### Propulsion and Power Plants

### Аuthors

^{1}

^{*},

^{2}

^{**},

^{1}

^{***},

^{1}

^{****}

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

2. Scientific and technical centre of rotor dynamic Alfa-Tranzit Co., Ltd, 1, Leningradskaya street, Khimky, Moscow region, 141400, Russia

*e-mail: davidovarc@gmail.com

**e-mail: degs@alfatran.com

***e-mail: maxim.kutakov@alfatran.com

****e-mail: lemk@alfatran.com

### Abstract

Object and purpose of the studyObject of the study is Unbalanced Magnetic Pull (UMP) which arises in electric motors and generators and must be taken into account in rotor dynamics tasks. Review of existing methods of UMP determination noted its nonlinear nature. The algorithm to solve the task of rotor dynamics behavior with UMP in nonlinear transient analysis was created. Hydraulic turbine generator with UMP was analyzed.

Methodology

UMP value in electric machines depends on the eccentricity of rotor, the geometric size of the machine, the value of magnetic field in the air gap, the magnetic properties of rotor material, presence of the stator winding parallel turns. In nonlinear definition the matrix

equation describing the nonlinear dynamic model of the rotor system is given by:

[

*M*]{

*ü*}+ [

*C*]{

*ù*}+ [

*K*]{

*u*} {

*F*(

*t*)}+{

*R*},

where [

*M*] inertial matrix; [

*C*] damping matrix; [

*K*] stiffness matrix; {

*ü*} {

*ù*} {

*u*} respectively columns of vibration acceleration, velocity and displacement; {

*F*(

*t*)} dynamic loading of any types internal or external; {

*R*} the nonlinear reaction, taking into account a magnetic force between rotor and stator. The equation can be integrated in accordance with the scheme shown in figure.

Findings

It is shown that the UMP has a major influence on the rotors vibrations of electric machines. It reduces the critical speed, changes the position of resonances and vibration amplitudes. The main advantage provided by the method and developed algorithm is its relative simplicity and minimum of input data. Application UMP model to the studied rotor showed that the significant difference between linear and nonlinear statements appears when the air gap is more than 40%.

Originality/value

The presented method and the algorithm was implemented in the software system Dynamics R4 which allows you to carry out quickly and accurately the design and analysis dynamical structures of electrical machines in nonlinear statement with the UMP, as well as other nonlinear properties.

### Keywords:

rotor dynamics, unbalanced magnetic pull, electric machines, rotor eccentricity, Dynamics R4### References

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