Analytical model of sliding friction in an overrunning clutch
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V
dimensionless elastic deformation
v
elastic deformation
W
load parameter
minimum film thickness, lm initial-minimum film thickness, lm
film thickness, lm mass moment of inertia of the output shaft (including out rim, rollers, planet, etc.) kgm2
Tribology International 38 (2005) 187–194
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Analytical model of sliding friction in an overrunning clutch
K. Liu a,Ã, E. Bamba b
K
constant, defined as K ¼ 6:173 Â 103 Á ZL0:85R2a0tgða0=2Þ.
L
effective length of the roller, mm
Mr resistance torque on the output shaft, Nm
n1,n4 input and output speed of the pulse-CVT, rpm
Because of the complexity of the operation of the overrunning clutch for Pulse-CVTs, both lubricated and non-lubricated friction states should be investigated. Also, because the contact stress in the clutch elements is high (greater than 2–4 GPa), an elastohydrodynamic lubricant (EHL) analysis is necessary. Recently, Sadeghi and Dow [2] reported a two-dimensional thermal elastohydrodynamic lubrication of rolling-sliding contacts for a wet clutch. Some work on the use of non-newtonian lubricants in concentrated line contacts has also been carried out. Johnson and Greenwood [3] have employed the Eyring fluid model to examine the effect of shear
heating on traction. However, limited information is currently available for the overrunning clutch of the pulse-CVT.
Reported in this paper is the development of an isothermal EHL model of the sliding friction of the overrunning clutch, which includes the Reynolds equation, and equations for the elastic-deformation, oil film thickness, and lubricate characteristics. A non-Newton rheogical model was utilized to calculate the frictional force and traction coefficient. An inverse solution is pursued to solve the simultaneous equations. An example problem of an overrunning clutch with Pulse-CVT with an input power of 1500 W is analyzed. The scientific and technological persons have tested the dynamic loading and friction behaviors of overrunning clutch and providing a better testimony and identifying the correctness of various models to the research in this paper [4].
q
pressure function
R, r inner radius of the outer rim, mm, roller radius, mm
S
geometric clearance
t
clutch engaging time, s
U
speed parameter
u
average rim speed, m/s
à Corresponding author. Tel.: +86-29-2312691; fax: +86-293240439.
0301-679X/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0301-679X(03)00033-1
Abstract
The overrunning clutch for pulse-continuously variable speed transmissions (Pulse-CVT) is a roller type of mechanism whose working condition is different from the conventional overrunning clutch. This paper studies the sliding friction of this clutch with the consideration of the dynamic effect of its operation. Both try and lubricated frictions are numerically analyzed. Distributions of the friction among the clutch components are numerically investigated and power loss is estimated. # 2003 Elsevier Ltd. All rights reserved.
a Xian University of Technology, Xian, 710048, China b Faculty of Science and Technology, Kinki University, 3-4-1 Kowakae, Higashiosaka, Osaka 577, Japan
2
¼ 1 À m21 þ 1 À m22
traction coefficient
E0
E1
E2
F
total frictional force, N
G
dimensionless material constant, G ¼ aE0
H, H0 h, h0 h1 J
dimensionless film thickness, dimensionless initial-minimum film thickness
188
K. Liu, E. Bamba / Tribology International 38 (2005) 187–194
Nomenclature
b
Hertzian-half length, mm
E1;E2 E0 f
Young’s modulus equivalent Young’ modulus,
2. The working principle of overrunning clutch
Fig. 1 schematically shows the structure of the overrunning clutch for the pulse-CVT. The clutch mainly contains of an outer rim, a few rollers, a planet wheel (inter rim), and springs. The outer rim is rigidly connected to the output rocker attached to the pulse-CVT, and the planet wheel is rigidly connected to the output shaft of the clutch. The spring retains the rollers in the wedged space between the planet wheel and the outer rim. When the rotor rotates in a given direction, it will convert the reciprocating motion of the rocker of the
1. Introduction
The overrunning clutch is the key element in a pulsecontinuously variable speed transmission (pulse-CVT). It converts the reciprocating motion of the rocker, which is attached to the pulse-CVT, into a pulse rotating motion in a single direction. It is a roller type of mechanism whose working condition is different from the conventional types of overrunning clutches. In general, the joint and release frequency is much higher than that of a conventional overrunning clutch, and can be thousands of times per minute. The overrunning clutch is also the most vulnerable portion of the pulse-CVT system [1]. Understanding the frictional characteristics of this clutch will provide necessary information to the future development of the pulse-CVT.