Periodic response analysis of a misaligned rotor system by harmonic balance method with alternating frequency/time domain technique

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.

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Time-Domain Harmonic Balance Method for Turbomachinery Aeroelasticity

AIAA Journal ◽

10.2514/1.j051848 ◽

2014 ◽

Vol 52 (1) ◽

pp. 62-71 ◽

Cited By ~ 11

Author(s):

Frédéric Sicot ◽

Adrien Gomar ◽

Guillaume Dufour ◽

Alain Dugeai

Keyword(s):

Time Domain ◽

Harmonic Balance ◽

Harmonic Balance Method ◽

Balance Method

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Multi-Harmonic Analysis of Dry Friction Damped Systems Using an Incremental Harmonic Balance Method

Journal of Applied Mechanics ◽

10.1115/1.3169175 ◽

1985 ◽

Vol 52 (4) ◽

pp. 958-964 ◽

Cited By ~ 128

Author(s):

C. Pierre ◽

A. A. Ferri ◽

E. H. Dowell

Keyword(s):

Time Domain ◽

Dry Friction ◽

Harmonic Balance ◽

Harmonic Balance Method ◽

Frequency Domain Analysis ◽

Balance Method ◽

Incremental Harmonic Balance Method ◽

Incremental Harmonic Balance ◽

The Time Domain ◽

Damped Systems

A multi-harmonic, frequency domain analysis of dry friction damped systems is presented which uses an incremental harmonic balance method. When compared with time domain solution methods, it is found that the incremental harmonic balance method can yield very accurate results with some advantages over the time domain methods. Both one and two degree-of-freedom systems are studied.

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The Development and Application of a Time-Domain Harmonic Balance Flow Solver

Volume 1: Symposia, Parts A and B ◽

10.1115/fedsm2012-72200 ◽

2012 ◽

Author(s):

Pengcheng Du ◽

Fangfei Ning

Keyword(s):

Time Domain ◽

Harmonic Balance ◽

Unsteady Flows ◽

Harmonic Balance Method ◽

Balance Method ◽

Computational Time ◽

Test Cases ◽

Flow Solver ◽

The Time Domain ◽

Time Periodic

Time periodic unsteady flows are often encountered in turbomachinery. Simulating such flows using conventional time marching approach is very time-consuming and hence expensive. To handle this problem, several Fourier-based reduced order models have been developed recently. Among these, the time-domain harmonic balance method solves the governing equations purely in the time domain and there is also no need for the turbulence model to be linearized, making it easy to be implemented in an existing RANS code. Thus, the time-domain harmonic balance method was chosen and incorporated into an in-house Navier-Stokes flow solver. Several test cases were performed for the validations of the developed code. They cover standard unsteady test cases such as the low speed vortex shedding cylinder flow and the Sajben transonic diffuser under periodically oscillating back pressure. Further, two different practical turbomachinery unsteady flows were considered. One is a transonic fan under circumferential inlet distortion and the other is the rotor-stator interactions in a single stage compressor. The results illustrate the capability of the harmonic balance method in capturing the dominant nonlinear effects. The number of harmonics should be retained in the harmonic balance method is depend on the strength of the nonlinear unsteady effects and differs from case to case. With appropriate number of harmonics retained, it can resolve the unsteady flow field satisfactory, meanwhile, reducing the computational time significantly. In a word, the harmonic balance method promise to be an effective way to simulate time periodic unsteady flows.

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Periodic Response of a Duffing Oscillator Under Combined Harmonic and Random Excitations

Journal of Vibration and Acoustics ◽

10.1115/1.4029993 ◽

2015 ◽

Vol 137 (4) ◽

Cited By ~ 10

Author(s):

Hai-Tao Zhu ◽

Siu-Siu Guo

Keyword(s):

Harmonic Balance ◽

Duffing Oscillator ◽

Harmonic Balance Method ◽

Solution Procedure ◽

Balance Method ◽

Periodic Response ◽

Coupled Equations ◽

The Mean ◽

Closure Method ◽

Gaussian Closure

This paper presents a solution procedure to investigate the periodic response of a Duffing oscillator under combined harmonic and random excitations. The solution procedure consists of an implicit harmonic balance method and a Gaussian closure method. The implicit harmonic balance method, previously developed for the case of harmonic excitation, is extended to the present case of combined harmonic and random excitations with the help of the Gaussian closure method. The amplitudes of the periodic response and the steady variances can be automatically found by the proposed solution procedure. First, the response process is separated into the mean part and the random process part. Then the Gaussian closure method is adopted to reformulate the original equation into two coupled differential equations. One is a deterministic equation about the mean part and the other is a stochastic equivalent linear equation. In terms of these two coupled equations, the implicit harmonic balance method is used to obtain a set of nonlinear algebraic equations relating to amplitudes, frequency, and variance. The resulting equations are not explicitly determined and they can be implicitly solved by nonlinear equation routines available in most mathematical libraries. Three illustrative examples are further investigated to show the effectiveness of the proposed solution procedure. Furthermore, the proposed solution procedure is particularly convenient for programming and it can be extended to obtain the periodic solutions of the response of multi degrees-of-freedom systems.

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Nonlinear Frequency Response Analysis of a Multistage Clutch Damper With Multiple Nonlinearities

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4026036 ◽

2014 ◽

Vol 9 (3) ◽

Cited By ~ 8

Author(s):

Jong-Yun Yoon ◽

Hwan-Sik Yoon

Keyword(s):

Frequency Response ◽

Harmonic Balance ◽

Piecewise Linear ◽

Dynamic Performance ◽

Harmonic Balance Method ◽

Balance Method ◽

Response Analysis ◽

Nonlinear Frequency ◽

System Equation ◽

Nonlinear Frequency Response

This paper presents the nonlinear frequency response of a multistage clutch damper system in the framework of the harmonic balance method. For the numerical analysis, a multistage clutch damper with multiple nonlinearities is modeled as a single degree-of-freedom torsional system subjected to sinusoidal excitations. The nonlinearities include piecewise-linear stiffness, hysteresis, and preload all with asymmetric transition angles. Then, the nonlinear frequency response of the system is numerically obtained by applying the Newton–Raphson method to a system equation formulated by using the harmonic balance method. The resulting nonlinear frequency response is then compared with that obtained by direct numerical simulation of the system in the time domain. Using the simulation results, the stability characteristics and existence of quasi-harmonic response of the system are investigated. Also, the effect of stiffness values on the dynamic performance of the system is examined.

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On the Extension of a Harmonic Balance Method for the Simulation of Compressor Casing Treatments

Volume 2C: Turbomachinery ◽

10.1115/gt2016-56990 ◽

2016 ◽

Author(s):

Christian Voigt ◽

Graham Ashcroft

Keyword(s):

Time Domain ◽

Harmonic Balance ◽

Harmonic Balance Method ◽

Balance Method ◽

Nonlinear Frequency ◽

Transonic Compressor ◽

Frequency Domain Methods ◽

Blade Tip ◽

The Time Domain ◽

Casing Treatments

In recent years both linear and nonlinear frequency domain methods have become increasingly popular in the simulation and investigation of time-periodic flows in turbomachinery. In this work the extension of an alternating frequency/time domain Harmonic Balance method to support arbitrary inter-domain block interfaces, with possibly different frames of reference, is described in detail. The approach outlined is based on the time-domain, area-based interpolation algorithm originally developed for the investigation of casing treatments. In this paper, it is shown that by solving the domain coupling problem in the time-domain it is possible to accurately and efficiently capture the flow physics of such complex, nonlinear problems as blade tip interaction with casing treatments in transonic compressors. To demonstrate and verify the basic algorithm the advection of a simple entropy disturbance in a subsonic duct flow is first computed. Secondly, unsteady flow due to rotor-stator interaction in a transonic compressor stage is simulated and the data compared with reference numerical methods. Finally, to validate the method a single stage transonic axial compressor with casing treatments is simulated and the results are compared with previously published time-domain simulations as well as experimental data based on particle image velocimetry measurements in the blade tip region.

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Application of the Harmonic Balance Method in Simulating Almost Periodic Turbomachinery Flows

Volume 2D: Turbomachinery ◽

10.1115/gt2014-25457 ◽

2014 ◽

Cited By ~ 2

Author(s):

Pengcheng Du ◽

Fangfei Ning

Keyword(s):

Time Domain ◽

Harmonic Balance ◽

Harmonic Balance Method ◽

Balance Method ◽

Time Sampling ◽

Almost Periodic ◽

Shift Method ◽

Shape Correction ◽

Phase Shift Method ◽

Correction Phase

The time-domain harmonic balance method is now popular in simulating unsteady turbomachinery flows. The essence of this method is that the time marching of a periodic or almost-periodic flow problem is substituted by several coupled steady computations at different time instants in the period of interest. The state-of-the-art non-uniform time sampling algorithm is adopted in our time-domain harmonic balance flow solver to simulate multistage turbomachinery unsteady flows. For a specific blade row in a multi-rows configuration, only the interactions from the adjacent blade rows are considered. A typical highly loaded 1.5 stage fan is studied as validation test case. The results showed that the non-uniform time sampling method is robust regardless of the frequencies considered. In this IGV-Rotor-Stator configuration, the interactions between the upstream-traveling rotor shock and IGV blades and the interactions between the rotor wakes and stator blades are all well captured. Thus, the time-averaged performance map obtained by the harmonic balance method with five resolved frequencies matches well with the reference time-accurate computations. The computational time of this five-frequency harmonic balance simulation is affordable, which ensures the code can be used in performing fast unsteady analysis in the design phase. Besides, the single passage unsteady calculation with the shape-correction phase shift method applied is also performed for comparison purpose. A simple interpolation technique is proposed to update the Fourier coefficients of each disturbance as frequently as possible, thus the convergence speed is enhanced. Similar results can be obtained by this shape-correction phase shift method, making it an alternative unsteady calculation module in an in-house CFD package.

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