When spools or webs of continuous paper, wire, cloth, or plastic are manufactured and converted, the material is typically pulled off a roll, processed, and rewound — in unwind, intermediate, and rewind zones. Knowing the unique tension values for each is important for making proper process adjustments and maintaining throughput and quality.

There are several ways to measure and control tension; as we discovered in the last installment of this series (*see the February 2007 issue at* motionsystemdesign.com) load cells are the most accurate. But selecting and sizing the right transducer for an application does require careful attention to detail; designers must fully understand their application and then formulate a basic equation for each transducer to be installed. As always, it's recommended that designers consult with suppliers before submitting orders. Sometimes, after evaluating requirements, they can recommend machine design improvements or alternatives.

### The importance of sizing

Load cells (also called tension transducers) are electromechanical devices that have inherent design limitations. If the tension or force on them is too high, the electromechanical elements become overstressed and fail. If the force is too low, the signal output may be too small to measure. So, because of these restrictions, load cells are manufactured with a range of maximum working force (*MWF*) ratings. The goal for a designer making use of load cells in a system is to select *MWF* ratings that meet *tension range* requirements without overstressing electromechanical elements.

What is tension range? It is the ratio of the maximum running tension to minimum running tension. For example, the range of a system with a maximum running tension of 80 lb and a minimum of 20 lb is 4:1. In fact, transducers for applications in which the tension range is 4:1 can be sized for a larger load and still produce a significant signal during low-tension operation. On the other hand, if the required tension range is wide (10:1 to 40:1) the *MWF* rating must be as small as possible, with the load cell's rating closely matching maximum tension requirements. This ensures that there is enough range remaining to provide sufficient measurement during the system's low-tension operation.

The formulas for *MWF* depend on the transducer design itself, but the range over which transducers can operate depends upon three things: transducer design, machine design, and how they are applied. So, factoring parameters into the formulas returns the *MWF* required by a specific application.

Force exerted on a transducer depends upon the magnitude and orientation of the web's wrap angle, as well as the actual tension in the material. So to design a web-monitoring system, the first step is to obtain the values for tension, roller weight, and a sketch of the web path.

### Applying sizing formulas

How does a designer best determine the wrap angle and angle of tension force? Web wraps around rollers, and transducers measure the force exerted on rollers by the moving web's tension. So assume we have roller mounted with a contained cartridge-style load cell. To use one example: For cartridge-style load cells, the maximum working force exerted on the transducers is then calculated:

where *T* = Maximum total tension

*K* = Transient tension overload factor (normally 1.4 to 2.0)

*A* = Wrap angle

*B* = Angle of tension force

*W* = Weight of roller, lb

The next step is to make a sketch that shows where the web enters and exits as it wraps around the roller. The point at which the web touches the roller as it enters and exits the wrap is referred to as the tangent. Draw a radius from the center of the circle and perpendicular to each tangent at entry and exit: These lines define angle *A*, which is the wrap angle. Then, draw a line that bisects angle *A*. The angle that this line makes with the horizontal is angle *B* — the angle of tension force. If *B* is below the horizontal, assume a positive value in the calculation; if angle *B* is above the horizontal, use a negative value.

The next step is to determine the maximum tension *T* and the minimum tension for your process. If this is not known, consult a transducer supplier. They often offer charts that indicate typical tensions for various materials.

Finally, weigh your design's rollers or calculate their weight to determine *W* and establish *K*. The latter is a safety factor that accounts for transient tension overloads; a value of 1.4 to 2.0 is typical, depending on the application. Plug these values into the equation for *MWF* exerted on each transducer — and then select a transducer rating that exceeds that *MWF*.

It's best to perform the calculation for the minimum tension value as well, because then resulting values predict force output at the lowest tension. If you find that it is a small percentage of the transducer rating (less than 1/20 or 1/40 the rating or so) you may need to increase wrap angle, reorient the web wrap, or reduce the roller weight to achieve a usable measurement at low tension.

### Case in point

In one application for printer RR Donnelley & Sons, Chicago, two transducers are used on each tension roller, one on each side. For one new printer design, initial calculations indicated that the main draw rollers (which are extremely important for maintaining steady tension on the entire web) were too heavy to take full advantage of load cell capabilities. The output signal wasn't strong enough to achieve optimum performance. So, the printer decided to upgrade the entire system, replacing existing rollers with much lighter composite versions. The result: Load-cell resolution improved significantly and boosted overall closed-looped system performance.

*Stay tuned for the final installment of this series. For more information, visit* cmccontrols.com.