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
22 DYNAMICS
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
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
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.
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.
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 70o
C and the trip at 80o
C.

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 60o
C 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.
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.
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
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

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