1. Engineering Measurements
Chapter One
Introduction to engineering measurements By
Dr. SAYEL M. FAYYAD
Home
Next
Previous
End

2. Engineering measurements
Introduction to engineering measurements
Definition
Measurement is a process of comparing one physical quantity with a prescribed standard other quantity by
Physical quantity could be: dimension, mass, temperature, …, etc.
For example, measuring the length of mechanical member in a mechanism is done by comparing the length of this member with prescribed standard (e.g. the meter) with aiding of an instrumentation (ruler)
in past, the measuring process was performed by a mechanical or chemical means. Nowadays, with the revelation of electrical sensing equipment, measurement is performed by electrical sensors which transform the physical quantity to electrical signal

3. Introduction to engineering measurements
Accepted measurement conditions
Proved measuring procedures
Proved measuring apparatus
Correct measuring instrumentation
Correct standard
Selection of meas. Sys. Factors
The required accuracy
Time of delivery of the measuring results
The type of presented data (e.g. mechanical, electrical, ..,etc)
Type of data needed to be measured
Cost criteria

4. Engineering measurements Measuring systems classification
Introduction to engineering measurements
Measuring systems classification
Measuring system
Operational method
Self – operated
Powered
Parts arrangements
Remote sensing
Self contained
Nature of operation
Manual
Automatic
It takes its power from the measured quantity
It needs auxiliary power source. Used in control sys.
The primary measuring element is separated from the secondary
All the elements are contained together
Operated by human
Operated without human assistant

5. Introduction to engineering measurements
Measuring phases
Detects the physical variable or parameter and transferred it into mechanical or electrical signal
Recording stage
Measurand
Transducer
Modifying
Output
Physical parameter (e.g. solid density) or variable (e.g. Temperature)
Modifying the signal from the transducer to be more useful. For example, magnify it.
Parameter does not change with time
Variable changes with time

6. Engineering measurements Introduction to engineering measurements
Basic concepts
Significant Figures: are the digits of a number we can use with confidence.
Significant Figures = number of certain digits + one digit
Examples:
3 Sign. Figs 1 2 3 4 5
26.5 mm
Uncertain
Digits
Certain

7. Special Cases: 2.55 & 25.5 & 255 & 2550 & 25500 have 3 Sig. Figs.
Engineering measurements
Introduction to engineering measurements
Significant figures
Special Cases:
2.55 & 25.5 & 255 & 2550 & have 3 Sig. Figs.
2.55 & & & have 3 Sig. Figs.
Representation : 2.55 x 101 & 2 & 3 & 4
Representation : 2.55 x 10-1 & -2 & -3 & -4

8. Introduction to engineering measurements
Accuracy and Precision
Accuracy refers to how closely a computed or measured value agree with the true value.
Precision refers to how closely individual computed or measured value agree with each other.
Bias (inaccuracy) is the opposite of accuracy. Systematic deviation from true value
Uncertainty (imprecision) is the opposite of precision. Magnitude of scatter.
Example:
Measurements must be
Inaccurate &
imprecise
accurate &
imprecise
Inaccurate &
precise
accurate &
precise

9. Engineering measurements Introduction to engineering measurements
More definitions
Sensitivity is the ratio between the action of measuring device and the change in the measured value.
Hysteresis is a difference between a several readings for one measured variable. This may be caused by mechanical, electrical, …, etc disturbance on the device.
Instrument accuracy is measured by a percentage from the true value must be recorded.
Instrument precision is its ability to reproduce a certain reading with the same accuracy. Precision depends on the mean value of a collection of recorded measurements.

10. Introduction to engineering measurements
Accuracy and precision
Example:
Let us have a thermometer is used to measure water temperature and is divided into 110 grades from 0C to 110C. If this device is used to measure the temperature of a boiling water at sea level (100C). 5 readings were recorded: 103, 103, 104, 105 and 105. assume that the distance between two consecutive grading is 2mm.
The sensitivity of this device equal 2mm/1C = 2 mm/C.
The deviation between these readings may be caused by heat disturbance. This disturbance is called hysteresis.
the accuracy of this device equal: ( )/100 *100% = 5%
The precision of this device equal 1C ( from the mean value which is 104C)

11. Accuracy and precision

12. Engineering measurements Introduction to engineering measurements
Calibration
Calibration is a process performed on measuring device after performing multi operation by it. This process depends on comparing a single measurement taken from the measurement device with well known standard value. This standard value may be:
Primary standard
Secondary standard with a higher accuracy than the device needed to be calibrated.
Known input source.
The main purpose behind the calibration is to increase the accuracy of a device. In many cases, to find a certain value to compare with it is a difficult process. However, there are self calibrated measuring devices which depends on a control system to measure the variable many times and compare it each time with the previous value to increase the precision.

13. Engineering measurements Introduction to engineering measurements
Dimensions and Units
Dimension is a physical variable used to specify the behavior or nature of a particular system. For example, the length of a body represent how long is that body is or the temperate of a system is the measure of how hot is this system is.
Unit is the measure of the dimension. For example, meter is the measure of length and Celsius is the measure of distance.
Units of Measurements
Length
(m or ft)
Mass
(kg or lbm)
Time
(sec)
Force
(N or lbf)
English ft
lbm
lbf SI m Kg N

14. Readability& Reproducibility
Repeatability
describes the closeness
of output readings when the same input is applied repetitively over a short period of time, with the same measurement conditions, same instrument and observer, same location and same conditions of use maintained throughout.
Reproducibility
describes the closeness of output readings for the same input when there are changes in the method of measurement, observer, measuring instrument, location, conditions of use and time of measurement. Both terms thus describe the spread of output readings for the same input. This spread is referred to as repeatability if the measurement conditions are constant and as reproducibility if the measurement conditions vary.

15. Tolerance
Tolerance is a term that is closely related to accuracy and defines the maximum error that is to be expected in some value. Whilst it is not, strictly speaking, a static characteristic of measuring instruments, it is mentioned here because the accuracy of some instruments is sometimes quoted as a tolerance figure. When used correctly, tolerance describes the maximum deviation of a manufactured component from some
specified value. For instance, crankshafts are machined with a diameter tolerance quoted as so many microns, and electric circuit components such as resistors have tolerances of perhaps 5%. One resistor chosen at random from a batch having a nominal value 1000W and tolerance 5% might have an actual value anywhere between 950W and 1050 W.

16. quantity that the instrument is designed to measure.
Range or span
The range or span of an instrument defines the minimum and maximum values of a
quantity that the instrument is designed to measure.

17. Sensitivity of measurement
The sensitivity of measurement is a measure of the change in instrument output that
occurs when the quantity being measured changes by a given amount. Thus, sensitivity (S)
is the ratio: ( if the relation is represented as linear, S=slope)

18. Example

19. Threshold
If the input to an instrument is gradually increased from zero, the input will have to
reach a certain minimum level before the change in the instrument output reading is
of a large enough magnitude to be detectable. This minimum level of input is known
as the threshold of the instrument. Manufacturers vary in the way that they specify
threshold for instruments. Some quote absolute values, whereas others quote threshold
as a percentage of full-scale readings. As an illustration, a car speedometer typically has
a threshold of about 15 km/h. This means that, if the vehicle starts from rest and accelerates,
no output reading is observed on the speedometer until the speed reaches 15 km/h.

20. Resolution
When an instrument is showing a particular output reading, there is a lower limit on the magnitude of the change in the input measured quantity that produces an observable change in the instrument output. Like threshold, resolution is sometimes specified as an absolute value and sometimes as a percentage of f.s. deflection. One of the major factors influencing the resolution of an instrument is how finely its output scale is divided into subdivisions. Using a car speedometer as an example again, this has subdivisions of typically 20 km/h. This means that when the needle is between the scale markings, we cannot estimate speed more accurately than to the nearest 5 km/h. This figure of 5 km/h thus represents the resolution of the instrument.

21. Sensitivity to disturbance
is a measure of the magnitude of the change in measurements values. Such environmental changes affect
instruments in two main ways, known as zero drift and sensitivity drift. Zero drift is
sometimes known by the alternative term, bias.

22. Sensitivity to disturbance forms
(a)zero drift; (b) sensitivity drift; (c) zero drift plus sensitivity drift

23. scale is a common example of an instrument that is prone to bias.
Zero drift
Zero drift or bias describes the effect where the zero reading of an instrument is
modified by a change in ambient conditions. This causes a constant error that exists
over the full range of measurement of the instrument. The mechanical form of bathroom
scale is a common example of an instrument that is prone to bias.

24. Sensitivity drift
Sensitivity drift (also known as scale factor drift) defines the amount by which an
instrument’s sensitivity of measurement varies as ambient conditions change. It is
quantified by sensitivity drift coefficients that define how much drift there is for a unit
change in each environmental parameter that the instrument characteristics are sensitive
to.

25. Example
Example 2.2
A spring balance is calibrated in an environment at a temperature of 20°C and has the following deflection/load characteristic.
It is then used in an environment at a temperature of 30°C and the following deflection/load characteristic is measured.
Determine the zero drift and sensitivity drift per °C change in ambient temperature.

26. Example soln.

27. Hysteresis effects
If the input measured quantity to the instrument is steadily increased from a negative
value, the output reading varies in the manner shown in curve (a). If the input variable
is then steadily decreased, the output varies in the manner shown in curve (b). The
non-coincidence between these loading and unloading curves is known as hysteresis.

28. Hysteresis

29. Hysteresis
Hysteresis is most commonly found in instruments that contain springs, such as the passive pressure gauge and the Prony brake (used for measuring torque). It is also evident when friction forces in a system have different magnitudes depending on the direction of movement, such as in the pendulum-scale mass-measuring device. Devices like the mechanical flyball (a device for measuring rotational velocity) suffer hysteresis from both of the above sources because they have friction in moving parts and also contain a spring. Hysteresis can also occur in instruments that contain electrical windings formed round an iron core, due to magnetic hysteresis in the iron. This occurs in devices like the variable inductance displacement transducer, the LVDT and the rotary differential transformer.

30. Dead space
Dead space is defined as the range of different input values over which there is no change in output value. Any instrument that exhibits hysteresis also displays dead space, as marked on last figure. Some instruments that do not suffer from any significant hysteresis can still exhibit a dead space in their output characteristics, however. Backlash in gears is a typical cause of dead space, and results in the sort of instrument
output characteristic. Backlash is commonly experienced in gear sets used to convert between translational and rotational motion (which is a common technique used to measure translational velocity).

31. Introduction to engineering measurements
Static and dynamic response
If the measured variable does not change with the time, then the measurement process is said to be static. For example, the measurement of the deflection of a beam under static load is a static measurement. However, measuring of the deflection of a vibrating beam is a dynamic measurement.
The measurement of the behavior of a dynamic system become more difficult when the rate of change in the system become larger.
The behavior of a dynamic system is described by a mathematical model. Generally, the mathematical model is described by a differential equation (DE). The general form for the DE is given as:

32. Engineering measurements Introduction to engineering measurements
Mathematical model
Where:
an, an-1, …, a0 are constants
x is the measured response of the system
F(t) is a forcing function imposed on the system.
0th order
1st order
2nd order

33. Engineering measurements Introduction to engineering measurements
0th order system
The solution : the term is called static sensitivity
If F(t) is constant (equal Fo) then the term is called the static response.
CASE 1: Assume that the system is subjected to a sudden STEP input F(t) = A at a time t=0 or
1st order system

34. Engineering measurements Introduction to engineering measurements
1st order system
The ratio a1/ao is called time constant and has a dimension of time.
The solution :
Assume x∞ is the steady state response and rearrange the terms
@ time , the value of x(t) will respond to 63.2 % of the step input.
We called the value of time needed to achieve this value time constant (τ)
Steady state response
Transient solution

35. Engineering measurements Introduction to engineering measurements
Time response
Rise time is the time is the time needed to achieve 90% response from the step input or or t = τ.
Measurement instrumentation does not reach the measured value immediately but it takes some time to reach it. This time is called settling time. Usually this time is assumed as: 5τ since 1-e-5 = 0.993

36. Introduction to engineering measurements
Time response
Graphical representation
Time
Measured
value
Input
Settling
time
62.3% τ
90%
Rise time
99.3%

37. CASE 2: First-order systems subjected to harmonic inputs

38. EXAMPLES

39. EXAMPLE 2

41. SECOND ORDER MEASU. SYSTEMS
Second-order systems described by Eq. (2.8) are those that have mass inertia or
electric inductance. There is no thermal analogy to inertia because of the second law of
thermodynamics. We shall illustrate second-order system behavior with a mechanical
example.

42. simple spring-mass damper system

43. 2nd order System solution

44. 2nd order system soln.

48. Some notes and def.

49. Notes and def.(cont…..)

50. Damping ratio

51. Examples on second order measu. Systems

52. Example2

53. Example 2 (cont…..)

54. Example3

55. System Response
Amplitude response pertains to the ability of the system to react in a linear way to
various input amplitudes. In order for the system to have linear amplitude response, the ratio of output-to-input amplitude should remain constant over some specified range of input amplitudes. When this linear range is exceeded, the system is said to be overdriven, as in the case of a voltage amplifier where too high an input voltage is used. Overdriving may occur with both analog and digital systems.
We have already noted the significance of phase-shift response and its relation to
frequency response. Phase shift is particularly important where complex waveforms are concerned because severe distortion may result if the system has poor phase-shift response.

56. Distortion Distortion is a very general term
that may be used to describe the variation of a signal from its true form. Depending on the system, the distortion may result from either poor frequency response or poor phase-shift response.
In electronic devices various circuits are employed to reduce
distortion to very small values. For pure electrical measurements distortion is easily controlled by analog or digital means.
For mechanical systems the dynamic response characteristics are not as easily controlled and remain a subject for further development.

57. Schematic of the generalized measurement system

58. Problems: HW
2.3
2.4
2.5
2.29
2.30
2.31
2.32
……………….

59. P2.3

62. P2.29

63. P2.30