# ERRORS IN DOSING SYSTEMS

Every system can generate errors and also dosing systems can be affected. However, there are ways to cancel these errors in order to obtain precise and reliable dosages. It is necessary to distinguish between two types of errors: measurement errors and control errors, respectively caused by instruments and the characteristics of machines. The analysis of errors is comparable to the same valid procedures of weighing systems.

MEASUREMENT ERRORS IN DOSING SYSTEMS

• Tolerance of cell rated output: usually neglected in dosing systems, it is necessary to consider it if high precision is required and it is compensated with the calibration of angles;
• Error of cell linearity: is caused by the weight of each component and its position on the measuring range; if weighing takes place in the centre of measuring range, the error will be zero; the closer it is to the end of measuring range, the greater the error will be; the formula for the calculation is:

El = (Tl / 100) * Pn * (8 – 0,08 * PM) * (S / Ln), in which:

El = error due to linearity (kg)

Tl = linearity amount (line of best fit) (% Ln)

Pn = component net weight (kg)

PM = mean value position of component weight (% f.s.)

S = width of measuring range (kg)

Ln = cell rated capacity (kg)

• Hysteresis error: during discharging dosages use downward linearity calculated as the difference between linearity and hysteresis;
• Drift under load: weight is acquired instantly, therefore it should not be considered;
• Measure resolution: considered in all applications;
• Repeatability error: it has to be calculated considering the weight of every single component to load;
• Stability of A/D converter: not to be considered because it is contained in the resolution;
• Thermal drifts of zero: it has not to be considered with the zeroing before the charge of each component starts;
• Thermal drifts of range: considered according to the weight of each component to load.

CONTROL ERRORS IN DOSING SYSTEMS

On equal terms, control errors in dosing systems are due to production speed. Less precision corresponds to a higher speed. The main causes of control errors are:

• Response time of instruments, even if very short, is a defined value and can significantly affect very short dosing cycles; response time is the time difference between the moment in which the weight exceeds the set value and the moment in which the instrument commands the intervention.
• Stopping time of the machine for component supply, during which a certain amount of material, not weighed yet, continues to supply the metered amount;
• Falling material between the supply machine and the material inside the hopper at the moment of the arrest;
• The total error resulting from the sum of above-mentioned errors, and highly influenced by supply capacity, which justifies what said before: higher speed causes a greater error in dosing; the early arrest of an amount equal to the total error (equivalent to the sum of the three above-mentioned errors) would undo the error unless supply capacity isn’t constant both as a result of the inability of many machines to give a constant volumetric capacity, and the variation of the material specific weight; the resulting dosing error is proportional to the variation of the supply capacity calculated by weight and is equal to the sum of above-mentioned errors multiplied by the percentage of capacity fickleness (between 5% and 20% according to the type of material and machine).

CALIBRATION ACCURACY

All measurement systems have an accuracy based on an ideal calibration line that isn’t always the same as the true calibration value. The difference between the ideal line and the true calibration value is called calibration error. Here are two examples to better understand it:

1. A very accurate balance (0.1%), but calibrated with a +10% error, will always provide different measurements from the true value (measurement error between +9.9% and +10.1%)
2. An inaccurate balance (2%), but exactly calibrated on the true value, will provide more accurate measurements (measurement error between -2% and + 2%)

The choice of calibration method aims at reducing calibration error together with cumbersome calibration operations.

MECHANICAL PROBLEMS

Calibration procedures of weighing systems in industrial plants often encounter problems. In particular, problems are classified according to:

• Static systems: the use of sample weights is extremely onerous for high full-scale capacity because of the position of silos, usually inserted in plants making the handling of big loads difficult;
• Dynamic systems: the use of material for calibration requires the handling of great quantity of material, usually belt balances are positioned in places difficult to reach.

There is the possibility of using simulated calibration methods, less onerous but that require a zeroing of mechanical errors, only possible through an impeccable installation. Among mechanical elements that influence errors in weighing systems, there are:

• The installation of load cells not perfectly vertical
• Differential thermal expansions between weighed part and supports
• Horizontal constraints that introduce a vertical load subtracted from weighing
• Pipes and other instruments for loading and unloading materials inside the hopper, if they aren’t released properly, they will interfere in weight measurement
• The lack of rigidity of the support surface of the hopper