The mechanics of the steered wheels of a road vehicle
Modern road vehicle suspension and steering systems may generally be classed as multi-loop spatial mechanisms, designed with links constrained and interconnected in such a manner as to attempt a preferred and prescribed motion of the steered wheels with regard to the inputs to the system. The mechanism incorporates elastic and damping elements and is terminated to the ground surface via the tyres. The complete system may be modelled as a multi-body system with spatial kinematics. This work demonstrates an analysis and simulation of the mechanics of a double wishbone/rack and pinion suspension and steering system modelled as a multi-body system. A 3-dimensional Newton-Euler based approach employing vector and matrix notation is used in deriving the coupled set of non-linear equations of motion, and these together with the kinematic equations of constraint are cast in state space form, and numerical solutions sought using a digital computer. The kinematic equations are derived from the velocity loop equations for the model, and deal with the so-called redundant degrees-of-freedom arising in models of this type in a completely general manner. The tyre, shock absorber, main spring, and steering gear are modelled from empirical data. A feature of the work is that the complete set of equations need not be excessively manipulated manually, and that use of a set of specially written computer program routines allows a numerical formulation of the equations in the machine, enabling the main program to be written from inspection of the 'raw' equations. Large displacements and therefore changes of geometry are considered, with the provision for partial numerical linearization of the geometric aspects if required. The kinematic behaviour of the model is also described. A supporting experimental programme of work with a vehicle on a rolling drum rig has been conducted in parallel to the simulation work. And results indicate good correlation between theory and experiment at low frequencies of vibration.