Evaluation of optimum profile modification curves of profile shifted spur gears based on vibration responses

• Mesh stiffness model of profile shifted gears with profile modification is developed.
• Optimum modification curves under different tooth profile modifications are determined.
• Optimum modification curves are related to the modification degree.
• Optimum modification curves are related to modification coefficients.
• Optimum modification curves should also be evaluated by vibration responses.

In this paper, a mesh stiffness model is developed for profile shifted gears with addendum modifications and tooth profile modifications (TPMs). The time-varying mesh stiffness (TVMS), load sharing factor (LSF), loaded static transmission error (LSTE) and non-loaded static transmission error (NLSTE) of a profile shifted spur gear pair with TPMs are obtained by the analytical model. The optimum profile modification curve under different amounts of TPM is determined by analyzing the LSTE first. Then, considering the effect of NLSTE, finite element (FE) model of a geared rotor system is established. The system vibration responses under different TPM curves are analyzed and the optimum modification curve is further evaluated by amplitude frequency responses. The results show that the optimum modification curve is related to the amount of TPM and modification coefficients. The comparison of the optimum profile modification curves is evaluated by LSTE and vibration responses, which shows that the optimum modification curve should be determined by evaluating the vibration response of the geared rotor system in the low mesh frequency range.