Description of sub- and superharmonic motion in rotor-stator contact using Fourier series

• Published in: Zeitschrift für angewandte Mathematik und Mechanik 2014-11, Vol.94 (11), p.945-950
• Main Authors: Alber, O., Mahner, M.
• Format: Article
• Language: English
• Subjects: Contact; Fourier analysis; Fourier series; harmonic balance; Kinematics; Mathematical models; Nonlinearity; Rotor stator contact; rub; Simplification; subharmonics; Superharmonics
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.201300250

This paper deals with the description of steady‐state sub‐ and superharmonic motion in rotor‐stator contact using truncated complex Fourier series. Two different approaches are presented with different stages of simplification. In particular, a kinematic contact condition describing continuous contact is used. The multi‐harmonic balance method is applied to solve the differential algebraic system of equations. A further simplification is implemented which uses the triangular inequality to approximate the nonlinear term in the kinematic contact condition. The Fourier coefficients of the nonlinear term are calculated using an integral expression. Reasonable initial values of the Fourier coefficients for the numerical solution are obtained by a hybrid approach. Results show good agreement with calculations by direct numerical integration using a pseudo‐linear viscoelastic contact model. This paper deals with the description of steady‐state sub‐ and superharmonic motion in rotor‐stator contact using truncated complex Fourier series. Two different approaches are presented with different stages of simplification. In particular, a kinematic contact condition describing continuous contact is used. The multi‐harmonic balance method is applied to solve the differential algebraic system of equations. A further simplification is implemented which uses the triangular inequality to approximate the nonlinear term in the kinematic contact condition. The Fourier coefficients of the nonlinear term are calculated using an integral expression. Reasonable initial values of the Fourier coefficients for the numerical solution are obtained by a hybrid approach. Results show good agreement with calculations by direct numerical integration using a pseudo‐linear viscoelastic contact model.