Lecture1 Mech SU

8/12/2019 Lecture1 Mech SU

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Mechanical Measurements

Dr. Eng. Adel Abdulrahman

Mechanical Engineering Department

Sanaa University


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Grade Distribution: Homework and attendance = 10%

Quizzes (Every Sunday in class) = 10%

Reports = 10% Midterm Exam = 10%

Final Exam = 60%

Total 100%


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Basic Concepts

Measurement: generally refers to the processof estimating or determining the ratio of amagnitude of a quantitative property or

relation to a unit of the same type ofquantitative property or relation.

Metrology: is the study of measurement. Ingeneral, a metric is a scale of measurementdefined in terms of a standard: i.e. in terms ofwell-defined unit.


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Why measurements?

A structural engineer might need to measure the strainresponse to loads on a structure such as a bridge or a

building to determine safety limits. A mechanical engineer may require measurements of the

pressure around an aircraft wing to determine its lift andlikelihood of stall.

A bioengineer might measure the blood pressure, the flowvelocity, and any pressure fluctuations in a blood vessel todetect obstructions and forestall failure.

A chemical engineer might measure the temperature,pressure, and chemical species concentration in a reactionvessel in a chemical plant to optimize product yield.

A systems engineer might measure amplitude andfrequency of a feed back signal in a controller to preventinstabilities.


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Purposes of Measurement:

Engineering experimentation - This is where we

new information, and is generally done whendeveloping a new product. Some examplequestions which may be asked by the engineerare: How hot does it get? How fast does it go?

Operational systems - This is where we monitorand control processes, generally on existingequipment rather than in the design of new

products. For example, consider the heatingand/or air conditioning control system in a room.The system measures the temperature, and thencontrols the heating or cooling equipment.


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Why Measure?

Generate Data for Design

Generate Data to Validate or Propose a Theory

For Commerce

Engineers design physical systems in the form of

machines to serve some specified functions. Thebehavior of the parts of the machine during theoperation of the machine needs to be examined oranalyzed or designed such that it functions reliably.

Such an activity needs data regarding the machineparts in terms of material properties. These areobtained by performing measurements in thelaboratory.


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The scientific method consists in the study of

nature to understand the way it works.

Science proposes hypotheses or theories

based on observations and need to be

validated with carefully performed

experiments that use many measurements.When once a theory has been established it

may be used to make predictions which may

themselves be confirmed by furtherexperiments.


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Experimental Test Plan

Effective measurements need a test plan:

(a) Parameter Design Plan:

What question am I trying to answer? What needs to be measured? What

variable and parameters will affect the results?

(b) System and Tolerance Design Plan:

How can I make the measurement? How gooddo the results need to

be?

(c) Data Reduction Plan:

How will I interpret the resulting data? How will I use this data to answer

my question? How goodis the answer? Does the answer make sense?


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Measurement Categories

1. Primary quantity:

It is possible that a single quantity that is

directly measurable is of interest. An example

is the measurement of the diameter of a

cylindrical specimen. It is directly measured

using an instrument such as vernier calipers.

We shall refer to such a quantity as a primaryquantity.


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Measurement Categories (cont)

2. Derived quantity:

There are occasions when a quantity of interest is notdirectly measurable by a single measurement process.The quantity of interest needs to be estimated by usingan appropriate relation involving several measuredprimary quantities. The measured quantity is thus aderived quantity. An example of a derived quantity isthe determination of acceleration due to gravity (g) by

finding the period (T) of a simple pendulum of length(L). T and L are the measured primary quantities whileg is the derived quantity.


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3. Probe or intrusive method:

Most of the time, the measurement of a

physical quantity uses a probe that is placed

inside the system. Since a probe invariably

affects the measured quantity the

measurement process is referred to as an

intrusive type of measurement.


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4. Non-intrusive method:

When the measurement process does not involveinsertion of a probe into the system the method isreferred to as being non-intrusive. Methods that use

some naturally occurring process like radiation emittedby a body is used to measure a desired quantityrelating to the system the method may be consideredas non-intrusive. The measurement process may beassumed to be non-intrusive when the probe has

negligibly small interaction with the system. A typicalexample for such a process is the use of laser Dopplervelocimeter (LDV) to measure the velocity of a flowingfluid.


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Direct Measurement: holding a measurand up to a calibratedstandard and comparing two ex meter stick

Indirect Measurement:Measuring something other than actualmeasurement this is typically done when direct measurement isdifficult to obtain or is danger ex blood pressure

Example blood pressure can be obtained using a catheter with pressuretransducer or can be obtained using Korotkoff Sounds

Neural activity of brain, direct measurement would be implanting ofelectrodes or use of indirect measurement of fMRI

Null Measurement:Compared calibrated source to an unknown

measurand and adjust till one or other until difference is zero Electrical Potentiometer used in Wheatstone Bridge


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Measurement system

It takes an input quantity and transforms it to anoutput quantity for observation or recording.

It includes all the components necessary for

producing a measurement.


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General components of measurement system:- sensor-transducer stageinput information

signal-conditioning stage

output stageoutput information

feedback-control stage

----------------------------------------------------------------------------

sensor - is a physical element that uses some natural

phenomenon to sense the variable being measured Transducer - converts this sensed information into a detectable

signal form, which might be electrical, mechanical, optical orotherwise.

Signal conditioning - modifies the transducer signal into a desired

form e.g. amplification, noise reduction. Output Stage - provides an indication of the value of the

measurement (readout device or recording)


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Example

The thermocouple produces a voltage which is proportional to a temperature difference.

The A/D converter converts this voltage to a digital value which is fed to the computer.

The program converts this voltage to the equivalent temperature. The value may be

plotted on the screen, or printed out, or stored.


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Example

The Bourdon Tube The bulb thermometer


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Some Definitions

Variable - a physical quantity that can change.Independent Variable - a variable you can change

without affecting other independent variables.

Dependent Variable - variable which changes when one

or more independent variable changes.Parameter - a combination of variables, usually

dimensionless - a dimensionless group.

Control of Variables- Variables that can be held

(controlled) at a constant value. This is used to find therelationship between independent and dependentvariables.


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Some Definitions (cont.)

Extraneous Variable - a variable which is not controlled

during a measurement. Ambient temperature is

frequently an extraneous variable.


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Noise - a random variation in the value of the measured

signal to a variations in extraneous variables.

Some Definitions (cont.)

Interference - a deterministic variation of the measured

signal to extraneous variables. 60 Hz signals from power

sources frequently cause interference.


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Minimizing the Effect of Extraneous

Variables

Hold all other independent variables

constant

Vary the independent variable in a random

order.

Replicate the test several times

Where possible, check result using a different

method


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Random Tests

Random Test:

A measurement matrix (set of tests) that imposes a random

order on the changes of the value of the independent

variable. Trends that may be introduced by the coupling of

a relatively slow and uncontrolled variation of an

extraneous variable with a sequential application of the

independent variable will be broken up.

Things to Randomize:

Instruments used, test operators, testing conditions,

samples, etc.


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Calibration

In order to determine the characteristics of the instrument, and toestimate its accuracy it is necessary to perform a calibration. Thisconsists of applying known values of the independent variable andobserving the output.

Types of calibration:

Static - steady state. A calibration procedure in which the values ofthe variable involved remain constant (do not change with time).

Dynamic - during changing input. When the variables of interest aretime dependent and time-based information is need. The dynamiccalibration determines the relationship between an input of knowndynamic behavior and the measurement system output.

The calibration should be performed as nearly as possible to theactual measurement conditions, and should follow the proceduresfor minimizing the effect of extraneous variables.


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Instrument characteristicsStatic Sensitivity - or static gain - The slope of the calibration curve.

Incremental ratio of the output signal to the desired input signal.

Range - maximum and minimum values to be used

Measurand range, operating range, full-scale range, span: the range of input variable (xmax

xmin) that produces a meaningful output.

Full scale output (FSO): Difference between the end points of the output. The upper limit of

output over the measurand range is called the full scale (FS).

Offset: The output of a transducer, under room temperature condition unless otherwise

specified, with zero measurand applied.


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Instrument characteristics (cont.)Linearity - is the output a linear function of input? Linearity is

desirable because it provides a constant static sensitivity overthe entire range and also because calculations are much

simpler.

Accuracy - the difference between the true (expected) and

measured values from the measurement system or sensor.Normally, it is quoted in as a fractional of the full scale output.

True Value - exact value of a variable (never known)

Measured Value - value of variable as indicated by measurement

system.


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Precision - The ability of the system to indicate a particular valueupon repeated but independent applications of a specific value

of input. The precision error is a measure of the random variation

found during repeated measurements.

Instrument characteristics (cont.)


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Resolution - the smallest increment in the value of the measurand

that results in a detectable increment in the output. It is

expressed in the percentage of the measurand range.


If the input is increased from zero, there will be some minimum value below which no

output change can be detected, This minimum value defines the Thresholdof theinstrument.

Repeatability - the ability of a measurement system to indicatethe same value on repeated measurements for a specific input

value.


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Error (e) - difference between the measured value and the truevalue of a variable.

e = measured value true value

There are two general categories of error: systematic (or bias) errors andrandom (or precision) errors.

Systematic errors (also called bias errors) are consistent, repeatable errors. Forexample, suppose the first two millimeters of a ruler are broken off, and the user is not

aware of it. Everything he or she measures will be too short by two millimeters a

systematic error.

Random errors (also called precision errors) are caused by a lack ofrepeatability in the output of the measuring system. The most common sign of random

errors is scatter in the measured data. For example, background electrical noise often

results in small random errors in the measured output.


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Bias Errors - consistent

inaccuracies in output for the

same input

0

5

10

15

20

25

0 100 200 300 400 500

Temperature,oC

Output,mV

Standard Reference

Individual Thermocouple Data

Poly. (Individual Thermocouple Data)

Bias

Error


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Systematic (or Bias) Errors

Systematic errors are consistent, repeatable errors in a set of measurements

The systematic error is defined as the average of measured values minus the true

value.

Systematic errors arise for many reasons. Here are just a few:

o calibration errors perhaps due to nonlinearity or errors in the calibration method.

o loading or intrusion errors the sensor may actually change the very thing it is trying to measure.

o spatial errors these arise when a quantity varies in space, but a measurement is taken only at one

location (e.g. temperature in a room - usually the top of a room is warmer than the bottom).

o human errors these can arise if a person consistently reads a scale on the low side, for example.

o defective equipment errors these arise if the instrument consistently reads too high or too low due to

some internal problem or damage (such as our defective ruler example above).

A nondimensional form of bias error is the mean bias error, defined as MBE =

systematic error / true value.


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Random (or Precision) Errors

Random errors are unrepeatable, inconsistent errors in the measurements, resulting in

scatter in the data.

The random error of one data point is defined as the reading minus the average ofreadings.

Example:

Given: Five temperature readings are taken of some snow: -1.30, -1.50, -1.20, -1.60, and -

1.50

o

C. To do: Find the maximum magnitude of random error in

o

CSolution:

The mean (average) of the five temperature readings is -1.42oC. The largest deviation

from this is the reading of -1.20oC. The random (or precision) error for this data point is

defined as the reading minus the average of readings, or -1.20 - (-1.42) = 0.22oC.


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Other Errorsozero error: The instrument does not read zero when the input is zero. Zero error is a type of bias error that offsets

all measurements taken by the instrument, but can usually be corrected by some kind of zero offset adjustment.

Zero balance is a term used by manufacturers to indicate the maximum expected zero error of their instrument.

o linearity error: The output deviates from the calibrated linear relationship between the input and the output (seefurther discussion in the next section on calibration). Linearity error is a type of bias error, but unlike zero error, the

degree of error varies with the magnitude of the reading.

o sensitivity error: The slope of the output vs. input curve is not calibrated exactly in the first place. Since this

affects all readings by the instrument, this is a type of systematic or bias error.

o resolution error: The output precision is limited to discrete steps (e.g., if one reads to the nearest millimeter on aruler, the resolution error is around +/- 1 mm). Resolution error is a type of random or precision error.

o hysteresis error: The output is different, depending on whether the input is increasing or decreasing at the time of

measurement. [This is a separate error from instrument repeatability error.] For example, a motor-driven traverse

may fall short of its reading due to friction, and the effect would be of opposite sign when the traverse arrives at

the same point from the opposite direction; thus, hysteresis error is a systematic error, not a random error.

o instrument repeatability error: The instrument gives a different output, when the input returns to the same value,and the procedure to get to that value is the same. The reasons for the differences are usually random, so

instrument repeatability error is a type of random error.

o drift error: The output changes (drifts) from its correct value, even though the input remains constant. Drift error

can often be seen in the zero reading, which may fluctuate randomly due to electrical noise and other random

causes, or it can drift higher or lower (zero drift) due to nonrandom causes, such as a slow increase in air

temperature in the room. Thus, drift error can be either random or systematic.


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Tactics to Decrease Error on Practical

Measurements:

1. Make Measurements several Times

2. Make Measurements on Several Instruments

3. Make successive Measurements on different

parts of instruments (different parts of ruler)


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Standards

Primary Standards - define the size of a unit

Interlaboratory Transfer Standards -maintained by national laboratories such as

the US National Institute for Science andTechnology

Local Standards - maintained by companiesand individual laboratories

Working Instruments - our laboratorythermometers


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Dimensions and Units

Primary (or Basic) Dimensions: Dimension

defines a physical variable used to describe

some physical quantity. There are seven

primary dimensions (also called basicdimensions). All other dimensions can be

formed by combinations of these. The primary

dimensions are: mass, length, time,temperature, current, amount of light, and

amount of matter.


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Unit Systems : Unit defines a quantitative measure ofa dimension, were invented so that numbers could be

assigned to the dimensions.

There are three primary unit systems in use today:

the International System of Units (SI units, from Le

Systeme International dUnites, more commonlysimply called the metric system of units)

the English Engineering System of Units (commonly

called English system of units)

the British Gravitational System of Units (BG)

P i di i S b l SI i t E li h i t BG i t


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Primary dimension Symbol SI uni t Engli sh uni t BG uni t

mass m kg (kilogram) lbm (pound-mass) slug

length L m (meter) ft (foot) ft (foot)

time t s (second) s (second) s (second)

thermodynamic temperature T K (kelvin) R (rankine) oR(oRankine

)

current I (or i) A (ampere) A (ampere) A (ampere)

amount of light (luminous

intensity)

C (or I) cd (candela) cd (candela) cd (candela)

amount of matter N mol (mole) mol (mole) mol (mole)

Secondary

dimension

Symbol SI uni t Engli sh uni t BG uni t

force F N (newton =

kgm/s2)

lbf (pound-

force)

lbf (pound-force)

acceleration a m/s2 ft/s2 ft/s2

pressure P (sometimes

p)

Pa (pascal = N/m2) lbf/in2 (psi) lbf/ft2 (psf)

energy E J (joule = Nm) ftlbf (foot-

pound)

ftlbf (foot-pound)

Power W (some

times P)

W(watt =J/s) ftlbf/s ftlbf/s


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Significant Digits (cont.)

Engineering measurements are generally

accurate to at most only a few digits. (Threedigits of accuracy is considered standard forengineering analysis.)

The number of significant digits is defined as thenumber of relevant or useful digits in ameasurement.

The best way to illustrate is to write the number

in standard exponential (scientific) notationinstead of common real number (engineering)notation, and then count the number of digits.

l


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Common

notation

Underlined

notationExponential notation

Number of

significant digitsComments

134.2 134.2 1.342 x 102 4 just count the number of digits

0.0056 0.0056 5.6 x 10-3 2 the leading zeroes are not significant

0.00506 0.00506 5.06 x 10-3 3the leading zeroes are not significant, but

any zeroes between two numbers are

significant

0.00560 0.00560 5.60 x 10-3 3the leading zeroes are not significant, but

the trailing zeroes are significant

400 400 4 x 102 infiniteinteger values have an infinite number of

significant digits

400. 400 4.00 x 102

3

a decimal point (or underline) indicates

that all digits to the left of the decimal

point are significant, and that this is notan integer value

400.0 400.0 4.000 x 102 4the zero to the right of the decimal point is

significant

40,300. 40,300 4.0300 x 104 5

a decimal point (or underline) indicates

that all digits to the left of the decimal

point are significant, and that this is not

an integer value

40,300 40,300 403 x 102 infinite

integer values have an infinite number of

significant digits; do not use a decimal

point when writing an integer in

exponential notation

400 (to 2

significant

digits)

400 4.0 x 102 2

words in parenthesis are necessary to

indicate a smaller number of significant

digits in common notation whenever

trailing zeroes are present

Here are some examples

Thi t littl t i k d bi h d li ith l b F


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Things get a little tricky and ambiguous when dealing with large numbers. For

example, suppose someone reports the population of a large city as

3,485,000, and says nothing about significant digits. Is it rounded to the

nearest thousand (3.485 106; 4 significant digits)? Is it rounded to the

nearest hundred (3.4850 106; 5 significant digits)? It is impossible to know.We suspect that it the population is not exactly 3,485,000 (7 significant

digits), although that is a remote possibility.

One way around this ambiguity is to underline the least significant digit. In

our population example, if the population were rounded to the nearest

thousand, we would write 3,485,000 since the first zero is not significant. Ifthe population were rounded to the nearest 100, we would write 3,485,000

since the first zero is significant, and so on.

When performing multiplication or division calculations, the answer has the

same number of significant digits as the component with the least number of

significant digits.


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Rounding Off There are standard rules for rounding off values to a desired number of

significant digits. First, the number is truncated to its desired length. Then, theexcess (leftover) digits are examined as if they were a decimal fraction:

If the decimal fraction is less than 0.5, truncate the excess digits.

If the decimal fraction is greater than 0.5, round up the least significant digit in

the number by one.

If the decimal fraction is equal to 0.5, the convention is to round up if the least

significant digit is odd, and to truncate (round down) if the least significant digit

is even. [Note: The number zero is even.]


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Presentation of Data

Graphs should be both concise and complete for ease of understanding

Its often easier to interpret data when they are presented as a line; only use

linear interpolation between single points, however,

Once the data has been linearized and plotted, a line may be fit byeye-

balling the data andMethod of least squares

Best fit means just thatall points will not be on the line

Goodness of fit is evaluated using the correlation coefficient: r2

closer to 1 implies better fit

Deviations from the line are often due to precision error

Packages such as Excel, MathCAD and MATLAB contain line-fitting

software

A i t f il bl d k d t i t i t t ( li


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A variety of axes are available, and may make data easier to interpret (e.g. linear versus

semi-logarithmic coordinates, full-log co-ordinate,or in the example shown below, drag is

plotted versus the square of velocity as opposed to just the velocity - this allows a linear

curve fit to be performed to the data

Lecture1 Mech SU

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