IComp Instructions and Terminology
Newtonâ€™s First Law of Motion
states that an object not subjected to any net external force moves at a constant velocity.
This is the principle of inertia. 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 pounds mass. A force will accelerate a mass.
In web handling, we are concerned with the inertia of rotating bodies (rollers). This is called the Moment of Inertia
Units of the Moment of Inertia are ft-lb2
(mass) or Kg-m2
. For a solid cylinder, it turns out the Moment of Inertia increases
as the 4th
power of the diameter.
Torque is required to accelerate a roller. The greater the inertia, the greater the torque required. The Acceleration
of a roller is Moment
of Inertia * Torque.
A driveâ€™s speed regulator 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). 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.
While Inertia Compensation should be considered for a fixed roller, it is almost always required for winding rolls if the line speed changes.
That is because there is a huge change in inertia between the core diameter and the maximum diameter of a roll. The inertia of the roll increases
with the 4th
power of the diameter.
Here are some examples of inertia for a 2m wide roll of several products.
|100mm core (kg*m2)||1.0||1.0||1.0||1.0|
|500mm roll (kg*m2)||11.2||7.2||31.0||94.9|
As the diameter changes, the RPM decreases. The torque required for accelerating the roll is Moment of Inertia * Angular Acceleration. The
Inertia of the roll increases as diameter4
, but the angular acceleration decreases with diameter. Therefore, torque increases as
but is shaped like a quadratic. Generally, the torque required is greatest at the maximum diameter, near minimum at
the spindle or core and its minimum value is at a diameter just a bit larger than the core.
The important outputs are:
- The maximum torque which generally occurs at the maximum roll diameter.
- The minimum torque which generally occurs just above the core diameter.
- The diameter at which minimum torque occurs.
- The actual power the roll requires to accelerate at maximum diameter.
- The required motor nameplate power required to accelerate at maximum diameter. This is higher than the actual power by the ratio of
maximum diameter/minimum diameter. This is lowered by increasing gear ratio.
Summary of Inputs and Outputs
The aim is to calculate the extra tension in the web caused by an increase in web speed of ΔV. This depends on the following inputs,
along with derived output values
|Span||Distance between rollers (m or in)|
|Gauge||Thickness of web (mm or mil)|
|Width||Web width (mm or in)|
|Speed||Web speed(m/min or ft/min)|
|Accel||Acceleration Rate (m/min² or ft/min²)|
|Density||Elastic Density of the web(GPa or MPSI)|
|Area||Cross-sectional area of the web (m² or in²)|
|Tc||Time Constant of the tension response to a change in speed at the 2nd roller (s)|
|Gain||Steady-state Gain of the tension response (N/m/min or lbf/ft/min)|
Final tension value (N or lbf), including T-in, can be read from the graph.
A few fun facts:
For unwinds (or winders), there is a specific diameter where the inertia compensation exactly matches the tension torque during acceleration (deceleration).
At this diameter the unwind brake (winder drive) produces no torque, but the tension is correct. Under this circumstance, we often hear the drive train gears
and couplings chattering.
For unwinds, the most thermal stress is put on the motor when decelerating with a large roll. That is because tension and deceleration both act in the same
direction. This occurs while stopping to patch a web defect just after accelerating with a large roll.
Moment of Inertia is the biggest factor in tuning the speed regulator.
If an unwind or winder drive is used for threading the line, the tuning should be optimized for the diameter at which the line is most often threaded. For
unwinds, that is at a large diameter. For winders that is at core diameter.