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Research Papers: Design of Direct Contact Systems

Compensated Conjugation and Gear Tooth Modification Design

[+] Author and Article Information
Bowen Yu

Center for Manufacturing Research,
Tennessee Technological University,
Cookeville, TN 38501
e-mail: byu42@students.tntech.edu

Kwun-lon Ting

Professor
Center for Manufacturing Research,
Tennessee Technological University,
Cookeville, TN 38501
e-mail: kting@tntech.edu

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 11, 2015; final manuscript received November 23, 2015; published online May 20, 2016. Assoc. Editor: Qi Fan.

J. Mech. Des 138(7), 073301 (May 20, 2016) (10 pages) Paper No: MD-15-1212; doi: 10.1115/1.4032264 History: Received March 11, 2015; Revised November 23, 2015

This paper addresses the fundamental issue on the conjugation for any gearing systems after tooth modification. It presents a rigorous theory on compensated conjugation for gear transmission error (TE) balance. The basic idea is that conjugation impaired by the loading condition can be compensated by modifying the transmission function. Thus, conjugation holds true after tooth modification. Because the modification is based on the universal concept of transmission rather than the tooth geometry, the proposed tooth modification method is universal rather than limited to involute or even planar gearing. A theorem about the continuity of motion and conjugate geometries is presented and proved for any desirable modification. The proposed theory is consistent with the standard manufacturing process for tooth modification. Tooth geometries and cutter geometries can be obtained after the theoretical TE function is designed. The proposed method is highlighted and demonstrated with an involute gear design, in which a convenient and practical method with a direct rack-cutter modification is presented and rigorously analyzed based on kinematics and differential geometry. Examples are presented to show the effectiveness of the methodology.

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Copyright © 2016 by ASME
Topics: Gears , Geometry , Design
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References

Houser, D. , 1985, “ Gear Noise Sources and Their Prediction Using Mathematical Models,” Gear Dynamics and Gear Noise Research Laboratory, Ohio State University, Columbus, OH.
Munro, R. , Yildirim, N. , and Hall, D. , 1990, “ Optimum Profile Relief and Transmission Error in Spur Gears,” Proc. Inst. Mech. Eng. C, 400(107), pp. 35–42.
Yildirim, N. , and Munro, R. , 1999, “ A New Type of Profile Relief for High Contact Ratio Spur Gears,” Proc. Inst. Mech. Eng., Part C, 213(6), pp. 563–568. [CrossRef]
Yildirim, N. , and Munro, R. , 1999, “ A Systematic Approach to Profile Relief Design of Low and High Contact Ratio Spur Gears,” Proc. Inst. Mech. Eng., Part C, 213(6), pp. 551–562. [CrossRef]
Velex, P. , Bruyère, J. , and Houser, D. , 2011, “ Some Analytical Results on Transmission Errors in Narrow-Faced Spur and Helical Gears: Influence of Profile Modifications,” ASME J. Mech. Des., 133(3), p. 031010. [CrossRef]
Velex, P. , and Maatar, M. , 1996, “ A Mathematical Model for Analyzing the Influence of Shape Deviations and Mounting Errors on Gear Dynamic Behaviour,” J. Sound Vib., 191(5), pp. 629–660. [CrossRef]
Maatar, M. , and Velex, P. , 1997, “ Quasi-Static and Dynamic Analysis of Narrow-Faced Helical Gears With Profile and Lead Modifications,” ASME J. Mech. Des., 119(4), pp. 474–480. [CrossRef]
Beghini, M. , Presicce, F. , and Santus, C. , 2004, “ A Method to Define Profile Modification of Spur Gear and Minimize the Transmission Error,” AGMA, Technical Paper No. 4FTM3.
Bonori, G. , Barbieri, M. , and Pellicano, F. , 2008, “ Optimum Profile Modifications of Spur Gears by Means of Genetic Algorithms,” J. Sound Vib., 313(3), pp. 603–616. [CrossRef]
Tharmakulasingam, R. , 2010, “ Transmission Error in Spur Gears: Static and Dynamic Finite-Element Modeling and Design Optimization,” Ph.D. thesis, Brunel University, School of Engineering and Design, Middlesex, England.
Li, Q. , Qiao, X. , Wu, C. , and Wang, X. , 2011, “ The Study on Gear Transmission Multi-Objective Optimum Design Based on SQP Algorithm,” Fourth International Conference on Machine Vision (ICMV 11), International Society for Optics and Photonics, p. 83502O.
Sankar, S. , and Nataraj, M. , 2011, “ Profile Modification—A Design Approach for Increasing the Tooth Strength in Spur Gear,” Int. J. Adv. Manuf. Technol., 55(1), pp. 1–10. [CrossRef]
Smith, J. , 1983, Gears and Their Vibration, Marcel Dekker, London, UK.
Harris, S. , 1958, “ Dynamic Loads on the Teeth of Spur Gears,” Proc. Inst. Mech. Eng., 172(1), pp. 87–112. [CrossRef]
Gregory, R. , Harris, S. , and Munro, R. , 1963, “ Dynamic Behavior of Spur Gears,” Proc. Inst. Mech. Eng., 178(8), pp. 261–266.
Terauchi, Y. , Nadano, H. , and Nohara, M. , 1982, “ On the Effect of the Tooth Profile Modification on the Dynamic Load and the Sound Level of the Spur Gear,” Bull. JSME, 25(207), pp. 1474–1481. [CrossRef]
Houser, D. , 1982, “ Research in the Gear Dynamics and Gear Noise Research Laboratory,” SAE Technical Paper No. 821066.
Umeyama, M. , Kato, M. , and Inoue, K. , 1998, “ Effects of Gear Dimensions and Tooth Surface Modifications on the Loaded Transmission Error of a Helical Gear Pair,” ASME J. Mech. Des., 120(1), pp. 119–125. [CrossRef]
Tavakoli, M. , and Houser, D. , 1984, “ Optimum Profile Modifications for the Minimization of Static Transmission Errors of Spur Gears,” ASME J. Mech. Trans. Automation, 108(1), pp. 86–94. [CrossRef]
Townsend, D. , and Dudley, D. , 1991, Dudley's Gear Handbook, McGraw-Hill, Noida, UP, India.
Lee, C. , Lin, H. , Oswald, F. , and Townsend, D. , 1990, “ Influence of Linear Profile Modification and Loading Conditions on the Dynamic Tooth Load and Stress of High Contact Ratio Gears,” NASA, Technical Report No. 103136.
Sankar, S. , Raj, M. , and Nataraj, M. , 2010, “ Profile Modification for Increasing the Tooth Strength in Spur Gear Using Cad,” Engineering, 2(9), pp. 740–749. [CrossRef]
Litvin, F. , and Fuentes, A. , 2004, Gear Geometry and Applied Theory, Cambridge University Press, Cambridge, UK.
Krantz, S. , and Parks, H. , 2002, The Implicit Function Theorem: History, Theory, and Applications, Birkhäuser, Boston, MA.
Litvin, F. , Wang, A. , and Handschuh, R. , 1998, “ Computerized Generation and Simulation of Meshing and Contact of Spiral Bevel Gears With Improved Geometry,” Comput. Methods Appl. Mech. Eng., 158(1), pp. 35–64. [CrossRef]
Litvin, F. , Fuentes, A. , Fan, Q. , and Handschuh, R. , 2002, “ Computerized Design, Simulation of Meshing, and Contact and Stress Analysis of Face-Milled Formate Generated Spiral Bevel Gears,” Mech. Mach, Theory, 37(5), pp. 441–459. [CrossRef]
Yu, B. , and Ting, K. L. , 2011, “ Free-Form Conjugation Theory,” ASME Paper No. DETC2012-71525.
Yu, B. , and Ting, K.-L. , 2013, “ Free-Form Conjugation Modeling and Gear Tooth Profile Design,” ASME J. Mech. Rob., 5(1), p. 011001. [CrossRef]
Piegl, L. , and Tiller, W. , 1997, The NURBS Book, Springer-Verlag, Berlin.

Figures

Grahic Jump Location
Fig. 1

Kinematic relationship for a rack cutter and a gear

Grahic Jump Location
Fig. 2

Line of action for right-hand tooth pair. Gear 1 is above gear 2. Gear 1 rotates clockwise while gear 2 counterclockwise. (a) The configuration of the gears. (b) The angles between the line of action and radial direction for both gear pairs.

Grahic Jump Location
Fig. 3

Line of action for left-hand tooth pair. Gear 1 is above gear 2. Gear 1 rotates counterclockwise while gear 2 clockwise. (a) The configuration of the gears. (b) The angles between the line of action and radial direction for both gear pairs.

Grahic Jump Location
Fig. 4

Modified rack-cutter curve (a) when r10 is modified into r11 and (b) when r20 is modified into r21

Grahic Jump Location
Fig. 5

Cutter profiles before (solid) and after (dotted) modification (unit is mm). The left figures show the complete cutter profiles and circle the modification parts, while the right figures zoom in the modified parts of tooth profiles on the left.

Grahic Jump Location
Fig. 6

Tooth profiles before (solid) and after (dotted) modification (unit is mm). The left figures show the complete tooth profiles and circle the modification parts, while the right figures zoom in the modified parts of tooth profiles on the left.

Grahic Jump Location
Fig. 7

TE distribution charts before (solid) and after (dotted) tooth modification

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