High Precision Gears

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Engineering Design Guide: GBHE-EDG-MAC-1102

High Precision Gears

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Engineering Design Guide: High Precision Gears CONTENTS 0 INTRODUCTION 1 SCOPE 2 TERMINOLOGY, SYMBOLS, ABBREVIATIONS, UNITS OF

MEASUREMENT 2. 1 Terminology 2.2 Symbols 2.3 Abbreviations 2.4 Units of Measurement SECTION TWO - INTEGRATION OF GEARS INTO THE MACHINE TRAIN 3 TYPES OF GEAR 3. 1 Parallel Shaft Gears 3.2 Epicyclic Gears 4 DEFINITION OF TERMS 4.1 Suffixes 4.2 Module 4.3 Speed 4.4 Power and Torque 4.5 Pitch line Velocity, Module and Transmitted Force 5 RATING OF GEARS 5. 1 Rated Speed 5.2 Application Factor KA 5.3 Rated Power, P 6 SELECTION OF GEARS 6. 1 Limit on Speed Ratio 6.2 Limit on Power



7 OTHER CONSIDERATIONS 7.1 Cyclic Torque 7.2 Rotation Direction 7.3 Offset Floor Area Requirement 8 VENDORS 8. 1 Approved Vendors 8.2 Co-coordinating Vendor SECTION THREE - TOPICS RELATING TO ALL GEARS 9 GENERAL 9. 1 Noise 9.2 Silver Plating 10 PITTING, BENDING AND SCUFFING 10. 1 Historical Note 10.2 General Influence Factors 10.3 Surface Durability <Pitting Factor) 10.4 Bending 10.5 Scuffing 11 PITCH LINE VELOCITY 11. 1 Accuracy 11.2 Pumping Effects with High PLV 11.3 Shear Wave Propagation 12 GEAR ELEMENTS 12. 1 Methods of Manufacture 12.2 Tooth Form 12.3 Accuracy 12.4 Fabrication 13 DYNAMICS 13. 1 Critical Speeds 13.2 Torsional Compliance 13.3 Balancing 13.4 Vibration and Vibration Detectors



14 LUBRICATION & COOLING OIL 14.1 Introduction 14.2 Tooth Flank Lubrication 14.3 Flash Temperature Theory 14.4 Viscosity 14.5 Oil Flow Requirements 15 INSTRUMENTATION 15.1 Bearing Temperature 15.2 Lube Oil System 16 SURFACE TEMPERATURE OF GEAR CASING 17 CLUTCHES SECTION FOUR - TOPICS RELATING TO PARALLEL SHAFT GEARS 18 SIZE OF PARALLEL SHAFT GEARS 18.1 Intershaft Distance 18.2 Notional Power 18.3 Centrifugal Forces 19. BEARINGS FOR PARALLEL GEARS 19.1 Radial Bearings 19.2 Thrust Bearings 19.3 Thrust Transfer System 19.4 Wire Wool Failure 19.5 Pinion Weight SECTION FIVE - TOPICS RELATING TO PLANETARY GEARS 20 SIZE AND SELECTION OF PLANETARY GEARS 21 BEARINGS FOR PLANETARY GEARS 21.1 Sun Wheel 21.2 Wheel Shaft - Bearings 21.3 Planet Wheels - Journal Bearings 21.4 Wire Wool Failure 22 DYNAMICS 22.1 Torsional Compliance 22.2 Excitation Frequencies



APPENDICES: A CHECK LIST FOR THE TECHNICAL COMPARISON OF GEARS B EXTRACT FROM BS 2519 : PART 2 1976. C FILM THICKNESS IN EHL LUBRICATION D VISCOSITY CHANGES WITH PRESSURE E BIBLIOGRAPHY FIGURES 2 MAAG EPICYCLIC GEAR, TYPE PU 3 3 MAAG EPICYCLIC GEAR, TYPE PF 3 4 SELECTION OF PARALLEL SHAFT GEARS FROM EQUATION 2 5 SELECTION OF PLANETARY GEARS 6 THRUST TRANSFER SYSTEM 7 ADJUSTED FILM THICKNESS VS PITCH LINE VELOCITY 8 EFFECT OF PRESSURE ON VISCOSITY/TEMPERATURE

CHARACTERISTICS TABLES 1 APPLICATION FACTOR KA FOR SPEED REDUCING GEARS 2 LIMITS OF ACCURACY WITH PITCH LINE VELOCITY 3 MINIMUM ACCURACY GRADES 4 SATISFACTORY VIBRATION LEVELS 5 OIL FLOW REQUIREMENTS FOR PARALLEL SHAFT GEARS 6 OIL FLOW AND FILTRATION REQUIREMENTS FOR PLANETARY

GEAR 7 TYPICAL VALUES OF COMPOSITE ROUGHNESS 8 GEAR EQUATIONS DOCUMENTS REFERRED TO IN THIS ENGINEERING DESIGN GUIDE



SECTION ONE – GENERAL 0 INTRODUCTIONS This Engineering Design Guide has several aims. It is intended to take an experienced mechanical engineer through the steps necessary to specify a gear and to carry out an assessment of gears offered against a particular specification for pumps, fans and compressors driven by electric motors, steam turbines, combustion gas turbines or expanders. It is not part of this Engineering Design Guide to show how to decide that a gear is or is not necessary for a particular duty. Background information is kept to a minimum and reference should be made to the list of articles and other reference data for further details. Several terms which are specific in gearing notation are explained in some detail. Further detail may be obtained from BS 2519, parts 1 and 2. Gears are necessary for several reasons: (a) To change rotational speed delivered by a driver to that required by the

driven equipment. A typical example is an electric motor driving a compressor at greater than 2 pole speed.

(b) To allow simultaneous drives to or from more than one item at the same or

different speeds. A typical example is the driving of axial and centrifugal compression sections of a compression set.

(c) To change the direction of the axis of rotation. This is not covered in this

Engineering Design Guide. 'Wheel' is preferred to 'gear' when describing the low speed part of the gear pair.



1 SCOPE The selection of high precision gears is covered for duties where one or more of the following apply: (a) Pinion shaft speed greater than 48 r/s. (b) Pitch line velocity between 25 m/s and 150 m/s. (c) Wheel or pinion shaft journal bearing peripheral speeds greater than 7.5

m/s. (d) Power transmitted is greater than 500 kW. Helical gears of both parallel shaft and epicyclic design are covered; spur gears are excluded. Slow running gears, or gears for machinery not dealing with fluid flow, are covered in other GBHE Design Guides. Using ISO DIS 6336 requires a familiarity with gear design greater than that necessary to use this document. The use of an independent gear consultant should be considered for assessment of gears offered when this Design Guide is inadequate. This Engineering Design Guide should be used in conjunction with API Standard 613, Special Purpose Gear Units for Refinery Services, 2nd Edition 1977 and with BS 2519 Parts 1 and 2 Glossary for Gears. An important change from the previous document is the use of Module in place of diametral pitch which reflects current practice in the gear manufacturing industry in 1980’s. Clutches are not normally permitted in drives covered by this Engineering Design Guide. Should a requirement arise for which a clutch is one solution then other means of achieving the objective should be examined vigorously.



2 TERMINOLOGY, SYMBOLS, ABBREVIATIONS, UNITS OF MEASUREMENT

2.1 Terminology

The terminology used throughout this Engineering Design Guide is that of BS 2519 Pt 1 which is dual numbered with ISO 1122/1.

2.2 Symbols

The notation used throughout this Engineering Design Guide is that of BS 2519 Pt 2 which is dual numbered with ISO 701. Pages 2, 3, 4

2.3 Abbreviations

BS (I) British Standard (Institution) ISO International Standards Organization DIN German Standards Organization VDl German Association of Engineers AGMA American Gear Manufacturers Association ASME American Society of Mechanical Engineers API American Petroleum Institute



2.4 Units of Measurement

The units of measurement used are those specified in GBHE Standard, Preferred Metric Units.

SECTION TWO - INTEGRATION OF GEARS INTO THE MACHINE TRAIN 3 TYPES OF GEAR 3.1 Parallel Shaft Gears These are cylindrical gear pairs with parallel shafts, usually in the same horizontal plane, so that a single horizontal split casing suffices for access. Vertical offset shaft units require careful examination of casing split to ensure good access and also to ensure that alignment is maintained. Gears may be either single helical or double helical, (herringbone). Single helical gears are preferred, because the effect of manufacturing error is less. Double helical gears balance thrust loads, and so require smaller thrust bearings. However, the effect of error between the two halves can be significant. The two flanks are to be separated by a gap; the use of jointed flanks is forbidden. 3.2 Epicyclic Gears This term is now specifically used to refer to gears containing a central floating sun wheel, with at least three planetary wheels moving around it within an annulus. The planetary wheels rotate on shafts fixed to a carrier. Two types of epicyclic fall within the scope of this Design Guide: (a) Planetary Gears, in which the annulus is stationary and fixed to the gear

casing by a flexible coupling. The planet carrier is part of the gear shaft, and the sun wheel is on the pinion shaft.

(b) Star Gears, in which the annulus rotates and the planet carrier is part of

the gear case. The sun wheel is on the pinion shaft, and the annulus is attached to the gear shaft by a large diameter coupling. Star gears are used in centrifuge screw conveyor drives and are not generally allowed elsewhere. For the remainder of this Design Guide planetary gears will be the only form of epicyclic gear considered.



Planetary gears need a flexibly mounted annulus with the sun wheel free to float to balance the loads. Do not accept gears which rely on accuracy only to balance the load, or gears which rely on flexibility of the planetary frame to balance the loads. FIGURE 2 - MAAG EPICYCLIC GEAR, TYPE PU3



FIGURE 3 - MAG EPICYCLIC GEAR, TYPE PF3



4 DEFINITION OF TERMS 4.1 Suffixes

Suffix 1 refers to pinion. Suffix 2 refers to wheel. 4.2 Module

4.3 Speed Input speed is the rated speed of the driver. Output speed is the rated speed of the driven equipment. It may not be possible for the Vendor to match exactly both input and output speed. One should be specified, the other speed should be indicated together with an allowable tolerance. The high speed shaft, whether input or output shaft, is the pinion, speed n1 The law speed shaft carries the wheel, speed n2.



4.4 Power and Torque The gear rated power, P, is the maximum power expected to be transmitted by the gear under continuous running conditions, and is stamped on the gear nameplate. The method of calculating rated power is given in Clause 5.3. The torque is the power d1vided by angular velocity.

The size of a gear is determined by the wear limit. It therefore depends on the maximum torque generated under continuous running conditions, TMAXCR. If the driver is an electric motor TMAXCR will occur at synchronous speed. If the driver is a turbine or machine train It may occur at some lower speed. It is imperative that the maximum torque, and the speed at which it occurs, is specified to the Vendor. The size of the gear teeth is determined by their strength in bending. It depends on the maximum torque generated under all transient conditions, TMAXT. If the machine train contains an alternator or electric motor TMAXT can be up to 15 times greater than TMAXCR. In this case the gear teeth will be designed for a lower value of TMAXT and the coupling selected to reduce the load on the gear teeth. There are limits on the standard size of gear teeth available. Therefore, in some particularly severe cases TMAXT will determine both the size of gear teeth and the size of gear.



4.5 Pitch Line Velocity, Module and Transmitted Force 4.5.1 Parallel Shaft Gears

4.5.2 Parallel Shaft Gears

Suffix 3 refers to planet, 4 refers to ring.

The diameter of the sun gear is denoted by d1 the diameter of the planet gears by d3 and of the ring gear by d4. The pitch line velocity of the sun wheel is v, where:

In a planetary gear the ring gear is fixed, so the velocity of the centre line of the planet wheel shafts is 1/2v. Hence the speed of rotation of the gear shaft is:



For planetary gears the transmitted force is the same as for parallel shaft gears. Let Z4 Z3 and Z1 be the number of teeth of the ring gear, planet gears and sun gear, respectively. The normal diametral pitch is:

but the relationships relating U to the diameters and the number of teeth are more complicated.



4.5.3 Overlap Ratio

5 RATING OF GEARS 5.1 Ra ted Speed

The input and output speed are defined in Clause 4. 5.2 Application Factor KA When gears are manufactured the teeth are made to give a small clearance, called backlash, between flanks on the pitch circle. This allows for errors in manufacture and thermal growth. The clearance, coupled with gear inertia, imposes a dynamic load on the teeth. This dynamic load reduces the rating of a given gear by reducing the permissible load for power transmission. It is not usually possible to calculate the dynamic load, so it is allowed for in gear design by introducing Application factor KA which depends on the types of machine in the machine train. See Table 1.



For installations of Reliability Class 1, 2 or 3, these values should be multiplied by 1.1. Previous plant operating experience has shown that this extra margin is necessary to give the reliability required to guarantee continuous three-year running of this class of machine. Reliability class, which is a characteristic of the machine train, is defined in GBHE-EDG-MAC-5100. 5.3 Rated Power, P 5.3.1 Gears Located Next to the Sole Driver The rated power of a gear used with a turbine driver is 105% of the turbine rated power. The rated power of a gear with an electric motor drive is the motor rated power multiplied by the service factor. 5.3.2 Gears in a Machine Train All modes of normal and abnormal operation are to be examined. Rated power will AT LEAST EQUAL each of the following: (a) 1.1 times the maximum power required to drive the equipment. (b) The power transmitted when the maximum power of all the drivers (as

calculated in Clause 5) is divided between the driven equipment in the ratio of normal power absorbed.

In some modes of operation power may be transmitted in the reverse direction. It is essential that the gear vendor is told of such modes as they will affect thrust bearing design and manufacturing tolerances. The following conditions apply: (1) The gear should be capable of running at rated power and speed from first

commissioning in both directions of power transmission. If necessary the teeth should be silver plated. It should be possible to commission the gear without the use of special oils.

(2) To maintain tooth contact, operation at near zero torque should be

avoided. Modes of operation where transmitted power is less than 5% of rated power are unwise.



This is because some tooth profiles are modified to allow for deflection under load and so at low loads noise and vibration levels may be unacceptable. Where the load varies greatly the gear rating should be based on teeth of unmodified profile.

5.3.3 Maximum Continuous Running Torque, TMAXCR For steam turbine drives the maximum torque generated may occur at a speed below the rated speed. If so this torque will be used to size the gear. The torque and the speed at which it occurs are required by the gear vendor. In a machine train containing one or more turbines, it is essential that the torque is calculated as in Clause 5 but using power absorbed in all possible start-up conditions. 5.3.4 Maximum Transient Torque, TMAXT The maximum transient torque on electrical fault will be specified by the electrical vendor. There is usually only one item of electrical equipment in a machine train. When the electrical equipment is next to the only gearbox, TMAXT is as specified by the electrical vendor. When it is between two gearboxes, or when there are other machines between it and the gearbox. TMAXT is not so clearly defined. TMAXT can be reduced by suitable choice of coupling. Use of a flexible coupling will reduce maximum torque by smoothing the peak of the transient. Use of a shear coupling will reduce maximum torque by providing a weak link to fail should the torque rise above a certain value. Examples of TMAXT are as follows: Induction motors: 6 times normal torque on short circuit Synchronous motors: 10 times normal tor qua on short circuit or

synchronization 1200o out of phase Alternators: 15 times normal torque on short circuit Actual values should be supplied by the electrical equipment vendor at the Vendor Co-ordination Meeting (see GBHE-EDP-MAC-3301).



6 SELECTION OF GEARS The size of gears depends on the transmitted torque. However, the maximum size of planetary gear available depends on the centrifugal loading of the planetary frame. Limits on the gear ratio arise from the geometry, and from excitation frequencies imposed by the low speed shaft on the high speed shaft. 6.1 Limit on Speed Ratio 6. 1.1 Parallel-shaft Gears Upper limits on gear ratio are imposed by geometry. Selection of a gear for a gear ratio greater than 8:1 requires special treatment. There is no lower limit imposed by geometry. At gear ratios of about 2.0 perturbations of the low speed shaft can excite the high speed shaft in a whirl mode, causing oil whip in extreme cases. If the gear ratio is between 1.5 and 2.5 the machines will have to be checked for rotor dynamic stability. To summarize:

6.1.2 Planetary Gears The geometry limits the speed ratio as follows:



6.2 Limit on Power 6.2.1 Parallel Shaft Gears The maximum power that can be transmitted by the largest parallel shaft gears is limited by tooth wear. This is covered in greater detail in Clause 21. In Clause 21 it is shown that tooth wear imposes the following limit. The maximum power that can be transmitted by a parallel shaft gear depends on U, n2, KA and the inter-shaft distance, a, as follows:

The largest gearboxes within the scope of this Design Guide currently available from German and Swiss manufacturers have Intershaft distance of 1.0 m and from British manufacturers 0.75 m. This imposes the limits on maximum torque sketched in Figure 1. 6.2.1 Parallel Shaft Gears The maximum power that can be transmitted by the largest planetary gearboxes is limited by the strength of the planet carrier, and the loads on the shafts carrying the planet wheels. Figure 2 shows maximum power that can be transmitted at different speeds and gear ratios by planetary gears currently available. Note that in each gear ratio there is also a lower limit to the power that can be transmitted. Figure 2 may be used to select planetary gears.



7 OTHER CONSIDERATIONS 7.1 Cyclic Torque The gear is said to be subject to cyclic torsional loading when the torque contains a period1c element such that:

This will occur with reciprocating machinery and may occur with centrifugal pumps with long discharge piping. Using a gear should be avoided if possible. If not, a double helical (herringbone) parallel shaft gear should be used, preferably with an elastomer coupling to provide torsional flexibility. Where fluctuations would be large enough to cause loss of tooth contact, viz:

(a) Fit a flywheel to the driven machine to reduce peak torque to 1.1 mean

torque. (b) Fit a torsionally compliant coupling, e.g. Holset WB or Bibby type. 7.2 Rotation Direction In planetary gears input and output shafts rotate in the same direction. In single stage parallel shaft gears they rotate in opposite directions.



7.3 Offset-Floor Area Requirement Parallel shaft gears have an offset between shaft centre 11nes. This can be considerable for high gear ratio. A gear w1th vert1cal shaft offset may require less floor space eyen when allowance is made for maintenance access space.





8 VENDORS 8.1 Approved Vendors A gearbox should be within a manufacturer's previous experience, in terms of maximum gear ratio, inter-shaft distance, pitch line velocity and tooth loading. 8.2 Coordinating Vendor The gearbox will usually be bought by the manufacturer coordinating the supply of the machine train - often the supplier of the driven machine. This practice is to ensure that there is undivided responsibility for the satisfactory performance of the train. SECTION THREE - TOPICS RELATING TO ALL GEARS Topics relating specifically to parallel shaft gears are covered in Section 4 and to planetary gears in Section 5. Topics are covered in the order in which they appear in API 613. Numbers in parenthesis after each heading are the appropriate section of API 613. Section 3, Section 4 or 5 and the check list in Appendix A may be used to conduct a technical comparison of manufacturer’s offers. 9 GENERAL (2. I) 9.1 Noise (2.1.3)

Noise in gear boxes is generated by tooth contact. Modern gear boxes have very accurate tooth form, and very small pitch error, and are therefore relatively quiet when running at their rated torque. Because tooth deflections at load are allowed for in gear design, gears often emit more noise when running at low load, than at full or over load.

Permissible noise levels are specified in accordance with the GBHE-EDS-MAC-2102. Normally the overall sound pressure level at 1m from the machine train should not exceed 90 dBA. This means that the noise from each component of the machine train, including the gear box, should not exceed 85 dBA.



The Octave Mid-Band Frequency Sound Pressure Levels, (SPL), corresponding to 90 dBA and 85 dBA are:

GBHE-EDS-MAC-2102 further requires that in any octave band in which there is an audibly recognizable pure tone, the permitted level in that band shall be reduced by 10 dB. Such a tone occurs at the tooth passing frequency, nm. For instance a gear box with pinion speed 100 RPS, and a pinion wheel with 50 teeth, the SPL at 4 KHz would be reduced to 71 dB and 66 dB respectively. The gear vendor is asked to supply estimated noise levels with his quotation, supported by measurements from similar machines.

9.1.1 Nitrided and Carburized Gears

It is not practicable to finish grind gears as the hard layer is too thin, there are always small imperfections, which increase the noise level, tooth flanks of nitride. The distortion is low, but giving tooth profile errors.

Carburizing creates a thick hard layer, which can be finish ground to remove distortions from the heat treatment. Thus although carburizing creates more distortion than nitriding, the final tooth profile is more accurate.

Nitrided gears need in general a K-factor 5-10% lower to give the same noise level.

9.1.2 Casings

Casings in the past were usually of cast iron, which give good attenuation. Fabricated steel casing may be used, especially for planetary gears. Flat surfaces should be stiffened by the use of ribs and curved construction to avoid drumming.



9.1.3 Noise Hoods Where these are used, they should not justify the use of noisy gears. Noise can indicate a shortfall in the standard of design and production quality.

9.2 Silver Plating (2.1.13)

Plating may be used to reduce scuffing during initial operation. Materials now available together with appropriate hardening and grinding techniques usually render plating unnecessary.

10 PITTING, BENDING & SCUFFING 10.1 Historical Note

It is convenient to assess allowable limiting conditions in gears by reference to Herzian pressures. Limiting values of Herzian pressure are derived from fatigue test. on gear specimens and so other relevant factors, e.g. direction and magnitude of sliding or influence of lubrication on distribution of pressure are included without being quantified. Values obtained from disc tests are less satisfactory. It is important that magnitude and direction of sliding are comparable with the working conditions with which the assessment is concerned. ISO DIS 6336 Parts 1 to 4 describe the basic principles and provide a uniform means of comparing and relating gear performances. Part 2 is confined to the calculation of surface durability (pitting). Part 3 refers to calculation of tooth strength. Part 4 relates to calculation of scuffing load capacity. Other documents detail simplified methods of calculating load capacity of industrial gears but they had not been issued for public use. Copies are held in Machines Section of EONEG. The K factor without suffix used in API 613 is used in parts of this document. It is still in widespread use. Note that many European manufacturers use radii instead of diameter in their calculations.



10.2 General Influence Factor.

The factors which influence gear design or assessment of gear capacity are determined either from gear geometry and for which equations have been established or are determined empirically based on research and field service. ISO DIS 6336 is aimed at gear designers and gives initial procedures to enable gears to be designed and final procedures which enable designed gears to be assessed. We are concerned here with the assessment of designed gears. Nominal tangential load, tangential to the reference cylinder and perpendicular to the axial plane is calculated directly from the power transmitted by the gear set (see Clause 9 of ISO DIS 6336/1).

NOTES (1) The values in the table, which correspond to the data given for the

overload factor in GBHE-EDP-MAC-6601, September 1966, are only valid for gears not running in the resonance speed range.

(2) Experience suggests that KA may be a little greater for a speed

increasing transmission than for a speed reducing transmission, (consequently increase the data above by 1.1).



Dynamic factor KY accounts for internally generated dynamic loads due to vibration. Method C of ISOIDIS 6336/1, Clause 11, is to be used unless V.Z :> 300 m/s. Longitudinal load distribution factors account for non-uniform distribution of load across the face width. This depends on mesh alignment and on mesh stiffness. Transverse load distribution factors. The distribution of total tangential load over several pairs of meshing teeth depends on gear accuracy. There are factors for contact stresses KH, for scoring load KB and for tooth root strength KF.

10.3 Surface Durability (Pitting Factor)

If the limit of fatigue surface stress is exceeded particles break out of tooth flanks leaving pits. A distinction may be made between initial pitting and destructive pitting. Pitting is not tolerable in gears covered by this Engineering Design Guide. It should be noted that in gears which are not within the scope of this Engineering Design Guide that pitting may be tolerable if it gives an adequate economic life and does not give rise to unacceptable operating risks (either safety or economics)

ISO DIS 6336 Part 2 gives the methods to be used to calculate the various factors required, together with tables and graphs to determine those factors which are material dependent.

The allowable contact (Herzian) stress is compared with the calculated stress to determine the achieved safety factor.



10.4 Bending

The maximum tensile stresses in the fillets of loaded flanks of gear teeth have been chosen as the criteria for gear tooth bending strength. These stresses are determined a. the products of nominal bending stresses and stress concentration factors. Method C of ISO DIS 6336 Part 3 should be used. Helical gear tooth root stresses are determined by analysis of the corresponding virtual spur gears. Tooth strength factor for nominal stress and the corresponding stress correction factor are calculated or determined from a series of charts. It is usual to choose a higher safety factor for tooth bending strength than for tooth surface damage as a broken tooth usually renders the gear pair inoperable much faster than does surface damage.

10.5 Scuffing

Scuffing is that form of tooth surface damage caused by sliding contact in which seizure or welding together of surfaces occurs due to absence or breakdown of the lubricant film. The incidence of scuffing is highest when sliding velocities are high and vice versa. When it occurs at low sliding velocities it is due mainly to uneven surface geometry. Lubricant films break down because of high loads or high sliding velocities which both cause high temperatures. The temperature at the tooth surface is partly due to the gear bulk temperature and partly due to what is termed the flash temperature. Blok (see list of references) and later other researchers have developed thermal network theories and hence means of calculating bulk temperatures. The flash temperature depends on the amount of heat generated when two surfaces are in contact and it varies from point to point depending on local geometry, velocities and pressures. It is a basis of the theory that there is a critical 'scuffing temperature' which is constant for a given combination of materials and lubricant. As usual a safety factor is introduced to make allowance for inaccuracies and uncertainties in calculations.



The flash temperature is dependent upon the local instantaneous coefficient of friction. Four factors are used in addition to calculate the required temperature.

11 PITCH LINE VELOCITY

The power transmitted by a gear is P = TYp where Yp is the pitch line velocity, PLV. Therefore, together with pitting and bending strength, PLV determines the power that may be transmitted by a gear. High pitch line velocities impose limits on gears. This Design Guide refers to gears of PLV 25 m/s to 150 m/s.

11.1 Accuracy

The higher the pitch line velocity the greater the need for accuracy of manufacture of the gear teeth. ISO 1328 defines accuracy required with increasing PLV. If the preferred grades are used, hunting tooth combinations are not required.

Accuracy grades are also defined in DIN 3962 and AGMA 309.02. Manufacturers may quote equivalent grades.

11.2 Pumping Effects with High PLV

A number of pumping effects can occur with high pitch line velocity. Precautions are required to overcome these.



11.2.1 Hydraulic Screw Pumping

The gear helix can act like a screw pump. At PLV over125 m/s this can become quite severe, the oil being heated as it is pumped. Resulting temperature gradient along the helix can reduce meshing accuracy. It can be avoided thus:

(a) Circumferential grooves are cut in the wheel/pinion to allow oil to

escape from the mesh. The gear works as two or more gears in parallel. This is the preferred method.

(b) Oil nozzles are sized to vary the amount of oil injected along the

tooth. Sizes are empirically determined on accurate full size models or existing gears.

(c) Tooth profile is adjusted for the expected thermal expansion.

The manufacturer will need to show considerable experience of using this method before it is acceptable.

11.2.2 Gear Pumping

Parallel shaft gears can act as gear pumps.

Downward meshing gears tend to cause a positive upward transfer of air and oil. This can lead to oil flooding in the top of the box and over lubrication of the mesh. The following precautions are desirable at PLV over 100 m/s.

(a) The gears should be upward meshing.

(b) Provide large voidage with air space at least twice gear and pinion

volume.

(c) Provide a large drain connection, discharging directly into the lube oil tank, sized so that when flooded the all velocity is no more than 0.1 m/s.

(d) Fit windage baffles to reduce air transfer.

(e) A 'dry' sump is preferred.



11.2.3 Aerodynamic Pumping

At high pitch line velocity a gear acts as a fan, creating a positive pressure gradient moving radially outward from the shafts. The effect is first noticeable above 60 m/s PLV and marked above 100 m/s PLV. It is of particular concern with planetary gears. The differential pressure created between the inside edge of the gear case and the shaft is typically of the order of 100 millibar. There are two consequences of this effect.

(a) It may blow oil mist out of the filler breather. If the filler breather

were to discharge into a noise hood the oil mist would create a fire hazard. At PLV greater than 100 m/s the filter breather should be piped back to the oil tank which will need a filtered vent. A small positive displacement blower with differential pressure about 100 millibar may be fitted to the tank.

(b) It may suck air into the bearing labyrinth. At PLV greater than100

m/s, an air purge should be fitted to the bearing labyrinths, especially if the atmosphere contains dirt or corrosive fumes. The purge typically has pressure about 1.1 bara, flow rate 30 m3/hour, and feeds into an annular groove in the outer labyrinth.

11.3 Shear Wave Propagation

When teeth mesh a shear wave is generated which propagates across the diameter and is reflected to the point of origin? If the time for the wave to traverse the diameter equals the time for the teeth to remesh the stress generated as the load is reapplied is amplified by the shear wave. This can give resonant failure. The tooth passing frequency is zn, and the distance travelled by the shear wave in the pinion is 2d. Let the shear wave velocity be Vw' Resonant failure will occur if:



For steel V w = 3.2 x 103 m/s. Therefore values of Z1Vw and Z2Vw between 4000 m/s. and 6000 m/s should be avoided. This is only likely to be a problem in the pinion only at low pitch line velocities and high gear ratios.

12 GEAR ELEMENTS 12.1 Methods of Manufacture

During manufacture the cutting and finishing process are done on one machine without interruption. The effect of temperature variation on accuracy can be significant. Gears covered by this Design Guide are normally machined in a temperature controlled environment. Teeth surface durability is improved by hardening either by carburizing or nitriding. Nitrided gears are usually cut from through hardened blanks. Most surface hardening processes cause distortion to the gear surface and therefore grinding must follow. The exception is nitriding. This produces a small and predictable growth of the surface (10 µ m). Gears are ground before nitriding since the hard layer is less than 50 µm and so too thin to grind.

12.2 Tooth Form

Most gears have modified involute tooth form with a pressure angle of 20o Pressure angle may be between 15o and 25o. Tooth deflection under load can be considerable. The profile is modified to give shock-free engagement of the unloaded teeth, their relative angular position being determined by the loaded teeth. This profile modification, known as tip relief, should be in accordance with BS 436. The amount of relief is determined by tooth loads. It is important that it is appropriate to normal load and, not overload, to reduce noise.

12.3 Accuracy

Accuracy of Table 2 needs to be achieved and the minimum grades in Table 3.



12.3.1 Pitch Errors

(a) Individual Pitch Error is the difference between nominal and actual pitch for each pair of teeth. It causes noise and wear.

(b) Cumulative Pitch Error is measured over a number of teeth, 6 - 12.

It can lead to cyclic variation of overall gear ratio at some multiple of notional speed. In extreme cases this can provide an exciting force for torsional oscillation.

12.3.2 Backlash

Backlash is the distance an individual tooth could be moved, when in mesh, to change contact from the leading flank to the trailing flank. It is an essential feature to allow for manufacturing errors and for deflections of teeth, of shafts or in bearings.

12.4 Fabrication

The pinion should be integral with its shaft and made from a forged bar. The wheel should also be forged and should be shrunk on to its shaft especially for machines in Reliability Class I, 2 or 3.

13 DYNAMICS 13.1 Critical Speeds

The co-ordinating vendor will normally calculate torsional and lateral critical speeds for the entire machine train. The gear vendor is to provide all information required for these calculations. The gear vendor should also do a critical speed analysis for the gearbox in isolation as specified in API 613.



The frequency of the lateral critical modes is load dependent. The bearing oil film stiffness varies with transmitted load. The critical speeds are to be calculated under all modes of normal and abnormal operation. Any unusual condition is to be indicated to the gear and machine vendor. In particular API 613 requires operating conditions of less than 50% maximum torque, or less than 70% maximum speed to be emphasized.

13.2 Torsional Compliance

Once built it is not possible to change the torsional compliance of a gear. If it is required to later change the torsional stiffness of machine train it is customary to use an elastomer coupling and alter stiffness by changing rubbers. This also has the beneficial effect of moving the antinodes’ from the gear to the coupling. When calculating the torsional compliance of parallel shaft gears it is necessary to account for the effect of lateral compliance of the bearing and housing (Reference 7). Couplings of torsional perturbations of frequency equal to second tooth meshing frequency with lateral compliance of bearings has been known to produce vibrations with peak acceleration of 1000 mi. (Reference 11). The effect of constructional features on the torsional compliance of planetary gears is covered in Section 5.

13.3 Balancing

Balancing tolerance is related to rotor weight and speed. Balance quality is specified for various rotor types in ISO 1940. The G factor is the residual unbalance at 1000 rad /s in g mm /kg.



ISO 1940 and BS 5265 Part 1 give values of G, in steps of 2.5, for different rotor types, but not for gearboxes. Use G2.5 for speeds up to 12,000 rpm and G1 for speeds over 12,000 rpm. Where the gear or pinion shaft is an extension of the machine shaft the gear elements should be balanced to the same grade as the machine.

13.4 Vibration and Vibration Detectors 13.4.1 In-service Vibration Detection

This sub-clause covers in-service vibration detectors, fixed to a machine to monitor its health throughout its life. API Standard 613 recommends the use of proximity probes to monitor vibration. Proximity' probes adequately measure vibration with frequency similar to gear and pinion speed, but not vibrations of higher frequency. Low frequency vibration is associated with out-of-balance or excitation of shaft natural frequencies. Acceleration detectors are better for detecting vibration with frequency similar to tooth meshing frequency or its harmonics. Such vibration is associated with tooth wear and similar faults. The most consistent results are obtained by measuring peak velocity. Use one pick-up over the input shaft extension and one over the output shaft extension. The transducers should be bolted to a flat machined surface on the gear case or bearing housing. The preferred transducer is an accelerometer with signal integrated to give velocity measurement. Measurement of RMS velocity or of peak or RMS acceleration is acceptable but do not give as consistent fault detection as does peak velocity. Recommended satisfactory vibration levels for gearboxes depend on the type of driven equipment. Values are given in Table 4. Maximum acceptable levels are three times these values.



*For double helical gears driving fans divide these numbers by 4.

The vibration meter should measure true peak and have a frequency range up to at least 5,000 Hz and preferably up to 10,000 Hz. The frequency range should extend above twice tooth meshing frequency.

14 LUBRICATION AND COOLING OIL 14.1 Introduction

Oil is used in gearboxes for both lubrication and cooling. Most of the oil is needed for cooling to restrict the bulk temperature of the gear pair to an acceptable value. Cooling oil is applied at the outgoing mesh at a suitable temperature in a suitable quantity.

Oil for bearings is supplied as it is to other machines at suitable pressure temperature quality and quantity.

The lubrication of mating gear teeth is different to most other lubrication duties because the pressures involved induce viscosity changes not encountered in other environments.



14.2 Tooth Flank Lubrication

The oil used to lubricate the working flanks of the gear teeth is subjected to pressures several orders of magnitude higher than in most other lubrication environments. When two curved surfaces are in contact the resultant surface pressures may be estimated using the method devised by Herz. In the special case of gears Herzian stress is defined in the following equation:

14.3 Flash Temperature Theory (see also Clause 12.5)

Blok (see bibliography) defines lubrication as a gear design factor. The gear manufacturer and lube oil supplier will need sufficient data to estimate the bulk temperature of the gear and the flash temperature. These two components determ1ne the operating oil temperature. There is a maximum value at which the oil remains liquid and at higher temperatures the film breaks allowing metal to metal contact - sliding at each side of the pitch line which produces the characteristic scuffing. Oil on the flank is assumed to reach the bulk metal temperature before it enters the mesh. Oil temperatures may be shown to determine oil film th1ckness, the viscosity should be inversely proportional to pitch line velocity.

14.4 Viscosity

Empirical equations may be used to estimate oil viscosity requirements when the pitch line velocity is known. ( Ref. 34).



Oil should have high viscosity at the operating temperature. It is preferable to avoid the use of EP additives as the action of gear teeth tends to break down the polymers and the viscosity then reverts towards that of the base oil. It should be noted that the viscosity of the oil used in a gearbox is vastly different at the pressures obtained between gear teeth. Teeth are lubricated in an elastohydrodynamic mode. The pressure in the contact zone is in the region of 109 N/m2 and this induces viscosities in the region of 105 cP. See refs 34, 35 for relationship between pressure, temperature and viscosity. See refs 36-41 for discussion on elastohydrodynamic lubrication.

14.5 Oil Flaw Requirements

Oil flaw requirements are different for planetary and parallel shaft gears.

14.5.1 Oil Supply for Parallel Shaft Gears

Total oil required depends on pitch line velocity and transmitted power. Table 5 gives a rough guide.

14.5.2 Oil Supply for Planetary Gears

Oil is supplied to gears for lubrication and cooling of bearings and of teeth.

Planetary gears require special care to avoid aver lubrication. The amount of oil required depends only on the power transmitted. Oil flow required is 1 liter/sec/MW for all planetary gears.



Planetary gears are lubricated by forcing oil outwards from the centre under the action of centrifugal forces. Very large accelerations are present, so a high filtration standard is required to avoid separation of solids in the gearbox. The planet journal bearings are particularly at risk. Table 6 gives filtration standard required aver different power ranges.

There is also a minimum oil pressure necessary to overcome centrifugal effect which will otherwise prevent the lubrication of the sun wheel. Use 2 bars as a minimum unless previous experience allows a relaxation.

15 INSTRUMENTATION 15.1 Bearing Temperature

Thermocouples should be placed in the radial and thrust bearings to measure bearing temperatures. In the radial bearings the thermocouples should be placed at the mid-length of the bearing. In the thrust bearing the thermocouple should be placed under the point of highest pressure. This is on the mid radius, three quarters of the way from the leading to the trailing edge, in the direction of rotation. The bearing thermocouples should be set to alarm on high bearing temperature and trip an extra high temperature. Typically the alarm will be set at 70oC and the trip at 80oC.



15.2 Lube Oil System

The lube oil system should be in accordance with GBHE-EDP-MAC-3602. On particularly arduous duties oil pressure indication on the line to each bearing should be considered.

16 SURFACE TEMPERATURE OF GEAR CASING

The surface temperature of a gear casing is not normally an important factor in gear assessment at the design stage. Casings should not normally be hot to touch (temp less than 60oC say). It should not therefore be necessary to have casings lagged for personnel protection. If personnel protection is deemed necessary then a machine guard which will allow unhindered ventilation is to be used. See Ref 42 for discussion on failures due to gear case distortion.

17 CLUTCHES

Clutches are not normally permitted in drives covered by this EDG. Should a requirement arise for which a clutch is one solution then other means of achieving the objective should be examined vigorously.



SECTION FOUR - TOPICS RELATING TO PARALLEL SHAFT GEARS 18 SIZE OF PARALLEL SHAFT GEARS 18.1 Intershaft Distance

The size of parallel shaft gears is characterized by the Intershaft distance, 'a'. Given the gear rated power, P, the gear ratio, U, the gear shaft speed, n2 , and the gear material, the minimum value of a can be calculated as follows:

The largest gears currently available and within the scope of this Design Guide have an Intershaft distance of about 1.0 m. The largest value of k allowable with carburized gears and EP oils is 3.7 MN/m2. Therefore:



18.2 Notional Power

This can be used to calculate the pitch circle diameter, d1, by an interactive procedure. Assume Vp calculate d and recalculate Vp. Check the value obtained against the value assumed and continue until convergence is obtained. This is clumsy when Fig 4 gives ‘a 'direct.

18.3 Centrifugal Forces

Equation 21 ceases to be the limit on power at very high speeds. In such cases centrifugal forces in the wheel will limit power. Centrifugal forces in the wheel are characterized by Fc = dn2. It can be shown that at given ‘a’. and 'KA’.



If there is some maximum allowable value of centrifugal force then the maximum obtainable value of A is inversely proportional to n2. Equation 23b implies that at low speeds the maximum obtainable value of KA is proportional to n2.

For a given gearbox maximum power transmission can occur at about n = 1500 RPM. Hence if a <0.7 :

19 BEARINGS FOR PARALLEL GEARS 19.1 Radial Bearings

The preferred arrangement is for the wheel and pinion shafts to be located in white metal journal bearings of the ported type, one bearing at each end of each shaft. Overhung wheel or pinion wheels are not allowed. In a gearbox direct coupled to either the driver or driven machine the total number of radial bearings on the gear and machine shaft may be reduced to three when there will be one bearing between the gear and the machine rotor.



19.2 Thrust Bearings The preferred arrangement for single helical gears is for each shaft to be located by two tilting pad thrust bearings rated to take the full load in each direction. Thrusts developed in double helical gears are mutually cancelling, so it is necessary to locate only one shaft by tilting pad thrust bearings. Care needs to be taken to avoid externally applied thrust loads to the free shaft as these causes the teeth to be loaded at one side only.

19.3 Thrust Transfer System

Single helical gears may use a thrust transfer system. One shaft is located by thrust bearings. The pinions are provided with shoulders within which the wheel runs. The thrust bearing may be on either the wheel or pinion shaft, whichever is likely to suffer the larger thrust loads. This arrangement is quite common and gives reliable service with less power loss and with capital cost saving compared to the preferred design (see Figure 6).



Shrunk-on collars may not be used with pitch line velocity greater than 130 m/s because of loss of interference fit at these and higher speeds. At pitch line velocity greater than 110 m/s oil pumping occurs along the gear tooth helix, causing under lubrication of one collar and over lubrication of the other. Heat generated by over lubrication causes thermal expansion which may result in loss of backlash.

19.4 Wire Wool Failure

Wire wool failure of the radial bearings can occur if all of the following occur together: (a) Shaft peripheral speed greater than 11 m/s. (b) Shaft chrome content greater than 1.8%. (c) Unwanted solids in the oil. The chrome content of a shaft should not exceed 1.5% when the peripheral speed in any Journal bearing exceeds 11 m/s.

19.5 Pinion Weight

Failure of the radial bearings has occurred in cases where the tooth contact force, F, is approximately equal to the pinion weight, wg, and acts upwards on the pinion. Calculate the force for all modes of normal and abnormal operation, except zero power transmission. If Fmax > wg > Fmin , then ensure the force acts downwards on the pinion. If the wheel is the driver the wheel and pinion should be downward meshing, and if the pinion is the driver they should be upward meshing.



SECTION FIVE - TOPICS RELATING TO PLANETARY GEARS 20 SIZE AND SELECTION OF PLANETARY GEARS

The individual gear wheels of a planetary gear need to comply with the wear and strength requirements of Section Three. However, the maximum power that can be transmitted by a gearbox is limited by the strength of the planet carrier and the loads in the planet wheel journal bearings. The loads are composed of those transmitting the torque, which depends upon Pin, and the centrifugal forces, which depend on (Pn3 (u+1)1/2. Therefore the maximum power that can be transmitted depends on both the gear shaft speed n2, and the gear ratio, u. There is also a minimum power that gearboxes w1thin the scope of this Design Guide can reliably transmit. Figure 5 is derived from accumulated knowledge. It shows the maximum and minimum power that can be transmitted by a planetary gear at different gear ratios. Also shown is maximum power that can be transmitted at different speeds. Figure 5 can be further used to make initial selection of planetary gears.

21 BEARINGS FOR PLANETARY GEARS 21.1 Sun Wheel

The sun wheel needs to be free to float to balance radial and thrust loads so it has neither radial nor thrust bearings. It is located within the planet wheels and is directly connected to the high speed flexible coupling. There is no thrust bearing locating the sun wheel, planetary gears are be double helical.

21.2 Wheel Shaft - Bearings

The planet carrier is overhung at the end of the gear shaft. There are two alternatives for the radial bearings. Double helical construction means internal thrust forces are balanced. (a) The gear shaft is an extension of the slow speed machine shaft.

The planet carrier is supported by the machine radial bearings. No thrust bearing is required, the machine bearing is used.



(b) The gear shaft is flexibly coupled to the machine shaft, and there are one or two radial journal bearings between the coupling and planet carrier. A thrust bearing or collar is required on the wheel shaft, rated for coupling thrust.

21.3 Planet Wheels - Journal Bearings

The planet wheels run on white metal radial journal bearings which are on shafts fixed to the planet carrier.

21.4 Wire Wool Failure

If the peripheral speed of the gear shaft in its radial bearings, or of the planet wheels on their bearings, exceeds 11 m/s 1.5% is the maximum allowed chrome content of the gear shaft, or of the shafts on the planet carrier.

22 DYNAMICS 22.1 Torsional Compliance

Power is transmitted simultaneously through three or more parallel paths in planetary gears. The internal parts are free to adjust their relative positions to allow the powers transmitted through all the paths to equalize. The following are preferred: (a) The sun wheel floats, finding its own centre relative to the planet

wheels by balancing the thrust loads. (b) The annulus is flexibly mounted within the gearbox. Do not accept boxes where the annulus is flexibly supported to permit mutual differential displacement of the planet gears, unless the annulus is also flexible. Torsional compliance is built in during manufacture and cannot be tuned.



Typical values for the torsional compliance of planetary gears are given in Reference 9. The report describes the simulation of the start-up of a torsionally compliant machine train containing two planetary gearboxes. Reference 9 and Reference 10 describe a system in which the torsional compliance was changed to improve the start-up response.

22.2 Excitation Frequencies

In all cases where gearboxes are used, perturbations in the slow speed machine can excite the high speed machine with frequencies equal to gear shaft speed. For gear ratio close to 2.0 this can cause oil whirl in the high speed machine. In a planetary gear the sun wheel is free to float between the planet wheels. Therefore excitation also occurs at frequencies of n p times gear shaft speed, where np is the number of planet wheels. Hence oil whirl can occur at gear ratios near 2.0 n p The effect of higher excitation frequencies on rotor dynamics needs to be considered.











APPENDIX B (continued)



APPENDIX C FILM THICKNESS IN EHL LUBRICATION INTRODUCTION Equations are given here for determining film thicknesses in involute gears of the following types: (a) Internal and external parallel, fixed axis spur and helical gears. (b) Simple planetary gear trains. This covers the majority of industrial gear configurations other than hypoid and worm gears, for which no detailed analysis of film thickness has yet been developed due to the complex contact conditions. The low speed gear in a gearset is usually the most critical in the formation of an EHL film. The calculations in this section are based on the lowest speed gear. In the case of a speed reducer, this would be the output gear. In very high speed gears and speed increasers, the calculations should be made on both the lowest speed and highest speed gears to determine the most critical value. The opposing teeth of involute gears meet in line contact and equation (3) is applicable for calculation of the pitch point film thickness under conditions of adequate lubrication:



Equations for determining the values of N, G and WT/b are given in Table 3 for the various types of gears. h will be in micrometers if length units are in meters and WT/b is in Newton’s, or will be in micro inches in length units are in inches and WT/b is in grounds force. The reduced modulus. ED, for steel gears is 2.20 x 1011 Nm- 2 or (3.3 x 10 7 psi). Although the film thickness varies throughout the meshing cycle, its value at the pitch point is taken as representative of the quality of lubrication in gears. The specific film thickness, λ = h/σ the critical value of is not constant but varies with pitch line velocity, V, as described here and shown in Fig 7. Equations for V are given in Table 8 and V will be in meters/sec when C or R values are in inches and N is in rpm. By determination of the value of pitch line velocity and reference to Fig 7 the critical value of λ may be found for a spur or helical gear. Although Wellauer and Holloway's work, from which Fig 7 is derived, did not, include bevel gears, their mode of operation is similar to helical gears and Fig 8 will give representative results, Table 7 gives values of composite roughness σ, for various types of gear finish. The results are derived from typical values given by Wellauer and Holloway and used in their analysis. For hobbed, shaved, and lapped gears, run-in values were used in the development of the data used for F'g 7. If actual values of σ are not known for the gearset being analyzed, the typical values of Table 7 should give reasonable results,



NOTES ON FIXED AXIS GEARS The load per unit length of the contact (WT/b) is determined using Ref 43 for helical gears and is applicable to spur gears by putting the helix angle φ equal to zero. Spiral bevel gears are treated as virtual helical gears using Tregold's approximation as described by Buckingham.



Table 8 – Gear Equations





APPENDIX D VARIATION OF VISCOSITY WITH PRESSURE Only at pressures of the order of 3000 Ib/in 2 (210 kg/cm2) and higher does pressure begin to cause a significant increase in the viscosity of mineral oils. At 5000 lb/in2 (350 kg/cm2) the Viscosity of a typical mineral all is approximately double its value at atmospheric pressure. As pressure is further increased, the rate of rise in viscosity accelerates, until at very high pressures mineral oils cease to behave like liquids and eventually tend to change their state to that of a waxy solid. For a mineral oil the most convenient mathematical relationship between absolute viscosity and pressure at any particular temperature is an exponential one of the form

This relationship becomes less satisfactory as pressures rise above 20,000 lb/in 2 for example in point contacts. The value of depends on the type of oil and operating range of temperature and pressure. Since the pressure/viscosity relationship is of an exponential form it is the general practice to present data on a logarithmic basis as in Fig.8 which shows the effect of increased pressure on viscosity/temperature characteristics. This graph shows viscosity in kinematic units.















