Vehicle_Handling_Model

1) Abstract 2) Introduction The aim of this project is to design and develop a simple vehicle handling model in either/both ADAMS/Matlab environment and to extend it to include rear wheel steering. The steering system is designed to ensure that the wheels point towards the desired direction with positive response to whatever directional signal driver may make on the steering wheel, in order to keep the deviation from the desired course low. This enables the driver to control and continuously adjust the steering path of the vehicle that is typically accomplished through series of mechanical linkages which is normally incorporated between the front steered wheels and driving wheel. However the correlation between turning angle of the steering wheel made by driver and the change in the driving direction is not linear and therefore there is no definite functional relationship because of these factors • Development of lateral tyre forces • Alteration of driving directions • Turns of the steering wheel • Alterations of the steer angle at the front wheels This arises from the elastic compliance in components of the chassis, so driver must adapt to the path and continually adjust the relation between the alteration in the direction of travel and turning of the steering wheel accordingly. To do so there is wealth of information the driver will take into perspective. This may include factors like the roll inclination of the body, transverse acceleration and the self-centring torque the driver would feel via steering wheel. It’s through steering moment or torque that the driver gets the information which provides him with the feedback of the forces acting on the wheels. Its therefore the steering system that has to convert the steering wheel angle into as clear relationship as possible to the steering angle of the wheels and carry the feedback about the state of the movement back to the steering wheel. The first approach that needs to be brought under consideration is to obtain the best steering control and handling behaviour to attempt to design the steering system so that two steering wheels run with equal slip angles during cornering. The way to assume to achieve this would be to actually design the steering system with Ackerman geometry .The principle of this geometry assumes a vehicle cornering with its tires running at zero slip angles. This derivation of such analysis could be valid only for vehicle moving very slowly, being a kinematic rather than dynamic so it could distinguish the need for side force generation. As soon as the vehicle picks up the speed, the tires must also comply and run at slip angles to generate cornering forces. This will modify the relation required between wheels, or toe-out on turns. Ackerman Geometry The steering system in its simplest form will have both the wheels pointing in the same direction. Ackerman steering geometry is an arrangement of linkages, while steering of the vehicles is actually designed to solve the problems of wheels on the inside and outside of a turn needing to trace out circles of different radii. When the vehicle steered, it’s actually to follow the path which is the part of the circumference of the turning and the centre point that will be around somewhere where the line is extending from the axis of the fixed axle. The angle of the both steered wheels must be at a 90 degree to a line drawn from the circle centre through the centre of the wheel. As the wheel on the outside turn will project a turn that would be larger than the wheel on the inside, so the wheels need to be set at different angle. The Ackerman steering geometry has automatic arrangement, by moving the steering pivot points inward as it lies on a line drawn between the steering kingpin and the centre of the rear axle centre. The pivot points of the steering are joined by a rigid bar, and steering components can be part of the mechanism for instance rack and pinion steering mechanism. This ensures that whatever angle steering is forced the centre point of all the circles traced by all wheels will lie at a common point. Modern cars do not purely operate on Ackerman steering, as a consequence that ignores important dynamic and compliant effects, but this system works sound for low speed manoeuvres. Rear Wheel Steering System Rear wheel as contrary to the front wheels steering could be distinguished on certain specialised vehicles such as mobile cranes forklift trucks and on Thrust SSC (land speed record car). It’s not usual to come across such system in road vehicles as it instigates dynamic instability. As from kinematics perspective, as with Ackerman geometry, rear wheel steering would seem to work. However when the forces require to corner at significant speed are taken into account, the dynamic difficulties become clearer. To introduce a turn to the right the rear wheels must be turned to the left, this would result into a situation where the front of the vehicle is nosed into a turn enabling front wheels to generate slip angle and cornering forces to the right towards the centre of the turn. At contrast the rear wheels would run at slip angle in the opposite direction, in a way that cornering forces are generated at the left away from the centre of turn. This will create conflict among the front and rear tire forces, yielding yaw moment and turning the vehicle more sharply – tend to oversteer. In theory it would be likely to change the rear-steer angle to reverse the direction of cornering forces and slip angles. But in practical humans reflexes are slow to cope with this control. In the context of road vehicles, rear wheel steering may be included as part of the four wheel strategy which the rear wheel steering has been always present. In the past years, the rear wheels of the most vehicles were to steer because of suspension kinematic and compliance characteristics that were difficult to overcome and were not understood. In most recent years suspension design had been accentuated, so passive rear wheel steering could be controlled, assumed to bring productive results. Steering Ratios All vehicles have steering ratio that is inherent to their design. You would never be able to turn the wheels if there was no steering ratio. Steering ratio provides you with mechanical advantage, enabling the driver to turn the load on the car, more importantly it means that you do not have to steer the wheel a large number of times to get the wheels moving. Steering ratio is the amount of steering wheel turned that is to be translated into degrees that front wheels are deflected. For instance if the steering wheels are to be turned at 20 degrees then the front wheels would turn at 1 degree, that gives the steering ratio of 20:1. For the most modern cars the steering ratio is between 12:1 and 20:1. The maximum interpretation of wheels that it is deflected to gives lock to lock turns for the steering wheel, for example if the car vehicle has steering ratio of 18:1 and the front wheels have deflection of 25 degree, it means the steering wheel has turned 25°x18 which is 450°. That’s only to one side, as the entire steering goes from -25° to 25° attaining a lock to lock angle at the steering wheel of 900°, or 2.5 turns(900°/360). 3) Background The simplest way to model a vehicle in order to study its dynamic behaviour is to make the following simplifications: 1) The vehicle is a rigid body. Suspension is not taken into account. 2) Each axle is considered as one wheel. Essentially, the width of the vehicle is ignored. 3) The pitch and roll motions are ignored. 4) The road surface is considered perfect. There are no variations in coefficient of friction during the test. 5) The steering is performed directly at the wheels and any steering input occurs instantaneously. 6) The bicycle model essentially causes the vehicle to behave as if it had Ackermann steering. 7) Aerodynamic effects are not taken into account. 8) Weight transfer during acceleration and braking is ignored. 9) The self-aligning moment generated by the wheels during cornering does not affect the dynamics. 10) The steering angle is small; therefore the equations of motion are linear. The bicycle model has 2 degrees of freedom, mainly yaw and lateral motion. Parameters and equations The parameters describing the vehicle behaviour and their notation are described below: L [m] – 2.4m – Wheelbase tf [m] - 1.15m - Track front tr [m] - 1.2m - Track rear a [m] – 1.15m – Front axle to centre of gravity b [m] – 1.25m – Rear axle to centre of gravity M [kg] – 1300kg – Vehicle Mass Ix [kgm2] – 1700 kgm2 – Moment of inertia about the x axis IY [kgm2] – 1700 kgm2 – Moment of inertia about the y axis IZ [kgm2] – 1900 kgm2 – Moment of inertia about the z axis Cf [N/rad] – 70000 N/rad – Front axle cornering stiffness Cr [N/rad] – 65000 N/rad – Rear axle cornering stiffness Wf [N] – Front static weight Wr [N] – Rear static weight g [m/s2] – 9.81 m/s2 – Acceleration due to gravity ay [m/s2] – Lateral acceleration K [rad/g] – Understeer gradient U [m/s] – Vehicle speed Uchar [m/s] – Characteristic speed Ψ’ [1/s] – Yaw rate β [] – Sideslip angle R [m] – Radius of turn Wf=mgbL (1) Wr=mgaL (2) K= WfCf-WrCr (3) ay=U2gR (4) δ=LR+Kay (4) Uchar=gLR (5) lateral acceleration gain=U2gL1+KU2gL (6) ψ'=UR (7) ψ'δ=UR1+KU2gL (8) β=57.3b-WrCrgU21R(9) static margin=bCr-aCfCf+Cr (10) * Steady-state and transient analysis The steady state analysis considers the steering angle and vehicle speed as constant. In transient analysis, these parameters are varied. * Rear wheel steering 4) Technical analysis and modelling a) Steady state model Fig 1. Steady state model Using this model, the values for the understeer gradient, lateral acceleration, steering angle, characteristic speed and static margin can be calculated. The speed is taken as 30 m/s and the turning radius as 100 m. K = 0.0008759 rad/g (understeer) Uchar = 164 m/s static margin = 0.005556 m (understeer) Plotting steering angle against speed going from 0 to 30 m/s shows typical understeer behaviour. For the same speed, showing steering angle as a function of lateral acceleration: This time, speed is held constant at 30 m/s but the radius of turn varies from 50 to 200 m. The yaw rate gain versus speed plot shows the characteristic speed is where the vehicle is most responsive. However, for this particular vehicle the characteristic speed is very large. Finally, plotting sideslip angle against speed shows that it is independent of turning radius: The eigenvalues for this vehicle, going from 10 to 50 m/s in steps of 10 m/s, are as follows: 10 m/s: -5.32e+000 + 6.83e+000i; -5.32e+000 - 6.83e+000i 20 m/s: -2.66e+000 + 8.08e+000i; -2.66e+000 - 8.08e+000i 30 m/s: -1.77e+000 + 8.29e+000i; -1.77e+000 - 8.29e+000i 40 m/s: -1.33e+000 + 8.36e+000i; -1.33e+000 - 8.36e+000i 50 m/s: -1.06e+000 + 8.39e+000i; -1.06e+000 - 8.39e+000i As for the frequency response: Time history for a step steering input of 2 degrees at 20 m/s: A lane change is equivalent to a sine input to the steering wheel. Using 2 degrees for the amplitude, the following results are obtained: 5) Review of design sensitivity In order to make the vehicle neutral steer, 2 changes are made to the parameters: a = b = 1.15 m (total vehicle length = 2.3 m) Cf = Cr = 70000 N/rad Therefore, the understeer gradient and the static margin are 0. Eigenvalues: 10 m/s: -4.87e+000 + 7.07e+000i; -4.87e+000 - 7.07e+000i 20 m/s: -2.44e+000 + 8.23e+000i; -2.44e+000 - 8.23e+000i 30 m/s: -1.62e+000 + 8.43e+000i; -1.62e+000 - 8.43e+000i 40 m/s: -1.22e+000 + 8.50e+000i; -1.22e+000 - 8.50e+000i 50 m/s: -9.74e-001 + 8.53e+000i; -9.74e-001 - 8.53e+000i Frequency response: Step input of 2 degrees at 20 m/s: Lance change response: Similarly, the vehicle can be caused to oversteer: a = 1.25 m; b = 1.15 m Cf = 65000 N/rad; Cr = 70000 N/rad The understeer gradient and static margin become: K = -0.0008759 Static margin = -0.005556 Eigenvalues: 10 m/s: -4.90e+000 + 6.57e+000i; -4.90e+000 - 6.57e+000i 20 m/s: -2.45e+000 + 7.99e+000i; -2.45e+000 - 7.99e+000i 30 m/s: -1.63e+000 + 8.22e+000i; -1.63e+000 - 8.22e+000i 40 m/s: -1.22e+000 + 8.30e+000i; -1.22e+000 - 8.30e+000i 50 m/s: -9.79e-001 + 8.34e+000i; -9.79e-001 - 8.34e+000i Frequency response: Step input of 2 degrees at 20 m/s: Lance change response: 6) Investigation of rear wheel steering * Four wheel steer scheme 1 * Four wheel steer scheme 2 7) Results and discussion 8) Conclusions 9) References 10) Appendix * Meetings minutes