Determining a Function for the Damping Coefficient of a laminated Stack

The design of electrical machines is determined by electrical as well as mechanical requirements. Possible lossesdue to eddy currents in the stator or the rotor are commonly reduced by using stacks of laminated sheet metal. On the other hand, the design of the stator and the rotor has a significant influence on the mechanical properties: Vibrations depend on the stiffness and the damping of the laminated stack. There are different methods to determine the stiffness coefficient of a stack, but it is much more difficult to obtain suitable values for the damping as there are more influencing factors. This paper describes an experimental procedure, which determines the influence of different parameters on the damping of a stack. The stack used during the experiments consists of 200 quadratic steel sheets with a side length of 80 mm and a thickness of 0.5 mm. In accordance with the measurement data, a functional dependance based on three variables is derived. The first one is the surface pressure between the steel sheets, the second one is the frequency of the applied lateral force, and the third one is the displacement between the steel sheets. It is the aim of this investigation to determine the influence of variations of these parameter values on the damping. The forces are applied onto the stack with hydraulic cylinders. The mechanical deformation of the stacked metal sheets is measured by a laser-speckle-based measurement system. This system detects the displacement of single steel sheets. The displacement is measured on two steel sheets, but they are not side by side. The difference between the two measurement points is equal to the displacement of the stack. Through the synchronization of the time signal of the lateral force and the displacement of the stack, a hysteresis loop can be calculated. This hysteresis depends on the lateral force and the displacement of the stack. The area of the hysteresis corresponds to the dissipation energy between the two measurement points on the stack, 140 sheets apart from each other. This area is calculated by numerical integration based on the trapezoidal rule. Through the conservation of energy for this system, it is possible to calculate an effective damping coefficient for the stack. Considering different influencing parameters, a function for the damping coefficient can be identified by the least square method. This function can be used for the parameters in a numerical simulation of an electrical machine