Skip to main content
SpringerLink
Log in

Road Torque Modeling for Electric Power Steering Systems

  • Published:
International Journal of Automotive Technology Aims and scope Submit manuscript

Abstract

The rack force transmitted to a rack bar through a tie-rod is regarded as a major external force to the electric power steering (EPS) system. However, since road torque generated between the tire and the road surface is transmitted to the rack bar under the influence of road wheels and various linkages and bushings, it is difficult to equalize the rack force and road torque. This paper proposes a road torque modeling method and identifies the characteristics of EPS systems, including road torque. To estimate the road torque acting on the tire, an EPS system model including road wheels is proposed. The proposed EPS system model and the road torque model in the vehicle driving situations are validated with vehicle experiment results. The experimental results show that the proposed road torque model represents the characteristics of road torque in both stop and driving conditions, and the newly proposed EPS system model expresses the characteristics of the actual system better than the conventional EPS system model in the stop state.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

J 1 :

moment of inertia of the steering wheel, kg·m2

J c :

moment of inertia of the steering column, kg·m2

J m :

moment of inertia of the motor, kg·m2

J fw :

moment of inertia of the road wheel, kg·m2

M r :

mass of the rack bar, kg

C 1 :

damping coefficient of the steering wheel, N·m/(rad/sec)

C c :

damping coefficient of the steering column, Nm/(rad/sec)

C m :

damping coefficient of the motor, Nm/(rad/sec)

C fw :

damping coefficient of the steering linkage bushing, N·m/(rad/sec)

C r :

damping coefficient of the rack bar, N·m/(rad/sec)

K :

torsional stiffness of the torque sensor, N-m/rad KOB: torsional stiffness of the ball joint, N-m/rad

N :

worm gear ratio

N L :

steering knuckle arm, m

θ 1 :

steering wheel angle, rad

θ m :

motor angle, rad

θ 2 :

steering column angle, rad

θ fw :

road wheel angle, rad

τ h :

driver torque, N·m

τ a :

motor torque, N·m

τ road :

road torque, N·m

b r :

radius of rotation of the ball stud, m

x r :

translational displacement of the rack bar, m

r p :

radius of pinion, m

References

  • Badawy, A., Zuraski, J., Bolourchi, F. and Chandy, A. (1999). Modeling and analysis of an electric power steering system. SAE Paper No. 1999-01-0399.

  • Canudas-de-Wit, C., Tsiotras, P., Velenis, E., Basset, M. and Gissinger, G. (2003). Dynamic friction models for road/tire longitudinal interaction. Vehicle System Dynamics 50, 3, 189–226.

    Article  Google Scholar 

  • Chen, X., Yang, T., Chen, X. and Zhou, K. (2008). A generic model-based advanced control of electric power-assisted steering systems. IEEE Trans. Control Systems Technology 50, 3, 1289–1300.

    Article  Google Scholar 

  • Fahami, S. M. H., Zamzuri, H. and Mazlan, S. A. (2015). Development of estimation force feedback torque control algorithm for driver steering feel in vehicle steer by wire system: Hardware in the loop. Int. J. Vehicular Technology, 2015, 1–17.

    Article  Google Scholar 

  • Fankem, S. and Müller, S. (2014). A new model to compute the desired steering torque for steer-by-wire vehicles and driving simulators. Vehicle System Dynamics 52, sup1, 251–271.

    Article  Google Scholar 

  • Illán, J. T., Ciarla, V. and De Wit, C. C. (2011). Oscillation annealing and driver/tire load torque estimation in electric power steering systems. IEEE Int. Conf. Control Applications (CCA), Denver, Colorado, USA.

  • Kang, J. (2011). Theoretical model of ball joint squeak. J. Sound and Vibration 50, 3, 5490–5499.

    Article  Google Scholar 

  • Lee, D., Jang, B., Han, M. and Kim, S. (2021) A new controller design method for an electric power steering system based on a target steering torque feedback controller. Control Engineering Practice, 106, 104658.

    Article  Google Scholar 

  • Lee, D., Kim, K. S. and Kim, S. (2017). Controller design of an electric power steering system. IEEE Trans. Control Systems Technology 50, 3, 748–755.

    Google Scholar 

  • Lee, D., Yi, K., Chang, S., Lee, B. and Jang, B. (2018) Robust steering-assist torque control of electric-power-assisted-steering systems for target steering wheel torque tracking. Mechatronics, 49, 157–167.

    Article  Google Scholar 

  • Ma, B., Yang, Y., Liu, Y., Ji, X. and Zheng, H. (2016). Analysis of vehicle static steering torque based on tire—road contact patch sliding model and variable transmission ratio. Advances in Mechanical Engineering 50, 3, 1–11.

    Google Scholar 

  • Pang, D. Y., Jang, B. C. and Lee, S. C. (2005). Steering wheel torque control of electric power steering by PD-control. Int. Conf. Control, Automation, and Systems (ICCAS), Gyeonggi, Korea.

  • Song, J., Boo, K., Kim, H. S., Lee, J. and Hong, S. (2004). Model development and control methodology of a new electric power steering system. Proc. Institution of Mechanical Engineers, Part D: J. Automobile Engineering 50, 3, 967–975.

    Google Scholar 

  • Sugitani, N., Fujuwara, Y., Uchida, K. and Fujita, M. (1997). Electric power steering with H-infinity control designed to obtain road information. American Control Conf. (ACQ), Albuquerque, New Mexico, USA.

  • Sugiyama, A., Kurishige, M., Hamada, H. and Kifiiku, T. (2006). An EPS control strategy to reduce steering vibration associated with disturbance from road wheels. SAE Paper No. 2006-01-1178.

  • Velenis, E., Tsiotras, P., Canudas-De-Wit, C. and Sorine, M. (2005). Dynamic tyre friction models for combined longitudinal and lateral vehicle motion. Vehicle System Dynamics 50, 3, 3–29.

    Article  Google Scholar 

  • Yasui, Y., Tanaka, W., Muragishi, Y., Ono, E., Momiyama, M., Katoh, H. and Imoto, Y. (2004). Estimation of lateral grip margin based on self-aligning torque for vehicle dynamics enhancement. SAE Trans., 632–637.

Download references

Acknowledgement

This research is supported by the Hyundai motor group.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, KAIST, Daejeon, 34141, Korea

    Byeonggwan Jang & Kyung-Soo Kim

  2. Korea Institute of Machinery and Materials, 156 Gajeongbuk-Ro, Yuseong-Gu, Daejeon, 34103, Korea

    Dongwook Lee

  3. Chassis Control Development Team, Hyundai Motor Company, 150 Hyundaiyeonguso-ro, Namyang-eup, Hwaseong-si, Gyeonggi, 18280, Korea

    Kyuwon Kim

Authors
  1. Byeonggwan Jang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dongwook Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kyuwon Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kyung-Soo Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kyung-Soo Kim.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jang, B., Lee, D., Kim, K. et al. Road Torque Modeling for Electric Power Steering Systems. Int.J Automot. Technol. 23, 765–773 (2022). https://doi.org/10.1007/s12239-022-0068-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12239-022-0068-0

Key Words

Search

Navigation