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 Inertia

The 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 AssembliesGearbox

J Motor

N Motor

Gearbox

 

 

 

 

Ratio I,

N Load

 

 

 

 

Efficiency E

J Load

 

 

 

Figure B-1 Practical Assemblies. Gearbox

Gearbox Ratio I = Nmotor/Nload

MICROMASTER Applications Handbook

61