## 1 Introduction
analyzed the effects of the steered wheel angle, friction coefficient, tire pressure and vertical load on the pivot steering resistance torque based on a vehicle road test [15], they also considered the contact between the tire and pavement in their research on the pivot steering resistance torque [16], however, the effect of the kingpin offset on the steering resistance torque is neglected in modeling. [PERSON], [PERSON] et al. introduced the LuGre friction model in their research on the pivot steering resistance torque, and the parameter identification and simulation calculation was carried out [17]. [PERSON], [PERSON] proposed the hypothesis of gradual distribution of tire load starting from contact and friction between the tire and pavement, and calculated the pivot steering resistance torque [18]. [PERSON], [PERSON] et al. proposed an estimation method of the static steering torque including the tire sliding torque and gravity aligning torque [19]. For the steering resistance torque under a medium and high speed steering condition, it is mainly composed of aligning torques caused by the alignment parameters of the front wheel, which is related to vehicle speed, the side-slip characteristics of the tire, pneumatic trail, the alignment parameters and steering angle of the front wheel, etc. [20; 21; 22] For example, [PERSON], [PERSON] et al. analyzed the effects of vehicle speeds (10 km/h, 20 km/h, 30 km/h, 40 km/h, 50 km/h) on the steering torque based on modeling and simulation [23]. [PERSON], [PERSON] et al. took the tire lateral force, the aligning torques due to kingpin inclination and the pneumatic trail into account in their research on hardware-in-the-loop simulations of an electrohydraulic power steering system [24]. [PERSON], [PERSON] et al. analyzed the relationships between the lateral force, the aligning torques of the tire and side-slip angle, the tire's rolling speed by establishing the simulation model of a rolling tire, and presented the change curve of the steering torque [25]. To sum up, domestic and foreign scholars mainly studied the steering resistance torque under pivot steering and medium or high speed steering conditions, but did not involve their research on low-speed steering resistance torque. According to analysis, the low-speed steering resistance torque mainly includes the tire/pavement friction torque and aligning torques caused by the alignment parameters of the front wheel. When the vehicle steers at a low speed, the friction generated between the tire and pavement includes the components of sliding and rolling friction. The proportion of the two friction components will transfer to each other as the vehicle speed changes, and thus the dynamic process is quite complex. There are no mature models to describe such dynamic processes so far. Judging from the above gap analysis, the study on low-speed steering resistance torque not only can provides a theoretical basis for the intervention and withdrawal mechanisms of a supercapacitor in SC-EPS, but can fill in the blank in the research field on low-speed steering resistance torque, providing a useful reference for the design of assist characteristics and control strategies for other new EPS systems as well. Considering that the low-speed steering resistance torque of heavy-duty commercial vehicles is not convenient for experimental verification, the model of low-speed steering resistance torque of a compact car was established and verified by real vehicle experiments in this paper. Then the proved modeling method of low-speed steering resistance torque would be generalized to heavy-duty commercial vehicles. Firstly, the finite element models of the tire and pavement were established to conduct the simulation and calculation of a low-speed steering friction force between the tire and pavement and to obtain the fitting expression of the equivalent steering friction coefficient with the running speed of the tire.