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Rotary Motion Calculator

$$ \Large T_{rms} = \sqrt{\left ( T_{a} \right )^2 \times t_{a} + \left ( T_{c} \right )^2 \times t_{c} + \left ( T_{d} \right )^2 \times t_{d} \over \left ( t_{on} + t_{off} \right )} $$
Variable Description Units Calculation
Tα Acceleration Torque
Tc Constant Velocity Torque
Td Deceleration Torque
ta Time to accelerate (sec)
tc Time at constant velocity (sec)
td Time to decelerate (sec)
ton ta + tc + td (sec)
toff Dwell time (sec)
Trms Average required torque 0
$$ \Large Duty Cycle\left ( \% \right ) ={ t_{on} \over \left ( t_{on} + t_{off}\right )} \times 100 $$
Variable Description Calculation
ton Time with power applied (sec)
toff Dwell time (sec)
Duty Cycle (%) Percentage of total time spent active 0
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.
$$ \Large T@100\% = Torque At DutyCycle \div \sqrt{ 1 \over DutyCycle} $$
Variable Calculation
Duty Cycle %
Torque at Duty Cycle
Torque at 100 % 0
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