Singular Value Decomposition Based Optimisation of Design Parameters of a Gearbox

Singular value decomposition based optimisation of geometric design parameters of a 5-speed gearbox is studied. During the optimisation, a four-degree-of freedom torsional vibration model of the pinion gear-wheel gear system is obtained and the minimum singular value of the transfer matrix is considered as the objective functions. The computational cost of the associated singular value problems is quite low for the objective function, because it is only necessary to compute the largest and smallest singular values (μmax and μmin) that can be achieved by using selective eigenvalue solvers; the other singular values are not needed. The design parameters are optimised under several constraints that include bending stress, contact stress and constant distance between gear centres. Thus, by optimising the geometric parameters of the gearbox such as, the module, number of teeth and face width it is possible to obtain a light-weight-gearbox structure. It is concluded that the all optimised geometric design parameters also satisfy all constraints.

Authors:

• Mehmet Bozca

Keywords:

• Singular value
• optimisation
• gearbox
• torsional vibration.

References:

[1] Saeed Ebrahimi, Peter Eberhard, “Rigid-elastic Modelling of meshing
gear wheels in multi-body systems”, Multi-body System Dynamics vol.
16, 2006.
[2] Kahraman, R. Singh, “Interactions between time varying mesh stiffness
and clearance nonlinearities in a geared system”, Journal of Sound and
Vibration vol. 146, 1990, pp. 135–156.
[3] M. Bozca, “Torsional vibration model based optimisation of gearbox
geometric design parameters to reduce rattle noise in an automotive
transmission”, Mechanism and Machine Theory vol. 45, 2010,pp. 1583–
1598.
[4] R.A. Horn, C.R. Johnson, Topics in Matrix Analysis, Cambridge
University Press, Cambridge, 1995.
[5] Roloff, Matek, Maschinenelemente, Vieweg & Sohn Verlag/Fachverlage
GmbH, Wiesbaden, 2005.
[6] H. Naunheimer, B. Bersche, J. Ryborz, W. Novak, Automotive
Transmissions, Springer, 2011.
[7] ISO 6336–1: calculation of load capacity of spur and helical gears, part
1:basic principle, introduction and general influence factors.