## What is metrology and engineering metrology?

Metrology is described as the science of measurement, precision, and accuracy. In other words, it is a method of measurement based on units and predefined standards.

Engineering metrology, on the other hand, is limited to the measurement of length and angle.

### Inspection and need for inspection

Inspection is a process in which a product's characteristics like dimensions and others are compared with standard dimensions or design specifications.

Following are the various needs or functions of inspection:

- To ascertain that the manufactured component conforms to the desired standard.
- To accomplish interchangeability of manufacture.
- To ensure no defective product reaches the customers.
- To provide the means of finding out inadequacies in manufacture.
- To provide good-quality raw material and pieces of equipment that govern the quality of a manufactured product.
- To coordinate the functions of quality control, production, feed receiver departments.
- To perform rework on defective parts so that they are accepted after minor repairs.
- To manufacture quality products in bulk by adopting better production methods.

### Accuracy and precision

Accuracy is described as a degree of agreement of the measured dimension with respect to its true dimension.

In other words, accuracy is the closeness of the measured value with the true value. It is determined with a single measurement and may be affected with systematic error. Accuracy is generally expressed in percentage.

Precision is described as a degree of the repetitiveness of the measuring process.

In other words, precision is a measure of the reproducibility of the measurement. It is determined by several numbers of measurements and may be affected with random error. If an instrument is not precise, it will give different results for the same dimension for repeated readings. Generally, precision assumes more significance than accuracy.

Accuracy of the system can be improved, but precision cannot be improved. Accuracy depends on the simple analysis technique, and precision depends on many factors and sophisticated techniques of analysis.

The diagrammatical representation of accuracy and precision cases is shown as:

The cost of the manufacturing product directly depends on its accuracy. The manufactured product comes with good quality, and higher cost, if the ideal quality raw material, manufacturing processes, and equipment are used. The relationship of accuracy with cost is shown as:

### Objectives of metrology and measurement

Following are the various objectives of metrology and measurement:

- To ascertain that the newly manufactured components are comprehensively evaluated and designed.
- To ensure uniformity of measurements.
- To achieve better component tolerances.
- To provide cost-effective inspection and optimal use of resources.
- To adopt quality control techniques to minimize material waste and rework.
- To establish inspection procedures from the design stage.
- To calibrate measuring instruments to maintain accuracy.
- To resolve measurement problems by designing gauges and special fixtures.
- To find and eliminate different sources of measuring errors.

The main objective of measurement in industries is to identify the quality of the manufactured part or element. The quality requirements check tolerance limit, surface finish, basic dimensions, flatness, and other product characteristics.

Following are the three basic elements of measurements:

- Measurand
- Comparator
- Reference

### Measurand

Measurand is a physical quantity to be measured like length, mass, weight, angle, and many more.

### Comparator

Comparator compares the measured physical quantity with the known standard reference for evaluation.

### Reference

Reference is the standard physical quantity to which quantitative comparisons are performed.

## Errors in measurements

Error is described as the variation within the measured value and the true value of the measured quantity.

The expression for error is given as,

$E={V}_{m}-{V}_{t}$

Here, *E* is the absolute error,

${V}_{m}$ is the measured value, and ${V}_{t}$ is the true value.

If an instrument measures ${V}_{m}$ instead of ${V}_{t}$ , then the percentage error is given as,

$\%error=\frac{Error}{Truevalue}\times 100\phantom{\rule{0ex}{0ex}}\%error=\frac{{V}_{m}-{V}_{t}}{{V}_{t}}\times 100$

Errors can be classified into two broad categories:

- Systematic or Controllable errors
- Random errors

### Systematic errors

Systematic error is described as an error that shows a fixed deviation in the measured value from the true value. Systematic error can be controlled in both magnitude and direction. It can be eliminated or minimized if efforts are made to analyze them.

Following are the reasons for the occurrence of systematic errors:

- Calibration errors
- Ambient conditions
- Deformation of workpiece
- Avoided errors

#### Calibration errors

Calibration error is defined as a small amount of variation in the measured value from the true value. It can be eliminated by using an accurate or calibrated measuring instrument.

#### Ambient conditions

Some measurement errors occur due to external ambient conditions of the instrument. Environmental conditions like change in temperature, relative humidity, vibration, or presence of an electric or magnetic field may generate an error in the measured value. Such errors are avoided by placing the instrument in a constant ambient condition.

#### Deformation of workpiece

The length of the solid workpiece is measured only by comparing it with another standard reference. If the workpiece is deformed, errors are obtained in the measured value.

#### Avoided errors

Errors obtained in measurement due to human mistakes are called avoided errors. Avoided errors include:

- Datum error
- Reading error
- Misalignment error
- Zero error

### Random errors

Random error is described as errors that occur due to a combination of small factors that fluctuate from one measured value to another. The sources of random errors are unknown, and they are minimized by repetitive measurement.

Random error can be statistically analyzed and their mean value and standard deviation determined.

If *n* number of measurement done by using an instrument gives values as

Then, the arithmetic mean is given as,

$\overline{)v}=\frac{{v}_{1}+{v}_{2}+{v}_{3}+........{v}_{n}}{n}$

And, the standard deviation is given as,

$\sigma =\pm \sqrt{\frac{\Sigma {\left(v-\overline{)v}\right)}^{2}}{n}}\phantom{\rule{0ex}{0ex}}\sigma =\pm \sqrt{\frac{{\left({v}_{1}-\overline{)v}\right)}^{2}+{\left({v}_{2}-\overline{)v}\right)}^{2}+{\left({v}_{3}-\overline{)v}\right)}^{2}+........{\left({v}_{n}-\overline{)v}\right)}^{2}}{n}}$

Following are some causes of random errors:

- Presence of transient fluctuations in friction of measuring instrument
- Error in operator's judgment in reading measurement
- Operator's failure in reading's collection due to fluctuations
- Positional errors due to small vibrations

The diagrammatical representation for the relationship between systematic and random errors with measured value is shown as:

## Methods of measurement

Following are the common methods of measurement:

### Direct method

In this method, the physical quantity to be measured is directly compared with the primary or secondary standard. Scale, micrometer, vernier caliper, gauges, and other instruments are used in the direct measurement method.

### Indirect method

In this method, the measurement of the quantity is carried out directly, and then the value is determined by using a mathematical relationship. Angle measurement using sine bar, measurement of strain in a bar due to applied force, and other instruments are examples of the indirect measurement method.

### Comparative method

In this method, the quantity to be measured is compared with the known value of equal quantity related to it.

### Coincidence method

It is a different method of measurement in which a very fine variation between the measured quantity and the true quantity is determined by careful observation of the coincidence of specific lines and signals.

### Null measurement method

In this method, the difference between the value of the quantity to be measured and the known value of the same quantity with which comparison is to be made is brought to zero.

### Contact method

In this method, surface contact is required between measured quantity and reference standard. Measurement using a vernier caliper, scale, micrometer, and other instruments are examples of contact methods.

### Contactless method

In this method, there is no physical contact needed for measurement. All-optical instruments like microscopes, telescopes, lenses, and others work on contactless measurement methods.

## Common Mistakes

Following are the common mistakes made by students:

- Sometimes, students get confused between precision and accuracy.
- They may also forget the objectives of meteorology.
- Another point of confusion is the basic elements of measurement.
- Students also get confused between the causes of systematic and random errors.

## Context and Applications

The topic of the basic principles of engineering metrology is significant in various courses and professional exams at undergraduate, graduate, postgraduate, and doctorate levels. For example:

- Bachelor of technology in mechanical engineering
- Bachelor of technology in instrumental engineering
- Bachelor of technology in production engineering
- Master of technology in machine design
- Doctor of philosophy in design

## Related Concepts

- Limit, fits and tolerances
- Measurement errors
- Allowance
- Inspection gauges

## Practice Problems

Q1.____ is a degree of the repetitiveness of the measuring process.

- Accuracy
- Precision
- Inspection
- Error

Correct option: **(b)**

**Explanation:** Accuracy is a degree of agreement of the measured dimension concerning its true dimension. In contrast, precision is a degree of the repetitiveness of the measuring process.

Q2. The cost and accuracy of the product are ______.

- Directly related
- Inversely related
- Not related
- None of these

Correct option: **(a)**

**Explanation:** The cost and accuracy of the product are directly related or proportional to each other. The product's cost increases with its accuracy.

Q3. Which of the following elements of measurement represents the physical quantity to be measured?

- Comparator
- Reference
- Measurand
- None of these

Correct option: **(c)**

**Explanation:** A measurand is a physical quantity to be measured like length, mass, weight, angle, and many more.

Q4. If a measuring device reads 55 cm in place of 50 cm, what will be percentage error for measured value?

- 10%
- 20%
- 1%
- 100%

Correct option: **(a)**

**Explanation:** The formula for percentage error is given as,

$\%error=\frac{{V}_{m}-{V}_{t}}{{V}_{t}}\times 100\%$

Substitute values in the above equation.

$\%error=\frac{55-50}{50}\times 100\%\phantom{\rule{0ex}{0ex}}\%error=10\%$

Q5. Zero error is a type of which error?

- Random error
- Systematic error
- Both systematic error and random error
- None of these

Correct option: **(b)**

**Explanation:** Zero error is a type of systematic error because random errors have no types.

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