Vibration analysis of planetary roller screw mechanism with time-varying mesh stiffness in non-circular gear engagement

The Planetary Roller Screw Mechanism (PRSM) enables high-precision power transmission via synchronized meshing of thread pairs and modified non-circular gear pairs. While the thread pairs maintain continuous contact, the non-circular gears exhibit periodic engagement-disengagement due to their helix-cut profiles. This inherent disparity in meshing mechanisms establishes the gear pair as the primary vibration excitation source. This study analytically resolves the time-varying mesh stiffness (TVMS) of non-circular gears and thread-pair contact stiffness to construct a multi-degree-of-freedom coupled dynamic model using lumped-parameter theory. The simulated vibration modes—classified as torsional, transverse, and roller modes—yield dynamic responses including displacement, velocity, and acceleration spectra for all components. Experimental validation confirms the model’s accuracy. The study found that the average TVMS of non-circular gears is 28 % lower than that of standard gears, and the internal ring gear is the vibration source of the PRSM system. The findings provide a quantifiable design basis for vibration control and condition monitoring in high-performance PRSM systems.