Bifurcation analysis of vehicle shimmy system exposed to road roughness excitation

2021 ◽  
pp. 107754632098779
Author(s):  
Heng Wei ◽  
Jian-Wei Lu ◽  
Sheng-Yong Ye ◽  
Hang-Yu Lu
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Averaging Method ◽  
Lagrange Equation ◽  
Response Characteristic ◽  
Lateral Force ◽  
Front Wheel ◽  
The Road ◽  
Road Roughness ◽  
The Stability

The vertical load of the tire has a significant influence on the lateral force, so the influence of the dynamic load on vehicle shimmy should be taken into account. Based on the dynamic model of a quarter vehicle, a three-degrees-of-freedom dynamic model of the shimmy system with consideration of the road roughness excitation is established by applying the second Lagrange equation. The response characteristic of the system is investigated by the numerical simulations. Moreover, the complexification-averaging method is used to obtain the analytical expression of the shimmy angle of the front wheel, and then, the stability of periodic solutions of the system is evaluated based on the bifurcation theory. Finally, the saddle-node bifurcation and Hopf bifurcation of the shimmy system are studied. The influence of the system parameters on the bifurcation characteristic of the system is also investigated, and the results obtained by using the complexification-averaging method are compared with the numerical examples.

Modal analysis and dynamic shimmy behavior of vehicle–road system

2021 ◽  
pp. 107754632110482
Author(s):  
Heng Wei ◽  
Jianwei Lu ◽  
Lei Shi ◽  
Hangyu Lu ◽  
Shengyong Ye
Keyword(s):  
Modal Analysis ◽  
Degrees Of Freedom ◽  
Front Wheel ◽  
System Stability ◽  
Largest Lyapunov Exponent ◽  
The Road ◽  
Road Roughness ◽  
Measurement Results ◽  
Wheel Track ◽  
Road System

To analyze the influence of the road roughness excitation on vehicle shimmy, a 12 degrees-of-freedom dynamic model of vehicle–road system is developed. The Hopf bifurcation theory is used to study the system stability. On this basis, the natural frequency and modal properties of the vehicle system are elaborated. It can be found that the roll mode plays a crucial role in the vehicle stability. Then, the dynamic shimmy behavior exposed to the sinusoidal and random road roughness excitations is investigated with the help of the modal analysis and the largest Lyapunov exponent. Furthermore, the numerical results are verified through the measurement results, and the influence of the front wheel track on vehicle shimmy is also examined. The results show that the decrease of the front wheel track is an effective way to attenuate vehicle shimmy for different road roughness excitations.

scholarly journals Effect of Road Profile on Suspension System of Heavy Truck

2019 ◽  
Vol 12 (2) ◽  
pp. 71-75
Author(s):  
Salem F. Salman
Keyword(s):  
Steering System ◽  
Suspension System ◽  
The Road ◽  
Road Profile ◽  
Road Roughness ◽  
Road Type ◽  
Heavy Truck ◽  
Main Factors ◽  
On The Road ◽  
The Stability

All vehicles are affected by the type of the road they are moving on it.  Therefore the stability depends mainly on the amount of vibrations and steering system, which in turn depend on two main factors: the first is on the road type, which specifies the amount of vibrations arising from the movement of the wheels above it, and the second on is the type of the used suspension system, and how the parts connect with each other. As well as the damping factors, the tires type, and the used sprungs. In the current study, we will examine the effect of the road roughness on the performance coefficients (speed, displacement, and acceleration) of the joint points by using a BOGE device.

scholarly journals Adhesion state estimation based on improved tire brush model

2018 ◽  
Vol 10 (1) ◽  
pp. 168781401774770
Author(s):  
Bei Shaoyi ◽  
Li Bo ◽  
Zhu Yanyan
Keyword(s):  
Lateral Force ◽  
Longitudinal Force ◽  
Lateral Acceleration ◽  
Stable Range ◽  
The Road ◽  
Nonlinear Compensation ◽  
The Stability ◽  
Standard Calculation ◽  
Double Nonlinear ◽  
Brush Model

On the basis of calculating the longitudinal force using the original brush model, we simplify the tire structure and consider the lateral force generated by the lateral elasticity of the tread. At the same time, the boundary conditions between the adhesion area and the slip zone in the contact area of the tire are fully discussed. By establishing an improved tire brush model, the error caused by neglecting the sideslip characteristics is avoided, and the adaptability of the tire model is improved. A double nonlinear compensation method based on the lateral acceleration deviation and the yaw rate deviation is employed to estimate the road adhesion coefficient, which is closer to the actual attachment situation than the standard calculation. Based on this model, the vehicle stability coefficient k is defined and calculated to describe the stability of the vehicle during the driving process. The modeling results show that the value of k is always in the stable range of [0, 1]. Therefore, the vehicle that utilizes the improved tire brush model is always within the controllable range in the driving process, which verifies the effectiveness of the model.

Steering and Stability of Single-track Vehicles

1951 ◽  
Vol 5 (1) ◽  
pp. 191-213 ◽  
Author(s):  
R. A. Wilson-Jones
Keyword(s):  
Lateral Force ◽  
Front Wheel ◽  
Slip Angle ◽  
Single Track ◽  
Motor Cycle ◽  
Low Mass ◽  
Low Speeds ◽  
The Stability ◽  
Straight Ahead

The author briefly states the elementary principles of equilibrium and claims that the stability of the conventional bicycle or motor cycle is automatic except at very low speeds. This is because the steering automatically turns in the direction in which the machine is leaning and returns to the straight ahead position when the machine is restored to the vertical. The achievement of these effects is largely due to the “trail” of the front wheel. The causes of “steering roll” and “steering wobble” and the purpose of the inclination of the steering head, are examined, as are the effects of high and low mass centres and of the rider leaning with and against the machine. It is shown how the elementary principles of steering apply to various types of vehicle, including single-track vehicles in which the necessary lateral force comes mainly from camber thrust rather than slip angle. The results are given of experiments on varying amounts of “trail”, and a method of measuring slip angles is described which is applicable to motor cycles. Finally, a method of indicating the direction of the torque applied to the handlebars when entering, holding, and leaving a bend is described.

Research on the Cornering Characteristics of Three-Axle Vehicle

2014 ◽  
Vol 945-949 ◽  
pp. 567-570
Author(s):  
Bo Xu ◽  
Sheng Min Cui ◽  
Xiang Yu Wu
Keyword(s):  
Degrees Of Freedom ◽  
Control Method ◽  
Front Wheel ◽  
Heavy Vehicle ◽  
Sideslip Angle ◽  
Motion Equations ◽  
Dynamic Steering ◽  
Angular Scale ◽  
Control Target ◽  
The Stability

A multi-axle dynamic steering technology was proposed to solve the steering stability and maneuverability problem of heavy vehicle. Two degrees of freedom linear steering-model and motion-equations of three-axle vehicle was established. Taking the zero sideslip angle as the control target and the proportional rear-front wheel angle as control method, we got the angular scale-factor equation and related matrix of the state space and transfer function. The MATLAB software was used to simulate the different steering modes stability steady-state and transient response. The results show that by using proportional control method the sideslip angle can be stabilized near zero and by using multi-axle dynamic steering technology the stability and maneuverability of the vehicle when steering can be improved effectively.

scholarly journals Analysis of Vehicle Steering and Driving Bifurcation Characteristics

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Xianbin Wang ◽  
Shuming Shi
Keyword(s):  
Degrees Of Freedom ◽  
Autonomous Vehicle ◽  
Lateral Force ◽  
Front Wheel ◽  
State Variables ◽  
Vehicle Model ◽  
Obvious Effect ◽  
Driving Mode ◽  
Lyapunov Index ◽  
Driving Torque

The typical method of vehicle steering bifurcation analysis is based on the nonlinear autonomous vehicle model deriving from the classic two degrees of freedom (2DOF) linear vehicle model. This method usually neglects the driving effect on steering bifurcation characteristics. However, in the steering and driving combined conditions, the tyre under different driving conditions can provide different lateral force. The steering bifurcation mechanism without the driving effect is not able to fully reveal the vehicle steering and driving bifurcation characteristics. Aiming at the aforementioned problem, this paper analyzed the vehicle steering and driving bifurcation characteristics with the consideration of driving effect. Based on the 5DOF vehicle system dynamics model with the consideration of driving effect, the 7DOF autonomous system model was established. The vehicle steering and driving bifurcation dynamic characteristics were analyzed with different driving mode and driving torque. Taking the front-wheel-drive system as an example, the dynamic evolution process of steering and driving bifurcation was analyzed by phase space, system state variables, power spectral density, and Lyapunov index. The numerical recognition results of chaos were also provided. The research results show that the driving mode and driving torque have the obvious effect on steering and driving bifurcation characteristics.

Dynamic Model of the Road Feel Generation System in Advanced Driving Simulators

2010 ◽  
Vol 44-47 ◽  
pp. 2448-2452 ◽  
Author(s):  
Li Wei Zhu ◽  
Zhi Yong Zhang ◽  
Zuo Jun Bao
Keyword(s):  
Dynamic Model ◽  
Control Algorithm ◽  
Lagrange Equation ◽  
Effective Control ◽  
Generation System ◽  
Driving Simulators ◽  
The Road ◽  
Model Based ◽  
Simulation And Experiment

Road feel Generation System (RFGS) is the key subsystem of Advanced Driving Simulators (ADS), and its performance is key index of ADS's fidelity and validity. In this paper, the composition and functions of RFGS is firstly introduced, and then the dynamic model of RFGS based on the Lagrange Equation is provided, and subsequently the simulation and experiment is executed to validating the proposed dynamic model. Based on this model, the effective control algorithm can be developed and the performance of RFGS can be improved, and then the fidelity and validity of ADS can be enhanced.

scholarly journals Robust Control Design of Active Front-Wheel Steering on Low-Adhesion Road Surfaces

2021 ◽  
Vol 12 (3) ◽  
pp. 153
Author(s):  
Chuanwei Zhang ◽  
Bo Chang ◽  
Jianlong Wang ◽  
Shuaitian Li ◽  
Rongbo Zhang ◽  
...  
Keyword(s):  
Robust Control ◽  
Control Strategy ◽  
Degrees Of Freedom ◽  
Reference Model ◽  
Front Wheel ◽  
Good Path ◽  
Road Surfaces ◽  
Robust Control Design ◽  
The Stability ◽  
Three Degrees Of Freedom

In order to improve the stability of vehicle steering on low-adhesion road surfaces, this paper designed a hybrid robust control strategy, H2/H∞, for active front-wheel steering (AFS) based on robust control theory. Firstly, we analyzed the influence of the sidewall stiffness and road adhesion coefficient of the tires on vehicle stability, through which we can study the wheel deflection characteristics of low-adhesion roads. Secondly, the reference yaw velocity of the vehicle was calculated using the three-degrees-of-freedom model as the reference model, through which, taking the norm H∞ as the objective function and the norm H2 as the limit to control the output, the hybrid robust control strategy H2/H∞ of the AFS system on a low-adhesion road surface was developed. Finally, the simulation experiment was carried out by the Simulink/CarSim co-simulation platform and a hardware-in-the-loop (HIL) experiment. In this paper, the results show that the AFS control strategy can improve the vehicle handling stability on low-adhesion road surfaces, and the controller has good path tracking performance and robustness.

Assessing the influence of the road-tire friction coefficient on the yaw and roll stability of articulated vehicles

2018 ◽  
Vol 233 (12) ◽  
pp. 2987-2999 ◽  
Author(s):  
André de Souza Mendes ◽  
Agenor de Toledo Fleury ◽  
Marko Ackermann ◽  
Fabrizio Leonardi ◽  
Roberto Bortolussi
Keyword(s):  
Friction Coefficient ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Lateral Force ◽  
Longitudinal Force ◽  
Convergence Region ◽  
The Road ◽  
Articulated Vehicles ◽  
Tire Friction

This article addresses the yaw stability of articulated vehicles by assessing the influence of the road-tire friction coefficient on the convergence region of a particular equilibrium condition. In addition, the boundaries of this region are compared to the boundaries of the non-jackknife and non-rollover regions to distinguish the instability phenomenon, jackknife or roll-over, responsible for this delimitation. The vehicle configuration considered in this analysis is composed by one tractor unit and one towed unit connected through an articulation point, for instance, a tractor-semitrailer combination. A nonlinear articulated bicycle model with four degrees of freedom is used together with a nonlinear lateral force tire model. To estimate the convergence region, the phase trajectory method is used. The equations of motion of the mathematical model are numerically integrated for different initial conditions in the phase plane, and the state orbits are monitored in order to verify the convergence point and the occurrence of instability events. In all cases, the longitudinal force on each tire, such as traction and braking, is not considered. The results show the existence of convergence regions delimited only by jackknife events, for low values of the friction coefficient, and only by rollover events, for high values of the friction coefficient. Moreover, the transition between these two conditions as the friction coefficient is changed is graphically presented. The main contributions of this article are the identification of the abrupt reduction of the convergence region as the value of the friction coefficient increases and the distinction of the instability events, jackknife or rollover, that define the boundaries of the convergence region.

Study on the LQG Control of Acceleration/Braking System Based on Wheelbase Preview

2011 ◽  
Vol 105-107 ◽  
pp. 566-570
Author(s):  
Gong Yu Pan ◽  
Yu Huang
Keyword(s):  
Optimal Control ◽  
Dynamic Model ◽  
Ride Comfort ◽  
Angular Acceleration ◽  
Front Wheel ◽  
Preview Control ◽  
The Road ◽  
Braking System ◽  
Air Suspension ◽  
Road Surface Roughness

A dynamic model of semi-vehicle under acceleration/braking condition based on air suspension was established. By applying wheelbase preview control to forecast the road surface roughness at the front wheel, the optimal controller based on wheelbase preview control theory was designed. Then the dynamic model was simulating with the MATLAB. The results show that both optimal control and optimal control with wheelbase preview can effectively reduce vibration of acceleration/braking system, which make an improvement in the vehicle’s ride comfort and handing stability. Finally, a controller based on wheelbase preview of air active suspension acceleration/braking system was designed, and then simulation was analyzed with white noise input. Centric acceleration, pitch angular acceleration and rear tire dynamic load of the back section were reduced significantly proving pre-wheelbase control can further improve the performance of the vehicle potentially, especially having an effect on decreasing the vibration of rear suppression.

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