Watch Hairspring Isochronism via Non-Linear Terminal Curves
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Solution Overview
Problem
Conventional mechanical watch hairsprings experience unbalance due to the movement of their center of gravity, leading to lateral pressure on the balance wheel axis, which disturbs isochronism and is difficult to produce with precise control using existing methods.
Innovation Solution
A flat hairspring design with a substantially constant thickness and variable radius of curvature, where the last turn's shape is optimized to compensate for the center of gravity displacement, reducing lateral pressure without modifying the thickness or material composition, and produced using photolithography for precise control.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If the hairspring is designed as a conventional Archimedean spiral with linearly increasing radius, then the manufacturing process is simple, but the center of gravity moves during expansion and contraction, creating unbalance and lateral pressure on the balance wheel axis
Solution Approach 1:
The patent modifies the radius function from linear (Archimedean spiral) to a non-linear function that maintains constant center of gravity position. The radius ρ is defined as a function of angle θ such that the mass distribution remains balanced throughout the expansion-contraction cycle, eliminating lateral pressure on the balance axis while preserving manufacturing feasibility through photolithography processes.
Solution Approach 2:
The patent transitions from a conventional two-dimensional Archimedean spiral to a three-dimensional configuration where the terminal curve is folded in a plane other than that of the hairspring. This adds a vertical dimension to the terminal portion, creating a more complex spatial arrangement that compensates for center of gravity displacement while maintaining flatness for manufacturing purposes.
2Reliability
If the terminal curve is folded in a plane other than that of the hairspring (Breguet hairspring), then the center of gravity unbalance is reduced, but additional height is required and the manufacturing becomes difficult with photolithography techniques
Solution Approach 1:
The patent modifies the radius function from linear (Archimedean spiral) to a non-linear function that maintains constant center of gravity position. The radius ρ is defined as a function of angle θ such that the mass distribution remains balanced throughout the expansion-contraction cycle, eliminating lateral pressure on the balance axis while preserving manufacturing feasibility through photolithography processes.
3Reliability
If the external curve is modified to improve isochronism and avoid collisions, then the timekeeping accuracy is improved, but the manufacturing precision requirements increase
Solution Approach 1:
The patent replaces mechanical manufacturing processes with photolithography techniques for producing the hairspring. This substitution enables precise control of complex non-linear curves and terminal configurations that would be difficult to achieve through traditional mechanical means, allowing for high manufacturing precision of the optimized external curve.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The solution improves isochronism by maintaining the center of gravity aligned with the balance wheel's center of rotation, reduces manufacturing complexity, and allows for precise production, minimizing bulk and internal tension, thus enhancing the watch's timekeeping accuracy.
Implementation Method 1
They are moreover difficult to achieve with photolithography techniques such as LIGA (Lithographie Galvanoformung Abformung) or deep etching DRIE (Deep Reactive Ion Etching) for example
Implementation Method 2
WO2012152843 describes a balance spring comprising a number of through or blind holes in order to increase the area of the oxidizable surface
Data Source
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AI summary
A planar spiral intended to be mounted on the balance staff of a mechanical watch regulator, the spiral being formed of a blade of substantially constant rigidity, the spiral comprising: several internal turns in which the distance (ρ) between each point and the center of rotation varies substantially linearly as a function of the angular position (θ) of the point when the spiral is at rest; an external turn in which the distance (r) between each point and the center of rotation is a non-linear function of the angular position (θ) of the point when the spiral is at rest; said non-linear function having the effect of reducing the lateral pressure exerted by the spiral on said balance staff when the spiral is mounted on this staff and/or having the effect of compensating for the delay due to the escapement at small amplitudes of oscillation.