Nonlinear vibration analysis and stability control of high-speed motorized spindles via parametric design

Abstract

This paper presents a nonlinear dynamic model for high-speed motorized spindles that accounts for multi-layer interface effects (interference fit, clearance, and gap configurations) coupled with thermomechanical interactions. A nonlinear stiffness function is formulated to derive the governing equations of motion. The influences of assembly parameters on critical speeds, stability boundaries, and bifurcation characteristics are systematically investigated using the Lyapunov exponent criterion and numerical simulations. The results demonstrate that the system exhibits pronounced Duffing-type softening nonlinearity, with the primary resonance occurring at 6200 rpm—representing a 36.5% reduction compared to the linear prediction of 9765 rpm. This resonance frequency reduction is primarily attributed to bearing load-zone narrowing and thermo-mechanical coupling effects combined with geometric nonlinearities. The nonlinear effects reach their maximum within an intermediate tolerance range. At high speeds (>15,000 rpm), the system exhibits quasi-linear behavior due to centrifugal forces and thermal expansion that enlarge the effective clearance. Based on parametric stability analysis, optimal assembly parameter ranges are identified: bearing radial clearance ( $C_3$ ) of 10–12 μm, outer ring-housing clearance ( $C_1$ ) of 12–18 μm, and inner ring-shaft interference ( $C_2$ ) of 14–18 μm. These findings provide a theoretical basis for optimizing assembly parameters and enhancing the operational stability of high-speed motorized spindles.