Conference article

Modelling and Simulating the Efficiency and Elasticity of Gearboxes

F. L. J. van der Lunden
German Aerospace Center (DLR), Institute of Robotics and Mechatronics, Oberpfaffenhofen, Germany

P. H. Vazques de Souza Silva
German Aerospace Center (DLR), Institute of Robotics and Mechatronics, Oberpfaffenhofen, Germany

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Published in: Proceedings of the 7th International Modelica Conference; Como; Italy; 20-22 September 2009

Linköping Electronic Conference Proceedings 43:29, s. 270-277

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Published: 2009-12-29

ISBN: 978-91-7393-513-5

ISSN: 1650-3686 (print), 1650-3740 (online)


Two elastic gearbox models with friction losses are presented; a 1-Degree Of Freedom (DOF) and a 3-DOF model.

The presented models have advantages over the existing lossy gear model of the Modelica Standard Library when gear vibrations are of interest. Care has been taken that also in the case of gear locking; the elasticity effects are treated adequately.

In addition to external excitations; it is now also possible to model internal excitations of the gearbox caused by the varying stiffness and/ or damping. This varying stiffness can be specified by the user for each gear wheel. This feature can for instance be used to model tooth interaction or broken gears.

Furthermore; the 3-DOF elastic model can simulate the elasticity of the support bearings in the load direction; which is impossible in the standard lossy gear model.


Elastic Gearbox; Efficiency; Gearbox


[1] I. Howard; S. Jia; and J. Wang. The dynamic modelling of a spur gear in mesh including friction and a crack. Mechanical Systems and Signal Processing; 15:831–853; 2001. doi: 10.1006/mssp.2001.1414.

[2] A. Kahraman and R. Singh. Interactions between time-varying mesh stiffness and clearance nonlinearities in a geared system. Journal of Sound and Vibration; 142:49–75; 1990. doi: 10.1016/0022-460X(90)90582-K.

[3] C. Kar and A. Mohanty. Determination of time-varying contact length; friction force; torque and forces at the bearings in a helical gear system. Journal of Sound and Vibration; 309:307–319 2008. doi: 10.1016/j.jsv.2006.09.031.

[4] C. J. Li; H. Lee; and S. H. Choi. Estimating size of gear tooth root crack using embedded modelling. Mechanical Systems and Signal Processing; 16:841–852; 2002. doi: 10.1006/mssp.2001.1452.

[5] H. Nevzat; Özgüven; and D. Houser. Dynamic analysis of high speed gear by using loaded static transmission error. Journal of Sound and Vibration; 125:71–83; 1988. doi: 10.1016/0022-460X(88)90416-6.

[6] M. Otter; H. Elmqvist; and S. E. Mattsson. Hybrid modeling in modelica based on the synchronous data flow principle. In CACSD; Hawaii; USA; August 1999.

[7] C. Pelchen; C. Schweiger; and M. Otter. Modeling and simulating the efficiency of gearboxes and of planetary gearboxes. In 2nd International Modelica Conference; pages 257–266; 2002.

[8] R. Sing and D. R. Houser. Non-Linear Dynamic Analysis of Geared Systems. PhD thesis; Ohio State University; February 1990.

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