Abstract
Considering the internal and external excitations such as time-varying mesh stiffness (TVMS), backlash, transmission error, torque of the traction motor, and load torque of the wheel/rail, a lumped mass model of the spur gear drive system for a railway locomotive is established. Based on Ma models in the relevant literatures, TVMS is calculated by simplifying a gear tooth as a cantilever beam on the root circle, taking into account the effects of extended tooth contact as well as revised foundation stiffness. The bifurcation diagrams and Lyapunov exponent curves of the model parameters are drawn by the numerical method, and the mechanism of chaos evolution of the gear transmission system is analyzed. According to the Floquet theory, variation curves of the maximum Floquet multiplier with pinion speed and support stiffness ratio are drawn by numerical methods. Combined with the bifurcation diagram of the system, the influences of model parameter on the stability of the system are analyzed, and the evolution laws of periodic motion and bifurcation phenomenon are gained. These research results provide the theoretical evidence of model parameter design of the locomotive transmission system.
Highlights
As an important device of rotating machinery, the gear transmission system has found extensive applications in many fields such as high-speed locomotive, petrochemical, and power generation industries
The characteristic analysis above is practically based on the modelling, and modelling of the gear system is considered as a fundamental problem which is still the research hotspot [4, 5]. e factors such as backlash [6, 7], time-varying mesh stiffness (TVMS) [8, 9], and transmission error and lateral-torsional coupled vibration [10, 11] will directly affect the dynamics including the stability and reliability of the gear system
finiteelement methods (FEMs) is time-consuming because every gear pair requires modelling, while analytical method can offer a general approach to evaluate TVMS. e relative contribution of individual components, such as bending, shear, and Hertzian contact stiffness, can be analyzed separately
Summary
As an important device of rotating machinery, the gear transmission system has found extensive applications in many fields such as high-speed locomotive, petrochemical, and power generation industries. In [16], Wei et al developed a six-degree-of-freedom dynamic model coupled flexional, torsional, and axial motion of the helical gear transmission system, which includes TVMS, bearing support stiffness, mesh damping, and backlash. Based on the nonlinear dynamic model of the three-degree-of-freedom gear system, Liu et al [19] studied the system stability and the type of bifurcation by Floquet theory and obtained the stable and unstable periodic orbits. On account of the harsh operation environment including high speed and heavy load, the driving system of locomotive often bears a high-frequency alternating load generated by single- and double-gear meshing in the process of operation For this reason, a three-degree-offreedom spur gear drive system model is derived for a typical locomotive, in which the parameters including TVMS, transmission error, mesh damping, and wheel/rail adhesion torque are considered as uncertain but bounded parameters. Some results are considered as references for the parameters design or vibration control of the gear transmission system for railway locomotive
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