Impact Severity in Drive Line Systems With Backlash

Numerical simulations are used to study the transient behavior of a four degree-of-freedom, rotational piecewise linear system. This study focusses on the impact between bodies in a system with backlash as a result of a sudden step input and the associated transient response. The subsequent Single Sided Impacts and Double Sided Impacts are studied as a function of the amplitude of the step input and the size of the backlash. Transitions have been observed between Double Sided Impact regions and Single Sided Impact regions which agree with earlier findings. However, in this paper a more complete overview of the boundaries is given. The severity of the impacts is quantified with the peak-to-peak acceleration of the impacting bodies. Increasing the size of the step input increases the severity of the impacts. However, increasing backlash size leads to an extremum in impact severity. This is a possible explanation for seeming contradictions in literature.

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Severity of Tip-Out Induced Impacts in Drive Line Systems With Backlash

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4000830 ◽

2010 ◽

Vol 5 (2) ◽

Cited By ~ 1

Author(s):

S. W. Boere ◽

A. Shukla ◽

R. H. B. Fey ◽

H. Nijmeijer

Keyword(s):

Linear System ◽

Numerical Simulations ◽

Transient Response ◽

Piecewise Linear ◽

Transient Behavior ◽

Degree Of Freedom ◽

Peak Acceleration ◽

Step Input ◽

Piecewise Linear System ◽

The Impact

Numerical simulations are used to study the transient behavior of a four degree-of-freedom, rotational piecewise linear system. This study focuses on the impact between bodies in a system with backlash as a result of a sudden step input and the associated transient response. The subsequent single sided impacts and double sided impacts are studied as a function of the amplitude of the step input and the size of the backlash. Transitions have been observed between double sided impact regions and single sided impact regions, which agree with earlier findings. However, in this paper a more complete overview of the boundaries is given. The severity of the impacts is quantified with the peak-to-peak acceleration of the impacting bodies. The increase in the size of step input increases the severity of the impacts. However, the increase in backlash size leads to an extremum in impact severity. This is a possible explanation for seeming contradictions in literature.

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A GLOBAL PERIOD-1 MOTION OF A PERIODICALLY EXCITED, PIECEWISE-LINEAR SYSTEM

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127405013071 ◽

2005 ◽

Vol 15 (06) ◽

pp. 1945-1957 ◽

Cited By ~ 19

Author(s):

SANTHOSH MENON ◽

ALBERT C. J. LUO

Keyword(s):

Linear System ◽

Numerical Simulations ◽

Piecewise Linear ◽

Dynamical Behavior ◽

Analytical Prediction ◽

Algebraic Equations ◽

Piecewise Linear System ◽

Nonlinear Algebraic Equations ◽

The Stability ◽

Nonsmooth Dynamical Systems

The period-1 motion of a piecewise-linear system under a periodic excitation is predicted analytically through the Poincaré mapping and the corresponding mapping sections formed by the switch planes pertaining to the two constraints. The mapping relationship generates a set of nonlinear algebraic equations from which the period-1 motion is determined analytically. The stability and bifurcation of the period-1 motion are determined, and numerical simulations are carried out for confirmation of the analytical prediction of period-1 motion. An unsymmetrical stable period-1 motion is observed. This investigation helps us understand the dynamical behavior of period-1 motion in the piecewise-linear system and more efficiently obtain other periodic motions and chaos through numerical simulations. The similar methodology presented in this paper can be used for other nonsmooth dynamical systems.

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Nonlinear Modal Analysis of a Cracked Beam

Volume 1A: 16th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc97/vib-3950 ◽

1997 ◽

Author(s):

M. Chati ◽

R. H. Rand ◽

S. Mukherjee

Keyword(s):

Linear System ◽

Modal Analysis ◽

Natural Frequencies ◽

Piecewise Linear ◽

Normal Modes ◽

Nonlinear Normal Modes ◽

Degree Of Freedom ◽

Mode Shapes ◽

Cracked Beam ◽

Piecewise Linear System

Abstract This paper addresses the problem of vibrations of a cracked beam. In general, the motion of such a beam can be very complex. This phenomenon can be attributed to the presence of the nonlinearity due to the opening and closing of cracks. The focus of this paper is the modal analysis of a cantilever beam with a transverse edge crack. The nonlinearity mentioned above has been modelled as a piecewise-linear system. In an attempt to define effective natural frequencies for this piecewise-linear system, the idea of a “bilinear frequency” is utilized. The bilinear frequency is obtained by computing the associated frequencies of each of the linear pieces of the piecewise-linear system. The finite element method is used to obtain the natural frequencies in each linear region. In order to better understand the essential nonlinear dynamics of the cracked beam, a piecewise-linear two degree of freedom model is studied. Perturbation methods are used to obtain the nonlinear normal modes of vibration and the associated period of the motion. Results of this piecewise-linear model problem are shown to justify the definition of the bilinear frequency as the effective natural frequency. It is therefore expected that calculating piecewise mode shapes and bilinear frequencies is useful for understanding the dynamics of the infinite degree of freedom cracked beam.

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