The Harmonic Balance Method with arc-length continuation in rotor/stator contact problems

By G. Groll, D. Ewins. 2001

384 citations recorded by the source corpus.

There are a variety of abnormal running conditions in rotating machinery which lead to rotor/stator interaction dynamics which, in turn, can cause a rich mixture of effects associated with rub-related phenomena. These effects manifest themselves in the occurrence of multiple solutions for steady state vibration response scenarios, including amplitude jumps during rotor acceleration, and vibration responses at different/multiple frequencies of excitation forces such as unbalance. This paper describes a numerical algorithm based on the harmonic balance method to calculate the periodic response of a non-linear system under periodic excitation. The algorithm also calculates the stability of the periodic solutions found, marks turning and bifurcation points, and follows a solution branch over varying system parameters via arc-length continuation.

Subfields: Control and Systems Engineering, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/035b776765ed7b7695d77ee6284e7ab7703c6d48

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In Control and Systems Engineering

In Mechanical Engineering

Citations in the corpus

Numerical computation of nonlinear normal modes in mechanical engineering (2016, methodology): “Stability can however be analyzed directly in the frequency domain using Hill’s method [53, 54].”
Computing multiple periodic solutions of nonlinear vibration problems using the harmonic balance method and Groebner bases (2015, methodology): “(4) is to introduce continuation methods [6,5].”
A new modal superposition method for nonlinear vibration analysis of structures using hybrid mode shapes (2018, methodology): “Recent studies on the use of HBM for MDOF nonlinear systems in different areas include the application for joints [23, 24], rotor/stator contacts [25], bladed disks [26], geometrically nonlinear beams [27] and plates [28].”
The Harmonic Balance Method for Advanced Analysis and Design of Nonlinear Mechanical Systems (2014, positive): “The quadratic eigenvalue problem proposed by von Groll et al. [10] for finding the Hill's coefficients as solutions of ∆2λ 2 + ∆1λ + Jz = 0 & with ∆1 =         C C −2 ω ν M 2 ω ν M C . . .”
Analytical model of bolted disk–drum joints and its application to dynamic analysis of jointed rotor (2014, background): “Then by referring equation (14), the total reaction of the left-side sub rotor can be obtained”
Rotor to stator contacts in turbomachines. Review and application (2013, methodology): “Several variants have been developed: HBM applied in the rotating frame using the fundamental contact frequency [22], HBM applied in the fixed frame with arc-length continuation [60], simple HBM [61], HBM with alternating time frequency algorithm [62] (the study neglects friction).”
The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems (2015, methodology): “Following the procedure described in [21], a periodic solution x∗(t) satisfying (1) is perturbed with a periodic solution s(t) modulated by an exponential decay: p(t) = x(t) + es(t) (35) Introducing this perturbation into expression (1) yields Mẍ + Cẋ + Kx + ( λ(2)Ms + λ (2Mṡ + Cs) + Ms̈ + Cṡ + Ks )”
Super- and sub-harmonic response calculations for a torsional system with clearance nonlinearity using the harmonic balance method (2005, methodology): “Eq. (26) is the so-called variational equation [ 26 ,34].”
Bifurcation tracking by Harmonic Balance Method for performance tuning of nonlinear dynamical systems (2017, methodology): “Periodic and quasiperiodic solutions are calculated by HBM and time integration respectively.”