Theoretical investigations on the linear and nonlinear damping force for an eddy current damper combining with rack and gear

To study the damping characteristics of a new type of eddy current damper with rack and gear recently proposed by the authors, the damping torque for the eddy current damper with rack and gear was theoretically investigated based on some fundamental assumptions, including evenly distributed magnetic field on a conductor plate and no magnetic leakage. A linear relationship between damping torque and velocity was obtained. Numerical simulations by using COMSOL Multiphysics were conducted to evaluate the accuracy of the linear theoretical formula. When angular velocity is less than 30 rad/s, it seems that the linear theoretical results agree well with the numerical results, and maximum relative error between them is about 6.58%. Then, by using COMSOL Multiphysics, a series of parametric studies on damping torque, including the effects of the air gap, the thickness of a back iron plate, the location and number of permanent magnets, and the thickness of a conductor plate, were carried out to further examine the linear theoretical formula. The results show the effects of the air gap and back iron plate on the relative error between linear theoretical and numerical results can be ignored, whereas the location and number of permanent magnets and the thickness of the conductor plate have significant influences on the relative error. Finally, a nonlinear theoretical formula was obtained by introducing three modified coefficients into the linear theoretical formula, and its accuracy was verified in some typical cases. It is proved that there is sufficient accuracy to adopt the nonlinear theoretical formula in preliminary design of the eddy current damper with rack and gear to determine the main structural parameters.