This document provides an overview of engineering measurements and measurement systems. It discusses key concepts such as: - Dimensions and units used to characterize physical quantities in measurements. The International System of Units (SI) and common English units are presented. - The components of a generalized measurement system, including sensor, transducer, signal conditioning, output, and feedback control stages. Examples of liquid-in-glass thermometer and Bourdon tube pressure gauge systems are described. - Definitions of variables involved in measurements like independent, dependent, discrete, continuous, and extraneous variables. Terms related to measurements such as sensitivity, least count, hysteresis, and repetitions are also defined.

1. PHM 131
Spring 2021
lecture 2
Engineering Measurements
Introduction to The Design of Measurement Systems
MCT 231
Fall 2023
Lecture 1
Dr. Hany Elsayed
Dr. Hamada Galal

2. Page 1 /Lecture 1
Introduction

3. Dimensions and Units
Physical variable is used to describe the
behavior or nature of a particular system
Units are terms used to measure the
magnitude of a dimension
Dimensions
Any physical quantity can be characterized by dimensions. The magnitudes assigned to the
dimensions are called units
Units
Page 2 /Lecture 1
Introduction

4. Dimensions and Units
There are two systems of units: International system(SI) and English system
Fundamental (primary) dimensions and their units
Physical variable Dimension SI units English units
Length 𝐿 Meter (𝑚) Foot (𝑓𝑡)
Mass 𝑀 Kilogram (𝑘𝑔) Pound mass (𝑙𝑏𝑚)
Time 𝑡 Second (𝑠) Second (𝑠)
Temperature 𝑇 Kelvin (𝐾) Rankine (𝑅)
1 𝑚 = 3.28 𝑓𝑡 1 𝑘𝑔 = 2.2 𝐼𝑏𝑚 1 𝐾 = 0.55 𝑅
Standard prefixes in SI units
Prefix tera, T giga, G Mega, M Kilo, k Hecto, h deka, da Deci, d centi, c milli, m micro,𝝁 nano, n Pico, p
Multiple 1012
109
106
103
102 101
10−1
10−2
10−3
10−6
10−9
10−12
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Introduction

5. Measurements and Metrology
Measurements Metrology
Measurement is the assignment of a specific
value to a physical variable and express in units
For engineering purposes
It presents a restrictions for measuring
length, angle, and other qualities which
are expressed in linear or angular
terms
Is the scientific study of measurements
For industrial inspections process
It provides a basis for judgments of
. Process information.
. Quality assurance.
. Process control
It basically encompasses all important aspects
pertaining to measurement and measurement
instruments
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Introduction

6. Measurements and Metrology
Measurement’s objectives
Evaluation of newly developed products
Measuring instrument capabilities
Ensuring a quiet sufficient for their
respective measurements
Minimizing the cost of inspection by
effective and efficient use of available
facilities
Maintain the accuracies of measurements
Reducing the cost of reject and rework
through the application of statical quality
control techniques
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Introduction

7. Generalized Measurement System
1- Sensor stage
2- Transducer stage
3- Signal conditioning stage
4- Output stage
5- Feed back control stage
Physical element that employs some natural phenomenon by
which it senses the variable being measured
It converts this sensed information into a detected signal
form which might be electrical, mechanical, optical or
otherwise
It takes the transducer signal and modifies it to a desired
magnitude. An optional stage can consist of one or more
devices.
It takes the signal and provide an indication of the value of the
measurements. Might be a simple read out display or might contain
devices that can record the signal for later analysis
It contains a controller that interprets the measured signal and makes a decision regarding the
control of the process. In simple magnitude of the signal of the sensed variable, whether it
exceeds some high or low set point, a value set by system operator
Sensor
stage
Transducer
stage
Output
stage
Control
stage
Calibration
Control signal
Signal Conditioning stage
Process
Signal
path
Page 6 /Lecture 1
Introduction

8. Schematic of the generalized measurement system
Detector-transducer
stage
Intermediate
stage
Recorder
Indicator
Analog/digital
meter
Controller
External
power
Calibration signal source
representing known
value of physical variable
Physical variable to be
measured
Feedback signal for control
Transduced
signal
Modified
signal
Calibrated
signal
Input
signal
Output stage
Signal processing
Signal
generation
Page 7 /Lecture 1
Introduction

9. Example1: Liquid in glass thermometer
Expansion Cavity
Stem
Liquid Column
Range Cavity
Bulb
Sensor-transducer stage
Sensor stage
Output stage
Page 8 /Lecture 1
Introduction

10. Example2: Bourdon-tube pressure gauge
Intermediate (Modifying) stage (Sector and Pinion)
Signal processing
Output (Indicator) stage (Pointer and the dial)
Detector-transducer stage (Bourdon tube)
Bourdon-tube (oval cross-section)
It converts the pressure signal into a mechanical
displacement signal of the tube
It amplifies the displacement of the end of the tube.
Small displacement to 3-quarters of a revolution of the center gear
When calibrated with known pressure inputs, gives an indication of the
pressure signal impressed on the bourdon tube
Physical signal Pressure
Signal generation Line or tank at which the gauge is fitted
Page 9 /Lecture 1
Introduction

11. Variable Definitions
Independent Variable
Dependent Variable
Control of Variable
Discrete Variable
Continuous Variable
Extraneous Variable
It can be changed independent of others.
It is affected by change in one or more other variables.
It hold at constant value or prescribed condition over duration of measurement.
Values can take on any level within range of operation (pressure, temperature).
It cannot be controlled during measurement but affect the measured variable
(operator or machine particular functioning).
Possible values can be enumerated (dice).
Page 10 /Lecture 1
Introduction

12. Variable Definitions
Control parameter
Noise
It has an effect on the behavior of the measured variable and should be controlled during
test period
A random variation of value of the measured signal due to variation in extraneous
variables.
• Most signals have some noise; the question is how much !
• A complete control
❑ Environmental conditions
❑ Thermal noise
❑ Radio frequency
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Introduction

13. Variable Definitions
Interference:
Produces undesirable deterministic trends
on measured values, such as a sinusoidal
wave superimposed on the signal path.
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Introduction

14. Variable Definitions
Repetitions: Repeated measurement of dependent variable during a signal test run
(diameter of ball bearing batch – multiple measurement on same batch/day) .
Replication: An independent duplication of a series of test measurements under similar operating conditions
(ball bearing batch on a separate days under similar conditions).
The least count: Is the smallest difference between two indications that can be detected on the instrument scale.
It depends on:
- Scale length
- Spacing of graduations
- Size of pointer
Page 13 /Lecture 1
Introduction

15. Variable Definitions
The sensitivity: Of an instrument is ratio of the linear movement of the pointer on an analog instrument to
the change in the measured variable causing this motion.
a 1-mV recorder might have a 25-cm scale length. Its sensitivity would be 25 cm/mV, assuming that the
measurement was linear all across the scale.
Example
An instrument is said to exhibit hysteresis when there is a difference in readings depending on whether the value
of the measured quantity is approached from above or below.
The hysteresis:
Hysteresis may be the result of
- mechanical friction - magnetic effects - elastic deformation - or thermal effects.
For a digital instrument read out the term “sensitivity” does not have the same meaning because different scale
factors can be applied with the push of a button. However, the manufacturer will usually specify the sensitivity for a
certain scale setting, for example, 100 nA on a 200-μA scale range for current measurement
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Introduction