$$ T = J \times \alpha $$
Torque = Inertia x Angular Acceleration
To size a stage properly the torque must be known. If torque is not known it must be calculated from this equation. The inertia is the total inertia of the customer payload plus the inertia of the moving components of the stage. If the acceleration component is not known it must be calculated. Calculators are provided under the Acceleration tab for estimating the acceleration of a system. Once the torque is determined, the duty cycle for all of the specific torques must be determined to calculate the RMS force, which is the average required torque. The Torque RMS tab provides the tools needed to determine the RMS Torque of a motion profile.
$$ \Large \alpha = \frac{4 \times \theta }{t^2} $$
$$ \Large \alpha = 2\pi^2 f^2 \theta $$
$$ \Large T_{rms} = \sqrt{\left ( T_{a} \right )^2 \times t_{a} + \left ( T_{c} \right )^2 \times t_{c} + \left ( T_{d} \right )^2 \times t_{d} \over \left ( t_{on} + t_{off} \right )} $$
$$ \Large Duty Cycle\left ( \% \right ) ={ t_{on} \over \left ( t_{on} + t_{off}\right )} \times 100 $$
| Example |
Duty Cycle = 1 sec on, 3 sec off
Duty Cycle = 1/(1+3) = 1/4
Duty Cycle = 25% |
Note: Duty Cycle is only for DC motors.
$$ \Large T@100\% = Torque At DutyCycle \div \sqrt{ 1 \over DutyCycle} $$
| Example |
Torque at 10% Duty Cycle = 1 N-m X (1/10%)1/2
Torque at 10% Duty Cycle = 1 N-m X 3.16
Torque at 10% Duty Cycle = 3.16 N-m
|
Note: This calculation is only for DC motors.
Use the following formula for AC motors:
| AC Duty Cycle Calculations |
| Torque @ 50% = Torque @ 100% * 1.75 |
| v@ 15% = Torque @ 100% * 5 |
| Torque @ 3% = Torque @ 100% * 8 |
