Skip to main content
Top
Published in: Meccanica 12/2023

21-11-2023

Transient lateral dynamic behavior of tire on μ-step road

Authors: Shengyong Ye, Jianwei Lu, Yingjie Zhu, Lei Shi, Hangyu Lu, Bofu Wu, Ping Jiang

Published in: Meccanica | Issue 12/2023

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this paper, the transient response of tire to step change in road friction coefficient is studied. The brush model is used to analyze the tread deformation, and a mathematical model is established to describe the transient behavior of the tire. The transient response curves of lateral force, aligning torque, slip angle, yaw angle and lateral displacement are obtained. For large initial slip angle, the transient expressions of tire force and torque are established by analyzing the change of tread deformation, and a second-order ordinary differential equation is established to describe the transient characteristics of tire by combining with the equations of motion. In addition, the rigid ring model is used to investigate the influence of flexible sidewalls. For small initial slip angle, a set of partial differential-integral equations of tread deformation and lateral displacement is established, and a numerical method is provided to solve these equations. Furthermore, an estimation method is proposed to make the calculation more efficient. The relevant conclusions of this paper can provide theoretical reference for vehicle dynamics and control.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Bobier CG, Gerdes JC (2013) Staying within the nullcline boundary for vehicle envelope control using a sliding surface. Veh Syst Dyn 51:199–217CrossRef Bobier CG, Gerdes JC (2013) Staying within the nullcline boundary for vehicle envelope control using a sliding surface. Veh Syst Dyn 51:199–217CrossRef
2.
go back to reference Pacejka HB (2012) Tire and vehicle dynamics, 3rd edn. Butterworth-Heinemann, Oxford Pacejka HB (2012) Tire and vehicle dynamics, 3rd edn. Butterworth-Heinemann, Oxford
3.
go back to reference Romano L, Bruzelius F, Jacobson B (2020) Brush tyre models for large camber angles and steering speeds. Veh Syst Dyn 60:1341–1392CrossRef Romano L, Bruzelius F, Jacobson B (2020) Brush tyre models for large camber angles and steering speeds. Veh Syst Dyn 60:1341–1392CrossRef
4.
go back to reference Riehm P, Unrau HJ, Gauterin F et al (2019) 3D brush model to predict longitudinal tyre characteristics. Veh Syst Dyn 57:17–43CrossRef Riehm P, Unrau HJ, Gauterin F et al (2019) 3D brush model to predict longitudinal tyre characteristics. Veh Syst Dyn 57:17–43CrossRef
5.
go back to reference Ozerem O, Morrey D (2019) A brush-based thermo-physical tyre model and its effectiveness in handling simulation of a Formula SAE vehicle. Proc Inst Mech Eng Part D J Automob Eng 233:107–120CrossRef Ozerem O, Morrey D (2019) A brush-based thermo-physical tyre model and its effectiveness in handling simulation of a Formula SAE vehicle. Proc Inst Mech Eng Part D J Automob Eng 233:107–120CrossRef
6.
go back to reference Davari MM, Jerrelind J, Trigell AS et al (2017) Extended brush tyre model to study rolling loss in vehicle dynamics simulations. Int J Veh Des 73:255–280CrossRef Davari MM, Jerrelind J, Trigell AS et al (2017) Extended brush tyre model to study rolling loss in vehicle dynamics simulations. Int J Veh Des 73:255–280CrossRef
7.
go back to reference Alagappan AV, Rao KVN, Kumar RK (2015) A comparison of various algorithms to extract Magic Formula tyre model coefficients for vehicle dynamics simulations. Veh Syst Dyn 53:154–178CrossRef Alagappan AV, Rao KVN, Kumar RK (2015) A comparison of various algorithms to extract Magic Formula tyre model coefficients for vehicle dynamics simulations. Veh Syst Dyn 53:154–178CrossRef
8.
go back to reference Guo K, Lu D (2007) UniTire: unified tire model for vehicle dynamic simulation. Veh Syst Dyn 45:79–99CrossRef Guo K, Lu D (2007) UniTire: unified tire model for vehicle dynamic simulation. Veh Syst Dyn 45:79–99CrossRef
9.
go back to reference Romano L, Sakhnevych A, Strano S et al (2019) A novel brush-model with flexible carcass for transient interactions. Meccanica 54:1663–1679MathSciNetCrossRef Romano L, Sakhnevych A, Strano S et al (2019) A novel brush-model with flexible carcass for transient interactions. Meccanica 54:1663–1679MathSciNetCrossRef
10.
go back to reference Romano L, Bruzelius F, Jacobson B (2021) Unsteady-state brush theory. Veh Syst Dyn 59:1643–1671CrossRef Romano L, Bruzelius F, Jacobson B (2021) Unsteady-state brush theory. Veh Syst Dyn 59:1643–1671CrossRef
11.
go back to reference Mavros G, Rahnejat H, King PD (2005) Transient analysis of tyre friction generation using a brush model with interconnected viscoelastic bristles. Proc Inst Mech Eng Part K: J Multi-body Dyn 219:275–283 Mavros G, Rahnejat H, King PD (2005) Transient analysis of tyre friction generation using a brush model with interconnected viscoelastic bristles. Proc Inst Mech Eng Part K: J Multi-body Dyn 219:275–283
12.
go back to reference Romano L, Timpone F, Bruzelius F et al (2002) Analytical results in transient brush tyre models: theory for large camber angles and classic solutions with limited friction. Meccanica 57:165–191MathSciNetCrossRefMATH Romano L, Timpone F, Bruzelius F et al (2002) Analytical results in transient brush tyre models: theory for large camber angles and classic solutions with limited friction. Meccanica 57:165–191MathSciNetCrossRefMATH
13.
go back to reference Romano L (2022) Advanced brush tyre modelling. Springer Briefs. Springer, Berlin, pp 57–85CrossRef Romano L (2022) Advanced brush tyre modelling. Springer Briefs. Springer, Berlin, pp 57–85CrossRef
14.
go back to reference Doria A, Taraborrelli L (2016) Out-of-plane vibrations and relaxation length of the tyres for single-track vehicles. Proc Inst Mech Eng Part D: J Automob Eng 230:609–622CrossRef Doria A, Taraborrelli L (2016) Out-of-plane vibrations and relaxation length of the tyres for single-track vehicles. Proc Inst Mech Eng Part D: J Automob Eng 230:609–622CrossRef
15.
go back to reference Shaju A, Pandey AK (2022) Modelling transient response using PAC 2002-based tyre model. Veh Syst Dyn 60:20–46CrossRef Shaju A, Pandey AK (2022) Modelling transient response using PAC 2002-based tyre model. Veh Syst Dyn 60:20–46CrossRef
16.
go back to reference Besselink IJM, Schmeitz AJC, Pacejka HB (2010) An improved magic formula/ SWIFT tyre model that can handle inflflation pressure changes. Veh Syst Dyn 48:337–352CrossRef Besselink IJM, Schmeitz AJC, Pacejka HB (2010) An improved magic formula/ SWIFT tyre model that can handle inflflation pressure changes. Veh Syst Dyn 48:337–352CrossRef
17.
go back to reference Schmeitz AJC, Alirezaei M (2016) Analysis of wheel speed vibrations for road friction classification. Veh Syst Dyn 54:492–509CrossRef Schmeitz AJC, Alirezaei M (2016) Analysis of wheel speed vibrations for road friction classification. Veh Syst Dyn 54:492–509CrossRef
18.
go back to reference Kuiper E, Van Oosten JJM (2007) The PAC2002 advanced handling tire model. Veh Syst Dyn 45:153–167CrossRef Kuiper E, Van Oosten JJM (2007) The PAC2002 advanced handling tire model. Veh Syst Dyn 45:153–167CrossRef
19.
go back to reference Hirschberg W, Rill G, Weinfurter H (2007) Tire model TMeasy. Veh Syst Dyn 45:101–119CrossRef Hirschberg W, Rill G, Weinfurter H (2007) Tire model TMeasy. Veh Syst Dyn 45:101–119CrossRef
20.
go back to reference Chen Ping Xu, Nan BF et al (2017) Tire transient cornering characteristics on mu-step road. J Mech Eng 53:143–151CrossRef Chen Ping Xu, Nan BF et al (2017) Tire transient cornering characteristics on mu-step road. J Mech Eng 53:143–151CrossRef
22.
go back to reference Khaleghian S, Ghasemalizadeh O, Taheri S et al (2019) A combination of intelligent tire and vehicle dynamic based algorithm to estimate the tire-road friction. SAE Int J Passeng Cars Mech Syst 12:81–97CrossRef Khaleghian S, Ghasemalizadeh O, Taheri S et al (2019) A combination of intelligent tire and vehicle dynamic based algorithm to estimate the tire-road friction. SAE Int J Passeng Cars Mech Syst 12:81–97CrossRef
23.
go back to reference Sharifzadeh M, Senatore A, Farnam A et al (2019) A real-time approach to robust identification of tyre-road friction characteristics on mixed-µ roads. Veh Syst Dyn 57:1338–1362CrossRef Sharifzadeh M, Senatore A, Farnam A et al (2019) A real-time approach to robust identification of tyre-road friction characteristics on mixed-µ roads. Veh Syst Dyn 57:1338–1362CrossRef
24.
go back to reference Zhang W, Guo XX (2015) An ABS control strategy for commercial vehicle. IEEE ASME Trans Mechation 20:384–392CrossRef Zhang W, Guo XX (2015) An ABS control strategy for commercial vehicle. IEEE ASME Trans Mechation 20:384–392CrossRef
25.
go back to reference Hoseinnezhad R, Bab-Hadiashar A (2011) Efficient antilock braking by direct maximization of tire-road frictions. IEEE Trans Ind Electron 58:3593–3600CrossRef Hoseinnezhad R, Bab-Hadiashar A (2011) Efficient antilock braking by direct maximization of tire-road frictions. IEEE Trans Ind Electron 58:3593–3600CrossRef
26.
go back to reference Kang MG, Li L, Li HZ et al (2012) Coordinated vehicle traction control based on engine torque and brake pressure under complicated road conditions. Veh Syst Dyn 50:1473–1494CrossRef Kang MG, Li L, Li HZ et al (2012) Coordinated vehicle traction control based on engine torque and brake pressure under complicated road conditions. Veh Syst Dyn 50:1473–1494CrossRef
27.
go back to reference Canudas-de-Wit C, Tsiotras P, Velenis E et al (2003) Dynamic friction models for road/tire longitudinal interaction. Veh Syst Dyn 39:189–226CrossRef Canudas-de-Wit C, Tsiotras P, Velenis E et al (2003) Dynamic friction models for road/tire longitudinal interaction. Veh Syst Dyn 39:189–226CrossRef
28.
go back to reference Tsiotras P, Velenis E, Sorine M (2004) A LuGre tire friction model with exact aggregate dynamics. Veh Syst Dyn 42:195–210CrossRef Tsiotras P, Velenis E, Sorine M (2004) A LuGre tire friction model with exact aggregate dynamics. Veh Syst Dyn 42:195–210CrossRef
29.
go back to reference Velenis E, Tsiotras P, Canudas-de-Wit C (2005) Dynamic tyre friction models for combined longitudinal and lateral vehicle motion. Veh Syst Dyn 43:3–29CrossRef Velenis E, Tsiotras P, Canudas-de-Wit C (2005) Dynamic tyre friction models for combined longitudinal and lateral vehicle motion. Veh Syst Dyn 43:3–29CrossRef
30.
go back to reference Deur J (2001) Modeling and analysis of longitudinal tire dynamics based on the Lugre friction model. In: IFAC Proceedings vol 34, pp 91–96 Deur J (2001) Modeling and analysis of longitudinal tire dynamics based on the Lugre friction model. In: IFAC Proceedings vol 34, pp 91–96
31.
go back to reference Deur J, Asgari J, Hrovat D (2004) A 3D brush-type dynamic tire friction model. Veh Syst Dyn 42:133–173CrossRef Deur J, Asgari J, Hrovat D (2004) A 3D brush-type dynamic tire friction model. Veh Syst Dyn 42:133–173CrossRef
32.
go back to reference Deur J, Ivanovic V, Troulis M et al (2005) Extensions of the LuGre tyre friction model related to variable slip speed along the contact patch length. Veh Syst Dyn 43:508–524CrossRef Deur J, Ivanovic V, Troulis M et al (2005) Extensions of the LuGre tyre friction model related to variable slip speed along the contact patch length. Veh Syst Dyn 43:508–524CrossRef
33.
go back to reference Kritayakirana K, Gerdes JC (2012) Using the centre of percussion to design a steering controller for an autonomous race car. Veh Syst Dyn 50:33–51CrossRef Kritayakirana K, Gerdes JC (2012) Using the centre of percussion to design a steering controller for an autonomous race car. Veh Syst Dyn 50:33–51CrossRef
Metadata
Title
Transient lateral dynamic behavior of tire on μ-step road
Authors
Shengyong Ye
Jianwei Lu
Yingjie Zhu
Lei Shi
Hangyu Lu
Bofu Wu
Ping Jiang
Publication date
21-11-2023
Publisher
Springer Netherlands
Published in
Meccanica / Issue 12/2023
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-023-01730-w

Other articles of this Issue 12/2023

Meccanica 12/2023 Go to the issue

Premium Partners