25.6.
Metrology i’s concerned with units of measurements, standards of measurements, measuring instruments and measuring procedures. Measuring is the experimental procedure whereby a special value of a physical or measured quantity or a multiple or fraction of such unit is determined. The measured value is the special value of the measured quantity to be determined and is expressed as a numerical value and a unit. Processing the data to the measuring results is also part of measuring. Calibration is the determination of the relationship between output quantity and intpu quantity. The indication error of the scale or dial of the measuring instrument is determined by calibration. On the other hand adjusting a measuring
instrument means setting the device so that the display deviates as less as possible from the correct value or the errors are kept within prescribed limits.
Unit of Mass. According to the International System of Units (SI) the unit of mass is kilogram and is defined as the mass of the International Prototype Kilogram kept under the custody of the International Bureau of Weights and Measures (BIPM) at Paris in France. The Interantional Prototype kilogram is a right circular cylinder whose height is 39 mm, and is equal to its diameter. It is made of a single-phase alloy of platinum-iridium with 10% iridium by weight. This is only weight in the world whose mass is taken exactly one kilogram and is called “international kilogram”.
Fig. 25.6. Hierarchy chart of mass standards.
Standards of Mass.
Fig. 25.6 shows the hierarchy chart of standards for mass. The grouping starts with the International Prototype kilogram and ends with the working standards in national and industrial metrology.
Next to international kilogram, BIPM has other 65 such cylinders whose mass values have been derived from the international kilogram. Six of them namely^1, k7, k8, k32, k43 and k41 are called the copies of the international kilogram and are preserved under the same conditions as the international kilogram. The remaining cylinders are serving as the national prototypes and transfer standards of BIPM. Every country, that is the member of the ‘Convention of meter1, is entitled to have one copy of the international prototype kilogram, which serves as its national prototype kilogram. This prototype is maintained as primary standard of mass at the national metrological laboratory of that country. The copy No. 57 of the International Prototype Kilogram serves as the National Primary Standard of Mass of our country and is kept under the custody of the National Physical Laboratory (NPL). National Physical Laboratory, under the subordinate legislation of the standards of Weights and Measures Act of 1976, is responsible for the realization, establishment, custody, maintenance, determination, reproduction and updating the national standards of weights and measures. The national prototype kilogram is periodically calibrated against the International Prototype Kilogram by BIPM at least once in a period of 10 years. In,addition to primary standard a number of transfer and laboratory standards are maintained by the NPL. The Department of Legal Metrology enforcing the laws of weights and measure Act maintains a series of standards at different levels. This ensures the traceability of mass measurement carried out in the country at any level to the national standards and hence the international kilogram.
Mass Measuring Instruments
. For high accuracy mass determination, analytical balances and comparator balances are used. An analytical balance is characterized by a small-scale interval (d) compared to the maximum capacity (Max.), the ratio d/Max generally being smaller than 10″5 and the maximum capacity usually not exceeding 10 kg. Analytical balances are grouped into weighing instrument of special accuracy (class I) and of high accuracy (class II). For weighing instruments of special accuracy, the following classification is generally used :
term comparator balance or mass comparator is used. The mass comparator allows only differential weighing whereas analytical balances can be used both for differential weighing as well as for proportional weighing. Differential weighing stands for mass comparison using mass standards or other suitable objects, whereas proportional weighing is the simple mass comparison without having recourse of reference standards.
Selection of Weighing Instrument.
For a given weighing task selection of suitable weighing instrument depends on the maximum load to be weighed and the resolution (also known as readability) required. The weighing instruments are often referred to number of decimal places in grams that the instrument is capable to indicate in its scale. A six-place balance will resolve up to sixth decimal place of a gram i.e. to a microgram. Sometimes not only the resolution but the maximum capacity is also specified for example a 200 g five place balance or a 5 g six place balance.
In legal metrology, as per OIML (International Organization on Legal Metrology) International Recommendation No. R 76-1, all non-automatic weighing instruments are classified in four accuracy classes. The maximum permissible error (MPE) of each class of weighing instrument is based on its verification scale interval (e) and is a function of the applied load on the instrument. The manufacturer for a particular weighing instrument specifies the value of e, if it is not given it is assumed to be equal to the scale interval (d).
The correctness of the instrument is defined through the value of the applied load i.e., mass of the weight used. This means certain accuracy is required for the standard weight used. All the weights used in trade, commerce, industry and other applications (up to 50 kg) are classified into seven accuracy classes as per OIMI International Recommendation No. R-111 and higher capacity weights into four other classes as per OIML R-47. Appropriate accuracy class weights are used depending on the required accuracy in measurement results.
The weighing instrument also contributes to the testing uncertainty and must therefore fulfill certain requirements with regard to its repeatability. Concerning the measurement uncertainty in the non-automatic weighing instrument, OIML R-76-1 states three important requirements as follows :
(i) Permissible differences between results. Regardless of what variation of results is permitted, the error of any single weighing result shall by itself not exceed the maximum permissible error for the given load.
(ii) Repeatability. The difference between the results of several weighing of the same load should not be greater than the absolute value of the maximum permissible error of the instrument for that load.
(iii) Weights. The standard weight used for the verification of an instrument should not have an error greater than 1/3 of the maximum permissible error of the instrument for the applied load. These three single demands are enough for correctly judging the performance of a weighing instrument, generally with 95% confidence level.
Adjustment of an Electronic Balance. Mechanically balances are normally not
adjusted because they indicate weighing differences in mass units using their sensitivity ditermined separately by independent measurement. But in the case of electromagnetic or electronic balance the indication is adjusted in mass units. Now-a-days, only electronic balances are commonly used.
Normally comparisons of two weights are carried out in air using suitable balance. Thus a balance serves to compare not only the weight forces but also buoyancy forces. For electromagnetic force compensation balances, the indication mw, in units of mass, is proportional to the electromagnetic force F which compensates the weight and buoyancy forces such that:
Measuring Procedure. The mass of a body is determined by weighing i.e. the comparison of the mass of the object to be weighed with mass of a reference weight of known
mass on a balance after allowing all necessary corrections, particularly, the buoyancy correction. In order to obtain relative uncertainties < 1 x 10-5, differential weighing is indispensable.
For differential weighing, following two different weighing principles are normally
used :
Transposition (Gauss) Weighing. This principle can be used only with equal-arm balances. The test weight and the reference weight are interchanged on the pans at least once and the results of the two weighing are averaged.
Substitution (Borda) Weighing. This principle can be used with all weighing instruments. The test weight and the reference weight are weighed one after another on the same pan. In the case of equal arm balances the second pan is loaded with a fixed auxiliary weight.
For modern analytical and comparator balance, the substitution principle is generally used because, unlike the Gaussian principle, it allows a simple balance design and offers more ease of handling and, thus, less time of measurement. It also makes it relatively simple to automate the weighing sequence and, thus, to increase the accuracy of measurement.
