Abstract

A novel planar ball reducer (NPBR) is invented in which the relative velocity of meshing surfaces is reduced to achieve high mechanical efficiency. In order to acquire an accurate quantitative analysis on the efficiency of a ball reducer, thorough comprehension of the reducer’s tribological behavior is required. To this end, the elastohydrodynamic lubrication (EHL) theory, for the first time, is used to reveal the tribological behavior of the planer ball reducer, and the equations of kinematics, EHL model, and theoretical efficiency of the transmission system are derived. The prototype of NPBR is developed, and its experimental efficiency is measured, which agrees well with the theoretical efficiency.

References

1.
Aliyev
,
A.
, and
Qasimova
,
A.
,
2021
, “
Perspectives of Cycloid Transmission
,”
ETM—Equipment, Technol. Mater.
,
5
(
1
), pp.
72
80
.
2.
Terada H
,
I. K.
,
2009
, “
Fundamental Analysis of a Cycloid Ball Reducer (5th Report)-Development of a Two Stage Type Reduction Mechanism
,”
JSPE
,
75
(
12
), pp.
1418
1422
.
3.
Terada
,
H.
,
2010
, “
The Development of Gearless Reducers With Rolling Balls
,”
J. Mech. Sci. Technol.
,
24
(
1
), pp.
189
195
.
4.
Blagojević
,
M.
,
Matejić
,
M.
, and
Kostić
,
N.
,
2018
, “
Dynamic Behaviour of a Two-Stage Cycloidal Speed Reducer of a New Design Concept
,”
Teh. Vjesn.
,
25
(
2
), pp.
291
298
.
5.
Sato
,
D.
, and
Hasegawa
,
S.
,
2015
, “
1P1-C07 Prototype Design of a Small and Quiet Cyclo Reducer With Eccentric Input by Planetary Gear Mechanism Using Rubber Roller
,”
Proceedings of JSME Annual Conference on Robotics and Mechatronics
,
Kyoto, Japan
,
May 17–19
, pp.
1
3
.
6.
Xu
,
L.
, and
Yang
,
J.
,
2018
, “
Vibration Analysis of a Two-Step Sine Movable Tooth Drive
,”
Shock Vib.
,
2018
, p.
4205273
.
7.
Xu
,
L.
, and
Men
,
M.
,
2019
, “
Meshing Efficiency for Sinusoidal Movable Tooth Drive
,”
J. Adv. Mech. Des. Syst. Manuf.
,
13
(
4
), pp.
1
11
.
8.
Xu
,
L.
, and
Wang
,
W.
,
2019
, “
Natural Frequency and Modes for a Sine Movable Tooth Drive
,”
Iran. J. Sci. Technol.—Trans. Mech. Eng.
,
43
(
s1
), pp.
267
273
.
9.
Ma
,
P.
,
Xing
,
J.
, and
Xu
,
L.
,
2022
, “
Forces and Stress for a Two-Stage Planar Sine-Wave Movable Tooth Drive
,”
Mech. Based Des. Struct. Mach.
,
50
(
3
), pp.
858
876
.
10.
Xu
,
L.
, and
Yang
,
X.
,
2021
, “
Relative Velocity and Meshing Efficiency for a Novel Planar Ball Reducer
,”
Mech. Mach. Theory
,
155
, p.
104057
.
11.
Duan
,
L.
,
An
,
Z.
,
Yang
,
R.
, and
Fu
,
Z.
,
2016
, “
Mechanical Model of Coupling Rolling and Sliding Friction in Real-Time Non-Clearance Precision Ball Transmission
,”
Tribol. Int.
,
103
, pp.
218
227
.
12.
Chen
,
S.
, and
Zhang
,
J.
,
2004
, “
Elastohydrodynamic Lubrication Analysis on Swing Movable Teeth Transmission
,”
J. Mechine Des.
,
21
(
3
), pp.
46
48
.
13.
Zhang Fujun
,
L. l.
,
2005
, “
Lubrication Performance and Influencing Factors Analysis of Swing Movable Tooth Transmission
,”
Lubr. Seal.
, (
3
), pp.
64
67
.
14.
Deng
,
Z.
, and
Zhang
,
J.
,
2007
, “
Multi-Objective Optimization Design of Swing Movable Tooth Transmission Considering Lubrication State
,”
Mech. Transm.
,
31
(
2
), pp.
45
48
. +108.
15.
Hamrock
,
B. J.
, and
Dowson
,
D.
,
1982
, “
Ball Bearing Lubrication: The Elastohydrodynamics of Elliptical Contacts
,”
New York Wiley
,
104
(
2
), pp.
279
281
.
16.
Liang
,
S.
,
Li
,
H.
, and
W
,
X.
,
2006
, “
Numerical Calculation and Analysis for the Elastohydrodynamic Lubrication of Swing Movable Teeth Transmission
,”
J. Sichuan Univ. Eng. Sci. Ed.
,
38
(
6
), pp.
135
139
.
17.
Liang
,
S.
,
Zhang
,
J.
, and
Yao
,
J.
,
2013
, “
Friction Power Loss of Swing Movable Teeth Transmission Under Elastohydrodynamic Lubrication
,”
Xinan Jiaotong Daxue Xuebao/J. Southwest Jiaotong Univ.
,
48
(
6
), pp.
1104
1109
.
18.
Liang
,
S. M.
,
Zhang
,
J.
, and
He
,
F. F.
,
2013
, “
Study on Flash Temperature of Swing Movable Teeth Transmission
,”
Sichuan Daxue Xuebao (Gongcheng Kexue Ban)/J. Sichuan Univ. (Engineering Sci. Ed.)
,
45
(
2
), pp.
176
181
.
19.
Blok
,
H.
,
1963
, “
The Flash Temperature Concept
,”
Wear
,
6
(
6
), pp.
483
494
.
20.
Kakoi
,
K.
,
2021
, “
Formulation to Calculate Isothermal, Non-Newtonian Elastohydrodynamic Lubrication Problems Using a Pressure Gradient Coordinate System and Its Verification by an Experimental Grease
,”
Lubricants
,
9
(
56
), p.
9050056
.
21.
Pu
,
W.
,
Zhu
,
D.
, and
Wang
,
J.
,
2014
, “
A Theoretical Analysis of the Mixed Elastohydrodynamic Lubrication in Elliptical Contacts With an Arbitrary Entrainment
,”
Soc. Tribol. Lubr. Eng. Annu. Meet. Exhib.
,
2014
(
136
), pp.
78
80
.
22.
He
,
T.
,
Wang
,
J.
,
Wang
,
Z.
, and
Zhu
,
D.
,
2015
, “
Simulation of Plasto-Elastohydrodynamic Lubrication in Line Contacts of Infinite and Finite Length
,”
ASME J. Tribol.
,
137
(
4
), p.
041505
.
23.
Cao
,
W.
,
Pu
,
W.
,
Wang
,
J.
, and
Xiao
,
K.
,
2018
, “
Effect of Contact Path on the Mixed Lubrication Performance, Friction and Contact Fatigue in Spiral Bevel Gears
,”
Tribol. Int.
,
123
, pp.
359
371
.
24.
Dong
,
Q.
,
Wang
,
Z.
,
Zhu
,
D.
,
Meng
,
F.
,
Xu
,
L.
, and
Zhou
,
K.
,
2019
, “
A Model of Mixed Lubrication Based on Non-Normalized Discretization and Its Application for Multilayered Materials
,”
ASME J. Tribol.
,
141
(
4
), p.
042101
.
25.
He
,
D.
,
Dong
,
Q.
, and
Zhao
,
G.
,
2021
, “
Modeling Mixed Lubrication in Point and Line Contact by Non-Normalized Discretization
,”
Int. J. Appl. Mech.
,
13
(
7
), pp.
1
23
.
26.
Meng
,
F.
,
Zheng
,
Y.
,
Liu
,
Y.
,
Gong
,
J.
, and
Wang
,
B.
,
2020
, “
Multi-Ellipsoid Contact Elastohydrodynamic Lubrication Performance for Deep Groove Ball Bearing
,”
Tribol. Int.
,
150
, p.
106367
.
27.
Yunlong
,
W.
,
Yulong
,
L.
,
Ziqiang
,
Z.
, and
Wenzhong
,
W.
,
2018
, “
Lubrication and Thermal Failure Mechanism Analysis in High-Speed Angular Contact Ball Bearing
,”
ASME J. Tribol.
,
140
(
3
), p.
031503
.
28.
Tian
,
J.
,
Zhang
,
C.
,
Liang
,
H.
, and
Guo
,
D.
,
2022
, “
Simulation of the Load Reduction Process of High-Speed Angular Contact Ball Bearing With Coupling Model of Dynamics and Thermo-Elastohydrodynamic Lubrication
,”
Tribol. Int.
,
165
, p.
107292
.
29.
Khonsari
,
M. M.
, and
Hua
,
D. Y.
,
1994
, “
Thermal Elastohydrodynamic Analysis Using a Generalized Non-Newtonian Formulation With Application to Bair-Winer Constitutive Equation
,”
ASME J. Tribol.
,
116
(
1
), pp.
37
46
.
30.
Bair
,
S.
, and
Winer
,
W. O.
,
1979
, “
Shear Strength Measurements of Lubricants at High Pressure
,”
ASME J. Tribol.
,
101
(
3
), pp.
251
257
.
31.
Cao
,
W.
,
Pu
,
W.
, and
Wang
,
J.
,
2019
, “
Tribo-Dynamic Model and Fatigue Life Analysis of Spiral Bevel Gears
,”
Eur. J. Mech. A/Solids
,
74
, pp.
124
138
.
32.
Zhou
,
C.
,
Pan
,
L.
,
Xu
,
J.
, and
Han
,
X.
,
2017
, “
Non-Newtonian Thermal Elastohydrodynamic Lubrication in Point Contact for a Crowned Herringbone Gear Drive
,”
Tribol. Int.
,
116
, pp.
470
481
.
33.
Wang
,
Z.
,
Pu
,
W.
,
Zhang
,
Y.
, and
Cao
,
W.
,
2020
, “
Transient Behaviors of Friction, Temperature and Fatigue in Different Contact Trajectories for Spiral Bevel Gears
,”
Tribol. Int.
,
141
, p.
105965
.
34.
Zhu
,
D.
, and
Cheng
,
H. S.
,
1989
, “
An Analysis and Computational Procedure for Ehl Film Thickness, Friction and Flash Temperature in Line and Point Contacts
,”
Tribol. Trans.
,
32
(
3
), pp.
364
370
.
35.
Martini
,
A.
,
Zhu
,
D.
, and
Wang
,
Q.
,
2007
, “
Friction Reduction in Mixed Lubrication
,”
Tribol. Lett.
,
28
(
2
), pp.
139
147
.
36.
Pu
,
W.
,
Wang
,
J.
, and
Zhu
,
D.
,
2016
, “
Friction and Flash Temperature Prediction of Mixed Lubrication in Elliptical Contacts With Arbitrary Velocity Vector
,”
Tribol. Int.
,
99
, pp.
38
46
.
37.
Zaretsky
,
E. V.
,
1987
, “
Fatigue Criterion to System Design, Life, and Reliability
,”
J. Propuls. Power
,
3
(
1
), pp.
76
83
.
38.
Zhu
,
D.
,
Ren
,
N.
, and
Wang
,
Q. J.
,
2009
, “
Pitting Life Prediction Based on a 3D Line Contact Mixed EHL Analysis and Subsurface von Mises Stress Calculation
,”
ASME J. Tribol.
,
131
(
4
), p.
014501
.
39.
Pu
,
W.
,
Zhu
,
D.
,
Wang
,
J.
, and
Jane Wang
,
Q. J.
,
2016
, “
Rolling-Sliding Contact Fatigue of Surfaces With Sinusoidal Roughness
,”
Int. J. Fatigue
,
90
, pp.
57
68
.
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