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.

Multiple Limit Cycles Shimmy of the Dual-Front Axle Steering Heavy Truck Based on Bisectional Road

2019 ◽  
Vol 14 (5) ◽  
Author(s):  
Daogao Wei ◽  
Yingjie Zhu ◽  
Tong Jiang ◽  
Andong Yin ◽  
Wenhao Zhai
Keyword(s):  
Dynamic Model ◽  
Limit Cycle ◽  
Dry Friction ◽  
Bifurcation Theory ◽  
Steering System ◽  
Front Axle ◽  
Adhesion Coefficient ◽  
The Road ◽  
Heavy Truck ◽  
Multiple Limit Cycle

The shimmy problem causes considerable harm to vehicles and is difficult to solve, especially multiple limit cycle shimmy. Moreover, the dynamic behavior of the multiple limit cycle shimmy of vehicles based on a bisectional road is more complex. Shimmy is practically observed in trucks of cooperative factories during utilization. Thus, we take a heavy truck of a cooperative factory as the prototype and establish a dynamic model of the vehicle-road coupling shimmy system, considering the road adhesion coefficient and dry friction between the suspension and steering system. Based on the dynamic model, the Hopf bifurcation theory is used to qualitatively analyze the existence of the limit cycle for the vehicle shimmy system, and the multiple limit cycle shimmy phenomenon is successfully reproduced using a numerical method. Moreover, the effect of the road adhesion coefficient on the multiple limit cycle shimmy characteristic is studied. Results show that the speed interval and amplitude of the multiple limit cycle shimmy decrease with the road adhesion coefficient; when the coefficient is reduced to a certain extent, the multiple limit cycle shimmy phenomenon is not observed. In addition, the adhesion coefficient of the second axle has a stronger effect on the shimmy characteristic than that of the first axle.

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.

Analysis of the non-periodic oscillations of a self-excited friction-damped system with closely-spaced modes

2021 ◽  
Author(s):  
Lukas Woiwode ◽  
Alexander F. Vakakis ◽  
Malte Krack
Keyword(s):  
Hopf Bifurcation ◽  
Limit Cycle ◽  
Dry Friction ◽  
The Self ◽  
Perturbation Approach ◽  
Friction Damping ◽  
Periodic Oscillations ◽  
Analytical Results ◽  
Fold Bifurcation ◽  
Phase Motion

Abstract It is widely known that dry friction damping can bound the self-excited vibrations induced by negative damping. The vibrations typically take the form of (periodic) limit cycle oscillations. However, when the intensity of the self-excitation reaches a condition of maximum friction damping, the limit cycle loses stability via a fold bifurcation. The behavior may become even more complicated in the presence of any internal resonance conditions. In this work, we consider a two-degree-of-freedom system with an elastic dry friction element (Jenkins element) having closely spaced natural frequencies. The symmetric in-phase motion is subjected to self-excitation by negative (viscous) damping, while the symmetric out-of-phase motion is positively damped. In a previous work, we showed that the limit cycle loses stability via a secondary Hopf bifurcation, giving rise to quasi-periodic oscillations. A further increase of the self-excitation intensity may lead to chaos and finally divergence, long before reaching the fold bifurcation point of the limit cycle. In this work, we use the method of Complexification-Averaging to obtain the slow flow in the neighborhood of the limit cycle. This way, we show that chaos is reached via a cascade of period doubling bifurcations on invariant tori. Using perturbation calculus, we establish analytical conditions for the emergence of the secondary Hopf bifurcation and approximate analytically its location. In particular, we show that non-periodic oscillations are the typical case for prominent nonlinearity, mild coupling (controlling the proximity of the modes) and sufficiently light damping. The range of validity of the analytical results presented herein is thoroughly assessed numerically. To the authors' knowledge, this is the first work that shows how the challenging Jenkins element can be treated formally within a consistent perturbation approach in order to derive closed-form analytical results for limit cycles and their bifurcations.

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.

Shimmy Characteristic Analysis for Steering System of Heavy Mining Dump Trucks

2020 ◽  
Vol 142 (2) ◽  
Author(s):  
Lulu Gao ◽  
Fei Ma ◽  
Chun Jin ◽  
Yanjun Huang ◽  
Zhipeng Feng
Keyword(s):  
Hopf Bifurcation ◽  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Steering System ◽  
Parameter Range ◽  
Characteristic Analysis ◽  
Excited Vibration ◽  
Tire Wear ◽  
Dump Trucks ◽  
Pneumatic Suspension

Abstract Tire wear cost accounts for a large proportion of the total cost of heavy mining dump trucks (HMDTs), and the shimmy of the steering system aggravates the tire wear severely. This study proposes a model-based approach to avoid the shimmy of the steering system for such trucks without replacement or destruction of steering structure. First, a five degrees-of-freedom (DOF) shimmy dynamic model of the steering system is established considering the tire lateral dynamics and the nonlinearity of the hydro-pneumatic suspension (HPS). Second, the unstable parameter range of the dynamic model is obtained based on the Lyapunov’s first approximation theorem and Hopf bifurcation theory. The stability analysis results show that the steering system of heavy mining dump trucks is a self-excited vibration system because of the Hopf bifurcation in the unstable parameter range, and this unstable parameter range is greatly affected by the load and the initial pneumatic volume of hydro-pneumatic suspension. In addition, the accuracy of the dynamic is verified by a field test. Therefore, how the load and initial pneumatic volume affect the shimming is analyzed numerically. In other words, how to match the load and initial pneumatic volume is uncovered to avoid the shimmy. For instance, it shows that the shimmy at full load can be avoided at the speed of 30 km/h by charging the initial pneumatic volume of hydro-pneumatic suspension to 14.5 l.

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.

scholarly journals Self-excited vibration of whole vehicle with multiple limit cycles induced by shimmy of front wheels

2019 ◽  
Vol 39 (4) ◽  
pp. 1052-1064 ◽  
Author(s):  
Daogao Wei ◽  
Wenhao Zhai ◽  
Yingjie Zhu ◽  
GenSheng Jiang ◽  
Andong Yin ◽  
...  
Keyword(s):  
Limit Cycles ◽  
Lateral Force ◽  
Steering System ◽  
Front Wheel ◽  
The Self ◽  
Vehicle Speed ◽  
Bifurcation Theorem ◽  
Excited Vibration ◽  
Speed Range ◽  
Existence And Stability

Front wheel shimmy may induce the self-excited vibration of whole vehicle with multiple limit cycles. This kind of shimmy is difficult to control and can do great harm to the vehicle. In order to obtain the mechanism of this phenomenon, a 7-DOF dynamic model of whole vehicle self-excited vibration induced by the shimmy of front wheels which take the nonlinear factor of tire lateral force and the dry friction force in suspension and steering system into consideration was established. By using Hopf bifurcation theorem and central manifold theorem, the existence and stability of limit cycles are qualitatively determined. By means of numerical analysis, the self-excited vibration with multiple limit cycles is found. The results show that in the speed range of 50–185 km/h, front wheels shimmy induced the self-excited vibration of whole vehicle and the amplitude of system’s vibration decreases with the increase of vehicle speed; in the speed range of 50–83 km/h and 149–185 km/h, the self-excited vibration with multiple limit cycles occurs; in the speed range of 83–149 km/h, the self-excited vibration with single limit cycle occurs.

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