Simulation of Elastic Gears with Non-Standard Flank Profiles

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There exist cases where precise simulations of contact forces do not allow modeling the gears as rigid bodies but a fully elastic description is needed. In this paper, a modally reduced elastic multibody system including gear contact based on a floating frame of reference formulation is proposed that allows very precise simulations of fully elastic gears with appropriately meshed gears in reasonable time even for many rotations. One advantage of this approach is that there is no assumption about the geometry of the gears and, therefore, it allows precise investigations of contacts between gears with almost arbitrary non-standard tooth geometries including flank profile corrections.

This study presents simulation results that show how this modal approach can be used to efficiently investigate the interaction between elastic deformations and flank profile corrections as well as their influence on the contact forces. It is shown that the elastic approach is able to describe important phenomena like early addendum contact for insufficiently corrected profiles in dependence of the transmitted load. Furthermore, it is shown how this approach can be used for precise and efficient simulations of beveloid gears.

[1] Bauchau O.A.: Flexible Multibody Dynamics. Dordrecht: Springer, 2011.

[2] Ziegler P., Eberhard P.: Simulative and Experimental Investigation of Impacts on Gear Wheels. Computer Methods in Applied Mechanics and Engineering, Vol. 197, No. 51-52, pp. 4653-4662, 2008.

[3] Ziegler P., Eberhard P.: Investigations of Gears Using an Elastic Multibody Model with Contact. Multibody Dynamics: Computational Methods and Applications, W. Blajer, K. Arczewski, J. Fraczek, and M. Wojtyra (eds.), 2010.

[4] Ziegler P.: Dynamische Simulation von Zahnradkontakten mit elastischen Modellen. Dissertation, Schiften aus dem Institut f¨ur Technische und Numerische Mechanik der Universit¨at Stuttgart, Band 23. Shaker Verlag, Aachen, 2012.

[5] Tamarozzi T., Ziegler P., Eberhard P., Desmet W.: On the Applicability of Static Modes Switching in Gear Contact. The 2nd Joint International Conference on Multibody Dynamics, May 29-June 1, 2012, Stuttgart, Germany.

[6] Sherif K., Witteveen W., Mayrhofer K.: Quasi-Static Consideration of High-Frequency Modes for More Efficient Flexible Multibody Simulations. Acta Mech 223, 1285-1305, Springer- Verlag, 2012.

[7] Wang S.P., Nakamachi E.: The Inside-Outside Contact Search Algorithm for Finite Element Analysis. International Journal for Numerical Methods in Engineering, Vol. 40, pp. 3665-3685, 1996.

[8] Chen Y.-C., Liu C.-C.: Contact Stress Analysis of Concave Conical Involute Gear Pairs with Non-Parallel Axes. Finite Elements in Analysis and Design, Vol. 47, pp. 443-452, 2011.

[9] Liu C.-C., Tsay C.-B.: Mathematical Models and Contact Simulations of Concave Beveloid Gears. Journal of Mechanical Design, Vol. 124, pp. 753-760, 2002.

[10] Liu C.-C., Chen Y.-C., Lin S.-H.: Contact Stress Analysis of Straight Concave Conical Involute Gear Pairs with Small Intersected Angles. Proceedings of the International MultiConference of Engineers and Computer Scientists 2010, Vol. III, IMECS, Hong Kong, March 17-19, 2010.

[11] Liu C.-C., Tsay C.-B.: Contact Characteristics of Beveloid Gears. Mechanism and Machine Theory, Vol. 37, pp. 333-350, 2002.

[12] Markovic K., Franulovic M.: Contact Stresses in Gear Teeth Due to Tip Relief Profile Modification, Engineering Review, Vol. 31-1, pp. 19-26, 2011.

[13] Brecher C., R¨othlingsh¨ofer T., Gorgels C.: Manufacturing Simulation of Beveloid Gears for The Use in a General Tooth Contact Analysis Software. Production Engineering Research and Development, Vol. 3, pp. 103-109, 2009.

[14] Zhu C., Song C., Lim T.-C., Vijayakar S.: Geometry Design and Tooth Contact Analysis Crossed Beveloid Gears for Marine Transmissions. Chinese Journal of Mechanical Engineering, Vol. 24, No. 5, 2011.

[15] Shabana A.A.: Dynamics of Multibody Systems. University Press, Cambridge, 1998.

[16] Schwertassek R., Wallrapp O.: Dynamik flexibler Mehrk¨orpersysteme (in German). Vieweg, Braunschweig, 1999.

[17] Lehner M., Eberhard P.: A Two-Step Approach for Model Reduction in Flexible Multibody Dynamics. (Special Issue Realtime, Ed. J. Cuadrado). Multibody System Dynamics, Vol. 17, No. 2-3, pp. 157-176, 2007.

[18] Eberhard P., Fehr J., Mathuni S.: Influence of Model Reduction Techniques on the Impact Force Calculation of Two Flexible Bodies. PAMM, Vol. 9, pp. 111-112, 2009.

[19] Fehr J., Eberhard P.: Simulation Process of Flexible Multibody Systems with Advanced Model Order Reduction Techniques. Multibody System Dynamics, Vol. 25, No. 3, pp. 313-334, 2011.

Archive of Mechanical Engineering

The Journal of Committee on Machine Building of Polish Academy of Sciences

Journal Information

CiteScore 2016: 0.44

SCImago Journal Rank (SJR) 2016: 0.162
Source Normalized Impact per Paper (SNIP) 2016: 0.459


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