2
nd Year Mechanical Engineering
School of Engineering
Engineering Manufacturing 2 –
Metrology (6.1)
Dr Robert Heinemann
Metrology – Dr R Heinemann 2
Content
▪ What is metrology
▪ Frequently used – and misunderstood – terms in metrology
▪ Measurement errors - The enemy
Metrology – Dr R Heinemann 3
What is metrology?
Metrology - from Ancient Greek metron (measure) and logos
(study of) - is the science of measurement. It includes all
theoretical and practical aspects of measurement.
The International Bureau of Weights and Measures defines
Metrology as "the science of measurement, embracing both
experimental and theoretical determinations at any level of
uncertainty in any field of science and technology.“
© International Bureau of Weights and Measures (BIPM)
Metrology – Dr R Heinemann 4
What does it include today
conventional
- +
micro-scale large-scale
Metrology
Metrology – Dr R Heinemann 5
Is it something new?
Did you know that, despite of its
size and the in today’s terms
rather primitive construction and
measurement equipment used
back then, the difference in
height of opposite corners of the
pyramid at its base is only 13
mm?
No! The science of measurement has been around for a long time.
The great pyramid of Cheops, built 4500 years ago, covers 52,000
square meters (13 acres) and contains 2,300,000 stone blocks having an
average mass of 2,270 kilograms (5,000 pounds) each. It has been
estimated that it took 100,000 men from 20 to 30 years to complete the
pyramid.
Metrology – Dr R Heinemann 6
Why is it so important in manufacturing today?
How were things made before the 18th century:
Mass production requires interchangeable parts, for which one
needs to define tolerances, which implies that parts are measured.
• One craftsman was in charge of manufacturing all parts of a product.
• Each part was made to “fit” the surrounding parts.
• Making parts did not require any information about measurements,
because one part was made to fit and only had to fit the parts around it.
How are things made today:
• Huge quantities of products require thousands of parts to be made, by
different people all over the world (→ mass production).
• To allow for a random combination, i.e. any part to fit any product, parts
need to be interchangeable, which means they are allowed to vary by a
certain amount only (→ they need to be almost “identical”).
Metrology – Dr R Heinemann 7
Some important technical terms
❑ Accuracy
❑ Trueness
❑ Precision
❑ Resolution
Don’t they
mean the
same?
Metrology – Dr R Heinemann 8
▪ Accuracy characterises the
closeness of agreement between a
measurement and the true value.
▪ If several measurements are
available from a series of
measurements, accuracy becomes
an umbrella term and is split up into:
❑ Trueness = closeness of
agreement between the mean
value of various measurements
and the true value.
❑ Precision = closeness of
agreement between individual
values among themselves.
Accuracy vs. trueness vs. precision
= one individual
measurement
= arithmetic mean of all
measurements
Accuracy (of one
measurement)
Trueness (of
several
measurements)
True value
Precision
Metrology – Dr R Heinemann 9
Accuracy, trueness, precision and resolution (cont’d)
Micrometer
Venier calliper
Tape measure
Resolution is related to the measuring device, and indicates the
smallest change it can detect and display in the quantity it measures.
It is not related to the actual measurement process, but often
considered to imply the level of accuracy a certain measurement
instrument exhibits.
Metrology – Dr R Heinemann 10
Measurement errors
Theoretically, the measured value x measured from an instrument should
be identical to the true value x true.
x measured = x true
In reality, however, these two values are not identical, because every
measurement is subject to some level of ‘Error’.
x measured = x true + Error
The ‘Error’ is a combination of many different types of errors, which
can be classified as systematic errors Es and random errors E r
.
x measured = x true + E s + E r
Maybe the biggest challenge in metrology is to keep these as
small a necessary.
Metrology – Dr R Heinemann 11
Measurement error (cont’d)
▪ Random Errors (‘Precision Errors’) are caused by unknown and
unpredictable changes in the experiment, such as:
❑ fluctuations in the readings of a measurement apparatus
❑ short-term environmental disturbances, e.g. vibrations
❑ subjective interpretation of an instrument’s reading.
▪ These changes result in the measured values not being constant.
▪ They are inherently unpredictable and therefore cannot be
corrected beforehand.
Question: Do you think that repeating a measurement over and over
again would allow us to be more certain of the “true” value?
Metrology – Dr R Heinemann 12
Measurement error (cont’d)
Answer: Yes. In the presence of only random errors, the mean value of
a set of measurements is more likely to be correct if you repeat the
measurement many times. Repeated measurements of the same thing
tend to be normally distributed.
Four measurements
19 measurements
One measurement
True value
n measurements
Normal
distribution curve
Metrology – Dr R Heinemann 13
Measurement error (cont’d)
▪ Systematic Errors (‘Bias Errors’) cause the mean value of many
separate measurements to be consistently too high or too low.
▪ Sources of systematic error are, e.g.,
❑ imperfect calibration of measuring devices
❑ faulty components or malfunctioning instruments
❑ long-term fluctuations in environmental conditions, e.g.
temperature, humidity, …
▪ If the source of error is known, corrections can be applied.
Question: In the presence of a systematic error, does it help to
repeat measurements?
Metrology – Dr R Heinemann 14
Measurement error (cont’d)
Answer: No! Repeating measurements in the presence of a
systematic error does not improve the trueness of the
measurements, because the same error is always there.
Although the measurements are normally distributed, the curve is
shifted towards the left; it is no longer centred around the true value. summarise info into 1 page for revision for my test