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Research Papers

Study on Deformed Limacon Gear and Motion Optimization of Its Serial Mechanism

[+] Author and Article Information
Liu Dawei

Ren Tingzhi

College of Mechanical Engineering,  Yanshan UniversityQinhuangdao, Hebei 066004, Chinartz@ysu.edu.cn

J. Mech. Des 133(6), 061004 (Jun 15, 2011) (8 pages) doi:10.1115/1.4004116 History: Received June 25, 2010; Revised April 13, 2011; Published June 15, 2011; Online June 15, 2011

In order to obtain the nonsinusoidal oscillation wave of continuous caster molds, a vibration generator comprised of an eccentric shaft and a new kind of noncircular gears called deformed limacon gear pair is proposed. The pitch curve equations of limacon gears are described based on the cosine rule. According to the closed property of noncircular pitch curves and residue theorem, the center distance between a limacon gear and its conjugate gear is deduced, as well as their transmission ratio and the pitch curve equations of the conjugate gear. Subsequently, the mathematical model of deformed limacon gears with dissymmetrical transmission ratio in one period is established and the kinematic formula of the serial mechanism is presented for optimization by a modified genetic algorithm. Here, a computer program is developed for optimizing the gear linkage mechanism to meet requirements in practice and results show that expected motion can be achieved by deformed gear linkage mechanism, which can provide a new choice for application.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Pitch curves of limacon gear and its conjugate gear

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Figure 2

Comparison of transmission ratio for three kinds of noncircular gears

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Figure 3

Pitch curves of two kinds of gear pairs

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Figure 4

Transmission ratio curves of two kinds of gear pairs

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Figure 5

Pitch curves of deformed limacon gear possessing several cycles

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Figure 6

Geometric sketch of the left tooth profile of noncircular gear generated by shaper cutter

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Figure 7

Meshing sketch of circular gear and rack

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Figure 8

Geometric sketch of the right tooth profile of noncircular gear generated by shaper cutter

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Figure 9

Left pressure angle of noncircular gears

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Figure 10

Right pressure angle of noncircular gear

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Figure 11

Maximal pressure angle of noncircular gears

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Figure 12

Movement sketch of mechanism combined with deformed limacon gear and eccentric shaft

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Figure 13

Tracking observation of evolutional calculation process

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Figure 14

Curve of optimized mold velocity

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Figure 15

Optimized pitch curves of deformed limacon gear pair applied to generate nonsinusoidal wave

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Figure 16

Tooth profile of driving gear

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Figure 17

Tooth profile of driven gear

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