International English | Appendix B |
B Some Useful Formulae
B.1 Torque and Power Relationships
If the steady state torque is known, the power requirement can be calculated:
Power [kW] = (Torque [Nm] X Speed [rev/min])/ 9550 or
Torque [Nm] = (9550 X Power [kW])/ Speed [rev/min]
Acceleration Torque.The amount of torque needed to accelerate (or decelerate) a rotating body is dependent on its moment of inertia:
Acceleration Torque [Nm] = Moment of Inertia [kg.m.m] X Acceleration [m/s.s] X 2p/60.
Often it is necessary to calculate the total torque requirement in order to determine the motor type and inverter power.
Total Torque = Acceleration Torque + Steady State Torque
Moment of InertiaThe moment of inertia is often specified for motors, gearboxes etc. It can be calculated for simple bodies, for example:
Solid Cylinder, Radius R, Length l, Mass m:
Moment of inertia = J = m.R2/2
If the cylinder is hollow, with inner radius r, outer radius R:
Moment of inertia = J = m.( R2 - r2)/2
Torque, Power and Moment of Inertia of Practical AssembliesGearboxJ Motor | N Motor | Gearbox |
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| Ratio I, | N Load | |
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| Efficiency E | J Load |
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Figure
Gearbox Ratio I = Nmotor/Nload
MICROMASTER Applications Handbook | 61 |