Crossed Blade Resonator Geometry for Isochronism
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Solution Overview
Problem
Cross-blade balance wheels in mechanical watches suffer from anisochronism due to non-linear elastic restoring torque and position-dependent frequency, making it difficult to achieve isochronism and independence from gravitational orientation.
Innovation Solution
Optimizing the geometry of the crossed blades by setting the first angle between 68° and 76°, particularly around 72°, to achieve a linear elastic restoring force and minimize center of mass displacement, thereby ensuring isochronism and independence from gravitational orientation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If crossed blades with 90° angle are used, then the quality factor is increased by eliminating rubbing pivot, but the system becomes highly anisochronous with strong dependence on oscillation amplitude
Solution Approach 1:
The patent changes the geometric parameter of the crossed blades from the conventional 90° angle to a specific angle between 68° and 76° (preferably 71.2°). This parameter change transforms the elastic restoring torque from non-linear to linear, making the oscillation frequency independent of amplitude and achieving isochronism while maintaining the quality factor benefits of the crossed-blade design.
2Device complexity
If crossed blades with 90° angle are used, then the structure is simple, but the resonator frequency depends on the watch's orientation in the gravitational field (position effect)
Solution Approach 1:
By changing the blade angle parameter to between 68° and 76°, the patent achieves two simultaneous benefits: the elastic restoring torque becomes linear (improving isochronism) and the center of mass displacement is minimized (reducing position effect). This single parameter change addresses both issues without increasing structural complexity.
3Ease of operation
If the blades cross at seven-eighths of their length with 90° angle, then the displacements of the virtual axis of rotation are minimized, but the anisochronism remains highly significant
Solution Approach 1:
The patent combines the known optimal crossing position (seven-eighths of blade length) with a newly optimized blade angle (68°-76°). The angle parameter change is the critical innovation that transforms the non-linear elastic restoring torque into a linear one, achieving isochronism while maintaining the virtual axis stability provided by the seven-eighths crossing position.
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 optimized geometry results in a balance resonator that is simultaneously isochronous and independent of gravitational orientation, reducing anisochronism and position effects, leading to improved timekeeping accuracy.
Implementation Method 1
crossed blades (3, 4) which are elastic blades
Implementation Method 2
at least one mass (1) oscillating with respect to a connecting element (2)
Implementation Method 3
whose projections of directions on one of said parallel planes intersect at the level of a virtual pivot axis of said mass
Implementation Method 4
the elastic restoring torque is non-linear, making the system anisochronous... find a blade geometry that cancels both the effect of the positions and the anisochronism produced by the non-linearity of the elastic restoring force
Data Source
Figure 1~1A
Figure 2~4
Figure 5~7
AI summary
Timepiece resonator (100) comprising a mass (1) oscillating with respect to a connecting element (2) fixed on a movement structure (200), said mass (1) being suspended on said connecting element (2) by resilient crossed blades (3, 4) which extend remotely from one another in two parallel planes, and the projections of which onto one of said planes cross at a virtual pivot axis (O) of said mass (1) and define a first angle (a) which is the apex angle opposite which extends the part of said connection element (2) situated between the fasteners of said crossed blades (3, 4) on the connecting element (2). Said first angle (a) is between 68° and 76°. Movement (200) comprising at least one such resonator (100). Timepiece (300), or watch, comprising at least one such resonator (100).