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Feedback Properties of Vehicle Controls
Published in Guy H. Walker, Neville A. Stanton, Paul M. Salmon, Vehicle Feedback and Driver Situation Awareness, 2018
Guy H. Walker, Neville A. Stanton, Paul M. Salmon
Joy and Hartley (1953/4) describe aligning torque as giving “a measure of the force required to steer the car, i.e. it gives a measure of the ‘feel’ at the steering wheel” (p. 113). This feel arises due to a characteristic of pneumatic tyres termed pneumatic trail (Setright, 1999). This is a speed- and load-sensitive distortion of the tyre's contact patch with the road which is fed back through the steering system. Pneumatic trail, and how this interacts with the geometry of steering and suspension components, is responsible for the weight and force needed to operate the steering wheel (Joy and Hartley, 1953/4). Up to a point, cornering force versus aligning torque is almost directly proportional, meaning it is possible to corner faster by imparting more effort to hold the steering wheel in a desired position. When this linear relationship between cornering force and aligning torque starts to falter, i.e. it is possible to corner harder and faster with no further increase in steering torque, most drivers perceive this to be the point at which control is about to be lost. Strictly speaking, as Figure 3.12 shows, it isn't.
Wheels and Tyres
Published in G. K. Awari, V. S. Kumbhar, R. B. Tirpude, Automotive Systems, 2021
G. K. Awari, V. S. Kumbhar, R. B. Tirpude
Pneumatic trail is caused by the progressive build-up of lateral force along the length of the contact patch, such that lateral forces are greater towards the rear of the contact patch (though less so when the rear of the contact patch begins sliding) and this creates a torque on the tyre called the self aligning. Self aligning torque helps steered tyres to return to the original position after negotiating a turn on the road. Self-aligning torque (SAT) may be defined as the product of the cornering force and the pneumatic trail.
Hopf bifurcation and energy transfer of automobile shimmy system with consideration of road roughness excitation
Published in Vehicle System Dynamics, 2022
Heng Wei, Jianwei Lu, Hangyu Lu, Lei Shi, Bofu Wu, Ping Jiang
The generalised forces corresponding to three DOF are: where is the lateral force of the right tire; R is the rolling radius of the tire; is the caster angle; n is the pneumatic trail; is the vertical resultant force of the wheel centre, is the vertical force of the road surface acting on the wheel centre, is the vertical force of the suspension acting on the wheel centre; A is the lateral distance from the wheel centre to the kingpin; is the inertia moment of the wheel about its rotation axis; B is the distance between the wheel centre and the hinge centre of the lower control arm and the subframe; v is the speed.
Modelling transient response using PAC 2002-based tyre model
Published in Vehicle System Dynamics, 2022
Aashish Shaju, Ashok Kumar Pandey
It is to be noted that the transient effects in the self aligning torque is approximated by including the lateral, and longitudinal, , forces and neglecting the possible changes in the pneumatic trail in the equation, where, , is the residual aligning torque which mainly comprise of PRAT (ply steer residual aligning torque). Here, one can see that both the Equations (7) and (9) depend upon the respective relaxation lengths and . In the subsequent section, we discuss about a reliable estimation of the relaxation lengths obtained based on Rill's work [41].
Actuator fault tolerant control for steer-by-wire systems
Published in International Journal of Control, 2021
Chao Huang, Hailong Huang, Fazel Naghdy, Haiping Du, Dazhong Ma
The state equation of the SbW system is given below: where is the moment of inertia, is the damping of the steering system at the road wheels, represents the coulomb friction, is the steering actuator torque, is the steering angle, is the steering ratio, is the motor voltage, is the motor constant, describes the self-aligning torque, and is the pneumatic trail (the distance between the resultant point of application of lateral force and the centre of the tyre). is the mechanical trail (the distance between the tyre centre and the point on the ground about which the tyre pivots as a result of the wheel caster angle), V is the longitudinal component of the centre of gravity (CG) velocity, is the front tyre cornering stiffness coefficient, is the yaw rate at the centre, a is the distance of the front axle to the CG, β is side slip angle, is the Coulomb friction constant, and is the sign function defined as Rewriting Equation (1) in state space form yields: where denotes the SbW systems state vector and The inputs of the front wheel subsystem include and , which are the voltage supplied to the front wheel motor and the self-aligning torque which represents the resistance offered by the road and coulomb friction, respectively.