Development of a steering-system model considering viscous friction and its verification

Abstract

A method to model the column-type electric power steering system considering viscous friction is proposed. In general column-type electric power steering systems, viscous friction occurs in the reducer. However, it is very difficult to predict with respect to modelling because it varies with the conditions, and accordingly many parameters should be considered. In this study, in order to estimate the dynamic behaviour of a column-type electric power steering system which uses a worm gear as a reducer, the viscous friction generated in the worm gear was derived through theoretical approaches, and the results were applied to modelling the steering system. In the theoretical approaches, the gear geometry and Hertz’s law were employed to derive parameters such as the normal load and the sliding velocity from the worm gear’s driving conditions. Then, the derived parameters were applied to a tribometer to measure the friction coefficients between the worm and the worm wheel. Finally, the friction coefficients were converted to the viscous friction torque of the steering system. By applying the converted viscous friction torque to the modelling, the entire steering system was modelled and the results were verified by comparative simulations and experiments. To model the entire steering system, the individual subparts of the steering system such as the steering column, the universal joint and the rack-and-pinion gear were modelled with MATLAB/Simulink. Then, for verification of the steering-system model, the dynamic behaviour of the steering system was measured experimentally and compared with the simulation results. Taking into account viscous friction and all the mechanical characteristics of the steering system, the established steering-system model which considers viscous friction was employed to estimate very accurately the dynamic behaviour of the steering system, whereas use of the steering-system model which does not consider viscous friction did not achieve accurate estimations.