Differential equations of air film in elastic bump foil journal bearing were deducted by the perturbation method with air lubrication Reynolds equation and series expansions of air film

air film thickness and foil deformation.The mathematics model of the relations among air film thickness

bump foil deformation and air film pressure was developed in consideration of air compressibility.Both finite difference method and Newton-Raphson method were applied to solve the coupled differential equations and air film thickness mathematics model equations

while the variation rules of air film stiffness and damping coefficients were achieved with different eccentricities

speeds

perturbation frequencies and different length-diameter ratios.This provides a basis for bump foil journal bearing design

optimization and theoretical and test analysis of rotor-elastic foil bearing system.The numerical results show that the main air film stiffness is enhanced when eccentricity and speed increase

and the value of air film stiffness and damping of bump foil journal bearing are connected strongly with the perturbation frequencies.