Electronic And Mechanical Engineering Laboratory Report Accounting Essay

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This calibration laboratory involves the calibration of a load cell and a spring balance using a 10kg mass, adjusted by 1kg per measurement recorded giving 11 distinct readings of 0kg to 10kg in 1kg steps. ANS/ISA recommend that this process should be repeated for a total of 5 up-down cycles to give a complete set of data which would consist of a total of 110 readings, however due to time constraints this lab will be restricted to 1 up-down cycles giving a total of 22 data points. The indicated values at atmospheric pressure increasing were recorded along with the indicated values decreasing and these values were entered into a regression equation using an excel spreadsheet. From this a graph was produced and a best fit curve fit to the measurements. We then set about determining the uncertainty limits associated with the recession curve fit, the results of this showed that the load cell had significantly less deviation from the true value over its entire range of values; 1 standard deviation for the spring balance equated to 0.1238 while with the load cell this was 0.00285. The load cell was also less susceptible to hysteresis with a full scale reading of 0.2% whereas the spring balance had a full scale reading of 6.1%, and also non line rarity with a full scale reading of 0.2% for the load cell and 4.2% for the spring balance.

Introduction

Calibration can be defined as a comparison between measurements, one of which has a known magnitude which has been set with a standard with a known or assigned correctness and another measurement made in as similar a way as possible with the unit under test (UUT) or test instrument (TI). For any measurement to be considered accurate the indicated output (O) of the measuring instrument must be as close as possible to the true value - which is also known as the measureand(I). This 'closeness' is quantified as a measurement error, as in the differential between the indicated value and the true value .To ensure the accuracy of equipment calibration is essential because the properties of components will inevitably drift away from their set values over time for many reasons such as stress on the component and environmental conditions, and the measurements made by these components become uncertain overtime. Calibration establishes the uncertainty specifications that are caused by systematic and random errors associated with an instrument to be determined along with the static characteristics of the instruments such as hysteresis and linearity.

Test Equipment

Load Cell: A load cell is a transducer which is used to convert a force into an electrical signal, it usually consists of 4 strain gauges in a Wheatstone bridge formation. This is an indirect conversion process, initially the force being sensed deforms the strain gauge and then this deformation is converted to an electrical signal which is usually a few millivolts and will need to amplified before it can be utilized.

Spring Balance: A spring balance is a weighing device that uses a usually linear relationship between a load applied and spring deformation. The spring balance works on the principle of Hooke's Law, this law states that the force needed to extend a spring is proportional to the distance that spring is extended from its rest position and for this reason the scale markings on the spring scale are equally spaced.

Method

This laboratory was carried out based on the ANS/ISA (1979) a standard procedure for static calibration. The influence of modifying (Im) and interfering (Ii) influences were ignored, so the calibration was carried out under standard environmental conditions ( 200C and 1 atmosphere)where Im=Ii=0.

The standard weights used were then applied incrementally from Imax to Imin in 10% increments giving 11 distinct readings on the up cycle, then the weights were removed incrementally on the down cycle providing a further 11 distinct readings. These readings were recorded from the spring balance scale in pounds, and also from the transducer output in millivolts.

For accuracy ANS/ISA recommend that this process should be repeated for another 4 up-down cycles to give a data set of 105 readings but for the purposes of this laboratory 22 data points were sufficient.

An excel spreadsheet was then used to fit a regression line to the data gathered. From here the true value, the systematic error and the random error for the load cell were specified .

The associated European Norm standards were then used to determine if both instruments lie within the specified linearity and hysteresis characteristics.

Results

Data recorded:

Regression Analysis:

Using a regression analysis the calibration data is fitted to a regression equation,

O = KI + a

Where O = Output or indicated value (Dependent variable)

I = Input or true value (Independent variable)

K = Slope of the line

a = Intercept on the vertical axis

K and a were then determined from regression analysis using the following equation where N = number of points:

For spring balance K = 22(1689.2) - (110)(242.55) = 10481.9 = 2.165

22(770) - 1102 4840

a = (242.55)(770) - (1689.2)(110) = 951.5 = 0.1965

22(770) - 1102 4840

Spring balance regression equation from manual calculation: O = 2.165I + 0.1965

Spring balance regression equation from excel: O = 2.1647I + 0.1994

Load cell regression equation from excel: O = 47.936I - 14.591

Post Calibration Application:

Post calibration in daily use, the load cell will show a value in mV and we need to be able to determine about what the true value this will represent in kg. To do this we rewrite the regression equation as a calibration equation as follows:

I = (O - a)/K = OK-1 - aK-1

Where I = an estimate of the true value using the calibration equation based on the indicated value O

Spring balance calibration equation: I = O(0.4615) - 0.0920

Load cell calibration equation: I = O(0.0208) - 0.3034

Uncertainty Limits associated with Regression Curve Fit

The uncertainty associated with the regression curve fit (O data) is given by:

Where: so = standard deviation associated with indicated values (O)

The uncertainty associated with using the inverse regression curve to predict the true value on the basis of an indicated value is given by:

Depending on the levels of uncertainty associated with the precision error the following specifications can be utilized:

0.674s (50% confidence interval) (50:100)

s (69.3% confidence interval) (32:100)

2s (95.4% confidence interval) (5:100)

3s (99.7% confidence interval) (3:1000)

Standard Deviation calculation for Load Cell:

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.9999991

R Square

0.99999821

Adjusted R Square

0.99999812

Standard Error

0.21298741

Observations

22

ANOVA

 

df

SS

MS

F

Significance F

Regression

1

505536.9

505536.9

11144099.8

6.10719E-59

Residual

20

0.907273

0.045364

Total

21

505537.8

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

-14.5909091

0.084953

-171.754

3.5923E-33

-14.768117

-14.4137

-14.7681

-14.4137

X Variable 1

47.9363636

0.01436

3338.278

6.1072E-59

47.90641003

47.96632

47.90641

47.96632

RESIDUAL OUTPUT

Observation

Predicted Y

Residuals

1

-14.5909091

0.090909

0.00826446

2

33.3454545

-0.04545

0.00206612

3

81.2818182

0.018182

0.00033058

4

129.218182

-0.01818

0.00033058

5

177.154545

0.045455

0.00206612

6

225.090909

-0.09091

0.00826446

7

273.027273

-0.02727

0.0007438

8

320.963636

0.036364

0.00132231

9

368.9

0.1

0.01

10

416.836364

-0.83636

0.69950413

11

464.772727

0.227273

0.05165289

12

464.772727

0.227273

0.05165289

13

416.836364

0.163636

0.02677686

14

368.9

0.1

0.01

15

320.963636

0.036364

0.00132231

16

273.027273

-0.02727

0.0007438

17

225.090909

-0.09091

0.00826446

18

177.154545

0.045455

0.00206612

19

129.218182

0.081818

0.00669421

20

81.2818182

0.018182

0.00033058

21

33.3454545

0.054545

0.00297521

22

-14.5909091

-0.10909

0.01190083

sum

0.90727273

So sqd

0.04123967

So

0.20307553

si

0.00423636

Calibration Equation for Load Cell:

0.674s (50% confidence interval) (50:100) = 0.00285

s (69.3% confidence interval) (32:100) = 0.00423636

2s (95.4% confidence interval) (5:100) = 0.008472

3s (99.7% confidence interval) (3:1000) = 0.0127

Standard Deviation for Spring Balance:

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.998318

R Square

0.996638

Adjusted R Square

0.99647

Standard Error

0.41699

Observations

22

ANOVA

 

df

SS

MS

F

Significance F

Regression

1

1030.865

1030.865

5928.58

3.26E-26

Residual

20

3.477611

0.173881

Total

21

1034.342

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

0.199432

0.166321

1.199075

0.244513

-0.14751

0.546372

-0.14751

0.54637205

X Variable 1

2.164659

0.028113

76.99728

3.26E-26

2.106015

2.223303

2.106015

2.223302693

RESIDUAL OUTPUT

Observation

Predicted Y

Residuals

1

0.199432

-0.07443

0.00554

2

2.364091

-0.23909

0.057164

3

4.52875

-0.27875

0.077702

4

6.693409

-0.19341

0.037407

5

8.858068

-0.10807

0.011679

6

11.02273

-0.22273

0.049607

7

13.18739

-0.18739

0.035114

8

15.35205

-0.15205

0.023118

9

17.5167

-0.2667

0.071131

10

19.68136

-0.38136

0.145438

11

21.84602

-0.64602

0.417345

12

21.84602

-0.64602

0.417345

13

19.68136

0.918636

0.843893

14

17.5167

0.733295

0.537722

15

15.35205

0.447955

0.200663

16

13.18739

0.312614

0.097727

17

11.02273

0.377273

0.142335

18

8.858068

0.391932

0.153611

19

6.693409

0.306591

0.093998

20

4.52875

-0.02875

0.000827

21

2.364091

0.135909

0.018471

22

0.199432

-0.19943

0.039773

sum

3.477611

So sqd

0.158073

So

0.397584

si

0.183671

Calibration Equation for Spring Balance:

0.674s (50% confidence interval) (50:100) = 0.1238

s (69.3% confidence interval) (32:100) = 0.18371

2s (95.4% confidence interval) (5:100) = 0.36742

3s (99.7% confidence interval) (3:1000) = 0.55113

Bias and Precision Error of the Instrument:

The process of calibration allows the total error to be separated into two separate parts, the bias error and the imprecision error. For example for a Load Cell reading of 230mV, the best estimate of true value is 4.85kg , the bias is observed as -0.3034 giving an unbiased best estimate of 4.5kg and the imprecision associated with this data is given by ± 0.0127 (3s) limits.

Linearity

A measurement instrument is determined to be linear if all the corresponding values of I and O are in a straight line over the range of the instrument if this is not the case the instrument is then said to be non linear. Most instruments would have some non linearity.

Non-Linearity

Non-Linearity (% FS)

Scale

Load Cell

Scale

Load Cell

0.13

0.09

0.6%

0.0%

0.24

0.07

1.1%

0.0%

0.28

0.03

1.3%

0.0%

0.20

0.10

0.9%

0.0%

0.12

0.06

0.6%

0.0%

0.23

0.22

1.1%

0.0%

0.20

0.19

0.9%

0.0%

0.17

0.15

0.8%

0.0%

0.29

0.11

1.3%

0.0%

0.40

1.08

1.9%

0.2%

0.67

0.04

3.2%

0.0%

0.67

0.04

3.2%

0.0%

0.90

0.08

4.2%

0.0%

0.71

0.11

3.4%

0.0%

0.43

0.15

2.0%

0.0%

0.30

0.19

1.4%

0.0%

0.37

0.22

1.7%

0.0%

0.38

0.06

1.8%

0.0%

0.30

0.00

1.4%

0.0%

0.03

0.03

0.2%

0.0%

0.13

0.03

0.6%

0.0%

0.20

0.11

0.9%

0.0%

0.90

1.08

4.2%

0.2%

Maximum non-linearity of Spring Balance = 0.90 = 4.2% Full scale reading

Maximum non-linearity of Load Cell = 1.08 = 0.2% Full scale reading

Hysterises

Hysteresis is described as for a given input, the output displayed by the instrument may be different depending if the value is increasing or decreasing. The hysterises measurement is the difference of the output measurement for the same input between the up cycle and the down cycle.

Maximum hysterises of Spring Balance = 1.3 = 6.1% Full scale reading

Maximum hysterises of Load Cell = 1.0 = 0.2% Full scale reading

Discussion and Conclusion

Calibration is essential to ensure the accuracy of measurement instrument and this laboratory set out to demonstrate the methods used to determine the accuracy levels of a load cell and a spring balance. This occurred under standard environmental conditions i.e. the modifying and interfering influences were ignored. Quite often the output from a measurement instrument could be affected by factors other than the input, such as atmospheric pressure, ambient temperature, supply voltage or relative humidity Standard environmental conditions are defined as 25oC ambient temperature, 1 bar atmospheric pressure, 50& relative humidity and 10V supply voltage. There are 2 types of environmental inputs, modifying that can cause the linear sensitivity of a measurement instrument to change most commonly temperature and interfering that can cause the intercept to change from standard value mostly caused by electrical interference. We chose to emit these factors due to the stable temperature in the room and the fact that there was virtually no possibility of electrical interference.

The accuracy of the load spring readings could be improved greatly if the scale had a better resolution also there would have been significant errors introduced to the data by virtue of the fact that the standards were not in 10% graduations. The loading and unloading between each reading most would have destroyed the accuracy of the hysteresis data gathered. Also if the recommended 105 readings had been gathered a more accurate set of data could be produced.

The calibration equation showed that the load cell was much more accurate that the spring balance with a 99.7% confidence interval with a standard deviation of just 0.0127 for the load cell as opposed to 0.55113 for the spring balace.There is much less hysteresis on the load cell with only 0.2% of full scale reading as opposed to 4.2% for the spring balance.

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