Investigation into the Traction王燕霜航空润滑油
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113
Investigation into the Traction Coefficient in Elastohydrodynamic Lubrication
Y.S. Wang Harbin Institute of Technology, Harbin, China and Henan University of Science and Technology, Luoyang, China B.Y. Yang Henan University of Science and Technology, Luoyang, China L.Q. Wang Harbin Institute of Technology, Harbin, China Abstract The elastohydrodynamic traction coefficients of two Chinese aviation lubricating oils were investigated for various loads, rolling velocities, and lubricant inlet temperatures iising a self-made test rig. Traction coefficient versus slide-to-roll ratio curves were generated. The concept of critical load varying with the lubricant temperature is proposed. This paper presents a new empirical formula f o r the dynamic pevforniance design of high-speed rolling bearings, that relates traction coefficient with normal load, rolling velocity, and lubricant inlet temperature. The coefficients of the formula may be computed by regression analysis of the experimental data. Two example calculations are presented. The predicted results from the formula agree well with experimental obserziations.
PREVIOUS METHOD TO CALCULATE TRACTION COEFFICIENT
The method that has been used in many studies5-’ to calculate the traction coefficient needs four basic equations that can be summarised as:
Figure 1 Construction of the test rig"
Disc soecimen
来自百度文库
Motor I
Ball specimen
Motor I I
dissipation. Eq. (3) is the momentum equation. Boundary conditions on temperature are calculated by Eq. (4)? Given the thickness of the lubricant film and rolling velocities, the above equations are solved simultaneously to obtain temperatures, velocities, and shear stress distributions over the contact. The traction force can be obtained by integrating the shear stress distribution. The traction coefficient is the ratio of the traction force to the applied normal load between the interacting surfaces. Eqs. (1)-(4), which may have to be calculated a great number of times before convergence solutions can be obtained, are quite computationally complex even after several simplifying assumptions are made about the operating cnvironment and film properties.@ The complexity of the traction model makes the computer program rather impractical to use. Therefore, the implementation o f this method for practical design tools is somewhat difficult, particularly in the case of dynamic performance simulation of rolling bearings. This situation has led to the simple method presented in this paper, in which an algebraic equation is used to predict the traction coefficient. The constitutive coefficients of the equation can be obtained by regression analysis of the available experimental data.
7
1 dT = -- + F(T, T*, q )
Gdt
where 7 is the shear rate, T is the shear stress, G and q are the shear modulus and the viscosity of the lubricant, T* is the reference stress or the limiting shear stress, p, c, and k are thermal characteristics of the lubricants, u, T, p , and p are the sliding velocity, absolute temperature, pressure, and lubricant density, x, y, and z are the coordinates along and perpendicular to the rolling velocity and across the lubricant film, respectively, and -a is the abscissa of the inlet of the Hertzian zone. Eq. (l), which was presented by Johnson and Tevaarwerk2and by Bair and Wir~er,~ has been the more widely accepted rheological model that describes the lubricant behaviour as a non-linear viscous flow superimposed on a linear elastic strain. Eq. (2) is an energy equation including the convection and heat
Tribotest journal 11-2, December 2004. (12) 114 ISSN 1354-4063 $35.00
lnuestigation into the traction coeflicient in elastohydrodynamic lubrication
115
Keywords
rolling bearings, elastohydrodynamic lubrication, traction coefficient, empirical formula, rolling velocity, lubricant temperature
INTRODUCTION
When a lubricated rolling bearing is operating at high speed an elastohydrodynamic (EHD) film is developed and excessive slip between rolling elements shears this oil film to generate a traction force. The traction force between the lubricant and the rolling element interfaces can cause balls and rollers to accelerate, decelerate, skid, or skew. Thus cage instabilities and the life of a rolling bearing are associated with the traction behaviour of the lubricant. Since the 1960s, many researchers14 have presented various rheological models to calculate the traction force. Unfortunately, the limitations of rheological models and
Tribotest journal 11-2, December 2004. (11) 113 lSSN 1354-4063 $35.00 (2630/1204)
114
Wang, Yung, and Wang
the lack of data for rheological parameters along with the complexity of numerical iteration techniques have restricted the practical application of those models for traction prediction in engineering. Therefore, the authors’ current aim is to model the traction behaviour with an empirical formula which can be conveniently and quickly used to compute the traction coefficient in simulating the dynamic performance of rolling bearings. Based on a large number of traction tests on two Chinese aviation lubricants, a new empirical formula for the traction coefficient is proposed. The method of calculating the traction coefficient used in this paper can be adapted to other lubricants working under the same operating conditions. This will not only be of significance in the dynamic behaviour design of rolling bearings, but will also help lay the foundations of further research on traction theory.
113
Investigation into the Traction Coefficient in Elastohydrodynamic Lubrication
Y.S. Wang Harbin Institute of Technology, Harbin, China and Henan University of Science and Technology, Luoyang, China B.Y. Yang Henan University of Science and Technology, Luoyang, China L.Q. Wang Harbin Institute of Technology, Harbin, China Abstract The elastohydrodynamic traction coefficients of two Chinese aviation lubricating oils were investigated for various loads, rolling velocities, and lubricant inlet temperatures iising a self-made test rig. Traction coefficient versus slide-to-roll ratio curves were generated. The concept of critical load varying with the lubricant temperature is proposed. This paper presents a new empirical formula f o r the dynamic pevforniance design of high-speed rolling bearings, that relates traction coefficient with normal load, rolling velocity, and lubricant inlet temperature. The coefficients of the formula may be computed by regression analysis of the experimental data. Two example calculations are presented. The predicted results from the formula agree well with experimental obserziations.
PREVIOUS METHOD TO CALCULATE TRACTION COEFFICIENT
The method that has been used in many studies5-’ to calculate the traction coefficient needs four basic equations that can be summarised as:
Figure 1 Construction of the test rig"
Disc soecimen
来自百度文库
Motor I
Ball specimen
Motor I I
dissipation. Eq. (3) is the momentum equation. Boundary conditions on temperature are calculated by Eq. (4)? Given the thickness of the lubricant film and rolling velocities, the above equations are solved simultaneously to obtain temperatures, velocities, and shear stress distributions over the contact. The traction force can be obtained by integrating the shear stress distribution. The traction coefficient is the ratio of the traction force to the applied normal load between the interacting surfaces. Eqs. (1)-(4), which may have to be calculated a great number of times before convergence solutions can be obtained, are quite computationally complex even after several simplifying assumptions are made about the operating cnvironment and film properties.@ The complexity of the traction model makes the computer program rather impractical to use. Therefore, the implementation o f this method for practical design tools is somewhat difficult, particularly in the case of dynamic performance simulation of rolling bearings. This situation has led to the simple method presented in this paper, in which an algebraic equation is used to predict the traction coefficient. The constitutive coefficients of the equation can be obtained by regression analysis of the available experimental data.
7
1 dT = -- + F(T, T*, q )
Gdt
where 7 is the shear rate, T is the shear stress, G and q are the shear modulus and the viscosity of the lubricant, T* is the reference stress or the limiting shear stress, p, c, and k are thermal characteristics of the lubricants, u, T, p , and p are the sliding velocity, absolute temperature, pressure, and lubricant density, x, y, and z are the coordinates along and perpendicular to the rolling velocity and across the lubricant film, respectively, and -a is the abscissa of the inlet of the Hertzian zone. Eq. (l), which was presented by Johnson and Tevaarwerk2and by Bair and Wir~er,~ has been the more widely accepted rheological model that describes the lubricant behaviour as a non-linear viscous flow superimposed on a linear elastic strain. Eq. (2) is an energy equation including the convection and heat
Tribotest journal 11-2, December 2004. (12) 114 ISSN 1354-4063 $35.00
lnuestigation into the traction coeflicient in elastohydrodynamic lubrication
115
Keywords
rolling bearings, elastohydrodynamic lubrication, traction coefficient, empirical formula, rolling velocity, lubricant temperature
INTRODUCTION
When a lubricated rolling bearing is operating at high speed an elastohydrodynamic (EHD) film is developed and excessive slip between rolling elements shears this oil film to generate a traction force. The traction force between the lubricant and the rolling element interfaces can cause balls and rollers to accelerate, decelerate, skid, or skew. Thus cage instabilities and the life of a rolling bearing are associated with the traction behaviour of the lubricant. Since the 1960s, many researchers14 have presented various rheological models to calculate the traction force. Unfortunately, the limitations of rheological models and
Tribotest journal 11-2, December 2004. (11) 113 lSSN 1354-4063 $35.00 (2630/1204)
114
Wang, Yung, and Wang
the lack of data for rheological parameters along with the complexity of numerical iteration techniques have restricted the practical application of those models for traction prediction in engineering. Therefore, the authors’ current aim is to model the traction behaviour with an empirical formula which can be conveniently and quickly used to compute the traction coefficient in simulating the dynamic performance of rolling bearings. Based on a large number of traction tests on two Chinese aviation lubricants, a new empirical formula for the traction coefficient is proposed. The method of calculating the traction coefficient used in this paper can be adapted to other lubricants working under the same operating conditions. This will not only be of significance in the dynamic behaviour design of rolling bearings, but will also help lay the foundations of further research on traction theory.