| Electromechanical integrated electromagnetic harmonic movable tooth drive system is a new electromechanical generalized complex transmission device which integrates drive, transmission and control, so the drive system realizes the fine combination of the harmonic drive, the electromagnetic drive, the movable tooth drive and the controller. There is no high-speed rotating components in the drive system, so its inertia is small, and the response is rapid. Thus, the high transmission ratio and the low-speed and high-torque power output can be obtained.Using electromagnetic principle, the changes of air-gap magnetic field with flexible gear deformation are studied. For two conditions of saturated and unsaturated magnetic circuits, the air-gap shape factor equations are given. In addition, the equivalent air-gap is analyzed, and the equations of air-gap flux density and electromagnetic force per unit area on flexible gear are presented.According to the non-swelling deformation theory of cylindrical shell, the key element of electromagnetic harmonic movable tooth drive system——flexible gear is simplified as cylindrical thin shell. Based on the geometry model, the force model of flexible gear under electromagnetic force is given, the displacement equation of the flexible gear under electromagnetic force is deduced, and the changes of the flexible gear displacement with system parameters are studied.Based on elastic mechanics theory, the force model of electromagnetic harmonic movable tooth drive system is established, the forces on each element in the system are analyzed. On this basis, the output torque equation is deduced. The comparison of the output torques between movable tooth type system and friction type system is done. The effects of the system parameters on the output torque is analyzed. Results show that the output torque of electromagnetic harmonic movable tooth drive is about 7 times of one of the friction type drive system.Using mechanical vibration theory, the electromechanical coupled dynamics equation of electromagnetic harmonic movable tooth drive system is deduced, the frequency equation and modal function of the free vibration are deduced. Based on the above equations, the frequency response functions of the drive system under radial and tangential excitation are solved. The influences of the electromechanical parameters on free vibration and force vibration are studied.The dynamic characteristics of the electromagnetic harmonic movable tooth drive system with the eccentric flexible gear is studied. The electromagnetic force equation is given and the modal function is deduced for the drive system with eccentricity. The influences of the electromechanical parameters on free vibration and force vibration of the drive system with eccentricity are studied, and the comparison of natural frequencies and vibration modes of the drive system with or without eccentricity is done.The parameters design, machining and vibration test of the prototype are performed. Using the ANSYS Workbench finite element analysis software, the deformation and vibration modal simulation of flexible gear is conducted. The frequency test of the prototype is performed. Comparing the calculation results with simulation and measuring results, the maximum error between simulation results and the theoretical values is 10.18%, and the maximum error between experimental results and theoretical values is 16.57%. The results show that theoretical values are in agreement with the experiment and simulation, which verifies the correctness of theoretical analysis in this paper. |
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