Real-Time Dynamics Modeling of Cryogenic Ball Bearings With Thermal Coupling

Abstract

Abstract Real-time dynamic modeling of cryogenic ball bearings, where the rotating inner race accelerates to the operating speed, is based on integration of classical differential equations of motion of bearing elements, when experimentally measured ball/race traction behavior is used to compute the imposed acceleration on the rolling elements. The dynamic performance simulation provides a realistic coupling between traction behavior in the ball-to-race contacts and dynamics of bearing element motion as the bearing goes through the transient speed variation. However, due to vastly different mechanical and thermal time scales, heat generation in the bearing is time-averaged over a relatively large thermal time-step to model temperature fields as a step change, while the bearing motion is simulated in real-time. The emphasis is on dynamic modeling with thermal coupling in a static sense. Under stable conditions, the step change in temperature field converges to operating value as the bearing approaches a dynamic steady-state condition, which demonstrates acceptable significance of the dynamic simulation with coupled thermal interactions. Both all steel and hybrid ball bearings for liquid oxygen (LOX) turbo pump applications are modeled. Bearing performance simulations are closely modeled over experimental time cycles in both transient and steady-state domains. Steady-state solutions are shown to be independent of initial conditions to demonstrate acceptable convergence of time domain integrations. Model predictions of heat transferred to circulating LOX is within the range of variation in experimental data. Parametric evaluation of bearing performance as a function of operating conditions demonstrate that while the ball/race contact stress is higher in a hybrid bearing, contact heat generation is significantly lower in comparison with that in the all steel bearings.