Accuracy Claims for Belt Weighers
There is a tendency for those who have purchased a 0.5% accurate instrument, to simply believe that the device could not have an error worse than 0.5%. The answers that come from it seem to have an unearthly authority and users seem to believe that the device will always tell the truth except perhaps on a bad day when it might have an error of as much as 0.5%.
Primary instruments that measure simple parameters such as temperature and pressure can have a known accuracy if used correctly, however, belt weighers, are more complex devices which measure two noisy, error prone inputs (weight and distance) and very often have to be ‘adjusted’ to get the right result. It is more the truth that a 0.5% belt weigher will read within +/-0.5% of the truth, if used correctly, on a good day, however, if not carefully maintained will more often give answers within +/-2 to 3% of the truth or even worse.
Given that a belt weigher that is really accurate and reliable would be a much sort after device, it’s important to know how belt weigher accuracy is determined by the manufacturers, and how their accuracy claims are best understood.
Most belt weighers use modern strain gauge load cells to measure the weight input of a belt scale, and process the information with a microprocessor. The microprocessor can be errorless in operation and almost any good modern load cell will hold accuracy within +/-0.1% for more than a year over a wide range of temperatures. Why then, does there seem to be a need to continually calibrate belt weighers? Why it is so hard to get a 0.25% belt weigher?
To answer the question, the concepts of Random and Systematic error need to be discussed and their application to belt weighing explained. Then it will be possible to respond in a more informed way to belt weigher sales talk and be better equipped to choose the right equipment for projects.
Random Error and Systematic Error
Random Error, also called “Non repeatability” is the name for the errors which are seen when the same measurement is repeated over and over. Systematic error, on the other hand, is the error that is always there.
As a simple example, if you weigh yourself on your bathroom scales many times over several days, you won’t always get the same answer. There are many potential reasons for this: the temperature has changed, you did not stand on the scale the same way, there is some vibration about, or the bathroom scale battery is going flat, just to name a few. We now have a list of weights, and we can work out the standard deviation and average weight from our list of measurements. (The standard deviation is a measure of the variability of the results).
We might be tempted to assume that our true weight is the calculated average weight; however, a trip to the Fair Trading calibration facility would soon confirm a weight in which you could have much more confidence. Let’s call the weight from Fair Trading, the True Weight, so we can do some calculations;
Systematic error= Average Weight – True Weight
Random Error: - related to the standard deviation of our list of measurements.
This can be the working understanding of random and systematic error. Random error is often easily found out by repeatedly testing equipment with the same ‘test sample’. The determination of systematic error is more difficult, requiring the use of an outside reference standard, usually from a standards authority.
You might argue that weighing yourself is not a good example because weight varies from day to day, hour to hour. The comment is correct. However, this example highlights the difficulty which is often faced with testing instruments using the ‘same’ test sample. The more complex the instrument, the more difficult it is to apply an identical test sample.
Having introduced the terms, we need to understand their role in belt weighing.
Random error affects calibration
Imagine first a belt weighing system with a +/-1% random error. In statistical terms, let’s say that two standard deviations is equal to 1% and therefore we expect 95% of all readings to lie within a +/-1% error band.
Suppose we want to calibrate this weighing system, and we apply a mass to it, taking only one reading as the basis of our calibration. It is easy to see that the calibration of the scale might now quite easily have a built in error of up to 1.0%, which will always be there. Now when the weighing system is used to weigh something, the error could be as much as 1%+/-1%.
It can be seen that in calibrating belt weighers, we need to have some understanding of the repeatability or randomness of the unit. Best practice is to always base calibration on a series of measurements. The more random the device, the more care is required in calibrating it, so as to reduce systematic error to a minimum. Calibration might be defined as “reducing systematic error to zero” or “reducing systematic error to acceptable levels”.
Sources of Random Error
In Belt Weighing, random errors come from “influence factors” such as belt tension affects, idler roll alignment and out of round, the general sensitivity of the belt scales weigh frame to alignment, temperature and belt tension. These factors move slowly around in circles so that over a year, a typical highly random belt scale may move around inside a few percent range. While there are only a few fundamental sources of variability, they take many forms; here is a brief list;
- Weigh frame deflection and belt stiffness
- Weigh frame sensitivity to the position at which calibration masses are applied
- Weigh frame friction, stiction and hysteresis.
- Belt tension, variability of belt tension (say sticky GTU or a screw take-up)
- Weigh frame initial alignment quality
- Uncontrolled spillage which is not zeroed off,
And, thinking now of the tachometer;
- Connection of the tachometer to belt, skip, slip, bounce
- Stability of diameter in the face of process material build-up
- Angle of wrap around pick-up pulley and belt tension variation
The apparent randomness of a belt weigher stems from the cross sensitivity of the units, two measuring sensors (weigh frame and tachometer) to other “influence factors” which come primarily from a weight measurement which is being conducted dynamically through a taught moving conveyor belt.
The knowledge of how to reduce influence factors to quantifiable and acceptable levels, is key to the design of good belt weighing equipment. As a weigh frame becomes more adequate in its ability to eliminate the randomness that comes from outside influence factors, its build cost increases.
It is the belt weigher supplier’s responsibility to ensure that the equipment is matched to the application, in terms of performance. This often leads to the cost of equipment being viewed as not competitive. One of the difficulties of the business is that in order to make a sale, an inadequate belt weigher is very often offered, and accepted by a customer who is not armed with sufficient knowledge to make the best choice.
Systematic Errors
Systematic errors come from
- the inherent randomness of the belt weigher itself, and
- the difficulty of simulating a live load of material on the belt.
The solution to this can only come from an appropriate combination of
- Always taking multiple measurements to overcome the affects of randomness or to verify repeatability;
- Choosing more inherently stable weigh frame and tachometer systems, which have known and acceptable immunity to influence factors; and
- Going to greater extremes in simulating live loads of material for calibration purposes.
Experienced belt weigher manufacturers know that the best way to minimise systematic errors in belt weighing is to choose substantial weigh frames which have a minimum of random error. These same weigh frames are the most amenable to allowing simple and accurate simulation of live load.