Watch stepper motor

Presented here is the internal mechanics of a watch employing a stepper motor. The watch is simulated using Infolytica's Transient 3D with Motion solver.

The device consists of a steel frame (12.1 mm across) with a stranded coil wrapped around it. The rotor of the stepper motor is made entirely of a neodymium permanent magnet with a fixed direction of magnetization. Instead of modeling all of the underlying gears attached to the rotor, a moment of inertia is applied to correctly simulate the motion. Friction is also applied to the moving body to simulate the contact between the rotor and its gears.

Results

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A 1-volt pulse is applied across the coil from 0 to 3.9 ms. The graph on the right shows the current reported for the coil by MagNet. Once the voltage pulse is complete, current is still flowing within the coil due to the induced currents from the spinning rotor and self-induced effects.

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The voltage applied to the coil for 3.9 ms imparts a spin to the neodymium rotor causing it to rotate 180 degrees. By alternating the sign of the consecutive voltage pulses, the rotor will begin achieving complete revolutions. The graph on the right displays the position vs time of the rotor. As well, below is an animation of the position of the rotor from 0 to 16.35 ms.

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Due to the permanent magnet rotor and the applied voltage, the flux density field creates a torque about the axis of rotation. This torque is responsible for the motion and it can be seen in the graph on the right. The net torque is the combination of the magnetic torque along with the friction that dampens the motion.

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Simulation time: 0 to 16.35 ms. (110 time steps).
CPU: AMD Opteron© 150 2.40 GHz.
Peak RAM used: 568 MB.
Average number of unknowns: 9 770 000.
Solving time per time step: 15 minutes 9 seconds.
Average number of tetrahedra: 295 000.
Average number of tetrahedra in remesh region: 3 500.
Time to generate initial mesh: 73 seconds.
Average time to remesh per time step: 2 seconds.

For each motion time step, the remesh region is recreated and reconnected to the surrounding mesh. With only 1% of the mesh elements in the remesh region, remeshing is a minor step when compared to the actual solving time.

In finite element analysis, the accuracy of a solution can be improved by increasing the polynomial order of each element. In MagNet, it is possible to use hierarchical elements which allow for different polynomial orders for different elements. This allows the user to increase the order in areas of interest and, conversely, lower it in unimportant areas. This leads to a more responsible use of the RAM resources present on the machine running the simulations. Consider the following for the same watch stepper motor presented above.

All elements polynomial order 1

• Number of unknowns: 482 825
• Peak RAM used: 165 MB

All elements polynomial order 2

• Number of unknowns: 6 076 312
• Peak RAM used: 323 MB

All elements polynomial order 3

• Number of unknowns: 34 537 097
• Peak RAM used: 990 MB

For the watch stepper motor presented here, hierarchical elements were used. In the rotor and its surrounding air the polynomial order is 3; in the frame of the watch it is set to 2; and the polynomial order of 1 is used for all remaining bodies.