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Research Papers

Research on Sliding Ratios of Conjugate Surfaces of Two Degrees of Freedom Meshing Transmission of Spherical Gear Pair

[+] Author and Article Information
Li Ting1

Jiuquan Satellite Launching Center, Gansubee.lt@163.com

Pan Cunyun

Gao Fudong

Changsha, Hunan 410073, Chinagaofudong2005@163.com

Wang Xiaocong

Luoyang, Henan Luoyang 410073, Chinawxcong1985@sina.com

1

Corresponding author.

J. Mech. Des 134(9), 091002 (Aug 06, 2012) (11 pages) doi:10.1115/1.4006322 History: Received November 09, 2010; Revised January 05, 2012; Published August 06, 2012; Online August 06, 2012

The spherical gear is a gear-driven mechanism with two degrees of freedom (DOF), which can transfer spatial motion. The spherical gear pairs have two types of basic assembly structures including an ideal mechanism and a gimbal mechanism, and whose kinematic characteristics are analyzed. The 2-DOF gearing principle of conjugate tooth surfaces of the spherical gear pair is introduced first. Then, the relative slide between two tooth surfaces in the mesh is analyzed. Finally, the equations of the meshing coned surface and the conjugate surface are established based on the meshing models of the spherical gear pairs. Furthermore, the sliding ratios of the tooth surfaces of the spherical gear pairs are obtained when they mesh in different meshing conditions based on two-parameter movement analysis. The computational results show that the sliding ratios of the spherical gear teeth are related to the angle velocity ratio in the ideal mechanism and they are not only related with angle velocity ratio but also related with the assembly axes in the gimbal mechanism, which are useful in theory for further studying the wear of the spherical gear.

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Copyright © 2012 by American Society of Mechanical Engineers
Topics: Gears , Mechanisms
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Figures

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Figure 1

Spherical gear mechanism: (a) ideal mechanism and (b) gimbal mechanism

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Figure 2

Coordinate system of spherical gear mechanism

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Figure 3

Coordinate transformation relationship of spherical gear pair in mesh

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Figure 4

Conjugate engagement of spherical gear pair

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Figure 5

Meshing cone of spherical gear transmission

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Figure 6

Sliding ratios of tooth surfaces of spherical gear pair

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Figure 7

Paths of contact point on tooth surfaces

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Figure 8

Relative movement and velocity of contact point

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Figure 9

Sliding ratio of every tooth of spherical gear pair

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Figure 10

Sliding ratios of conjugate tooth meshing

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Figure 11

Sliding ratios of spherical gears teeth: (a) ɛ = 2, (b) ɛ = 1, (c) ɛ = 0.1, and (d) ɛ = 0.05

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Figure 12

Conjugate tooth surfaces of spherical gear pair

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Figure 13

Sliding ratio of spherical gear pair in gimbal mechanism: (a) ɛ = 0, (b) ɛ = 1, and (c) ɛ = ∞

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