Research Papers

Robust Optimization of Cylindrical Gear Tooth Surface Modifications Within Ranges of Torque and Misalignments

[+] Author and Article Information
Alessio Artoni

e-mail: alessio.artoni@ing.unipi.it

Massimo Guiggiani

e-mail: massimo.guiggiani@ing.unipi.it
Dipartimento di Ingegneria Civile e Industriale,
University of Pisa,
Largo Lucio Lazzarino 2, Pisa 56122, Italy

Ahmet Kahraman

e-mail: kahraman.1@osu.edu

Jonny Harianto

e-mail: harianto.1@osu.edu
Gear and Power Transmission
Research Laboratory,
Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
201 West 19th Avenue,
Columbus, OH 43210

m is defined here as a nondimensional number, being expressed as the net displacement at one side of the tooth divided by the face width (slope).

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 31, 2013; final manuscript received July 23, 2013; published online September 18, 2013. Assoc. Editor: Matthew B Parkinson.

J. Mech. Des 135(12), 121005 (Sep 18, 2013) (9 pages) Paper No: MD-13-1045; doi: 10.1115/1.4025196 History: Received January 31, 2013; Revised July 23, 2013

Tooth surface modifications are small, micron-level intentional deviations from perfect involute geometries of spur and helical gears. Such modifications are aimed at improving contact pressure distribution, while minimizing the motion transmission error to reduce noise excitations. In actual practice, optimal modification requirements vary with the operating torque level, misalignments, and manufacturing variance. However, most gear literature has been concerned with determining optimal flank form modifications at a single design point, represented by fixed, single load and misalignment values. A new approach to the design of tooth surface modifications is proposed to handle such conditions. The problem is formulated as a robust design optimization problem, and it is solved, in conjunction with an efficient gear contact solver (Load Distribution Program (LDP)), by a direct search, global optimization algorithm aimed at guaranteeing global optimality of the obtained microgeometry solutions. Several tooth surface modifications can be used as microgeometry design variables, including profile, lead, and bias modifications. Depending on the contact solver capabilities, multiple performance metrics can be considered. The proposed method includes the capability of simultaneously and robustly handling several conflicting design objectives. In the present paper, peak contact stress and loaded transmission error amplitude are used as objective functions (to be minimized). At the end, two example optimizations are presented to demonstrate the effectiveness of the proposed method.

Copyright © 2013 by ASME
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Ghribi, D., Bruyère, J., Velex, P., Octrue, M., and Haddar, M., 2012, “Design Optimization for Robustness Using Quadrature Factorial Models,” ASME J. Mech. Des., 134(6), p. 061011. [CrossRef]
GearLab, Load Distribution Program Manual, The Ohio State University, Columbus, OH.
Walker, H., 1938, “Gear Tooth Deflection and Profile Modification,” Engineer, 166, pp. 409–412 and 434–436.
Dudley, D. W., 1949, “Modification of Gear Tooth Profiles,” Prod. Eng., pp. 126–131.
Tavakoli, M. S., and Houser, D. R., 1986, “Optimum Profile Modifications for the Minimization of Static Transmission Errors of Spur Gears,” ASME J. Mech. Trans., 108(1), pp. 86–94. [CrossRef]
Simon, V., 1989, “Optimal Tooth Modifications for Spur and Helical Gears,” ASME J. Mech. Trans., 111(4), pp. 611–615. [CrossRef]
Wagaj, P., and Kahraman, A., 2002, “Influence of Tooth Profile Modification on Helical Gear Durability,” ASME J. Mech. Des., 124(3), pp. 501–510. [CrossRef]
Beghini, M., Presicce, F., and Santus, C., 2005, “Proposal for Tip Relief Modification to Reduce Noise in Spur Gears and Sensitivity to Meshing Conditions,” VDI-Berichte1904, Vol. II, pp. 1719–1734.
Bonori, G., Barbieri, M., and Pellicano, F., 2008, “Optimum Profile Modifications of Spur Gears by Means of Genetic Algorithms,” J. Sound Vib., 313, pp. 603–616. [CrossRef]
Artoni, A., Kolivand, M., and Kahraman, A., 2010, “An Ease-Off Based Optimization of the Loaded Transmission Error of Hypoid Gears,” ASME J. Mech. Des., 132(1), p. 011010. [CrossRef]
Artoni, A., Gabiccini, M., Guiggiani, M., and Kahraman, A., 2011, “Multi-Objective Ease-Off Optimization of Hypoid Gears for Their Efficiency, Noise, and Durability Performances,” ASME J. Mech. Des., 133(12), p. 121007. [CrossRef]
Sundaresan, S., Ishii, K., and Houser, D. R., 1991, “A Procedure Using Manufacturing Variance to Design Gears With Minimum Transmission Error,” ASME J. Mech. Des., 113(3), pp. 318–324. [CrossRef]
Yu, J.-C., 1998, “Design Optimization for Robustness Using Quadrature Factorial Models,” Eng. Optimiz., 30, pp. 203–225. [CrossRef]
Harianto, J., and Houser, D., Sept. 4–7, 2007, “A Methodology for Obtaining Optimum Gear Tooth Micro-Topographies for Noise and Stress Minimization Over a Broad Operating Torque Range,” Proceedings of the ASME 2007 International Design Engineering Technical Conference and Computers and Information in Engineering Conference, Paper No. IDETC/CIE 2007.
Gabiccini, M., Bracci, A., and Guiggiani, M., 2010, “Robust Optimization of the Loaded Contact Pattern in Hypoid Gears With Uncertain Misalignments,” ASME J. Mech. Des., 132(4), p. 041010. [CrossRef]
Houser, D., Harianto, J., and Talbot, D., 2006, “Gear Mesh Misalignment,” Gear Solutions (June 2006), pp. 34–43.
Jones, D. R., 2001, “Direct Global Optimization Algorithm,” Encyclopedia of Optimization, C. A.Floudas and P. M.Pardalos, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 431–440.
Kelley, C. T., “Implicit Filtering,” Retrieved Jan. 12, 2013, www4.ncsu.edu/∼ctk/iffco.html
Beyer, H.-G., and Sendhoff, B., 2007, “Robust Optimization—A Comprehensive Survey,” Comput. Methods Appl. Mech. Eng., 196, pp. 3190–3218. [CrossRef]
Miettinen, K. M., 1999, Nonlinear Multiobjective Optimization, Kluwer Academic Publishers, Norwell, MA.
Deb, K., 2001, Multi-Objective Optimization Using Evolutionary Algorithms, John Wiley & Sons, Chichester, West Sussex, England.


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Fig. 1

Some typical tooth surface modifications

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Fig. 2

Optimal total surface modification for problem (1). (3 μm profile crown; 14 μm lead crown.)

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Fig. 3

Variation of PPTE with torque (design point optimization)

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Fig. 4

Selected weight distribution functions and corresponding robust counterparts (shown for torque only)

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Fig. 5

A multi-objective optimization problem with two design variables and two objectives

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Fig. 6

Reference points F˜1 (infeasible) and F˜2 (feasible) projected onto the Pareto front and their corresponding Pareto-optimal objective vectors

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Fig. 7

Pareto front exploration: reference points and their corresponding Pareto-optimal objective vectors

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Fig. 8

Robust optimization of PPTE: optimal tooth surface (total) modifications corresponding to the three proposed robustness measures

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Fig. 9

Robust optimization of PPTE: optimized PPTE curves (thicker) versus those obtained in Ref. [14] (thinner)

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Fig. 10

Robust optimization of PPTE and pmax: reference points and robust Pareto-optimal objective vectors

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Fig. 11

Robust optimization of PPTE and pmax: Pareto-optimal tooth surface (total) modifications

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Fig. 12

Robust multi-objective optimization of PPTE and pmax: optimized PPTE and pmax curves versus those obtained in Ref. [14]



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