kl800.com省心范文网

API11E2008版


"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

Specification for Pumping Units
API Specification 11E, Eighteenth Edition, Xxxx 2008

i

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

Contents

Page

Foreword ......................................................................................................................................................... ii Introduction..................................................................................................................................................... ii 1 2 3 4 5 5.1 5.2 Scope ...................................................................................................................................................2 Normative references .........................................................................................................................2 Terms and definitions.........................................................................................................................2 Abbreviations and symbols ...............................................................................................................2 Product requirements.........................................................................................................................2 Functional requirements ...............................................................................................................2 Technical requirements.................................................................................................................2 5.2.1 General ......................................................................................................................................2 5.2.2 Stroke and torque factors ........................................................................................................2 5.2.3 Design requirements ................................................................................................................2 5.2.4 Design documentation .............................................................................................................2 5.2.5 Design changes ........................................................................................................................2

6

Beam pump structure requirements..................................................................................................2 General ...........................................................................................................................................2 Design loads for all structural members except walking beams ...............................................2 Design stresses for all structural members except walking beams, bearing shafts, and cranks .............................................................................................................................................2 6.4 Design loads for walking beam.....................................................................................................2 6.5 Maximum allowable stress for walking beams ............................................................................2 6.6 Other structural components........................................................................................................2 6.6.1 Shafting .....................................................................................................................................2 6.6.2 Hanger .......................................................................................................................................2 6.6.3 Horseheads ...............................................................................................................................2 6.6.4 Cranks .......................................................................................................................................2 6.7 Structural bearing design..............................................................................................................2 6.7.1 General ......................................................................................................................................2 6.7.2 Anti-friction bearings................................................................................................................2 6.7.3 Sleeve bearings ........................................................................................................................2 6.8 Brakes.............................................................................................................................................2 6.1 6.2 6.3 Speed reducer requirements..............................................................................................................2 General ...........................................................................................................................................2 Gear reducers.................................................................................................................................2 7.2.1 General ......................................................................................................................................2 7.2.2 Standard sizes, peak torque ratings and speed .....................................................................2 7.2.3 Rating factors............................................................................................................................2 7.2.4 Metallurgy..................................................................................................................................2 7.2.5 Residual stress .........................................................................................................................2 7.2.6 Minimum effective case depths ...............................................................................................2 7.3 Chain reducers...............................................................................................................................2 7.3.1 Design........................................................................................................................................2 7.3.2 Rating Factors...........................................................................................................................2 7.3.3 Metallurgy..................................................................................................................................2 7.3.4 Dimensions ...............................................................................................................................2 7.3.5 Alignment ..................................................................................................................................2 7.3.6 Peak Torque Rating ..................................................................................................................2 7.4 Components ...................................................................................................................................2 7.4.1 Housing .....................................................................................................................................2 7.4.2 Bearings ....................................................................................................................................2 7.1 7.2

7

ii

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

7.4.3 7.4.4 7.4.5 7.4.6 7.4.7 7.4.8 7.4.9 8 8.1 8.2 8.3 8.4

Sleeve bearings ........................................................................................................................2 Anti-friction bearings................................................................................................................2 Shafts.........................................................................................................................................2 Key stresses..............................................................................................................................2 Peak loading (overloads) .........................................................................................................2 Fastener stresses .....................................................................................................................2 Special seals and breathers.....................................................................................................2

Product identification .........................................................................................................................2 Beam pump structure name plate ................................................................................................2 Speed reducer name plate ............................................................................................................2 Installation markings .....................................................................................................................2 Supplier/manufacturing requirements .........................................................................................2 8.4.1 Quality control ..........................................................................................................................2 8.4.2 Data sheet..................................................................................................................................2

9

Storage and maintenance...................................................................................................................2 Shipping and handling ..................................................................................................................2 9.1.1 General ......................................................................................................................................2 9.1.2 Packaging..................................................................................................................................2 9.1.3 Storage ......................................................................................................................................2 9.1.4 Handling and transport ............................................................................................................2 9.2 Lubrication .....................................................................................................................................2 9.1

Annex A (normative) Beam pumping unit designations..............................................................................2 Annex B (informative) Recommended data forms .......................................................................................2 B.1 General ...........................................................................................................................................2 B.2 Rating form for crank counterbalances .......................................................................................2 B.3 Stroke and torque factors .............................................................................................................2 B.4 Gear reducer data sheet ................................................................................................................2 Annex C (informative) Torque factor on beam pumping units with rear mounted geometry class I lever systems with crank counterbalance..................................................................................................2 C.1 General ...........................................................................................................................................2 C.2 Symbols..........................................................................................................................................2 C.3 Method of calculation ....................................................................................................................2 C.3.1 Torque factors...........................................................................................................................2 C.3.2 Submission form ......................................................................................................................2 C.3.3 Data submission .......................................................................................................................2 C.3.4 Calculation method...................................................................................................................2 C.4 Application of torque factors ........................................................................................................2 C.4.1 General ......................................................................................................................................2 C.4.2 Changes due to structural unbalance .....................................................................................2 C.4.3 Polish rod effects......................................................................................................................2 C.4.4 Rotary counterbalance moment ..............................................................................................2 C.4.5 Torque determination ...............................................................................................................2 C.4.6 Alternative crank rotation ........................................................................................................2 C.4.7 Alternative techniques .............................................................................................................2 C.4.8 Geometrical influences ............................................................................................................2 C.4.9 Interpolation ..............................................................................................................................2 Annex D (informative) Torque factor on beam pumping units with front mounted geometry class III lever systems with crank counterbalance ........................................................................................2 D.1 General ...........................................................................................................................................2 D.2 Symbols..........................................................................................................................................2 D.3 Method of calculation ....................................................................................................................2 D.3.1 Torque factors...........................................................................................................................2 D.3.2 Submission form ......................................................................................................................2 D.3.3 Data submission .......................................................................................................................2 D.3.4 Calculation method...................................................................................................................2 D.4 Application of torque factors ........................................................................................................2 D.4.1 General ......................................................................................................................................2 D.4.2 Changes due to structural unbalance .....................................................................................2 D.4.3 Polished rod effects..................................................................................................................2

iii

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

D.4.4 D.4.5 D.4.6 D.4.7 D.4.8

Rotary counterbalance moment ..............................................................................................2 Torque determination ...............................................................................................................2 Alternative techniques .............................................................................................................2 Geometrical influences ............................................................................................................2 Interpolation ..............................................................................................................................2

Annex E (informative) Torque factor on beam pumping units with front mounted geometry class III lever system with air counterbalance................................................................................................2 E.1 General ...........................................................................................................................................2 E.2 Symbols..........................................................................................................................................2 E.3 Method of calculation ....................................................................................................................2 E.3.1 Torque factors...........................................................................................................................2 E.3.2 Submission form.......................................................................................................................2 E.3.3 Data submission .......................................................................................................................2 E.3.4 Calculation method...................................................................................................................2 E.4 Application of torque factors ........................................................................................................2 E.4.1 General ......................................................................................................................................2 E.4.2 Changes due to structural unbalance .....................................................................................2 E.4.3 Alternative crank rotation.........................................................................................................2 E.4.4 Alternative techniques .............................................................................................................2 E.4.5 Geometrical influences ............................................................................................................2 E.4.6 Interpolation ..............................................................................................................................2 Annex F (informative) Torque factor on beam pumping units with rear mounted geometry class I lever systems with phased crank counterbalance ....................................................................................2 F.1 General ...........................................................................................................................................2 F.2 Symbols..........................................................................................................................................2 F.3 Method of calculation ....................................................................................................................2 F.3.1 Torque factors...........................................................................................................................2 F.3.2 Submission form.......................................................................................................................2 F.3.3 Data submission .......................................................................................................................2 F.3.4 Calculation method...................................................................................................................2 F.4 Application of torque factors ........................................................................................................2 F.4.1 General ......................................................................................................................................2 F.4.2 Changes due to structural unbalance .....................................................................................2 F.4.3 Polished rod effects..................................................................................................................2 F.4.4 Rotary counterbalance moment ..............................................................................................2 F.4.5 Torque determination ...............................................................................................................2 F.4.6 Alternative techniques .............................................................................................................2 F.4.7 Geometrical influences ............................................................................................................2 F.4.8 Interpolation ..............................................................................................................................2 Annex G (informative) Examples for calculating torque ratings for pumping unit reducers .....................2 G.1 Illustrative example, pitting resistance ........................................................................................2 G.2 Illustrative example, bending strength.........................................................................................2 G.2.1 General ......................................................................................................................................2 G.2.2 Pinion.........................................................................................................................................2 G.2.3 Gear ...........................................................................................................................................2 G.3 Illustrative example, static torque ................................................................................................2 Annex H (informative) System analysis..........................................................................................................2 H.1 System analysis .............................................................................................................................2 Annex I (informative) Product nomenclature .................................................................................................2 I.1 General ...........................................................................................................................................2 Annex J (informative) API Monogram……………………………………………………………………………… 86 Bibliography...................................................................................................................................................89

iv

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

Foreword
API will add standard language

v

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

Introduction
This Specification under the jurisdiction of the API Executive Committee on Standardization and was developed with oversight from API Subcommittee 11 on Field Operating Equipment. This Specification is intended to give requirements and information to both parties in the design, selection, and manufacture of beam pumping units. Furthermore, this Specification addresses the minimum requirements with which the manufacturer is to comply so as to claim conformity with this Specification. Users of this Specification should be aware that requirements above those outlined in this Specification may be needed for individual applications. This Specification is not intended to inhibit a manufacturer from offering, or the user/purchaser from accepting, alternative equipment or engineering solutions. This may be particularly applicable where there is innovative or developing technology. Where an alternative is offered, the manufacturer should identify any variations from this Specification and provide details. Forms are provided in Annex B for rating of crank counterbalances (Figure B.1) and for recording pumping unit stroke and torque factors (Figure B.2). Recommendations and examples for the calculation and application of torque factors are contained in Annexes C to F and examples for calculating torque ratings for pumping unit reducers are contained in Annex G. Recommendations and considerations for conducting a system analysis are contained in Annex H. Annex I contains an illustration of a typical beam pumping unit and the nomenclature associated with it. Finally, Annex J contains information on the application of the API Monogram for those organizations licensed to API Specification 11E.

vi

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

1

Scope

This Specification provides the requirements and guidelines for the design and rating of beam pumping units for use in the petroleum and natural gas industry. Included are all components between the carrier bar and the speed reducer input shaft. This includes the following: a) Beam pump structures; b) Pumping unit gear reducer; c) Pumping unit chain reducer. Only loads imposed on the structure and/or gear reducer by the polished rod load are considered in this Specification. Also included are the requirements for the design and rating of enclosed speed reducers wherein the involute gear tooth designs include helical and herringbone gearing. The rating methods and influences identified in this Specification are limited to single and multiple stage designs applied to beam pumping units in which the pitch-line velocity of any stage does not exceed 5,000 ft/min and the speed of any shaft does not exceed 3,600 r/min. This standard does not cover chemical properties of materials, installation and maintenance of the equipment, beam type counterbalance units, prime movers and power transmission devices outside the gear reducer, or control systems.

2

Normative references

The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ANSI/AGMA 1012–G05, Gear Nomenclature, Definitions of Terms with Symbols AGMA 2001-D04, Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth AGMA 908-B89, Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur, Helical and Herringbone Gear Teeth ASME B29.100, Precision Power Transmission, Double-Pitch Power Transmission, and Double-Pitch Conveyor Roller Chains, Attachments, and Sprockets – Incorporating ASME B29.1, B29.3, and B29.4 API Spec 11B, Specification for Sucker Rods

3

Terms and definitions

For the purposes of this document, the following terms and definitions apply. Additionally, the terms provided in ANSI/AGMA 1012--G05 also apply. See Figure I.1 for an illustration of a beam pumping unit. 3.1 beam pumping unit machine for translating rotary motion from a crankshaft to linear reciprocating motion for the purpose of transferring mechanical power to a down-hole pump 3.2 beam pump structure all components between the carrier bar and the speed reducer output shaft

1

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

3.3 brake component of a pumping unit designed to restrain motion in all rotary joints
NOTE It is often composed of a disk or drum mounted on the reducer input shaft combined with a mechanism to impart a restraining friction torque.

3.4 carrier bar part of the pumping unit that supports the load of the sucker rod string through the polished rod clamp 3.5 class I lever system lever system in which the fulcrum is located between the load and the applied force or effort
NOTE An example of this is a beam pumping unit with the fixed saddle bearing located along the walking beam between the equalizer and the well.

3.6 class III lever system lever system in which the applied force (effort) is located between the load and fulcrum
NOTE the well. An example of this is a beam pumping unit with the equalizer located between the fixed samson post bearing and

3.7 cranks driving link in the four-bar linkage of a beam pumping unit that is located between the output shaft of the gear reducer and the pitman link 3.8 diametral along a diameter 3.9 equalizer connects the pitman links to the rear of the walking beam 3.10 hanger component of a pumping unit designed to interface with the fluid well
NOTE Transmits well load from the polished rod to the pumping unit wireline.

3.11 horsehead component of a beam pumping unit designed to transmit force and motion from the walking beam to the flexible wireline
NOTE Its shape is such that the imparted motion is directed vertically above the well head allowing the polished rod to move without undue side loads.

3.12 pitmans Connecting link in the pumping unit mechanism between the cranks and the equalizer 3.13 crank rotation direction of rotation, either clockwise or counter-clockwise as viewed from the side of the beam pumping unit with the horsehead to the right.

2

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

3.14 samson post bearing bearing mounted to a fixed location atop the samson post of the pumping unit that is attached to and provides the fulcrum location for the walking beam 3.15 speed reducer mechanism located between the belt drive and the cranks to transmit rotary power while reducing speed and increasing torque 3.16 structural unbalance force required at the polished rod to balance the beam in a horizontal position with the pitmans disconnected from the crank pin and no applied well load
NOTE The structural unbalance is considered positive when the force required at the polished rod is downward, and negative when upward.

3.17 torque factor factor, for any given crank angle, that, when multiplied by the load at the polished rod, gives the torque at the crankshaft of the beam pumping unit speed reducer
NOTE The torque factor has units of length.

4

Abbreviations and symbols

The symbols and definitions used in this specification may differ from other specifications. Users should assure themselves that they are using these symbols and definitions in the manner indicated herein. See Annexes C, D, E, F for additional symbol definitions that are exclusive to those annexes. a A As C area of cross section distance from the center of the saddle bearing to the centerline of the polished rod tensile area of fastener distance from the center of the saddle bearing to the center of the equalizer bearing

Cs standard center distance between gear shafts C1 pitting velocity factor C3 pitting stress for external helical gears C5 velocity factor for pitting resistance Cg geometry factor for pitting resistance CJ geometry factor for bending strength Cm load-distribution factor for pitting resistance Cp elastic coefficient d de operating pitch-diameter of pinion outside diameter minus two standard addendums for enlarged pinions

3

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

D

operating pitch diameter of gear

Dm major diameter of fastener ds E shaft diameter, (for tapered shaft use mean diameter) modulus of elasticity

Eg modulus of elasticity for gears Ep modulus of elasticity for pinions fac allowable contact stress fat allowable bending stress

fay allowable yield strength of the gear or pinion material fcb allowable compressive stress in bending fs,b maximum stress due to bending fs,t maximum stress due to torsion G h1 he shear modulus height of key in the shaft or hub that bears against the keyway minimum effective case depth

HB,g Brinell hardness for gears HB,p Brinell hardness for pinions Iy J k kh weak axis second moment of inertia torsional constant bearing rating factor factor applied to account for any uncorrected distortion due to hardening the gears

K1 strength velocity factor K2 strength contact number K4 strength geometry number K5 velocity factor for bending strength Km helical gear load distribution factor Kms load distribution factor, static torque Ky yield strength factor

4

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

l L

un-braced length of column length of key

Lmin minimum total length of lines of contact in contact zone mg gear ratio n end restraint constant

nO rotational speed of output shaft, equal to the pumping speed nP pinion rotational speed

Ng number of teeth on gear Np number of teeth on pinion Nt p threads per inch of fastener thread pitch of metric fastener

pN normal base pitch P maximum applied load on column

Pb maximum load on bearing Pb,m bearing manufacturer's specific dynamic rating Pd diametral pitch in plane of rotation (transverse) Pnd the normal diametral pitch (the number of teeth per inch of diameter of the gear) PR polished rod load r R radius of gyration of section radius of the crank or of large sprocket

R1 bearing load ratio S Sx T ultimate tensile strength of chain section modulus of walking beam peak torque rating

Tac allowable transmitted torque at output shaft, based on pitting resistance Tas,i allowable static torque at the gear or pinion being checked Tat allowable transmitted torque at output shaft based on bending strength Tt transmitted shaft torque

5

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

vt w

pitch-line velocity width of key

Wb walking beam rating Wc pitting contact width factor Wf net face width Z length of line of action in the transverse plane normal operating pressure angle operating transverse pressure angle tensile stress in extreme fibers in bending

φn φt
ftb

σy yield strength of material σc compressive stress of key σs shear stress of key ψ
operating helix angle

5
5.1

Product requirements
Functional requirements

The user/purchaser shall determine the applicable well and environmental operational conditions to order products which conform to this Specification, and specify the requirements and/or identify the manufacturer’s specific products. These requirements may be conveyed by means of dimensional drawing, data sheet, or other suitable documentation. To ensure proper interfaces with the other elements of the beam pumping system such as the complete sucker rod string and the downhole reciprocating pump, the following requirements shall be specified: a) required well lifting capacity by identification of the applicable downhole pump; b) required sucker rod size in alignment with well depth, rod design, or other mechanical well parameters; c) the total sucker rod string mass(weight) in the well; d) potential extra loads due to the well configuration, friction, and dynamic loading; e) required gear configuration and resulting gear loading expressed as gear reducing rating, defining the required lifting energy input; f) required load capability of the beam pump structure to accommodate the sucker rod string weight and additional loads;

g) the required maximum stroke length. The combined requirements of gear reduction rating, structure loading capacity, and maximum stroke length shall be used to identify the specific beam pumping unit to be ordered as indicated by the designation number provided in Table A.1.

6

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

It is recommended that beam pumping units furnished to this specification adhere to the gear reducer rating, structure capacity, and stroke length as given in Table A.1, although the combinations of these items that make up the pumping unit designation need not be identical to those in the table. Recommended forms are provided in Annex B for rating of crank counterbalances (Figure B.1) and for recording pumping unit stroke and torque factors (Figure B.2). Recommendations and examples for the calculation and application of torque factor on pumping units are contained in Annexes C to F and examples for calculating torque ratings for pumping unit reducers are contained in Annex G. A recommendation for conducting a system analysis is contained in Annex H.

5.2
5.2.1

Technical requirements
General

Designs developed after the publication of this Specification shall be conducted according to the methods and assumptions as defined in Clauses 6 and 7. Beam pumping unit designs developed prior to this Specification for which the manufacturer can document satisfactory compliance/performance to the requirements included in this standard, shall be considered as meeting this standard. 5.2.2 Stroke and torque factors

For the torque on a reducer to be determined conveniently and accurately from dynamometer test data, manufacturers of beam pumping units shall, if requested by the purchaser, provide stroke and torque factors for each 15° position of the crank. Figure B.2 is an example form for recording this data. 5.2.3 Design requirements

Design requirements shall include those criteria defined in clauses 6 and 7 and other pertinent requirements upon which the design is based. Additive dimensional tolerances of components shall be such that proper operation of the beam pumping unit is assured. This requirement applies to manufacturer-assembled equipment and to replacement components or sub-assemblies. 5.2.4 Design documentation

Documentation of designs shall include methods, assumptions, calculations and design requirements. Design documentation shall be reviewed and verified by a qualified individual other than the individual who created the original design. Design documentation according to the list below shall be maintained for ten years after date of last manufacture. a) One complete set of drawings, written specifications/standards, including material type and yield strength as designated in clauses 6 and 7. b) Instructions providing methods for the safe assembly and disassembly of the beam pumping unit and stating the operations which are permitted and preclude failure and/or non-compliance with the stated performance. 5.2.5 Design changes

The manufacturer shall, as a minimum, consider the following when making design changes: stress levels of the modified or changed components; material changes; and functional changes. All design changes and modifications shall be identified, documented, reviewed, and approved before their implementation. Design changes and changes to design documents shall require the same control features as the original design.

7

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

6
6.1

Beam pump structure requirements
General

Requirements for beam pump structures are specified in the following clauses. Only loads imposed on the structure and/or gear reducer by the polished rod load are considered in this Specification. Polished rod load ratings are specified in API Spec 11B. Additional loads on the beam pumping unit imposed by add-on devices (such as compressors and stroke increasers) attached to the reducer, walking beam, or other structural components are not covered by this Specification. No dimensional requirements, other than stroke length, are given.

6.2

Design loads for all structural members except walking beams

For all pumping unit geometries, and unless otherwise specified, the maximum load exerted on the component being considered shall be determined by examining the loads on the component at each 15° crank position on the upstroke of the pumping unit. The polished rod load, PR, shall be used for all upstroke crank positions. For units with bi-directional rotation and non-symmetrical torque factors, the direction of rotation used for design calculations shall be that which results in the highest forces in structural components. Due consideration shall be given to the direction of loading on all structural bearings and on the structural members supporting these bearings.

6.3

Design stresses for all structural members except walking beams, bearing shafts, and cranks

Allowable stress levels are based on simple stresses without consideration of stress risers. Adequate stress concentration factors shall be used when stress risers occur. Design stresses for all structural components shall be a function of the yield strength of the material, σy. Components subjected to simple tension or compression and non-reversing bending shall have a limiting stress of 0,3 σy. If stress risers occur in critical zones of tension members, the limiting stress shall be 0.25 σy. Components subjected to reverse bending shall have a limiting stress of 0.2 σy. The following equation (1) shall be used for all components acting as columns:
P= a σy ? σ y ? l ?2 ? ?1 ? ? ? ? 4 ? 4 n π2 E ? r ? ? ? ? (1)

where P a is the maximum applied load on column expressed in pounds is the area of cross section expressed in square inches

σy is the yield strength of material expressed in psi
n E is the end restraint constant, assumed to be 1,0 is the modulus of elasticity expressed in psi

8

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

l r

is the un-braced length of column expressed in inches is the radius of gyration of section expressed in inches

?l? ?l? The value for ? ? shall not exceed 90. For ? ? values of 30 or less, columns may be assumed to be acting in r? ? ?r? simple compression.

6.4

Design loads for walking beam

Equation (2) shall be used for rating conventional walking beams as shown in Figure 1:
Wb = fcb

A

( Sx )

(2)

where Wb is the walking beam rating, equal to the design polished rod load expressed in pounds fcb is the allowable compressive stress in bending expressed in psi (see Table 1 for maximum allowable stresses) Sx A is the section modulus of the walking beam expressed in cubic inches is the distance from centerline of saddle bearing to centerline of the polished rod expressed in inches(see Figure 1)

Equation (2) is based on conventional beam construction using a single rolled section. The gross section of the rolled beam may be used to determine the section modulus, however, holes or welds are not permissible on the tension flange in the critical zone (see Figure 1). With unconventional construction or built-up sections, consideration shall be given to changes in loading, to checking stresses at all critical sections, and to the inclusion of stress concentration factors where applicable.

6.5

Maximum allowable stress for walking beams

The maximum allowable stress, f cb, for the walking beam rating equation, Equation (2), shall be determined from Table 1. For standard rolled beams having cross sections symmetrical with the horizontal neutral axis, the critical stress is compression in the lower flange. The maximum value of this stress, f cb, is the smaller of the values determined from lines 3 and 4 in Table 1.

9

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

Table 1 — Maximum allowable stresses in pumping unit walking beams of structural steel (See Figure 1)
Line 1 2 3 Stress Specified minimum yield strength of material Maximum allowable tensile stress in extreme fibers in bending Maximum allowable compressive stress in extreme fibers in bending, not to exceed value in line 4 Maximum allowable compressive stress in extreme fibers in bending except, if limited by line 3 Symbol Values 36,000 psi 11,000 psi

σy
f?tb f?cb

EI y GJ S xl

4

f?cb

11,000 psi

Where

J l E Iy G

is the torsional constant of the beam section expressed in inches

4

is the longest laterally, un-braced length of beam expressed in inches [longer of LC or A (see Figure 1)] is the modulus of elasticity;(29,000,000 psi) is the weak axis second moment of inertia expressed in inches is the shear modulus; (11,200,000 psi) is the section modulus expressed in cubic inches
4

Sx

10

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

1 4

Lc / 2

LA / 2

5

3

2

Lc
Key 1 2 3 4 Critical zone in tension flange Saddle bearing Equalizer bearing Horsehead

LA

Figure 1 — Walking beam elements

6.6
6.6.1

Other structural components
Shafting

The limiting stresses for all bearing shafts as well as other structural shafting are given in clause 7.4.5.1.

6.6.2

Hanger

Wire lines for horseheads shall have a minimum factor of safety of 5 with respect to breaking strength. For allowable stresses on carrier bar, end fittings, etc., see clause 6.3.

6.6.3

Horseheads

Horseheads shall be either hinged or removable to provide access for well servicing and shall be attached to the walking beam in such a manner as to prevent detachment in event of a high rod failure or other sudden load changes. The distance from the pivot point of the horsehead to the tangent point of the wire line on the horsehead shall have a maximum dimensional tolerance at any position of the stroke of the following values: a) ±1/2 in for stroke lengths up to 100 in;

11

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

b) ±5/8 in for stroke lengths from 100 in up to 200 in; c) ±3/4 in for stroke lengths of 200 in and longer.

6.6.4

Cranks

All combined stresses in cranks resulting from operational loads shall be limited to a maximum value of 0.15 σy.

6.7
6.7.1

Structural bearing design
General

Structural bearing shafts shall be supported in sleeve or anti-friction bearings.

6.7.2

Anti-friction bearings

For bearings subject to oscillation or rotation, the bearing load ratio R1 shall be determined using Equation (3) but shall not be less than the minimum values given below. For bearings subject to only oscillation, R1 shall be 2.0 or greater. For bearings subject to full rotation, R1 shall be 2.25 or greater:
R1 = k Pb,m Pb

(3)

where R1 is the bearing load ratio k is a bearing rating factor k = 1.0 for bearings rated at 331/3 r/min and 500 h or k = 3.86 for bearings rated at 500 r/min and 3,000 h. Pb,m is the bearing manufacturer's specific dynamic rating expressed in pounds Pb is the maximum load on bearing expressed in pounds

6.7.3

Sleeve bearings

The design of sleeve bearings is outside the scope of this Specification. The pumping unit manufacturer shall design sleeve bearings, based on available test data and field experience that are comparable in performance to anti-friction bearings designed for the same operating loads and speeds.

6.8

Brakes

Pumping unit brakes shall have sufficient braking capacity to withstand the torque exerted by the cranks at any crank position with the maximum amount of counterbalance torque designed by the manufacturer for the particular unit involved. This braking torque shall be effective with the pumping unit at rest under normal operating conditions with the well disconnected. The pumping unit brake is not intended as a safety stop but is intended for operational stops only.
NOTE When operations or maintenance are to be conducted on or around a pumping unit, it is recommended that the position of the crank arms and counter weights be securely fixed in a stationary position by chains or by other acceptable means.

12

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

7
7.1

Speed reducer requirements
General

Speed reducers for beam pumping units shall be designed for the unusual external loads encountered in this service. All components are subject to loading determined by the structural geometry and the load rating of the pumping unit. The data in this clause are general in nature and should only be used after careful consideration of all factors that influence the loading. Reducers rated under this Specification and properly applied, installed, lubricated, and maintained shall be capable of safely carrying the rated peak torque under normal oil field conditions. Requirements for beam pump speed reducers are specified in the following clauses. Included are the following types: a) b) Gear reducers; Chain reducers.

7.2
7.2.1

Gear reducers
General

Gear reducers typically consist of a set of gears enclosed in a housing located between the prime mover and the cranks to transmit rotary power while reducing speed and increasing torque. The gear rating equations contained in this Specification apply only to gear elements possessing involute tooth form geometry.

7.2.2

Standard sizes, peak torque ratings and speed

The pumping unit reducer of a given size shall have a capacity, calculated as provided herein, as near as practical to, but not less than, the corresponding peak torque rating in Table 2. Gear peak torque ratings shall be based on a nominal pumping speed (strokes per minute), see Table 3.

13

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

Table 2 — Pumping unit reducer sizes and ratings
Size 6.4 10 16 25 40 57 80 114 160 228 320 456 640 912 1280 1824 2560 3648 Peak Torque Rating, in-lbs 6,400 10,000 16,000 25,000 40,000 57,000 80,000 114,000 160,000 228,000 320,000 456,000 640,000 912,000 1,280,000 1,824,000 2,560,000 3,648,000

Table 3 — Speeds for peak torque rating for gear reducers
Strokes Per Minute 20 16 16 15 14 13 11 Peak Torque Rating, in-lbs 320,000 and smaller 456,000 640,000 912,000 1,280,000 1,824,000 2,560,000 and larger

7.2.3 7.2.3.1

Rating factors General

The allowable stresses in this Specification are maximum allowed values. Less conservative values for other rating factors in the document shall not be used.

14

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

7.2.3.2 7.2.3.2.1

Peak torque rating General

The peak torque rating of the gear reducer is the lower of the pitting resistance torque rating, bending strength torque rating, or static torque ratings as determined by the use of the formulas in this section.

7.2.3.2.2

Pitting resistance torque rating

Pitting is considered to be a fatigue phenomenon and is a function of the stresses at the tooth surface. The two kinds of pitting, initial pitting and destructive pitting, are illustrated in AGMA 1010-E95. The aim of the pitting resistance equation is to determine a load rating at which destructive pitting of the teeth does not occur during their design life. Equation (4) or the equivalent Equation (17) shall be used for rating the pitting resistance of gears: Tac = C1 Wc C3 where Tac is the allowable transmitted torque at output shaft, based on pitting resistance expressed in in-lbs C1 is the pitting velocity factor, Equation (5) Wc is the pitting contact width factor, Equation (8) C3 is the pitting stress for external helical gears, Equation (11) The pitting velocity factor is given by:
nP d e C5 2 nO
2

(4)

C1 =

(5)

where
nP

is the pinion rotational speed, expressed in rotations per minute

nO is the rotational speed of output shaft expressed in rotations per minute and equal to the pumping speed expressed in strokes per minute de outside diameter minus two standard addendums for enlarged pinions, expressed in inches

C5 is the velocity factor for pitting resistance
C5 =

78 78 + ν t

(6)

where vt is the, pitch line velocity (do not use enlarged pinion pitch diameter), expressed in feet per minute
vt = 0, 262nP d

(7)

where

15

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

d

is the operating pitch diameter of pinion expressed in inches

The pitting contact width factor Wc is given by:
Wc = Wf kh Cm

(8)

where
Wf is the net face width of the narrowest of the mating gears, expressed in inches. For herringbone or double helical gearing, the net face width is the sum of the face widths of each helix. kh

is a factor applied to account for any uncorrected distortion due to hardening the gears

When gears are hardened after cutting and the profiles and leads are not corrected or otherwise processed to ensure high accuracy, the tooth distortion will affect load distribution. This makes it necessary to apply the distortion factor kh. kh = 1.0 if no hardening has been undertaken, kh = 0.95 when one element is hardened after cutting and kh = 0.90 when both elements are hardened after cutting.
Cm is a load-distribution factor for pitting resistance given by Equations (9) and (10) and which, for Wf ≤ 16 in may be read from Figure 2 Cm = 1,24 + 0,031 2 Wf Cm = Wf / (0,45 Wf + 2,0)

for Wf ≤ 16 in for Wf > 16 in

(9) (10)

If deflections or other sources of misalignment are such that the values of Cm from Figure 2 do not represent the actual mal-distribution of load across the face, then it is recommended that the load distribution factor be calculated using AGMA 2001-D04 and AGMA 908-B89. The Wc values from Equation (8) can only be attained with well-controlled heat-treating processes. If the as-heattreated accuracy is such that the required Cm values (for above Wc values) can not be attained, it is recommended that Cm be calculated in accordance with AGMA 908-B89.

16

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition
2,0

1,5

Cm

1,0

0,5

0 0 50 100 150 200 250 8 10 300 350 400 mm in

0

2

4

6

12

14

16

Wf

Figure 2 — Helical gear load distribution factor, Cm, for helical and herringbone gears and well controlled heat-treating processes
The pitting stress for external helical gears C3 is given by:
? mg ? ? fac C3 = 0, 225 ? ?? ? mg + 1 ? ? Cp ? ?? ? ? ? ?
2

(11)

where
fac is the allowable contact stress expressed in psi from Figure 3 or Table 4
NOTE Recommended gear and pinion hardness combinations are given in Table 6.

Cp the elastic coefficient. See Table 5. mg is the gear ratio mg = Ng / Np Ng number of teeth in gear Np number of teeth in pinion

17

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

Table 4 — Maximum allowable contact stress number— f ac (For other than through hardened and tempered steel gears)
Material AGMA Class Commercial designation Heat treatment Flame or induction hardeneda Steel AISI 4140 AISI 4340 20 Cast iron 30 40 A-7-a A-7-c Nodular (ductile) iron A-7-d A-7-e 60-40-18 80-55-06 100-70-03 120-90-02 120-90-02 mod A-8-c Malleable Iron (pearlitic) A-8-e A-8-f A-8-i
a b

Minimum hardness at surface 50 HRC 54 HRC 55 HRC 60 HRC 48 HRC 46 HRC 175 BHN 200 BHN 140 BHN 180 BHN 230 BHN 270 BHN 300 BHN 165 BHN 180 BHN 195 BHN 240 BHN

f ac psi 170,000 175,000 180,000 200,000 155,000 155,000 57,000 70,000 80,000 90 % to 100 %d of f ac value of steel with same hardness (see Figure 4)

Carburized and case hardenedb Nitridedc Nitridedc As cast As cast As cast Annealed Quenched & tempered Quenched & tempered Quenched & tempered Quenched & tempered -

45007 50005 53007 80002

68,000 74,000 79,000 89,000

Minimum effective case depth requirements are given in 7.2.5.2 Minimum effective case depth requirements are given in Figure 9 Minimum effective case depth requirements are given in Figure 10 The higher allowable stress for nodular iron is determined by metallurgical controls as defined by the manufacturer.

c
d

Table 5 — Elastic coefficient— Cp for gear/pinion material combinations
MPa-1, (psi-1)
Pinion Materials Steel Malleable Iron Nodular Iron Cast Iron Modulus of Elasticity Ep 30 x 106 psi 25 x 106 psi 24 x 106 psi Gear Materials & Modulus of Elasticity, Eg, MPa (psi) Steel 30 x 106 psi 2,300 2,180 2,160 2,100 Malleable Iron 25 x 106 psi 2,180 2,090 2,070 2,020 Nodular Iron 24 x 106 psi 2,160 2,070 2,050 2,000 Cast Iron 22 x 106 psi 2,100 2,020 2,000 1,960

22 x 106 psi

18

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

Table 6 — Minimum gear and pinion Brinell hardness combinations for through hardened and tempered steel gears
Gear, HB,g 180 210 225 245 255 270 285 300 335 350 375 Pinion, HB,p 210 245 265 285 295 310 325 340 375 390 415

The values of C3 determined from Equation (11) are minimums for acceptable gear design. C3 may be determined more precisely as follows:
? f C3 = Cg ? ac ? Cp ? ? ? ? ?
2

(12)

where
Cg is a geometry factor for pitting resistance (wear) given by Equation (13):
? cosφt sinφt Cg = ? 2 ? ? ? mg ? ? Lmin ? ? ? m + 1? ? W ? ? ? ?? g ?? f ?

(13)

where
Lmin is the minimum total length of lines of contact in contact zone, expressed in inches Wf is the net face width of the narrowest element, expressed in inches

φt

is the operating transverse pressure angle, expressed in degrees

φt = tan?1 ?
where

? tanφ n ? ? ? cosΨ ?

(14)

φ n is the normal operating pressure angle, expressed in degrees ψ is the operating helix angle, expressed in degrees

19

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

For most helical gears having a face contact ratio of 2 or more; a conservative estimate of Lmin / Wf is
Lmin 0, 95 Z = Wf pN where Z is the length of line of action in the transverse plane, expressed in inches (15)

pN is the normal base pitch, expressed in inches With acceptable gear design, the above value of Lmin / Wf is acceptable for a face contact ratio of 1.0 to 2.0. Equation (16) incorporates the expansion of Cg into a more precise equation for C3 as:
? cosφt sinφt C3 = ? 2 ? ? ? mg ? ? 0, 95 Z ? ? fac ?? ?? ?? ? ? mg + 1 ? ? pN ? ? Cp ? ? ? ? ? ? ?
2

(16)

The method used in this Specification for determining the geometry factors for pitting resistance Cg is simplified. A more precise and detailed analysis may be made using the method in AGMA 2001-D04 and AGMA 908-B89. The more precise method mentioned previously shall be used for face contact ratios less than 1.0. When I is determined in accordance with AGMA 2001-D04 and AGMA 908-B89 and if 2Cs / (mg+1) is not equal to outside diameter minus two standard addendums, the operating pitch diameter of the pinion in all of the preceding rating equations shall be defined in accordance with AGMA 2001-D04 and AGMA 908-B89. Incorporating the Equations for C1, Wc and C3 into Equation (4) gives the following Equation (17) for Tac:

Tac

? n d 2C5 ? ? Wf ? ? fac ? =? P kh ? ? Cg ? ?? ? ? 2 nO ? ? Cm ? ? Cp ? ?

2

(17)

or

Tac

? n d 2C5 ? ? Wf ? ? cosφt sinφt kh ? ? =? P ?? 2 ? 2nO ? ? Cm ? ?

? ? mg ? ? 0,95 Z ? ? fac ? ?? ? ?? ?? ? ? ? ? ? ? mg + 1 ? ? pN ? ? Cp ?

2

20

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

1 000 lbf/in 2 175 150

1 200 1 100 1 000 900

ac

f

125 800 700 600 75 150 200 250 300 350 400

100

MPa

H B,g

Figure 3 — Allowable contact fatigue stress for through hardened and tempered steel gears f ac for helical and herringbone gears 7.2.3.2.3 Bending strength torque rating

Bending strength rating is related to fracture at the gear tooth root fillet. Fracture in this area is considered to be a fatigue phenomenon and is a function of the bending stress in the tooth as a cantilever plate. Typical fractures are illustrated in AGMA 1010-E95. The aim of the bending strength rating equation is to determine a load rating at which tooth root fillet fracture does not occur during the anticipated design life of the teeth. The following Equation (18) or the expanded Equation (27) shall be used for rating the bending strength of helical and herringbone gears: Tat = K1 K2 f at K4 where Tat is the allowable transmitted torque at output shaft based on bending strength expressed in in-lbs K1 is the strength velocity factor, see Equation (19) K2 is the strength contact number, see Equation (22) f at is the allowable bending stress from below or Table 7 K4 is the strength geometry number, see Equation (25) (18)

21

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

The strength velocity factor K1 is given by Equation (19)
K1 = nP d K 5 2 nO

(19)

where nP d is the pinion speed, expressed in rotations per min is the operating pitch-diameter of pinion, expressed in inches

nO is the speed of output shaft, pumping speed, expressed in strokes per minute K5 is the velocity factor for bending strength
K5 = 78 78 + vt

(20)

where vt is the pitch-line velocity, expressed in feet per second
vt = 0, 262nP d

(21)

The strength contact number K2 is given by Equation (22):
K2 = Wf kh Km

(22)

where Wf is the face width of the narrowest of the mating gears. For herringbone or double helical gearing, the net face width is the sum of the face width of each helix, expressed in inches kh is a factor applied to account for any uncorrected distortion due to hardening the gears

When gears are hardened after cutting and the profiles and leads are not corrected or otherwise processed to ensure high accuracy, the tooth distortion will affect load distribution. kh = 1.0 if no hardening has been undertaken, kh = 0.95 when one element is hardened after cutting and kh = 0.90 when both elements are hardened after cutting. Km is the load distribution factor from Equations (23) to (24) and shown in Figure 5 for Wf ≤ 16 in
Km = 1 0, 872 ? 0,176 Wf

for Wf ≤ 16 in for Wf > 16 in

(23) (24)

Km = 1,7

If deflection or other sources of misalignment are such that the values of Km from Figure 5 do not represent the actual mal-distribution of load across the face, then the load distribution factor should be calculated using AGMA 2001-D04 and AGMA 908-B89. The K2 values from Equation (22) can only be attained with well-controlled heat-treating processes. If the as-heattreated accuracy is such that the required Km values (for above K2 values) can not be attained, Km should be calculated in accordance with AGMA 2001-D04 and AGMA 908-B89.

22

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

The strength geometry number K4 is given by Equation (25):
K4 = CJ Pd

(25)

where CJ is the geometry factor for bending strength in accordance with AGMA 908-B89 Pd is the diametral pitch in plane of rotation (transverse) Pd = Pnd cos ψ where Pnd is the normal diametral pitch, nominal, expressed in in-1 (26)

ψ

is the operating helix angle, expressed in degrees

The bending strength rating shall be calculated for both pinion and gear. The lower of the two values is the bending strength rating of the gear set. Incorporating the Equations for K1, K2 , and K4 into Equation (4) gives the following Equation (27) for Tat:
Tat = ?

? nP dK5 ? ? Wf ? ? CJ ? kh ? fat ? ?? ? ? 2 nO ? ? Km ? ? Pd ?

(27)

where

fat = 142 H B ? 0,13 H B

2

(See Figure 4)

23

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition
1 000 2 lbf/in

40 250

30

200

150 20

f

at

100 10 50

MPa

150

200

250

300

350

400

HB

Figure 4 — Allowable bending fatigue stress for through hardened and tempered steel gears - fat

2,0

1,5

K m 1,0

0,5

0 0 1 50 2 100 4 150 6 200 8 250 10 300 12 350 14 400 mm 16 in

WF

Figure 5 — Helical gear load distribution factor – Km for helical and herringbone gears

24

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

Table 7 — Allowable bending fatigue stress, f at (For other than through hardened and tempered steel gears)
Material AGMA Class Commercial designation Heat treatment Flame or induction d hardened Steel AISI 4140 AISI 4340 20 Cast iron 30 40 A-7-a A-7-c Nodular (ductile) iron A-7-d A-7-e 60-40-18 80-55-06 100-70-03 120-90-02 120-90-02 mod A-8-c Malleable Iron (pearlitic) A-8-e A-8-f A-8-i
a

Minimum hardness at surfacea 50 - 54 HRC 55 HRC 60 HRC 48 HRC 46 HRC 175 BHN 200 BHN 140 BHN 180 BHN 230 BHN 270 BHN 300 BHN 165 BHN 180 BHN 195 BHN 240 BHN

f at psi 38 300 47,000 47,000 29,000 31,000 4,200 7,200 11,000

Carburized and case hardenedb Nitridedc Nitrided As cast As cast As cast Annealed Quenched & tempered Quenched & tempered Quenched & tempered Quenched & tempered -

90 % to 100%e of fat value of steel with same hardness

45007 50005 53007 80002

8,500 11,000 13,600 17,900

Core hardness for nitrided gears to be a minimum of 300 BHN. Core hardness for case hardened and ground gears and pinions to be shown in Manufacturer's Gear Reducer Data Sheet (Figure B.3). Minimum effective case depth requirements are given in Figure 9 Minimum effective case depth requirements are given in Figure 10

b

c

d For minimum flame or induction hardened hardening pattern, see Figure 8. Pattern 8A is limited to approximately 5DP and finer. Process control is important to the achievement of correct hardening pattern. Parts of this type should be carefully reviewed since residual compressive stresses are less than with pattern 8B. Tooth distortion and lack of ductility may necessitate a reduction of allowable stress numbers. e

The higher allowable stress for nodular iron is determined by metallurgical controls.

7.2.3.2.4

Static torque rating

Static torque loads on the gear teeth are caused by resisting the torque exerted by the counterbalance or other non-operating conditions. A description of the many conditions of installation, maintenance, and use of pumping unit reducers that can cause high static torques is not covered in this Specification. The static torque rating of the gear reducer to resist these loads shall be equal to or greater than 500 % of the reducer name plate rating. Certain pumping unit geometries can require a higher static torque rating. The system analysis (see Annex H) should be used to determine when a higher static torque rating is required. The following Equation (28) shall be used to determine static torque rating of helical and herringbone gears:
Tas,i = ?

? D ? ? CJ ?? Wf ? ? fay K y ? ? ?? ? 2 ? ? Pd ?? Kms ?

(28)

25

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

where Tas,i is the allowable static torque at the gear or pinion being checked, expressed in inch-pounds
NOTE 1: Tas,1 = 1 reduction, Tas,2 = 2
st nd

reduction, Tas,n = n reduction

th

NOTE 2: Torque on output shaft may be calculated as Tas,2 = Tas,1·mg2, etc.

D

is the operating pitch diameter of gear, expressed in inches

f ay is the allowable yield strength of the gear or pinion material taken from Figure 6 for steel and nodular iron; for case hardened (flame, induction, nitrided, carburized) material, the core hardness from the Gear manufacturer's data sheet (see Figure B.3) shall be used to determine yield strength, expressed in psi where f ay = 482 HB - 32 800 (See Figure 6) Ky is the yield strength factor from Table 8 Kms is the load distribution factor, static torque Kms = 0,014 4 Wf + 1,07 Kms = 1.3 for Wf measured in inches and Wf ≤ 16 in for Wf > 16 in (30) (31) (29)

The allowable static torque rating determined using this formula is conservative since the geometry factor CJ includes a stress concentration factor for fatigue. It should be noted that some gear materials do not have a welldefined yield point and the ultimate strength is approximately equal to the yield. For these materials, a much lower value of Ky shall be selected. The user of this Specification should satisfy himself that the yield values selected are appropriate for the materials used.

26

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

1 000 Ibf/in 2 160 140 120

1 200

1 000

800

f ay

100

600 80

60 400

40 150 200 250 300 350 400 450

MPa

HB

Figure 6 — Allowable yield strength number for steel and nodular iron, f ay Table 8 — Yield strength factor, Ky
Material Steel (through hardened) Nodular iron Steel (flame or induction hardened) Steel (case carburized) Steel (nitrided) Cast iron Malleable iron Ky 1.00 1.00 0.85 1.20 0.85 0.75 1.00

27

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

7.2.4

Metallurgy

The allowable stresses, f ac and f at, included in this Specification are based on commercial ferrous material manufacturing practices. Hardness, tensile strength, and microstructure are the criteria for allowable stress values. Reasonable levels of cleanliness and metallurgical controls are required to permit the use of the allowable stress values contained in this Specification.
7.2.5 Residual stress

Any material having a case-core relationship is likely to contain residual stresses. If properly managed, these residual stresses will be compressive and will enhance the bending strength performance of the gear teeth. Shot peening, case carburizing, nitriding, and induction hardening are common methods of inducing compressive prestress in the surface of the gear teeth. Grinding the tooth surface after heat treatment can reduce the residual compressive stresses. Grinding the root fillet area can introduce tensile stresses in the root. Care shall be taken to avoid changes in microstructure during any grinding process. Shot peening may be performed after grinding to assure the presence of residual compressive stresses.
7.2.6 7.2.6.1 Minimum effective case depths General

The effective case depth is the depth of the case which has a minimum Rockwell 'C' hardness of 50 RC. The minimum effective case depth is a function of Pnd, the normal diametral pitch.
7.2.6.2 Flame and induction hardened gears

The minimum effective case depth for flame or induction hardened gears shall be as defined in Equation (32), see Figure 7:
he = 0,264 693 Pnd
?1,124 81

(in)

(32)

28

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright11E, Eighteenthreserved." API Specification API. All rights Edition

10 9 8 7 6 5 4

Pnd

3

2

1 0,3 0,010 0,4 0,5 2 0,7 3 1,0 4 5 6 7 2,0 3,0 0,100 6,0 0,300 10,0 mm in

he

Figure 7 — Minimum effective case depth for flame or induction hardened gears, he
Note: The minimum effective case depth is defined as the depth below the surface at which the Rockwell C hardness has dropped to 50 Rc or 5 points below the surface hardness, whichever is the lower hardness.

Induction coil or flame head

Inductor or flame head

Pattern 8A

Pattern 8B

Figure 8 — Acceptable flame and induction hardening patterns

7.2.6.3

Carburized gears

The minimum effective case depth in inches for carburized gears shall be in the ranges as defined in Equation (33) and Equation (34), see Figure 9:

29

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

he,1 = 0,119 935 Pnd

-0,861 05

(33) (34)

he,2 = 0,264 693 Pnd

-1,124 81

20 15 2 10 9 8 7 6 5 4 3 2 3 4 5 6 8 10 12 15 20 25 0,1 0,2 0,3 0,4 0,5 0,010 2 0,7 3 1,0 4 2,0 5 6 7 3,0 0,100 6,0 mm 0,300 in 1

mm 1

mn

Pnd

in

2

0,004 5 6 7

he
Key 1 2

See Equation 33 See Equation 34

Figure 9 — Effective case depth for carburized gears, he
NOTE 1: The values and ranges shown on the case depth curves are to be used as guides. For gearing in which maximum performance is required, detailed studies must be made of the application, loading, and manufacturing procedures to obtain desirable gradients of both hardness and internal stress. Furthermore, the method of measuring the case as well as the allowable tolerance in case depth should be a matter of agreement between the customer and the manufacturer. NOTE 2 : The effective case depth is defined as the depth below the surface at which the Rockwell C hardness has dropped to 50 Rc.The total case depth to core carbon is approximately 1.5 x effective case depth.

7.2.6.4

Nitrided gears

The minimum effective case depth in inches for nitrided gears shall be in the ranges as defined in Equation (35) to Equation (36), see Figure 10:

30

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

he,1 = 4,328 96 × 10

?2

? 9,681 15 × 10

?3

Pnd + 1,201 85 × 10
3

?3

Pnd

2

? 4

6,797 21× 10 he,1 = 6,600 90 × 10
?2

?5

Pnd + 1,371 17 × 10

?6

(35)

Pnd
2

? 1,622 24 × 10

?2

Pnd + 2,093 61× 10
3

?3

Pnd

? 4

1,177 55 × 10

?4

Pnd + 2,331 60 × 10

?6

(36)

Pnd

20 15 10 9 8 7 6 5 4 3 2

he,1

he,2

Pnd

1 0,1 0,001 2 3 4 0,2 5 6 7 0,3 0,4 0,5 0,010 2 0,7 3 1,0 4 2,0 5 6 7 mm 0,1 in

he
Key 1 2 See Equation 34 See Equation 35

Figure 10 — Minimum total case depth for nitrided gears, he
NOTE: The values shown have been successfully used for nitrided gears and can be used as a guide. For gearing requiring maximum performance, especially large sizes, coarse pitches, and high working stresses, detailed studies must be made of application, loading, and manufacturing procedures to determine the desired gradients of hardness, strength, and internal residual stresses throughout the tooth.

7.3
7.3.1

Chain reducers
Design

Chain drives shall be either single, double, or triple reduction.

31

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

Single, or multiple strand roller chain, conforming to ASME B29.100 heavy series, shall be used. Link plates may be thicker than specified in ASME B29.100. Center link plates of multiple strand chains shall be press fitted on the pins. Sprockets shall have the ASME tooth form. The small sprocket shall have not less than eleven teeth.
7.3.2 Rating Factors

Chain and sprocket ratings shall be based on a nominal pumping speed of 20 strokes per minute.
7.3.3 Metallurgy

The small sprocket shall be of steel and of a minimum of 225 Brinell hardness. The large sprocket shall be of steel or cast iron.
7.3.4 Dimensions

The distance between sprocket centerlines shall not be less than the sum of the pitch circle radius of the large sprocket plus the pitch circle diameter of the small sprocket. Chain length shall be selected to obtain an even number of pitches (no offset link). A minimum take-up of two pitches, or 3 percent of chain length, whichever is less, shall be provided.
7.3.5 Alignment

Shafts and sprockets shall be aligned to provide proper distribution of load across the width. Where a shaft is movable for take-up, reference marks shall be provided for checking parallelism.
7.3.6 Peak Torque Rating

The peak torque rating of the first reduction shall be calculated as follows: a) For double reduction reducers, the peak torque rating of the first (high speed) reduction shall be related to the crankshaft peak torque rating by multiplying the high-speed reduction peak torque by the ratio of the second (low-speed) reduction. b) For triple reduction reducers, the peak torque rating of the first (high-speed) reduction shall be related to the crankshaft peak torque rating by multiplying the high-speed reduction peak torque by the product of the ratios of the second (intermediate-speed) and third (low-speed) reductions. The following Equation (37) shall be used for rating of chain:
T = SR 12

(37)

where T S R is the peak torque rating expressed in in-lbs is the ultimate tensile strength of chain in accordance with ASME B29.100 expressed in pounds is the pitch radius of large sprocket expressed in inches

7.4
7.4.1

Components
Housing

The housing may be of any design, provided it is sufficiently rigid to maintain shaft positions under the maximum gear and structural loads for which it is intended.

32

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

7.4.2

Bearings

Shafts may be supported in sleeve bearings or in anti-friction bearings.
7.4.3 Sleeve bearings

Sleeve bearings shall be designed for bearing pressures not in excess of 750 psi of projected area, based on actual loading (internal and external), at the rated peak torque.
7.4.4 Anti-friction bearings

Anti-friction bearings shall be selected according to the bearing manufacturer's recommendations based on actual loads (internal and external) at rated peak torque and rated speed for not less than 15,000 hours L-10 life.
7.4.5 7.4.5.1 Shafts Shaft stresses

For steel shafts and for the torque rating of the unit, the maximum stress due to torsion fs,t and the maximum stress due to bending fs,b shall not exceed the values shown in Figure 11. These allowable stress limitations allow for stress concentrations arising from keyways, shoulders, and grooves, etc., not exceeding a factor of 3.0. More detailed analysis is required where stress concentrations (considering notch sensitivity) exceeding a factor of 3.0, where press fit components are used or where there are unusual deflections.

33

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

1,000 Ibf/in 2 24 20

150

MPa

16 100

f

s,b

f s,t f s,b

12

f

s,t

8

50

4

0

0 600 160 80 200 100 800 240 120 1 000 280 140 320 160
2

1 200 360 180

1 400 400 200

σ y (MPa)
440 220

HB

σ y (1000 lbf/in )
Figure 11 — Allowable stress – shafting 7.4.5.2 Shaft deflections

Shaft deflections causing tooth misalignment shall be analyzed regardless of stress levels to ensure satisfactory tooth contact as required to achieve the Cm (see 7.2.2.1.1) and Km (see 7.2.2.1.2) values used to rate the gearing.
7.4.6 Key stresses

The shear and compressive stress in a key shall be calculated using Equations (38) and (39):

σs =

2 Tt ds wL

(38)

34

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

σc =
where

2 Tt d s h1 L

(39)

σs is the shear stress of key, expressed in psi. See Table 9. σc is the compressive stress of key, expressed in psi. See Table 9.
Tt ds w L is the transmitted shaft torque, expressed in inch-pounds is the shaft diameter, expressed in inches. For tapered shaft, use mean diameter. is the width of key, expressed in inches is the length of key, expressed in inches

h1 is the height of key in the shaft or hub that bears against the keyway, expressed in inches. For designs where unequal portions of the keyway are in the hub or shaft, h1 is the minimum portion. Maximum allowable key stresses based on peak torque rating are shown in Table 9 for AISI materials, appropriate allowable stresses should be developed if non-AISI materials are used. These stress limits are based on the assumption that an interference fit is used with a torque capability equal to or greater than the reducer rating at the shaft.
Table 9 — Allowable key stresses
Allowable shear stressa Key Material Hardness (BHN) psi AISI 1018 AISI 1045 AISI 4140
a

Allowable compressive stressa

psi 20,000 30,000 40,000 60,000

None specified 225-265 265-305 310-360

10,000 15,000 20,000 30,000

The values tabulated assume an interference fit with a torque capacity equal to or greater than the reducer rating. When other methods of attachment are used a detailed stress analysis shall be performed.

7.4.7

Peak loading (overloads)

The shaft to hub interface shall be capable of withstanding the manufacturer specified maximum anticipated loads associated with beam pumping units.
7.4.8 Fastener stresses

Fastener stresses shall be determined from the forces developed at the torque rating of the gear reducer in addition to any external structure loading. The maximum allowable stress at the tensile area of threaded fasteners (bolts, studs, or capscrews) shall not exceed the values given in Table 10. The tensile area (As) is calculated as follows:

35

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

0,97 ? ? As = 0,785? Dm ? ? Nt ? ?

2

(40)

where As = tensile area of fastener, expressed in square inches

Dm = major diameter of fastener, expressed in inches Nt = threads per inch of fastener
Table 10 — Maximum allowable tensile stress, fasteners
SAE and/or ASTM Designation SAE 2 Threaded fastener diameter, Dm Mm Over 6 to 19 incl. Over 19 to 38 incl. SAE 5 (ASTM A-449) Over 6 to 25 incl. Over 25 to 38 incl. ASTM A-449 ASTM A-354 Grade BB ASTM A-354 Grade BC Over 38 to 75 incl. Over 6 to 64 incl. Over 64 to 100 incl. Over 6 to 64 incl. Over 64 to 100 incl. SAE 7 SAE 8 (ASTM A-354 Grade BD) Over 6 to 38 incl. Over 6 to 38 incl. Inches Over ? to ? incl. Over ? to 1? incl. Over ? to 1 incl. Over 1 to 1? incl. Over 1? to 3 incl. Over ? to 2? incl. Over 2? to 4 incl. Over ? to 2? incl. Over 2? to 4 incl. Over ? to 1? incl. Over ? to 1? incl. Hardness (BHN) 149-241 121-241 241-302 223-285 183-235 217-285 217-285 255-321 255-321 277-321 302-352 Ultimate yield strength psi 55,000 33,000 85,000 74,000 55,000 80,000 75,000 109,000 99,000 105,000 120,000 MPa 379 228 586 510 379 552 517 752 683 724 827 Allowable applied tensile strength psi 74,000 60,000 120,000 105,000 90,000 105,000 100,000 125,000 115,000 133,000 150,000 MPa 510 414 827 724 621 724 689 862 793 917 1,034 Tensile stress maximum psi 11,000 11,000 20,000 18,000 13,000 17,000 17,000 22,000 22,000 24,600 27,700 MPa 75.8 75.8 138 124 89.6 117 117 152 152 170 186

NOTE: The basis for the values in Table 10 is to prevent joint opening at a peak-rated load.

7.4.8.1

Tensile preload

The tensile preload in the bolt, stud, or cap screw should be 70 % of the yield strength of the material as determined at the tensile area of the thread.
7.4.9 Special seals and breathers

Beam pumping units operate outdoors under potentially adverse atmospheric conditions and shall be equipped with seals and breathers designed for these conditions.

8
8.1

Product identification
Beam pump structure name plate

Each beam pump structure shall be provided with a name plate similar to that shown in Figure 12. At the discretion of the manufacturer, the name plate may contain other non-conflicting and appropriate information, such as model number or lubrication instructions. When structural unbalance is negative the minus (-) sign shall be stamped on the nameplate.

36

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

API Spec 11E

BEAM PUMP STRUCTURE

BEAM PUMP STRUCTURE STRUCTURAL UNBALANCE (+ UNITS) SERIAL NUMBER (NAME OF MANUFACTURER) (ADDRESS OF MANUFACTURER)

Figure 12 — Beam pump structure nameplate

8.2

Speed reducer name plate

Each pumping unit reducer shall be provided with a name-plate substantially as shown in Figure 13. The size (peak torque rating in 1,000 in-lbs) shown on the nameplate shall be one of those listed in Table 2. No other rating marking shall be applied to the reducer. The nameplate may contain information such as model number, lubrication instructions, etc., provided such marking does not conflict with the rating marking.

API Spec 11E

PUMPING UNIT GEAR REDUCER

SIZE (PEAK TORQUE RATING IN THOUSANDS OF INCH-POUNDS RATIO SERIAL NUMBER
(NAME OF MANUFACTURER) (ADDRESS OF MANUFACTURER)

Figure 13 — Pumping unit reducer nameplate

8.3

Installation markings

Clearly defined and readily usable markings shall be provided on the end cross members of the base to indicate the vertical projection of the walking beam centerline. The markings shall be applied with a chisel, punch, or other suitable tool.

37

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

8.4
8.4.1

Supplier/manufacturing requirements
Quality control

The manufacturer is responsible for complying with all of the provisions of this Specification. All quality control work shall be controlled by documented instructions which include acceptance criteria. Only products in full compliance with this Specification shall be considered as being in accordance with this Specification. Where a user/purchaser appoints an inspector to verify the manufacture, the inspector shall have unrestricted access to all works related to the manufacture of items for the purchaser. The manufacturer shall afford the inspector all reasonable facilities to satisfy him that the material is being furnished in accordance with this Specification. Any inspection made at the place of manufacture shall be considered process inspection and shall be conducted so as not to interfere unnecessarily with the operation of the works.
8.4.2 Data sheet

The manufacturer shall retain in his files, and make available upon request, a completed Manufacturer's Gear Reducer Data Sheet (see Figure B.3) for each gear reducer size manufactured.

9
9.1

Storage and maintenance
Shipping and handling
General

9.1.1

Products shall be packaged, stored and transported in such a manner as to preserve the full integrity of the equipment prior to installation in conformance with the manufacturer’s written specifications.

9.1.2

Packaging

Products shall be packaged in such a way as to prevent physical damage during typical transport and deterioration during storage. Products shall be prevented from contact with contaminants.
9.1.3 Storage

Products shall be stored in conditions that meet the manufacturer’s written specifications. Equipment shall be stored in an unstressed condition and shall be protected from the effects of abrasives and chemicals that may cause product damage. Where applicable the application of manufacturer approved anti-corrosion fluids prolongs the products effective storage duration.
9.1.4 Handling and transport

At each occasion the handling of the product shall meet the written requirements of the manufacturer/ supplier to prevent any operational damage to the product. Transportation regulations governing size, weight, hazardous materials, etc. as set forth by state, regional, or national authorities and manufacturer recommendations shall be observed when shipping/transporting products.

9.2

Lubrication

Lubrication is recommended to be in accordance with API RP 11G.

38

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

Annex A (normative) Beam pumping unit designations

The designation of a particular pumping unit is composed of a 3 number sequence containing the reducer rating, structure capacity and stroke length. It is recommended that pumping units furnished to this specification adhere to the gear reducer rating, structure capacity, and stroke length as given in Table A.1. The particular combinations in the table are typical, but combinations other than those listed are acceptable under this standard.
Table A.1 — Pumping unit designations
Designation 6.4-32-16 6.4-21-24 10-32-24 10-40-20 16-27-30 16-53-30 25-53-30 25-56-36 25-67-36 40-89-36 40-76-42 40-89-42 40-76-48 57-76-42 57-89-42 57-95-48 57-109-48 57-76-54 80-109-48 80-133-48 80-119-54 80-133-54 80-119-64 114-133-54 114-143-64 114-173-64 114-143-74 114-119-86 160-173-64 160-143-74 160-173-74 160-200-74 160-173-86 228-173-74 228-200-74 228-213-86 228-246-86 228-173-100 Reducer rating in-lb 6,400 6,400 10,000 10,000 16,000 16,000 25,000 25,000 25,000 40,000 40,000 40,000 40,000 57,000 57,000 57,000 57,000 57,000 80,000 80,000 80,000 80,000 80,000 114,000 114,000 114,000 114,000 114,000 160,000 160,000 160,000 160,000 160,000 228,000 228,000 228,000 228,000 228,000 Structure capacity lb 3,200 2,100 3,200 4,000 2,700 5,300 5,300 5,600 6,700 8,900 7,600 8,900 7,600 7,600 8,900 9,500 10,900 7,600 10,900 13,300 11,900 13,300 11,900 13,300 14,300 17,300 14,300 11,900 17,300 14,300 17,300 20,000 17,300 17,300 20,000 21,300 24,600 17,300 Max. stroke length in 16 24 24 20 30 30 30 36 36 36 42 42 48 42 42 48 48 54 48 48 54 54 64 54 64 64 74 86 64 74 74 74 86 74 74 86 86 100

39

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition
Designation 228-213-120 320-213-86 320-256-100 320-305-100 320-213-120 320-256-120 320-256-144 456-256-120 456-305-120 456-365-120 456-256-144 456-305-144 456-305-168 640-305-120 640-256-144 640-305-144 640-365-144 640-305-168 640-305-192 912-427-144 912-305-168 912-365-168 912-305-192 912-427-192 912-470-240 912-427-216 1280-427-168 1280-427-192 1280-427-216 1280-470-240 1280-470-300 1824-427-192 1824-427-216 1824-470-240 1824-470-300 2560-470-240 2560-470-300 Reducer rating in-lb 228,000 320,000 320,000 320,000 320,000 320,000 320,000 456,000 456,000 456,000 456,000 456,000 456,000 640,000 640,000 640,000 640,000 640,000 640,000 912,000 912,000 912,000 912,000 912,000 912,000 912,000 1,280,000 1,280,000 1,280,000 1,280,000 1,280,000 1,824,000 1,824,000 1,824,000 1,824,000 2,560,000 2,560,000 Structure capacity lb 21,300 21,300 25,600 30,500 21,300 25,600 25,600 25,600 30,500 36,500 25,600 30,500 30,500 30,500 25,600 30,500 36,500 30,500 30,500 42,700 30,500 36,500 30,500 42,700 47,000 42,700 42,700 42,700 42,700 47,000 47,000 42,700 42,700 47,000 47,000 47,000 47,000 Max. stroke length in 120 86 100 100 120 120 144 120 120 120 144 144 168 120 144 144 144 168 192 144 168 168 192 192 240 216 168 192 216 240 300 192 216 240 300 240 300

40

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

Annex B (informative) Recommended data forms

B.1 General
Example data forms are provided for the manufacturer to communicate information on the crank counterbalances and stroke and torque factors.

B.2 Rating form for crank counterbalances

Manufacturers are recommended to use the form below when providing pumping unit crank counterbalances.
Name of manufacturer Designation of unit Total mass(weight) Descriptiona (include units) Maximumb moment about crankshaft (include units) Date prepared

a

Describe parts in use accurately enough to avoid any possible misunderstanding, showing on separate lines a series of practical combinations from minimum to maximum. Equals total weight (column 2) times distance to center of gravity, with crank in horizontal position.

b

Figure B.1 — Rating form for crank counterbalances

41

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

B.3 Stroke and torque factors
Manufacturers are recommended to use the form below when providing pumping unit stroke and torque factors. Name of manufacturer Designation of unit Pumping unit structural imbalance
Position of cranka (degrees) 0° 15° 30° 45° 60° 75° 90° 105° 120° 135° 150° 165° 180° 195° 210° 225° 240° 255° 270° 285° 300° 315° 330° 345° A C R1 R2 R3
a

Date prepared

Pounds/N rodsb Torque factorc Length of stroke, (include units)

Position of Length of stroke, (include units)

P K H I G

For crank counterbalance units with Class I Geometry, the position of the crank is the angular displacement measured clockwise from the 12 o'clock position, viewed with the wellhead to the right. For crank counterbalanced units with Class III Geometry, the position of the crank is the angular displacement measured counter-clockwise from the 6 o'clock position, viewed with the wellhead to the right. For air counterbalanced units with Class III Geometry, the position of the crank is the angular displacement measured clockwise from the 6 o'clock position, viewed with the wellhead to the right. b Position is expressed as a fraction of stroke above lowermost position.
c

Torque factor =

T P R

, where T = torque on pumping unit reducer due to polished rod load PR.

NOTE: See Annexes C, D, E, or F for symbol identification.

Figure B.2 — Pumping unit stroke and torque factor form

42

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

B.4 Gear reducer data sheet
Manufacturers are recommended to use this form below when providing gear reducer information. Manufactured by: Nominal reducer size Calculated Values Pitting resistance torque First reduction Second reduction Third reduction Bending strength torque First reduction: Gear Second reduction: Gear Third reduction: Gear
Notes: 1. First reduction is high-speed reduction. 2. Second reduction is slow-speed reduction on double reduction gear reducers and the intermediate reduction on triple reduction gear reducers. 3. Third reduction is the slow-speed reduction on triple reduction reducers and is not applicable on double reduction reducers.

Date submitted

Units:

Static torque First reduction: Gear Second reduction:

Units: Pinion Pinion Pinion

Units: Pinion Pinion Pinion

Gear Third reduction: Gear

Construction Features Type of reducer (Cross out if not applicable) (Single) (Single) Teeth Number of teeth and normal diametral pitch or transverse diametral pitch: First reduction Second reduction Third reduction Np Np Np Ng Ng Ng Pnd Pnd Pnd Pd Pd Pd (Double) (Double) (Triple) Reduction Helical gearing

Center distance and net face width: First reduction Second reduction Third reduction Cs, Cs, Cs, Wf Wf Wf

Figure B.3 - Manufacturer’s gear reducer data sheet

43

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

Helix angle and normal pressure angle or transverse pressure angle (degrees): First reduction Second reduction Third reduction ψ, ψ, ψ,

φn, φn, φn,
CJ,P CJ,P CJ,P process Teeth finished by CJ,G CJ,G CJ,G

φt φt φt

Geometry factors, I and J (for pinion and gear) First reduction geometry factor Second reduction geometry factor Third reduction geometry factor Manufacturing methods Teeth generated by Tooth hardening method Gear and pinion materials and hardness First reduction Gear material Pinion material Second reduction Gear material Pinion material Third reduction Gear material Pinion material Other components Crankshaft material Housing material Housing type (Check Bearing sizesb pinionc High speed pinion Intermediate speed Low speed pinion Low speed gear
a b

I I I

process

Surface BHC/Rc Surface BHC/Rc Surface BHC/Rc Surface BHC/Rc Surface BHC/Rc Surface BHC/Rc Hardness ): Split One piece Bearing loadingd

Core BNHa Core BNHa Core BNHa Core BNHa Core BNHa Core BNHa

High speed pinion Intermediate speed pinionc Low speed pinion Low speed gear

Core hardness required for surface hardened gears and pinions only. For journal bearings indicate projected area; for roller bearings indicate the American Bearing Manufacturer’s Association (or equivalent) size. List all bearings on each shaft. (State if bearings are mounted in carriers or directly in gear housing.) Not applicable on double reduction reducers. For journal bearings, list loading on each bearing. For roller bearings, list L-10 life as calculated in 7.4.4.

c d

Figure B.3 - Manufacturer’s gear reducer data sheet (continued)

44

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

Annex C (informative) Torque factor on beam pumping units with rear mounted geometry class I lever systems with crank counterbalance

C.1 General
The following calculation technique is generally accepted. More precise results are dependent on the true stroke length which can vary with changes in the beam position relative to the centerline of the saddle bearing. This can be due to an adjustment provided on most medium- to large-size units or due to manufacturing tolerances. Any dimensional deviation will produce some change in the angular relationships with a resultant minor change in the torque factors furnished by the manufacturer. Determinations made with a dynamometer can determine more specific performance characteristics of the individual pumping unit.

C.2 Symbols
In addition to those listed in clause 2, the following system of nomenclature and symbols is used in this Annex (See Figure C.1): FT Torque factor for a given crank angle θ H G I LJ K P M Height from the center of the saddle bearing to the bottom of the base beams Height from the center of the crankshaft to the bottom of the base beams Horizontal distance between the centerline of the saddle bearing and the centerline of the crankshaft Distance from the center of the crankpin bearing to the center of the saddle bearing Distance from the center of the crankshaft to the center of the saddle bearing Effective length of the pitman (from the center of the equalizer bearing to the center of the crankpin bearing) Maximum moment of the rotary counterweights, cranks, and crankpins about the crankshaft

PB Structural unbalance, equal to the force at the polished rod required to hold the beam in a horizontal position with the pitmans disconnected from the crankpins
NOTE This force is positive when acting downward and negative when acting upward.

PRn Net polished rod load PRn = PR - PB Tn Net torque at the crankshaft for a given crank angle θ Tn = Twn - Tr Tr Torque due to the rotary counterweights, cranks, and crankpins for a given crank angle θ ,

45

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

Tr = M sin θ Twn Torque, due to the net polished rod load for a given crank angleθ Twn = FT PRn XPR Polished rod position expressed as a fraction of the stroke length above the lowermost position for a given crank angle θ

α β θ ρ φ χ ψ

Angle between P and R measured clockwise from R to P Angle between C and P Angle of crank rotation in a clockwise direction viewed with the wellhead to the right and with zero degrees occurring at 12 o'clock Angle between K and LJ Angle between the 12 o'clock position and K Angle between C and LJ Angle between C and K

ψ=χ-ρ ψ b Angle between C and K, at bottom (lowest) polished rod position ψ t Angle between C and K, at top (highest) polished rod position

C.3 Method of calculation
C.3.1 Torque factors
Torque factors (as well as the polished rod position) may be determined by a scale layout of the unit geometry so that the various angles involved can be measured. They may alternatively be calculated from the dimensions of the pumping unit by mathematical treatment only.

C.3.2 Submission form
A form for submission of torque factor and polished rod position data is shown on Figure B.2.

C.3.3 Data submission
Torque factors and polished rod positions shall be furnished by pumping unit manufacturers for each 15° crank position with the zero position at 12 o'clock. Other crank positions shall be determined by the angular displacement in a clockwise direction viewed with the wellhead to the right. The polished rod position for each crank position should be expressed as a fraction of the stroke above the lowermost position.

C.3.4 Calculation method
Application of the laws of trigonometric functions give the following expressions. All angles are calculated in terms of a given crank angle θ .

46

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

? AR ? ? sinα ? FT = ? ? ?? ? C ? ? sinβ ?

(C.1)

Sin α is positive when the angle α is between 0° and 180° and is negative when angle α is between 180° and 360°. Sin β is always positive because the angle β is always between 0° and 180°. A negative torque factor (FT) only indicates a change in direction of torque on the crankshaft.

φ = tan?1 ?

? I ? ? ?H?G?

(C.2)

This is a constant angle for any given pumping unit.

β = cos?1 ?

? C2 + P2 ? K 2 ? R 2 + 2 KRcos (θ ? φ ) ? ? 2 CP ? ? ? ?

(C.3)

cos (θ -φ ) is positive when (θ -φ ) is between 270° and 90° moving clockwise and is negative from 90° to 270° moving clockwise. When the angle (θ -φ ) is negative, it should be subtracted from 360°, and the following equations, C.4 and C.5, apply.

χ = cos?1 ? ?

? C2 + LJ2 ? P2 2 C LJ ?

? ? ? ?

(C.4)

ρ = sin

?1

±

? Rsin(θ ? φ ) ? ? ? LJ ? ?

(C.5)

The angle ρ should be taken as a positive angle when sin ρ is positive. This occurs for crank positions between (θ - φ ) = 0° and (θ - φ ) = 180°. The angle ρ should be taken as a negative angle when sin ρ is negative. This occurs for crank positions between (θ - φ ) = 180° and (θ - φ ) = 360°.

ψ =χ -ρ
α = β + ψ ? (θ ? φ )
X PR =

(C.6) (C.7) (C.8)

ψ b ?ψ ψ b ?ψ t
? C2 + K 2 ? ( P + R ) 2 ? ? 2CK ? ? ? ?

ψ b = cos?1 ?

(C.9)

ψ t = cos?1 ?

? C2 + K 2 ? ( P ? R )2 ? ? 2CK ? ? ? ?

(C.10)

C.4 Application of torque factors
C.4.1 General
Torque factors are used primarily for determining peak crankshaft torque on operating pumping units. The procedure is to take a dynamometer card and then use torque factors, polished rod position factors, and counterbalance information to plot the net torque curve. Example forms for recording calculations are provided in Figure C.4.

47

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

Points for plotting the net torque curve are calculated from the following equation (see note):
Tn = FT ( P ? P ) ? M sinθ R B
NOTE

(C.11)

This equation applies to pumping units where maximum counterbalance moment is obtained at θ equals 90° or 270°.

C.4.2 Changes due to structural unbalance
The equation for net crankshaft torque, Tn, does not include the change in structural unbalance with change in crank angle; neglects the inertia effects of beam, beam weights, equalizer, pitman, crank, and crank counterweights; and neglects friction in the saddle, tail, and pitman bearings. For units having 100 % crank counterbalance and where crank-speed variation is not more than 15 % of average, these factors usually can be neglected without introducing errors greater than 10 %. When beam weights are used, the inertia effects of the weights should be included to determine peak torque with any degree of accuracy. The procedure for including the inertia effect of beam counterweights has been omitted because of the limited use of this type of counterbalance. Some non-dynamic factors that can have an effect on the determination of instantaneous net torque loadings, and which accordingly should be recognized or considered, are outlined in C.4.7, C.4.8, and C.4.9.

C.4.3 Polish rod effects
Torque factors may be used to obtain the effect at the polished rod of the rotary counterbalance. This is done for a given crank angle by dividing the counterbalance moment, M sin θ, by the torque factor for the crank angle θ . The result is the rotary counterbalance effect at the polished rod.

C.4.4 Rotary counterbalance moment
Torque factors may also be used to determine the maximum rotary counterbalance moment. This is done by placing the cranks in the 90° or 270° position and tying off the polished rod. Then, with a polished rod dynamometer, the counterbalance effect is measured at the polished rod. Using this method, the measured polished rod load (PR) is the combined effect of the rotary counterbalance and the structural unbalance. The maximum rotary counterbalance moment can then be determined from the following equation:
M = FT ( PR ? P ) B

(C.12)

To check measurements, the maximum moment, M, should be determined with the cranks in both the 90° and 270° positions. If there is a significant difference in the maximum moments calculated from measurements at 90° and 270°, a recheck of polished rod measurements and crank positions should be made. However, if there is only a slight difference, a satisfactory check is indicated and it is recommended that an arithmetic average of the two maximum moments be used.
EXAMPLE 1 To illustrate the use of torque factors, an example dynamometer card taken on a 4,000 ft well is shown in Figure C.2. The first step in calculating the net crankshaft torque is to divide the dynamometer card so that the load may be determined for each 15° of crank angle θ . Lines are projected down from the ends of the card, as shown, to determine its length, which is proportional to the length of the stroke. The length of the baseline or zero line is then divided into 10 equal parts and these parts are subdivided. This may easily be done with a suitable scale along a suitable diagonal line as shown (see note). NOTE Using the polished rod position data, vertical lines representing each 15° of crank angle θ are projected upward to intersect the dynamometer card. Then the polished rod load may be determined for each 15° of crank angle θ . EXAMPLE 2 To further illustrate, a calculation is made considering the point where the crank angle θ equals 75°. From polished rod stroke and torque factor data for the particular 64 in stroke 160-D pumping unit used for this example, it is found that the position of the polished rod at 75° is 0.397 and that the torque factor FT is 34.38 in. A vertical line is drawn from the 0.397 position on the scale up to the point of intersection with the load on the upstroke (Figure C.2). The dynamometer deflection at this point is read to be 1.16 in, which, with a scale constant of 7,450 lbs/in, makes the load (PR) at that point 8,650 lbs. EXAMPLE 3 In a similar manner, the polished rod load may be obtained for each 15° angle of crank rotation. The dynamometer card has been marked to show the load and position involved for each 15° of crank angle. The structural unbalance, PB, for the example unit equals +650 lbs. Therefore, the net polished rod load, PRn, at θ = 75 is:

48

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition
PRn = PR - PB = 8,650 - (+650) = 8,000 lbs The torque, Twn, due to the net polished rod load is given by: Twn =FT x PR = 34.38 x 8,000 = 275,000 in-lbs

C.4.5 Torque determination
To find the torque, Tr, due to the crank counterbalance, the maximum moment, M, has to be determined. This may be done either from manufacturers' counterbalance tables or curves, or as described in C.4.4. Because of the lack of manufacturers' counterbalance data in a majority of the cases, the polished rod measurement technique will be used more frequently in determining the maximum moment. Should the manufacturers' counterbalance data be used, it is suggested that a check be made using a polished rod measurement technique.
EXAMPLE The horizontal dotted line drawn across the dynamometer card in Figure C.2 is the counterbalance effect measured with the dynamometer at the 90° crank angle and is 6,250 lbs. The maximum moment can then be calculated as follows, using Equation (C.12): M = FT (PR -PB ) = 32.76 x (6,250 - 650) = 183,000 in-lbs (The torque factor of 32,76 in is the value at the 90° crank position for the example unit.) Although not shown, the measured counterbalance effect for the 270° crank position was 6,410 lbs. Using the torque factor of 32.04 in at the 270° crank position for the example unit, the maximum moment is M = 32.04 x (6,410 - 650) = 185,000 in-lbs The maximum moments determined at the 90° and 270° crank positions are in good agreement, and the average maximum moment of 184,000 in-lbs will be used. The torque, Tr , due to the counterbalance at the 75° crank position would therefore be equal to: 184,000 x sin 75° = 184,000 x 0.966 = 178,000 in-lbs) The net torque at the crankshaft for the 75° crank position would then be calculated from Equation (C.11) as follows: Tn = FT x (PR - PB) – M sin θ = 34.88 x (8,650 - 650) – (184,000 x 0.966) = 275,000 -178,000 = 97,000 in-lbs) These values may be calculated for other crank angle positions in the same manner as outlined above. Shown in Figure C.3 is a plot of torque versus crank angle that includes the net polished rod load torque curve, the counterbalance torque curve, and the net crankshaft torque curve.

C.4.6 Alternative crank rotation
The foregoing example on the use of torque factors has been based on the pumping unit operating with the cranks rotating toward the well from top dead center If the pumping unit is operating with the cranks rotating away from the well from top dead center, the calculation technique is changed only in the use of the torque factor in polished rod position data form (Figure B.2). The angle of the crank (column 1) is reversed, starting from the bottom with 15° and counting up in 15° increments to 360°.

49

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

C.4.7 Alternative techniques
The foregoing technique is generally accepted. More precise results are dependent on the true stroke length which can vary with changes in the beam position relative to the centerline of the saddle bearing. This can be due to an adjustment provided on most medium- to large-size units or due to manufacturing tolerances. Any dimensional deviation will produce some change in the angular relationships with a resultant minor change in the torque factors furnished by the manufacturer.

C.4.8 Geometrical influences
The geometry of the dynamometer can influence the determination of instantaneous load values for the various specified or selected crank angles. The dynamometer manufacturer should be contacted for the performance characteristics of the particular dynamometer being used and the procedures that should be followed to adjust the recorded card when completely accurate data are required.

C.4.9 Interpolation
Maximum and minimum loads will most frequently fall at points other than the 15° divisions for which torque factors are provided. Interpolation between 15° divisions is permissible without significant error.

50

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

β

LC

χψ
LP ρ LK H1

LA

θ
R

LJ

PR

2

L
a) Upstroke

β

LC


LP LJ LK

ψ χ

LA

H1 PR

R

θ
H2

LI

b)

Downstroke

Figure C.1 — Pumping unit geometry
NOTE: Crank rotation is defined as either clockwise or counter-clockwise as viewed from the side of the pumping unit with the well head to the right.

51

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

15 30

75

PR
CB

1
135 150 165 180 240
0 ,8 0 ,9

45

60

90

345

330

315

300

285

270

105

255

120

0

2

0 ,1

0 ,2

0 ,3

0 ,4

0 ,5

0 ,6

0 ,7

1

Upstroke

Key 2

Downstroke

Figure C.2 — Division of dynamometer card by crank angle using polished rod position data

1000 in-lb

300
kN.m

30

100

T

200

Net 10,9 kNm 97 000 in-lb +31,0 kNm +275 000 in-lb

1 2

20

10

225 210
1 ,0

0

0

θ
120 150 180 240 270 300 330 360
3

30
-10

60

90

-100

-20,1 kNm -178 000 in-lb

-200

-20

4
5

6

Key 1 Well torque 4 Counterbalance torque

2 5

160 D Reducer limit Upstroke

3 6

Net gear torque Downstroke

Figure C.3 — Torque curves using torque factors

52

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition
NET REDUCER TORQUE CALCULATION SHEET (CONVENTIONAL CRANK BALANCED UNIT ONLY—CLOCKWISE ROTATION) Well No.: Unit size: ___________________________________________ ___________________________________________ sin θ 0 0.259 0.500 0.707 0.866 0.966 1.000 0.966 0.866 0.707 0.500 0.259 0 -0.259 -0.500 -0.707 -0.866 -0.966 -1.000 -0.966 -0.866 -0.707 -0.500 -0.259 Date Prepared
Note

Company: Location: FT

________________________________ ________________________________ FT (PR - PB) -M(sinθ ) 0 0 + + + + + + + + + + + Tn

θ
0° 15° 30° 45° 60° 75° 90° 105° 120° 135° 150° 165° 180° 195° 210° 225° 240° 255° 270° 285° 300° 315° 330° 345°

PR

PB

PR - PB

Tn = FT ( P ? P ) ? M sinθ R B
Tn = Net reducer torque, in-lbs FT = Torque factor at θ , in PCB at 90° = _______________ M = (PCB at 90° - PB (FT at 90°)) = _____________

Where

θ = Position of crank

M = Maximum moment of counterbalance, in-lbs PR = Measured polished rod load at θ , lbs PB = Unit structural unbalance, lbs

Figure C.4 – Calculation sheet – Clockwise rotation

53

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition
NET REDUCER TORQUE CALCULATION SHEET (CONVENTIONAL CRANK BALANCED UNIT ONLY—COUNTER-CLOCKWISE ROTATION) Well No.: Unit size: ___________________________________________ ___________________________________________ sinθ 0 -0.259 -0.500 -0.707 -0.866 -0.966 -1.000 -0.966 -0.866 -0.707 -0.500 -0.259 0 0.259 0.500 0.707 0.866 0.966 1.000 0.966 0.866 0.707 0.500 0.259 Date Prepared Note Where
Tn = Net reducer torque, in-lbs

Company: Location: FT

________________________________ ________________________________ FT (PR - PB) -M(Sin θ ) 0 + + + + + + + + + + + 0 Tn

θ
0° 345° 330° 315° 300° 285° 270° 255° 240° 225° 210° 195° 180° 165° 150° 135° 120° 105° 90° 75° 60° 45° 30° 15°

PR

PB

PR - PB

Tn = FT ( P ? P ) ? M sinθ R B
FT = Torque factor at θ , in PCB at 270° = _______________ M = (PCB at 270° - PB (FT at 270°)) = _____________

θ = Position of crank

M = Maximum moment of counterbalance, in-lbs PR = Measured polished rod load at θ , lbs PB = Unit structural unbalance, lbs

Figure C.4 – Calculation sheet – Counter-clockwise rotation

54

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

Annex D (informative) Torque factor on beam pumping units with front mounted geometry class III lever systems with crank counterbalance

D.1 General
The following calculation technique is generally accepted. More precise results are dependent on the true stroke length which can vary with changes in the beam position relative to the centerline of the saddle bearing. This can be due to an adjustment provided on most medium- to large-size units or due to manufacturing tolerances. Any dimensional deviation will produce some change in the angular relationships with a resultant minor change in the torque factors furnished by the manufacturer. Determinations made with a dynamometer can determine more specific performance characteristics of the individual pumping unit.

D.2 Symbols
In addition to those listed in clause 2, the following system of nomenclature and symbols is used in this Annex (See Figure D.1): FT Torque factor for a given crank angle θ G H I P LJ K M Height from the center of the crankshaft to the bottom of the base beams Height from the center of the Samson Post bearing to the bottom of the base beams Horizontal distance between the centerline of the Samson Post bearing and the centerline of the crankshaft Effective length of the pitman (from the center of the equalizer, or cross yoke, bearing to the center of the crankpin bearing) Distance from the center of the crankpin bearing to the center of the Samson Post bearing Distance from the center of the crankshaft to the center of the Samson Post bearing Maximum moment of the rotary counterweights, cranks, and crankpins about the crankshaft

PB Structural unbalance, equal to the force at the polished rod required to hold the beam in a horizontal position with the pitmans disconnected from the crankpins
NOTE This force acts upward on Class III Geometry Units and is negative.

Pc

Counterbalance at the polished rod, determined using a dynamometer with crankpin at 90° position

PRn Net polished rod load PRn = PR – PB Tn Net torque at the crankshaft for a given crank angle θ Tn = Twn - Tr

55

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

Tr

Torque due to the rotary counterweights, cranks, and crankpins for a given crank angle θ Tr = M sin (θ + τ)

Twn Torque, due to the net polished rod load for a given crank angle θ Twn = FT PRn XPR Polished rod position expressed as a fraction of the stroke length above the lowermost position for a given crank angle θ

α β θ ρ τ φ χ ψ

Angle between P and R measured clockwise from R to P Angle between LC and P Angle of crank rotation in a counter-clockwise direction viewed with the wellhead to the right and with zero degrees occurring at 6 o'clock Angle between K and LJ Angle of crank counterweight arm offset for front mounted geometry (Class III lever systems) Angle between the 6 o'clock position and K Angle between C and LJ Angle between C and K

ψ=χ-ρ ψ b Angle between C and K, at bottom (lowest) polished rod position ψ t Angle between C and K, at top (highest) polished rod position

D.3 Method of calculation
D.3.1 Torque factors
Torque factors (as well as the polished rod position) may be determined by a scale layout of the unit geometry so that the various angles involved can be measured. They may alternatively be calculated from the dimensions of the pumping unit by mathematical treatment only.

D.3.2 Submission form
A form for submission of torque factor and polished rod position data is shown on Figure B.2.

D.3.3 Data submission
Torque factors and polished rod positions shall be furnished by pumping unit manufacturers for each 15° crank position with the zero position at 6 o'clock. Other crank positions shall be determined by the angular displacement in a counter-clockwise direction viewed with the wellhead to the right. The polished rod position for each crank position should be expressed as a fraction of the stroke above the lowermost position.

56

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

D.3.4 Calculation method
Application of the laws of trigonometric functions give the following expressions. All angles are calculated in terms of a given crank angle θ .
FT =

AR sinα C sinβ

(D.1)

Sin α is positive when the angle α is between 0° and 180° and is negative when angle α is between 180° and 360°. Sin β is always positive because the angle β is always between 0° and 180°. A negative torque factor (FT) only indicates a change in direction of torque on the crankshaft.

φ = tan?1 ?

? I ? ? + 180 ° ?H?G?

(D.2)

This is a constant angle for any given pumping unit.

β = cos?1 ?

? C2 + P2 ? K 2 ? R 2 + 2 K Rcos (θ ? φ ) ? ? 2CP ? ? ? ?

(D.3)

It is important to get the sign of cos (θ -φ) correct. Cos (θ -φ ) is negative when (θ -φ ) is between 90° and 270° and positive for all other angles. When the angle (θ -φ) is negative, it should be subtracted from 360°, and the following equations, D.4 and D.5, apply.

χ = sin?1 ?

? Psinβ ? ? ? LJ ? ? φ)?

(D.4)

ρ = sin

?1 ? Rsin(θ

? ?

LJ

? ?

(D.5)

In regards to the diagrams in Figure D.1, ρ shall be taken as positive in the upstroke diagram (Fig. D.1a), and negative in the downstroke diagram (Fig. D.1b). For Equation (D.6) to be correct it is necessary to use the correct sign for the angle ρ . The angle ρ should be taken as positive when sin ρ is positive. This occurs for crank positions when 0° < (θ -φ ) < 180°. The angle ρ is taken as negative when sin ρ is negative. This occurs for crank positions when 180° < (θ -φ ) < 360°.When the angle (θ -φ ) is negative it can be subtracted from 360°, and this new angle can be used to determine the proper sign.

ψ =χ?ρ
sin α = sin (θ ?φ ) ? ψ ? β
X PR =

(D.6)

[

]

(D.7) (D.8)

ψ b ?ψ ψ b ?ψ t
? C 2 + K 2 ? ( P + R )2 ? ? 2CK ? ? ? ? ? C 2 + K 2 ? ( P ? R )2 ? ? 2CK ? ? ? ?

ψ t = cos?1 ?

(D.9)

ψ b = cos?1 ?

(D.10)

57

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

D.4 Application of torque factors
D.4.1 General
Torque factors are used primarily for determining peak crankshaft torque on operating pumping units. The procedure is to take a dynamometer card and then use torque factors, polished rod position factors, and counterbalance information to plot the net torque curve. Points for plotting the net torque curve are calculated from the following equation: Tn = FT ( PR ? PB ) ? M sin (θ + τ ) (D.11)

D.4.2 Changes due to structural unbalance
The equation for net crankshaft torque, Tn, does not include the change in structural unbalance with change in crank angle; neglects the inertia effects of beam, beam weights, equalizer (or cross yoke), pitman, crank, and crank counterweights; and neglects friction in the bearings. For units having 100 % crank counterbalance and where crank-speed variation is not more than 15 % of average, these factors usually can be neglected without introducing errors greater than 10 %. Some non-dynamic factors that can have an effect on the determination of instantaneous net torque loadings, and which accordingly should be recognized or considered, are outlined in D.4.6, D.4.7, and D.4.8.

D.4.3 Polished rod effects
Torque factors may be used to obtain the effect at the polished rod of the rotary counterbalance. This is done for a given crank angle by dividing the counterbalance moment, M sin (θ + τ), by the torque factor for the crank angle θ . The result is the rotary counterbalance effect at the polished rod.

D.4.4 Rotary counterbalance moment
Torque factors may also be used to determine the maximum rotary counterbalance moment. This is done by placing the cranks in the 90° position and tying off the polished rod. Then, with a polished rod dynamometer, the counterbalance effect is measured at the polished rod. Using this method, the measured polished rod load (Pc) is the combined effect of the rotary counterbalance and the structural unbalance. The maximum rotary counterbalance moment can then be determined from the following equation:
M = FT ( Pc ? P ) B

sin ( 90 ° + τ )

(D.12)

EXAMPLE 1 To illustrate the use of torque factors, an example dynamometer card taken on a 2,872ft well is shown in Figure D.2. The first step in calculating the net crankshaft torque is to divide the dynamometer card so that the load may be determined for each 15° of crank angle θ . Lines are projected down from the ends of the card, as shown, to determine its length, which is proportional to the length of the stroke. The length of the baseline or zero line is then divided into 10 equal parts and these parts are subdivided. This may easily be done with a suitable scale along a suitable diagonal line as shown (see Note). NOTE Using the polished rod position data, vertical lines representing each 15° of crank angle θ are projected upward to intersect the dynamometer card. Then the polished rod load may be determined for each 15° of crank angle θ . To further illustrate, a calculation is made considering the point where the crank angle θ equals 60°. From polished rod stroke and torque factor data for the particular 86 in. stroke 160-D pumping unit used for this example, it is found that the position of the polished rod at 60° is 0.405 and that the torque factor FT is 35.45 in. A vertical line is drawn from the 0.405 position on the scale up to the point of intersection with the load on the upstroke (Figure D.2). The dynamometer deflection at this point is read to be 0.99 in, which, with a scale constant of 7,500 lbs/in, makes the load (PR) at that point 7,425 lbs. In a similar manner, the polished rod load may be obtained for each 15° angle of crank rotation. The dynamometer card has been marked to show the load and position involved for each 15° of crank angle. The structural unbalance, PB, for the example unit equals -1,535 lbs. Therefore, the net polished rod load, PRn, at θ = 60 is: PRn = PR - PB = 7,425 - (-1,535) = 8,960 lbs

58

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition
The torque, Twn, due to the net polished rod load is given by: Twn =FT?PR = 36.45 x 8,960 = 326,592 in-lbs

D.4.5 Torque determination
To find the torque, Tr, due to the crank counterbalance, the maximum moment, M, has to be determined. This may be done either from manufacturers' counterbalance tables or curves, or as described in D.4.4. Should the manufacturers' counterbalance data be used, it is suggested that a check be made using a polished rod measurement technique.
EXAMPLE The horizontal dotted line drawn across the dynamometer card in Figure D.2 is the counterbalance effect measured with the dynamometer at the 90° crank angle and is 4,594 lbs. The maximum moment can then be calculated as follows, using Equation (D.12):

M

=

sin ( 90° + τ )

FT ( Pc ? P ) B

= 38.38 x (4,594 + 1,535)/0.891) = 264,008 in-lbs) (The torque factor of 38.38 in is the value at the 90° crank position and angle τ is 27°for the example unit.) The torque, Tr , due to the counterbalance at the 60° crank position would therefore be equal to Tr = 264,008 x sin(60° + 27°)) = 264,008 x 0.999 = 263,744 in-lbs The net torque at the crankshaft for the 60° crank position would then be calculated from Equation (D.11) as follows: Tn Tn = FT?(PR -PB) – M sin (θ + τ) = Twn – Tr = 362,592 - 263,744 = 62,848 in-lbs These values may be calculated for other crank angle positions in the same manner as outlined above. Shown in Figure D.3 is a plot of torque versus crank angle that includes the net polished rod load torque curve, the counterbalance torque curve, and the net crankshaft torque curve.

D.4.6 Alternative techniques
The foregoing technique is generally accepted. More precise results are dependent on the true stroke length which can vary with changes in the beam position relative to the centerline of the saddle bearing. This can be due to an adjustment provided on most medium- to large-size units or due to manufacturing tolerances. Any dimensional deviation will produce some change in the angular relationships with a resultant minor change in the torque factors furnished by the manufacturer.

D.4.7 Geometrical influences
The geometry of the dynamometer can influence the determination of instantaneous load values for the various specified or selected crank angles. The dynamometer manufacturer should be contacted for the performance characteristics of the particular dynamometer being used and the procedures that should be followed to adjust the recorded card when completely accurate data are required.

59

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

D.4.8 Interpolation
Maximum and minimum loads will most frequently fall at points other than the 15° divisions for which torque factors are provided. Interpolation between 15° divisions is permissible without significant error.

LA

ψ ρ

χ
LK LJ

LC

β
LP PR

1

α

θ τ

H2

L
a) Downstroke

LA LC

ψ ρ

β

χ
LP PR

LJ LK

H1

α θ
H2

τ

L
b) Upstroke

60

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

Figure D.1 — Front mounted geometry, class III lever system
NOTE: Crank rotation is defined as either clockwise or counter-clockwise as viewed from the side of the pumping unit with the well head to the right.

P R
30 75 120 45 135 0,9
2 360 5

90

105

15

60

330 345 0

P CB
315 300 285 270

33,0 kN 7 425 lbf 240 255

1 210 2 225

0

195

180 1,0 0,8

0,1

0,2

0,3

0,4

0,5

0,6

0,7

1

Key Upstroke 2 Downstroke

Figure D.2 — Division of dynamometer card by crank angle using polished rod position data
1000 in-lb

kNm

400 300 200 100 0

40

1 36,9 kNm 326 592 in-lb

T

T

30 20 10 0 300 -10 -20 -30 -300 6 5 29,7 kNm 263 744 in-lb 7,2 kNm 62 848 in-lb

3

θ
60 120 180 240 300

0

-100 -200

4 6

150 165

61

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition
Key 1 Well torque 4 Counterbalance torque

2 5

160 D Reducer limit Upstroke

3 6

Net gear torque Downstroke

Figure D.3 — Torque curves using torque factors

62

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

Annex E (informative) Torque factor on beam pumping units with front mounted geometry class III lever system with air counterbalance

E.1 General
The following calculation technique is generally accepted. More precise results are dependent on the true stroke length which can vary with changes in the beam position relative to the centerline of the saddle bearing. This can be due to an adjustment provided on most medium- to large-size units or due to manufacturing tolerances. Any dimensional deviation will produce some change in the angular relationships with a resultant minor change in the torque factors furnished by the manufacturer. Determinations made with a dynamometer can determine more specific performance characteristics of the individual pumping unit.

E.2 Symbols
In addition to those listed in clause 2, the following system of nomenclature and symbols is used in this Annex (See Figure E.1): FT Torque factor for a given crank angle θ G H I LJ Height from the center of the crankshaft to the bottom of the base beams Height from the center of the Samson Post bearing to the bottom of the base beams Horizontal distance between the centerline of the Samson Post bearing and the centerline of the crankshaft Distance from the center of the crankpin bearing to the center of the Samson Post bearing where
LJ = C2 + P2 ? ( 2CPcosβ )

K P

Distance from the center of the crankshaft to the center of the Samson Post bearing Effective length of the pitman (from the center of the equalizer bearing to the center of the crankpin bearing)

Ma Geometry constant for a given unit (distance from Samson Post bearing to air tank bearing multiplied by the area of the piston in the air cylinder divided by the distance from the Samson Post bearing to the centerline of the polished rod) Pa Pressure in air counterbalance tank for a given crank position θ Pc Counterbalance effect at the polished rod at any specific crank angle θ Pc = Ma (Pa - S) S Pressure in air counterbalance tank required to offset the weight of the walking beam, horsehead, equalizer, pitmans, etc.

63

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

Tn

Net torque at the crankshaft for a given crank angle θ

XPR Polished rod position expressed as a fraction of the stroke length above the lowermost position for a given crank angle θ

α β θ ρ φ χ ψ

Angle between P and R measured clockwise from R to P Angle between C and P Angle of crank rotation in a clockwise direction viewed with the wellhead to the right and with zero degrees occurring at 6 o'clock Angle between K and LJ Angle between the 6 o'clock position and K Angle between C and LJ Angle between C and K

ψ =χ -ρ ψ b Angle between C and K, at bottom (lowest) polished rod position ψ t Angle between C and K, at top (highest) polished rod position

E.3 Method of calculation
E.3.1 Torque factors
Torque factors (as well as the polished rod position) may be determined by a scale layout of the unit geometry so that the various angles involved can be measured. They may alternatively be calculated from the dimensions of the pumping unit by mathematical treatment only.

E.3.2 Submission form
A form for submission of torque factor and polished rod position data is shown on Figure B.2.

E.3.3 Data submission
Torque factors and polished rod positions shall be furnished by pumping unit manufacturers for each 15° crank position with the zero position at 6 o'clock. Other crank positions shall be determined by the angular displacement in a clockwise direction viewed with the wellhead to the right. The polished rod position for each crank position should be expressed as a fraction of the stroke above the lowermost position.

E.3.4 Calculation method
Application of the laws of trigonometric functions give the following expressions. All angles are calculated in terms of a given crank angle θ .
FT =
AR sinα C sinβ

(E.1)

64

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

Sin α is positive when the angle α is between 0° and 180° and is negative when angle α is between 180° and 360°. Sin β is always positive because the angle β is always between 0° and 180°. A negative torque factor (FT) only indicates a change in direction of torque on the crankshaft.

φ = 180° ? tan?1 ?

? I ? ? ?H?G?

(E.2)

This is a constant angle for any given pumping unit.

β = cos?1 ?

? C2 + P2 ? K 2 ? R 2 + 2 K Rcos (θ ? φ ) ? ? 2CP ? ? ? ?

(E.3)

Cos (θ -φ ) is positive when (θ -φ) is between 270° and 90° moving clockwise and is negative from 90° and 270° moving clockwise. When the angle (θ -φ) is negative, it should be subtracted from 360°, and the following equations, E.4 and E.5, apply.

χ = sin?1 ?

? Psinβ ? ? ? LJ ? ? φ)?

(E.4)

ρ = sin

?1 ? Rsin(θ

? ?

LJ

? ?

(E.5)

The angle ρ should be taken as positive when sin ρ is positive. This occurs for crank positions when 0° < (θ φ) < 180°.The angle ρ should be taken as negative when sin ρ is negative. This occurs for crank positions when 180° < (θ -φ ) < 360°.

ψ =χ+ρ
sinα = sin ? β + ψ + (θ ? φ ) ? ? ?

(E.6) (E.7) (E.8)

X PR =

ψ b ?ψ ψ b ?ψ t
? C 2 + K 2 ? ( P + R )2 ? ? 2CK ? ? ? ? ? C 2 + K 2 ? ( P ? R )2 ? ? 2CK ? ? ? ?

ψ t = cos?1 ?

(E.9)

ψ b = cos?1 ?

(E.10)

E.4 Application of torque factors
E.4.1 General
Torque factors are used primarily for determining peak crankshaft torque on operating pumping units. The procedure is to take a dynamometer card and then use torque factors, polished rod position factors, and counterbalance information to plot the net torque curve. Points for plotting the net torque curve are calculated from the following equation (see Note):
Tn = FT ( P ? Pc ) R

(E.11)

65

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

E.4.2 Changes due to structural unbalance
The equation for net crankshaft torque, Tn, does not include the change in structural unbalance with change in crank angle; neglects the inertia effects of beam, beam weights, equalizer, pitman, and crank, and neglects friction in the Samson Post, equalizer and pitman bearings. For units where crank-speed variation is not more than 15 % of average, these factors usually can be neglected without introducing errors greater than 10 %. Some non-dynamic factors that can have an effect on the determination of instantaneous net torque loadings, and which accordingly should be recognized or considered, are outlined in E.4.4, E.4.5, and E.4.6.
EXAMPLE 1 To illustrate the use of torque factors, an example dynamometer card taken on a 1 700 m (5 560 ft) well is shown in Figure E.2. The first step in calculating the net crankshaft torque is to divide the dynamometer card so that the load may be determined for each 15° of crank angle θ . Lines are projected down from the ends of the card, as shown, to determine its length, which is proportional to the length of the stroke. The length of the baseline or zero line is then divided into 10 equal parts and these parts are subdivided. This may easily be done with a suitable scale along a suitable diagonal line as shown (see Note). NOTE Using the polished rod position data, vertical lines representing each 15° of crank angle are projected upward to intersect the dynamometer card. Then the polished rod load may be determined for each 15° of crank angle. The counterbalance line may then be drawn on the card. To avoid time-consuming geometrical considerations, it may be assumed that the counterbalance line is straight between the two end points of maximum and minimum counterbalance. The assumed counterbalance will be 3 % to 4 % lower than the actual counterbalance around the mid-point of the stroke, slightly higher at the bottom of the stroke, and nearly equal at the top of the stroke. For the example calculation, the recorded maximum air counterbalance tank pressure at the bottom of the stroke, 0° crank position, was 328 psig and the minimum air pressure at the top of the stroke, 180° crank position, was 262 psig. Using the equation, Pc = Ma (Pa - S), where Ma = 52.5 in2 and S is 73 psi (as furnished by the pumping unit manufacturer), we calculate the following results: a) b) Maximum counterbalance at the 0° crank position is Pc = 52.5 (328 - 73) = 13,388 lbs counterbalance at the polished rod. 13,388 lbs divided by the scale constant, 11,300 lbs/in, gives 1,185 in; Minimum counterbalance at the 180° crank position is Pc = 52.5 (262 -73) = 9,923 lb. 9,923 divided by 11,300 lbs/in gives 0.878 in.

The counterbalance line can now be drawn on the dynamometer card as shown in Figure E.2. EXAMPLE 2 To further illustrate, a calculation is made considering the point where the crank angle θ equals 75°. From polished rod stroke and torque factor data for the particular 86 in stroke 300-D pumping unit used for this example, it is found that the position of the polished rod at 75° is 0.332 and that the torque factor FT is 39.02. A vertical line is drawn from the 0.332 position on the scale up to the point of intersection with the load on the upstroke (Figure E.2). The dynamometer deflection at this point is read to be 1.45 in, which, with a scale constant of 11,300 lbs/in, makes the load (PR) at that point 16,385 lbs. In a similar manner, the polished rod load may be obtained for each 15° angle of crank rotation. The dynamometer card has been marked to show the load and position involved for each 15° of crank angle. However, it is usually only necessary to determine the maximum polished rod load, which in the example case occurs between the 105° and 120° crank position. The maximum dynamometer deflection at this point is 1.60 in which when multiplied by the scale constant of 11,300 lbs/in gives 18,080 lbs polished rod load. The net torque, Tn, can now be determined. In the equation Tn = Ft(PR - Pc) the value (PR - Pc) is represented by the difference in the dynamometer deflection between the card and the counterbalance line. Referring to the card in Figure E.2, the difference in the dynamometer deflection between the counterbalance line and the well card is 0.36 in at 75° crank position. This value multiplied by the scale constant of 11,300 lbs/in and the torque factor of 39.25 in at 75° crank position gives 159,669 in-lbs net torque. These values may be calculated for other crank positions in the same manner. Figure E.3 is a plot of the net torque curve.

E.4.3 Alternative crank rotation
The foregoing example on the use of torque factors has been based on the pumping unit operating with the cranks rotating toward the well from top dead center If the pumping unit is operating with the cranks rotating away from the well from top dead center, the calculation technique is changed only in the use of the torque factor in polished rod position data form (Figure B.2). The angle of the crank (column 1) is reversed, starting from the bottom with 15° and counting up in 15° increments to 360°.

66

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

E.4.4 Alternative techniques
The foregoing technique is generally accepted. More precise results are dependent on the true stroke length which can vary with changes in the beam position relative to the centerline of the saddle bearing. This can be due to an adjustment provided on most medium- to large-size units or due to manufacturing tolerances. Any dimensional deviation will produce some change in the angular relationships with a resultant minor change in the torque factors furnished by the manufacturer.

E.4.5 Geometrical influences
The geometry of the dynamometer can influence the determination of instantaneous load values for the various specified or selected crank angles. The dynamometer manufacturer should be contacted for the performance characteristics of the particular dynamometer being used and the procedures that should be followed to adjust the recorded card when completely accurate data are required.

E.4.6 Interpolation
Maximum and minimum loads will most frequently fall at points other than the 15° divisions for which torque factors are provided. Interpolation between 15° divisions is permissible without significant error.

67

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

LA

χ ρ

LC

ψ

β

LJ H1 LK

LP PR

θ
R H2

α

L
a) Downstroke

ψ ρ χ
LJ LK

LC

LA

β
LP PR

H1

H2

α θ
LI
b)

R

Upstroke

Figure E.1 — Pumping unit geometry

68

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

105

P R
60 75 90 45

120

30

135

345 330

315

0

300 72,9 kN 16 385 lbf 285

2 270 255

165 180 195 1,0

CB

80,4 kN 18 080 lbf

9,1 mm 0,36 in

15

1

0

240

225 0,8
θ 360

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,9

1

Upstroke

Key 2

Downstroke

Figure E.2 — Division of dynamometer card by crank angle using polished rod position data
400
1000 in-lb

T

300

T kNm

40

2

30

1

200

20

100

10

0

0

0

60

120

180

240

300

-100

-10

-200

-20 5 6

Key 1 Theoretical net torque 5 Upstroke

2 6

320 D Reducer limit Downstroke

Figure E.3 — Torque curves using torque factors

210

150

69

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

Annex F (informative) Torque factor on beam pumping units with rear mounted geometry class I lever systems with phased crank counterbalance

F.1 General
The following calculation technique is generally accepted. More precise results are dependent on the true stroke length which can vary with changes in the beam position relative to the centerline of the saddle bearing. This can be due to an adjustment provided on most medium- to large-size units or due to manufacturing tolerances. Any dimensional deviation will produce some change in the angular relationships with a resultant minor change in the torque factors furnished by the manufacturer. Determinations made with a dynamometer can determine more specific performance characteristics of the individual pumping unit.

F.2 Symbols
In addition to those listed in clause 2, the following system of nomenclature and symbols is used in this Annex (See Figure F.1): FT Torque factor for a given crank angle θ G H I LJ K P M Height from the center of the crankshaft to the bottom of the base beams Height from the center of the saddle bearing to the bottom of the base beams Horizontal distance between the centerline of the saddle bearing and the centerline of the crankshaft Distance from the center of the crankpin bearing to the center of the saddle bearing Distance from the center of the crankshaft to the center of the saddle bearing Effective length of the pitman (from the center of the equalizer bearing to the center of the crankpin bearing) Maximum moment of the rotary counterweights, cranks, and crankpins about the crankshaft

PB Structural unbalance, equal to the force at the polished rod required to hold the beam in a horizontal position with the pitmans disconnected from the crankpins. This force is positive when acting downward and negative when acting upward. PRn Net polished rod load PRn = PR - PB Tn Net torque at the crankshaft for a given crank angle θ Tn = Twn - Tr Tr Torque due to the rotary counterweights, cranks, and crankpins for a given crank angle θ Tr = M sin (θ + τ)

70

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

Twn Torque, due to the net polished rod load for a given crank angleθ Twn = FT PRn XPR Polished rod position expressed as a fraction of the stroke length above the lowermost position for a given crank angle θ

α β θ ρ τ φ χ ψ

Angle between P and R measured clockwise from R to P Angle between C and P Angle of crankpin rotation in a clockwise direction viewed with the wellhead to the right and with zero degrees occurring at 12 o'clock Angle between K and LJ Angle of crank counterweight arm offset (negative when weights are counter-clockwise relative to crankpin bearings) Angle between the 12 o'clock position and K Angle between C and LJ Angle between C and K

ψ =χ-ρ ψ b Angle between C and K, at bottom (lowest) polished rod position. ψ t Angle between C and K, at top (highest) polished rod position.

F.3 Method of calculation
F.3.1 Torque factors
Torque factors (as well as the polished rod position) may be determined by a scale layout of the unit geometry so that the various angles involved can be measured. They may alternatively be calculated from the dimensions of the pumping unit by mathematical treatment only. Example forms for recording calculations are provided in Figure F.4.

F.3.2 Submission form
A form for submission of torque factor and polished rod position data is shown on Figure B.2.

F.3.3 Data submission
Torque factors and polished rod positions shall be furnished by pumping unit manufacturers for each 15° crank position with the zero position at 12 o'clock. Other crank positions shall be determined by the angular displacement in a clockwise direction viewed with the wellhead to the right. The polished rod position for each crank position should be expressed as a fraction of the stroke above the lowermost position.

F.3.4 Calculation method
Application of the laws of trigonometric functions give the following expressions. All angles are calculated in terms of a given crank angle θ .

71

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

FT =

AR sinα C sinβ

(F.1)

Sin α is positive when the angle α is between 0° and 180° and is negative when angle α is between 180° and 360°. Sin β is always positive because the angle β is always between 0° and 180°. A negative torque factor (FT) only indicates a change in direction of torque on the crankshaft.

φ = tan?1 ?

? I ? ? ?H?G?

(F.2)

This is a constant angle for any given pumping unit.

β = cos?1 ?

? C2 + P2 ? K 2 ? R 2 + 2 K Rcos (θ ? φ ) ? ? 2CP ? ? ? ?

(F.3)

cos (θ -φ ) is positive when (θ -φ ) is between 270° and 90° moving clockwise and is negative from 90° to 270° moving clockwise. When the angle (θ -φ ) is negative, it should be subtracted from 360°, and the following equations apply.

χ = cos?1 ? ?

? C2 + LJ2 ? P2 ? ? ? 2 C LJ ? ?

(F.4)

ρ = sin

?1

±

? Rsin(θ ? φ ) ? ? ? LJ ? ?

(F.5)

The angle ρ should be taken as a positive angle when sin ρ is positive. This occurs for crank positions between (θ - φ ) = 0° and (θ - φ ) = 180°. The angle ρ should be taken as a negative angle when sin ρ is negative. This occurs for crank positions between (θ - φ ) = 180° and (θ - φ ) = 360°.

ψ =χ-ρ
sinα = sin ? β + ψ ? (θ ? φ ) ? ? ?

(F.6) (F.7) (F.8)

X PR =

ψ b ?ψ ψ b ?ψ t
? C2 + K 2 ? ( P + R ) 2 ? ? 2CK ? ? ? ?

ψ b = cos?1 ?

(F.9)

ψ t = cos?1 ?

? C2 + K 2 ? ( P ? R )2 ? ? 2CK ? ? ? ?

(F.10)

F.4 Application of torque factors
F.4.1 General
Torque factors are used primarily for determining peak crankshaft torque on operating pumping units. The procedure is to take a dynamometer card and then use torque factors, polished rod position factors, and counterbalance information to plot the net torque curve. Points for plotting the net torque curve are calculated from the following equation:

72

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

Tn = FΤ ( P ? P ) ? M sin (θ ? τ ) R B

(F.11)

F.4.2 Changes due to structural unbalance
The equation for net crankshaft torque, Tn, does not include the change in structural unbalance with change in crankpin angle; neglects the inertia effects of beam, beam weights, equalizer, pitman, crank, and crank counterweights; and neglects friction in the saddle, tail, and pitman bearings. For units having 100 % crank counterbalance and where crank-speed variation is not more than 15 % of average, these factors usually can be neglected without introducing errors greater than 10 %. Some non-dynamic factors that can have an effect on the determination of instantaneous net torque loadings, and which accordingly should be recognized or considered, are outlined in F.4.6, F.4.7, and F.4.8.

F.4.3 Polished rod effects
Torque factors may be used to obtain the effect at the polished rod of the rotary counterbalance. This is done for a given crankpin angle by dividing the counterbalance moment, M sin (θ + τ ), by the torque factor for the crankpin angle θ . The result is the rotary counterbalance effect, in pounds, at the polished rod.

F.4.4 Rotary counterbalance moment
Torque factors may also be used to determine the maximum rotary counterbalance moment. This is done by placing the cranks in the 90° position and tying off the polished rod. Then, with a polished rod dynamometer, the counterbalance effect is measured at the polished rod. Using this method, the measured polished rod load (PR) is the combined effect of the rotary counterbalance and the structural unbalance. The maximum rotary counterbalance moment can then be determined from the following equation:
M = FT ( PR ? P ) B

sin ( 90° + τ )

(F.12)

EXAMPLE 1 To illustrate the use of torque factors, an example dynamometer card taken on a 1 800 m (5 954 ft) well is shown in Figure F.2. The first step in calculating the net crankshaft torque is to divide the dynamometer card so that the load may be determined for each 15° of crank angle θ . Lines are projected down from the ends of the card, as shown, to determine its length, which is proportional to the length of the stroke. The length of the baseline or zero line is then divided into 10 equal parts and these parts are subdivided. This may easily be done with a suitable scale along a suitable diagonal line as shown (see Note). NOTE Using the polished rod position data, vertical lines representing each 15° of crank angle θ are projected upward to intersect the dynamometer card. Then the polished rod load may be determined for each 15° of crank angle θ . To further illustrate, a calculation is made considering the point where the crankpin angle θ equals 120°. From polished rod stroke and torque factor data for the particular 86 in stroke 114-D pumping unit used for this example, it is found that the position of the polished rod at 120° is 0.629 and that the torque factor FT is 35.446 in. A vertical line is drawn from the 0.629 position on the scale up to the point of intersection with the load on the upstroke (Figure F.2). The dynamometer deflection at this point is read to be 1.672 in, which, with a scale constant of 5,000 lbs/in, makes the load (PR) at that point 8,360 lbs. In a similar manner, the polished rod load may be obtained for each 15° angle of crankpin rotation. The dynamometer card has been marked to show the load and position involved for each 15° of crank angle. The structural unbalance, PB, for the example unit equals +231 lbs. Therefore, the net polished rod load, PRn, at θ = 120° is: PRn = PR - PB = 8,360 - (+231) = 8,129 lbs

The torque, Twn, due to the net polished rod load is given by: Twn =FT x PRn = 35.446 x 8,129 = 288,140 in-lbs)

73

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

F.4.5 Torque determination
To find the torque, Tr, due to the crank counterbalance, the maximum moment, M, has to be determined. This may be done either from manufacturers' counterbalance tables or curves, or as described in F.4.4. Because of the lack of manufacturers' counterbalance data in a majority of the cases, the polished rod measurement technique will be used more frequently in determining the maximum moment. Should the manufacturers' counterbalance data be used, it is suggested that a check be made using a polished rod measurement technique.
EXAMPLE The horizontal dotted line drawn across the dynamometer card in Figure F.2 is the counterbalance effect measured with the dynamometer at the 90° crank angle and is 7,000 lbs. The maximum moment can then be calculated as follows, using Equation (F.12):

M =

sin ( 90° + τ )
1,005× ?31100- +1 000 ? sin ?90°+ -14° ?

FT ( P ? P ) R B

M =

(

(

)? ?

)? ?

? ?M ? ?

=

39,575× ?7 000- +231 ? sin ?90°+ -14° ?

(

(

)? ?

)? ? ?
? ? ?

M = 276,084 in-lbs (The torque factor of 1,005 m (39,575 in) is the value at the 90° crankpin position and angle τ is -14° for the example unit.) The torque, Tr , due to the counterbalance at the 120° crank position would therefore be equal to: Tr = = 276,084 x sin [120° + (-14°)] = 276,084 x 0.961 = 265,389 in-lbs. The net torque at the crankshaft for the 120° crankpin position would then be calculated from Equation (F.11) as follows:

Tn = FT ( P ? P ) M sin (θ + τ ) R B

Tn = Twn - Tr
Tn = 288,140 - 265,389 = 22,751 in-lbs These values may be calculated for other crankpin angle positions in the same manner as outlined above. Shown in Figure F.3 is a plot of torque versus crankpin angle that includes the net polished rod load torque curve, the counterbalance torque curve, and the net crankshaft torque curve.

F.4.6 Alternative techniques
The foregoing technique is generally accepted. More precise results are dependent on the true stroke length which can vary with changes in the beam position relative to the centerline of the saddle bearing. This can be due to an adjustment provided on most medium- to large-size units or due to manufacturing tolerances. Any dimensional deviation will produce some change in the angular relationships with a resultant minor change in the torque factors furnished by the manufacturer.

F.4.7 Geometrical influences
The geometry of the dynamometer can influence the determination of instantaneous load values for the various specified or selected crank angles. The dynamometer manufacturer should be contacted for the performance characteristics of the particular dynamometer being used and the procedures that should be followed to adjust the recorded card when completely accurate data are required.

74

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

F.4.8 Interpolation
Maximum and minimum loads will most frequently fall at points other than the 15° divisions for which torque factors are provided. Interpolation between 15° divisions is permissible without significant error.

75

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

β
LP

LC

χ
LK L J ρ

ψ

LA

α
θ

τ
H1
R

PR

H2

L
a) Upstroke

β
LP LJ

LC

χ ψ


LA

LK

τ

α
R

H1

PR

θ
H2

L
b) Downstroke

Figure F.1 — Rear mounted geometry, class I lever system with phased crank counterbalance

76

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

PR
75 105 120 150 135 165 240 0,9 1,0 180 195 225 210 90

60

PCB

315

0

37,2 kN 8 360 lbf

45

1

2 255 0,8

15 30

345

330

300

285

θ
0,7

0,1

0,2

0,3

0,4

0,5

0,6

Key 1 Upstroke 2 Downstroke
Figure F.2 — Division of dynamometer card by crank angle using polished rod position data
1000 in-lb

400
kNm

40 30 20 10 0 32,6 kNm 288 140 in-lb

1 2,6 kNm 22 751 in-lb

T

200 100

T

300

270

2 3

0 -100 -200 -300

-10

30,0 kNm 265 389 in-lb

0

60

120

180

240

300

360

θ

-20 -30

4 5
Key 1 Well torque 4 Counterbalance torque

6

2 5

114 D Reducer limit Upstroke

3 6

Net gear torque Downstroke

Figure F.3 — Torque curves using torque factors

77

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition
NET REDUCER TORQUE CALCULATION SHEET (REAR MOUNTED GEOMETRY, CLASS I LEVER SYSTEM WITH PHASED CRANK COUNTERBALANCE —CLOCKWISE ROTATION) Well No.: Unit size: ___________________________________________ ___________________________________________ Company: Location: FT ________________________________ ________________________________

θ
0° 15° 30° 45° 60° 75° 90° 105° 120° 135° 150° 165° 180° 195° 210° 225° 240° 255° 270° 285° 300° 315° 330° 345°

sin (θ + τ )

PR

PB

PR - PB

FT ( P ? PB ) R

M [sin(θ + τ )]

Tn

Date Prepared

Note Tn = FT ( P ? P ) M sin (θ + τ ) R B
Where
Tn = Net reducer torque, in-lbs PCB at 90° = _______________
M =

θ = Position of crank
M = Maximum moment of counterbalance, in-lbs PR = Measured polished rod load at θ , lbs PB = Unit structural unbalance, lbs FT = Torque factor at θ , in

(PCB at 90° ? B )(FT at 90° ) sin (90° + τ )

= __________________

τ = Angle of crank counterweight arm offset (negative when weights are counter-clockwise relative to crankpin bearings) = __________________

Figure F.4 — Net reducer torque calculation sheet

78

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API.Eighteenthreserved." API Specification 11E, All rights Edition

Annex G (informative) Examples for calculating torque ratings for pumping unit reducers

G.1 Illustrative example, pitting resistance
This clause contains an example calculation of the allowable transmitted torque at the output shaft based on the pitting resistance for a first reduction helical gear set. For the example the pinion speed is 588 revolutions per minute (r/min ), and the reducer output speed is 20 r/min . Example in US Customary units Gear set data: d = 3,167 in D = 16,833 in NP = 19 NG = 101 Pd = 6,0 in-1 Wf = 3 in

φ n = 17,495 2° ψ = 30°
np = 588 r/min No = 20 r/min Minimum pinion hardness = 340 BHN (steel) Minimum gear hardness = 300 BHN (steel) Determine pitting resistance torque rating as follows: From Equation (7): vt = 0,262 x 3,167 x 588 =487 ft/min From Equation (6): C5 =
78 78 + 487, 5

= 0,779

From Equation (5):
C1 =
(588)(3,167)2 (0, 779) = 114, 85 2(20)

Cm = 1,33 (from Figure 2) From Equation (8): Wc =
3 × 1 = 2,25 1, 33

fac = 129 100 psi (see Figure 4)

79

"This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved." API Specification 11E, Eighteenth Edition

From Equation (11):

? 5,316 ? ? 129 100 ? C3 = ( 0, 225 ) ? ?? ? = 596,7 ? 5,316 + 1 ? ? 2 300 ?
From Equation (4): Tac = (114,9)(2,25)(597) = 154 300 in-lbs
NOTE The pitting resistance rating of this gear set is 154,300 in-lb. The final rating is the lowest calculated value of pitting resistance rating and bending strength ratings as determined in Equations (4) and (18) of this Specification, but not to exceed one of the standard pumping unit reducer sizes listed in Table 2.

2

G.2 Illustrative example, bending strength
G.2.1 General
This clause contains an example calculation of the allowable transmitted torque at the output shaft based on bending strength for a first reduction helical (or double helical) gear set. For the example the pinion speed is 588 r/min , and the reducer output speed in 20 r/min .
NOTE This is the same gear set used in the pitting resistance calculation example.

G.2.2 Pinion
Determine strength numbers for pinion as follows: Example in

赞助商链接