# Steering Pull Model and Its Sensitivity Analysis
## 7 Conclusions  
A complete steering pull model is developed, and the sensitivity of steering pull factors is analyzed based on the model in this study. To develop the steering pull model, an approach organized into three steps--tire pulling force model, steering system model, and the model integration--is achieved in this study. First, the factors of tire pulling forces, such as road bank angle, polyester and conicity, kingpin and caster angles, and camber angle, are investigated and mathematically modeled. Second, a steering system that consists of lower body linkages, rack and pinion gear, universal joint, and steering column is modeled. For the steering column modeling, a C-EPS system and the friction generated in the system, which includes Coulomb and viscous friction, are also considered. Then, each model is integrated into a complete steering system model. Finally, a steering pull model is developed by integrating the tire pulling force model and the steering system model. All models are built on SIMULINK environment.  
Prior to a sensitivity analysis on the steering pull, the developed steering pull model is experimentally verified. A vehicle is designated, and its driving conditions and design parameters are adopted into the model. Two profiles of the steering pull distance at \(0.7\) and \(1.6\) degrees of bank angle are estimated by the model. For an experimental verification, a steering pull measurement system using a GPS device is set up in the designated vehicle. The experimental steering pull distances by the measurement system are compared with the estimated. The estimated and the experimented show the same tendency, i.e., the steering pull distance increases with the increase of vehicle moving distance. There are slight differences between the estimated and the experimented but throughout the entire steering pull distance, the steering pull model developed in this study provided very accurate estimation results.  
As the final procedure, sensitivity analysis on the steering pull is performed. First, the sensitivity of bank angle is analyzed, and then, the sensitivity of design parameters, such as caster angle, kingpin angle, camber angle, rack friction force, and ARS stiffness, are analyzed. Among the design parameters, the rack friction force has the highest sensitivity on the steering pull, and the ARS stiffness has the second highest sensitivity. On the other hand, the caster angle has the lowest sensitivity, which means that it hardly has any influence on the steering pull.  
The steering pull causes an annoying steering feel to the driver in that it forces the driver to exert a constant steering torque to the steering wheel. Therefore, many automotive engineers have been trying to improve the steering pull. The steering pull model proposed in this study can be used as a basic model in designing automotive components and help the improvement of steering pull.  
Conceptualization, S.H.K.; Methodology, S.H.K. and M.C.S.; Software, S.H.K. and M.C.S.; Validation, S.H.K. and M.C.S.; Formal Analysis, S.H.K. and M.C.S.; Investigation, S.H.K. and M.C.S.; Resources, M.C.S.; Data Curation, M.C.S.; Writing-Original Draft Preparation, S.H.K.; Writing-Review & Editing, M.C.S.; Visualization, M.C.S.; Supervision, M.C.S.; Project Administration, S.H.K.; Funding Acquisition, S.H.K. All authors have read and agreed to the published version of the manuscript.  
This research was supported by Korea Institute for Advancement of Technology (KIAT) grant funded by the Korea Government (MOTIE) (N0002431, The Competency Development Program for Industry Specialist). This research was supported by the MSIT (Ministry of Science and ICT), Korea, under the ITRC (Information Technology Research Center) support program (IITP-2020-2016-0-00312) supervised by the IITP (Institute for Information & communications Technology Planning & Evaluation).  
The authors declare no conflict of interest.