The analytical beam element model: novel approach for fast calculation of vibrations in electric machines

The vibration and acoustic behavior of electric machines is an important aspect of the design process. A crucial part of the modeling is the correct prediction of the stator's vibration behavior, characterized by the stator's eigenfrequencies and eigenmodes. For this purpose, a calculation approach called the analytical beam element model (ABM) was presented in a previous paper [18], where Euler-Bernoulli beams were used to describe the vibration behavior of the stator. The ABM introduced offers an alternative to the finite element (FE) method and to classical analytical models. In this paper, the model is examined and extended further. Different approaches conceived to better describe the influence of the stator yoke's thickness by using Timoshenko beams and a multi-layer discretization are presented and discussed. Furthermore, a new feature that considers the lever arm effect of the stator teeth with respect to the yoke is introduced. The results are compared to FE calculations and measurements. Lastly, the improved ABM is used to calculate the vibration behavior of four stators with outer diameters ranging from 160 mm to 7 m. The results are compared to FE results to prove the accuracy of the ABM.