Coupled multi-DOF dynamic contact analysis model for the simulation of intermittent gear tooth contacts, impacts and rattling considering backlash and variable torque

Variable torque conditions in geared powertrain applications are known to lead to tooth contact loss, contact reversal, tooth impacts, rattling vibration and noise. Displacements/ deflections dominate the low-torque high-vibration responses and, besides backlash, the real-time dynamic lateral deflections of the gear bodies and the occurrence of simultaneous double-sided tooth contact influence the instantaneous mesh excitation strongly. The faster deterministic and stochastic analytical models do not consider this coupling, whereas the numerical models that do so implicitly by simulating the contact of discretised tooth surfaces/ volumes are significantly limited by the accuracy and computational overhead of their discrete meshes. To provide a both fast and accurate solution of the contact problem, especially in displacement-dominated operating conditions, this work analyses the dynamic contact of gears starting from basic principles and derives an accurate analytical model for the coupling between the compliance, contact geometry, the backlash, and the torsional and lateral displacements and deflections in the general three-dimensional multi-DOF system. This serves as a foundation for a series of dynamical simulations of a single-stage spur gear transmission under different variable-torque excitations to predict tooth contact loss and contact reversal and the basic interactions that lead to impacts and rattling vibration. This approach can be used to predict critical torque fluctuation levels, beyond which these phenomena emerge.