Abstract

Harmonic reducers are generally supported by flexible bearings. The elastic deformation of the flexible bearing enables the harmonic reducer to satisfy high reduction ratio performance. By considering the flexible outer ring and noncircular inner ring of the flexible bearing, a universal static analysis model was developed to calculate the ball load distribution of flexible bearings in harmonic reducers. The validity of the proposed model was proved by studying two types of flexible bearings mounted on an elliptical cam and a four-force action-type cam, respectively. Several results validate the use of the model to assess the ball load distribution instead of a more time-consuming finite element method. Influences of design parameters in the flexible bearing on the load distribution were investigated, which makes reference for the optimal design of the flexible bearing.

References

1.
Yang
,
S. Y.
,
2018
, “
Study of Wear Failure Mechanism of Harmonic Reducer’s Flexible Wheel
,” M.S. thesis,
Shaanxi University of Science and Technology
,
Xi’an, China
.
2.
Lyuminarsky
,
I. E.
,
Lyuminarsky
,
S. E.
, and
Lyuminarskaya
,
E. S.
,
2018
, “
Increased Durability of Flexible Gear of Harmonic Drive Due to Flexible Bearing Modification
,”
Proceedings of the 4th International Conference on Industrial Engineering, ICIE 2018
,
Moscow, Russian Federation
,
May 15–18
,
Springer
,
Cham
, pp.
1287
1292
.
3.
Shen
,
Y. W.
, and
Ye
,
Q. T.
,
1985
,
Theory and Design of Harmonic Gear Transmission
,
Machine Industry Press
,
Beijing
, Chap. 5.
4.
Ostapski
,
W.
,
2010
, “
Analysis of the Stress State in the Harmonic Drive Generator-Flexspline System in Relation to Selected Structural Parameters and Manufacturing Deviations
,”
Bull. Polish Acad. Sci.: Tech. Sci.
,
58
(
4
), pp.
683
698
. 10.2478/v10175-010-0073-8
5.
Harris
,
T. A.
, and
Kotzalas
,
M. N.
,
2007
,
Rolling Bearing Analysis: Advanced Concepts of Bearing Technology
, Chap. 1,
Taylor & Francis
,
London
.
6.
Jones
,
A. B.
, and
Harris
,
T. A.
,
1963
, “
Analysis of a Rolling-Element Idler Gear Bearing Having a Deformable Outer-Race Structure
,”
J. Basic Eng.
,
85
(
2
), pp.
273
278
. 10.1115/1.3656576
7.
Mignot
,
L.
,
Bonnard
,
L.
, and
Abousleiman
,
V.
,
2010
, “
Analysis of Load Distribution in Planet Gear Bearings
,” AGMA Technical Paper.
8.
Harris
,
T. A.
, and
Broschard
,
J. L.
,
1964
, “
Analysis of an Improved Planetary Gear-Transmission Bearing
,”
J. Basic Eng.
,
86
(
3
), pp.
457
461
. 10.1115/1.3653139
9.
Jiang
,
Y.
,
Wang
,
Y. Z.
,
Tong
,
Q.
,
Su
,
D. S.
, and
Song
,
L.
,
2017
, “
Theoretical Calculation and Simulation Analysis of Internal Load Distribution of Flexible Bearing in Harmonic Drive
,”
Mach. Des. Res.
,
33
(
3
), pp.
91
94
.
10.
Le
,
K. X.
, and
Shen
,
Y. W.
,
1990
, “
Load Distribution on the Wave Generator of Harmonic Gear Transmission
,”
Mech. Sci. Technol. Aerosp. Eng.
,
34
(
2
), pp.
38
45
.
11.
Shao
,
F. C.
, and
Wen
,
S. Z.
,
1991
, “
Internal Load Analysis of Flexible Rolling Bearings for Harmonic Gear Transmission
,”
Mach. Des. Manuf.
, (
1
), pp.
34
37
.
12.
Guan
,
C. F.
,
1994
, “
Calculation for the Contact Pressure of Flexible Bearings Under Dynamic Load
,”
J. Northeast Heavy Mach. Inst.
,
18
(
3
), pp.
220
226
.
13.
Le
,
K. X.
,
Quan
,
Y. X.
,
Zhou
,
G. R.
,
Cheng
,
Z. N.
, and
Zhang
,
M. J.
,
1994
, “
A New Method for Calculating Load Distribution on Harmonic Rolling Bearing
,”
J. Zhejiang Univ. Nat. Sci.
,
28
(
4
), pp.
396
404
.
14.
Li
,
L.
,
You
,
B. D.
, and
Wen
,
J. M.
,
2016
, “
Load Distribution Calculation of Flexible Ball Bearing With Elliptical Cam Wave Generator
,”
Proceedings of the 2016 International Conference on Mechanics, Materials and Structural Engineering, ICMMSE 2016
,
Jeju Island, South Korea
,
Mar. 18–20
, pp.
26
32
.
15.
Li
,
S. T.
, and
Shen
,
Y. W.
,
2004
, “
Fatigue Failure Patterns and Strength Design Methods of a Harmonic Drive Device
,”
Proceedings of the 11th World Congress in Mechanism and Machine Science
,
Tianjin, China
,
Apr. 1–4
,
China Machine Press
, pp.
805
810
.
16.
Li
,
L.
,
2016
, “
Static and Dynamic Analysis of Flexspline and Flexible Bearing Under the Cam With Typical Profile
,” M.S. thesis,
Harbin Institute of Technology
,
Harbin
.
17.
Xiang
,
X. Q.
,
Zhang
,
W. W.
,
Wang
,
X. J.
,
Yu
,
G. Y.
,
Dong
,
J.
, and
Zhang
,
J.
,
2017
, “
Stress Characteristics’ Analysis of Flexible Bearings at Different Speeds
,”
Metrol. Meas. Tech.
,
44
(
4
), pp.
6
8
.
18.
Jiang
,
Y.
,
Wang
,
Y. Z.
,
Zhao
,
K.
, and
Su
,
D. S.
,
2017
, “
Mechanical Property Analysis of Flexible Thin Bearing in Harmonic Drive
,”
Bearing
, (
1
), pp.
10
14
. 10.19533/j. issn1000-3762.2017.01.003
19.
Shao
,
F. C.
,
1990
, “
Lubrication Analysis and Experimental Study of Flexible Rolling Bearing in Harmonic Gear Drive
,” M.S. thesis,
Tsinghua University
,
Beijing
.
20.
Ma
,
C.
,
2018
, “
Vibration Research and Fatigue Analysis of Harmonic Reducer
,” M.S. thesis,
Shaanxi University of Science and Technology
,
Xi’an, Shaanxi
.
21.
Ma
,
J. F.
,
Li
,
C.
,
Luo
,
Y. C.
, and
Cui
,
L. L.
,
2018
, “
Simulation of Meshing Characteristics of Harmonic Reducer and Experimental Verification
,”
Adv. Mech. Eng.
,
10
(
3
), pp.
1
8
. 10.1177/1687814018767494
22.
Peng
,
P. D.
,
2018
, “
Design and Finite Element Analysis of Harmonic Drive With Short Flexspline
,” M.S. thesis,
South China University of Technology
,
Guangzhou
.
23.
Tian
,
L.
,
Wang
,
Y. Z.
,
Tong
,
Q.
,
Su
,
D. S.
, and
Song
,
L.
,
2017
, “
Analysis on EHL of Flexible Bearing Based on Deformation of Ring
,”
Lubr. Eng.
,
42
(
11
), pp.
69
73
.
24.
Ostapski
,
W.
, and
Mukha
,
I.
,
2007
, “
Stress State Analysis of Harmonic Drive Elements by FEM
,”
Bull. Polish Acad. Sci.: Tech. Sci.
,
55
(
1
), pp.
115
123
.
25.
Liu
,
J. Y.
, and
Chiu
,
Y. P.
,
1974
, “
Analysis of a Thin Elastic Ring Under Arbitrary Loading
,”
J. Eng. Ind.
,
96
(
3
), pp.
870
876
. 10.1115/1.3438455
26.
Harris
,
T. A.
, and
Kotzalas
,
M. N.
,
2007
,
Rolling Bearing Analysis: Essential Concepts of Bearing Technology
, Chap. 7,
Taylor & Francis
,
London
.
27.
He
,
X. F.
,
2008
, “
Study on Some Problems About Long Distance Pipeline Crossing Engineering
,” M.S. thesis,
Northeastern University
,
Shenyang
.
28.
Zhang
,
C. L.
,
Wang
,
J. X.
,
Qin
,
D. C.
, and
Zhu
,
S. S.
,
2013
, “
Effects of the Groove Curvature Radius Coefficients on the Flexible Bearing’s Stress
,”
Mech. Sci. Technol. Aerosp. Eng.
,
32
(
5
), pp.
652
655
.
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