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Technical Briefs

A General Approach to Locate Instantaneous Contact Lines of Gears Using Surface of Roll Angle

[+] Author and Article Information
M. Kolivand1

Department of Mechanical Engineering, Ohio State University, 201 West 19th Avenue, Columbus, OH 43210kolivand.1@osu.edu

A. Kahraman

Department of Mechanical Engineering, Ohio State University, 201 West 19th Avenue, Columbus, OH 43210kahraman.1@osu.edu

1

Corresponding author. Currently with the Gleason Works.

J. Mech. Des 133(1), 014503 (Jan 10, 2011) (6 pages) doi:10.1115/1.4003142 History: Received May 02, 2010; Revised November 10, 2010; Published January 10, 2011; Online January 10, 2011

Determining the locations and orientation of potential instantaneous contact lines between two contacting tooth surfaces of gears is one major step in the prediction of unloaded and loaded gear tooth contacts. This study defines and utilizes new general concept based on the construction of a surface of roll angle to simplify the task of locating instantaneous contact lines of any type of gearing. The position and normal vectors of points on one of the mating surfaces and axes of both gears are used in conjunction with the equation of meshing to define the surface of action and the surface of roll angle. With the surface of roll angle defined, instantaneous contact lines are determined by a novel approach based on an analogy to parallel-axes gears. At the end, the proposed method is applied to various parallel- and cross-axis gear pairs to demonstrate its effectiveness.

FIGURES IN THIS ARTICLE
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Copyright © 2011 by American Society of Mechanical Engineers
Topics: Gears
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References

Figures

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Figure 1

Potential instantaneous contact line on the action and projection planes of a sample helical gear

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Figure 2

Conventional method of approximating the gear contact surfaces as two paraboloids in order to orient instantaneous contact lines

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Figure 3

Construction of the surface of roll angle Q

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Figure 4

(a) The surface of roll angle Q and (b) the instantaneous contact curves on the projection plane of an example hypoid gear pair having a 50 deg pinion mean spiral angle and 20 deg pressure angle

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Figure 5

(a) A pinion surface with large deviations and (b) the resultant deviations in the instantaneous contact lines on the projection plane. Solid lines represent the conjugate surfaces and the dashed line represents the surfaces with deviations.

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Figure 6

(a) The surface of roll angle Q and (b) the instantaneous contact curves on the projection plane of an example spur gear pair having a 20 deg pressure angle

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Figure 7

(a) The surface of roll angle Q and (b) the instantaneous contact lines on the projection plane of an example helical gear pair having a 20 deg pressure angle and a 20 deg helix angle. The number to the right of each contact curve denotes the roll angle while the number to the left represents the angle between the tangent to the contact curves at the midpoint of the contact curve and the root line of the tooth.

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Figure 8

Instantaneous contact lines of basic helical gear pair design with 20 deg pressure angle on the projection plane for the helix angles of (a) 5 deg and (b) 40 deg

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Figure 9

(a) The surface of roll angle Q and (b) the instantaneous contact curves on the projection plane of an example straight bevel gear pair having a 25 deg pressure angle

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Figure 10

(a) The surface of roll angle Q and (b) the instantaneous contact curves on the projection plane of an example cycloidal gear pair with gear ratio r2/r1=2, and generating circle radii half of the pitch circle

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