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ความรูพ้ืน้ฐานเกีย่วกบัการวดั
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AU 351 Sensor Technology in Automotive EngineeringFaculty of Engineer ingThammasat University
AU 351Sensors Technology
in Automotive Engineering
by
Asst. Prof.Dr. Channarong Asavatesanupap
Faculty of Engineer ingThammasat University
AU 351 Sensor Technology in Automotive Engineering
ความรูพ้ืน้ฐานเกีย่วกบัการวดั
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Chap 1 Fundamentals of Measurement
Measurementprocess
Reference
Physical Quantity
magnitude ofthe quantity
Measurement is the process of determining the magnitude of a physical quantity, such as length or mass, relative to a unit of measurement (Reference).
Faculty of Engineer ingThammasat University
AU 351 Sensor Technology in Automotive Engineering
คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
What important?
- Accuracy
- Margin of error
- Confidence level
Example
Physical quantityHeight (Length)
Measurementprocess
ReferenceMeasuring tape
magnitude ofthe quantity
= 1.60 m
AU 351 Sensor Technology in Automotive Engineering
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Measuring devices
คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
distance
MassTemperature
Pressure
Measuring deviceconverts this sensed information into a
detectable signal
PhysicalQuantity
Signalelectrical, mechanical,
optical, or otherwise
AU 351 Sensor Technology in Automotive Engineering
คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
Basic measuring devices
Sensor
Transducer
Output
Sensor
Transducer
Output on display scale
is a physical element that employs some natural phenomenon by which it senses the variable being measured.
converts the sensed information into detectable signal.
AU 351 Sensor Technology in Automotive Engineering
ความรูพ้ืน้ฐานเกีย่วกบัการวดั
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คณะวิศวกรรมศาสตร์
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Example: Thermometer
bulb
Thermometersensor
TemperatureThermal Expansion
of the liquid
Liquid contained within the bulb exchanges energy with its surrounding until they reach thermal equilibrium. As a result, the liquid moves up and down the stem due to the thermal expansion.
AU 351 Sensor Technology in Automotive Engineering
คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
Electronic measurement system
Transducer
Conditioningcircuits
Amplifier
Recorder
Dataprocessor
Controller
Powersupply
Commandgenerator
For engineering analysis- Graphs or Tables
Process control
AU 351 Sensor Technology in Automotive Engineering
ความรูพ้ืน้ฐานเกีย่วกบัการวดั
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คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
Transducer
Conditioningcircuits
Amplifier
Recorder
Dataprocessor
Controller
Powersupply
Commandgenerator
Transducer converts the physical change from the sensor into the signal.
T VThermocouple
Amplifier increases the power of the desired signal to the desired magnitude.
Conditioning circuit takes the transducer signal and modifies it to a desired signal.
Electronic measurement system
AU 351 Sensor Technology in Automotive Engineering
คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
Data processor is used with the measurement system that incorporate analog-to-digital converters (A/D) and provides the output signal representing the measurement in a digital code.
Recorder is a voltage-measuring device used to display the measurement.
Analog recorders
Digitalrecorders
Controller is used to monitor and adjust any quantity that must be maintained at a specified value to produce a material or product in a controlled process.
Transducer
Conditioningcircuits
Amplifier
Recorder
Dataprocessor
Controller
Powersupply
Commandgenerator
Electronic measurement system
AU 351 Sensor Technology in Automotive Engineering
ความรูพ้ืน้ฐานเกีย่วกบัการวดั
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คณะวิศวกรรมศาสตร์
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Transducer
TransducerMechanical energy
orThermal energy
Electrical energy
converts the physical change from the sensor into the detectable signal. In other words, transducer is a device that converts one form energy to another.
Resistance,Voltage,Current,
etc
Strain,Temperature,
Pressure,etc
Input, Qi Output, Qo
AU 351 Sensor Technology in Automotive Engineering
คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
Calibration
is a comparison between measurements – a known input value (standard) is applied to a measurement system for the purpose of observing the system output value. The relationship between the input and output values is then established.
1. Static calibration: a known value is input to the system under calibration and the system output is recorded. The input values remain constant, i.e. they do not vary with time or space.
Qo = f (Qi)
2. Dynamic calibration: when the inputs are time (or space) dependent.
AU 351 Sensor Technology in Automotive Engineering
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คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
***The calibration curve will have the form y=f(x) and can be used in later measurements to ascertain the unknown input value based on the output value.
AU 351 Sensor Technology in Automotive Engineering
คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
Calibration curve interpretation
Qo
Qi
Least-squaresfit to data
ZeroOffset , Z0
Deviationfrom linearity
Span
Allowable deviation
Slope = S = senstivity
Range
Many instruments are designed to achieve a linear relationship between the applied input and indicated output values as shown in the figure
AU 351 Sensor Technology in Automotive Engineering
ความรูพ้ืน้ฐานเกีย่วกบัการวดั
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คณะวิศวกรรมศาสตร์
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Characteristics of measurement system
2) Slope of a calibration curve provides the static sensitivity, S (calibration constant) of the measurement system.
S = Qi
QO
Qo,L = S Qi + Z0
1) Calibration curve represents the characteristics of the measurement system. It can be written in the form
Linear function
AU 351 Sensor Technology in Automotive Engineering
คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
Characteristics of measurement system
3) Range is the difference between the maximum and the minimum values.
Input operating range, ri = Qi, max – Qi, min
Output operating range, ro = Qo, max – Qo, minFull-Scale-Operating range (FSO)
AU 351 Sensor Technology in Automotive Engineering
ความรูพ้ืน้ฐานเกีย่วกบัการวดั
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คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
Characteristics of measurement system
4) Zero offset, Z0 is the deviation measured at the intercept with the ordinate.
eL(Qi) = Qo(Qi) – Qo,L(Qi)
Maximum error as a percentage of FSO range is calculated from
%eL,max = eL,max x 100 ro
5) Linearity error is the difference between the measured value and the value obtained from the calibration curve.
AU 351 Sensor Technology in Automotive Engineering
คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
Characteristics of measurement system
6) Resolution is the ability of the measurement system to detect and indicate small changes in the characteristic of the measurement result.
the smallest least significant digit the smallest scale increment
0.001 kg0.01 C
AU 351 Sensor Technology in Automotive Engineering
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คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
Characteristics of measurement system
7) Accuracy and Error
Accuracy of a measurement refers to the closeness of agreement between the measured value and the true value.
Error is defined as the difference between the measured value and the true value.
True value = the exact value of a variableMeasured value = The value of the variable indicated by a measurement system
Error, e = measured value – true value
Relative error, er = |measured value – true value| / true value x 100%
AU 351 Sensor Technology in Automotive Engineering
คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
True value Measured value
Accuracy and Precision
Accurate but not precise(random error)
Precise but not accurate(systematic error)
AU 351 Sensor Technology in Automotive Engineering
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คณะวิศวกรรมศาสตร์
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Accuracy and Precision (cont.)
Precision is sometimes stratified into:
Repeatability — the variation arising when all efforts are made to keep
conditions constant by using the same instrument and operator, and
repeating during a short time period.
Reproducibility — the variation arising using the same measurement
process among different instruments and operators, and over longer time
periods.
AU 351 Sensor Technology in Automotive Engineering
คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
Significant figures
In any measurement, the number of significant figures is critical and refers to the number of digits that carry meaning contributing to its precision. It is equal to the number of digits that are known with some degree of confidence plus the last digit which is an estimate.
For example, 2.402 has four significant digits;
the first three digits (2, 4, 0) are known for sure but
the last digit (2) is estimated.
AU 351 Sensor Technology in Automotive Engineering
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คณะวิศวกรรมศาสตร์
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Significant figures (cont.)
Rules for counting significant figures1) Leading zeros are not significant.
(e.g. 00042 => 2 significant digits)2) Zeros within a number are always significant.
(e.g. 00402 => 3 significant digits)3) Trailing zeros that aren’t needed to hold the decimal point are
significant. (e.g. 042.00 => 4 significant digits)4) Zeros that do nothing but set the decimal point are not
significant. (e.g. 42,000 => 2 significant digits)
AU 351 Sensor Technology in Automotive Engineering
คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
Significant figures (cont.)
A rule of thumb: reading the scale to 1/10 of the smallest division.
40
30
20
The smallest division is 1 unit, so we can read the scale to ± 1/10 of 1 unit or ± 0.1 unit. Therefore, the value we read from the scale is 31.6 ± 0.1 unit.
We have 3 significant digits of which the “3” and the “1” are known for sure and the “6” is estimated.
AU 351 Sensor Technology in Automotive Engineering
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คณะวิศวกรรมศาสตร์
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Significant figures (cont.)
Significant Digits in Addition and Subtraction
When quantities are being added or subtracted, the number of decimal places (not significant digits) in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted.
Example:5.67 J (two decimal places)1.1 J (one decimal place)0.9378 J (four decimal place)7.7078 J (one decimal place)
AU 351 Sensor Technology in Automotive Engineering
คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
Significant figures (cont.)
Significant Digits in Multiplication, Division, Trig. functions, etc.
In a calculation involving multiplication, division, trigonometric functions, etc., the number of significant digits in an answer should equal the least number of significant digits in any one of the numbers being multiplied, divided etc.
Example: In evaluating sin(kx), where k = 0.097 m-1 (two significant digits) and
x = 4.73 m (three significant digits), sin (kx) = 0.44288 (the answer should have two significant digits).
Note that whole numbers have essentially an unlimited number of significant digits. As an example, if a hair dryer uses 1.2 kW of power, then 2 identical hairdryers use 2.4 kW:1.2 kW {2 sig. dig.} ´ 2 {unlimited sig. dig.} = 2.4 kW {2 sig. dig.}
AU 351 Sensor Technology in Automotive Engineering
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คณะวิศวกรรมศาสตร์
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Instrument error
1. Hysteresis error
2. Linearity error
3. Sensitivity error
4. Zero-shift error
5. Repeatability error
Sensitivityerror
Actual
Expected
Linearity errorActual
Expected
Upscale
Downscale
Hysteresis
Occur in the ferromagnetic material or the deformation of some materials
AU 351 Sensor Technology in Automotive Engineering
คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
Instrument error
Zero-shifterror
Actual
Expected
Data scatter band
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22 ⋯ 2Overall error,
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คณะวิศวกรรมศาสตร์
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Dual sensitivity errors
is the error that occurs in the instrument due to the effect of other parameters
other than that of the primary parameter
Anticipated
Non-controlled environment
Actual
Zerodrift
Totalerror
Sensitivity change
Controlled environment
Anticipated response
AU 351 Sensor Technology in Automotive Engineering
คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
Example of dual sensitivity errors
If a transducer is employed to measure some quantity (say, pressure) in
the process, and if the temperature also changes as the measurement is
made, error will result in the dual sensitivity of the transducer.
Primary quantity(pressure)
Secondary quantity(Temperature)
Zero offset
Sensitivity error
Dual sensitivity
AU 351 Sensor Technology in Automotive Engineering
ความรูพ้ืน้ฐานเกีย่วกบัการวดั
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Example: Thermocouple calibration curves
Output
InputZero-offset
Sensitivity
Non-linearity
AU 351 Sensor Technology in Automotive Engineering
คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
When a measurement system is calibrated, its indicated value is compared directly with a reference value. This reference value forms the basis of the comparison and is known as the standard. This standard may be based on the output
(1) from a piece of equipment,
(2) from an object having a well-defined physical attribute to be
used as a comparison, or
(3) from a well-accepted technique know to produce reliable value.
Standards
Primary standard > Secondary standard > Working standard
AU 351 Sensor Technology in Automotive Engineering
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คณะวิศวกรรมศาสตร์
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Standards
1 meter
Platinum-Iridium meter bar
defined as the length of the path travelled by light in a vacuum in 1⁄299,792,458 of a second
1 kilogram
Platinum-Iridium weight
defined as being equal to the mass of the international prototype kilogram which is almost exactly equal to the mass of one liter of water at 4 C
AU 351 Sensor Technology in Automotive Engineering
คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
Dimensions and Units
A dimension defines a physical quantity that is used to describe some aspect of a physical system, e.g. mass, length, time, etc.
A unit defines a quantitative measure of a dimension
For example: If we want to measure a distance (length), then its dimension is the L which has a unit of meter (for SI system)
Physical quantity Dimension Unit
Distance, Length L meter
AU 351 Sensor Technology in Automotive Engineering
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คณะวิศวกรรมศาสตร์
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Base dimensions in the SI system
Physical quantity Dimension Unit Unit symbol
Length L meter m
Mass M kilogram kg
Time T second s
Temperature Kevin K
Current I ampere A
Amount of substance N mole mol
Luminous intensity J candela cd
AU 351 Sensor Technology in Automotive Engineering
คณะวิศวกรรมศาสตร์
มหาวิทยลยัธรรมศาสตร์
Dimension SI unit Imperial unit Conversion
L m ft 1ft = 0.3048 m1 in = 0.0254 m
M kg lbm 1lbm = 0.45359 kg
T s s -
K C
RF
R = 1.8 KF = 1.8 C +32
Unit systems
SI units Imperial units
AU 351 Sensor Technology in Automotive Engineering
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คณะวิศวกรรมศาสตร์
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Derived units
Other dimensions and their associated units are defined in terms of and derived from the base dimensions and units
L
m
T
s
divided by
equal
a
m/s2
divided by
equal
F
Kg. m/s2 = N
multiplied by
equal
V
m/s
T
s
M
kg
AU 351 Sensor Technology in Automotive Engineering
คณะวิศวกรรมศาสตร์
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Derive quantity Derive unit Symbol
Area Square meter m2
Volume Cubic meter m3
Speed Meter per second m/s
Pressure, Stress Pascal Pa
Work, energy, or heat Joule J
Force Newton N
Power Watt W
Voltage Volt V
Resistance Ohm
Derived units
AU 351 Sensor Technology in Automotive Engineering
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Question #1
For the temperature calibration data as shown in table below, plot the result and determine the static sensitivity of the transducer.
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Resistance (Ohm) Temperature (C)
307 200.2
314 230.1
321 259.8
328 289.5
335 320.2
342 350.1
349 379.5
Question #2
The temperature of the water in the boiling process needs to be monitored. It is known that the temperature should be in the range as shown in the figure. If there are three temperature transducers available, which transducer would you select for this purpose? Explain.
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AB
C
Output [mV]
Input [°C]
Range
ความรูพ้ืน้ฐานเกีย่วกบัการวดั
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Question #3
Determine the relative error that may occur if the actual sensitivity of an instrument is S1 but the anticipated (manufacturer) sensitivity is S2.
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