STATIC CHARACTERISTICSMECHANICAL MEASUREMENTS &

METROLOGY

By- Chirag Solanki Wasim Kazmi Mayur Veer Macklinbrett Veigas

STATIC CHARACTERISTICS The characteristics involved in measurement of quantities that are either

constant or slowly varying with time to define a set of criteria that gives meaningful description of quantity of measurement are called static characteristics.

Static Calibration

Static Sensitivity

Static Error

Linearity

Threshold

Resolution

Hysteresis

Drift

Span & Range

STATIC CALIBRATION The static calibration refers to a situation wherein all inputs whether it is

desirable or non desirable , modifying or non modifying, interfering or non interfering are kept at constant values.

In general calibration is defined as process in which the measurand is compared with known standard.

Steps for calibration:

1. Identify all the possible inputs of the instrument.

2. Decide which of the inputs will be significant in your application.

3. Determine the apparatus and methods to control (vary or maintain constant) all significant inputs over the desired range.

4. By varying one input and holding the other inputs constant, develop the sensor input-output relations.

The characterization is related with input-output relationship. We cannot change characteristics but we can calibrate. e.g. Consider a junction of thermocouple is subjected to high temperature and one at a lower temp. The o/p of thermocouple is emf generated due to difference in temp of two junctions .By varying temperature difference we can obtain relation between temp. change i.e. i/p and emf generated i.e. o/p.

EXAMPLE: PRESSURE GAUGE/SENSOR

The objective in this example is to determine the relationship between the desired input (pressure) and the output (scale reading). The first step of the calibration process requires identifying the desired, interfering and modifying inputs of the pressure gauge.

In the second step you must determine how, or in what conditions, you are going to use the sensor. For example, what will be the surrounding temperature? If the temperature (which is an interfering input for this sensor) varies over a large range during the normal use of the sensor, maybe you will have to do the (desired-input/output) calibration for different value of the temperature.

Then you must ensure that, by choosing the appropriate experimental conditions, all the inputs of the pressure gauge, except the fluid pressure, are kept constant. The fluid pressure (true value) must be varied with another instrument, in increments, over some range, causing the measured value also to vary:

STATIC SENSITIVITYStatic sensitivity of instrument or measurement system is ratio of the

magnitude of output signal or response to the magnitude of input signal or quantity being measured.

Reciprocal of static sensitivity is called deflection factor or inverse sensitivity.

Deflection Factor = 1/ K

Load Cell

Force, F

Output, Vo

Output, Vo (V)

Input, Fi (kN)

Slope = 5 V/kN

Input,

F(kN)

K=5V/kN

Output,

Vo(V)

EXAMPLE OF SENSITIVITY The resistance value of a Platinum Resistance Thermometer changes when the temperature increases. Therefore, the unit of sensitivity for this equipment is Ohm/°C.

Most Sensitive

Variation of physical variables

Slope =output/input

Input(°C) Output(Ohm)

0 0

100 200

200 400

300 600

400 800

The output of a platinum resistance thermometer (RTD) is as follows:

Calculate the sensitivity of the equipment.Answer :

Draw an input versus output graph. From that graph, the sensitivity is the slope of the graph.

K = Δθο , graph = (400-200) ohm = 2 ohm/°C Δθi slope (200-100) °C

STATIC ERROR The most important characteristic of an instrument is its accuracy,

which is the agreement of the instrument reading with the true value of quantity being measured. The accuracy of an instrument is measured in terms of its errors.

Measurement always introduces errors.

Error may be expressed either as absolute or percentage of error :nXnY Absolute error,

e = nY

nX

where,

– expected value

– measured value

100nYnXnY% Error =

n

nn

Y

XYA

1

100A

n

nn

X

XX 1

nX

nX

Relative accuracy,

% Accuracy, a = 100% - % error

=

Precision, P =

- value of the nth measurement- average set of measurement

EXAMPLE

Given expected voltage value across a resistor is 80V. The measurement is 79V. Calculate,i. The absolute errorii. The % of erroriii.The relative accuracyiv.The % of accuracy

Given that , Expected value = 80V Measurement value = 79V

i. Absolute error, e = = 80V – 79V = 1V

ii. % error = = = 1.25%

iii. Relative accuracy, = 0.9875

iv. % accuracy, a = A x 100% = 0.9875 x 100%=98.75%

nXnY

100nYnXnY 100

80

7980

n

nn

Y

XYA

1

TYPES OF ERRORS Types of error in measurement:

1)Gross error/human error2)Systematic Error3)Random Error

1) Gross Error

- caused by human mistakes in reading/using instruments.

- cannot eliminate but can be minimized.

2) Systematic Error - due to shortcomings of the

instrument (such as defective or worn parts)

- 3 types of systematic error :-(i) Instrumental error(ii) Environmental error(iii) Observational error

3) Random error - due to unknown causes, occur when all systematic error has accounted - accumulation of small effect, require at high degree

of accuracy - can be avoided by- (a) increasing number of reading (b) use statistical means to obtain best approximation

of true value

Linearity :Basically, a mathematical equation is said to be linearif the following properties hold.

• homogeneity

• additivity

What does this mean? We first look at theproperty of homogeneity.

Linearity

Linearity : Homogeneity

Homogeneity requires that if the input (excitation)of a system (equation) is multiplied by a constant,then the output should be obtained by multiplyingby the same constant to obtain the correct solution.

Sometimes equations that we think are linear, turnout not be linear because they fail the homogeneityproperty. We next consider such an example.

Linearity

LinearityLinearity e.g. : Homogeneity (scaling).

Illustration: Does homogeneity hold for the following equation?

Given,

y = 4x Eq 1.1

If x = 1, y = 4. If we double x to x = 2 and substitutethis value into Eg 1.1 we get y = 8.

Now for homogeneity to hold, scaling should hold for y.that is, y has a value of 4 when x = 1. If we increase x by a factor of 2 when we should be able to multiplyy by the same factor and get the same answer and whenwe substitute into the right side of the equation for x = 2.

LinearityLinearity : Additivity Property

The additivity property is equivalent to thestatement that the response of a system to a sum of inputs is the same as the responsesof the system when each input is applied separately and the individual responses summed (added together).

This can be explained by considering the following illustrations.

LinearityLinearity : Additivity Property

Illustration: Given, y = 4x.

Let x = x1, then y1 = 4x1

Let x = x2, then y2 = 4x2

Then y = y1 + y2 = 4x1 + 4x2 Eq 1.3

Also, we note, y = f(x1 + x2) = 4(x1 + x2) = 4x1 + 4x2 Eq 1.4

Since Equations (1.3) and (1.4) are identical, the additivity property holds.

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ThresholdIf the instrument input is very gradually increased from zero there will be a minimum value required to give a detectable output change. This minimum value defines the threshold of the instrument.

input

Output

RESOLUTION

Ability to discriminate between nearly equal values.

Difference between two input values corresponding to smallest changes in output.

Smallest measurable input changes.

HYSTERESIS

Phenomenon depicts different output effects when loading and

unloading.

Input output graph do not coincide.

Causes a difference in the output curve.

Causes – Internal friction , Free play , Looseness of mechanical

joint , Backlash, Mechanical strain , etc.

The region between the limits within which an instrument is designed to operate for measuring is called as range of instrument.

RANGE

Has a positive value e.g..:The range of span of an instrument which has a reading range of –100°C to 100 °C is 200 °C.

The range of variable that an instrument is designed to measure is sometimes called scale of instrument.

If X max and X min are the highest and lowest limit of calibration then X max - X min is called as the span of the instrument.

In the case of a thermometer, its scale goes from −40°C to 100°C. Thus its span is 140°C

SPAN

If the instrument input is very gradually increased from zero there will be some minimum value below which no output change can be observed or detected .

This minimum value defines threshold of the instrument.

THRESHOLD

The smallest change in input reading that can be traced accurately.

Given in the form ‘% of full scale (% fs)’.

Available in digital instrumentation.

RESOLUTION

When the process of measurement takes place there are some changes taking place in the environment such as changes in the temperature ,pressure etc .

Such environmental changes affect the output of an instrument and this is termed as drift.

DRIFT

Drift is classified mainly into 3 types:1. Zero drift 2. Sensitivity drift

3. Zonal drift

TYPES OF DRIFT