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Research Papers

Dynamic Model of Variable Speed Process for Herringbone Gears Including Friction Calculated by Variable Friction Coefficient

[+] Author and Article Information
Changzhao Liu

State Key Laboratory
of Mechanical Transmission,
Chongqing University,
Chongqing 400044, China
e-mail: lczcq@qq.com

Datong Qin

State Key Laboratory
of Mechanical Transmission,
Chongqing University,
Chongqing 400044, China
e-mail: dtqin@cqu.edu.cn

Yinghua Liao

State Key Laboratory
of Mechanical Transmission,
Chongqing University,
Chongqing 400044, China
e-mail: liaoyinghua118@163.com

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 9, 2013; final manuscript received January 2, 2014; published online February 26, 2014. Assoc. Editor: Zhang-Hua Fong.

J. Mech. Des 136(4), 041006 (Feb 26, 2014) (12 pages) Paper No: MD-13-1116; doi: 10.1115/1.4026572 History: Received March 09, 2013; Revised January 02, 2014

A dynamic model that includes friction and tooth profile error excitation for herringbone gears is proposed for the dynamic analysis of variable speed processes. In this model, the position of the contact line and relative sliding velocity are determined by the angular displacement of the gear pair. The translational and angular displacements are chosen as generalized coordinates to construct the dynamic model. The friction is calculated using a variable friction coefficient. The tooth profile error excitation is assumed to depend on the position along the contact line and to vary with the angular displacement of the driving gear. Thus, the proposed model can be used in the dynamic analysis of the variable speed process of a herringbone gear transmission system. An example acceleration process is numerically simulated using the model proposed in this paper. The dynamics responses are compared with those from the model utilizing a constant friction coefficient and without friction in cases where the profile error excitations are included and ignored.

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References

Figures

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Fig. 1

Illustration of meshing process of helical gears

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Fig. 2

Contact between circular truncated cones with opposite orientations

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Fig. 3

Snapshot of pair of helical gears in plane perpendicular to axis of rotation and containing point K

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Fig. 6

Illustration of motion of contact line of herringbone gears: (a) εα ≥ εβ and (b) εα < εβ

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Fig. 5

Lumped-parameter dynamic model of herringbone gears, including friction

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Fig. 4

Definition of positive rotating orientation of driving gear and starting point of L: (a) right hand and (b) left hand

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Fig. 7

Typical friction coefficient curve for Xu's formula

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Fig. 8

Simulated profile error excitation with pseudo-random numbers

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Fig. 15

Wigner–Ville distributions of translational displacements and angular acceleration of driving gear when profile error excitations are ignored (a), (d), and (g) show results for translational displacements in x-direction and y-direction and angular acceleration of driving gear for model with variable friction coefficient, respectively; (b), (e), and (h) show results for translational displacements in x-direction and y-direction and angular acceleration of driving gear for model with constant coefficient of 0.02, respectively; (c), (f), and (i) show results for translational displacements in x-direction and y-direction and angular acceleration of driving gear for model without friction, respectively

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Fig. 16

Time domain responses of meshing force (a)–(c) show results for model with variable friction coefficient, with constant friction of 0.02, and without friction, respectively, when profile error excitations are included; (d)–(f) show results for model with variable friction coefficient, with constant friction of 0.02, and without friction, respectively, when profile error excitations are ignored

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Fig. 17

Wigner–Ville distributions of meshing force (a)–(c) show results for model with variable friction coefficient, with constant friction of 0.02, and without friction, respectively, when profile error excitations are included; (d)–(f) show results for model with variable friction coefficient, with constant friction of 0.02, and without friction, respectively, when profile error excitations are ignored

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Fig. 9

Time domain responses of translational displacements of driving gear when profile error excitations are included ((a), (d), and (g) show results for model with variable friction coefficient; (b), (e), and (h) show results for model with constant friction coefficient of 0.02; c, f, and i show results for model without friction)

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Fig. 10

Wigner–Ville distributions of translational displacements of driving gear when profile error excitations are included: (a), (d), and (g) show results for translational displacements of driving gear in x-direction, y-direction, and z-direction for model with variable friction coefficient, respectively; (b), (e), and (h) show results for translational displacements of driving gear in x-direction, y-direction, and z-direction for model with constant coefficient of 0.02, respectively; (c), (f), and (i) show results for translational displacements of driving gear in x-direction, y-direction, and z-direction for model without friction, respectively

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Fig. 11

Time domain responses of angular acceleration of driving gear when profile error excitations are included (a) shows results for model with variable friction coefficient; (b) shows results for model with constant friction coefficient of 0.02; (c) shows results for model without friction

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Fig. 12

Wigner–Ville distributions of angular accelerations of driving gear when profile error excitations are included: (a) shows results for model with variable friction coefficient; (b) shows results for model with constant friction coefficient of 0.02; (c) shows results for model without friction

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Fig. 13

Time domain responses of angular velocity of driving gear when profile error excitations are included (blue solid line shows results for model with variable friction coefficient; red dashed line shows results for model with constant friction coefficient of 0.02; black dotted line shows results for model without friction)

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Fig. 14

Time domain responses of translational displacements and angular acceleration of driving gear when profile error excitations are ignored (a), (d), (g), and (j) show results for model with variable friction coefficient; (b), (e), (h), and (k) show results for model with constant friction coefficient of 0.02; (c), (f), (i), and (l) show results for model without friction

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