MECHANICAL MEASUREMENTS

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MECHANICAL MEASUREMENTS
Prof. Dr. Ing. Andrei Szuder Tel.
40.2.1.4112604 Fax. [phone] www.labsmn.pub.
ro szuder_at_labsmn.pub.ro
2
INTRODUCTION TO MEASUREMENT
LECTURE 1
Prof. Dr. Ing. Andrei Szuder Tel.
40.2.1.4112604 Fax. [phone] www.labsmn.pub.
ro szuder_at_labsmn.pub.ro
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INTRODUCTION TO MEASUREMENT
Aims What is measurement? Why measurement?
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INTRODUCTION TO MEASUREMENT
Measurement Systems Measurement
Standards Variables Tests Measurement
Instruments Accuracy Calibration
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AIM OF COURSE
To develop the following skills To understand
existing systems To design outline systems To
communicate with system designers and
manufacturers
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MEASUREMENT SYSTEM
Measures a physical quantity Displays and/or
records the result of the measurement in an
appropriate form
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MEASUREMENT IN MANUFACTURING

• To ensure compatibility of processes
• To ensure compatibility of products
• Essential for quality control
• Frequently required in automatic control

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MEASUREMENT STANDARDS

• All measurement is relative
• Measurement involves the comparison of a physical
  quantity with a similar physical quantity
• Agreed reference standards are required
• A combination of several international agencies
  are responsible for maintaining the primary
  standard measures of various quantities. The
  standard kilogram and the standard second are
  maintained by the French. Others are kept
  elsewhere. It extremely important that these
  standards do not change with time, even over
  hundreds of years.

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HIERARCHY OF STANDARDS
These primary standards cant be passed around to
any that wants to take some measurements if we
expect them to maintain their values, so
secondary standards are kept which may be
somewhat less accurate, but much more accessible.
These are calibrated against the primary
standards. In this manner, a hierarchy of
standards exist. In addition, there are Test
Standards which specify test procedures,
terminology, methods of construction and data
reduction. These are often dictated from
professional societies such as the ASME.
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MEASURAND (definition)

• This is the quantity being measured

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PRIMARY STANDARDS (SI Units)

• Length Metre
• Defined as the distance travelled by light in
  1/299 792 458 seconds
• Reproducible to 1 in 108
• Time Second
• Defined by the rotation time of a specific atom
• Reproducible to 1 in 1011
• Mass Kilogram
• Defined as mass of cylinder held in France
• Reproducible to 1 in 109

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PRIMARY STANDARDS (SI Units)

• Temperature K
• International practical scale
• Defined by various physical properties
• Reproducibility varies with temperature

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DERIVED STANDARDS

• All other quantities are defined in terms of
  primary standards.
• Examples
• Force Mass x length/time
• Current - defined as the force between two
  current carrying wires.

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STANDARDS LABS

• In all major industrial countries.
• ROMANIA
• National Physical Laboratory
• National Engineering Laboratory

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VARIABLES
CONTROL VARIABLE A variable that we are able to
hold constant at a known value. In math,
this is called an independent
variable. DISCRETE VARIABLE Takes on discrete
values, like theroll of the dice. More
important examples are things like different
pieces of equipment that may effect
measurements. CONTINUOUS VARIABLE Not
discrete, anything else. EXTRANEOUS
VARIABLE Cannot be controlled and can effect the
value (e.g. room temp).
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EXEMPLE
The book talks about measuring the gas mileage of
a car. In order to determine this quantity, we
need to measure the miles driven and the volume
of gas used. These are both continuous
variables. Several examples of extraneous
variables are given, including the weather and
the driver.
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MORE DEFINITIONS
PARAMETER A functional relationship between
several variables.
For example, in fluid mechanics, say we have
measured/determined the variables velocity, u,
kinematic viscosity, v, and the length scale D.
Then the Reynolds number is a parameter ReD
uD/v
Noise a random variation of the value due to
effects of extraneous variables. Interference
a deterministic variation in the value due to
extraneous variables.
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TEST MATRICES
If we have a phenomenon y that is a function of
one control variable x, then in order to
determine how y varies with x, we will set x to
several values, x1, x2, x3 and measure the
corresponding y values y1, y2, y3 until we have
enough data to determine the functional form of
y(x). Generally, phenomenon depend on more than
one control variable. Say z(x,y). In this case,
it is necessary to hold one of the control values
(say x x1) constant while varying the other
(y). Then, a second value of x is chosen, and in
best case, the same values of y are repeated.
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RANDOM TESTS
Random tests attempt to minimize the effect of
extraneous variables. If tests are made by
randomly varying the independent variables
(controls) rather than making the tests in order,
we should make interference effects look more
like noise. Noise can be averaged out of a
result by making more and more tests, while
interference can not.
REPETITION Decreases random errors.
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CONCOMITANT METHODS

• It is never smart to believe any single piece of
  information.
• Instruments let you down more often that you
  would hope, as do other methods of getting
  results (e.g. computer simulations).
• Do not bank on any result until you have verified
  it independently with a different method.

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MEASUREMENT INSTRUMENTS

• A measurement instrument gives an estimate of the
  value of a physical quantity defined in terms of
  the standard
• It is essential that the accuracy of this
  estimate is known

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ACCURACY

• Accuracy is an estimate of the likely difference
  between the measured value and the true value.
  
• The true value is that which would be obtained
  by direct comparison with a primary standard.
• Error is basically the same thing as accuracy -
  it is a better term but is used less often.
• Accuracy is determined by calibration

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ACCURACY
Accuracy can be determined during a calibration.
It is the ability of the system to indicate the
true value exactly. We define the error as e
true value - indicated value. The accuracy is
the error relative to the true value expressed in
a percentage, or
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ACCURACY

• Deviation of the reading from a known input.

Instrument reading
45 deg
accuracy
Known Input
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CALIBRATION

• This is the process which relates the measurement
  given by an instrument to the measurement
  standard
• It enables a set of parameters for the
  instruments to be quantified.

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CALIBRATION DEFINITIONS

• Say we have a sensor that has the relationship
  y(x) and that we calibrate it by varying x
  between xmin and xmax. As a result, we measure
  values of y between ymin and ymax.
• (Note that ymin is not necessarily the value when
  x xmin). Then our input range ri is xmax- xmin
  and our output range ro is ymax- ymin. Any
  measurements outside of this domain are not
  valid.

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CALIBRATION
A sensor is something that changes its value as a
result of some phenomenon that we want to
measure. A good sensor is sensitive to only one
variable. The manner in which the value changes
with the control variable is not theoretically
known in most cases. Therefore, we compare the
output of our sensor/transducer to a known value
(standard) as we vary the control variable. A
thermometer is an example.
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CALIBRATION EXAMPLES
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CALIBRATION EXAMPLES
Thermal Anemometry uses the fact that many
materials change their resistance with
temperature. A hot-wire anemometer is a device
that heats a wire by pumping current through it
and keeps its resistance (and thus its
temperature) constant. When air blow on the wire
the current required to keep the wire hot goes
up. Therefore this instrument is sensitive to
velocity. It needs to be calibrated against a
known velocity, however.
A2, V2, P2
A1, V1, P1
A1 is 100 times larger than A2, so V1 is close to
zero. So, Bernoulli says that
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TRACEABILITY

• All measurement systems should be traceable to
  the primary standard via a calibration chain.

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CALIBRATION

• Two kinds of calibration will be considered
• calibrating a new instrument
• calibrating an existing instrument
• We will also look at how the specification of a
  commercial instrument is defined and assessed

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MAKING A NEW INSTRUMENT

• An instrument is a device which has an output
  which varies in response to changes in the
  measurand
• The output may be a voltage, a current instrument
• , the position of a pointer, etc.
• The relationship between the output value and the
  measurand must be established
• This is done by calibration of the instrument

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HOW CALIBRATION IS DONE

• A "known" instrument which measures the same
  measurand is required - this instrument must have
  already been traceably calibrated
• The quantity being measured must be variable over
  the range of interest
• All other parameters which might affect the
  performance of the instrument must be kept
  constant as far as possible

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CALIBRATION DATA
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CALIBRATION DATA

• Output may be in Volts, mm, degrees, mA etc.
• The operating range of the instrument can be
  found from this data
• The calibration data enables the instrument to be
  used subsequently for measurement
• Systematic and random errors can also be
  determined - these define the accuracy of the
  instrument

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OPERATING RANGE (definition)

• This defines the range of measurand values which
  the instrument can measure
• Examples
• Temperature 50 - 250C
• Length 5 - 200 mm
• Pressure 10 - 200 Kpa
• Also called Span, Full Scale Output (FSO), Full
  Scale deflection (FSD)

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DETERMINING THE CALIBRATION PARAMETERS

• This is usually done using regression analysis
• If this is not possible, they will have to be
  individually estimated.

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LINEAR REGRESSION ANALYSIS

• The value of the measurand, M, is varied in
  suitable steps over the operating range,
  increasing and decreasing several times.
• The instrument output X (usually, but not always
  volts) is noted.
• A straight line is fitted to the data
  X SMb
• S is the slope of the line, i.e. the sensitivity
• b is the intercept with the axis

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LINEAR REGRESSION ANALYSIS

• The regression data can then be used to find the
  measurand value when the output has a particular
  value
• output value X
• measurand (X-b)/S
• This is only an approximation since the
  relationship is not truly linear
• The errors incurred in using this approximation
  enable the sources of error to be determined and
  quantified.
• This is done using the residual values

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ACCURACY AND ERRORS
LECTURE 2
Prof. Dr. Ing. Andrei Szuder Tel.
40.2.1.4112604 Fax. [phone] www.labsmn.pub.
ro szuder_at_labsmn.pub.ro
42
SYSTEMATIC AND RANDOM ERRORS

• Systematic errors are constant for a given
  instrument
• The values are found by the calibration
• Their effects can be removed
• Random errors cannot be removed
• However, their effects can be reduced by taking
  several measurements

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ERROR

• The deviation of a reading from a known input.
  Systematic errors can be reduced by calibration.

Reading (cts)
EU value
error
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PARAMETERS DEFINING ACCURACY (ERROR)

• Parameters found from calibration which are used
  to define the accuracy (error)
• - Precision
• Resolution
• Sensitivity
• Linearity (or non-linearity)
• Hysteresis
• Repeatability/precision/reproducibility
• Environmental errors

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DEFINING ACCURACY

• For a given instrument, only a few of these
  errors will be significant
• The overall error (and accuracy) will be given by
  the combination of the individual errors.

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ACCURACY

• Deviation of the reading from a known input.

Instrument reading
45 deg
accuracy
Known Input
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PRECISION

• Ability to reproduce a certain reading with a
  given accuracy.

Standard deviation
samples
Readings
Mean reading
Input value
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LEAST COUNT

• Smallest difference that can be detected.

Counts
1 ct
Volts
Least Count
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RESOLUTION

• The smallest change in the measurand which can be
  detected by the instrument
• This is normally determined by how the output is
  displayed
• Straightforward with a digital display
• Not fully defined with an analogue system
• The resolution is sometimes limited by a
  particular aspect of the instrument itself (e.g.
  a potentiometer)
• Sometimes called discrimination

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RESOLUTION OF AN ANALOGUE DISPLAY

• What is the resolution?

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SENSITIVITY AND LINEARITY

• Sensitivity is the rate of change of output vs
  input
• May be in mV/mm, A/mbar, mm/C
• An ideal instrument has constant sensitivity
• Linearity is a measure of how the sensitivity
  varies over the operating range of the instrument

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HYSTERESIS

• This is a measure of the variation in output for
  a given measurand value when approached both
  upwards and downwards.
• It arises due to stiffness, backlash, friction,
  magnetic effects

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REPEATABILITY (PRECISION,
REPRODUCIBILITY)

• Repeatability is a measure of the random error
• Strictly speaking, it should be called
  repeatability error

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ENVIRONMENTAL ERRORS

• Changes in instrument output due to changes in
  environment, not measurand changes
• Humidity
• Acceleration
• Vibration
• Temperature
• Pressure
• Mounting effects

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RESIDUAL VALUES AND ERRORS

• The residuals show the difference between the
  real points and the fitted curve
• For a perfect straight line, the residuals would
  all be zero.
• The bigger the residual values, the greater the
  errors
• The form of the residual curve is related to the
  types of error

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ERROR

• The deviation of a reading from a known input.
  Can be reduced by calibration.

Reading (cts)
EU value
error
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UNCERTAINITY

• The portion of the error that cannot or is not
  corrected for by calibration.

Uncertainty 3 sd
Standard deviation (sd)
samples
Readings
Mean calibrated reading
Input EU value
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CALCULATING ERRORS FROM RESIDUALS

• The real value is not on the straight line
• The difference between the output value and the
  value indicated by the straight line is ?X, the
  residual value
• Using the straight line gives an error in the
  measured value of ?M
• The error, ?M, is related to the residual value,
  ?X by ?M ?X/S where S is the slope or
  sensitivity

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SOURCES OF ERROR

• These can be determined by looking at the form of
  the residuals
• Each type of error produces a specific form of
  residual variation
• If there is more than one type of error, these
  will be combined

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FORM OF RESIDUALS

• Linearity error shows a systematic deviation from
  the straight line
• Hysteresis error shows as residuals with opposite
  signs for increasing and decreasing measurand
• Repeatability error has random variation in the
  residuals

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QUANTIFYING THE ERRORS

• If there is one predominant error
• find the largest positive and negative residual
  values
• divide by S, the sensitivity, to give the
  measurand errors
• quote as ?m or mmax , -mmin

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QUANTIFYING THE ERRORS

• If there are several sources of errors
• estimate the amount of residual error due to each
  source
• divide each value by S to give the measurand
  error due to that source
• The total error is then found by combining these
  errors - see Unit 3.

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• EXAMPLES

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CALIBRATION OF A POSITION MEASURING SYSTEM

• The sensitivity is found to be 3.35V/mm
• The residual errors are plotted on the next slide
• Assume that the vertical axis is in Volts

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Position measuring system - residuals
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SAQ 3

• The maximum error is
• a) ? 0.3 mm
• b) ? 0.03V
• c) ? 0.003mm
• d) ? 0.003mV

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Speed measurement system

• The output of the system is the position of a
  needle on a circular display
• Calibration gives the sensitivity as 0.5420 per
  mph.
• The residuals are shown on the next slide
• Assume the vertical scale is in 0 (degrees)

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Speed measurement calibration - residuals
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SAQ 4

• The main source of error here is
• a) non-linearity
• b) repeatibility
• c) speeding
• d) hysteresis

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SAQ 5

• The maximum error is
• a) ? 5mph
• b) ? 0.50
• c) ? 1mph
• d) ? 0.01mph

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Calibration of a mercury thermometer

• Output is the position of the mercury level on a
  vertical scale
• The sensitivity is found to be 0.132mm/0C
• The residuals are plotted on the next slide
• Assume the vertical scale is in mm

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Mercury thermometer - residuals
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SAQ 6

• The main source of error here is
• a) non-linearity
• b) draughts
• c) repeatability
• d) hysteresis

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SAQ 7

• The maximum error is
• a) ?.04mm
• b) ? 0.040 C
• c) ? 0.4 0 C
• d) ?.04V

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Position sensor

• The output is in the form of a voltage
• The sensitivity is found to be 2.43V/mm
• The residuals are plotted on the next slide
• Assume the vertical axis is in V

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Position sensor - residuals
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SAQ 8

• The main source(s) of error is/are
• a) non-linearity
• b) hysteresis
• c) repeatibility and hysteresis
• d) hysteresis and non-linearity

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SAQ 9

• The maximum error is
• a) .02V
• b) .008mm
• c) 0.5mm
• d) 0.02mm

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Pressure sensor - residuals
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SAQ 10

• The main source(s) of error is/are
• a) Repeatability
• b) Repeatability and hysteresis
• c) Hysteresis
• d) Non-linearity and hysteresis

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SAQ 11

• The maximum error is
• a) ?.012V
• b) ? 0.2kPa
• c) ? 0.07kPa
• d) ? 0.1mm

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MEASURING ERRORS DIRECTLY

• Applies to
• repeatability
• hysteresis
• May be necessary if it is not possible to perform
  a complete calibration.

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REPEATABLITY

• Random departures from the ideal line indicate a
  repeatability error

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REPEATABILITY AND RESIDUALS

• When the variation in the residuals is random,
  repeatability is the only source of error
• The repeatability error can be calculated
  statistically
• If ? is the rms residual value
• The random error (repeatability) is less than
  2?/S with a confidence of 95

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MEASURING REPEATABILITY DIRECTLY

• The instrument output is noted for a fixed value
  of the measurand several times
• This is repeated for several different values of
  the measurand
• The repeatability error can be taken as the
  largest difference which occurs for a given
  measurand value
• Usually quoted as ? this difference

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HYSTERESIS

• A difference in output for increasing and
  decreasing measurand indicates hysteresis

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MEASURING HYSTERESIS DIRECTLY

• The measurand is set to the same value approached
  from both directions
• The instrument output is noted
• This is done for several values
• The hysteresis error can be taken as the largest
  difference which occurs for a given measurand
  value when it is approached in opposite
  directions.
• Usually quoted as ? this difference

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SENSITIVITY ERROR

• If the line is not at 450, then there is a
  sensitivity error

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Sensitivity error

• The manufacturer may quote a sensitivity error
• e.g. sensitivity 12.3V/mm, error ??0.5
• When the manufacturers sensitvity value is used
  in setting up the instrument, each value will
  have an associated error
• e.g. position 12.5 mm, sensitivity error
  12.5mm x 0.5 0.06mm
• Can be avoided by doing your own calibration

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MEASURING ENVIRONMENTAL ERRORS

• If the appropriate environmental parameter can be
  varied, its effect on the instrument can be
  measured
• For example, the variation in output of the
  instrument may be noted as the temperature
  changes

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MEASURING ENVIRONMENTAL ERRORS

• It is also possible to correct for such errors,
  but this makes the measurement much more complex
• These errors may be negligible
• They are normally treated as part of the cause of
  random errors (repeatability)

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CALIBRATION RESULTS

• An ideal instrument gives a straight line at 45o
  through the origin
• Deviations from this indicate the errors that are
  present

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BIAS

• If the points lie on a line which is parallel but
  displaced from the ideal line, then the
  instrument is biased

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NON-LINEARITY

• Systematic deviation from the ideal line
  indicates non-linearity error

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SPECIFICATION OF A COMMERCIAL INSTRUMENT

• This is found partly from the manufacturer's data
  sheet, and partly from investigation in use

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MANUFACTURER'S DATA SHEET

• Commercial transducers and instruments are
  supplied with a specification sheet containing
  values for relevant parameters
• It is not always easy to find the information you
  are looking for!
• May quote an overall accuracy which combines all
  errors
• May quote various sources of error, (linearity,
  hysteresis, temperature etc) which will need to
  be combined.

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HOW CALIBRATION PARAMETERS ARE QUOTED

• range or FSO (Full Scale Output)
• reading
• number of l.s.d. (least significant
  digits)
• units of measurand
• combinations of these

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HOW CALIBRATION PARAMETERS ARE QUOTED - examples

• 2lsd
• 0.02 Range
• 0.1 FSO
• 0.1 mm
• 20 kPa
• 0.1 FSO 0.2 reading
• 0.2 reading 3lsd

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Accuracy of the reference instrument

• The accuracy of the known instrument should be 10
  times the accuracy you expect in the instrument
  you are calibrating
• The minimum acceptable is 3 times.

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CALIBRATING AN EXISTING INSTRUMENT

• The instrument gives a direct reading of the
  quantity being measured (mm, oC, etc)
• Calibration enables its accuracy to be assessed
• It may also indicate that the instrument should
  be adjusted
• Another known instrument is required
• It must be possible to vary the measurand in
  appropriate steps

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Assessing a commercial instrument

• Check the range
• Check all the different sources of error
• non-linearity error
• repeatability error
• hysteresis error
• sensitivity error - see later
• temperature error - see later
• any other environmental errors
• any other sources of error mentioned

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Assessing a commercial instrument

• Other important parameters
• Dimensions
• Weight
• Drive voltage required
• Sensitivity
• Temperature operating range
• Cost!!!

106
Temperature error

• This is a measure of how the sensitivity varies
  with temperature
• Such a variation in sensitivity give srise to an
  error
• If the sensitivity error is 0.01/oC, and the
  temperature varies during use by 10oC, this will
  give rise to an error of 0.1 of the reading

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CALIBRATION AND QUALITY ASSURANCE (ISO9000)

• An effective system for control and calibration
  of measurement standards and equipment must be
  maintained
• All personnel shall have adequate training
• The calibration system should be reviewed to
  maintain its effectiveness
• All measurements should take into account errors
  and uncertainties in the measurement

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CALIBRATION AND QUALITY ASSURANCE

• Calibration procedures shall be documented
• Objective evidence of the measurement system's
  effectiveness should be available
• Calibration must be done using equipment
  traceable to national standards