13. Metrology

13.1 The Role of Metrology

• modern manufacturing can produce features that are more accurate than we can measure by hand, therefore we need tools to assist us.

• These tools allow us to quantitatively evaluate physical properties of objects.

• EVERY industry uses these tools to some extent, for example,

machine shops



automotive manufacturers


13.2 Definitions

Accuracy: The expected ability for a system to discriminate between two settings.

Assembly: the connection of two or more separate parts to make a new single part.

Basic Dimension: The target dimension for a part. This typically has an associated tolerance.

Dimension: A size of a feature, either measured, or specified.

Dimensional Metrology: The use of instruments to determine object sizes shapes, form, etc.

English System: See Imperial.

Error: a discrepancy between expected, and actual values.

Imperial System: An older system of measurement, still in use in some places, but generally replaced by the metric system.

Limits: These typically define a dimensional range that a measurement can be expected to fall within.

Machine Tool: Generally use to refer to a machine that performs a manufacturing operation. This is sometimes confused with the actual cutting tools, such as a drill bit, that do the cutting.

Measurement: The determination of an unknown dimension. This requires that known standards be used directly, or indirectly for comparison.

Metric System: A measurement system that has been standardized globally, and is commonly used in all modern engineering projects.

Metrology: The science of measurement. The purpose of this discipline it to establish means of determining physical quantities, such as dimensions, temperature, force, etc.

Precision: Implies a high degree of accuracy.

Repeatability: Imperfections in mechanical systems can mean that during a Mechanical cycle, a process does not stop at the same location, or move through the same spot each time. The variation range is referred to as repeatability.

Standards: a known set of dimensions, or ideals to compare others against.

Standard Sizes: a component, or a dimension that is chosen from a table of standard sizes/forms.

Tolerance: The allowable variation in a basic dimension before a part is considered unacceptable

13.3 Standards

• Standards are the basis for all modern accuracy. As new methods are found to make more accurate standards, the level of accuracy possible in copies of the standard increase, and so on.

• A well known metric standard is the metric 1m rod.

• Many standards are available for measuring, and many techniques are available for comparison.

13.3.1 Scales

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• The most common tool for crude measurements is the scale (also known as rules, or rulers)

• Although plastic, wood and other materials are used for common scales, precision scales use tempered steel alloys, with graduations scribed onto the surface.

• These are limited by the human eye. Basically they are used to compare two dimensions.

• The metric scales use decimal divisions, and the imperial scales use fractional divisions.


• Some scales only use the fine scale divisions at one end of the scale.

• It is advised that the end of the scale not be used for measurement. This is because as they become worn with use, the end of the scale will no longer be at a ‘zero’ position. Instead the internal divisions of the scale should be used.

• Parallax error can be a factor when making measurements with a scale.


13.3.2 Calipers

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• A tool used to transfer measurements from a part to a scale, or other instrument.

• calipers may be difficult to use, and they require that the operator follow a few basic rules,

do not force them, they will bend easily, and invalidate measurements made

try to get a feel, or personal technique for using these instruments.

if measurements are made using calipers for comparison, one operator should make all of the measurements (this keeps the feel factor a minimal error source).

• These instruments are very useful when dealing with hard to reach locations that normal measuring instruments cannot reach.

• Obviously the added step in the measurement will significantly decrease the accuracy

13.3.3 Transfer Gages

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• Small hole gages can be inserted into a hole, as an adjustment knob is turned, the head expands to the size of the hole. The gauge can be removed and measured to determine the diameter of the hole. The end of this gauge appears as if a sphere with a shaft in it has been split into two halves.

• Telescope gages have two plungers that are springy, until locked in place. This can be put in holes or hard to reach locations, and used to transfer measurements to other measurement devices.

13.4 Instruments

13.4.1 Vernier Scales

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• Vernier scales have normal scale components, but also incorporate a small secondary scale that subdivides major increments.

• This secondary scale is based on a second scale that is one increment shorter than a main scale. If the secondary scale is compared to the main scale, it will indicate relative distance between two offsets.


• The scale pictured above would normally be on an instrument, and the main and vernier scales would slide relative to each other. The ‘0’ on the vernier scale would be used to take the reading from the main scale. In this example the main scale would read a value that is between 0.4 and 0.6. (Note: it is not considered good practice to round this to 0.5)

• The vernier scale can then be used to find the internal division, by looking for where the divisions in the top and bottom scales align. In this case the second internal division aligns with 1. Using the values on the vernier scale, we can see that the value for this division would be 0.08. The value from the vernier scale is added directly to the main scale value to get the more accurate results. 0.4+0.08 = 0.48.

• On imperial sliding vernier scales the main scale divisions are 0.050” apart, and on the vernier scale they are 0.049”, giving a reading of 0.001” per graduation.

• On metric sliding vernier scales the main scale divisions are 1mm apart, and the vernier scale they are 0.98 mm, giving a reading of 0.02mm per graduation.

• Angular vernier scales are used on protractors, and are identical in use to linear vernier scales. The major protractor scales have divisions of 1 degree, and the vernier scale is divided into 5 minute intervals. One interesting note is that the vernier scale has two halves, one in the positive direction, and one in the negative direction. If reading from the left division, on the main scale, the right vernier scale should be used. And, when measuring from the right hand division on the major scale, the left vernier scale should be used.

13.4.2 Micrometer Scales

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• This is a very common method for measuring instruments, and is based on the thread principle.

• In effect, as a thread is turned, a large motion on the outside of the thread will result in a very small advance in the position of the thread.


• The micrometers pictured above have major scales, as well as minor scales. The major scales are read first, and the micrometer scales are read second and the readings added on.

• The metric micrometer above reads 13.5 = 13.5mm on the major scale, and 31 = .31mm on the thimble, for a total of 13.81mm

• The Imperial scale above shows a micrometer reading of 4.5 = .45” on the main scale, and 9 = .009” on the thimble, for a total of .459

• On imperial micrometers the divisions are typically .025” on the sleeve, and 0.001” on the thimble. The thread used has 40 T.P.I. = a pitch of 0.025”

• Metric micrometers typically have 1 and 0.5 mm divisions on the sleeve, and 0.01mm divisions on the thimble. The thread has a pitch of 0.5mm.

• A vernier micrometer has the scales as pictured above, but also a vernier scale is included to provide another place of accuracy.

• Depth micrometers have an anvil that protrudes, out the end, and as a result the scales are reversed to measure extension, instead of retraction. - The Principle of Magnification

• The operation of micrometers is based on magnification using threads.

• A large movement on the outside of the micrometer thimble will result in a small motion of the anvil.

• There are two factors in this magnification. First, the difference in radius between the thread, and the thimble will give a change in sensitivity relative to the difference in radii. Second, the pitch of the thread will provide a reduction in motion.

• The basic relationship can be seen below,


13.4.3 The Principle of Alignment

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• Basically, the line of the physical measurement should be such that it is coincident with the measurement axis of the instrument.

• If the measurement is out of line, it may lead to misreadings caused by deflections in the instrument.


• micrometers are generally better than sliding vernier calipers when considering this principle.

13.4.4 Dial Indicators

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• Converts a linear displacement into a radial movement to measure over a small range of movement for the plunger.


• The radial arm magnification principle is used here.

• these indicators are prone to errors caused by errors that are magnified through the gear train. Springs can be used to take up any play/backlash in the rack and pinion to reduce these errors.

• The gears are small, but friction can result in sticking, thus reducing accuracy

• A spring is used on the rack to return the plunger after depression.

• The problems mentioned earlier will result in errors in these instruments. If the dial indicator is used to approach a dimension from two different sides, it will experience a form of mechanical hysteresis that will bias the readings. An example of this effect is given below.


• In the graph shown, as the dial indicator is raised in height (taking care not to change direction), the errors are traced by the top curve. As the height of the dial indicator is decreased, the bottom curve is traced. This can be observed using gauge blocks as the known heights to compare the readings against.

• The causes of this hysteresis are bending strain, inertia, friction, and play in the instrument.

• Applications include,

centering workpieces to machine tool spindles

offsetting lathe tail stocks

aligning a vise on a milling machine

checking dimensions

• These indicators can be somewhat crude for accurate measurements, comparators have a higher degree of sensitivity.

13.4.5 The Tool Makers Microscope

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• Quite basically this is a microscope. But, it has lines added to the optics for visual reference, and micrometer dials, and angular verniers added to the stage to measure distances.

• Parts are put on the stage, and the microscope is focused. The stage can then be rotated, and translated precise distances to allow visually referenced measurements

• Such a microscope might have two micrometer heads for x-y translation of the stage. In addition, the stage can be rotated, and angular positions measures.

13.5 Metrology Summary

• We can discuss various instruments, and what they are used for.


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13.6 Problems

Problem 13.1 1. What are measurement standards?

Answer 13.1 Standards are objects of known size, quantity, roughness, etc. These standards are used to calibrate and verify measuring instruments. As a result, measured values are more accurate.

Problem 13.2 What effect will temperature variation have on precision measurements?

Answer 13.2 Temperature control during measurement is important because as materials are heated they expand. Each material expands at a different rate. This leads to distortion of parts and measuring devices that results in measurement errors.

Problem 13.3 How can a vernier scale provide higher accuracy?

Answer 13.3 A vernier scale uses a second elongated scale to interpolate values on a major scale.

Problem 13.4 What are dimensional tolerances, and what are their primary uses?

Answer 13.4 Dimensional tolerances specify the amount a dimension may vary about a target value. These are supplied by a designer to ensure the correct function of a device. If these tolerances are controlled the final product will work as planned.

Problem 13.5 Why is an allowance different from a tolerance?

Answer 13.5 A tolerance is the amount a single dimension can vary. An allowance is an intentional difference between two dimensions to allow for press fits, running fits, etc.

Problem 13.6 What are fits?

Answer 13.6 There are standard for different types of fits (e.g. press fit, running clearance). These specify the allowance of two parts, so that they may be made separately and then joined (mated) in an assembly.

Problem 13.7 What is the difference between precision and accuracy?

Answer 13.7 Precision suggests a limit of technology, accuracy is the ability to achieve a value consistently. These are often interchanged because we are usually concerned with the accuracy when producing precision parts.

Problem 13.8 If a steel ruler expands 1% because of a temperature change, and we are measuring a 2” length, what will the measured dimension be?

Answer 13.8 If we assume that only the steel rule expands, and not the steel part, we can calculate,

Problem 13.9 Draw the scales for a vernier micrometer reading 0.3997”.


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