ELASTIC MOMENT (TORQUE)
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The elastic moment (torque) (sometimes called stiffness) is the restoring torque generated by an elastic element when it is deformed in rotation. It is a rotational force that tends to bring the system back to its equilibrium position. Thus, when a spring is twisted by an angle θ, it develops a torque proportional to this deformation:
M = C · θ
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M = elastic moment (torque) (N·m)
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C = stiffness (spring rate) constant (N·m/rad)
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θ = torsion angle (rad)
The elastic moment (torque) is the rotational force exerted by a deformed elastic component — hairspring (balance spring), mainspring, blade suspension — to return to its rest position. In watchmaking, it plays a fundamental role in the behavior of the regulating organ: it is the elastic moment (torque) of the hairspring which, combined with the moment of inertia of the balance, determines the frequency of oscillation according to the relation f = (1/2π) × √(C/I), where C is the Stiffness (spring rate) of the Hairspring (balance spring) and I the Inertia of the Balance.
An excessively high Elastic moment (torque) gives a high Frequency and a low Amplitude; too low, it produces the opposite. The Stiffness (spring rate) depends on the Young’s modulus of the material, on the dimensions of the Blade (thickness, width, active length) and on the temperature. Nivarox or silicon hairsprings were developed in particular to minimize variations in the Elastic moment (torque) with Temperature, thereby improving chronometric stability.
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