Watch Gear Tooth Profile for Constant Torque Transmission
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
In watchmaking, existing gear wheels with teeth profiles based on geometric curves like cycloids and involutes face issues with constant torque transmission due to friction, leading to variations in force transmission and chronometric performance degradation.
Innovation Solution
A method for manufacturing a second gear wheel with a defined flank geometry that maintains a constant torque ratio with a given first gear wheel by using a man-machine interface to input parameters, solving equations for torque balance and kinematic relationships, and interpolating points to construct the tooth flank, ensuring consistent torque transmission.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If gear teeth profiles are based on geometric curves (cycloid, epicycloid, hypocycloid, or involute), then the speed of rotation transmission remains substantially constant, but friction forces cause torque transmission to vary during tooth drive
Solution Approach 1:
The invention changes the geometric parameters of the tooth profile from traditional curves (cycloid, epicycloid, hypocycloid, or involute) to a new profile defined by specific mathematical equations (equations 1-4). This parameter change allows the tooth flanks to maintain constant torque transmission while accounting for friction forces, resolving the contradiction between speed transmission and torque constancy.
Solution Approach 2:
The invention introduces a dynamic approach by defining the tooth profile based on friction coefficients and torque balance equations rather than static geometric curves. The profile adapts to the friction conditions during tooth engagement, allowing the system to maintain constant torque transmission despite the presence of friction forces.
2Ease of manufacture
If variable torque transmission is accepted due to friction, then manufacturing is simpler with standard geometric curves, but chronometric performance degrades due to force variations
Solution Approach 1:
The invention changes the manufacturing approach from standard geometric curves to profiles defined by equations (1-4) that incorporate friction coefficients. While this requires more complex calculation, it ensures constant torque transmission and improved chronometric performance. The manufacturing process uses these equations to generate precise tooth profiles that account for friction forces.
Solution Approach 2:
The invention incorporates friction coefficients as feedback parameters in the tooth profile design equations. By considering the friction forces that will act during operation and incorporating them into the profile design, the system achieves constant torque transmission and improved chronometric performance without sacrificing manufacturability.
3Device complexity
If traditional geometric curve profiles are used, then the gear structure is simpler, but the torque ratio varies during tooth drive due to friction forces
Solution Approach 1:
The invention changes the tooth profile parameters from traditional geometric curves to profiles defined by equations (1-4) that incorporate friction coefficients. This parameter change maintains relatively simple gear structures while achieving constant torque ratio transmission by accounting for friction forces in the profile design.
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 method ensures a quasi-constant or constant torque ratio between meshed gear wheels, enhancing chronometric precision and reducing variations in force transmission, thereby improving the reliability and accuracy of watch movements.
Implementation Method 1
considering a first equation defining the power or torque balance of at least a pair of teeth in contact of the two gear wheels
Implementation Method 2
entering a coefficient of friction of a pair of teeth in contact of the two gear wheels
Implementation Method 3
constructing the flank of said tooth of the second gear wheel, for example by interpolation, in particular by interpolation by a succession of straight lines and/or curves, in particular splines, between said points
Data Source
Figure 1
Figure 2
Figure 3
AI summary
Gear wheel (R2) for a watch movement, adapted to cooperate with a given first gear wheel (R1), characterized in that it comprises teeth whose flank is defined so that the torque ratio j between the two gear wheels (R1, R2) meshed is constant at least over a given angular pitch.