We often think of inertia as resistance to change in velocity in a straight line. In this case the inertia is identical to mass, with units of kilograms or poundsmass.
In web handling, we are concerned with the inertia of rotating bodies (rollers). This is called the Moment of Inertia (but we will refer to it simply as inertia in future blogs). Units of the Moment of Inertia are ft-lbmass^2 or Kg-m^2. It turns out the Moment of Inertia increases as the 4th power of diameter. That is to say the inertia of a hollow cylinder (typical of a roller) is nearly as large as the inertia of a solid cylinder.
The inertia of a roller requires torque for acceleration. The greater the inertia, the greater the torque required. The Acceleration of a roller is Moment of Inertia * Torque.
Inertia is important to variable speed drives in two ways. One is that the tuning of the speed regulator compensates for the inertia of the roller. More inertia requires more gain. Gain can be increased with a larger number or a larger motor.
Second is that the speed regulator by itself is incapable of accurately accelerating the roller with the line pacer. The speed will always lag behind the speed reference when the speed is changing (ramping). Regulators with a single integrator have an error while ramping. We can compensate for this speed lag with inertia compensation. Inertia compensation for a fixed roller adds a torque proportional to the inertia when accelerating at a fixed rate. Inertia compensation is suggested for all rollers if tension requirements indicate that all rollers accelerate together.
Most drives have inertia compensation available, but this compensation is disabled by default. If there are tension variations during speed change, consider using inertia compensation on the driven fixed rollers.