Abstract
Deviations from isochronism for the osciliating system of spiral hairspring and balance wheel are investigated. Only those deviations caused by non-linearity of the hairspring are considered. It is shown that, in the case of springs manufactured from wire of a circular cross section, the deviations are related to the displacement of the outer end point of the hairspring, where the latter is arranged such that this end point is free to move in the plane of the spring, while its tangent is held constant in direction. Such an arrangement, proposed by Bouasse (12), is called a "free end" spring. Hairsprings of the more common flat strip are subject to the influence of additional effects that modify the above relationship. The modifications are investigated experimentally. The influence of manufacturing errors, and certain modifications to the spring shape are considered for round wire hairsprings, and approximate formulae derived that predict the deviations from isochronism of the oscillator in terms of the spring parameters and values of introduced errors. The theoretical predictions are verified experimentally. The formulae describing the deviation from isochronism are stated such that they can be used in the design of balance wheel and hairspring oscillators. A design example is included.