Approximate analytical solution of the self-excited vibration of piecewise-smooth systems induced by dry friction —The vibration mechanism of the Chinese cultural relic Dragon Washbasin

1998 ◽  
Vol 14 (1) ◽  
pp. 78-84 ◽  
Author(s):  
Liu Xijun ◽  
Wang Dajun ◽  
Chen Yushu
Keyword(s):  
Analytical Solution ◽  
Dry Friction ◽  
Approximate Analytical Solution ◽  
Piecewise Smooth ◽  
The Self ◽  
Piecewise Smooth Systems ◽  
Excited Vibration ◽  
Vibration Mechanism ◽  
Cultural Relic

The Investigation of the Influence of Structure Parameters on the Friction-Induced Self-Excited Vibration

2011 ◽  
Vol 66-68 ◽  
pp. 933-936
Author(s):  
Xian Jie Meng
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Method ◽  
Calculation Result ◽  
Dry Friction ◽  
Vibration Amplitude ◽  
The Self ◽  
Structure Parameters ◽  
Dynamics Model ◽  
Excited Vibration ◽  
Nonlinear Dynamics Model

A one degree of freedom nonlinear dynamics model of self-excited vibration induced by dry-friction was built firstly, the numerical method was taken to study the impacts of structure parameters on self-excited vibration. The calculation result shows that the variation of stiffness can change the vibration amplitude and frequency of the self-excited vibration, but can not eliminate it, Along with the increase of system damping the self-excite vibration has the weakened trend and there a ritical damping, when damping is greater than it the self-excite vibration will be disappeared.

scholarly journals Suppression of Self-Excited Vibrations in Rotating Machinery Utilizing Leaf Springs

2019 ◽  
pp. 599-608
Author(s):  
Chang Wang ◽  
Jun Liu ◽  
Zhiwei Luo
Keyword(s):  
Dry Friction ◽  
Critical Speed ◽  
Rotating Machinery ◽  
The Self ◽  
Internal Damping ◽  
Structural Damping ◽  
Leaf Springs ◽  
Excited Vibration ◽  
Hysteretic Damping ◽  
Theoretical Analyses

When rotating machinery is operated above the major critical speed, self-excited vibrations appear due to internal friction of the shaft. Internal frictions are classified into hysteretic damping due to the friction in the shaft material and structural damping due to the dry friction between the shaft and the mounted elements. In this paper, a method to suppress the self-excited vibration using leaf springs are proposed. The structural damping is considered as the internal damping. The characteristics of a rotor with leaf springs are investigated systematically by using simulative and theoretical analyses. The validity of the proposed method is also proved by experiments.

scholarly journals Hopf Bifurcation Characteristics of Dual-Front Axle Self-Excited Shimmy System for Heavy Truck considering Dry Friction

2015 ◽  
Vol 2015 ◽  
pp. 1-20 ◽  
Author(s):  
Daogao Wei ◽  
Ke Xu ◽  
Yibin Jiang ◽  
Changhe Chen ◽  
Wenjing Zhao ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Dry Friction ◽  
Steering System ◽  
Front Axle ◽  
Friction Torque ◽  
The Self ◽  
Lagrange’S Equation ◽  
Excited Vibration ◽  
Heavy Truck ◽  
Manifold Theory

Multiaxle steering is widely used in commercial vehicles. However, the mechanism of the self-excited shimmy produced by the multiaxle steering system is not clear until now. This study takes a dual-front axle heavy truck as sample vehicle and considers the influences of mid-shift transmission and dry friction to develop a 9 DOF dynamics model based on Lagrange’s equation. Based on the Hopf bifurcation theorem and center manifold theory, the study shows that dual-front axle shimmy is a self-excited vibration produced from Hopf bifurcation. The numerical method is adopted to determine how the size of dry friction torque influences the Hopf bifurcation characteristics of the system and to analyze the speed range of limit cycles and numerical characteristics of the shimmy system. The consistency of results of the qualitative and numerical methods shows that qualitative methods can predict the bifurcation characteristics of shimmy systems. The influences of the main system parameters on the shimmy system are also discussed. Improving the steering transition rod stiffness and dry friction torque and selecting a smaller pneumatic trail and caster angle can reduce the self-excited shimmy, reduce tire wear, and improve the driving stability of vehicles.

The Investigation of the Influence of Dynamics Parameters on the Friction-Induced Self-Excited Vibration

2011 ◽  
Vol 295-297 ◽  
pp. 2223-2226
Author(s):  
Xian Jie Meng
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Method ◽  
Calculation Result ◽  
Dry Friction ◽  
Initial Velocity ◽  
Normal Pressure ◽  
The Self ◽  
Dynamics Model ◽  
Excited Vibration ◽  
Nonlinear Dynamics Model

A one degree of freedom nonlinear dynamics model of self-excited vibration induced by dry-friction is built firstly, the numerical method is taken to study the impacts of dynamics parameters on self-excited vibration. The calculation result shows that Along with the variation of system dynamics parameters such as initial velocity or normal pressure the self-excite vibration has the weakened trend or the enhanced trend, so the self-excite vibration could be controled through the control of dynamics parameters.

The Analytical Solution and The Existence Condition of Dry Friction Backward Whirl in Rotor-to-Stator Contact Systems

2006 ◽  
Vol 129 (2) ◽  
pp. 260-264 ◽  
Author(s):  
Jun Jiang
Keyword(s):  
Analytical Solution ◽  
Contact Surface ◽  
Dry Friction ◽  
Existence Condition ◽  
Good Correspondence ◽  
Continuous Contact ◽  
Vibration State ◽  
Analytical Results ◽  
Excited Vibration ◽  
Backward Whirl

Dry friction backward whirl is a self-excited vibration state in rotor-to-stator contact systems, by which the rotor is in continuous contact with the stator, slipping continuously on the contact surface and whirling backward at a supersynchronous frequency. To correctly cope the response of dry friction backward whirl, the effect of dry friction must be taken into account in rotor/stator models. From the knowledge on the characteristics of dry friction backward whirl, the whirl frequency, the existence condition and the solution of this response are derived analytically in this paper. The analytical results are verified by simulations and shown in good correspondence to the experimental observations.

scholarly journals Forced-self-excited System of Iced Transmission Lines under Planar Harmonic Excitations

2021 ◽  
Author(s):  
Xiaohui Liu ◽  
Shuguang Yang ◽  
Guangyun Min ◽  
Ceshi Sun ◽  
Haobo Liang ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Transmission Lines ◽  
Forced Vibration ◽  
Approximate Analytical Solution ◽  
Excitation Amplitude ◽  
Principal Resonance ◽  
Periodic Response ◽  
Excited System ◽  
Excited Vibration ◽  
Harmonic Resonance

Abstract This paper is concerned with the analysis of the self-excited vibrations and forced vibrations of the iced transmission lines. By introducing the external excitation load, the effect of dynamic wind on the nonlinear vibration equations of motion is reflected by vertical aerodynamic force. The approximate analytical solution of the non-resonance, and the amplitude frequency response relation of the principal resonance of the forced self-excited system are obtained by using the multiple scale method. With the increase in excitation amplitude, the nonlinearity of the system is enhanced, and the forced-self-excited system experiences three vibration stages (self-excited vibration, the superposition form of self-excited vibration and forced vibration, forced vibration controlled by nonlinear damping). Among them, the accuracy of the approximate analytical solution decreases with the increase of the nonlinear strength. And the excitation amplitude is greater than the critical value, the quenching phenomenon appear in the forced-self-excited system, and the discriminant formula is derived in this paper. In addition, the frequency of excitation term determines the vibration form of the system. The principal resonance, super-harmonic resonance and sub-harmonic resonance of the forced-self-excited system are analyzed by using different excitation frequencies. Compared with the principal resonance and the harmonic resonance, the meaningful transition from periodic response to quasi periodic response is easy to appear with the condition of the 1/3-order sub-harmonic and the 3-order super-harmonic. The conclusions would be helpful to the practical engineering of the iced transmission lines. More important, as a combination of Duffing equation and Rayleigh equation, the forced-self-excited system also has high theoretical research value.

scholarly journals Nonsmooth Behavior of Sliding Bifurcations in a General Piecewise Smooth Rotor/Stator Rubbing System

2021 ◽  
Vol 31 (02) ◽  
pp. 2150085
Author(s):  
Shunzeng Wang ◽  
Ling Hong ◽  
Jun Jiang
Keyword(s):  
Dry Friction ◽  
Vector Fields ◽  
Initial Conditions ◽  
Piecewise Smooth ◽  
The Self ◽  
Stick Slip ◽  
System Parameters ◽  
Contact Points ◽  
Topological Features ◽  
Contact Surfaces

Sliding bifurcations of different types are defined to characterize the topological features of trajectories around the switching manifolds of nonsmooth dynamical systems. In this paper, the stick-slip transitions, which are related to the dynamical scenarios of sliding bifurcations, of the self-excited dry friction backward whirls of a general rotor/stator rubbing system, are investigated. The four-degree-of-freedom piecewise smooth rotor/stator rubbing model is said to be general because it takes into account main factors in the rotor/stator rubbing systems, including both the dynamics of the rotor and the stator as well as the dry friction and the flexibility on the contact surfaces. The switching manifold that separates two discontinuous vector fields is defined as the curved hypersurface in a nine-dimensional extended state space where the relative velocity at the contact points equals zero. After deriving the formulae defining the sliding regions and their boundaries for the piecewise smooth system, two extreme cases with rigid and soft contact surfaces are theoretically analyzed and confirmed to correspond respectively to a continuous pure rolling with full sliding region and a continuous crossing without sliding region on the switching manifold. Furthermore, three types of sliding bifurcations, namely, crossing-sliding, grazing-sliding and switching-sliding, are observed in the dry friction backward whirls of the present model in a semi-analytical way. Moreover, hybrids of the three kinds of the sliding solutions in one period of oscillation are also identified with the variation of system parameters and initial conditions. The main scenarios of the switching transition of sliding bifurcations in the self-excited dry friction backward whirl of the general rotor/stator rubbing system with the variation of system parameters are also summarized.

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