MECHANICAL ENGINEERING SYSTEMS LABORATORY

Transcription

1 MECHANICAL ENGINEERING SYSTEMS LABORATORY Group 02 Asst. Prof. Dr. E. İlhan KONUKSEVEN

2 FUNDAMENTAL CONCEPTS IN MEASUREMENT AND EXPERIMENTATION

3 MEASUREMENT ERRORS AND UNCERTAINTY

4 THE ERROR IN A MEASUREMENT IS THE DIFFERENCE BETWEEN THE MEASURED VALUE AND THE TRUE VALUE OF THE MEASURAND

5 The error in a measurement is not known since the true value of the measurand is not normally known. But, estimates ofthenatureandthe magnitude of the error can be given. SINCE THE TRUE VALUE IS UNKNOWN THE DIFFERENCE BETWEEN THE TRUE VALUE AND MEASURED VALUE CAN ONLY BE ESTIMATED

6 THE ESTIMATION OF THE DIFFERENCE BETWEEN THE TRUE VALUE AND THE MEASURED VALUE IS CALLED UNCERTAINTY Measurement Error and Uncertainty Measurement Uncertainty Error Measured Value True Value

7 TYPES OF ERRORS 1. GROSS ERRORS 2. SYSTEMATIC (FIXED) ERRORS (BIAS) 3. RANDOM ERRORS

8 1. GROSS ERRORS LARGELY HUMAN ERRORS DUE TO MISREADING INSTRUMENTS INCORRECT ADJUSTMENT or IMPROPER USE OF INSTRUMENTS COMPUTATIONAL MISTAKES This type of errors can be minimized by proper training and experience of the personnel involved in measurement processes.

9 2. SYSTEMATIC (FIXED) ERRORS (BIAS) THESE ERRORS ARE DUE TO INSTRUMENTS OR THEIR ENVIRONMENTS

10 TYPICAL INSTRUMENT CHARACTERISTICS WHICH LEAD TO SYSTEMATIC ERRORS ARE : FRICTION IRREGULAR SPRING TENSION IMPROPER CALIBRATION

11 TYPICAL ENVIRONMENTAL BASED SYSTEMATIC ERRORS ARE : EFFECT OF CHANGES IN SURROUNDING TEMPERATURE HUMIDITY BAROMETRIC PRESSURE MAGNETIC OR ELECTRICAL FIELDS

12 ENVIRONMENTAL BASED SYSTEMATIC ERRORS CAN BE MINIMISED BY PROPER CONDITIONING OF THE ENVIRONMENT ISOLATING OR SHIELDING

13 IN GENERAL SYSTEMATIC ERRORS CAN BE OVERCOME BY APPLYING CORRECTION FACTORS AFTER DETERMINING THE AMOUNT OF ERROR OR BY CALIBRATING THE INSTRUMENTS

14 EXAMPLE : A THERMOMETER IS CALIBRATED AND THUS MARKED AT THE FACTORY. THIS CALIBRATION MAY BE DONE BY EITHER FULLY OR PARTIALLY IMMERSING THE THERMOMETER INTO THE CALIBRATION ENVIRONMENT. IF A FULL IMMERSION THERMOMETER (ROOM THERMOMETER) IS PARTIALLY IMMERSED IN A FLUID THEN A STEM CORRECTION WILL BE NECESSARY

15 3. RANDOM ERRORS THESE ERRORS ARE MOSTLY DUE TO UNKNOWN AND RANDOMLY OCCURRING CAUSES THEY ARE DIFFICULT TO DETERMINE AND PREDICT THEY ARE DEALT WITH BY STATISTICAL METHODS The only way to offset them is to increase the size of the data and to use statistical techniques so that the best estimate of the true value of the measured is obtained.

16 CALIBRATION BY CALIBRATION THE STATIC RESPONSE OF AN INSTRUMENT IS DETERMINED DURING CALIBRATION ALL INPUTS TO THE MEASUREMENT SYSTEM ARE KEPT CONSTANT EXCEPT THE MEASURAND WHICH IS VARIED IN A CONTROLLED MANNER

17 CALIBRATION A CALIBRATION STANDARD SHOULD, IF POSSIBLE, BE ABOUT 10 TIMES MORE ACCURATE THAN THE INSTRUMENT BEING CALIBRATED

18 ACCURACY DEGREE OF CLOSENESS OF MEASUREMENTS TO THE TRUE VALUE OF THE MEASURAND ACCURACY IS DETERMINED BY COMPARISON WITH CALIBRATED VALUES

19 ACCURACY THE ACCURACY OF AN INSTRUMENT IS EXPRESSED AS : * ABSOLUTE ACCURACY * RELATIVE ACCURACY RELATIVE ACCURACY IS DEFINED WITH RESPECT TO * ACTUAL READING * FULL SCALE READING OF THE INSTRUMENT

20 PRECISION (REPEATABILITY) THIS IS THE DEGREE OF AGREEMENT BETWEEN REPEATED MEASUREMENTS A precise data implies a small degree of dispersion (scattering) which may or may not be close to the true value of the measurand.

21 ACCURACY AND PRECISION Instrument Readings True Value Accurate & precise Inaccurate but precise Imprecise but accurate Inaccurate & imprecise

22 RESOLUTION IS A MEASURE OF THE SMALLEST CHANGE IN THE INPUT SIGNAL THAT THE MEASUREMENT SYSTEM CAN DETECT

23 RESOLUTION MEASURAND AS MEASURED BY MORE ACCURATE INSTRUMENT (True Value) MEASURAND AS MEASURED BY LESS ACCURATE INSTRUMENT (Measurement) Resolution ? 16 bit Digital A/D 2 16 =65536 Range = 0-10 Volt Res= 1 bit Volt Res= Volt

24 THRESHOLD STARTING FROM ZERO INPUT, IF A SIGNAL IS SLOWLY INCREASED, THERE WILL BE SOME MINIMUM SIGNAL LEVEL BELOW WHICH NO OUTPUT CHANGE CAN BE DETECTED

25 HYSTERESIS If an instrument provides different readings for the same measurand values depending on whether measurand is increased or decreased, then the I/O characteristic of this instrument is said to have an hysteresis. Measurement Output Measurand

26 SPAN THIS IS NORMALLY ACCEPTED AS THE INPUT SIGNAL RANGE THAT THE MEASUREMENT SYSTEM WILL MEASURE EXAMPLE THERMOMETERS USED BY DOCTORS HAVE A SPAN OF 7 C RANGING FROM 35 C TO 42 C

27 DYNAMIC RANGE THIS IS THE SPAN OF AN INSTRUMENT EXPRESSED IN TERMS OF RATIO OF THE HIGHEST AND LOWEST VALUES OF THE MEASURAND

28 SENSITIVITY THE SENSITIVITY OF AN INSTRUMENT IS THE RATIO OF THE CHANGE PRODUCED IN THE INSTRUMENT OUTPUT TO THE CHANGE IN THE MEASURED VARIABLE q o SENSITIVITY q q O i q i

29 SENSITIVITY O Higher Sensitivity Lower Sensitivity O High Sensitivity Regions Low Sensitivity Region I I

30 ZERO DRIFT AND SENSITIVITY DRIFT DRIFT IS A VARIATION IN THE OUTPUT OF A MEASUREMENT DEVICE WHICH IS NOT CAUSED BY ANY CHANGES IN THE INPUT SIGNAL

31 ZERO DRIFT AND SENSITIVITY DRIFT A shift in calibration curve in vertical direction is called Zero Drift.

32 ZERO DRIFT AND SENSITIVITY DRIFT A shift in calibration curve to change the sensitivity is called Sensitivity Drift.

33 LINEARITY IF AN INSTRUMENT IS SUPPOSED TO BE LINEAR, THE LINEARITY GIVES THE INDICATION OF THE MAXIMUM DEVIATION OF ANY CALIBRATION POINTS USUALLY FROM A LEAST SQUARES BEST STRAIGHT LINE FIT THROUGH THE CALIBRATION DATA

34 LINEARITY An instrument is called LINEAR when its I/O relation (calibration curve) İs a straight line, indicating that the output is proportional to the input O Best straight line I

35 LINEARITY The most common method to find the best fitted straight line for a series of calibration data is the least squares. Linearity is desirable in most applications. It eliminates the need of referring to a calibration chart or a conversion data. However, the linearity does not imply a better accuracy, a higher precision, or greater sensitivity.

36 INDEPENDENT LINEARITY An indication on the max deviation of any calibration point from the best fitted line expressed as O ± x % of the full scale I

37 O PROPORTIONAL LINEARITY An indication on the max deviation of any calibration point from the best fitted line expressed as ± x % of the actual reading I