Engineering - Metrology

Metrology is the study of measurement.

There are 2 methods of inspecting a component :

  1. By using measuring equipment to determine the components actual dimensions. This is measurement.
  2. By using Gauges to simply determine whether the component is 'good or bad'. This is gauging.


Standards of Measurement

There are 2 main Standards of Measurement in use in the world today :

  1. Metric
  2. Imperial

The metric system of measurement uses the decimal, (base 10), system of numbering. It is the most commonly used system of measurement in use in the world. Since the 1960s, the International System of Units (SI) is the internationally recognized standard metric system.

The 7 SI Base Units are:

  • metre (m)  : SI unit of length
  • second (s)  : SI unit of time
  • kilogram (kg) : SI unit of mass
  • kelvin (K)  : SI unit of temperature
  • ampere (A) : SI unit of electric current
  • candela (cd) : SI unit of luminousintensity
  • mole (mol) : SI unit of amount of substance

Other units of measure are derived from these 7 Base units and are called Derived SI Units. eg : Speed = m/s


Before SI units were widely adopted around the world, the British systems of Imperial units were used in Britain, the Commonwealth and the United States. The Imperial system works on base 12.

In reality people use a combination of both standards in everyday vocabulary. However in Engineering and Science the Metric, (SI), system is used.


Grades of Accuracy

In order for the correct use of measuring devices they must be callibarted as accuratly as possible within appropriate cost limits. As a result there are different Grades of Accuracy. The main reason for having a hierarchial standard system is to avoid handling or damage to the higher grades and thus preserve their accuracy.

Primary Standard
Secondary Standard
Working Standard

The metre is defined as the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. From this definition prototype bars are manufactured at the Primary or International level. Subsequent levels are measured form the preceding level. The tools used in the workshop are Grade A.


Systems of Limits

Limits, Tolerances, and Allowances


When machining it is impossible to manufacture a number of pieces to an exact measurement. There will always be some difference in size. As a result Limits are set. This means that what the machinist manufactures can differ from the proper size by the small amount stated by the Limits, and still be able to be used.

The required size of the component, before the Limits are set, is called the Basic Size or Nominal Size. Then the Upper Limit and the Lower Limit are set.

The Limits are the maximum and minimum sizes allowable.

E.g. 22.00mm ---- Nominal Size
22.02mm ---- Upper Limit
21.97mm ---- Lower Limit

To get the :

Upper Deviation ---- Subtract the Nominal Size from the Upper Limit. i.e. 0.02mm
Lower Deviation ---- Subtract the Lower Limit from the Nominal Size. i.e. 0.03mm

Limits are usually written in this way : 22.00

These Limits tell the manufacturer that the component can be any size between 22.02mm and 21.97mm.


The Tolerance is the difference between the Upper Limit and the Lower Limit.

i.e. 0.05mm

The Tolerance is the total amount by which the size of the component can differ from the Nominal Size.

A Tolerance is said to be Bilateral if it is spread over both sides of the Nominal Size. The above example is an example of a Bilateral Tolerance.

A Tolerance is said to be Unilateral if it is only on one side of the Nominal Size. E.g. 22.00

These Limits tell the manufacturer that the component can be any size between 22.00mm and 22.02mm.


Allowance is basically the size difference between components that work together. Allowance between parts that are assembled is very important. For example, the axel of a car has to be supported in a bearing otherwise it will fall to the ground. If there was no gap between the axel and the bearing then there would be a lot of friction and it would be difficult to get the car to move. If there was too much of a gap then the axel would be jumping around in the bearing. It is important to get the Allowance between the axel and the bearing correct so that the axel rotates smoothly and easily without judder.


Types of Fit

In any machine, parts must fit togehter in certain ways in order to operate. An axle must be able to rotate in a bearing, but the bearing itself must be fixed into it's housing. The Fit is determined by the size of the mating parts. Allowance is what determines the type of Fit.

There are 3 Types of Fit :

  • Clearance Fit
  • Transition Fit
  • Interference Fit

Clearance Fit

In the case of a Clearance fit, the shaft is always smaller than the hole.
eg. Axle in a bearing, the axle must be free to rotate without friction.

Transition Fit

With a Transition Fit some shafts may be a little smaller than the hole and some may be a little larger.
eg. The lid of a pen. The lid must fit on securly but not be too difficult to remove. This is a push fit.

Interference Fit

In the case of an Interfenence Fit, the shaft is always larger than the hole.
eg. Bearing in a chassis. The bearing must not rotate in the chassis. This is a force fit.

Determination of Limits and Tolerances from given data

When a machine is being designed the engineer decides on the tolerances of different mating parts. Depending on the situation required two different systems can be chosen from.

The Hole Basis System

In this system the holes are drilled to a specific size and the shaft varies. This is the preffered system as drills and reamers come in standard sizes and it is relatively easy to modify the size of a shaft.

The Shaft Basis System

In this system the shaft has a fixed size and the holes are varied to suit the type of fit necessary. This is a relatively expensive system as a wide range of drills and reamers are required.

Examples of Designations

A tolerance designation is made up of three parts, the nominal size of the hole or the shaft, a letter and number combination showing the system being used, followed by another letter number combination.

25 H7/g6 : This is a designation using the Hole Basis System. It is recognisable by a capital letter H.
25 K7/h6 : This is a designation using the Shaft Basis System. It is recognisable by a small letter h.

These designations are standards and available in tabular form. Here you can find the British Standards ISO Fits - Hole Basis, (BS 4500 A). (It will open in a new window.)

Worked example of determining the sizes of parts using BS 4500 A

Find the sizes of the Hole and Shaft and type of fit for a 45 H8/f7 Hole Basis designation.

  • Look under Nominal Size on the BS 4500 A sheet and find the row for 45mm. (You should be be at the row which says 40 in the Over column and 50 in the To column.)
  • Move across the row until you are under the Tolerance H8 f7. (Negative numbers in this box mean subtract.)
  • The Upper Limit for the Hole is the Nominal Size added to the top number under the H8 column,
  • The Lower Limit for the Hole is the Nominal Size added to the bottom number under the H8 column,
  • The Upper Limit for the Shaft is the Nominal Size added to the top number under the f7 column,
  • The Lower Limit for the Shaft is the Nominal Size added to the bottom number under the f7 column,
  • The Upper Deviation is the difference between the Nominal Size and the Upper Limit.
  • The Lower Deviation is the difference between the Nominal Size and the Lower Limit.
  • The Tolerance is the difference between the Upper Limit and the Lower Limit.
  • Now find the Maximum Allowance and the Minimum Allowance.
  • The numbers calculated here tell you what type of fit this is. Two positive numbers mean a Clearance Fit. A positive and a negative number mean an Transition Fit. Two negative numbers mean an Interference Fit.
45 H8 Hole
45 f7 Shaft
Nominal Size : 45 Nominal Size : 45
Upper Limit : 45.039 Upper Limit : 44.975
Lower Limit : 45.000 Lower Limit : 44.95
Upper Deviation : 0.039 Upper Deviation : -0.025
Lower Deviation : 0.000 Lower Deviation : -0.050
Tolerance : 0.039 Tolerance : 0.025
Maximun Allowance : Largest Hole - Smallest Shaft = 45.039-44.95 = 0.089
Minimum Allowance : Smallest Hole - Largets Shaft = 45.000-44.975 = 0.025
This is a Clearance Fit


Interchangeability of Parts and Selective Assembly

Back before the Industrial Revolution machines were manufactured independently of one another. One engineer might make the whole machine. If a part broke on a machine it would have to be manufactured again to suit the machine in question. It was not possible to use the same part from another machine. Screws and nuts were manufactured to suit the machinist and their use. Standardisation had not yet arrived.

During the Industrial Revolution a new concept in manufacturing was developed. Parts were manufactured by individualsand the individual stuck to making that part. Then the whole machine was assembled from these parts. Now that the parts were the same, if a part broke in a machine it could be replaced by the same part from another machine. This concept led to what we now call Interchangeability of Parts.

Interchangeability of Parts and other inventions around the same time revolutionised mass manufacture and reliability of machines. A machine could have spares at the ready that the owner new would work. If a screw or nut broke, another screw or nut of the same dimensions could be easily obtained. It also ensured that machinists became more specialised and therefore more accurate as their skills were honed in a specific direction as opposed to needing to have an overall knowledge.

Selective Assembly was the next step in the evolution of improved assembly manufacturing. A machinist would produce a large number of parts with a low tolerance. A mating part would be produced in the same numbers and to the same tolerance by another machinist. Each machinist would then grade the parts that they manufactured to similar higher tolerances. The parts could then be assembled by taking parts from the same grade and assembling them.

Selective Assembly has a number of advantagesover earlier manufacturing methods. There is a larger number of acceptable parts as original tolerances are greater. This in turn allows the manufacture of cheaper parts as less will be consigned to the waste bin.

Selective Assemblyassures betterand more accurate assembly of parts bu insuring closer tolerances between the mating parts.

Limit Gauges


Measurement of Screw Threads


Use of Thread Form Gauges and Profile Projector


Honours Only Section

Principles involved in using Sine Bar, Slip Gauges. Precision Balls and Rollers

Slip Gauges

Slip Gauges are small blocks of alloy Steel or tungsten carbide. They are usually rectangular in shape. They have two very flat parallel surfaces at opposite ends. The measuring faces of Slip Gauges have such a good surface finish that when you place two gauges together with their measuring faces in contact, and slide one gauge over the other, they will wring together. Basically this means that they are almost stuck together, and that they will not slide off eachother easily.

Slip Gauges are designated by a code. E.g. M32/1

M : Metric gauges

32 : there are 32 Slip Gauges in the set

1 : the smallest Slip Gauge has a thickness of 1mm

Try and work out what the two following Slip Gauge codes mean :

  • M42/1
  • M52/2

To Make Up A Slip Gauge Pile To 41.125mm

A Slip Gauge pile is used to set up or simulate a height that you may require for other purposes. The Gauges are wrung together. Generally the top and bottom Slip Gauges in the pile are 2mm wear gauges. This is so that they will be the only ones that will wear down, and it is much cheaper to replace two gauges than a whole set.


A Slip Gauge pile is set up with the use of simple maths.

Decide what height you want to set up, in this case 41.125mm. Take away the thickness of the two wear gauges, and then use the gauges in the set to remove each place of decimal in turn, starting with the lowest.

- 4.000
- 1.005
- 1.020
- 1.100
- 4.000

two x 2mm wear gauges

third decimal

second decimal

first decimal




Specification of Surface Finish