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Technical Briefs

The Mechanics of Spiral Springs and Its Application in Timekeeping

[+] Author and Article Information
Longhan Xie

School of Mechanical and Automotive Engineering,
South China University of Technology,
Guangzhou 510640, China

Ruxu Du

Institute of Precision Engineering,
The Chinese University of Hong Kong,
Hong Kong, China

Manuscript received October 6, 2011; final manuscript received May 13, 2013; accepted manuscript posted May 29, 2013; published online September 23, 2013. Assoc. Editor: Alexander F. Vakakis.

J. Appl. Mech 81(3), 034504 (Sep 23, 2013) (7 pages) Paper No: JAM-11-1360; doi: 10.1115/1.4024669 History: Received October 06, 2011; Revised May 13, 2013; Accepted May 29, 2013

Spiral spring is widely used in mechanisms, such as mechanical watch movements and clocks where the spiral spring is used for timekeeping. According to literature, there are only a few studies on spiral springs. In this paper, the mechanics of spiral springs is analyzed in details, and its dynamic performance in mechanical watch movements is further studied to find out its natural frequency, which is the most critical parameter for mechanical watch movements. Based on Castigliano's theorem, the mathematical model of dynamic deformation and natural frequency of the spiral spring under external axial torque is developed, and computer simulation with Matlab® is also conducted. Experimental validations are carried out, which confirm the simulation results. Experiments show that the analytical method in this paper can be used to guide and facilitate the design of spiral spring.

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References

Figures

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Fig. 1

Hairspring and its assembly

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Fig. 2

Schematic diagram of the hairspring structure [18]

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Fig. 3

The hairspring in its rest state (solid line) and its deformed position after it is rotated 360 deg counterclockwise

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Fig. 4

Locus of the center of mass of the hairspring when rotating from −360 deg to 360 deg

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Fig. 5

Equivalent stiffness of the hairspring with respect to the balance wheel rotation

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Fig. 6

Moment of inertia of the hairspring with respect to the balance wheel rotation

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Fig. 7

Natural frequency of the hairspring-balance wheel system [18]

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Fig. 8

The coordinate measuring machine used in the experiment—Mitutoyo Quick Vision Pro

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Fig. 9

Hairspring sample on the fixture in the experiment

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Fig. 10

Software interface of the CMM (a) measuring a segment of the sample spring; (b) focus view of the segment

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Fig. 11

Comparison of simulation results (blue line) and experimental measurements (red circles) of hairspring sample in x–y plane (in mm) for center shaft rotation angle = 60 deg

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