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How to mathematically calculate the accuracy and resolution of weighing system

2011-07-08 09:25   Article Source:N/A   View Times:

If you are only measuring after you remove weight from your system in batch format, you should use the hysteresis specification of your load cells combined with the accuracy of your electronics to determine accuracy.

If you measure after adding AND removing weight from your system, you can use the combined error (linearity and hysteresis) of your load cells combined with the accuracy of your electronics to determine system accuracy. You have to take into account the error of your controller, load cells, gravity correction, and verify that there are no other issues that may affect your accuracy reading (like EMI/RFI noise, scale binding, correct load cell placement, etc) and environmental variations (such as humidity, temperature and wind). For example, using a 16,500lb Hardy load cell: Linearity 0.012% = 1.98lb or approximately 1 in 10,000 Hysteresis 0.025% = 4.125lb or approximately 1 in 3000 Combined error 0.02% = 3.3lb or approximately 1 in 5000 The above does not including mechanical, electronic or electrically induced errors. Before designing a system, an engineer should consider carefully what he or she expects from it and then relate this to the component accuracies making up the system. No physical measuring system can be completely accurate. An error band must be defined for a system which gives an indication of any expected deviations from true value. The parameters under which this applies must also be clear and concise. Accuracy terms such as "1 part in 3000" are commonly used. Calculating true weigh system accuracy is very difficult, and many customers do not know what they really require from their system.

They often request a "system to be as accurate as possible". Proper installation is critical to maximize a systems accuracy, but other considerations such as connecting pipes and conduits must be taken into account. One thing is certain, good load cells do not make a poor system good, but poor load cells can make a good system poor. Hardy Instruments and load cells are considered by many to be the most accurate available in today’s process weighing market.

In the vast majority of applications, weighing occurs in only a small portion of the load cell’s range. Thus non-repeatability is the most important specification for most system designers. LOAD SENSOR NON-REPEATABILITY: A standard non-repeatability for a typical load sensor is 0.01% of Full Scale. This is the equivalent of one part in 10,000 of total system load cell capacity. In a 300 pound example the non-repeatability would be + or - 0.03 pounds. The simple definition for non-repeatability is: the maximum error seen if the same amount of material was repeatedly add to or removed from the same vessel, under the same environmental conditions. This situation is often encountered in batching applications. SYSTEM STATISTICAL ERROR: In a multiple load cell system the “combined error” parameters are not added together but are combined using the following formula: The square root of the sum of load cell number one’s “combined error” squared, plus load cell number two’s “combined error” squared, plus load cell number three’s “combined error” squared, etc. In a system using three 10,000 lb load cells, the “combined error” of each load cell is 3 pounds. Entering this data in the formula: Square root of (32 + 32 + 32) or Square root of (9 + 9 + 9) or Square root of 27 or 5.196 lbs (the square root of 27). SYSTEM RESOLUTION: The stability of the weight reading (often referred to as useful resolution) is affected by electrical noise in the form of both Radio Frequency Interference (RFI), and Electro Magnetic Interference (EMI).

These sources of interference affect the signal to noise ration of the load censor input to the weight controller. Following standard electrical wiring procedures a weight stable to 0.3 micro volt is typical for Hardy controllers. Utilizing 2 mV/V load cells and a 5 volt excitation this translates to one part in 30,000. In a 300 lb example, a stable weight reading of + or - 0.01 pound would be obtained. To insure good results attention must be paid to shielding, grounding and cable routing. EQUIPMENT DISPLAYED RESOLUTION: The high internal and displayed resolution of the Hardy Instrument weight controller line allows precise mathematical computations. This resolution yields good results for such features as WAVERSAVER and development of various digital and analog outputs without introducing errors in either displayed or transmitted data. The Internal Resolution is one part in 654,000 for a 2 mV/V load cell and one part in 985,000 for a 3 mV/V load point. SYSTEM ACCURACY: All of the above terms relate only to the electrical specifications of the system. Mechanical errors often introduce system errors. Mechanical errors can at times be difficult to identify. Proper system performance requires that the mechanical system be properly designed. In a properly designed system all of the weight will be vertically applied to the load points. In addition, there will be no redundant load paths from non-flexible connections, such as piping, ducting, tubing, etc. As you can see the proper installation of load cells is critical to a scale systems accuracy. Mechanical errors caused by binding is the number one cause of inaccuracy in a scale system. By using the above terms and formula’s you can calculate your weighing system’s accuracy.

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