ME 646 Pressure Tap – Mechanical Matlab coding report Solving the Deliverable part on page 2. ALL six data wll be provided. ME 646 – Pressure Tap Lab Sprin

ME 646 Pressure Tap – Mechanical Matlab coding report Solving the Deliverable part on page 2. ALL six data wll be provided. ME 646 – Pressure Tap Lab
Spring 2019
A pressure tap is expected to exhibit the dynamics of a second order system. The system dynamics of a
pressure tap are explained in the “Pressure Measurement Lecture” and in Chapter 9 section 8 in the
Figliola and Beasley text. You are asked to compare the measured response of a pressure tap system to
the predicted response based on estimates of the natural frequency and damping ratio from the
experimental data. You are also asked to determine if the dependence of natural frequency and
damping ratio on tube length is consistent with the model predictions.
The text and the notes provide a solution for the response of a second order system to a step function
input. We have two proposed methods for applying a step function input to the pressure tap system.
One involves flipping a valve switch as fast as you can and the other utilizes popping a balloon. You will
measure the system response for both of those methods, analyze the resultant response to estimate the
natural frequency and damping ratio of the system, and then compare the actual performance to
performance predicted using the constants you determined.
In lab tasks:
A diagram of the setup has been provided in lecture. The pressure transducer is a differential
diaphragm transducer manufactured by Validyne. The specifications are at the end of this document.
The pressure tanks will be charged to 10-15 psi. The actual value is not that important. You are provided
with three pressure tap tubes of differing length. Use the measuring tape to measure the tube length
and use a caliper to measure the inner diameter of the tube. Record this data in your notebook along
with a brief description of the system and a diagram (which you may tape in).
Use the oscilloscope to record the pressure pulse from a popping balloon and from flipping the manual
valve switch for each tube length. The magnitudes of each signal will be significantly different because
the maximum pressure in the balloon is smaller than the pressure in the tank. This means you will need
to adjust the gain on the oscilloscope (volt/div). We will adjust the output of the oscilloscope so that it
saves twice as many points. This will enable you to record data for twice as long which will improve the
frequency resolution of the FFT. Save the data for subsequent analysis.
Analysis:
You should have at least six individual data sets (both pressure pulses for each tube length). The
magnitude of the response will be very different because the pressure for the balloon is much lower
than the pressure in the tank. The sign of the transition will be opposite because the balloon releases
pressure and the tank applies pressure. Use FFT methods to determine the frequency of the oscillation.
Create plots comparing the measured response to the predicted response for a step pressure pulse
using your best estimates of damping ratio and damped natural frequency) for both pressure pulse
methods. The code provided in Lecture 5 will be very useful in providing the predicted response.
The data sheet provides the transducer volume and you can calculate the tube volume. The assumption
of pressure tap system model is that the transducer volume is small with respect to the tube volume.
Verify that this assumption is correct. Plot ?n vs.1/ l and ? vs. l . Compare these plots to the expected
dependence. Does the data lie on a positive slope straight line? Do the slopes of the two plots agree
with the model predictions? (You must evaluate the model predictions to answer this question).
Deliverables:
All plots must be carefully labelled. Use dashed lines for simulations and solid lines for data.
1. A precisely and concisely written paragraph or two describing the method you used to extract
the constants from the data.
2. FFT plots for each tube length and pressure pulse application method where the frequencies for
each FFT peak are labeled on the plot. State the frequency resolution in the caption. Propose a
value for the damped natural frequency for each length and pulse application method.
3. Plots using peakfinder to show the positions of the peaks for the valve data only. List the
apparent damped natural frequency on the plot obtained by ?d ? 2? / T where T is the period
obtained using multiple peaks.
4. Six plots comparing the actual p-t response to the simulated response for a step input. Each plot
should have a caption that describes which situation the plot refers to. List the value of ?d and ?
on each plot.
5. Individual plots showing the dependence of the natural frequency and the damping ratio on
length.
6. Write a concise and precise paragraph that describes how well the prediction from Equations
9.30 and 9.31 matches the data. Consider both the dependence on length and the magnitude of
the slope. Avoid qualitative descriptions like good and bad. Use descriptions like, ‘exhibits the
same dependence on length (or not)’ and the predicted slope ‘is exactly equal to, approximately
equal to, is the same order of magnitude, or is more than one order of magnitude different’.
List the values of the constants (with units) in the equation.
Strategies and expectations for analyzing the pressure tap data
1. The predicted data from the Matlab step function can be stored in an array that you can
manipulate using the syntax [y,t] = step(sys). This allows you to shift t to match your data.
Alternatively, you can shift the time vector in your data to match the t=0 predicted data. It also
allows you to use two x,y data sets in a single plot command.
2. Peakfinder or peakdet will not work for the balloon data. Use the FFT results for the damped
natural frequency and iterate to find the damping ratio that best matches the data by eye. You
must be careful with your initial signal and final signal values to determine the KA in the
numerator (num in the program). It will require several iterations to get the prediction to
closely match the data. It will not be perfect.
3. The step Matlab function will generate much larger amplitudes than those observed for the
valve data. It will be close to the observed data for the balloon but it will not contain the higher
frequency data.
4. If your initial and final value are nearly the same, you probably acquired the data using AC
coupling which attempts to remove the DC component. I have data that you can use if you find
your data has similar initial and final values. Email me if you have this issue.

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