Abstract
The numerical simulation of temperature distribution of point contacts in mixed lubrication is presented. The calculating includes two steps. First, temperature rises on two surfaces are obtained by a temperature integration method of transient point heat source. Second, the partition coefficients of heat flux are determined by matching the temperature of two surfaces. Similar to the calculation of elastic deformation, double linear interpolation function is used to get a better accuracy, and moving grid method is used to increase the efficiency of the computation. Due to the symmetry of influence coefficient matrix in the direction perpendicular to the velocity, storage and computational work are further reduced by 50%. Numerical samples validate the algorithm and program. The calculating results of the cases of smooth surface and isotropic sinusoidal surface are presented.
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Abbreviations
- a :
-
Hertzian contact radius
- c :
-
specific heat of solid
- C1, C2:
-
influence coefficients of body 1 and body 2. f. heat partition coefficient
- h, \(\bar h\):
-
oil film thickness and its dimensionless parameter, \(\bar h = h/a\)
- Ks, Kf:
-
thermal conductivities of solid and fluid
- p, \(\bar p\):
-
pressure and its dimensionless parameter, \(\bar p = p/p_h \)
- P h :
-
maximum Hertzian pressure, q, \(\bar q\), heat flux density and its dimensionless parameter, q=μpV s , \(\bar q = \mu \bar p\bar V_s \); S=π 3/2 K s/K f
- t, \(\bar t\):
-
time and its dimensionaless parameter, \(\bar t = t \cdot 4\alpha /a^2 \)
- \(T_{1b} ,T_{2b} ,\bar T_{1b} ,\bar T_{2b} \) :
-
bulk temperatures of body 1 and body 2 and the dimensionless forms, \(\bar T = T \cdot \pi ^{3/2} \rho c/(2p_h )\)
- \(\Delta \bar T_1 ,\Delta \bar T_2 \) :
-
dimensionless temperatures rises of body 1 and body 2; \(u = \bar t - \bar t'\)
- \(V_1 ,V_2 ,\bar V_1 ,\bar V_2 \) :
-
velocities of body 1 and body 2 and the dimensionless forms \(\bar V = Va/(4\alpha )\)
- V s , \(\bar V_s \):
-
sliding velocity and its dimensionless parameter, V a=|V 1−V 2|, \(\bar V_s = \left| {\bar V_1 - \bar V_2 } \right|\)
- x, y, \(\bar x,\bar y\):
-
Cartesian coordinates and nondimensional, \(\bar x = x/a, \bar y = y/a\)
- \(\Delta \bar x,\Delta \bar y\) :
-
mesh spacing in the direction of \(\bar x\) and \(\bar y\) axis
- α=K g/gc :
-
thermal diffusivity of solid
- μ:
-
friction coefficient
- σ:
-
density of solid
- μ:
-
solution domain
- Pe=Va/2α) :
-
Peclet number
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Liu, Y., Hu, Y., Wang, W. et al. Simulation of temperature distribution of point contacts in mixed lubrication. Sci. China Ser. E-Technol. Sci. 45, 365–372 (2002). https://doi.org/10.1360/02ye9043
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DOI: https://doi.org/10.1360/02ye9043