### Development of a simulation model for the investigation of vibrations in large asynchronous machines

Software development for rotor dynamic analysis of supercritically operated asynchronous motors

In the development of asynchronous motors, rotor-dynamic calculations are an important part of the machine design. The position of the critical speeds resulting from the natural frequencies relative to the operating speed is decisive for the permanent operability of a machine. If the distance between critical speed and operating speed is too small, the machine can be directly destroyed by strong resonance increases or can be reduced in its service life by the resulting, strong alternating loads. Since large asynchronous motors often have to be operated supercritically (i. e. above the first critical speed), resonance-induced vibration increases can occur when the machine is started and stopped. These must be recorded mathematically in order to avoid excessive oscillations in advance by design measures. Development of a simulation model for the investigation of vibrations in large asynchronous machines

Objectives of the simulation program

A simulation program adapted to the problem area of large asynchronous motors can greatly reduce the time required for the necessary rotor-dynamic calculations. With the help of the application-specific simulation program, it is possible to estimate not only the critical speeds but also the behaviour of the rotor during resonance transits, both qualitatively and quantitatively. Due to its modular structure, the program can be easily extended and thus adapted to new problems. The calculation software is implemented in the Matlab environment, using the Finite Element Method (FEM), which is widely used for the numerical solution of technical problems.

Fig. 1: Considered rotor dynamic influences

Special boundary conditions for asynchronous motors

When analyzing asynchronous motors, there are various boundary conditions that must be taken into account depending on the question. Fig. 1 provides an overview of the boundary conditions and influences currently and in the future taken into account in the programme.

Fig. 2: Developed GUI for the Matlab application

Developed Matlab GUI

The modeling is done in a graphical user interface (GUI) tailored to the problem (see Figure 2). The rotor of the motor is represented by beam elements, where the user can choose between Bernoulli beam and Timoshenko beam. When choosing the bearing, it is possible to consider an idealized rigid bearing as well as a linear elastic bearing or a hydrodynamic plain bearing.

Distributed unbalances can be installed at any angle over the entire rotor. In this way, different unbalance scenarios can be simulated and evaluated. The unilateral magnetic tensile forces occurring in asynchronous motors can be taken into account by spring elements with negative stiffness in the area of the rotor plate stack. In future, the housing and foundation will be represented by discrete spring-damper and mass models.

Fig. 3: Example of the displacement time course of a point on the shaft

Post-processing

In addition to support for modeling, the GUI also offers possibilities for the systematic evaluation of simulation results. In this way, the entire rotor can be animated during operation in addition to the displacement time curves (see Fig. 3).

Fig. 4: Result representation of the eigenfrequency analysis Part 1

The results of natural frequency analyses can be displayed in different ways. On the one hand, the calculated frequencies (respectively critical speeds) can be displayed in tabular form, on the other hand the individual eigenforms can also be viewed on the 3D model (see Fig. 4).

Fig. 5: Result representation of the eigenfrequency analysis Part 2

In addition, circular effects can also be taken into account in the eigenfrequency analysis by taking different speeds into account. Here, the results can also be displayed in tabular form, but also in a Campbell diagram (see Fig. 5).

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RWTH Aachen University

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