Transformation between polar and rectangular coordinates of stiffness and dampness parameters in hydrodynamic journal bearings

Abstract

The stiffness and dampness parameters of journal bearings are required in rectangular coordinates for analyzing the stability boundary and threshold speed of oil film bearings. On solving the Reynolds equation, the oil film force is always obtained in polar coordinates; thus, the stiffness and dampness parameters can be easily obtained in polar coordinates. Therefore, the transformation between the polar and rectangular coordinates of journal bearing stiffness and dampness parameters is discussed in this study.

Threshold speed of short journal bearings considering the non-Gaussian longitudinal surface roughness

“…At equilibrium point, the non-dimensional accelerations of the journal equal 0, and the attitude angle φ and the Sommerfeld number S could be deduced from equations (21) and (22) Applying the state vector as follows Taking the derivation of state vector above with respect to time, the state equation could be obtained When the journal is on equilibrium location, the Jacobi matrix of state equation (26) is The subscript s indicates the journal in equilibrium state, and K i j * and C i j * (i,j = X,Y) are stiffness and damping coefficients. The definition of K i j * and C i j * are: And the expressions of K i j * and C i j * are 20 : The values of the middle matrix in the right of equations (29) and (30) are The definite integration in equations (17)- (18) and (31)-(32) are not easy to get the analytical results, so the values of these definite integration are obtained by seven-point Gauss–Legendre integral formula in (13)-(14).…”