Spiral spring

The arises spiral standard, with nonjointed whorls and thus without friction, is composed of a ribbon of rectangular section embedded at an end B and interdependent at other end 0 of an axis perpendicular to the plan of rolling up.

In clock industry, the spiral spring is small a Ressort rolled up in spiral and constituting with the beam the regulating body of the mechanical watch. It brings back the beam to its starting position at the end of each alternation.

Us will suppose that the axis is mobile without friction and, which is less obvious, that it does not tend to move radially when one makes it turn under the effect of a couple C.

Under these conditions, any couple perpendicular to the plan of rolling up, applied out of O, is transmitted completely out of B, which would not be the case so in this point the end was not embedded but simply not hung, as it will be probably the case for this industrial realization:

Condition of resistance

If the elastic blade has for width B (counted perpendicular to the plan of rolling up) and as a thickness E, then:

$\ sigma_ {maximum} = \ frac {6 \, C} {B \, e^2} \ the \ sigma_ {adm}$

Condition of deformation

For a beam subjected to the inflection, a variation of the bending moment involves a variation of the curve (opposite radius of curvature), such as:

$\ Delta \ left (\ frac {1} {R} \ right) = \ frac {\ Delta (M_f)}{E \, I}$

Integration on the whole the length L of the ribbon provides the swing angle θ of the end O:

$\ theta = \ frac {12 \, C \, L} {E \, B \, e^3}$ (θ is obviously in radians)

While eliminating C between the two formulas, it comes:

$\ theta = \ frac {2 \, \ sigma_ {maximum} \, L} {E \, E}$

Manufacture

The spiral spring, primarily used in the equipment of precision (watches, electricals appliance,…) fact the object of a very special manufacture whose procedures and tests are codified by the Technical center of Clock making Industry. Obtaining nonjointed and equidistant whorls requires, at the beginning, a special conformation of the ribbon. This last, if it were right at the beginning, would be laid out indeed naturally in the shape of a roller with jointed whorls of very different behavior because of frictions. One finds such a provision in the case of the springs which point out the tape-measures in their case.

When the ends of the spiral spring are normally dependant, i.e. embedded, any variation of the bending moment to the one of the ends is completely transmitted to the other end: this made that in all the cases the bending moment along the ribbon is constant.

In a given point, the curve of the blade is defined like the reverse of the local radius of curvature. However, as the section of the blade is constant, any variation of the bending moment is accompanied by a proportionate change of the curve:

$\ Delta (\ frac {1} {R}) = \ frac {\ Delta (M_f)}{I.E.(internal excitation)}$

We will agree to say that all along the spring rolled up in load, the curve is positive. The figure opposite represents in top a spiral spring rolled up and below, with vacuum. On the level of the interior end has and of the point M, the curve of the outline is positive and the remainder after rolling up. The point B corresponds to a point of inflection of the preform, where the curve is null. At the point NR and the external end C, the curves of the preform are negative and they become positive once the rolled up spring.

Working of the spring “in S” with vacuum is a complex operation which requires much know-how and experiment!

For other types of hair springs like those of the beams used in clock industry, the form with vacuum is a spiral of Archimedes whose curves increase or decrease with the liking of the oscillations. By regulating the length of the flexible ribbon by an adapted device, one varies the stiffness of the spring and thus the frequency of the oscillations of the beam, one thus as far as possible reduces the advance or the delay of the watch or the clock.

Any more how very other, the spiral spring is not a business of specialists!

Assembly

We supposed that the end of the spring was embedded and affirmed that under these conditions the couple transmitted by the blade was identical in any point of the latter. So on the other hand the end of the spring is simply hung out of B, the moment is null in this point and variable throughout the ribbon, with a maximum reaching 2C almost!

The mode of fixing thus influences enormously the maximum constraint.

History

The spiral spring was invented as of the Antiquité, probably by chance after steeping of a wire of iron or bronze rolled up in reversed spiral spiral or double. This shape of spring for example was used for the closing of the Fibule S which played the part of safety pin. One finds it in the Serrure S of the Middle Ages, then to later animate the mechanisms of watches to spiral spring.

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