On the Number of Idle and Working Revolutions of the Spring Motor of Wristwatches
Abstract Generated abstract
This paper examines the relationship between winding, working, and idle revolutions in wristwatch spring motors using spiral mainsprings made from the cobalt alloy K40TYu, which had become widely used for its anticorrosion and antimagnetic properties. After 1000 preliminary winding and unwinding cycles, experimental data were collected for springs used in Polet, Baltika, and Slava watches and averaged across groups with different working lengths. The authors approximate the dependence of arbor winding revolutions on barrel working revolutions and the spring geometry ratio by a least squares formula with a reported root mean square deviation of 3.7 percent. From this relation they also derive an expression for the number of idle barrel revolutions needed to reach the working portion of the spring characteristic.
Full Text
ON THE NUMBER OF IDLE AND WORKING REVOLUTIONS OF THE SPRING MOTOR OF WRISTWATCHES
Yu. Ya. Kovylin, V. I. Kalyagina
(Presented by the scientific-methodological seminar of the Department of Applied Mechanics)
Let \(n_{\text{work}}\) be the number of working revolutions of the winding barrel corresponding to the rectilinear portion of the characteristic of the spring in the barrel; \(n_{\text{wind}}\) be the number of revolutions of the arbor when the spring is transferred from the fully run-down state to the wound state; \(m\) be the coefficient equal to the ratio of the maximum moment \(M_{\max}\) of the wound spring to the minimum moment \(M_{\min}\) during unwinding of the spring within the limits of the working portion of its characteristic (Fig. 1).
For springs made of steels U8A and 70S2KhA, on the basis of experimental materials presented in the monographs of T. A. Gevondyan [1] and a number of other authors, an approximate relation had previously been obtained [2]
\[ n_{\text{wind}} \approx n_{\text{work}}\left(1+\frac{0.4}{\sqrt{m-1}}\right). \]
At present, the anticorrosion and antimagnetic cobalt alloy K40TYu is widely used in the watch industry. In this connection, it became necessary to carry out additional investigations of springs made of the specified alloy. The objects of the investigation were spiral springs manufactured by the Leningrad Steel-Rolling Plant according to the existing technology.
The parameters of interest for the springs were recorded after preliminary running-in on a stand for 1000 winding–unwinding cycles. As a result of the experiments, a set of experimental data was obtained for three brands of wristwatches—“Polet,” “Baltika,” and “Slava”—which are presented in generalized form in the table.
The experimental dependences \(n_{\text{wind}}(n_{\text{work}})\) (Fig. 2) for the springs of the listed watch brands can be approximated by a single formula
\[ n_{\text{wind}} \approx 1.56\,n_{\text{work}} + 10.41 \cdot 10^3 \left(\frac{R}{h}\right)^{-2} - 6.67, \tag{1} \]
where \(\dfrac{R}{h}\) is 41.6 for “Polet” watches, 43.1 for “Baltika” watches, and 39.7 for “Slava” watches.
The coefficients in formula (1) were found by the method of least squares. The root-mean-square deviation of the experimental points—
Table 1
Experimental values of \(n_{\text{wind}}\), \(n_{\text{work}}\), \(n_{\text{idle}}\), \(m\), averaged over five springs in each group (springs made of KChOTYu alloy)
| Group no. | “Polet” watches: working length \(L\), mm | \(n_{\text{wind}}\) | \(n_{\text{work}}\) | \(n_{\text{idle}}\) | \(m\) | “Baltika” watches: working length \(L\), mm | \(n_{\text{wind}}\) | \(n_{\text{work}}\) | \(n_{\text{idle}}\) | \(m\) | “Slava” watches: working length \(L\), mm | \(n_{\text{wind}}\) | \(n_{\text{work}}\) | \(n_{\text{idle}}\) | \(m\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| I | 599.6 | 4.92 | 3.59 | 1.33 | 1.276 | 485 | 5.28 | 4.11 | 1.17 | 1.35 | 265.4 | 3.85 | 2.44 | 1.41 | 1.238 |
| II | 479.8 | 6.24 | 4.30 | 1.94 | 1.398 | 385 | 6.32 | 4.67 | 1.65 | 1.51 | 223 | 4.68 | 2.98 | 1.70 | 1.348 |
| III | 386.8 | 6.51 | 4.52 | 1.99 | 1.580 | 314 | 6.42 | 4.74 | 1.67 | 1.68 | 189 | 4.94 | 3.18 | 1.74 | 1.486 |
| IV | 326 | 6.29 | 4.38 | 1.91 | 1.770 | 262 | 6.27 | 4.65 | 1.62 | 1.87 | 155 | 4.85 | 3.22 | 1.63 | 1.663 |
| V | 281.4 | 5.97 | 4.26 | 1.71 | 1.950 | 216 | 5.79 | 4.50 | 1.29 | 2.19 | 120.8 | 4.58 | 3.10 | 1.48 | 1.870 |
the deviation of the points from the approximating curve is 3.7%. The applicability boundary of formula (1) is given by the inequality \(n_{\text{wind}} > n_{\text{work}}\).
The number of idle revolutions of the barrel \(n_{\text{idle}}\) required to reach the working portion of the characteristic when winding the spring from the fully run-down state (Fig. 1) is one of the most important parameters of the spring motor.
Fig. 1
Fig. 2
According to [1], for spiral springs made of alloys U8A and 70S2KhA,
\[ n_{\text{idle}} \approx \frac{n_{\text{wind}}}{1 + 2.5\sqrt{m - 1}} . \]
On the basis of [2], for spiral springs made of alloy K40TYu we obtained
\[ n_{\text{idle}} \approx 0.56\, n_{\text{work}} + 10.41 \cdot 10^3 \left( \frac{R}{h} \right)^{-2} - 6.67 . \]
REFERENCES
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T. A. Gevondyan. Spring Motors. Moscow, Oborongiz, 1956.
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Yu. Ya. Kovylin. Determination of the number of idle revolutions of the barrel of a spring motor with a spiral mainspring. In: Collection of Materials of the Jubilee Scientific-Technical Conference of Tomsk Polytechnic Institute Dedicated to the 50th Anniversary of October, issue 2, Tomsk, 1968.