WatchTech - Simulation and Mechanical Design in Watchmaking

Simulation and Mechanical Design in Watchmaking

Simulation and Mechanical Design in Watchmaking
by Xavier Clement

Introduction
Finite element simulation is a powerful tool that allows to optimise the geometry of parts by simulating their function. Using finite element simulation it is possible to reduce the time necessary to fine-tune parts in prototyping by eliminating as many unknowns as possible in the design phase. At the same time this technology requires a profound knowledge of the mechanisms being simulated and a rigorous design. Setting the parameters for the simulation is critical for a good result and can take more time than the simulation itself. With bad parameters a simulation is often not possible or is not realistic. Of course the goal is to have realistic and reliable results. To this end it is essential to estimate the reliability of the results by identifying the approximations used in converting the real mechanism into a simulation model. In the following I propose a succinct description of the different steps in a 2-dimensional simulation of a common mechanism (jumper and star wheel) using the Ansys finite element program.

Parameters
- For each piece of the model it is necessary to define :
- Thickness
- Material
- Character (deformable of not deformable)

Then one defines the zones of contact between the different parts and the corresponding coefficients of friction.

Mesh
The dimensioning of the mesh elements for the finite element analysis determines the precision of the results, but also the necessary computing time. To optimize the processing time while maintaining reliable results the object is to have a fine mesh in the areas that may be deformed, but a course mesh otherwise.

Border conditions
This step determines the degrees of liberty of movement of the pieces allong with the external actions that the pieces will react to (forces, torques, movements…).
For this simulation we will start by moving the jumper until it comes into contact with the teeth of the star.
Then the star will be animated with a rotating movement corresponding to the passage of one tooth.

Results
Calculation time: about 5 minutes
Objectives of the simulation:
- Verify that the part remains in its elastic zone (where it will bend but not retain the new shape after the force is removed ( ?max < ?e ))
- Calculate the torque caused by the jumper as one tooth of the star passes.

Distribution of the stress :
- The stress is highest at the surface of the bent portions of the jumper, shown here in red.

Evolution of the stress and torque:
This graph shows the stress and torque on the jumper when the star wheel turns the distance between 2 teeth, as there are 7 teeth this is 51.42°. The stress is in red

Observations :
- As we see the jumper starts pushing the star wheel at 32° which is 64% of the turn and not 50% as we would expect. This is due the non-symmetrical form of the jumper head and the friction at the point of contact between the jumper and the star.
- The holding stress of the jumper is about 180 MPa.
- The movement of the jumper causes a rotation of the star by about 1° compared to its theoretical starting position.

English translation Don Corson

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