This study proposed a new model to estimate the manual steering torque of steer-by-wire systems. The current steerby-wire system uses the steering-actuator torque at the end of the rack-and-pinion gear to obtain the manual steering torque. However, there is a need for a new method to obtain the manual steering torque because a steer-by-wire system is expected to develop as it eliminates or at least simplifies more mechanical parts in order to enable them to be combined with other technologies such as an in-wheel motor. In order to propose a new estimation model, this study employs vehicle dynamics modeling and steering-system modeling. Vehicle dynamics modeling is used to estimate the self-aligning moment that arises between the tires and the ground. The slip angle and the normal force, as well as the tire properties of the vehicle, were considered to obtain the self-aligning moment. In addition, the steering system was also considered in this study because the calculated self-aligning moment is transferred through the steering system. The universal joint, the rack-and-pinion gear, and the lower-body linkages were modeled to calculate the manual steering torque delivered to the driver's hands. For validation of the new model, there are two sets of simulation and verification processes in this study. First, the steering-system model was verified through experiments. A steering system was set as the target system, and its mechanical characteristics such as the inertial coefficient, the damping coefficient, and the stiffness were adopted for modeling and verification. Second, the manual steering torque estimation model was verified using field tests. A vehicle was set as the target vehicle, and its specifications such as the dimensions, the steering system, and the lower-body linkages were adopted for modeling and verification. The verification results were presented and show accurate estimation results. The new model proposed in this study does not need mechanical parts to estimate the manual steering torque apart from the steering actuator and the steering feedback actuator and, therefore, it can contribute to the development of a steer-by-wire system.

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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.

This study proposes hardware-in-the-loop simulations to develop the motor speed map of electrohydraulic power steering systems for heavy commercial vehicles. The current method that relies on the test driver’s hands and feet to obtain electrohydraulic power steering motor speed maps causes a number of problems, such as inaccurate steering rates and vehicle speeds and the risk of rollover during tests. In order to overcome these weaknesses, this study employs a hardware-in-the-loop simulation system, a vehicle model, and an experimental development method. A hardware-in-the-loop simulation system was set up to simulate a steering system on the road. The system includes a system drive, data acquisition, system controller sets, and an electrohydraulic power steering system. This hardware-in-the-loop simulation system is controlled in real time because the amount of the torque from the resistant torque motor, which applies the self-aligning moments generated between the ground and the tires to the steering system, is affected by the steering angle of the steering-wheel motor. For calculation of the resistant torque with respect to various driving conditions, a vehicle model was employed in this study. It includes calculation of the self-aligning moments with the tire property data, the moments due to the kingpin inclination, the vehicle dynamics, and the steering-system modeling. The resultant values were input into the resistant torque motor. In addition to the hardware-in-the-loop simulation system and the vehicle model, the concept of a desirable steering torque which parameterizes the steering feel was introduced in this study. Using the desirable steering torque, the steering feel could be quantified, and desirable steering feels were established. In this study, in order to validate the hardware-in-the-loop simulations, a heavy commercial vehicle was designated as the target vehicle. The target vehicle’s tire and specifications such as the dimensions, the weight, the steering system, and the mechanical links were adopted, and a desirable steering-torque map was established by a professional test driver. The development results were presented.