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Research Papers: Elastohydrodynamic Lubrication

Efficient Simulation of Gear Contacts Including Transient Elastohydrodynamic Effects

[+] Author and Article Information
Peter Fietkau

e-mail: Peter.Fietkau@ima.uni-stuttgart.de

Bernd Bertsche

Institute of Machine Components,
University of Stuttgart,
Pfaffenwaldring 9,
Stuttgart, 70569, Germany

Contributed by the Tribology Division of ASME for publication in the Journal of Tribology. Manuscript received October 8, 2012; final manuscript received March 2, 2013; published online May 2, 2013. Assoc. Editor: Dong Zhu.

J. Tribol 135(3), 031502 (May 02, 2013) (9 pages) Paper No: TRIB-12-1169; doi: 10.1115/1.4024212 History: Received October 08, 2012; Revised March 02, 2013

This paper describes an efficient transient elastohydrodynamic simulation method for gear contacts. The model uses oil films and elastic deformations directly in the multibody simulation, and is based on the Reynolds equation including squeeze and wedge terms as well as an elastic half-space. Two transient solutions to this problem, an analytical and a numerical one, were developed. The analytical solution is accomplished using assumptions for the gap shape and the pressure in the middle of the gap. The numerical problem is solved using multilevel multi-integration algorithms. With this approach, tooth impacts during gear rattling as well as highly loaded power-transmitting gear contacts can be investigated and lubrication conditions like gap heights or type of friction may be determined. The method was implemented in the multibody simulation environment SIMPACK. Therefore it is easy to transfer the developed element to other models and use it for a multitude of different engineering problems. A detailed three-dimensional elastic multibody model of an experimental transmission is used to validate the developed method. Important values of the gear contact like normal and tangential forces, proportion of dry friction, and minimum gap heights are calculated and studied for different conditions. In addition, pressure distributions on tooth flanks as well as gap forms are determined based on the numerical solution method. Finally, the simulation approach is validated with measurements and shows good consistency. The simulation model is therefore capable of predicting transient gear contact under different operating conditions such as load vibrations or gear rattling. Simulations of complete transmissions are possible and therefore a direct determination of transmission vibration behavior and structure-borne noise as well as of forces and lubrication conditions can be done.

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Figures

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Fig. 1

Gearwheel model with circumferentially moveable teeth

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Fig. 2

Flow chart of gear pair simulation

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Fig. 3

Dimensions of fluid gap between meshing teeth

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Fig. 4

Different grids used by the multigrid method for pressure and deformation calculation

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Fig. 5

Stick diagram and multibody model of the experimental transmission

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Fig. 6

Total normal force, dry contact normal force, total tangential force, and minimum gap height at a single tooth flank for different viscosities

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Fig. 7

Fluid pressure, dry contact pressure, and gap height at a single tooth flank in the middle of the mesh for different viscosities

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Fig. 8

Total normal force, dry contact normal force, total tangential force, and minimum gap height at a single tooth flank different viscosities

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Fig. 9

Comparison of measurement and simulation for a loaded gear pair

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Fig. 10

Comparison of measurement and simulation for a rattling gear pair and different backlashes

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Fig. 11

Comparison of frequency spectra of measured and simulated housing acceleration for a rattling gear pair

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