Tooth flank modifications

For involute high speed gears and

gears of similar requirements

For Leaders
Introduction

The gear teeth in gear-driven produc- In a torque-transmitting gear, the along the path of contact and an even
tion plants and marine main propulsion toothed parts of the rotors are sub- load distribution along the face width
units occupy very little space. However, ject to elastic deflections due to the are achieved at a certain load – usually
this very specific space, along with many tooth load. nominal load – and oil temperature in
other factors, is essential for successful spite of the all load and temperature
plant operation. Optimum, highly re- The teeth bend, the pinion and wheel influences. Moreover the teeth should
liable torque transmission between the bodies twist, bend and expand under move into and out of mesh with as little
two gear rotors by the tooth flanks is the effect of the centrifugal force. The impact as possible so as to minimize
also crucial. churning and frictional losses in the gear noise.
teeth and the frictional losses in the
Maximum-precision grinding of pure bearings heat up the gear drive com- The necessary magnitudes (degrees) of
involute tooth flanks as shown in ponents, causing additional thermal modification are relatively small. They
Figure 1 is not in itself sufficient to distortions. The mean temperature of normally amount to a few thousandths
achieve such high reliability. A contact the pinion usually settles at a higher or hundredths of a millimetre. But even
check of the mating tooth flanks on a level than that of the wheel. The tem- these small modifications substantially
contact checking stand using Prussian perature varies across the face width. improve the tooth load bearing pattern
blue would show contact over the full The temperature distribution is also in- and the safety of power transmission.
tooth height and over 100% of the fluenced by the type of tooth lubrica- The inevitable conclusion to be drawn
face width – geometrically ideal, but tion (cooling). For this reason, the the- from this is that high precision is es-
potentially disastrous in nominal opera- oretical tooth form must be modified sential in the manufacturing of tooth-
ting conditions. such that a «trapezoidal» load variation modified gears. If the tooth deviations
are roughly of the same dimensional
order as the degree of modification,
modification loses its sense.
Base cylinder helix Involute helicoid
To reap the full benefits of flank modi-
fications it is very important to accu-
rately measure the finished machined
Straight line generator gears. This involves not only measuring
pitch (single and cumulative pitch devi-
ations), but also profile and helix con-
tours.

In determining the form and degree of

Base cylinder the modifications, the various influen-
cing factors are investigated separately;
Transverse involute the total modification is the sum of the
resulting modifications.
Rolling plane unwrapped from base cylinder

Figure 1: Involute helicoid tooth flank surface with helix angle (bb) and base lead angle (cb)
Tooth load distribution along the path of contact
in the transverse section, profile modification

In order to prevent engagement shocks

due to tooth bending deflections and Interference
to obtain a «trapezoidal» tooth load Driven
distribution along the path of contact
in the transverse section, profile modi- Bending deflection
fications are always applied by tip and of teeth 1 and 2
root relief of the pinion or tip reliefs of
the mating gears. The shape and mag-
nitude of these modifications have to
be carefully determined on the basis of
the calculated tooth stiffness of the Path of contact Tip circle
gear mesh and results gathered in the
Driving
field.

Figure 2: Deformation and meshing interference in loaded, pure involute spur gears
Figure 2 shows the interference at the
first point of contact (point A) of a pure
involute tooth form without profile
modifications. This interference is due (Root) (Tip)
to the bending deflections of teeth 1
and 2, which are in contact with each
other at point D. The resulting shock
100% Load
generates noise and may diminish the
strength of the gear teeth in all their Load
aspects, including the oil film on the
tooth flanks with the risk of scuffing at
0% Load
the tips and roots of the mating gear
teeth.

Gear driven
Figure 3 shows the profile modification
(profile diagram) of the pinion and the
«trapezoidal» tooth load distribution
obtained along the path of contact
without engagement shock by ap-
plying tip and root relief to the pinion
(A, H, I, E).
Path of contact

Tip relief

Root relief
Pinion driving

Fig. 3: Load variation & profile diagram for involute spur gears with tip & root relief
Even tooth load distribution along
the face width, lead modification

In order to obtain an even tooth load side (leading end of face width) to the The mean temperature of the pinion is
distribution along the face width (face warmer exit side (trailing end of face higher than the mean temperature of
load factor KHß, KFß close to unity) a lead width). The side faces of the rotors, the mating gear-wheel. This tempera-
modification is always applied to the especially the larger side face of the ture difference causes a pitch difference
pinion to compensate for the bending gear-wheel, have a cooling effect. between between the pinion and gear-
and torsional deflections and thermal wheel which should be compensated
distortions of the gear mesh. Careful Figure 4a shows typical measurements in the transverse section by the profile
consideration of thermal distortions is with thermocouples of the bulk tem- modification and in the axial direction
essential for gears with pitch line velo- peratures of a high speed pinion. The by the lead modification. A simple rule
cities above approximately 80 m/s. resulting thermal tooth flank distor- exists for the axial pitch difference.
tions of the pinion and wheel have an
Those distortions originate from heat asymmetric barrel shape (figure 4b). If the pinion is driving (reduction gear)
arising from the power loss in the heavy tooth contact occurs at the trail-
meshing zone caused by the displace- ing end of the face width; if the pinion
ment of the air / oil mixture out of the is driven (increasing gear) heavy tooth
tooth spaces. In a helical gear this dis- contact occurs on the leading end of
placement moves along the face width the face width.
(screw pump effect) from the cooler

Pinion without lead Pinion with lead

modification modification

Lead when cold

Lead when cold

exit side exit side

Gear-wheel Gear-wheel

Face width Face width

Lead at full speed Mean temp. difference

pinion – gear-wheel

Figure 4b: Gear contact at nominal speed with / without lead modification
Pinion, face width in mm

Leading end Trailing end

of face width, of face width,
cooler side warmer exit side

Figure 4a: Measurements of bulk temperature of a high speed pinion

If these thermal distortions are not com- Very extensive tests performed by gears. The shape and considerable
pensated for, they cause a high local MAAG with pitch line velocities up to amount of bending deflection (slope
overload between the tooth flanks, 200 m/s using thermocouples installed of the toothed parts) strongly influence
seriously endangering the safe opera- in the gear rotors clearly indicated that the lead modification of the double
tion of the gear. To obtain an even even with all kinds of asymmetric oil helical gear. Working flanks with such
tooth load distribution along the face injections into the gear mesh or gear lead modifications cannot be used
width, the tooth flanks of the pinion housing it is practically impossible to to align a gear because the contact
have a conical / concave lead modifi- obtain a uniform temperature distribu- bearing pattern (Prussian blue) is much
cation. tion in pinion and gear which would too short. Therefore, the non-working
permit the omission of this conical / flanks of the pinion and gear are
concave lead modification. ground absolutely parallel and used as
the basis for the correct alignment of
Figures 5 and 6 depict the separate the gear (contact checking in the gear
and combined bending and torsional casing).
deflections and thermal distortions of
the rotors, as well as the lead modifi-
cation of the pinion for typical single
helical and double helical high-speed

100 100
Torque [%] 50
0 Torque [%]
0
even tooth load Pinion driving
distribution
even tooth load even tooth load
distribution distribution

gear mesh axially self-adjusting

Face width 1
/2 face width gap 1
/2 face width
Bending deflection 1st helix 2nd helix

Bending deflection
Torsional deflection
Torsional deflection

Thermal distortion Thermal distortion

Exit side
Exit side Exit side
Combined deflections Combined deflections
and distortion and distortion
Lead modification Lead modification
of single helical pinion of double helical pinion

Figure 5: Single helical gear – deflection, thermal distortion and lead modification Figure 6: Double helical gear – deflection, thermal distortion and lead modification
 Marine gears with special low noise re- Figure 9 shows the actual deflections
quirements operate mainly under part- and thermal distortions of a MAAG high-
load conditions. speed turbo gear with a pitch line velo-
city of approximately 170 m/s. At this
Figures 7 and 8 show the lead modifi- high speed the thermal distortions exert
cation of a single helical and a double a major influence in absolute terms.
helical marine gear. The advantage of
the single helical gear, which stems Figure 9 also shows the resulting lead
from the extremely long tooth contact modification and the tooth bearing pat-
over the net face width – even at no terns of the working and non-working
load – is clearly visible. flanks as obtained during contact check-
ing with Prussian blue and used to align
the gear, as well as the full-load, full-
speed bearing pattern checked with
Dykem Red.

1410

225 960 225

1180
170 365 230 365 170
1070
170 730 170
1300
130 40 130 40
ø 637.03

ø 637.03

ø 560

55 55 55 55

327 861 327

327 1091 327

Coupling Coupling 1st helix 2nd helix

0.020

0.031

Single helical Even tooth load Double helical

0.010

pinion driving distribution along face width pinion driving

Even tooth load
distribution along net face width
Lead modification to compensate for bending and Lead modification to compensate for bending and
torsional deflections at maximum continuous torque torsional deflections at maximum continuous torque
(also excellent for part load conditions) (also adequate for part load conditions)

Figure 7: Lead modification of a single helical marine gear Figure 8: Lead modification of a double helical marine gear
 Concluding statement

Properly designed profile and lead modifications of the work-

Bending (pinion) ing flanks (and also of the non-working flanks, if required)
Torsion (pinion) are of utmost importance for the safe, satisfactory and suc-
Bending+torsion (pinion) cessful operation of a gear drive. These modifications should
be based on many years of observation and experience. But
Thermal (pinion+gear)
be aware that – despite all the applied calculation methods,
standards, the help of computers and numerically controlled
Total (pinion+gear) machine tools – a gear is ultimately a work of art. Satis-
factory results essentially depend on the know-how of the
people involved and above all on their will to do their best
every day. This is mainly true for the staff of the heat treat-
Lead modification (pinion) ment, gear cutting, gear grinding and gear checking depart-
ments, but it is also true for the assembly shop and for those
out in the field.
Face width
Gears from different gear manufacturers may conform to
Torque side identical safety or service factors, determined in accordance
Exit side
with gear standards to calculate their load capacity, but their
reliability can neverthless vary greatly due to the disparity in
Non-working flank Working flank quality of workmanship. Even if a gear is properly designed
and manufactured, it might still suffer damage if it is put into
Contact checking with Prussian blue service without the correct alignment.

Working flank Accordingly, every possible effort has to be made in relation to

the gear teeth.
Full load, full speed bearing pattern (Dykem red)
A gear customer is well advised if he selects a gear manufac-
Figure 9: Actual deflection and distortion, respective lead modification and
contact check with/without load and speed
turer that he can trust.
Representatives Worldwide

Representatives worldwide

MAAG can be contacted through our

world-wide network of agents.
Our skilled service specialists are ready
to provide rapid and expert assistance
at any time.

MAAG Gear AG
Sulzer-Allee 46
P.O.Box 65
CH-8404 Winterthur
Switzerland
Tel. +41 (0) 52 26 28 888
Fax +41 (0) 52 26 28 707
maag-gear@maag-gear.ch
www.maag-gear.com

MAAG Gear Zamech Sp. z o.o.

ul. Stoczniowa 2
PL 82-300 Elblag / Poland

MAAG is a Member of the

F.L.Smidth Group
www.flsmidth.com

MAAG Gear AG MG-TFModifications 1000.09.03

All rights reserved.

Printed in Switzerland.