A novel contact dynamics modeling method for profile-shifted spur gear pairs considering geometric eccentricity

The profile shift coefficient, as an active design parameter, optimizes transmission performance by adjusting the meshing point displacement, while geometric eccentricity arises from manufacturing or assembly errors, causing meshing center distance deviation. These two factors respectively characterize active modification and passive deviation in gear systems, jointly influencing dynamic characteristics. Focusing on a pair of profile-shifted spur gears considering geometric eccentricity, a contact dynamics modeling method is adopted to investigate their vibration characteristics. The contact dynamics model for profile-shifted spur gear pairs with geometric eccentricity comprises five core components: tooth profile mathematical model, time-varying meshing stiffness (TVMS) model, dynamic differential equations, contact model, and unknown variable solving model. Based on the proposed model, the study analyzes the effects of different profile shift coefficients, geometric eccentricity values, and their coupled interactions on the dynamic response of the gear system. It reveals the regulatory role of profile shift coefficients in eccentricity sensitivity. By constructing a dynamic simulation model for profile-shifted spur gear pairs with geometric eccentricity, the accuracy of the proposed model is validated. This research provides theoretical foundations for profile-eccentricity collaborative optimization in high-precision gear systems, particularly applicable to dynamically sensitive transmission devices such as aerospace reducers and precision machine tools.