CHOICE OF THE DEFLECTIONAL INSTRUMENT RANGE AND ACCURACY CLASS FOR MEASUREMENT OF THE QUANTITY WITH THE GIVEN ADMISSIBLE DEVIATION

In everyday practice, engineers often face this problem. For example, it is stated in a technical documentation that a voltage across the object must be:

U = (145 ± 10) V.

When developing a technological scheme or a user's manual, an engineer has to choose an instrument to measure the prescribed voltage from those available at the plant or motivate a need to buy the necessary instrument.

Measurement range selection rules:

1. The measurement range M has to be not less than the sum of a quantity being measured and its admissible deviation:

               М ≥ (145 V + 10 V),

i.e.:

                         М ≥ 155 V .

A voltmeter with the measurement range of 150 V is not acceptable, as not all from the permissible voltage values across the object (from 135 V till 155 V) can be measured with this instrument. But all the voltmeters with the measurement range 155 V and more are acceptable.

2. Among all voltmeters available at the plant which correspond to this requirement, one should choose an instrument with the least measurement range. For example, there are the voltmeters with the measurement ranges of (200; 250; 300; 500) V. The most rational way is to choose an instrument with the measurement range of 200 V. As it will be understood from the rule below, in this case the requirements to its accuracy are the least.

The accuracy class selection rule: the permissible absolute error of an instrument must be at least 3-5 times less than the admissible deviation of a quantity being measured:Δ_{max i} ≤[Δ_{max q} / (3…5)],

where: ∆_maxi is the permissible absolute error of the instrument, ∆_maxq is the admissible deviation of the quantity being measured. For technical measurements it is quite enough to apply coeficient 3 to this formula. It may be increased according to the responsibility of the measurement, for example, for the measurements, connected with the material valuables distribution, flight safety, etc.

For the example given:

i.e.

Having calculated the voltmeter permissible absolute error and having chosen previously its measurement range ( the fiducial value) using the known formula of the fiducial error, that defines the accuracy class of the deflectional instrument, let us calculate:

i.e.

It means that all voltmeters with the range of 200V of the accuracy classes 1.5; 1.0; 0.5; 0.2; 0.1 and 0.05 meet the requirements prescribed.

From practical and economic considerations, the instrument with the lowest of the given here accuracy classes, i.e. 1,5 is expedient to be chosen. Instruments of higher classes , as a rule, are substantially expensive to purchase and maintenance, often need the peculiar service conditions, more qualified personnel, etc.

Let us return to the grounding of the rationality in choosing the least instrument measurement range (200V). If an instrument with the range of 500V is chosen, its permissible fiducial error is:

γ

i.e.                        

γ %max i ≤ 0,67%.

It means, that the accuracy class must be not worse than 0,5, i.e., three times higher than for an instrument with the measurement range of 200 V.

CHOICE OF A MEASUREMENT RANGE AND ACCURACY CLASS OF A DEFLECTIONAL REFERENCE INSTRUMENT FOR VERIFICATION OF A DEFLECTIONAL INSTRUMENT BY THE JUXTAPOSITION METHOD

This problem by its solution is very similar to the previous one, that’s why we will consider it using the same procedure with a concrete numerical example.

It’s necessary to verify a deflectional voltmeter with a measurement range of 250V and accuracy class of 2,5.

Rules of choosing the range of the reference deflectional instrument.

1.The upper limit of the reference deflectional instrument range has to be not less than the sum of the instrument being verificated measurement range and its permissible absolute error.

Let us calculate the permissible absolute error of the instrument, offered for the verification. It may be determined as 2,5% from 250V (see the accuracy class definition on fiducial error), that is 6,25V. Consequently, a measurement range of the reference instrument has to be not less than (250+6,25)V=256,25V

2. Among the reference instruments available at the metrological service of your enterprise, that satisfy the calculated result, of previous point, it is expendient to choose an instrument with the least measurement range (then the requirements to its accuracy will be also the least).

Note. In many instructions on the verification, the same measurement ranges of the reference instruments and those being verificated are tolerated. In this case, however, there could be some complications on the errors estimation on the last scale mark. For example, for the indication of the instrument under verification of 250V, the readings of the reference instrument up to 256,25V are tolerated. But how can it be done, if the reference instrument measurement range is 250V?

Therefore, let us choose the reference instrument with the measurement range of, for example, 300V.

The rule of the reference instrument accuracy class choice.

The permissible intrinsic absolute error of the reference instrument must be at least 3…5 times less than that of the instrument under verification.

A ratio 1:3 is tolerated for the verification of the ammeters and voltmeters with the accuracy class of 0,5 and more precise and 1:4 for verification of the instruments with accuracy class of 1,0 and less precise.

Herewith a hysteresis error of the reference instrument has not exceed a half of its permissible intrinsic absolute error,

 i.e.:

 where is the permissible intrinsic absolute error of the reference instrument; is the permissible absolute intrinsic error of the instrument under verification.

Let’s calculate the permissible intrinsic absolute error of the reference voltmeter for the given example, using a ratio 1:4:     

i.e.

Hence it is possible to determine the permissible intrinsic fiducial error of the reference instrument γ_maxr in percentage and to choose its accuracy class:

γ

that is:

γ

and   

γ_{max r}% ≤ 0,52% .

This requirement is satisfied by the instruments with the accuracy class of 0,5 and more precise with the measurement range of 300V.

From the practical and economic points of view, it is recommended to use the reference instrument of the lowest possible accuracy that satisfied the above-mentioned requirements.