Multibody Dynamics for Assessing Tolerance Effects in Roller-Bearing-Supported Rings

The accurate motion of roller-bearing-supported rings is critically influenced by shape and positional tolerances, which are often underestimated in conventional modeling approaches. The aim of this study is to develop and validate a multibody dynamic framework capable of quantifying the impact of roundness and positional errors on the motion accuracy of roller-bearing-supported rings. Shape errors are modeled using Fourier series and incorporated into a high-fidelity multibody simulation environment. Experimental validation using laser triangulation reveals a maximum runout error of 72.9 μm, compared to a numerically predicted value of 88.6 μm, resulting in a quantified numerical overestimation of 21.5%. Parametric studies investigated the effects of harmonic order, error amplitude, and combined error scenarios on key performance metrics, including trajectory runout and initial offset displacement. Results reveal that the trajectory errors range between 0.29 mm and 0.63 mm for shape error orders and can escalate to 2.84 mm for high amplitude errors, demonstrating the critical role of error order and amplitude. Furthermore, combined simulations show that bearing position errors exert a more pronounced effect on radial accuracy than shape deviations alone. The proposed approach enables precision design evaluation and tolerance optimization in high-accuracy applications, including robotics, aerospace mechanisms, and optical alignment systems.