When webs of continuous paper, wire, cloth, or plastic are manufactured, 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 maintaining throughput and quality.
There are several ways to measure and control tension; as we discovered in the last installments of this series (see the February and June 2007 issues at motionsystemdesign.com) selecting and sizing the right transducer for an application requires careful attention to detail. Let's now discuss how orientation and size affects the performance of these sensors.
Get the most from load cells
Assume we're using a cartridgestyle transducer. (The formulas for other styles may be different so the specifics may change, but the principles for application are the same.) First things first: Load cells must be oriented properly. This is because the force exerted on the roller by tension in the material must bend the transducer beam to produce measurements. The force from tension in the material always points along the bisector of the angle of wrap. The bisector is the line that splits the angle in half, also called the angle of tension force. If the bisector of the wrap angle is vertical and the material pulls down on the roller, this force points straight down. If the bisector of the wrap angle is vertical and the material is pulling up on the roller, the force points straight up. Pulling horizontally on the roller is often used to negate the effect of the roller weight on the transducer.
There is an arrow on the coupling face of our example cartridge transducer. Installation instructions require that the transducer body be rotated so that the arrow is in line with the bisector of the wrap angle. When oriented this way, force is always perpendicular to the beam. So the beam undergoes maximum bending/deflection, which makes for a larger output measurement signal. For this reason, under a given tension and wrap angle, no other orientation yields stronger measurements. If the transducer is not installed to align with the bisector of the wrap angle, measurement power is diminished.
Generally, eyeballing is sufficient to achieve proper alignment. The resultant signal output is a function of the sin of the included angle between the direction of the force and beam surface. 5° of misalignment results in less than a 1% decrease in signal strength. Being 15° off results in only a 4% drop.
Consider roller weight
Keep in mind that load cells not only measure force due to material tension, but also that from roller mass. The force measured by the transducer due to the mass of the roller is called tare weight. It's a function of the roller mass and orientation of the transducer with respect to gravitational force. Gravity always pulls a mass toward the earth — so force due to gravity (weight) points vertically downward and bends (or deflects) the transducer beam most when it is perpendicular to it. As part of calibration, tare weight is zeroed so that only the signal due to tension is measured. This is accomplished by various means with electronic amplifiers or controllers, either automatically or by adjusting a potentiometer.
If the output signal due to the tare weight is too great, less of the total transducer output signal can be utilized for measuring the tension force. This is especially important to consider when roll weight is large in comparison to required tension. As a general rule of thumb, tare weight should be no greater than two-thirds of the transducer load rating MWF. This preserves enough signal to measure tension load.
There are exceptions to this — say, if the tension range is small, 2:1 or 4:1. But for a large tension range (20 or 30:1) tare weight must be reduced to zero or used to extend the transducer range, by working in the opposite direction of the load. In other words, either the roller weight must be reduced or the web path changed so that the transducer can be oriented differently. One option is to use rollers of aluminum or composite material to reduce their weight.
Make weight work for you
The tare weight term ±W sin(B)/2 is gravitational force exerted on the transducer beam by roller mass. Angle B is the angle between the horizontal and the bisector of the wrap angle. So, B is always between 0° and 90°.
When B is exactly 90° it means that force is either pulling straight up or down on the roller. The sin of 90° is 1, so with B = 90° tare weight is ±W/2 — half the weight of the roller, as there are two transducers supporting the roller. When tension pulls down on a roller, tare weight W/2 acts in the same direction as the tension force, and is positive. It adds to the tension force to increase total load on the transducer.
By setting the web to pull up on the transducer, you can make roller weight work for you. Here, tare weight W/2 acts in the opposite direction of the tension force and is negative. It's subtracted from tension force to decrease the total load on the transducer. For example, assume maximum tension in the material is 50 lb, roller weight is 60 lb, and wrap angle is 180°. With a cartridge-style transducer, if force is pulling straight down, MWF is 80 lb per transducer. (50 lb is the force due to the tension and 30 lb is the tare weight.) You'll have to select a transducer that meets or exceeds an 80-lb rating for this application.
On the other hand, if the web path is changed so that force is pulling straight up, MWF is 20 lb per transducer. 50 lb is the force due to the tension and 30 lb is the opposing tare weight — which is subtracted. Pulling up on the roll allows a lower MWF rating, for higher transducer output and sensitivity. One caveat: Though a transducer with a 20-lb rating meets the minimum MWF rating in this situation, it is not enough to support the 30-lb tare weight. So, a transducer with a rating greater than 30 lb must be selected.
That said, by pulling up instead of down on the roll, reduced transducer size increases sensitivity, cuts costs, and increases the ability to measure lower tensions — and expands the range of measurable tensions. How? A transducer with a lower MWF force rating is more sensitive to lighter loads than one with a higher MWF rating. That's why the recommended orientation for most applications is a 180° wrap angle, pulling straight up on the roller.
When B is 0° force pulls horizontally on the roller. The sin of 0° is 0, so B = 0° yields a tare weight of zero. In other words, pulling horizontally against the roller negates any effects of roller weight.
Horizontal setting exercise
For the same application we just explored, calculate MWF when the material is pulling horizontally against the roller. Ignore the safety factor by making K = 1. Maximum working force is 5 lb (the force due to the tension) and 0 lb is the tare weight. Now assume the closest transducer rating that meets or exceeds this MWF is 25 lb. Output signal is only that due to tension force. So, only 20% (5 lb) of the available transducer output signal (good to 25 lb) is being utilized for the maximum tension measurement — but there is no output due to the roller weight. This means that everything being measured is actual tension signal.
This technique improves the measurements of small signals when roll weight is appreciably larger than the tension. Note that transducer MWF rating should not be less than the weight it might support. Otherwise, you could damage it by overloading, or find yourself unable to zero out the roller weight with the electronics.
Something else to consider: Even though the tare weight is zero, the transducer is subjected to the weight of the roller while it is being installed and rotated into position.
Make wrap angle work for you
The force due to tension and wrap angle is part of the sizing formula. As we reviewed in previous installments, the term 2T x sin (A/2)/2 is the force exerted by the tension in the material as it wraps around the roller. (The term is divided by two because there are two transducers supporting this roller, and they divide the total load.) Tension T pulls in opposite directions, away from the roller, and this puts double the load (or 2T) on the roller. The portion of tension that is transmitted to the roller and the transducer is dependent upon the amount of wrap around the roller. Wrap angle is the angle between where the web first touches the roller as it enters, and where it last touches as it exits.
The portion of tension transmitted through the wrap angle is sin (A/2) and its maximum value is one — which occurs when angle A is 180° — sin (180°/2) = sin (90°) =1. The largest amount of tension is transmitted to the roller when the wrap angle is 180°. (Think about it: When A is 0° there is no wrap around the roller and the tension force is zero.) So, for typical applications, and especially for low tension, make the wrap angle as large as possible. This produces the greatest tension force giving more signal output resulting in a better measurement.
Many machine designers use a minimum of 30° of wrap as a general rule of thumb. A wrap angle of 30° transmits 25% of the line tension to the transducer. This is still a significant value, so the signal will be manageable. In most cases, this also gives enough wrap to ensure that the material stays in contact with the roller surface. There is another reason for the 30° rule. Particularly with light material running at low tension and at high speeds, air may blow under the material and cause it to rise and lose contact with the roller surface.
In fact, transducers are applied at much lower angles of wrap, but these applications require scrutiny to ensure proper performance. For some applications it is desirable to slightly decrease the wrap angle, to use a smaller transducer with a smaller MWF rating. This is generally the approach when large tension ranges are required. In this case, we want to use the entire transducer output signal in order to get maximum resolution.
Maintain a fixed angle of wrap throughout the process. Otherwise, if the angle of wrap varies, the tension force on the transducer changes. This results in inaccurate measurements. Only use transducers on rollers where the wrap angle is fixed.
Safety factor: Use judiciously
A safety factor K is assigned to ensure that the MWF rating of the transducer is high enough to protect it from transient overloads. Overload conditions may damage the transducers, and some transducers are rated for higher overloads than others. A typical overload rating is 150% of MWF. A value for K of 1.4 to 2 is typically used for these transducers, which effectively extends the overload protection to 210% and 300%. But it is not always necessary to assign a K value greater that 1; it depends upon the application and the transducer overload rating. Some overload limits reach 500% and even 1,000%. If the maximum tension value is conservative, and the machine has tight controls, the K value doesn't need to be large. Making the K value too big may make for an oversized transducer, which limits the low end of the effective tension range.
Of course, undersized and overloaded transducers may become damaged. But when a large tension range is required (say, 20:1 or 40:1) oversizing the transducer limits its low-end performance. When a small tension range is required (2:1 to 4:1) oversizing the transducers gives it extra protection.
Be realistic about tension control and tension range. How well tension can be controlled (and over what range) depends upon many factors not related to load cells. Some of these factors are the mechanical design of the machine, mechanical wear of the components, line speed, and the mechanical and electrical system response. All systems have natural resonant frequencies that limit their ability to be controlled and to respond to corrective changes.
Controlling tension above a 20:1 or 30:1 range with acceptable tolerances is extremely difficult. In fact, some system integrators won't even accept jobs specifying a tension range over 10:1. For this reason, although load cell signal output is linear all the way down to zero, try not to exceed a 40:1 tension range from an individual load cell. These applications require special attention. (Steps can be taken to extend the measuring range such as routing the web over an idler roller to change the wrap angle.) But many applications require much less range than this — 4:1 to 8:1.
Bandwidth and response
These two quantities quantify a system's capability to react to command changes. Bandwidth for any system is the maximum frequency at which a system can be excited and still remain stable. The value of this bandwidth is less than the natural frequency of a system. For example, in a mechanical system, the natural frequency of a mass attached to a spring is expressed:
w = square root of k/m
where w = natural frequency
k = spring stiffness, N/m, and
m = the inertial mass, kg.
If this type of system is excited at its natural frequency, the system oscillates uncontrollably and becomes unstable. Well, electrical systems operate in a similar manner. For a servo system, bandwidth is the frequency of small signal change (10% or less) that, applied to the input, reduces output to 0.707 (-3 dB) of input. Servo bandwidth is expressed in Hertz (cycles per second) and radians per second. To convert from Hz to rad/sec, multiply the Hz value by 2π. For example, a hypothetical servo system has a bandwidth of 100 Hz. This can also be expressed as 628 rad/sec.
Response time indicates the time (in seconds or milliseconds) for output to reach the speed or position commanded by a small input change. For slightly underdampened systems — and most servo systems fall into this category — response time is approximately three times the reciprocal of the bandwidth when expressed in rad/sec. To illustrate: A servo with a 100-Hz (628-rad/sec) bandwidth has a response time of 3(1/628) = 0.005 sec. Thus, the servo reaches the full value of a small input change in 5 msec.
Typically, for small input changes, ac brushless servo drives have a bandwidth of 100 Hz and response times of 0.005 sec. For systems where a large change (more than 10%) is required, system response must usually be added to acceleration time because of load inertia, maximum accelerating current, and other factors.
To learn more about using load cells for web tension control, visit the archives of motionsystemdesign.com, and scroll to the February and June 2007 issues to read Part I and Part II of this article series, or visit cmccontrols.com.
Questions to ask
Is the primary sensor type well accepted?
For primary sensing elements, load cells use strain gages, LVDTs, and magnetoelastic units. Strain gages as primary measuring elements are extremely linear in their response and reliable. They are also utilized and proven in highly accurate applications including weigh scales, Formula One and NASCAR racecars, and aerospace and defense applications.
Will the load cell disrupt the web path?
A primary consideration in tension sensing is keeping the path of the moving web undisrupted as measurements are being taken. This means that the deflection of the load cell must be minimal. The more deflection, the more likely the web path will be disturbed and not track properly. Low deflection at the rated tension load is between 0.002 and 0.004 in. Here, twin-beam designs keep any beam deflection perpendicular to the web path, to prevent steering to one side. Note that load cells using strain gages have significantly less deflection than those using LVDTs.
Will the load cell allow for shaft misalignment?
In a perfect world, all rollers in every web line would be perfectly aligned from end to end and with respect to their neighbors. But even with the best installations, misalignment occurs. Where rollers are mounted to pillow block bearings, the bearing must be one designed to accommodate shaft misalignment. When the load cell is coupled to the roller shaft, the load cell must be able to accommodate the shaft misalignment.
Some load cells are designed to accommodate up to ±1° of misalignment from one end of the roller shaft to the other, some with a Teflon-coated aircraft-grade alignment bearing. The Teflon eliminates fretting corrosion, which occurs when metal surfaces are knocked together by vibration. This corrodes the metal over time, weakening it, and creating a rust-like condition.
Not all manufacturers offer load cells that accommodate for shaft misalignment. In these cases, binding may occur and make the load cell measure stress as a force that interferes with the true tension measurement. Some designs use a diaphragm to accommodate for misalignment, but they weaken with repeated bending, and can eventually crack and break.
What is the strength of the output signal?
The signal output of the load cell must be large enough for it to operate over a large tension range — typically 20:1 to 40:1. Semiconductor strain gages have very high gage factors (100) and provide high signal output at small deflections to provide up to 400 mV output at rated load. Other designs provide as little as 21 mV at rated load.
How responsive is the load cell?
Load cells must respond quickly to tension changes. This is especially true in closed-loop applications. Some load cells are designed to have a high natural frequency, to respond quickly to changing web tension. Electronics such as amplifiers, indicators, and controllers are also designed to accommodate this rapid response. High inertia limits their response capability, and suppliers should be able to calculate the response of their load cell in your application. Stay away from designs that require movement of substantial mass; they yield sluggish response.
Is the load cell's signal linear and repeatable?
Look for a combined nonlinearity and hysteresis no more than ±0.5% of rated output, and repeatability of ±0.2% maximum of rate output. Manufacturers provide specifications for these ratings. They are not consistent on how they present their ratings so take this into account. One caveat: All systems have natural resonant frequencies that limit their controllability and response to corrective changes.
Is the load cell temperature compensated?
Look for a sensitivity change (in the output signal) of less than 0.02% per degree Fahrenheit. To this end, some load cells incorporate a temperature compensation network.
Will the load cell accommodate shaft expansion?
Roller shafts expand in length as temperature increases. This creates a stress on the mounting components. If not properly relieved, load cells measure this stress, and that interferes with true tension measurement. Where a roller is mounted to a pillow block bearing, the bearing must be designed to accommodate shaft expansion. When the load cell is coupled to the roller shaft, the load cell must accommodate shaft expansion. Some load cells are designed to accommodate 0.10 in. of shaft expansion per transducer. Where twin load cells are utilized, shaft expansion of 0.20 in. can be accommodated.
Many designs require one end of the roller shaft to be tightened to a transducer coupling, and a free end to float in the transducer coupling. While this relieves the stress due to shaft expansion, it requires special mounting procedures and the use of feeler gages to set the appropriate gaps. Ensuring that the gap is even may require the use of shims, and adhering to these requirements places much responsibility on the expertise and judgment of the installer. This can lead to improper installation or inconsistencies, especially during replacement of roller bearings, for example.
Will the load cell be reliable and durable?
Look at the construction of the load cell. Is it open or sealed? Dust entering into the sensing elements can shorten the operating life. Is the body cast, machined, or made from sheet metal? Sheet metal designs are not very rugged. Does the design require moving parts, mechanical springs, or offsets? These wear over time and present calibration problems. How reputable is the load cell manufacturer? A good reputation is generally derived from producing a reliable product. The most reliable load cells have no moving parts and last 20 years or longer.