On the basis of the Hertz contact theory,the mechanical models of high-speed four-point contact ball bearings in the cases of high speeds and zero-speed are constructed respectively.In order to solve the problems that the initial values of the constructed mechanical model at high speeds is undeterminable and their convergence is difficult,a numerical solution algorithm for the constructed mechanical model at high speeds is proposed on the basis of the Newton-Raphson theory,and the range of iteration variables and the selection principle of convergence factors are presented.For the purpose of reducing the solving difficulty,the number of unknown variables is reduced by a half through the mathematical transformation of the constructed mechanical model at high speeds.In order to tackle the stuck phenomenon of the program for larger-scale nonlinear equations,the proposed algorithm is optimized and the computational efficiency is improved.Finally,the results of the proposed algorithm are compared with those of Jones’program.It is found that the convergence and convergence rate of the proposed algorithm can be controlled by adjusting the convergence factor.Thus,the proposed algorithm is proved to be correct.