Multiparameter Vibration Characteristics Of The Speed Integrated Gear

The speed integrated gear can realize the transmission function of the two-stage series mechanism of circular gear and non-circular gears,which is composed of ordinary involute cylindrical gear and non-circular face gear.It has broad application prospects in high-end fields such as aerospace,instruments and robots,which have strict requirements for transmission performance,space and weight.Due to the special time-varying instantaneous center excitation,it is of great significance to research the variable multi-parameter vibration characteristics of the speed integrated gear for its design and application.Clarifying the transmission principle of the speed integrated gear,pitch curve and transmission ratio equations are given.According to the space meshing theory,the tooth profile equations of non-circular gear are derived and based on the shaping principle of non-circular gear,the simulation program of non-circular gear is developed by UG,which provides a geometric model for the finite element calculation of gear stiffness.The instantaneous center variation law of the integrated gear was disscussed,and the excitation mechanism of the instantaneous center on the gear was revealed.It is found that the instantaneous center excites the gear system by changing the relative normal displacement between the teeth,the arm of the circumferential force and the dynamic inertia torque.In view of the lumped parameter method,the pure torsion dynamic model of the speed integrated gear is established considering the instantaneous center,meshing stiffness,damping and tooth error.The dynamic response of the gear is solved by numerical method.It is found that the speed integrated gear has multi-frequency response characteristics.With the increase of frequency and amplitude of instantaneous center excitation,the increase of the torsional vibration of the speed gear is intensified.Furthermore,considering the bearing stiffness,the torsional-lateral-axial coupled dynamic model of the speed integrated gear is established.The numerical analysis shows that the multi-frequency response also appears in the axial and torsional vibration of the gear.Finally,the noncircular face gear is processed by advanced 5 axis CNC milling machine.The torsional and axial vibrations acceleration of the speed integrated gear are measured by using acceleration sensors.The results show that the instantaneous center frequency and meshing frequency are similar to the theoretical calculation results,and the multi-frequency response characteristics of the speed integrated gear are verified.