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A power assisted rack and pinion steering gear is mathematically modelled, enabling the development of quantitative definitions for power steering ‘stiffness’ and ‘feel’. Both these quantities are defined as instantaneous derivatives, being a function of various valve parameters such as differential boost rate, effective pinion pitch radius, piston area, torsion bar stiffness, etc. The resulting stiffness and feel relations are plotted for two types of valve boost curve: a conventional tan-function-like boost curve and a linear boost curve. The latter is shown to yield proportional feel and stiffness in the cornering region of valve operation. The application of this theory to the performance evaluation of two families of speed sensitive valve systems is also addressed.

Mathematical modeling of the mesh friction of a rack and pinion system has been carried out in order to predict the mesh friction of a steering gear. The three dimensional gear geometry and force diagram of a rack and pinion gear is represented in vector form. With proper boundary conditions applied to the equations, the mathematical model simulates the friction forces resulting from the mesh. An experimental apparatus was also built to measure mesh friction between a rack and pinion. A number of rack and pinion steering gears have been tested under several load conditions. Experimental results are then compared with the simulation results to verify the mathematical model.