A new model for the dynamics of the mechanical part of a belt CVT (Continuously Variable Transmission) is presented. The model takes into account the mass of the belt, assuming it to be uniformly distributed over its length. The model can therefore be used as a benchmark for FE models, which focus on every element of the belt or chain, as well as for much simpler models that neglect the belt mass or imply significant simplifications in the respective kinematics. Although a nonholonomic system has to be investigated, the result is surprisingly simple, i.e., an algebraic solution is provided that is not much more complicated than the solutions derived with more stringent assumptions. The equations of motion derived here are especially suitable for use in control applications.

Issue Section:
Technical Briefs
Keywords:
mechanical engineering, finite element analysis
Topics:
Belts, Chain, Equations of motion, Kinematics, Drive chain
1.
Srnik, J., and Pfeiffer, F., 1996, “Dynamik von CVT-Kettengetrieben: Modellbildung und -verifikation,” in Schwingungen in Maschinen, Fahrzeugen und Anlagen, VDI-Berichte 1285, pp. 441–455. VDI-Verlag GmbH, Du¨sseldorf.
2.
Srnik
,
J.
, and
Pfeiffer
,
F.
,
1999
, “
Dynamics of CVT chain drives
,”
Int. J. Veh. Des.
,
22
(
1/2
), pp.
54
–
72
.
3.
Micklem
,
J. D.
,
Longmore
,
D. K.
, and
Burrows
,
C. R.
,
1994
, “
Modelling of the steel pushing V-belt continuously variable transmission
,”
J. Mech. Eng. Sci.
,
208
(
C1
), pp.
13
–
27
.
4.
Luh, J., 1994, “Modell eines stufenlosen Umschlingungsgetriebes im Triebstrang,” Berechnung im Automobilbau, VDI-Berichte 1153, pp. 625–639. VDI-Verlag GmbH, Du¨sseldorf.
5.
Shafai, E., Simons, M., Neff, U., and Geering, H. P., 1995, “Model of a Continuously Variable Transmission,” Proceedings of the 1st IFAC Workshop on Advances in Automotive Control, pp. 99–107.
6.
Gesenhaus, R., 2000, “Audi Multitronic: The New Generation of Automatic Transmission,” Proceedings of the 1st Ricardo International Conference, Vehicle Systems Integration-the Way Ahead, Brighton, UK.
7.
Chen
,
C.-K.
, and
Freudenstein
,
F.
,
1998
, “
Toward a More Exact Kinematics of Roller Chain Drives
,”
ASME Journal of Mechanisms, Transmissions and Automation in Design
,
110
(
1
), pp.
269
–
275
.
8.
Sauer, G., 1996, Grundlagen und Betriebsverhalten eines Zugketten-Umschlingungsgetriebes, Fortschritt-Berichte VDI, Reihe 12, Nr. 293. VDI-Verlag GmbH.
9.
Hiller, M., 1983, Mechanische Systeme—Eine Einfu¨hrung in die analytische Mechanik und Systemdynamik, Springer-Verlag.
10.
Naunheimer, H., 1995, “Beitrag zur Entwicklung von Stufenlosgetrieben mittels Fahrsimulation,” Dissertation, Universita¨t Stuttgart, Germany.
11.
Pfiffner, R., 2001, “Optimal Operation of CVT-Based Powertrains,” Dissertation no. 14136, Swiss Federal Institute of Technology, Zu¨rich, Switzerland.
12.
Pfiffner
,
R.
, and
Guzzella
,
L.
,
2001
, “
Optimal Operation of CVT-Based Powertrains
,”
Int. J. Robust Nonlinear Control
,
11
(
11
), pp.
1003
–
1021
.
Copyright © 2002
 by ASME
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