On stochastic processes in the dynamics of planetary transmissions

Abstract

In addition to the theoretical analysis of the nonlinear dynamics of dissipative mechanical systems with the possibility of stochastic and chaotic processes, the paper also includes a numerical experimental example of a planetary transmission. The most common non-linear effects of operation and their influence on the behavior of the planetary gear as a system were analyzed. A simplified model of planetary gears as dissipative dynamic systems whose operation is a complex dynamic process with different effects was considered. These operating effects can appear in many different ways and can be the cause of stochasticity in the operation of the planetary gear. A numerical analysis of planetary gear lubrication was made, as one of the effects of stochasticity, where turbulent damping occurs. The turbulent damping force, due to oil splashing, is taken to be proportional to the second power of the angular velocity of the sun gear. Based on the experiment, it is concluded that the phase space in this system is not preserved and the system is dissipative because the trajectories spiral down into a certain singularity.

Keywords

• stochasticity
• chaoticity
• dissipative system
• nonlinear
• phase curve