1.6.
In precision measurements various methods of measurement are followed depending upon
the accuracy required and the amount of permissible error.
There are numerous ways in which a quantity can be measured. Any method of measurement
should be defined in such a detail and followed by such a standard practice that there is little scope
for uncertainty. The nature of the procedure in some of the most common measurements is described
below. Actual measurements may employ one or more combinations of the following.
(i) Direct method of measurement.
In this method the value of a quantity is obtained directly
by comparing the unknown with the standard. It involves, no mathematical calculations to arrive
at the results, for example, measurement of length by a graduated scale. The method is not very
accurate because it depends on human insensitiveness in making judgement.
(ii) Indirect method of measurement.
In this method several parameters (to which the
quantity to be measured is linked with) are measured directly and then the value is determined by
mathematical relationship. For example, measurement of density by measuring mass and geometri-
cal dimensions.
(iii) Fundamental method of measurement.
Also known as the absolute method of measure-
ment, it is based on the measurement of the base quantities used to define the quantity. For example,
measuring a quantity directly in accordance with the definition of that quantity, or measuring a
quantity indirectly by direct measurement of the quantities linked with the definition of the quantity
to be measured.
(iv) Comparison method of measurement.
This method involves comparison with either a
known value of the same quantity or another quantity which is function of the quantity to be
measured.
(v) Substitution method of measurement.
In this method, the quantity to be measured is
measured by direct comparison on an indicating device by replacing the measuring quantity with
some other known quantity which produces same effect on the indicating device. For example,
determination of mass by Borda method.
(vi) Transposition method of measurement.
This is a method of measurement by direct
comparison in which the value of the quantity to be measured is first balanced by an initial known
value A of the same quantity ; next the value of the quantity to be measured is put in the place of
that known value and is balanced again by a second known value B. When the balance indicating
device gives the same indication in both cases, the value of the quantity to be measured is VAB. For
example, determination of a mass by means of a balance and known weights, using the Gauss double
weighing method.
(vii) Differential or comparison method of measurement.
This method involves measuring the
difference between the given quantity and a known master of near about the same value. For
example, determination of diameter with master cylinder on a comparator.
(viii) Coincidence method of measurement.
In this differential method of measurement the very
small difference between the given quantity and the reference is determined by the observation of
the coincidence of scale marks. For example, measurement on vernier caliper.
(ix) Null method of measurement.
In this method the quantity to be measured is compared
with a known source and the difference between these two is made zero.
(x) Deflection method of measurement.
In this method, the value of the quantity is directly*
indicated by deflection of a pointer on a calibrated scale.
(
xi) Interpolation method of measurement.
In this method, the given quantity is compared
with two or more known value of near about same value ensuring at least one smaller and one
bigger than the quantity to be measured and the readings interpolated.
(xii) Extrapolation method of measurement.
In this method, the given quantity is compared
with two or more known smaller values and extrapolating the reading.
(xiii) Complimentary method of measurement.
This is the method of measurement by com-
parison in which the value of the quantity to be measured is combined with a known value of the
same quantity so adjusted that the sum of these two values is equal to predetermined comparison
value. For example, determination of the volume of a solid by liquid displacement.
(xiv) Composite method of measurement.
It involves the comparison of the actual contour of a
component to be checked with its contours in maximum and minimum tolerable limits. This method
provides for the checking of the cumulative errors of the interconnected elements of the component
which are controlled through a combined tolerance. This method is most reliable to ensure
inter-changeability and is usually effected through the use of composite “Go” gauges, for example,
checking of the thread of a nut with a screw plug “GO” gauge.
(xv) Element method.
In this method, the several related dimensions are gauged individually,
i.e. each component element is checked separately. For example, in the case of thread, the pitch
diameter, pitch, and flank angle are checked separately and then the virtual pitch diameter is
calculated. It may be noted that value of virtual pitch diameter depends on the deviations of the
above thread elements. The functioning of thread depends on virtual pitch diameter lying within
the specified tolerable limits.
In case of composite method, all the three elements need not be checked separately and is
thus useful for checking the product parts. Element method is used for checking tools and for
detecting the causes of rejects in the product.
(xvi) Contact and contactless methods of measurements. In contact methods of measurements,
the measuring tip of the instrument actually touches the surface to be measured. In such cases,
arrangements for constant contact pressure should be provided in order to prevent errors due to
excess contact pressure. In contactless method of measurements, no contact is required. Such
instruments include tool-maker’s microscope and projection comparator, etc.
For every method of measurement a detailed definition of the equipment to be used, a
sequential list of operations to be performed, the surrounding environmental conditions and
descriptions of all factors influencing accuracy of measurement at the required level must be
prepared and followed.
1.6.1.
Classification of Measuring Instruments.
According to the functions, the measur-
ing instruments are classified as :
(1) Length measuring instruments.
(2) Angle measuring instruments.
(3) Instruments for checking the deviations from geometrical forms.
(4) Instruments for determining the quality of surface finish.
According to the accuracy of measurement, the measuring instruments are classified as
follows:
(1) Most accurate instruments e.g., light-interference instruments.
(2) Second group consists of less accurate instruments such as tool room microscopes,
comparators, optimeters etc.
(3) The third group comprises still less accurate instruments e.g., dial indicators, vernier
calipers and rules with vernier scales.
1.6.2.
Metrological characteristics of Measuring Instruments.
Measuring instru-
ments are usually specified by their metrological properties, such as range of measurement, scale
graduation value, scale spacing, sensitivity and reading accuracy.
Range of Measurement. It indicates the size values between which measurements may be
made on the given instrument.
Scale range. It is the difference between the values of the measured quantities corresponding
to the terminal scale marks.
Instrument range. It is the capacity or total range of values which an instrument is capable
of measuring. For example, a micrometer screw gauge with capacity of 25 to 50 mm has instrument
range of 25 to 50 mm but scale range is 25 mm.
Scale Spacing. It is the distance between the axes of two adjacent graduations on the scale.
Most instruments have a constant value of scale spacing throughout the scale. Such scales are said
to be linear.
In case of non-linear scales, the scale spacing value is variable within the limits of the scale.
Scale Division Value. It is the measured value of the measured quantity corresponding to
one division of the instrument, e.g., for ordinary scale, the scale division value is 1 mm. As a rule,
the scale division should not be smaller in value than the permissible indication error of an
instrument.
Sensitivity (Amplication or gearing ratio). It is the ratio of the scale spacing to the division
value. It could also be expressed as the ratio of the product of all the larger lever arms and the
product of all the smaller lever arms. It is the property of a measuring instrument to respond to
changes in the measured quantity.
Sensitivity Threshold. It is defined as the minimum measured value which may cause any
movement whatsoever of the indicating hand. It is also called the discrimination or resolving power
of an instrument and is the minimum change in the quantity being measured which produces a
perceptible movement of the index.
Reading Accuracy. It is the accuracy that may be attained in using a measuring instrument.
Reading Error. It is defined as the difference between the reading of the instrument and the
actual value of the dimension being measured.
Accuracy of observation. It is the accuracy attainable in reading the scale of an instrument.
It depends on the quality of the scale marks, the width or the pointer/index, the space between the
pointer and the scale, the illumination of the scale, and the skill of the inspector. The width of scale
mark is usually kept one-tenth of the scale spacing for accurate reading of indications.
Parallax. It is apparent change in the position of the index relative to the scale marks, when
the scale is observed in a direction other than perpendicular to its plane.
Repeatability. It is the variation of indications in repeated measurements of the same
dimension. The variations may be due to clearances, friction and distortions in the instrument’s
mechanism. Repeatability represents the reproducibility of the readings of an instrument when a
series of measurements in carried out under fixed conditions of use.
Measuring force. It is the force produced by an instrument and acting upon the measured
surface in the direction of measurement. It is usually developed by springs whose deformation and
pressure change with the displacement of the instrument’s measuring spindle.
