Paper 5: Vehicle Behaviour in Combined Cornering and Braking

1968 ◽  
Vol 183 (8) ◽  
pp. 19-34 ◽  
Author(s):  
A. J. Harris ◽  
B. S. Riley
Keyword(s):  
Steady State ◽  
Load Transfer ◽  
Equations Of Motion ◽  
Rear Wheel ◽  
Front Wheel ◽  
Slip Angle ◽  
Vehicle Model ◽  
Force Coefficient ◽  
Wheeled Vehicle ◽  
Non Linear

This paper considers first the steady-state motions of a simple two-wheeled vehicle model having non-linear sideway force relationships with respect to tyre slip angle. It is shown that any steady-state conditions may be represented and their solutions found by simple graphical means, using only the non-linear curves. The curves can be modified to take into account the influence of vehicle parameters such as compliance, roll steer, wheel camber, and load transfer. Stability boundaries are discussed and criteria are presented showing that stability of the motion depends only on the slopes of the curves and the speed of the manoeuvre at the cornering acceleration being considered. A more involved four-wheeled vehicle model is then considered when subjected to braking while cornering on a fixed radius path of 45·8 m on a wet Bridport macadam surface. Actual sideway force–slip angle curves for combined braking and cornering, as presented by Holmes and Stone (see reference (6))†, are used with the equations of motion derived for the quasi-steady state conditions of decelerating while cornering. The effects of front wheel steered angle and body slip angle on the forces necessary for the manoeuvre are also considered. An envelope of maximum cornering acceleration at various braking decelerations is presented. This shows that for those particular conditions up to about 70 per cent of maximum deceleration may be obtained before there is more than about 10 per cent loss in maximum cornering ability. Outside the envelope the vehicle fails to maintain the path. At the lower deceleration the car spins, and at higher values it continues tangentially to its original path without spinning. It is also shown that the total sideway force–slip angle curve for a pair of front or rear wheels, when one or both wheels have a high braking force coefficient, can have a sharp peak, such that for small increase in slip angle there is a rapid fall in sideway force. It is suggested that this is why a rear wheel skid which occurs while braking and cornering is more difficult to correct than one which occurs when only cornering.

Enhanced braking and steering yaw motion controllers with a non-linear observer for improved vehicle stability

2008 ◽  
Vol 222 (3) ◽  
pp. 293-304 ◽  
Author(s):  
Jeonghoon Song
Keyword(s):  
Load Transfer ◽  
Rear Wheel ◽  
Front Wheel ◽  
Driver Model ◽  
Lateral Acceleration ◽  
Slip Angle ◽  
Vehicle Stability ◽  
Motion Controller ◽  
Non Linear ◽  
Linear Observer

This study proposes two enhanced yaw motion controllers that are modified versions of a braking yaw motion controller (BYMC) and a steering yaw motion controller (SYMC). A BYMC uses an inner rear-wheel braking pressure controller, while an SYMC uses a rear-wheel steering controller. However, neither device can entirely ensure the safety of a vehicle because of the load transfer from the rear to front wheels during braking. Therefore, an enhanced braking yaw motion controller (EBYMC) and an enhanced steering yaw motion controller (ESYMC) are developed, which contain additional outer front-wheel controllers. The performances of the EBYMC and ESYMC are evaluated for various road conditions and steering inputs. They reduce the slip angle and eliminate variation in the lateral acceleration, which increase the controllability, stability, and comfort of the vehicle. A non-linear observer and driver model also produce satisfactory results.

Investigation of the tyre characteristics under non-steady-state conditions on the basis of road tests

2016 ◽  
Vol 231 (1) ◽  
pp. 3-15 ◽  
Author(s):  
Hubert Sar ◽  
Andrzej Reński ◽  
Janusz Pokorski
Keyword(s):  
Steady State ◽  
Computer Simulations ◽  
Dynamic Characteristics ◽  
Slip Angle ◽  
Real Motion ◽  
Side Force ◽  
The Real ◽  
Different Types ◽  
Non Linear ◽  
The Difference

This paper presents a method of identifying the dynamic characteristics of tyres for non-steady-state conditions on the basis of road measurements on a vehicle. The side force acting on the tyre is presented as a function of not only the slip angle but also the slip angle derivative (i.e. the velocity of the change in the slip angle). Hence, the influence of the manoeuvre dynamics on the tyre characteristics and the difference between the characteristics obtained for steady-state conditions and the characteristics for non-steady-state conditions are shown. Also the results of computer simulations prepared for different types of tyre characteristics are presented in this paper. It is evident from the presented graphs that applying dynamic non-linear tyre characteristics for computer simulations instead of steady-state characteristics enables us to describe the real motion of a vehicle better.

Analysis of Vehicle Lateral Response During Regenerative Braking in a Turn

2016 ◽  
Author(s):  
C. S. Nanda Kumar ◽  
Shankar C. Subramanian
Keyword(s):  
Rear Wheel ◽  
Front Wheel ◽  
Lateral Acceleration ◽  
Regenerative Braking ◽  
Steering Wheel ◽  
Slip Angle ◽  
Lateral Response ◽  
Wheel Drive ◽  
Reference Track ◽  
The Impact

Regenerative braking is applied only at the driven wheels in electric and hybrid vehicles. The presence of brake force only at the driven wheels reduces the lateral traction limit of the corresponding tires. This impacts the vehicle lateral response, particularly while applying the regenerative brake in a turn. In this paper, a detailed study was made on the impact of regenerative brake on the vehicle lateral response in front wheel drive and rear wheel drive configurations on dry and wet asphalt road surfaces. Simulations were done considering a typical set of vehicle parameters with the IPG CarMaker® software for different drive conditions and braking configurations along the same reference track. The steering wheel angle, yaw rate, lateral acceleration, vehicle slip angle, and tire forces were obtained. Further, they were compared against the conventional all wheel friction brake configuration. The regenerative braking configuration that had the most impact on vehicle lateral response was analyzed and response variations were quantified.

Non-Linear Diffusion - Non-linear diffusion I. Diffusion and flow of mixtures of fluids

1963 ◽  
Vol 255 (1064) ◽  
pp. 607-633 ◽  
Keyword(s):  
Mechanical Properties ◽  
Steady State ◽  
Body Force ◽  
Equations Of Motion ◽  
Plane Waves ◽  
Viscous Fluids ◽  
Rigid Plate ◽  
Linear Diffusion ◽  
Diffusion Effects ◽  
Non Linear

A theory for the flow and non-linear diffusion effects in mixtures of fluids is formulated based upon hydrodynamical considerations. It is assumed that each point of the mixture is occupied simultaneously by all constituents in given portions. The motion of each constituent is governed by the usual equations of motion and continuity. The mechanical properties of each component are specified by means of constitutive equations for the stresses; diffusion effects are accounted for by means of a body force acting on each constituent which depends upon the composition and relative motion of the substances in the mixture. The theory is extended to deal with the diffusion of a mixture of fluids through a rigid solid. The theory is applied to a number of steady-state problems involving non-Newtonian fluids including the diffusion of a fluid through a rigid plate, the laminar flow of a mixture and the flow of a mixture between rotating cylinders. The propagation of plane waves through a homogeneous mixture of viscous fluids at rest is also examined.

Vehicle Braking Stability Analysis in Turn Condition

2014 ◽  
Vol 607 ◽  
pp. 604-607 ◽  
Author(s):  
Ling Zhao
Keyword(s):  
Stability Analysis ◽  
Dynamic Model ◽  
Load Transfer ◽  
Rear Wheel ◽  
Front Wheel ◽  
Vertical Load ◽  
Steering Angle ◽  
Braking Distance ◽  
Simulation Results

Considering the influence of wheel vertical load transfer and Steering angle, the paper establishes a dynamic model of 7 degrees freedom for vehicle under Braking in Turn Condition. Based on this model, wheel lock braking and ABS braking were researched and simulated. The simulation results show directly that first lock of front wheel loses vehicle steering performance, first lock the rear wheel sideslips, ABS braking can prevent loss of vehicle steering performance and sideslip, but slightly long braking distance.

The Control of the Braking Stability of Active Rear Wheel Steering Vehicle Based on LQR

2013 ◽  
Vol 416-417 ◽  
pp. 909-913
Author(s):  
Qi Jia Liu ◽  
Si Zhong Chen
Keyword(s):  
Slip Rate ◽  
Linear Quadratic Regulator ◽  
Rear Wheel ◽  
Front Wheel ◽  
Slip Angle ◽  
Linear Quadratic ◽  
Wheel Slip ◽  
Side Slip Angle ◽  
Braking Distance ◽  
Lock Mode

The aim of this article is to improve the brake stability of active rear wheel steering vehicle. The optimal theory of linear quadratic regulator is used to construct a controller, and the aim of the controller is to maintain the side slip angle is zero, and the control parameter is set according to the change of velocity when braking. An antilock brake model based on the door limit of wheel slip rate is constructed. The analysis is carried on a front wheel steering vehicle, which has two kinds of unti-lock mode. Meanwhile, an active rear wheel steering vehicle with two kinds of unti-lock mode is performed, also. All tests are performed on the bisectional road. The results of analysis show that the active rear wheel steering vehicle using the anti-lock mode of four wheels independent control can give the shortest braking distance, the smaller side slip angle and the smaller deviation from the lane. So it can give more contribution to the braking safety.

scholarly journals LINEARIZATION OF A NONLINEAR VEHICLE MODEL

2021 ◽  
pp. 33-37
Author(s):  
Lubica Miková
Keyword(s):  
Dynamic Models ◽  
Equations Of Motion ◽  
Lateral Position ◽  
Front Wheel ◽  
Driver Assistance ◽  
Vehicle Model ◽  
Driver Assistance Systems ◽  
Nonlinear Vehicle Model ◽  
Mathematical Equations ◽  
Assistance Systems

The purpose of this article is to create a mathematical model of a vehicle using dynamic equations of motion and simulation of perturbations acting on a vehicle. It is assumed that the tire in the car model behaves linearly. Because the vehicle model is nonlinear, the model will need to be linearized in order to find the transfer function between the angle of rotation of the front wheel and the lateral position of the vehicle. For this purpose, simple dynamic models of the car were created, which reflect its lateral and longitudinal dynamics. These types of models are usually used with a linearized form of mechanical and mathematical equations that are required when designing controllers, active suspension and other driver assistance systems.

Hands-free circular motions of a benchmark bicycle

2007 ◽  
Vol 463 (2084) ◽  
pp. 1983-2003 ◽  
Author(s):  
Pradipta Basu-Mandal ◽  
Anindya Chatterjee ◽  
J.M Papadopoulos
Keyword(s):  
Nonlinear Equations ◽  
Dynamic Balance ◽  
Equations Of Motion ◽  
Ground Plane ◽  
Rear Wheel ◽  
Front Wheel ◽  
Static Equilibrium ◽  
Straight Line ◽  
Nonlinear Equations Of Motion

We write nonlinear equations of motion for an idealized benchmark bicycle in two different ways and verify their validity. We then present a complete description of hands-free circular motions. Three distinct families exist. (i) A handlebar-forward family, starting from capsize bifurcation off straight-line motion and ending in unstable static equilibrium, with the frame perfectly upright and the front wheel almost perpendicular. (ii) A handlebar-reversed family, starting again from capsize bifurcation but ending with the front wheel again steered straight, the bicycle spinning infinitely fast in small circles while lying flat in the ground plane. (iii) Lastly, a family joining a similar flat spinning motion (with handlebar forward), to a handlebar-reversed limit, circling in dynamic balance at infinite speed, with the frame near upright and the front wheel almost perpendicular; the transition between handlebar forward and reversed is through moderate-speed circular pivoting, with the rear wheel not rotating and the bicycle virtually upright. Small sections of two families are stable.

Influence of Frame Stiffness and Rider Position on Bike Dynamics: Analytical Study

2015 ◽  
Author(s):  
Trevor Williams ◽  
Sudhir Kaul ◽  
Anoop Dhingra
Keyword(s):  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Critical Role ◽  
Rear Wheel ◽  
Front Wheel ◽  
Rigid Bodies ◽  
Limited Attention ◽  
Structural Stiffness ◽  
Bicycle Frame

Dynamic characteristics of a bicycle such as handling and stability can be studied during the design phase to comprehend specific aspects associated with the overall layout as well as the frame architecture. Bicycles demonstrate unique properties such as static instability that is overcome by getting them into motion with a minimum velocity threshold. The structural stiffness of a frame plays a critical role in the handling behavior of a bike. However, the influence of structural stiffness has received limited attention in the existing literature. This paper attempts to fill the gap by presenting analytical results from a study that includes the influence of rider positions on three bicycle layouts. The analytical model consists of four rigid bodies: rear frame, front frame (front fork and handle bar assembly), front wheel and rear wheel. The overall model exhibits three degrees-of-freedom: the roll angle of the frame, the steering of the front frame, and the rotation of the rear wheel with respect to the frame. The rear frame is divided into two parts, the rider and the bicycle frame, that are assumed to be rigidly connected. This is done in order to allow the model to account for varying rider positions. The influence of frame flexibility is studied by coupling the structural stiffness of the frame to the governing equations of motion. Layouts from a benchmark bicycle, a commercially manufactured bicycle, and a cargo bicycle are used for this study in conjunction with rider positions ranging from a relaxed position to an extreme prone position. All the results are analyzed and compared with some proven analytical and experimental results in the existing literature. Results indicate that some of the rider positions can play a significant role in influencing the dynamic characteristics of the bike. Structural stiffness is seen to significantly affect the weave mode, only when the stiffness is reduced substantially.

Mechanical Structural Optimization and Research for an Intelligent Vehicle Model

2013 ◽  
Vol 302 ◽  
pp. 486-489
Author(s):  
Chong Jie Leng ◽  
Hui Yu Xiang ◽  
Xiao Zhuang Zhou ◽  
Jia Jun Huang
Keyword(s):  
College Students ◽  
Structural Optimization ◽  
Rear Wheel ◽  
Front Wheel ◽  
Intelligent Vehicle ◽  
Main Study ◽  
Vehicle Model ◽  
Steering Mechanism ◽  
Wheel Alignment ◽  
Control Procedures

This paper utilized an intelligent vehicle model for the “Freescale” Cup National College Students' Intelligent Vehicle competition as the main study object. Under the prerequisite of adopting the same control procedures and algorithms, the mechanical structures and its parameters of the model vehicle which influence the running performance, such as front wheel alignment, steering mechanism and rear wheel deceleration mechanism are optimally designed and adjusted .It has been proved that the scheme induced the model vehicle driving fast and stable on the path-complex track and thus to achieve reasonable effects.

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