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In this study, a nonlinear translation-torsion model of spur gear pair with flexible support of gearbox is proposed. The time-varying meshing stiffness, transmission error and backlash are considered in this model. Lagrange’s equations are used for establishing the mathematic model. The numerical method is presented for solutions of nonlinear differential equations. The effect of rotating speed and support stiffness of gearbox is analyzed. The numerical results show that the flexibility of the support of gearbox has a significant effect on the amplitude-frequency characteristic of the spur gear pair at low rotating speeds. The response shows flexibility while the support stiffness is smaller than the bearings and rigidity while the support stiffness is larger than the bearings. The maximum deformation of the driving gear bearings under the flexible support is generally greater than the one under rigid support.

Dynamic characteristic of spur gear with flexible support of gearbox