General harmonic balance solution of a cracked rotor-bearing-disk system for harmonic and sub-harmonic analysis: Analytical and experimental approach

2010 ◽  
Vol 48 (10) ◽  
pp. 921-935 ◽  
Author(s):  
Mohammad A. AL-Shudeifat ◽  
Eric A. Butcher ◽  
Carl R. Stern
Keyword(s):  
Harmonic Analysis ◽  
Harmonic Balance ◽  
Experimental Approach ◽  
Cracked Rotor ◽  
Disk System ◽  
Rotor Bearing ◽  
Balance Solution

Generalized Harmonic Analysis of Nonlinear Ship Roll Dynamics

1996 ◽  
Vol 40 (04) ◽  
pp. 316-325
Author(s):  
J. C. Peyton Jones ◽  
I. Cankaya
Keyword(s):  
Harmonic Analysis ◽  
Harmonic Balance ◽  
Initial Conditions ◽  
Balance Equations ◽  
Validation Process ◽  
Algebraic Expressions ◽  
Resonant Modes ◽  
Ship Roll ◽  
Righting Moment ◽  
Simulation Time

Algebraic expressions are presented which enable the harmonic balance equations to be written down directly in terms of the coefficients of a general nonlinear ship roll equation, without restriction on the number of harmonics considered. The rolling response is then readily computed, as illustrated by an investigation of the resonant modes of ships with angle-dependent cubic damping, or quintic terms in the righting moment. Details are also given of the validation process, showing how simulation time can be reduced by an appropriate choice of initial conditions.

Nonlinear vibration characteristics of the rotor bearing system with bolted flange joints

2019 ◽  
Vol 233 (4) ◽  
pp. 910-930
Author(s):  
Yifu Zhou ◽  
Zhong Luo ◽  
Zifang Bian ◽  
Fei Wang
Keyword(s):  
Nonlinear Vibration ◽  
Time Domain ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Rolling Bearing ◽  
Vibration Characteristics ◽  
Rotor System ◽  
Rotor Bearing ◽  
Bolted Flange ◽  
Bearing System

As sophisticated mechanical equipment, the rotor system of aero-engine is assembled by various parts; bolted flange joints are one of the essential ways of joints. Aiming at the analysis of the nonlinear vibration characteristics of the rotor-bearing system with bolted flange joints, in this paper, a finite element modeling method for a rotor-bearing system with bolted flange joints is proposed, and an incremental harmonic balance method combined with arc length continuation is proposed to solve the dynamic solution of the rotor system. In order to solve the rotor system with rolling bearing nonlinearity, the alternating frequency/time-domain process of the rolling bearing element is deduced. Compared with the conventional harmonic balance method and the time-domain method, this method has the characteristics of fast convergence and high computational efficiency; solving the rotor system with nonlinear bearing force; overcome the shortcoming that the frequency–response curve of the system is too sharp to continue solving. By using this method, the influence of bearing clearance and stiffness on vibration characteristics of the rotor system with bolted flange joints is studied. The evolution law of the state of the rotor system with bolt flange is investigated through numerical simulation and experimental data. The results indicated that the modeling and solving method proposed in this paper could accurately solve the rotor-bearing system with bolted flange joints and analyze its vibration characteristics.

scholarly journals Harmonic Balance Solution Of Coupled Nonlinear Non-Conservative Differential Equation

2013 ◽  
Vol 32 ◽  
pp. 1-14
Author(s):  
M Saifur Rahman ◽  
M Majedur Rahman ◽  
M Sajedur Rahaman ◽  
M Shamsul Alam
Keyword(s):  
Differential Equation ◽  
Numerical Solution ◽  
Limit Cycle ◽  
Nonlinear Differential Equation ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Approximate Solutions ◽  
Balance Method ◽  
Balance Solution ◽  
Good Agreement

A modified harmonic balance method is employed to determine the second approximate solutions to a coupled nonlinear differential equation near the limit cycle. The solution shows a good agreement with the numerical solution. DOI: http://dx.doi.org/10.3329/ganit.v32i0.13640 GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 32 (2012) 1 – 14

Unbalanced Response of Cracked Rotor-Bearing System Under Time-Dependent Base Movements

2013 ◽  
Author(s):  
Qinkai Han ◽  
Fulei Chu
Keyword(s):  
Harmonic Balance Method ◽  
Response Spectra ◽  
Element Model ◽  
Time Dependent ◽  
Cracked Rotor ◽  
Transverse Cracks ◽  
Response Characteristics ◽  
Equivalent Time ◽  
Rotor Bearing ◽  
Bearing System

Unbalanced response of cracked rotor-bearing system under time-dependent base movements is studied in this paper. Three base angular motions, including the rolling, pitching and yawing motions, are assumed to be sinusoidal perturbations superimposed upon constant terms. Both the open and breathing transverse cracks are considered in the analysis. The finite element model is established for the base excited rotor-bearing system with open or breathing cracks. Considering the time-varying base movements and transverse cracks, the second order differential equations of the system will not only have time-periodic gyroscopic and stiffness coefficients, but also the multi-frequency external excitations. An improved harmonic balance method is introduced to obtain the steady-state response of the system under both base and unbalance excitations. The whirling frequencies of the equivalent time-invariant system, orbits of shaft center, response spectra and frequency response characteristics, are analyzed accordingly. The effects of various base angular motions, frequency and amplitude of base excitations, and crack depths on the system dynamic behaviors are considered in the discussions.

Periodicity and Stability in Transverse Motion of a Nonlinear Rotor-Bearing System Using Generalized Harmonic Balance Method

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Zhiwei Liu ◽  
Yuefang Wang
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Iteration Scheme ◽  
Balance Method ◽  
Transverse Motion ◽  
Harmonic Load ◽  
Mass Eccentricity ◽  
Rotor Bearing ◽  
Generalized Harmonic Balance Method ◽  
Bearing System

Many rotor assemblies of industrial turbomachines are supported by oil-lubricated bearings. It is well known that the operation safety of these machines is highly dependent on rotors whose stability is closely related to the whirling motion of lubricant oil. In this paper, the problem of transverse motion of rotor systems considering bearing nonlinearity is revisited. A symmetric, rigid Jeffcott rotor is modeled considering unbalanced mass and short bearing forces. A semi-analytical, seminumerical approach is presented based on the generalized harmonic balance method (GHBM) and the Newton–Raphson iteration scheme. The external load of the system is decomposed into a Fourier series with multiple harmonic loads. The amplitude and phase with respect to each harmonic load are solved iteratively. The stability of the motion response is analyzed through identification of eigenvalues at the fixed point mapped from the linearized system using harmonic amplitudes. The solutions of the present approach are compared to those from time-domain numerical integrations using the Runge–Kutta method, and they are found to be in good agreement for stable periodic motions. It is revealed through bifurcation analysis that evolution of the motion in the nonlinear rotor-bearing system is complicated. The Hopf bifurcation (HB) of synchronous vibration initiates oil whirl with varying mass eccentricity. The onset of oil whip is identified when the saddle-node bifurcation of subsynchronous vibration takes place at the critical value of parameter.

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