Research Papers

Differential Contact Path and Conjugate Properties of Planar Gearing Transmission

[+] Author and Article Information
Huimin Dong1

 School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, P.R. Chinadonghm@dlut.edu.cn

Kwun-Lon Ting

 Center for Manufacturing Research, Tennessee Technological University Associate Professor, Cookeville, TNkting@tntech.edu

Bowen Yu

 Center for Manufacturing Research, Tennessee Technological University, Cookeville, TN

Jian Liu

 Dalian University of Technology, Dalian 116024, P.R. China

Delun Wang

 School of Mechanical Engineering,Dalian University of Technology, Dalian 116024, P.R. China


Visiting scholar (March 2009–April 2010), Center for Manufacturing Research, Tennessee Tech University, Cookeville, TN.

J. Mech. Des 134(6), 061010 (May 23, 2012) (11 pages) doi:10.1115/1.4006654 History: Received August 01, 2011; Revised April 06, 2012; Published May 23, 2012; Online May 23, 2012

This paper presents a general conjugation model based on the intrinsic kinematical properties of the contact path. The model is truly general for any planar transmission through contact curves, such as gearing. The effectiveness of the method is not affected by the type of centrodes or motion and path of contact. With the method, for any given centrodes and any chosen path of contact, the corresponding conjugate curves can be identified and the geometric properties of the conjugation can be determined even before the conjugate curves are found. The method is demonstrated with straight, circular, and polynomial paths of contact in both circular and noncircular gears. The versatility of the theory and the outstanding features of the method become obvious with treating arbitrary centrodes or any planar motion transmission. The freedom of selecting contact path suggests the possibility of optimal conjugation design.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

A centrode and its coordinate system.

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Figure 2

The motion of a pair of centrodes (a) motion at s = 0; (b) motion at s-position

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Figure 3

A tooth curve Γi and the centrode ci of gear i

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Figure 4

Conjugate curves and their centrodes

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Figure 5

Centrodes and convenient coordinate systems

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Figure 6

Straight line POC

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Figure 7

The tooth profiles with a straight line POC (a) a circular gear set; (b) an elliptic gear set

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Figure 8

The tooth curve of a straight line centrode

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Figure 9

POC of a rack cutter tip and first tooth profile at right side (a) POC of the rack cutter tip; (b) first tooth curve and fillet: Point 4: on the centrode; Point 7: joint point between the tooth curve and fillet; Point 10: joint point between the fillet and bottom (dedendum curve)

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Figure 10

The circle path of contact and centrode ci

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Figure 11

The tooth curve of the circular path of contact

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Figure 12

Circular arc POC with a = 6 mm, a = −10 mm

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Figure 13

The tooth profiles with circular POC (a) a circular gear set and (b) an elliptic gear set

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Figure 14

The tooth profiles of elliptic gears with polynomial POC (a) a quadratic POC and (b) a cubic POC

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Figure 15

The path of contact and λ

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Figure 16

The curvature interference

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Figure 17

The properties of noncircular gears in Sec. 21

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Figure 18

The properties of noncircular gears in Sec. 23

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Figure 19

The properties of the elliptic gears with polynomial POC in Sec. 23




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