Multibody dynamics simulation of thin-walled four-point contact ball bearing with interactions of balls, ring raceways and crown-type cage

Abstract

The dynamic characteristics of thin-walled four-point contact ball bearing with crown-type cage are important to the dynamic performance and motion accuracy of an industrial robot. Considering multi-clearances, dynamic contact and impact relationships of the ball, ring raceway and crown-type cage, a general methodology for dynamic simulation analysis of the bearing is investigated in the proposed work. In accordance with the geometry of torus, the geometric equation of accurate ring raceway is derived and integrated into the three-dimensional ring raceway using user’s subroutines. The parameterized and assembled three-dimensional model of the bearing is established using ADAMS’s macro-programs. Applying a penalty formulation and a unilateral nonlinear spring–damper model to the bearing, the internal contact interaction is represented as the compliant contact force model using IMPACT function. The multibody contact dynamic models of the bearing are solved by HHT algorithm with ADAMS/Solver. The dynamic results of the contact force, impact force and motion stability of the bearing are discussed under the condition of different loads. The static load distribution and cage’s angular velocity of simulation model are verified by the theoretical values. The motion trajectory of outer ring’s center is circular with a whirling motion. The sphere-to-partial torus surface contacts (ball–racetrack contact) are always four contact points in the load zone of the bearing. Applying pure radial load or rotating radial load, the impact force of ball-to-cage small pocket contact is much larger than that of radial and axial load combination in the non-load zone of the bearing. As a result of the large impact force of ball-to-cage small pocket contact, the angular velocities of the ball and cage are varying greatly in the non-load zone. The impact force of ball-to-cage big pocket contact is very small. The angular velocity of the ball is always that of pure rolling in the load zone and varying slightly in the non-load zone. The new method can be applied to investigate dynamic analysis and design of high-precision industrial robots with multi-clearances, multi-ball bearings under complex, time-varying working conditions.