Modelling, analysis and experimental validation of vibration of electric motors

Electric motors are fundamental components of many machines and processes which provide mechanical power to the systems they are coupled to. Consequently, the performance and efficiency of these motors directly affect the performance and efficiency of the machines or processes they power. Therefore, it is always in engineers' best interest to improve the designs of electric motors in order to obtain higher efficiency, higher reliability as well as better performance from vibration and acoustics points of view. In most design processes in industrial applications, numerical simulations are extensively utilised to minimise the number of design iterations and to reduce testing and prototyping costs. Finite element and multibody dynamic simulations are often used in these simulations and methodologies to build numerical models of electric motors which represent the real behaviour of these motors with acceptable accuracy are widely sought after in industry. The aim of this thesis is to develop a comprehensive methodology to build robust numerical models of electric motors and demonstrate the validity of the models using experimental data. The Atlas motor, which is a small brushless DC motor manufactured by Arcelik A.S. to power Arcelik brand washing machines, is selected as a specimen to demonstrate the modelling and validation procedure proposed and used in this thesis. Firstly, the individual components of the Atlas motor are identified as the front and back covers, the stator, the bearings, the rotor and the flywheel. The flywheel is used here to simulate the loading the Atlas motor is subjected to during its operation in a washing machine. Then, each component is subjected to frequency response function measurements and their natural frequencies in the frequency range of interest (0 – 3200 Hz) are determined experimentally for model validation purposes. Finally, the Campbell Diagrams of the specimens are obtained using measured data between 1000 RPM – 10000 RPM range and this data is used later for the validation of the multibody dynamic models of the Atlas motor for the same frequency range of interest. After the required tests and measurements are completed, finite element models are developed for individual components and their natural frequencies and corresponding mode shapes are calculated by means of modal analyses within the frequency range of interest. The results are compared with the test results and the models are then validated. The components which do not have elastic modes within the frequency range of interest are modelled as rigid bodies. Subsequently, flexible body models of the parts are created based on their finite element models. The generated flexible and rigid body models are then assembled using multibody dynamics simulation software, MSC Adams, by means of appropriate kinematic constraints between the parts. Although the rings and the balls of the ball bearing are modelled as rigid bodies, the nonlinear elastic contacts between the ball bearing elements (the rings and the rolling elements) are included in the model using Hertzian contact approach. Both steady-state and Campbell Diagram simulations are conducted and the numerical results are compared with the experimental results for model validation purposes. In this thesis, the complex contact mechanism between the front and back covers of the motor and the stator is simplified by assuming that these parts are perfectly joined (welded) together at the matching surfaces in the modelling stage. It is shown that this modelling approach yields results with less than 5 percent error in terms of natural frequencies of the assembly of the front cover, the back cover and the stator. Another important finding of this thesis is that, the use of primitive joints or bushings to model the ball bearings does not produce satisfactory results as the nonlinear behaviour of the ball bearings due to the contacts between their elements are neglected in this approach. It is further shown that the detailed bearing model developed in this thesis, which is based on the Hertzian contact theory, is able to produce results with satisfactory accuracy in terms of the nonlinear effects. Finally, it is discovered that the frequencies of the sidebands around the shaft rotation frequency and its harmonics are strongly affected by the contact angle and bearing clearance. A comparison between the results obtained from two different motor models, one with a bearing model that includes the effects of contact angle and bearing clearance and one that does not, revealed that the sidebands are predicted with less than 4 percent error in the former model. It is concluded that the proposed model can be used to predict not only the natural frequencies, but also the forced response characteristics of electric motors as a function of rotational speed with acceptable accuracy.