Research Papers

Calibration of an Articulated Vehicle Model and Analysis of Friction Model in the Connection Between Two Vehicle Units

[+] Author and Article Information
Adamiec-Wójcik Iwona

University of Bielsko-Biala,
Willowa 2,
Bielsko-Biała 43-309, Poland
e-mail: i.adamiec@ath.bielsko.pl

Drąg Łukasz

University of Bielsko-Biala,
Willowa 2,
Bielsko-Biała 43-309, Poland
e-mail: ldrag@ath.bielsko.pl

Grzegożek Witold

Cracow University of Technology,
Warszawska 24,
Kraków 31-155, Poland
e-mail: witek@mech.pk.edu.pl

Wojciech Stanisław

University of Bielsko-Biala,
Willowa 2,
Bielsko-Biała 43-309, Poland
e-mail: swojciech@ath.bielsko.pl

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 10, 2018; final manuscript received January 13, 2019; published online March 14, 2019. Assoc. Editor: Corina Sandu.

J. Comput. Nonlinear Dynam 14(5), 051008 (Mar 14, 2019) (12 pages) Paper No: CND-18-1397; doi: 10.1115/1.4042638 History: Received September 10, 2018; Revised January 13, 2019

This paper describes models of dynamics for articulated vehicles (tractor with a semitrailer and a tractor with a trailer). The models are obtained by using joint coordinates and homogenous transformations. Yawing velocities of the vehicle units have been measured during a sharp turn maneuver. The results of experimental measurements are then used to calibrate the mathematical models, which means the parameters of tires for the Dugoff–Uffelman model are chosen in such a way that the results of calculations and measurements are compatible. In order to solve this problem, an optimization method is used. Satisfactory results have been achieved and they are presented in this paper. Further, the model calibrated is used to analyze how the friction in the connections between the tractor and semitrailer, as well as between the dolly and the trailer, influences the motion of the vehicle.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.


Langwieder, K. , Gwehenberger, J. , Hummel, T. , and Bende, J. , 2003, “ Benefit Potential of ESP and Real Accident Situations, Involving Car and Trucks,” 18th International Technical Conference on the Enhanced Safety of Vehicles, Nagoya, Japan, May 19–22, p. 10. https://udv.de/en/publications/other-publications/benefit-potential-esp-real-accident-situations-involving-cars-and-trucks-0305
Regulation (EC) No. 661/2009, 2009, “Official Journal of the European Union L200,” Vol. 52, Aberdeen, UK, Report No. L:2009:200:TOC.
Andrzejewski, R. , and Awrejcewicz, J. , 2005, Nonlinear Dynamics of a Wheeled Vehicle, Springer, Cham, Switzerland.
Fencher, P. S. , Winkler, C. , Ervin, R. , and Zhang, H. , 1998, “ Using Braking to Control Lateral Motion Full Trailers,” Veh. Syst. Dyn., 29(Suppl. 1), pp. 462–468. [CrossRef]
van den Molengraft-Luiten, M. F. J. , Besselink, I. J. , Verschuren, R. M. A. F. , and Nijmeijer, H. , 2012, “ Analysis of the Lateral Theoretical Dynamic Behaviour of Articulated Commercial Vehicles,” Veh. Syst. Dyn., 50(Suppl. 1), pp. 169–189. [CrossRef]
Bolzern, P. , DeSantis, R. M. , and Locatelli, A. , 2001, “ An Input-Output Linearization Approach to the Control of an n-Body Articulated Vehicle,” ASME J. Dyn. Syst. Meas. Control, 123(3), pp. 309–316. [CrossRef]
Wu, D.-H. , 2001, “ A Theoretical Study of the Yaw/Roll Motions of a Multiple Steering Articulated Vehicle,” J. Mech. Eng., 215(12), pp. 1257–1265.
Kaneko, T. , and Kageyama, I. , 2003, “ A Study on the Braking Stability of Articulated Heavy Vehicles,” JSAE Rev., 24(2), pp. 157–164. [CrossRef]
Hussain, K. , Stein, W. , and Day, A. J. , 2005, “ Modelling Commercial Vehicle Handling and Rolling Stability,” Proc. Inst. Mech. Eng. Part K, 219, pp. 357–369. [CrossRef]
Bouteldja, M. , and Cerezo, V. , 2011, “ Jackknifing Warning for Articulated Vehicles Based on a Detection and Prediction System,” Third International Conference on Road Safety and Simulation, Indianapolis, IN, Sept. 14–16.
Yang, X. , Song, J. , and Gao, J. , 2015, “ Fuzzy Logic Based Control of the Lateral Stability of Tractor Semitrailer Vehicle,” Math. Probl. Eng., 2015, p. 16.
Szczotka, M. , and Wojciech, S. , 2008, “ Application of Joint Coordinates and Homogenous Transformations to Modeling of Vehicle Dynamics,” Nonlinear Dyn., 52(4), pp. 377–393. [CrossRef]
Adamiec, I. , 2009, Modelling Dynamics of Multibody Systems. Use of Homogenous Transformations and Joint Coordinates, Lambert Academic Publishing, Köln.
Dugoff, H. , Fancher, P. S. , and Segel, L. , 1970, “ An Analysis of Tire Traction Properties and Their Influence on Vehicle Dynamics Performance,” SAE Paper No. 700377.
Pacejka, H. B. , and Bakker, E. , 1993, “ The Magic Formula Tyre Model,” Int. J. Veh. Syst. Dyn., 21(Suppl. 001), pp. 1–18.
Lu, L.-Y. , Chung, L.-L. , Wu, L.-Y. , and Lin, G.-L. , 2006, “ Dynamic Analysis of Structures With Friction Devices Using Discrete-Time State-Space Formulation,” Comput. Struct., 84(15–16), pp. 1049–1071. [CrossRef]
Andersson, S. , Söderberg, A. , and Björklund, S. , 2007, “ Friction Models for Sliding Dry, Boundary and Mixed Lubricated Contacts,” Tribol. Int., 40(4), pp. 580–587. [CrossRef]
Marques, F. , Flores, P. , and Lankarani, H. M. , 2015, “ On the Frictional Contacts in Multibody System Dynamics,” ECCOMAS Thematic Conference on Multibody Dynamics, Barcelona, Spain, Sept. 1–3.
Muller, S. , Uchanski, M. , and Hedrick, K. , 2003, “ Estimation of the Maximum Tire-Road Friction Coefficient,” ASME J. Dyn. Syst. Meas. Control, 125, pp. 607–617. [CrossRef]
Toumi, M. , Bouazara, M. , and Richard, M. J. , 2013, “ Development of Analytical Model for Modular Tank Vehicle Carrying Liquid Cargo,” World J. Mech., 3(2), pp. 122–138. [CrossRef]
Craig, J. J. , 1988, Introduction to Robotics, Addison-Wesley, Boston, MA.
Hegazy, S. , Rahnejat, H. , and Hussain, K. , 2000, “ Multi-Body Dynamics in Full-Vehicle Handling Analysis Under Transient Manoeuvre,” Veh. Syst. Dyn., 34(1), pp. 1–24. [CrossRef]
Masoudi, R. , Uchida, T. , and McPhee, J. , 2015, “ Reduction of Multibody Dynamic Models in Automotive Systems Using the Proper Orthogonal Decomposition,” ASME J. Comput. Nonlinear Dyn., 10(3), p. 031007. [CrossRef]
Jung, H. K. , Kim, S. S. , Shim, J. S. , and Kim, C. W. , 2004, “ Development of Vehicle Dynamics Model for Real-Time ECU Evaluation System,” Advanced Vehicle Control (AVEC '04), Arnhem, The Netherlands, Aug. 23–27, pp. 555–560. http://citeseerx.ist.psu.edu/viewdoc/download?doi=
Adamiec-Wójcik, I. , Awrejcewicz, J. , Grzegożek, W. , and Wojciech, S. , 2015, “ Dynamics of Articulated Vehicles by Means of Multibody Methods,” Dynamical Systems: Mathematical and Numerical Approaches, J. Awrejcewicz , M. Kaźmierczak , J. Mrozowski , and P. Olejnik , eds., TU of Lodz, Łódź, Poland.
Nelder, J. A. , and Mead, R. , 1965, “ A Simplex Method for Function Minimization,” Comput. J., 7(4), pp. 308–313. [CrossRef]
Trelfall, D. C. , 1978, “ The Inclusion of Coulomb Friction in Mechanisms Programs With Particular Reference to DRAM Au Programme DRAM,” Mech. Mach. Theory, 13, pp. 475–483. [CrossRef]
Ambrósio, J. A. C. , 2003, “ Impact of Rigid and Flexible Multibody Systems: Deformation Description and Contact Model,” Virtual Nonlinear Multibody Syst., 103, pp. 57–81. [CrossRef]


Grahic Jump Location
Fig. 1

The tree structure of an articulated vehicle

Grahic Jump Location
Fig. 2

Models of units: (a) pth  unit in the chain, and (b) first unit

Grahic Jump Location
Fig. 3

Model of the connection between the wheel and the road and coordinate systems

Grahic Jump Location
Fig. 4

Model of a semitrailer

Grahic Jump Location
Fig. 5

A truck with a trailer as a system of four units

Grahic Jump Location
Fig. 6

Forces acting on wheel k of unit pXp′,Yp′,Zp′—coordinate system with axes parallel to Xp,Yp,ZpXk(p),Yk(p),Zk(p)—coordinate system assigned to wheel k of link pτk(p),nk(p)—normal and tangential directions of the wheel motion, fk(p)—coefficient of rolling friction

Grahic Jump Location
Fig. 7

Tractor with semitrailer (case A): (a) sensor for measurements of the steer angle of the steering wheel and (b) Correvit sensor for velocity measurements

Grahic Jump Location
Fig. 8

Tractor with trailer (case B): (a) general view and (b) Correvit sensor for velocity measurements

Grahic Jump Location
Fig. 9

Experimental measurements for case A: (a) steer angle of the front wheels, (b) yawing velocity of the tractor, and (c) yawing velocity of the semitrailer

Grahic Jump Location
Fig. 10

Experimental measurements for vehicle B: (a) steer angle of the front wheels, (b) yawing velocity of the tractor, and (c) yawing velocity of the semitrailer

Grahic Jump Location
Fig. 11

Yawing velocity of vehicle units of vehicle A

Grahic Jump Location
Fig. 12

Yawing velocities of vehicle units for vehicle B

Grahic Jump Location
Fig. 13

Forces and moments in joint connecting links m and m−1

Grahic Jump Location
Fig. 14

Course of the steer angle of the front wheels of the tractor for the maneuvers analyzed: (a) lane change, and (b) double lane change

Grahic Jump Location
Fig. 15

Course of the relative rotation in the fifth wheel for a semitrailer (vehicle A): (a) lane change and (b) double lane change

Grahic Jump Location
Fig. 16

Course of the relative rotation in the connection between the trailer and the dolly (vehicle B): (a) lane change and (b) double lane change

Grahic Jump Location
Fig. 17

Course of the friction moment in the fifth wheel for a semitrailer (vehicle A): (a) lane change and (b) double lane change

Grahic Jump Location
Fig. 18

Course of the friction moment in the connection between the trailer and the dolly (vehicle B): (a) lane change and (b) double lane change



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In