Super- and sub-harmonic response calculations for a torsional system with clearance nonlinearity using the harmonic balance method

Kim, T.C.; Rook, Todd E.; Singh, Rajendra

doi:10.1016/j.jsv.2004.02.039

Cited by 138 publications

(122 citation statements)

References 21 publications

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“…From Equations (1)-(3) with a multi-degree-of-freedom (MDOF) system model, the Galerkin scheme of the governing equations is expressed by the residual formulation as follows [14,24,[25][26][27][28][29]: sub-system can be expressed with the following equations in the same formulation as Equation (2):…”

Section: Harmonic Balance Methods With Multi-staged Clutch Dampersmentioning

confidence: 99%

“…In addition, consider Ψ as a function of ω. The Jacobian matrix ω J is obtained by parameterizing the frequency ω on the basis of the arc-length continuation technique [14,[24][25][26][27][28][29].…”

Section: T T Tc T T T Tc T T Tc T Tc T Tcmentioning

confidence: 99%

“…The stability analysis is determined by Hill's method [14,24,30]. When the dynamic responses are examined at these unstable zones, jumping phenomena are clearly observed, especially in Figure 3b.…”

Section: Examination Of System Responses Of Severe Excitation Conditionmentioning

confidence: 99%

“…Piecewise-type nonlinearities such as multi-staged clutch dampers will be employed to simulate the nonlinear dynamic behaviors in terms of relative motions in a simple driveline system model. The large body of literature for piecewise-type nonlinearities and other problems can be reviewed [13][14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

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Effect of Various Excitation Conditions on Vibrational Energy in a Multi-Degree-of-Freedom Torsional System with Piecewise-Type Nonlinearities

Yoon

Kim

2015

Energies

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Dynamic behaviors in practical driveline systems for wind turbines or vehicles are inherently affected by multiple nonlinearities such as piecewise-type torsional springs. However, various excitation conditions with different levels of magnitudes also show strong relationships to the dynamic behaviors when system responses are examined in both frequency and time domains. This study investigated the nonlinear responses of torsional systems under various excitations by using the harmonic balance method and numerical analysis. In order to understand the effect of piecewise-type nonlinearities on vibrational energy with different excitations, the nonlinear responses were investigated with various comparisons. First, two different jumping phenomena with frequency up-and down-sweeping conditions were determined under severe excitation levels. Second, practical system analysis using the phase plane and Poincaré map was conducted in various ways. When the system responses were composed of quasi-periodic components, Poincaré map analysis clearly revealed the nonlinear dynamic characteristics and thus it is suggested to investigate complicated nonlinear dynamic responses in practical driveline systems.

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Section: Harmonic Balance Methods With Multi-staged Clutch Dampersmentioning

confidence: 99%

Section: T T Tc T T T Tc T T Tc T Tc T Tcmentioning

confidence: 99%

Section: Examination Of System Responses Of Severe Excitation Conditionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Effect of Various Excitation Conditions on Vibrational Energy in a Multi-Degree-of-Freedom Torsional System with Piecewise-Type Nonlinearities

Yoon

Kim

2015

Energies

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“…The FRF displays predominant and small resonance peaks. The small resonance peaks are super harmonic resonances, which are typical phenomena of nonlinear vibration systems caused by the nonlinearity of the restoring force (Kim et al, 2005). These resonances are not the stick-slip phenomenon caused by the negative damping coming from the difference between the static and dynamic friction forces because the difference of the static and dynamic frictions is not be considered in the proposed friction model.…”

Section: Influence Of Nsb On Frequency Responsementioning

confidence: 99%

Influence of nonlinear spring behavior of friction on dynamic characteristics of a rolling guideway

Sakai

Tanaka

Yoshioka

et al. 2015

JAMDSM

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The friction of rolling guideways in the prerolling region displays hysteretic behavior known as nonlinear spring behavior (NSB). NSB deteriorates motion accuracy and causes vibration in the feed direction. Therefore, the influences of NSB on the dynamic characteristics of rolling guideways should be clarified. This paper describes the influence of NSB on the dynamic characteristics of a rolling guideway. A simple friction model is constructed based on the Masing rule. Because the proposed friction model is described with only three parameters, the factor that inherently affects the dynamic characteristics can be clearly identified. To clarify the influence of NSB, the impulse response, frequency response, and steady state motion are analyzed by numerical analysis. According to the results, the dynamic characteristics in the feed direction depend only on the change rate of friction in the prerolling region, which is introduced to the friction model as the shape factor, n. The stiffness and damping are high when the change rate of friction is high in the prerolling region. The frequency response function is forcedependent, and its tendency is varied by n. The frequency response function includes harmonic and super harmonic resonances. When the carriage is excited with a frequency lower than that of the super harmonic resonance, a displacement spike (quadrant glitch) is observed. Additionally, the nonlinearity cannot be ignored when the carriage is excited with a frequency lower than the harmonic resonance. Finally, an experiment with a roller guideway is conducted to prove the validity of the analysis. The resonance frequency and compliance at the harmonic resonance measured by the experiment accurately conform to the analytical results. IntroductionRolling guideways are widely used in machine tools because they can achieve high speed and precise motion at low cost. The rolling elements circulating inside of a carriage elastically support loads. The elastic deformation of rolling elements and raceways causes rigid-body vibration of a carriage in five degrees of freedom, excluding the feed direction (Ohta and Hayashi, 2000). Additionally, the circulation of rolling elements causes the rolling element passage vibration owing to the variations in stiffness (Matsumoto, 2004). Moreover, the nonlinear elastic behavior of friction causes vibration in the feed direction. This elastic behavior of friction is known as nonlinear spring behavior (NSB) (Otsuka and Masuda, 1998) (Futami et al., 1990) (Koizumi and Kuroda, 1990. These vibrations deteriorate the motion accuracy of a feed drive equipped with rolling guideways.NSB particularly causes the force dependency of the dynamic characteristics of a rolling guideway in the feed and pitch directions (Sakai et al., 2014). The cutting force varies periodically over a wide range during the machining process. Thus, the dynamic characteristics of a feed drive equipped with a rolling guideway vary throughout the machining process. This variation in dynamic characteristics ...

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Numerical Continuation of Periodic Orbits for Harmonically Forced Nonlinear Systems

Sracic

Allen

2011

Civil Engineering Topics, Volume 4

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A nonlinear structure will often respond periodically when it is excited with a sinusoidal force. Several methods are available that can compute the periodic response for various drive frequencies, which is analogous to the frequency response function for a linear system. The simplest approach would be to compute a sequence of simulations where the equations of motion are integrated until damping drives the system to steady state, but that approach suffers from a number of drawbacks. Recently, numerical methods have been proposed that use a solution branch continuation technique to find the free response of unforced, undamped nonlinear systems for different values of a control parameter. These are attractive because they are built around broadly applicable time-integration routines, so they are applicable to a wide range of systems. However, the continuation approach is not typically used to calculate the periodic response of a structural dynamic system to a harmonic force. This work adapts the numerical continuation approach to find the periodic, forced steady-state response of a nonlinear system. The method uses an adaptive procedure with a prediction step and a mode switching correction step based on Newton-Raphson methods. Once a branch of solutions has been computed, it explains how a full spectrum of harmonic forcing conditions affect the dynamic response of the nonlinear system. The approach is developed and applied to calculate nonlinear frequency response curves for a Duffing oscillator and a low order nonlinear cantilever beam.

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Super- and sub-harmonic response calculations for a torsional system with clearance nonlinearity using the harmonic balance method

Cited by 138 publications

References 21 publications

Effect of Various Excitation Conditions on Vibrational Energy in a Multi-Degree-of-Freedom Torsional System with Piecewise-Type Nonlinearities

Effect of Various Excitation Conditions on Vibrational Energy in a Multi-Degree-of-Freedom Torsional System with Piecewise-Type Nonlinearities

Influence of nonlinear spring behavior of friction on dynamic characteristics of a rolling guideway

Numerical Continuation of Periodic Orbits for Harmonically Forced Nonlinear Systems

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