westkid85

We know that the equation for DC motor to calculate the torque is

Tm = T(load) + J dw/dt + T(friction)

How do we calculate the J dw/dt provided we do not know the value of dw/dt which is the acceleration?

J = (mr^2)/2

Papabravo

As a first approximation assume T(load) and T(friction) are zero. The remaining term is set equal to (Kt * i).

Kt is the torque constant of the motor and i is the current. Now you can get some idea of the acceleration that the motor is capable of with just the shaft and the rotor as a load. As you add in the requirement to accelerate the actual load and overcome additional friction in bearings and so forth, the required torque will go up and the maximum available accleration will decrease accordingly.

Of course you need to confirm your calculation with testing. As a rule of thumb I would start with an available torque (Kt * i) that is 50% to 100% greater than you need to accelerate the shaft and the rotor with no load and zero friction.

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