SAMPLE ONLY 10/31/06FOR ME 435L DEMOSTRATION PURPOSES ONLY 1 Pressure Transient Fourier Analysis...

10/31/06 FOR ME 435L DEMOSTRATION PURPOSES ONLY

1

SAMPLE

ONLY

Pressure TransientFourier Analysis

Experimentby

Student XGroup Y

ME 435L Winter 2007


2

SAMPLE

ONLY Objectives

• Calibrate a strain gage pressure transducer and compare to manufacturer’s calibration data

• Study transient response pressure fluctuations generated by rapid release of water from a raised tank

• Create a computer generated curve fit of analog pressure transient curve using a Discrete Fourier Transform

• Compare physical system to computer generated model

• Find pressures at t=120° and t=180°


3

SAMPLE

ONLY Background Theory

• Strain Gage Pressure Transducer– Strain gages bonded to diaphragm in Wheatstone Bridge

configuration.– Pressure gradient causes deflection in diaphragm– Resistance in strain gages is proportional to diaphragm

deflection


4

SAMPLE

ONLY Background Theory

• Strain Gage Pressure Transducer (Continued)– Low mass and relative stiffness of diaphragm lead to a high

natural frequency and quick response time– Well suited to transient measurements


5

SAMPLE

ONLY Background Theory• Fourier Analysis

– Infinite expression of coefficients multiplied by sines and cosines to approximate a continuous, complex function

• Fourier Transform– Method for decomposition of a measured signal (y(t))

into its amplitude-frequency components– Discrete Fourier Transform (DFT)

• Approximation of the Fourier Transform for use with finite data sets

– Fast Fourier Transform (FFT)• Algorithm to compute DFT quickly• Uses N log2 N operations as opposed to N2 in the DFT


6

SAMPLE

ONLYFourier Analysis Theory

2n

2nn BAC

40

1nnno ) tsin(nCAF(t)

t)2

Ncos(

2

A t)sin(nB t)cos(nA

2

AF(t) 2

N12

N

1nnn

o

4096

VA

4096

1ii

o

n

n1n A

Btan


7

SAMPLE

ONLY Equipment

• Viatran Corp. Model 119 Pressure Transducer– FSO Range:

• 0-40” WCD

– Static Sensitivity:• K = 100.54 +/- 15.3% mVDC / in WCD

• Agilent Technologies HP34970A Data Acquisition / Switch Unit – Operating Range:

• 0-10 VDC

– Bias Error:• 0.0035% of Reading + 0.0005% of Range


8

SAMPLE

ONLY Equipment

• Agilent Technologies HP35670A Dynamic Signal Analyzer– Range:

• 90 dB

– Accuracy• +/- 0.15dB

• Operational Amplifier Bridge

Signal Conditioning board– Gain potentiometer set to obtain 0.993

VDC at 10” WCD– Gain, G=120


9

SAMPLE

ONLYEquipment

• Water Supply Tank– Hole in bottom plugged by

stopper

• Ruler– Accuracy

• +/- 0.0625”

• PC with LABVIEW installed


10

SAMPLE

ONLYPressure Transducer Calibration Curve

Figure G2: Calibration curve calculated after shifting the y-intercept.

y = 87.193x - 44

R2 = 1

y = 100.54x - 44

R2 = 0.9882

-100

100

300

500

700

900

0 1 2 3 4 5 6 7 8 9 10

Water Column Depth (in. WCD)

Tra

nu

cer

Ou

tpu

t V

olt

age

(m

VD

C)

Experimental Cal Curve

Mfg. Cal Curve

Linear (Mfg. Cal Curve)

Linear (Experimental Cal Curve)

Graph of the Experimental and Manufacturer's Calibration Curves for Viatran Model 119 Pressure TransducerStatic Sensitiviy: Experimental = 100.54 mVDC / in WCD Manufacturer = 87.193 mVDC / in WCDResulting % difference: % difference = [(100.54 - 87.193) / 87.193] * 100 = 15.3%

Mechanical Engineering DepartmentCal Poly Pomona UniversityMeasurements Lab9/30/02


11

SAMPLE

ONLYUncertainty Analysis

2FAE

2SA

2DAQ

2Tape

2PTFAE PBBBBu

2ZB

2REP

2HYS

2LIN

2SEPT BBBBBB

WCD 0.740" BPT

BSE= 0.04” WCD BLIN= 0.16” WCD

BHYS= 0.08” WCD BREP= 0.004” WCD

BZB= 0.716” WCD

eFAE 1.96 P

WCD 0.03125" BTAPE

WCD "10x 8.54 B -4DAQ

WCD 0.0667" BSA

WCD 0.0995" e

WCD .1949"0 PFAE WCD "766.0uFAE


12

SAMPLE

ONLY

Figure 6: Actual Pressure Transient Curve superimposed on the Fourier Pressure Transient Curve

0.00

2.00

4.00

6.00

8.00

10.00

12.00

0 0.5 1 1.5 2 2.5

Time (s)

Head

(in

. W

CD

)

Actual Pressure TransientFourier Analysis Pressure Transient

Graph of Pressure Transient

Mechanical Engineering DepartmentCal Poly PomonaMeasurments Lab

Fourier Analysis ofPressure Transient Curve


13

SAMPLE

ONLYFigure 7: Chart of the frequency spectrum for the full pressure transient curve

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

0.5

1.5

2.5

3.5

4.5

5.5

6.5

7.5

8.5

9.5

10

.5

11

.5

12

.5

13

.5

14

.5

15

.5

16

.5

17

.5

18

.5

19

.5

Frequency

He

ad

(in

. WC

D)

Frequency Spectrum ChartPressure Transient Curve

Mechanical Engineering DepartmentCal Poly PomonaMeasurements Lab

Fourier Analysis ofPressure Transient Curve


14

SAMPLE

ONLYFourier Analysis of

Pressure Transient Curve

P(t) = 2.986 + 11.936 sin (πt ) + 3.282 sin (2πt + 1.512) + 1.482 sin (3πt - 1.557) + 1.064 sin (4πt - 1.408) + 0.577 sin (5πt - 1.164) + 0.577 sin (6πt + 1.152) + 0.656 sin (7πt - 1.198) + 0.318 sin (8πt - 1.222) + 0.239 sin (9πt - 0.246) + 0.328 sin (10πt + 0.653) + 0.537 sin (11πt + 1.241) + 0.477 sin (12πt - 0.931) + 0.129 sin (13πt + 0.766) + 0.368 sin (14πt + 0.436) + 0.517 sin (15πt + 1.57) + 0.338 sin (16πt - 0.349) + 0.169 sin (17πt - 0.733) + 0.338 sin (18πt + 0.960) + 0.348 sin (19πt - 1.132) + 0.129 sin (20πt + 0.069) + 0.149 sin (21πt + 0.155) + 0.288 sin (22πt - 1.247) + 0.239 sin (23πt - 0.944) + 0.050 sin (24πt + 0.724) + 0.199 sin (25πt + 0.91) + 0.159 sin (26πt + 1.479) + 0.119 sin (27πt - 1.136) + 0.030 sin (28πt - 1.217) + 0.099 sin (29πt + 0.973) + 0.139 sin (30πt + 1.533) + 0.099 sin (31πt - 1.139) + 0.050 sin (32πt + 1.529) + 0.090 sin (33πt + 1.187) + 0.109 sin (34πt + 1.546) + 0.080 sin (35πt + 1.299) + 0.050 sin (36πt + 1.57) + 0.070 sin (37πt + 1.294) + 0.090 sin (38πt + 1.516) + 0.070 sin (39πt -1.391) +0.050 sin (40πt -1.528) [in. WCD]


15

SAMPLE

ONLYFigure 8: Actual static noise curve superimposed on the Fourier static noise curve

-0.3000000

-0.2000000

-0.1000000

0.0000000

0.1000000

0.2000000

0.3000000

0.4000000

0.5000000

0.6000000

0 0.01 0.02 0.03 0.04 0.05 0.06

Time (s)

Hea

d (in

. WC

D)

Actual Static Noise

Fourier Equation Static Noise

Graph of Static Noise Curves

James Beale and Tyler HaraMechanical Engineering DepartmentCal Poly PomonaSystem Dynamics Lab 9/30/02

Fourier Analysis of Noise in Static Region


16

SAMPLE

ONLY

Fourier Analysis of Noise in Static Region

Figure 9: Chart of frequency spectrum for the Static Noise Curve

0.0000000

0.0200000

0.0400000

0.0600000

0.0800000

0.1000000

0.1200000

0.1400000

0.1600000

0.1800000

0.2000000

50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

Frequency

Frequency Spectrum ChartStatic Noise Curve

Mechanical Engineering DepartmentCal Poly PomonaMeasurements Lab

P(t) = 0.039 + 0.149 sin (100πt ) + 0.020 sin (200πt - 0.233) + 0.030 sin (300πt - 1.238) + 0.189 sin (400πt + 1.477) + 0.010 sin (500πt - 0.406) + 0.020 sin (600πt - 0.098) + 0.109 sin (700πt + 0.871) + 0.030 sin (800πt + 1.216) + 0.010 sin (900πt + 1.431) +

0.010 sin (1000πt + 1.045) + 0.010 sin (1100πt - 1.161) + 0.010 sin (1200πt + 0.139)+ 0.040 sin (1300πt + 0.507) + 0.020 sin (1400πt + 0.314) + 0.020 sin (1500πt + 0.015)+

0.020 sin (1600πt - 1.327) + 0.010 sin (1700πt + 1.121) + 0.010 sin (1800πt - 0.81) + 0.010 sin (1900πt + 0.458) + 0.010 sin (2000πt + 0.078) [in. WCD]

SAMPLE ONLY 10/31/06FOR ME 435L DEMOSTRATION PURPOSES ONLY 1 Pressure Transient Fourier Analysis...

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Transcript of SAMPLE ONLY 10/31/06FOR ME 435L DEMOSTRATION PURPOSES ONLY 1 Pressure Transient Fourier Analysis...