The Impact of Gear Meshing Nonlinearities on the Vehicle Launch Shudder

During the launch of a car, severe torsional vibration sometimes may occur in its driveline due to somewhat the slipping of the clutch, its intuitive sense for an occupant is the longitudinal vibration of the vehicle, referred to as the launch shudder whose characteristic frequency is from 5 to 25 Hz generally. As the main vibration sources of the driveline and its crucial nonlinear components, the variable stiffness and backlash of the gear meshing are considered, their impacts on the launch shudder are analyzed in this paper. Conformal mapping, finite element method and regression method etc. are the main approaches to calculate the variable meshing stiffness of a gear pair. If this stiffness is get, it can usually be substituted for its approximate analytical expression, just with finite harmonic terms, in Fourier Series form into Ordinary Differential Equations(ODEs) to calculate the vehicle responses with its nonlinearity considered. There are two methods to model gear backlash, one is to introduce nonlinear backlash function to the stiffness matrix of the system, the other is to model and add restoring torques to its generalized force vector with the original stiffness matrix. The latter is more appropriate for the consideration of backlash as for the tandem gear pairs combination in multiple Degrees of Freedom(DOFs) system. Aimed at analyzing launch shudder, a certain passenger sedan is taken as the research object, 12 DOFs branched torsional vibration model of the vehicle driveline is established, the nonlinearity for two-stage gear variable meshing stiffness and backlash are modeled, further their restoring torques deduced respectively. Vehicle responses, in both time and time-frequency domain are provided; meanwhile transmission errors of two-stage gear pairs with variable meshing stiffness considered and clunk phenomenon of loaded gears caused by the backlash are calculated under the typical launch operating scenario. Through the results of simulation, it is revealed that variable meshing stiffness has very small impact on the launch shudder and can be replaced by the averaged one for the corresponding gear pair in numerical analysis; moreover, the gear backlash may aggravate the shudder when it is larger, while in its rational range, its impact on launch shudder is also smaller.