## 1 Introduction  
With the rapid development of China's national economy and advanced highway networks, the driving speed of heavy-duty commercial vehicles, such as coaches and lorries, has greatly increased, while high-speed safety has becoming increasingly prominent. The steering system as a key part in vehicle chassis is crucial for the driving safety of vehicles. Nowadays, heavy-duty commercial vehicles are widely equipped with a hydraulic power steering (HPS) system, with an assist characteristic that is relatively single and an assist effort cannot vary with vehicle speed, which would easily cause poor road feel and affect handling stability during high-speed steering. On the other hand, whether the vehicle is going straight or steering, the steering pump in HPS is always running along with the engine, which causes a large amount of energy loss [1; 2]. Recently, the electric power steering (EPS) system has been widely used in passenger cars and light commercial vehicles for its advantages of safety, energy saving and environmental protection. The assist effort of EPS can vary with vehicle speed, which is conducive to improving handling stability. In addition, the motor in EPS provide steering assist effort directly, thus EPS hardly consumes electric energy under no-steering conditions, which is more energy saving [3; 4]. Nevertheless, EPS is not suitable for heavy-duty commercial vehicles due to a large steering resistance torque and the power limitation of existing power supply systems in heavy-duty commercial vehicles, especially under the condition of pivot or low-speed steering [5]. It is known that heavy-duty commercial vehicles travel at medium or high speeds most of the time. In this case, the steering resistance torque is lower and the power supply system can meet the steering power demand. So the issue of insufficient power provided by existing vehicle power systems during pivot or low-speed steering needs to be emphatically solved to promote the application of EPS in heavy-duty commercial vehicles. Supercapacitors (SC) have been widely used in electric vehicles and the braking system of trains for its advantages of high power density, short charging time, large current discharge capacity, etc. [6; 7; 8] Therefore, a new type of EPS system based on the hybrid power system constituted by the vehicle power system and the supercapacitor, which is defined as SC-EPS here, is proposed in this paper. When vehicle speed is low, the vehicle power system and supercapacitor jointly provide electric power for EPS. When the vehicle speed is high, the vehicle power system solely provides electric power for EPS while charging the supercapacitor. In order to provide a theoretical basis for the intervention and withdrawal mechanisms of a supercapacitor in the new EPS structure, the law of steering resistance torque at a low or extremely low vehicle speed needs to be explored first. In other words, the power supply modes of the SC-EPS system are determined by the change laws of the steering resistance torque. Domestic and foreign scholars have carried out relevant research on the compositions, calculations and influences of the steering resistance torque. The pivot steering resistance torque is related to various factors such as the front axle load, the alignment parameters and steering angle of the front wheel, the tire/pavement friction, etc. [9; 10; 11; 12] For example, empirical formulas are usually used to calculate the pivot steering resistance torque at present [13; 14], however, empirical formulas do not reflect the relationship between the steering resistance torque and the steered wheel angle. [PERSON], [PERSON] et al.