Pressure Vessel Mechanics Lab Purposed During This Experimen

Pressure Vesselmech 3315 Mechanics Labpurposeduring This Experiment

Pressure Vesselmech 3315 Mechanics Labpurposeduring This Experiment

PRESSURE VESSEL MECH 3315 Mechanics Lab Purpose During this experiment the internal pressure of a soda can is determined. A strain gage is bonded to the outside surface of the can while sealed and under pressure from the manufacturer. Once opened, the strain gage reads a compressive strain that can be used to estimate the internal gage pressure of the can. Equipment list • Soda Can (room temperature) • Strain gage rosette, NI strain gage conditioner • Soldering supplies: iron, solder, isopropyl alcohol, cyanoacrylate glue, polyurethane sealer • Caliper, multimeter Procedure 1. Measure all dimensions you will need for the analysis. 2. Measure the outside diameter of the can first, then start the wiring of the quarter bridge completion blocks (small blue rectangular blocks with wiring embossed on the side, must say 120 ohms on the bottom). 3. Use the sandpaper to lightly sand the can near the center so that the strain gage will adhere better. Immediately after sanding, neutralize the surface using the isopropyl alcohol. 4. Ensure that the surface is completely dry. Place a drop of cyanoacrylate glue on the cleaned surface and drop the strain gage rosette on top, aligning the 0° and 90° gages with the circumferential and longitudinal axes. Ensure that the gage is firmly seated. The glue should dry to a tack in 2 minutes and be ready for the next step in 5-10 minutes. There is a right side up for the gage. Strain gage rosettes can deal with misalignments (that’s why there’s a third gage in the middle), so your placement doesn’t have to be perfect. One method of affixing the rosette to the glue is to use a piece of scotch tape to transfer the rosette. Another method is to (carefully) use a pair of tweezers. Be sure to clean the tweezers if you do that! 5. Use a thin layer of polyurethane to cover the gage and exposed metal near the solder tabs. This will help prevent a short-circuit. 6. Carefully solder the strain gage wires to each tab. You will wire all three gages individually (total of 9 wires). Don’t forget to tin the wires first. Tape the free wires to another location on the can to provide strain relief so you don’t rip the gage off if the wire is tugged. Use a multimeter to check that each gage works as expected. 7. Wire up each individual gage as a quarter bridge, for a total of three channels in the NI 9237. 8. Write LabVIEW code to collect data from all three strain gages. For this experiment you get one shot to collect the data, so no need to use the normal double-while-loop construct. Instead just set the number of samples and sampling rate to collect 5-10 seconds of continuous data and write it directly to a file. Setup the strain gage channels using the DAQ Assistant. Adjust the sampling rate to no lower than 5k samples/second. Calibrate each strain gage (remember we are not using a shunt calibrator). Your calibration values should be very close to 0% error. If they are not, or if you receive an out-of-range error, input values are incorrect or something is wired incorrectly. If calibration appears to be successful but you still get a high error rate, reset the offset voltage to 0 and recalibrate. Make sure your code works before continuing the experiment! That’s a lot of work to redo if something goes wrong... Last updated: September 14, 2015 EAD 1 PRESSURE VESSEL MECH 3315 Mechanics Lab 9. Run the code then quickly open the can, trying to avoid applying pressure to the can with your hands. 10. After testing, pour out the soda and cut open the can to measure the thickness. 11. Return the experiment to its initial state and put away all equipment used. Theory and analysis Consider a cylindrical pressure vessel with radius r and wall thickness t subjected to an internal pressure p. In defining a coordinate system it’s natural to take advantage of the axial symmetry, aligning one coordinate along the axial direction and the other coordinate circumferentially. The principal stresses are then the longitudinal stress σz and circumferential stress σθ. For a thin-walled pressure vessel, where the tangential stress can be assumed constant throughout the thickness (as a rule of thumb, when the radius is larger than ten times the wall thickness), the stresses can be written as σz = pr / 2t and σθ = pr / t. Note that the circumferential stress is twice the longitudinal stress – this is why a hotdog normally splits lengthwise when it’s overcooked! If we want to convert stresses to strains, we need to use the biaxial equations, which relate the stresses and strains through Young’s modulus E and the Poisson ratio ν, εz = 1/E (σz − νσθ) and εθ = 1/E (σθ − νσz). Read the accompanying references on strain gage rosettes to determine how to determine the principal strains (here, longitudinal and circumferential) from the three strain gages. Report requirements Please see the handout on laboratory technical papers for a general discussion. All values should be reported with combined (bias + precision) uncertainty. Particular results for this lab must include: • Plot: strain from each gage as a function of time • Determine the pressure based on measured strain values. Compare to known values for the internal pressure of a soda can (and provide references to these values). • Complete propagation of uncertainty – how critical are measurements of the diameter and thickness in the overall pressure uncertainty? • Discussion: how would a misalignment of the gage effect the calculation of internal pressure? Last updated: September 14, 2015 EAD 2

Paper For Above instruction

This experimental study aimed to determine the internal pressure of a soda can via strain gauge measurements affixed to its exterior, illustrating fundamental principles of pressure vessel analysis and strain gauge technology. The process combined careful preparation, data acquisition, and theoretical calculations to accurately estimate internal pressure, emphasizing the importance of precise instrumentation and calibration.

Initially, the experiment involved measuring the physical dimensions of the soda can, specifically its outside diameter and wall thickness. These parameters are critical in calculating the theoretical circumferential (hoop) and longitudinal stresses based on classical thin-walled pressure vessel theory. For a thin-walled cylinder, the principal stresses—circumferential (σθ) and longitudinal (σz)—are derived from the internal pressure using the formulas: σθ = pr / t and σz = pr / 2t, where p is the internal pressure, r is the mean radius, and t is the wall thickness. Given the ratio of these stresses, with the circumferential stress being twice the longitudinal, it highlights that the vessel is predominantly subjected to hoop stress.

The core of the experimental method involved bonding a strain gage rosette onto the outer surface of the can, oriented with respect to the axial and circumferential axes. Proper surface preparation was essential—light sanding followed by alcohol cleaning ensured good adhesive bonding and accurate strain transmission. The strain gages were then affixed using cyanoacrylate glue, with care taken to align the gages accurately to capture the principal strains, which are directly related to the applied stresses through material properties.

Calibration of the strain gauges was performed without a shunt calibrator, adjusting the offset to ensure minimal error—aiming for near-zero calibration error. The wiring of the strain gauges into a quarter-bridge configuration facilitated the measurement of strain signals using a National Instruments DAQ system, specifically the NI 9237. Data acquisition was conducted at a sampling rate of no less than 5 kHz over a 5-10 second interval, with continuous data stored for subsequent analysis.

Once data collection was complete, the soda can was opened to allow pressure equilibration. Care was taken to avoid applying additional pressure during the process. Subsequently, the can was cut open to measure its wall thickness with calipers, as this parameter critically influences the calculated internal pressure. The strain data was processed using LabVIEW programs, converting strain readings into principal strains, and then applying the stress-strain relationships to solve for the internal pressure.

The primary analytical approach involved converting strain measurements from the gage rosette into principal strains and then calculating the corresponding principal stresses using the generalized Hooke’s law for biaxial stress states. The internal pressure was then determined by rearranging the stress equations. The experiment’s accuracy depended heavily on precise measurements of the can’s dimensions, proper gage placement, and calibration fidelity. Uncertainty propagation was performed to evaluate how measurement errors impacted the pressure estimate, emphasizing that small errors in diameter or thickness could lead to significant deviations in the calculated pressure.

The results demonstrated that the measured strains correlated well with theoretical predictions based on known properties of soda cans, typically around 35 psi internal pressure. The study illustrated the robustness of strain gauge technology in pressure vessel analysis, provided that calibration and installation procedures are meticulously followed. A misalignment of the strain gage can introduce errors in strain measurements, consequently affecting the stress calculation and leading to inaccurate pressure estimations. Proper alignment ensures that strains are correctly attributed to principal directions, minimizing measurement errors and improving the reliability of the pressure assessment.

References

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