American Institute of Mathematical Sciences

Advanced
2003, 2003(Special): 610-617. doi: 10.3934/proc.2003.2003.610

Dynamics of torque-speed profiles for electric vehicles and nonlinear models based on differential-algebraic equations

Roderick V.N. Melnik 1, , Ningning Song 1, and  Per Sandholdt 2,

1. 

University of Southern Denmark, MCI, Faculty of Science and Engineering, Sonderborg, DK-6400, Denmark, Denmark
2. 

Sauer-Danfoss A/S, Nordborg, Denmark

Received  September 2002 Revised  March 2003 Published  April 2003

The so-called $\mu - \lambda$ curves, where $\lambda$ is the slip ratio and $\mu$ is the normalised traction force or the friction index, are nonlinear functions of the velocity of the vehicle and the wheel rotational velocity. Despite their predominant use in the literature, linear approximations of such curves may fail to predict correctly key characteristics of vehicle performance efficiency such as torque-speed profiles. Although attempts to model these characteristics in the context of slip phenomena have been made before, to our best knowledge a general model with respect to the vehicle velocity, the wheel rotating velocity, the slip ratio, the traction force, and the torque, has never been formulated and solved as a coupled nonlinear problem based on a system of differential-algebraic equations arising naturally in this context. In this paper, such a model is formulated, solved numerically, and some results of numerical simulation of driving an electric vehicle on different surface conditions are presented.
Keywords: differential-algebraic models., Nonlinear slip phenomena.
Mathematics Subject Classification: 37M05,65P40,65L80.
Citation: Roderick V.N. Melnik, Ningning Song, Per Sandholdt. Dynamics of torque-speed profiles for electric vehicles and nonlinear models based on differential-algebraic equations. Conference Publications, 2003, 2003 (Special) : 610-617. doi: 10.3934/proc.2003.2003.610
[1]

Yingjie Bi, Siyu Liu, Yong Li. Periodic solutions of differential-algebraic equations. Discrete and Continuous Dynamical Systems - B, 2020, 25 (4) : 1383-1395. doi: 10.3934/dcdsb.2019232
[2]

Vu Hoang Linh, Volker Mehrmann. Spectral analysis for linear differential-algebraic equations. Conference Publications, 2011, 2011 (Special) : 991-1000. doi: 10.3934/proc.2011.2011.991
[3]

Jason R. Scott, Stephen Campbell. Auxiliary signal design for failure detection in differential-algebraic equations. Numerical Algebra, Control and Optimization, 2014, 4 (2) : 151-179. doi: 10.3934/naco.2014.4.151
[4]

Kerioui Nadjah, Abdelouahab Mohammed Salah. Stability and Hopf bifurcation of the coexistence equilibrium for a differential-algebraic biological economic system with predator harvesting. Electronic Research Archive, 2021, 29 (1) : 1641-1660. doi: 10.3934/era.2020084
[5]

Sergiy Zhuk. Inverse problems for linear ill-posed differential-algebraic equations with uncertain parameters. Conference Publications, 2011, 2011 (Special) : 1467-1476. doi: 10.3934/proc.2011.2011.1467
[6]

Anna Marciniak-Czochra, Andro Mikelić. A nonlinear effective slip interface law for transport phenomena between a fracture flow and a porous medium. Discrete and Continuous Dynamical Systems - S, 2014, 7 (5) : 1065-1077. doi: 10.3934/dcdss.2014.7.1065
[7]

Heikki Haario, Leonid Kalachev, Marko Laine. Reduction and identification of dynamic models. Simple example: Generic receptor model. Discrete and Continuous Dynamical Systems - B, 2013, 18 (2) : 417-435. doi: 10.3934/dcdsb.2013.18.417
[8]

Jaume Llibre, Claudia Valls. Algebraic limit cycles for quadratic polynomial differential systems. Discrete and Continuous Dynamical Systems - B, 2018, 23 (6) : 2475-2485. doi: 10.3934/dcdsb.2018070
[9]

Claudio Giorgi. Phase-field models for transition phenomena in materials with hysteresis. Discrete and Continuous Dynamical Systems - S, 2015, 8 (4) : 693-722. doi: 10.3934/dcdss.2015.8.693
[10]

Alfonso Ruiz Herrera. Paradoxical phenomena and chaotic dynamics in epidemic models subject to vaccination. Communications on Pure and Applied Analysis, 2020, 19 (5) : 2533-2548. doi: 10.3934/cpaa.2020111
[11]

Sergio Albeverio, Sonia Mazzucchi. Infinite dimensional integrals and partial differential equations for stochastic and quantum phenomena. Journal of Geometric Mechanics, 2019, 11 (2) : 123-137. doi: 10.3934/jgm.2019006
[12]

Aaron W. Brown. Nonexpanding attractors: Conjugacy to algebraic models and classification in 3-manifolds. Journal of Modern Dynamics, 2010, 4 (3) : 517-548. doi: 10.3934/jmd.2010.4.517
[13]

Jędrzej Śniatycki. Integral curves of derivations on locally semi-algebraic differential spaces. Conference Publications, 2003, 2003 (Special) : 827-833. doi: 10.3934/proc.2003.2003.827
[14]

J. M. Cushing. Nonlinear semelparous Leslie models. Mathematical Biosciences & Engineering, 2006, 3 (1) : 17-36. doi: 10.3934/mbe.2006.3.17
[15]

James M. Hyman, Jia Li. Differential susceptibility and infectivity epidemic models. Mathematical Biosciences & Engineering, 2006, 3 (1) : 89-100. doi: 10.3934/mbe.2006.3.89
[16]

Xin Liu. Compressible viscous flows in a symmetric domain with complete slip boundary: The nonlinear stability of uniformly rotating states with small angular velocities. Communications on Pure and Applied Analysis, 2019, 18 (2) : 751-794. doi: 10.3934/cpaa.2019037
[17]

Zhiqing Liu, Zhong Bo Fang. Blow-up phenomena for a nonlocal quasilinear parabolic equation with time-dependent coefficients under nonlinear boundary flux. Discrete and Continuous Dynamical Systems - B, 2016, 21 (10) : 3619-3635. doi: 10.3934/dcdsb.2016113
[18]

Michael E. Filippakis, Donal O'Regan, Nikolaos S. Papageorgiou. Positive solutions and bifurcation phenomena for nonlinear elliptic equations of logistic type: The superdiffusive case. Communications on Pure and Applied Analysis, 2010, 9 (6) : 1507-1527. doi: 10.3934/cpaa.2010.9.1507
[19]

Masatoshi Shiino, Keiji Okumura. Control of attractors in nonlinear dynamical systems using external noise: Effects of noise on synchronization phenomena. Conference Publications, 2013, 2013 (special) : 685-694. doi: 10.3934/proc.2013.2013.685
[20]

Monica Marras, Stella Vernier-Piro, Giuseppe Viglialoro. Blow-up phenomena for nonlinear pseudo-parabolic equations with gradient term. Discrete and Continuous Dynamical Systems - B, 2017, 22 (6) : 2291-2300. doi: 10.3934/dcdsb.2017096

 Impact Factor: 

Tools

Metrics

  • PDF downloads (48)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy