Weak nonlinear free vibration study of electromechanical integrating toroidal drive

As for a new-style generalized composite transmission-electromechanical integrated toroidal drive,the nonlinear changes of the electromagnetic mesh stiffness between worm and planets were analyzed.Firstly,weak nonlinear motion differential equation of toroidal drive in the form of perturbation was presented.Then,approximative analytic solution of frequency and displacement response were obtained by Linstedt-Poincare(L-P) perturbation method.Lastly,influences of the changes of the electromagnetic mesh stiffness on frequencies and amplitudes of system vibration were discussed,a number of useful results were given.Amplitudes of every direction vibration are not affected almost by increasing order of the small parameter ε,while free vibration frequencies change obviously..