The process of winding has been described as pulling one truck with another truck and the web as the chain. In the paper industry, we talked about 10-ton trucks.
Not all lines require inertia compensation. If a continuous process line is threaded, brought up to speed and then the product is brought into spec, no inertia compensation is required.
To prevent breaking the web on speed changes, a few key drive system items are needed. The first is that S Ramps should be used. An S Ramp eases into acceleration and reduces jerk on the web. The S time cuts into the productivity of the line and should be kept as short as possible. For newsprint, the S time is often 6 to 10 seconds. Many plastic films can accept an S time shorter than 1 second. Inertia compensation is used only when the speed is changing.
An interesting fact about drive speed regulators is that they are incredibly accurate at a steady speed. It is well known that single integrating (type 1) speed regulators lag behind a ramping speed reference. A feed-forward technique is used to compensate for the rotational moment of inertia of the wound roll or any roller. The rotational inertia can be measured or calculated and compensated with inertia compensation. Inertia increases as the 4th power of diameter and is quite significant for some materials.
Inertia compensation depends on accurate diameter measurement of the roll. The density of the product is then one parameter (for large diameter). We assume the density is constant from day to day and product to product. Inertia compensation also depends on the inertia of the motor, roller, and shafts (for small diameter). Drive vendors have techniques for setting the inertia compensation by accelerating empty shafts and full rolls. One of the simplest measurements is to monitor the output of the speed regulator and make adjustments to the small diameter or large diameter inertia compensation factors while accelerating a taped up roll. The speed regulator output will not change if the inertia compensation is correct.
Any errors in calibrating inertia compensation will be seen at the output of the tension regulator while changing speed. There is no value in setting the inertia compensation to better than 3 significant figures as the product density varies by more than that. Spend time calibrating the diameter calculator.