Derek: 2007 06 20 - Fixing the X-Y arms

Progress Report

Fixing the X-Y arms

1. The X-Y motors were unable to rotate the worm axles. Hence, we asked ourselves if the failure was caused by an electrical fault, where the stepper driver does not provide enough current to drive the motor, or a mechanical fault, where there is not enough torque to rotate the axles.

2. Parameters for the motor, before we began to analyse the problem
- Speed of rotation = 272 rpm (using a tachometer)
- Input power = Input current * Input voltage = 1.69 A * 12 V ≈ 20.28 W
=> Torque provided by motor = Input power / Angular velocity ≈ 0.716 Nm

3. In our electrical findings, we realized that the motor driver is providing enough current to rotate the motor. The input current into the motor, measured using a current probe, showed that the current is well below the absolute maximum rating (2 A) of the motor driver. As there was nothing wrong with the electrical components, we concluded that there was no electrical fault.

4. Hence, we narrowed down to the mechanical fault. We came out with three solutions:

a. use a larger motor that has provides a larger torque but this would mean a total change in the circuit boards, which would us back to breadboard prototyping and it just takes up too much time.

b. the axles had to be placed precisely horizontal so that there will not be a large resultant reaction force on the coupling. However, this did not seem feasible as it would make the system not very robust.

c. to reduce the weight of the axles to reduce the moment of inertia and hence reduce the amount of torque required to rotate the axle. This proved to be a better and more viable solution.

5. Calculating the torque required to rotate the old axle, we took the parameters of the axle to find:
- Mass of axle = 933 g
- Radius of axle = 8 mm
=> Torque required to rotate the axle = moment of inertia * angular acceleration ≈ 0.850 Nm

6. Hence, we see that torque provided by the motor was below the torque required to rotate the old axle. That meant that the axle was too heavy at 933 g. We proceeded to try with a lighter rod of 400 g with a smaller radius and the motors started to rotate without any problems. We concluded that the new axle should have a lower mass and a smaller diameter.

7. Currently to match the speed of the hamster with our current motor speed, we would require a lead screw with a pitch of 30mm. I have checked with the supplier and he mentioned that the diameter of the lead screw would need to be large to compensate for the large pitch. Furthermore, the material used for the lead screw is commonly carbon steel and we were not able to get a custom made lead screw with a metal of a lower density. We cannot go ahead with the larger diameter and weight as this would greatly increase the torque required. We decided to stick with market available standard sizes (10 mm diameter with a 2 mm screw pitch) and we made orders for three of them.

8. To try to bring the speed of the motor up, we will try to up ratio the speed with a planetary gear to get an optimal speed without reaching the threshold of our torque required.

End.

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