Basics of Metrology Need for Measurement

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BASICS OF METROLOGY

Metrology is the name given to the science of pure measurement. Engineering Metrology is restricted to measurements of length & angle.

Need for Measurement:

• To ensure that the part to be measured conforms to the established standard.

• To meet the interchangeability of manufacture.

• To provide customer satisfaction by ensuring that no faulty product reaches the customers.

• To coordinate the functions of quality control, production, procurement & other departments of the organization.

• To judge the possibility of making some of the defective parts acceptable after minor repairs.

Precision & Accuracy of Measurement

Precision : It is the degree which determines how well identically performed measurements agree with each other. It is the repeatability of the measuring process. It carries no meaning for only one measurement. It exists only when a set of observations is gathered for the same quantity under identical conditions. In such a set, the observations will scatter about a mean. The less is the scattering, the more precise is the measurement.

Basic units in SI system

1) For Length : Metre (m) which is equal to 1650763.73 wavelengths in vacuum of the red-orange radiation corresponding to the transition between the levels 2p10 & 5d5 of the krypton-86 atom. (Definition by wavelength standard)

By Line standard, Metre is the distance between the axes of two lines engraved on a polished surface of the Platinum – Iridium bar 'M' (90% platinum & 10% iridium) kept at Bureau of Weights & Measures (BIPM) at Sevres near Paris at 0°C, the bar kept under normal atmospheric pressure, supported by two rollers of at least 1 cm diameter symmetrically situated in the same horizontal plane at a distance of 588.9 mm (Airy points) so as to give minimum deflection.

2) For Mass: Kilogram (kg) which is equal to the mass of International prototype of the kilogram.

3) For Time : Second (s) which is equal to the duration of 9192631770 periods of the radiation corresponding to the transition between the hyper fine levels of the ground state of the Caesium 133 atom.

4) For Current : Ampere (A) is that constant current which, if maintained in two straight parallel conductors of infinite length of negligible circular cross section & placed one metre apart in vacuum would produce between these conductors, a force equal to 2 x 10-⁷ Newton per unit length.

5) For Temperature: Kelvin (K) is the fraction 1/273 of thermodynamic temperature of the triple point of water.

6) For Luminous intensity: Candela (cd) is the luminous intensity in the perpendicular direction of a surface of 1/6,00,000 m² of a black body at the temperature of freezing platinum under a pressure of 101325 N/m².

7) For amount of substance: Mole (mol) is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kg of Carbon-12.

Supplementary SI units:

​1) For Plane angle: Radian (rad)

2) For Solid angle: Steradian (sr)

Derived SI units:

1) For Frequency: Hertz (1 Hz = 1 cycle per second)

2) For Force: Newton (1 N = 1 kg-m/s²)

3) For Energy: Joule (1 J = 1 N-m) 4) For Power: Watt (1 W = 1 J/s)

Errors In Measurements:

During measurement several types of error may arise as indicated and these error can be broadly classified into two categories.

Systematic error and random error:

For statistical study and the study of accumulation of errors, errors are categorized as controllable errors and random errors.

(a) Systematic or controllable errors:

Systematic error is just a euphemism for experimental mistakes. These are controllable in both their magnitude and sense. These can be determined and reduced, if attempts are made to analyse them. However, they can not be revealed by repeated observations. These errors either have a constant value or a value changing according to a definite law. These can be due to:

1. Calibration Errors: 

The actual length of standards such as slip gauges and engraved scales will vary from nominal value by small amount. Sometimes the instrument inertia, hysteresis effects do not let the instrument translate with complete fidelity. Often signal transmission errors such as drop in voltage along the wires between the transducer and the electric meter occur. For high order accuracy these variations have positive significance and to minimize such variations calibration curves must be used.

2. Ambient Conditions: 

Variations in the ambient conditions from internationally agreed standard value of 20°C, barometric pressure 760 mm of mercury, and 10mm of mercury vapour pressure, can give rise to errors in the measured size of the component. Temperature is by far the most significant of these ambient conditions and due correction is needed to obtain error free results.

3. Styles Pressure: 

Error induced due to styles pressure is also appreciable. Whenever any component is measured under a definite stylus pressure both the deformation of the workpiece surface and deflection of the workpiece shape will occur.

4. Avoidable Errors: 

These errors include the errors due to parallax and the effect of misalignment of the workpiece centre. Instrument location errors such as placing a thermometer in sunlight when attempting to measure air temperature also belong to this category.

5. Experimental arrangement being different from that assumed in theory. 

6. Incorrect theory i.e., the presence of effects not taken into account.

(b) Random Errors:

​These occur randomly and the specific cases of such errors cannot be determined, but likely sources of this type of errors are small variations in the position of setting standard and workpiece, slight displacement of lever joints in the measuring joints in measuring instrument, transient fluctuation in the friction in the measuring instrument, and operator errors in reading scale and pointer type displays or in reading engraved scale positions.

Characteristics of random errors:

The various characteristics of random errors are:

• These are due to large number of unpredictable and fluctuating causes that can not be controlled by the experimenter. Hence they are sometimes positive and sometimes negative and of variable magnitude. Accordingly they get revealed by repeated observations.

• These are caused by friction and play in the instrument‘s linkages, estimation of reading by judging fractional part of a scale division, by errors in position the measured object, etc.

• These are variable in magnitude and sign and are introduced by the very process of observation itself.

• The frequency of the occurrence of random errors depends on the occurrence probability for different values of random errors.

• Random errors show up as various indication values within the specified limits of error in a series of measurements of a given dimension.

• The probability of occurrence is equal for positive and negative errors of the same absolute value since random errors follow normal frequency distribution.

• Random errors of larger absolute value are rather than those of smaller values.

• The arithmetic mean of random errors in a given series of measurements approaches zero as the number of measurements increases.

• For each method of measurement, random errors do not exceed a certain definite value. Errors exceeding this value are regarded as gross errors (errors which greatly distort the results and need to be ignored).

• The most reliable value of the size being sought in a series of measurements is the arithmetic mean of the results obtained.

• The main characteristic of random errors, which is used to determine the maximum measuring error, is the standard deviation.

• The maximum error for a given method of measurement is determined as three times the standard deviation.

• The maximum error determines the spread of possible random error values

• The standard deviation and the maximum error determine the accuracy of a single measurement in given series.

From the above, it is clear that systematic errors are those which are repeated consistently with repetition of the experiment, whereas Random Errors are those which are accidental and whose magnitude and sign cannot be predicted from knowledge of measuring system and conditions of measurement.