# Steering Pull Model and Its Sensitivity Analysis
###### Abstract  
When a vehicle goes on the straight road with a bank angle, a steering pull makes the driver exert a constant steering torque to the steering wheel, which causes an annoying steering feel to the driver. This paper proposes a steering pull model and sensitivity analysis on the steering pull. In order to develop the steering pull model, pulling forces on the tires, such as polyester and conicity forces, lateral force due to slip angle, lifting forces due to cast and kingpin, and camber force are modeled. A steering system is also modeled because the generated pulling forces are attenuated as it is transmitted through the steering system. Each component of the steering system, such as lower body linkages, rack and pinion gear, universal joint, and steering column with electric power steering (EPS) system is modeled, and then they are integrated into a complete steering system. Finally, the steering pull model is developed by integrating the pulling force model with the steering system model. For verification, the steering pull of a vehicle is estimated based on the model, and the results are compared with the experimental results. For the verification experiments, a steering pull measurement system using a global positioning system (GPS) and its accessories are used. The result comparison showed that the developed steering pull model provides very accurate estimation results. Based on the steering pull model, the sensitivity of steering pull factors, such as caster angle, kingpin angle, camber angle, rack friction force, and anti-rattle spring (ARS) stiffness is analyzed. steering pull; vehicle pull; steering drift; vehicle dynamics; vehicle system model  
parameters as rigid links joined with flexible bushes so as to access their effect on the vehicle during braking. [PERSON] and [PERSON] studied the sensitivity of suspension compliances and steering offset on braking-related steering pull and presented the experimental results from kinematic and compliance (K&C) tests [4]. [PERSON] et al. analyzed the effects on handling due to suspension component and assembly tolerances focusing on steering pull [5]. The paper focused on the causes and reduction of steering pull in the specific case of vehicles with front double wishbone suspension and rear five arms suspension. The improvement of steering pull in electric power steering (EPS) systems has been also studied by researchers. They developed the control strategies of EPS systems to reduce steering pull. [PERSON] et al. developed a new algorithm to reduce steering pull in an EPS system [6]. A compensation method applying corrective steering torque using an EPS motor was developed and then, it was validated through field tests. [PERSON] and [PERSON] proposed a control method using an EPS system to improve steering maneuverability and reduce steering pull on rutted roads [7]. The proposed method detects the amount of disturbance torque caused by the ruts in the road, and only when disturbance torque is detected, the EPS system applies compensation torque to the steering system. For parameter studies on steering pull, many researchers focused on the steering pull generated by tire characteristics. [PERSON] et al. studied the simulation procedure of a ply steer residual aligning torque (PRAT) using a stationary global rolling finite-element method (FEM) tire model combined with a detailed local FEM tread pattern model [8]. The simulated results of the PRAT for eight pattern variants are compared with measured values of experimental tires to show a high correlation. [PERSON] studied the behaviors of tires and vehicle system in the straight-line motion and identified the effect of tires using two degrees of freedom vehicle model [9]. Then, the results were verified through field tests and simulations with a full-car model. This paper proposes a complete steering pull model and the sensitivity of steering pull factors based on the model.