The transient thermal performance of rolling bearings affects the mechanical performance and system safety of traction motors. Most of the traditional empirical formulas used in temperature analysis have been simplified and cannot be completely applied to the calculation of heat generation and convection heat transfer coefficients. Based on the comparative analysis of finite element transient temperature and experimental data, this paper proposes a correction method of mathematical model and derives an accurate calculation formula for the heat generation and lubricant convection heat transfer coefficient of ball bearings applicable for the non-driving end in the traction motor of a high-speed EMU (Electric Multiple Unit). The accuracy of the results has been verified by durability experiment data. In addition, with changes in speed, radial load and other factors taken into account, we have analyzed the influence of these time-varying factors on ball bearing temperature, as well as the temperature distribution law of each component in a grease-lubricated bearing, in a bid to lay a foundation for follow-up research on the heat transfer laws of traction motors and rolling bearings.

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In this paper we present a novel, closed three-dimensional (3D) random vortex dynamics system, which is equivalent to the Navier-Stokes equations for incompressible viscous fluid flows. The new random vortex dynamics system consists of a stochastic differential equation which is, in contrast with the two-dimensional random vortex dynamics equations, coupled with a finite-dimensional ordinary functional differential equation. This new random vortex system paves the way for devising new numerical schemes (random vortex methods) for solving three-dimensional incompressible fluid flow equations by Monte Carlo simulations. In order to derive the 3D random vortex dynamics equations, we have developed two powerful tools: the first is the duality of the conditional distributions of a couple of Taylor diffusions, which provides a path space version of integration by parts; the second is a forward type Feynman-Kac formula representing solutions to nonlinear parabolic equations in terms of functional integration. These technical tools and the underlying ideas are likely to be useful in treating other nonlinear problems.