Applied Mechanics and Materials Vols. 10-12 (2008) pp 317-321
© (2008) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMM.10-12.317
Online: 2007-12-06
The Tooth Profile Modification in Gear Manufacture
Z. Li1,a and K. Maob
1
School of Engineering and Design, Brunel University, Uxbridge, London, UK, UB8 3PH
a
[email protected], [email protected]
Keywords: Transmission error, Tooth profile modification
Abstract. The gear design always be focus on analyzing the static performance (strength, stress,
friction) and dynamic performance (inertia, noise, vibration), and especially for dynamic, the noise
and vibration of gear are big problems. Actually, the main reason of noise and vibration is
transmission error between master and slave gears, but the error must exist in any manufacture
process. To decrease harmful noise and vibration, the most effective method is “tooth profile
modification”, which is by tip relief or root relief for modifying geometry profile of gear tooth to
regulate transmission error. In the paper, the transmission error of original model and modified
model will be compared to show the gear profile modification will influence the transmission error
obviously.
Introduction
Transmission error (TE) is defined as the difference between the actual position of the output gear
and the position it would occupy if the gear drive were perfect, it can be seen a kind of geometry
error in design and manufacture because of the deformation, friction and transmission wasting and
so on. Actually, transmission error is an important kind of deformation for the gear set and it is the
main source of noise and vibration because the deformation will cause harmful impact and friction.
In actual design and manufacture processes, the deformation and friction must exist, which means
the transmission error can’t be eliminated. The main purpose of the research of transmission error
analysis is trying to find a method to predict the static transmission error of the gears because it is a
necessary condition to reduce noise radiated and harmful vibration from gearbox. According to
primary research, many results of literatures indicated the “tooth profile modification” is very
effective to control transmission error.
Tooth Profile Modification
The noise and vibration of gear set are not only caused by dynamic reasons such as transmission
error, but also can be caused by some geometrical reasons. For example, if a pair of gear starts to
engage, because of tiny error in tooth profile’s geometry, it may cause horrible impact between two
contact surfaces. If the kind of impact exists in meshing process once, the performance of the gear
set will be destroyed by serious distortion. To solve this problem, it’s necessary to modify the
profile of gear tooth to avoid such impact and some serious friction (some kinds of friction should
not be ignored); this is “Tooth profile modification”.
There are many kinds of gear tooth profile forms (e.g. involute, liner, circular and so on), and the
performances of various profile forms are different. For profile modification of any form, the
general process contains short tip relief and long profile modification, but in this paper, the gear
model with standard involute tooth profile will be modified in the simplest method which is tip
relief only, so the following figure just shows the general tip relief process. Actually, the different
profile forms can be gained by modifying the original model, and the core of modification is
controlling the positions of point T1 and point S (amount of Ca and ∆La ). For the purpose of
decreasing noise and vibration, the amount of tip relief is very tiny, and it should be decided
carefully before manufacture because too much modification will change the profile form, and will
cause other dynamic performances distortion.
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Fig.1 Tip relief of tooth profile
Actually, the modification is not unlimited, if the modification is too large the TE and other
harmful parameter will be more serious, if it is too small, the request will not be met. The
conventional amount of tip relief is as given in the existing standards such as British Standard (BS
1970) and ISO (ISO/DIS 1983), the maximum amount of relief (magnitude) Camax =0.02M and the
length of relief (extend) ∆Lamax =0.6M to prevent the possibility excess relief in general. The
standard tip relief limitations can be chosen as the reference values to calculate the actual profile
modification amount.
Cn =
Ca
Ca max
∆Ln =
∆La
∆La max
(1)
(2)
where Cn and ∆Ln are the normalised relief parameters that clearly show the applied relief
(parameters) relative to the limits used in the standards, Ca and ∆La are actual amount relief and
length.
Finite Element Analyze
Model. To analyze the stresses and transmission error of gear, a finite element model should be
built. In the research, a pair of gear model used to be analyzed in ABAQUS. The following figure
shows the model and mesh stiffness:
The primary parameters of the gears are:
Number of teeth: n=24
Module: m=2
Pressure angle: α=20˚
Applied Mechanics and Materials Vols. 10-12
319
Fig.2 Finite Element Mesh Model
There is a simple introduction of the finite element model: the tooth profile of the gear is standard
involute, and the mesh stiffness has been considered that the contact area has dense mesh element.
Anyway, the integrated model is not necessary for analyzing because it will take so much time. In
actual research, just bases on the error of Lewis and AGMA stresses (the static contact stresses of
gear teeth) within 5%, the finite elements of the model have been decreased to reduce analyzing
time (7 out of 24 teeth), and the result of reduced model can be accepted. Finally, there is an
important parameter should be defined, the friction, it will influent the stresses of the model
obviously and can’t be eliminated. But according to some researches of comparing the transmission
error of model with and without friction, the effect is not very seriously, the friction only makes the
transmission error line not regular and doesn’t change the peak values and general trend, it still can
be regulated by reasonable tooth profile modification. So, in this paper, the effect of friction has
been ignored, just for predigesting analyze processes and optimizing the final results.
Profile Modification Amount. As above introduction, the relief amount should be decided
before modification. For tip relief of the research, the relief parameters can be chosen as an
example:
Cn = 0.5
∆Ln = 0.83
So, the actual amount relief can be calculated:
Ca max = 0.02M = 0.02 × 2 = 0.04
∆La max = 0.6M = 0.6 × 2 = 1.2
Ca
⇒ Ca = Cn × Ca max ⇒ Ca = 0.5 × 0.04 = 0.02(mm)
Ca max
∆La
∆Ln =
⇒ ∆La = ∆Ln × ∆La max ⇒ ∆La = 0.83 × 1.2 = 0.996(mm)
∆La max
Cn =
Results and Discussion. The purpose of the research is comparing transmission error between
original model and modified model. For the analyzed processes, two different situations will be
discussed which means the results will be calculated in different input torque with the same time
increment.
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- 0. 5
- 0. 5
- 0. 4
- 0. 4
- 0. 4
- 0. 3
- 0. 3
- 0. 3
- 0. 3
- 0. 2
- 0. 2
- 0. 2
- 0. 1
- 0. 1
-0
-0
0
- 0. 1
(1) Input torque = 20Nm, time increment is 0.02 second, ignore friction:
- 0. 0005
- 0. 001
Or i gi nal
Modi f i ed
- 0. 0015
- 0. 002
- 0. 0025
- 0. 003
Fig.3 Transmission Error (20Nm, Time increment = 0.02s)
Discussion: The blue line indicates the TE trend of original model and the pink line for modified
model. Because the input torque is not very large, the transmission error is inerratic. Although the
transmission error has changed a little by profile modification, there is not very significative effect
at all, and by reason of regular transmission error transfer, the dynamic performance of gear set will
be easy to control, and harmful noise and vibration can be limited.
Actually, with the input torque increase gradually, the transmission error will not be regular any
more, the trend line will become complicated. In that case, the meshing gear teeth will make serious
impact, and will produce terrible noise and vibration; it is very harmful for gear manufacture. In that
time, the reasonable profile modification can regulate complicated TE line to decrease harmful
dynamic response.
- 0. 5
- 0. 5
- 0. 4
- 0. 4
- 0. 4
- 0. 3
- 0. 3
- 0. 3
- 0. 3
- 0. 2
- 0. 2
- 0. 2
- 0. 1
- 0. 1
-0
- 0. 0005
- 0. 1
0
-0
(2) Input torque = 30Nm, time increment = 0.02 second, ignore friction.
- 0. 001
- 0. 0015
- 0. 002
- 0. 0025
Or i gi nal
Modi f i ed
- 0. 003
- 0. 0035
- 0. 004
- 0. 0045
Fig.4 Transmission Error (30Nm, Time increment = 0.02s)
Applied Mechanics and Materials Vols. 10-12
321
Discussion: The input torque has increased to 30Nm; TE line of the original model is not regular
any more. The figure shows the blue line looks ugly, which means the transmission error is ruleless,
and the effect of this situation is making impact to produce noise and vibration. After profile
modification, the TE line become more static, some complicated area of original line has been
modulated, and the noise and vibration have been decreased successfully.
Summary
The paper analyzed the effect of profile modification for transmission error, and the results showed
that the transmission error can be modulated by modifying tooth profile, but above analysis just
based on perfect situation (ignore friction, no inertia, no thermal response), if the research will
consider all conditions, the situation of transmission error will be more complicated, so profile
modification is very important for optimizing the gear performance. Actually, profile modification
will not only influence transmission error but also static stresses distributing. For gear manufacture,
profile modification of the model should be paid more attention to research, because it is the best
method to decrease noise and vibration of gear set.
References
[1]
J. Wang and I. Howard, Comprehensive Analysis of Spur Gears in Mesh with Various Types of
Profile Modifications: Department of Mechanical Engineering, Curtin University of
Technology, Perth, WA, Australia. (2005).
[2]
J. D. Smith: Gear Noise and Vibration (Marcel Dekker, Inc., New York 1999, pp. 32-34).
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The Tooth Profile Modification in Gear Manufacture
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