Application of the Month
Tension Determines Torque
November, 2012  View all Application Examples
Winding and unwinding coils of material, including paper, film, and plastic, among others, usually requires variable speed operation and precise tension control. Tension is important for maintaining material thickness throughout the process and variable speed is necessary to control linear throughput.
We have many winder/unwind manufacturers as customers. It seems that each one calls in every time they have a project to go over the specifications and get help selecting a gearbox. This is fine. It’s what we do. But it’s probably because these applications don’t quite follow the normal torque calculation formula used for continuous speed gearbox selection.
In most cases a gearbox can be selected by calculating the horsepower given times a unit of measure factor, divided by output speed. Of course, efficiency and applied service factors may affect the final selection, but that’s the basic calculation.
However, in winder applications the output speed is always changing. This is because as the roll takes up material it’s diameter changes by getting larger. With the larger diameter comes a larger circumference. And with the larger circumference more material is picked up per roll revolution. So, to maintain a fixed material linear speed through the machine, the rotational speed slows down as the roll gets bigger.
With the speed change there is also a torque change. Obviously as the roll gets larger and heavier, it’s just tougher to turn. However, that isn’t the real reason for the torque level increase. The culprit is the tension force from the material at a growing distance from the center of the roll.
This is where we can use the other common torque formula. The one that states that torque is equal to force times distance.
In this case the distance is the growing radius from the roll core to the outside edge. For the force we need a little help from the customer.
Depending on the product being produced there is a specific tension applied. This is usually specified as PLI, or pounds per linear inch. Multiplying this value by the width of the roller, or more specifically the material, will give us the overall material tension, which is the force we need.
So, this leads us to the short cut for sizing gearboxes in winder/unwind applications. The highest operational torque required will be at the maximum roll diameter. By multiplying the full roll radius by the tension value we will get a torque value at a given rpm (ft/min divided by circumference), which will be the slowest within the cycle. As long as the gearbox can handle the torque at this stage, the first hurdle is passed.
There are two other elements that may need consideration. The first is core speed. To take up the material at the required linear speed the core must rotate very quickly, often at a higher speed than the continuous rating of the gearbox. However, as the material builds on the roll this high speed is rapidly reduced before the gearbox can get hot. Therefore this is rarely an issue.
The second element is emergency stops. Whether it be from a web jam or someone pushing the big red button, the roll has to be stopped quickly. It’s now an inertia issue. For this a different torque calculation is used, more like a accel/decel motion control application, to determine the estop torque to stop the load in a given time frame. And the time part is most critical. With a given inertia at a given change in speed, the time to stop has a linear effect on the torque required to stop.
We’ve found that the estop torque is quite often lower than the operational torque. At maximum inertia the speed is lowest. At highest speed, the inertia is the least. And even if the torque required is higher, gearboxes can easily handle 2x3x their rating for short periods.
The product that most of our customers use is the Tandler spiral bevel right angle gearbox, series HW, usually in ratios of 4:1 or 5:1. The shaft mount allows direct mounting on the roll journal shaft and we often fabricate a custom motor adapter to create a gearmotor effect. Output shafts are available in metric bores with keyways, spline shafts, and hollow bores with shrink discs. There are 8 sizes of gearboxes available for machines of all sizes.
These ratios allow for a reasonable motor speed at the low end to maintain motor efficiency and some torque multiplication at the high speed end in case they have to over speed the motor, which would reduce torque output, to maintain linear speed at the core.
Another advantage of the Tandler box is the very accurate rotary velocity within each revolution. Especially in film or coating applications, where tension and linear velocity is critical, the predictable tooth to tooth velocity provides extremely smooth operation.
For something called a turret winder, there are often two rolls that allow change over while the machine is still running. For these machines the turret rotates 180 degrees to move the second roll into position to be spliced into the web while the first roll can be replaced. For these applications, low backlash is helpful. To drive this part of the mechanism we have low backlash worm and helical bevel gearboxes in sizes that can handle the weight of very large rolls.
Providing customers with selection assistance is a prime function of DieQua product support personnel. With the wide variety of gearbox solutions and the vast experience applying them, allowing us to help choose the appropriate product assures you the gearbox will perform at the optimal level.
Chris Popp
Director of Marketing

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