Measurements and Instrumentation

ME-313Fall’15

ME@DSU

Dr. Bilal A. Siddiqui

Course Outline• Significance of measurement• planning of experiments,• general measurement systems• Calibration• static and dynamic measurement sensitivity• range, accuracy, precision, repeatability, and uncertainty of instruments• measurement errors• instruments for measurement of

• Length• Force• Torque• Strain• Pressure• Flow• Temperature

• Introduction to data acquisition systems, A/D and D/A converters.

Course Objectives and Texbook• To understand the methods and principles of instrumentations of

various systems.• To learn the basic method to measure various parameters.

Textbook• Theory and Design for Mechanical Measurements by Figliola and

Beasley.• Class Notes.

Measurements and Instruments• We measure things every day. Think of examples.• Measuring instrument: a device for measuring a physical quantity.• Process of measurement gives a number relating the item under study

and the referenced unit of measurement. • Measuring instruments are the means by which these relations of

numbers are obtained. • Selection of measurement instruments and techniques and their

interpretation depends on the task at hand.• You may not worry about how much a “pinch of salt” actually weighs

when cooking pakoray, but your life depends on it if it is a life saving drug to be taken in exactly 2.56 mg doses.

Mechanical Measurements• By mechanical measurements, we mean quantities to be measured

are related to mechanical engineering and processes.• Force• Torque• Length• Pressure• Temperature• Humidity• Flow rate• Speed• Acceleration etc etc

Emotional Measurements• We may instrument emotions too ….

Objective behind Measurements• The objective in any measurement is to answer a question. • Measurements = value or the tendency of some variable to answer our question. • Output of the measurement device should be a reliable indication of the true

value of the measured variable.• How can a measurement or test plan be devised so that the measurement provides the

information we need?• How can a measurement system be used so that the engineer can easily interpret the

measured data and be confident in their meaning?• Specifying a measurement system and measurement procedures represents an

open-ended design problem • Several approaches to solving a measurement problem, some better than others.

General Measurement System• All measurement systems consist of the following components

Sensor• A physical element that employs some natural

phenomenon to sense the variable being measured.• Provide various types of outputs. Typically electrical or

optical. • All living organisms contain biological sensors with

functions similar to those of the mechanical devices.• A chemical sensor is a self-contained analytical device

that can provide information about chemical composition.

• A biosensor uses a sensitive biological element (cell, bacteria etc) to measure some quantity, e.g. “miner’s canary” to detect gas in mines.

Transducer• A transducer is a device that converts the sensed value from the

sensor into a detectable signal.• Often sensor and transducer are interchangeable terms.• ‘‘Transducer’’ is also often used in reference to a packaged device

(instrument), which may contain a sensor, transducer, and even some signal conditioning elements and readouts.

• It is important to note that like all practical engineering, many terms have more than one usage.

Signal Conditioning• The signal-conditioning stage takes the transducer signal and modifies

it to a desired magnitude.• Used to perform tasks such as

• increasing the magnitude of the signal by amplification• removing portions of the signal through some filtering• providing mechanical or optical linkage between the transducer and the

output stage.

Output Stage• The output stage indicates or records the value measured. • This might be a simple readout display, a marked scale, or even a

recording device such as a computer disk drive. • Additionally, we may need to log the data.

An Example – Atomic Force Microscope• Measure the profile of a surface

at a nanometer scale. • Very small cantilever beam

placed near the surface is deflected by atomic forces

• Cantilever is the sensor

Example 2 - Thermometer• Identify the components

Experimental Test Plan• An experimental test serves to answer a question, so the test should be

designed to answer that question reasonably. • E.g. design a test to answer , ‘‘What is the mileage of my car?’’• What will be your test plan?• What are the sensors you will deploy?• What are the variables?

• Driver and driving habits• Highways vs downtown• Road conditions• Weather

• How accurate do you need the test to be?

Steps in Experiment Test Plan1. Parameter design plan:

o Determine the test objectiveo identify the process variables and parameterso Identify the means for controlling these variables and parameters. o Ask:

‘‘What question am I trying to answer? What needs to be measured?’’ ‘‘What variables and parameters will affect my results?’’

2. System and tolerance design plan. based on some tolerance limits for error, select:o measurement techniqueo equipmento test procedureo Ask:

‘‘In what ways can I do the measurement” “how good do the results need to be to answer my question?’’

3. Data reduction design plan: Plan how to do the following with the datao Analyze ito Present ito Ask:

‘‘How will I interpret the resulting data?” “How will I use the data to answer my question?” “How good is my answer?” “Does my answer make sense?’’

Variables and their Types• Variables are things that influence the test. • Besides the targeted measured variable, there may be other variables that will

affect the test result. • All known process variables should be evaluated for any possible cause-effect

relationships. • A variable that can be changed independently of other variables is an

independent variable.• A variable that is affected by changes in other variables is a dependent variable. • A variable may be continuous or discreet, controlled or extraneous .• Identify the type of variables in the car fuel consumption example.

Continuous and Discrete VariablesAnalog and Digital Measurements• Continuous variables which can take any real numbered value

in an interval.• E.g. the time from elapsed since sunrise today is continuous• Discrete variables can take only a finite number of values in

an interval.• E.g. the time you can measure since sunrise using a wall clock

can be measured with intervals of 1 second only! In one hour you can measure 3600 discrete time values using wall clock, not more!

• Continuous measurements are called analog, discrete measurements and systems are digital.

Controlled and Extraneous Variables• The control of variables is very important. • The cause-and-effect relationship between the independent variables and the

dependent variable is found by controlling the values of the independent variables while measuring the dependent variable.

• A controlled variable is one that can be held at a constant value or within some margin. • Variables that are not (or cannot be) controlled during measurement are called

extraneous variables. • Extraneous variables can introduce differences in repeated measurements of the same

measured variable taken under seemingly identical operating conditions. • They can also impose a false trend onto the behavior of that variable. • Due to extraneous variables, the measured signal will be corrupted by noise and drift.

Example of Extraneous Variable’s Influence• Consider a thermodynamics

experiment to establish the boiling point of water.

• The apparatus for measuring the boiling point gives the results shown for three test runs conducted on separate days.

• Why should the data from three seemingly identical tests show such different results?

• Measurement system accuracy accounts for only 0.1 F of the test data scatter.

• Where is the rest of the scatter coming from?

• Control important variables or be prepared to solve a puzzle!

Random and Deterministic Variables• A variable’s value may be exactly predicted due to some

information we possess about the phenomena causing the variation.

• Such variables are called deterministic.• If I know the force applied on a known mass, in the

absence of any friction I can exactly determine it’s acceleration.

• However, if there is some friction I cannot measure or predict, I cannot determine exactly its acceleration.

• The error of my prediction will be a random variable.• Random variable’s next value does not depend on its

previous value.• Dependent variable’s value depends on its history.

Noise and Bias/Interference• Noise is a random variation of the value of the measured signal as a

consequence of the variation of the extraneous variables. • Noise increases data scatter. Noise is random, it’s not a trend.• Bias or interference is a deterministic trend on the measured value. • Any uncontrolled influence that causes the signal or test outcome to behave

in a manner different from its true behavior is a bias or interference.• Noise is easier to take care of using filters.• Bias removal needs more attention.• Noise is a short term effect, biases are longer term.

Noise and Bias Examples

Getting Rid of Bias• We can easily sift through the noise to get the desirable signal using

statistics. • But interference imposes a false trend on the signal. • The measurement plan should be devised to break up such trends so that

they appear as random variations in the data set. • In other words, we want to randomize a deterministic phenomenon.• Although this will increase the scatter in the measured values of• a data set, noise can be handled by statistics. It is far more important to

eliminate false trends in the• data set.

Randomization• A random test is a measurement matrix in which the independent variable is randomly varied..• Recall our car fuel-usage example in which the question is: ‘‘What fuel usage should I expect from

this car?’’

• Let y be the fuel use, which depends on xa, fuel volume consumption, and xb, distance traveled.• We determine y by varying these two variables (i.e. , we drive the car) randomly in our test

matrix. • But the test result can be affected by discrete extraneous variables such as the traffic, weather,

and road conditions. Driver and route are controlled variables.• The effect of the random order on the results of the test is termed randomization..

• Let the dependent variable y be a function of independent variables, xa, xb, . . . . extraneous variables, zj, where j =1, 2, . . .

• Although the influence of the zj variables on these tests cannot be eliminated, the possibility of their introducing a false trend on y can be minimized by a proper test strategy (randomization).

Replication and Repetition -2 strategies of Randomization• Repeated measurements made during any single test run or on a single batch are

called repetitions. • An independent duplication of a set of measurements using similar operating

conditions is referred to as a replication.• Repetition quantifies variation during any one test or batch while the operating

conditions are held under nominal control. • Repetition don’t tell how precisely operating conditions can be set.• Replication quantifies variation between different tests or batches, each having

the same nominal values of operating conditions.• In our fuel economy examples, using different drivers and routes is replication.

Driving the same route again and again by the same driver is repetition. Which one is better?

Example 1.5• Consider a room A/C thermostat. • Set to some temperature, we can make repeated measurements (repetition)

of room temperature and come to a conclusion about the average value and the variation in room temperature at that particular thermostat setting.

• Repetition permits an assessment of how well we can maintain (control) the operating condition.

• If we change the thermostat to another level and then return it to the original setting and duplicate the measurements. The two sets of test data are replications of each other.

• If average temperature in the second test differs from the first, it shows how well we could set and control the temperature.

• Replication permits the assessment of how well we can duplicate a set of conditions.

Example 1.1

• In the pressure calibration system shown, a sensor–transducer is exposed to a known pressure, p.

• The transducer, powered by an external supply, converts the sensed signal into a voltage that is measured by a voltmeter.

• The measurement approach is to control the applied pressure by the measured displacement of a piston that is used to compress a gas contained within the piston-cylinder chamber.

• Identify the independent and dependent variables in the calibration and possible extraneous variables.

Solution to Problem 1.1• Piston displacement x sets the volume in chamber • From the ideal gas law, • For constant cross section, • Therefore, displacement x and excitation voltage Vin is independent• Pressure p, temperature T and voltmeter reading Vout is dependent.• T and Vin are controlled.• Fluctuations z1 in T, fluctuations z2 in Vin and electromagnetic interference z3

in Vout are extraneous.• Therefore,

Concomitant Methods• A strategy to find if the instrument is working or to get a ball park

estimate of the expect result, we use alternate methods.• Goal is to obtain two or more estimates for the result, each based on

a different method, which can be compared as a check. • May affect the experimental design as additional variables may need

to be measured or controlled.• Discuss concomitant methods in the problem of finding volume of a

cylinder.

Example 1.2• Develop a test matrix that will minimize the interference effects of any

extraneous variables in Example 1.1• Solution

• Our test strategy is to vary x, control T, and measure p.• This strategy should minimize the false trends in the data set by the extraneous

variables. • Since z1, z2, and z3 are continuous extraneous variables, their influence on p can

be randomized by a random test.• This means we should shuffle x in the experiments.• Say we pick 5 tests, then we need to shuffle x1, x2, x3, x4, x5 such that they are

randomly chosen from a probability distribution (normal or uniform?)

Example 1.3 and 1.4• The manufacture of a glass reinforces plastic (GRP) requires mixing a a

binder with resin to produce a gel for strengthening glass fibers. • After lay-up, the material is cured at elevated temperature T.• Strength σ of the composite depends on the percent binder in the gel. • However, strength may also be “lay-up” operator as well as curing

temperature dependent• Formulate a test matrix by which the strength to binder–gel ratio

under production conditions can be established.

Solution to Example 1.3 and 1.4• The dependent variable σ is to be tested against the independent variable:

binder–gel ratio. Curing temp. is a controlled variable.• The operator is an extraneous variable in actual production, but during tests,

s/he is a controlled variable.• Let’s test relation b/w 3 binder–gel ratios, x1, x2 and x3 and measure σ • Choose 3 typical operators (v good, good, avg): z1, z2 and z3

• Also choose three different curing temperatures T1, T2 and T3

Test Matrix Z1 Z2 Z3

X1 T1 T1 T1

X2 T2 T2 T2

X3 T3 T3 T3

Calibrated Measurements• Calibration is the process of finding a relationship between a known and an

unknown quantity.• The known quantity is measured with one accurate instrument called the

“standard” or “calibrator”.• The unknown quantity is the measurement made using the instrument to be

calibrated called the “test instrument”.• Calibration “teaches” the instrument to produce results that are more accurate

than those that would occur if it is uncalibrated. • The instrument can then provide more accurate results when samples of

unknown values are tested in the normal usage of the product.• Calibration is used to remove bias or interference.

Gas pump with rotary flow indicator (yellow) and nozzle (red)

calibration procedure on a temperature test gauge

Basic Steps of Static Calibration• The term ‘‘static’’ implies that the values of the variables involved

remain constant; i.e., they do not vary with time or space. • In static calibrations, only the magnitudes of the known input and the

measured output are important.• Selection of reference standards with known values to cover the range

of interest.• Measurements on the reference standards with test• Finding relationship between the measured and standard values. This is

usually a least-squares regression fit to the data called a calibration curve.

• Correction of all measurements by the inverse of the calibration curve.• If a thermometer always reads 25o higher, this error can not be

eliminated by taking averages, because this error is constant (bias). • Easiest way to determine if it is accurate and fix it is to send the

thermometer to a calibration laboratory. Representativestatic calibration curve.

Static Sensitivity or Static Gain

• The slope of a static calibration curve provides the static sensitivity of the measurement system. As

• The gain, K, at any particular static input value x1, is evaluated as

• The more the instrument’s gain, the more ‘sensitive’ it is for a small change in measured variable, it gives a large output.

Dynamic Calibration• When the variables of interest are time (or space) dependent, we

need dynamic information (i.e. space/time behavior). • Dynamic variables are time (or space) dependent in both their

magnitude and frequency. • Dynamic calibration determines the relationship between an input of

known dynamic behavior and the measurement system’s output.• This known input signal is often either a sinusoid or a step signal.• Think of an impulse test on metal. Is this static or dynamic behavior?

When do instruments need to be calibrated?

• Before major critical measurements• Before measurements that requires highly accurate data, send the instruments for calibration and do not use before the test.

• After major critical measurements• Sending instrument for calibration after the test helps user decide whether the data obtained were reliable or not. Also, when using

an instrument for a long time, the instrument's conditions will change.

• After an event• The event here refers to any event that happens to the instrument. For example, when something hits the instrument or any kinds

of accidents that might impact the instrument's accuracy. A safety check is also recommended.

• When observations appear questionable• When you suspect the data's accuracy that is due to instrumental errors, send the instrument to calibrate.

• Per requirements• Some experiments require calibration certificates. Check the requirements first before starting the experiment.

• Indicated by manufacturer• Every instrument will need to be calibrated periodically to make sure it can function properly and safely. Manufacturers will indicate

how often the instrument will need to be calibrated.

 pH electrode used in titration experiments must be calibrated before the beginning of data collection. 

Scale Range• A calibration applies known inputs ranging from the minimum to the maximum

values for which the instrument is to be used. • These limits define the operating or scale range of the instrument. • The input operating range is defined as

• This is equivalent to specifying the output operating range of the instrument. The full-scale operating range (FSO) is expressed as

• It is important to avoid extrapolation beyond the range of known calibration during measurement

• The range of calibration should be carefully selected.

Resolution, Dynamic Range and Turndown Ratio• The resolution represents the smallest increment in the measured value that can

be discerned. • For a measuring instrument, it the smallest scale increment or least count (least

significant digit) of the output readout indicator.• The ratio of the range to the number of intervals the range can be divided in, is

called ‘dynamic range’ or least count.

• Turndown ratio is the ratio of maximum to minimum measurement possible by the instrument

• A ‘good’ instrument will have small LC and high TR. Why?

Bias in Measurements

An example of a device whose calibration is off: a weighing scale that reads ½ ounce without any load.