Constant Torque Gear Contour for Watch Accuracy
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Solution Overview
Problem
Watch gear trains fail to transmit a constant torque during tooth engagement due to variations in center distance between wheels, leading to fluctuations in the amplitude of balance wheel oscillations, which affects timekeeping accuracy.
Innovation Solution
A gear profile design that ensures a constant torque transmission by optimizing the efficiency, inclination, and base radii of tooth flanks, with specific formulas to calculate the profiles of functional and non-functional portions of the teeth, ensuring the force direction intersects a common point throughout the meshing process, even with deviations in center distance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional gear profiles (involute, cycloid, epicycloid, hypocycloid) are used, then proportional transmission is achieved, but torque transmission varies during tooth drive
Solution Approach 1:
The patent changes the geometric parameters of the gear tooth profiles by introducing a new family of curves (limaçons, epitrochoïdes, hypotrochoïdes) with specific mathematical formulations. These curves are defined by parameters such as base radius, eccentricity, and shape coefficients that are optimized to maintain constant torque transmission. The key parameter change is in the radial distance function r(θ) that defines the tooth flank geometry, transitioning from conventional involute profiles to these new curves where the contact force direction consistently passes through a fixed point on the center line.
2Ease of manufacture
If manufacturing tolerances in wheel positioning are present, then center distance deviates from theoretical value, but torque transmission becomes highly sensitive to this deviation
Solution Approach 1:
The patent creates a universal gear profile design that functions correctly across a range of center distances. The tooth profiles are designed with inherent geometric properties that allow them to maintain constant torque transmission whether the center distance is exactly nominal or slightly deviated due to manufacturing tolerances. This universality is achieved through the specific mathematical form of the limaçon and related curves, which have the property that their normal lines at contact points consistently pass through a fixed point on the center line regardless of small center distance variations.
3Ease of operation
If the point of contact moves radially during tooth drive, then gear meshing occurs, but torque ratio varies during the drive cycle
Solution Approach 1:
The patent introduces a geometric intermediary concept: a fixed reference point on the center line that serves as the intersection point for all contact force directions. By designing the tooth profiles such that their normals at any contact point pass through this intermediary fixed point, the patent ensures that the torque transmission remains constant. This intermediary point acts as a geometric mediator that decouples the varying contact position from the torque variation, allowing smooth meshing while maintaining constant force transmission.
Data Source
Figure 1~3
Figure 2A~2B
Figure 4~5
AI summary
The wheel (1) has a set of teeth, where each tooth (17) comprises an edge whose functional portion has a profile complying with a parametric double formula comprising parameters u and mu, where mu corresponds to a coefficient of friction at a contact between the edge and an edge of a tooth (18) of another toothed wheel (2) with values comprised between 0.05 and 0.5, and u is a variable that varies in an interval such that the profile is covered by varying the u. The portion and another functional portion of edge of tooth are contiguous.