REPORT as a partial requirement for the course on ENGINEERING EXPERIMENTATION

Transcription

1 REORT as a parial requiremen for he course on ENGINEERING EXERIMENTATION DETERMINATION OF RESSURE WITHIN A THIN WALLED CYLINDER USING AN EXTERNALLY ALIED STRAIN GAGE Submied by: Signed Name(s) Suden_A and Suden_B Submied o: rofessor John M. Sullivan, Jr. Monh Day, Year

2 Lis of Figures: Figure 1: Thin wall cylinder schemaic wih cross secional lines A--A and B--B indicaed. Figure : Cross secion A--A showing ha hoop wall sress mus 3 balance inernal pressure. Figure 3: Cross secion B--B showing ha axial wall sress mus 3 balance inernal pressure. Figure 4: Wheasone bridge configuraion wih R1 acing as srain gage. 4 Figure 5: Connecing a Quarer-Bridge srain gage o channel 0. 5 Figure 6: Srain.vi fron panel showing required inpu parameers. 5 Figure 7: Diagram view of srain.vi cenered on he offse 6 poeniomeer configuraion. Lis of ables: NA Sample Lab Wrie Up for ME

3 ABSTRACT: The ASME boiler codes requires coninuous monioring of pressure in hin walled pressure vessels. Unforunaely our produc lines conain highly viscous fluids which have fowled mechanical and elecrical pressure gages and ransducers repeaedly. The viscous fluids experience dramaic flucuaions in emperaure, and hence pressure, during he curing sage of he process. A srain gage was mouned exernally in he circumferenial direcion of a es pressure vessel o measure he hoop sress. The pressure wihin he vessel is direcly relaed o he hoop sress. I was deermined ha he pressure was 5.3 psig +/- 1%. The exernal srain gage is insensiive o he fowling problems experienced wih more radiional pressure measuring devices. This pressure monioring sysem is recommended for our full produc line. INTRODUCTION: The ASME boiler codes requires coninuous monioring of pressure in hin walled pressure vessels. A hin walled cylinder has a wall hickness < r/10, wih r being he radius of he cylinder. In his siuaion only he membrane sresses are considered and he sresses are assumed o be consan hroughou he wall hickness,. Our produc lines conain highly viscous fluids which have fowled mechanical and elecrical pressure gages and ransducers repeaedly. The viscous fluids experience dramaic flucuaions in emperaure, and hence pressure, during he curing sage of he process. Unforunaely, he diaphragm wihin he mechanical pressure gages becomes encrused wih cured producs wihin cycles. Elecrical pressure ransducers have experienced similar problems. The man-hour effor o clean and/or replace he fowled gages has reduced he profi margin by 6%. Consequenly, a new mehod of measuring pressure is required. Consider a hin-walled pressure vessel as shown in Fig. 1. A B B A Figure 1: Thin wall cylinder schemaic wih cross secional lines A---A and B---B indicaed. Sample Lab Wrie Up for ME 3901

4 The hoop sress can be deermined from a sress analysis of he ank cross secion, such as along line A--A of figure 1 and is shown in Fig..[1] r σ Hoop = (1) Diameer σ hoop ressure Effec r/ = σ hoop σ hoop (Thickness, ) Figure : Cross secion A--A showing ha hoop wall sress mus balance inernal pressure. Similarly, figure 3 illuminaes he analysis mehodology for deermining he longiudinal sress (along cross secion B---B of figure 1). r σ Loop = () πr = πrσ r σ Long = Long Figure 3: Cross secion B--B showing ha axial wall sress mus balance inernal pressure. Recall ha he srain is relaed o sress in his siuaion via: ε Hoop = (σ Hoop - ν σ Long )/E (3) which can be rearranged for pressure by subsiuing Eqs. 1 and ino 3: = E ε /[ r (1 - ν/)] (4) Sample Lab Wrie Up for ME

5 where oisson s raio ν = 0.30 and elasic modulus E = 1.7 x 10 6 psi for our es pressure vessels. Consequenly, a srain gage mouned exernally in he circumferenial direcion of he vessel can be direcly relaed o he pressure wihin he ank. ROCEDURE: A 10 Ω srain gage (R1) was mouned on he es pressure vessel (a 1 oz Die Coke Can) while he soda can was unopened. The diameer of he can was measured wih a vernier caliper. The vessel surface was prepared according o he specificaions lised in he srain gage insallaion manual.[] A second 10 Ω srain gage (R) was mouned on a fla sock of aluminum which is used as he maching resisor in he srain circui bridge. The NI Terminal module (13) conained he oher half of he bridge circui shown in figure 4 (R3 and R4). Figure 4: Wheasone bridge configuraion wih R1 acing as srain gage. The wo srain gages were conneced o he daa acquisiion sysem as shown in figure 5. Srain gage R1 used a 3 wire lead whereas he balancing resisor (R) used a wire lead configuraion as shown in figure 5.[3] Sample Lab Wrie Up for ME

6 Vexciaion (+) R1 Channel 0 (+) Channel 0 (-) Vexciaion/ R SCXI-13 Terminal Block Vexciaion (-) Figure 5: Connecing a Quarer-Bridge srain gage o channel 0. A vi o measure srain was creaed (srain.vi) and is fron panel is presened in figure 6. This virual insrumen had an inernal poeniomeer balance which was used o balance he bridge shown in figure 4 a he sar of he experimen. Figure 6: Srain.vi fron panel showing required inpu parameers. Sample Lab Wrie Up for ME

7 The programming logic of he poeniomeer is shown in he diagram view of he VI in figure 7. Figure 7: Diagram view of srain.vi cenered on he offse poeniomeer configuraion. Once he uni was balanced, he flip op of he lid was released and he soda poured ou of he conainer. The srain gage reading on he empy soda can was measured and repored. This procedure was repeaed for 4 separae soda cans for saisical confidence. Each can was cu in half and he wall hickness measured wih a micromeer. Sample Lab Wrie Up for ME

8 FACILITIES: A 300 MHz enium II CU wih 64 Mbyes of RAM and 4 Gbye hard drive. LabVIEW version 5.0 NI DAQ Board: AT-MIO-16E-10 NI SCXI 1000: NI SCXI 11 module NI SCXI 13 erminal srip Srain gages (R1 and R): Measuremens Groups EA-13-40LZ-10 Srain gage wire: 3 wire, 6 gage, Measuremens Groups SS Solder: 35 Wa Soldering iron: Micromeer Vernier caliper Surface preparaion maerial (emery cloh, glue, solven cleaners and neuralizers) 1 oz soda cans, unopened RESULTS: The wall hickness of he soda cans averaged in. +/ in. The soda can diameer averaged.597 in +/ in. The average srain recorded was in/in +/- 3%. Saisical rials can be found in he Appendix. The pressure was calculaed based on Eq. 4 = E ε / [ r (1 - ν/)] = 1.7 x 10 6 (0.004) / [.597in/)(1-.3/)] = 5.3 psi The corresponding hoop and longiudinal sresses in he es vessel were: r σ = Hoop = ksi r σ Loop = = 8.49 ksi Sample Lab Wrie Up for ME

9 The uncerainy measuremen in is a funcion of he srain, radius measuremen and wall hickness. Each measuremen was done by independen means such ha he uncerainy can be expressed as: ω = r ε ( ω ) + ( ω r ) + ( ω ε ) ω r ε = ( ω ) + ( ωr ) + ( ωε ) ω 1 1 = ( ) + ( ) (0.03) ω = 1.86% This uncerainy is primarily a funcion of he error in he hickness measuremen. CONCLUSIONS: The exernal srain gage is compleely insensiive o he fowling problems experienced wih more radiional pressure measuring devices. This sysem is capable of coninuous pressure monioring. Replacemen of he srain gages does no require any significan down ime in he process. We recommend his sysem for all our produc line pressure vessels. REFERENCES: 1. Baumeiser, T. and L.S. Marks, Sandard Handbook for Mechanical Engineers, Chaper 5, McGraw-Hill, Measuremens Group Inc., Suden Manual for Srain Gage Technology, Bullein 309B, O Box 7777, Raleigh, NC, Naional Insrumens, Geing Sared wih SCXI, ar No C-01, June Sample Lab Wrie Up for ME

10 AENDIX: Wall hickness measuremens using a micromeer accurae o +/ in. Soda Can Trial Thickness (in) A B C D Diameer measuremens using a vernier caliber accurae o +/ in. Soda Can Trial Diameer (in) A B C D Srain recorded afer empying he soda cans A in/in B in/in C in/in D in/in Sample Lab Wrie Up for ME