Small Perturbation Method in Kinetic Theory

1968 ◽  
Vol 11 (4) ◽  
pp. 906
Author(s):  
L. K. Chi
Keyword(s):  
Kinetic Theory ◽  
Perturbation Method ◽  
Small Perturbation ◽  
Small Perturbation Method

A Derivation of Stiffness and Damping Coefficients for Short Hydrodynamic Journal Bearings with Pseudo-Plastic Lubricants

2020 ◽  
Vol 36 (6) ◽  
pp. 943-953
Author(s):  
Zhuxin Tian ◽  
Runchang Chen
Keyword(s):  
Perturbation Method ◽  
Small Perturbation ◽  
Integral Formula ◽  
Journal Bearings ◽  
Damping Coefficients ◽  
Non Linear ◽  
Small Perturbation Method ◽  
Plastic Lubricants ◽  
Factor Α ◽  
Stiffness And Damping

ABSTRACTA new derivation considering the non-linear terms has been proposed to calculate stiffness and damping coefficients for short hydrodynamic journal bearings lubricated with pseudo-plastic fluids. The proposed method has relaxed the constraint of small perturbation method applicable to only small values of non-Newtonian factor α. An analytical solution is also given. The non-linear Reynolds equation is solved with a more reasonable boundary condition ∂p*/∂z* = 0 at the location of z*=0 while the analytical pressure distribution is obtained by seven-point Gauss-Legendre integral formula. When the non-dimensional non-Newtonian factor α is small, the stiffness and damping coefficients of computed by the proposed method can agree well with those from small perturbation method, which could verify the proposed derivation. As for large non-dimensional non-Newtonian factor α, the stiffness coefficients $K_{XX}^*$ , $K_{XY}^*$ and $K_{YX}^*$ as well as the damping coefficients $C_{XX}^*$ , $C_{XY}^*$ and $C_{YX}^*$ decrease with the increasing of non-dimensional non-Newtonian factor α. The significance of the derivation is that it can relax the constraint of small α and simplify the computation process.

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