In this paper, an exact vibration model for helical gear pairs, is developed assuming no spacing error and no shaft run-out, in consideration of nonlinear tooth separation phenomenon. Inside the model, a simple modified stiffness function, including the effect of tooth numbers and addendum modification coefficients, is proposed for a helical involute tooth pair. This new stiffness function is verified by comparing its results with theoretical calculation and experiment. The rotational vibration of helical gear pairs with comparative narrow face width is simulated clearly on a 16-bit personal computer using the finite difference method in Fortran. The total contact ratio, including transverse and overlap contact ratios, is changed in the range of 1 ≤ ε ≤ 3. As a result, the simulated vibration time waveforms and their frequency characteristics agreed precisely with Umezawa’s calculation and experiment. This simulator is also used to investigate the effect of shaft deviation and pressure angle errors on the vibration of helical gears.

1.
Walker
H.
,
1946
, “
Helical Gears
,”
The Engineer
, July, Vol.
21
, pp.
24
26
, pp. 46–48, pp. 70–71.
2.
Jaramillo
T. J.
,
1950
, “
Deflections and Moments Due to A Concentrated Load on a Cantilever Plate of Infinite Length
,”
ASME Journal of Applied Mechanics
, Vol.
25
, pp.
67
72
.
3.
Trbojevic
M. D.
,
1957
, “
Load Distribution on Helical Gear Teeth
,”
The Engineer
, Vol.
32
, Aug. 9. pp.
187
190
, Aug. 16. pp. 222–224.
4.
Houser
D. R.
, and
Seireg
A.
,
1970
, “
An Experimental Investigation of Dynamic Factors in Spur and Helical Gears
,”
ASME Journal of Engineering for Industry
, Vol.
45
, pp.
495
503
.
5.
Seireg
A.
, and
Houser
D. R.
,
1970
, “
Evaluation of Dynamic Factors for Spur and Helical Gears
,”
ASME Journal of Engineering for Industry
, Vol.
45
, pp.
504
515
.
6.
Umezawa, K., 1972, “Fundamental Investigation on the Design of Power Transmission Helical Gears,” Doctoral Dissertation, Tokyo Institute of Technology
7.
Umezawa
K.
,
1972
, “
Deflection and Moments Due to A Concentrated Load on a Rack-Shaped Cantilever Plate with Finite Width for Gears
,”
Bulletin of JSME
, Vol.
15
, No.
79
, pp.
116
124
.
8.
Umezawa
K.
, and
Ishikawa
J.
,
1973
, “
Deflection Due to Contact between Gear Teeth with Finite Width
,”
Bulletin of JSME
, Vol.
16
, No.
97
, pp.
1085
1092
.
9.
Umezawa
K.
,
1974
, “
The Meshing Test on Helical Gears under Load Transmission (3rd Report; The Static Behaviours of Driven Gear)
,”
Bulletin of JSME
, Vol.
17
, No.
112
, pp.
1348
1355
.
10.
Umezawa
K.
, and
Ishikawa
J.
,
1975
, “
On Cylindrical Gear Without Statical Behaviours of Driven Gears under any Load
,”
Bulletin of JSME
, Vol.
18
, No.
122
, pp.
897
904
.
11.
Kasuba
R.
, and
Evans
J.
,
1981
, “
An Extended Model for Determining Dynamic Loads in Spur Gearing
,”
ASME JOURNAL OF MECHANICAL DESIGN
, April 1981, Vol.
103
, pp.
398
409
.
12.
Umezawa
K.
,
Suzuki
T.
,
Houjou
H.
, and
Sato
T.
,
1985
, “
Vibration of Power Transmission Helical Gears (The Effect of Contact Ratio on the Vibration)
,”
Bulletin of JSME
, Vol.
28
, No.
238
, pp.
694
700
.
13.
Umezawa
K.
,
Suzuki
T.
, and
Sato
T.
,
1986
, “
Vibration of Power Transmission Helical Gears (Approximate Equation of Tooth Stiffness)
,”
Bulletin of JSME
, Vol.
29
, No.
251
, pp.
1605
1611
.
14.
Suzuki, T., 1987, “Vibration of Power Transmission Helical Gears,” Doctoral Dissertation, Tokyo Institute of Technology, Supervised by Prof. K. Umezawa.
15.
Sundaresan, S., Ishii, K., and Houser, D. R., 1991, “Design of Helical Gears with Minimum Transmission Error under Manufacturing and Operating Variances,” Proceedings of the International Conference on Motion and Power Transmissions, MPT’91 Hiroshima, pp. 92–97.
16.
Cai
Y.
, and
Hayashi
T.
,
1994
, “
The Linear Approximated Equation of Vibration of a Pair of Spur Gears (Theory and Experiment)
,”
ASME JOURNAL OF MECHANICAL DESIGN
, June, Vol.
116
, pp.
558
564
.
17.
Cai, Y., and Hayashi, T., 1992, “The Optimum Modification of Tooth Profile for a Pair of Spur Gears to Make Its Rotational Vibration Equal Zero,” Proceedings of 1992 International Power Transmission and Gearing Conference, Scottsdale, AZ, Vol. 2, pp. 453–460.
18.
Cai, Y., 1992, “The Evaluation Method of Spur Gear Accuracy to Predict US Running Performance,” Doctoral Dissertation, Tokyo Institute of Technology, Supervised by Prof. T. Hayashi.
19.
Draft International Standard ISO/DIS 6336-1.2, 1990, “Calculation of Load Capacity of Spur and Helical Gears, Part 1: Basic Principles,” Introduction and Influence Factors,” pp. 87–95.
This content is only available via PDF.
You do not currently have access to this content.