I want you to answer my 7 Lab Questions.

INSTRUCTIONS 

I have 7 questions, need to be answered in 7 pages. I need help with this lab, it’s only asking for a couple of simple things in the outside of lab sections. 

 there are three steps in page #2, and four steps in page #4 

the 7 questions, there are 3Q on page #2, and 4Q on page #4. 

see the attached

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Attachment 1;

Lab 7 – Velocity, and Acceleration

Format

This lab will be conducted during your regularly scheduled lab time in a group format. You may ask the lab instructors for assistance if needed, but successful completion of the lab is your responsibility.

Report

An individual, informal report is due from each student at the beginning of the next lab (Lab 8).

 
Background  

Velocity and acceleration measurements are of obvious importance to mechanical engineers. To learn more about these measurements, you will do the following during this laboratory:

I. Measurement of rotational speed using a proximity sensor and an incremental encoder. You will be provided a laboratory test-stand with a DC motor and the associated motor driver. You will then measure the motor shaft speed using a proximity sensor and a toothed-gear and then with an incremental encoder. In your laboratory report, you will compare the two methods for measuring shaft speed.

II. Measurement of beam vibration using a piezoelectric accelerometer.

You will be provided an accelerometer and accelerometer signal conditioner. You will then use the combination to measure the vibration of a mass-ended aluminum beam clamped to the lab station. The acceleration data will be used to determine the natural frequency of the mass-ended beam with two different sets of masses on the beam. In turn, you are to use the natural frequency of the beam to estimate the beam stiffness. In your report, you must compare the measured and theoretical beam stiffnesses.

 
Because there are two parts to the lab and because there are limited test-stands available for each part of the lab, you will be rotating among different laboratory workstations. You will have approximately 45 minutes to make all measurements at a given test stand before rotating to the next workstation. As such, please be sure to stay focused and on-task during the laboratory.   

 
I. Angular Velocity Measurement  

This section of the laboratory will examine three different methods for measuring the rotational speed of a motor’s shaft. The different sensors that you will use are:

1. Optical Tachometer

2. Incremental Encoder

3. Magnetic pickup

These are all shown in Figure 1 below.

In the first example, a handheld tachometer is pointed at an optical reflective tape on the shaft coupling. The shaft speed in rpm is read directly off of the display on the front of the tachometer.

In the second example, a commercial incremental encoder is used. It has a resolution of 360 slots per revolution and is attached to the end of the DC motor/tachometer. The output of this device can be read with the Waveforms oscilloscope. To convert that reading into the motor speed in rpm, use the following formula:

 rev slots 1 rev 60sec

Motor' s  * * . min sec 360 slots min

Finally, a circular plate with ferrous metal “gear-teeth” has been installed on the shaft of the motor and is used to generate pulses as the teeth pass an external, fixed magnetic pickup coil. There are 30 teeth on the plate and thirty “spaces.” As such, 30 pulses are generated for each revolution of the plate. Those pulses are translated into the speed in rpm, which can be read on the readout at the front of the experimental setup.

The process for testing these rotary velocity transducers is as follows:

1. Set the speed controller to a desired (low) setting.

2. •Measure the rotational speed of the shaft using each of the transducers listed above:

• Handheld tachometer (direct reading in RPM)

• Incremental encoder frequency in Hz from Waveforms oscilloscope. Make sure there are between 5 and 20 complete cycles on the screen.

• Magnetic gear pickup readout (direct reading in RPM)

3. Change the speed setting and repeat step #2.

4. •Continue step #3 until at least 10 different motor speeds (including the maximum speed) have been tested and the data has been recorded for the report.

•Outside Lab:

5. Treat the angular velocity from the magnetic gear pickup readout as ideal (ideal) and plot the other 2 directly measured speeds (handheld, encoder) on the vertical axis of one plot.

6. Plot the deviations (handheld – ideal) vs. ideal and (encoder – ideal) vs. ideal on a second plot.

 
7. The optical encoder is equipped with what is known as an “open collector output.” That is, the transducer does not, on its own, provide a voltage output. Instead, you must provide (in the lab you this was done for you) a load resistor that is connected between the high voltage source (that provides power for the encoder) and a photo-transistor in the encoder. To learn more about this, search for information about open-collector outputs. Show a schematic detailing how to connect an open-collector output to your data acquisition system. Explain (in a paragraph or two) how to make the connections and how they work.   

 
Figure 3. Velocity sensors and DC motor controller.  

II. Vibration Measurement with Accelerometers

 
As discussed in class, accelerometers are perhaps the most widely used sensors in the field of vibration measurement. As you will see in the lab, they are quite easy to use, provided you have the appropriate signal conditioning equipment.   

 
For this portion of the lab, you will be measuring the acceleration response of a mass-ended, cantilevered, aluminum beam. If the end-mass is significantly larger than the mass of the beam, then as a first approximation, the system can be treated as a second-order mass-spring-damper system. The natural frequency of such a system is given by the equation  

 n  , K  3EI3 ,

L

where E is the elastic modulus of aluminum, I is the cross-sectional inertia of the beam, and L is the length from the base of the beam to the center of the mass at the end.

 
If the beam is pulled to a non-equilibrium position and released, then the beam displacement response will be x t  x0ent sinn 12t. If you take the second derivative of that expression, you will see (some algebra later) that the acceleration response of the beam will also be a decaying sine with the same frequency. As such, if you measure the frequency of the acceleration signal, you will be measuring the damped natural frequency which, for lightly damped systems, is almost the same as the natural frequency. You can also use the logdecrement method on the acceleration response to get an approximation of the system damping ratio.   

 
You will find a mass-ended, cantilevered beam clamped to the lab bench. An accelerometer will be attached to the end-mass; it is mounted using a synthetic wax (as opposed to bee’s wax, which was one of the original accelerometer mounting adhesives). A thin layer of wax is all that is necessary; thicker layers allow for compliance between the device under test and the accelerometer itself (which is a fancy way of saying that a thicker layer may act as an additional spring-damper between the accelerometer and the mass to which it is attached). The accelerometer will be wired to an XDCR (“transducer”) input on an ICP (integrated circuit piezoelectric) signal conditioner (some lab stations will have multi-channel ICP signal conditioners). The signal conditioner will have three gain settings: x1, x10, and x100. If a 10mV/g accelerometer is plugged into the ICP signal conditioner and that channel’s gain is set to x10, then the output voltage on that signal conditioner will be 100mV/g, where one “g” is one “gravity,” also known as an acceleration of 9.81m/s2 or 32.2ft/s2.   

 
1. Measure the distance from the edge of the lab bench (where the beam is clamped) to the center of the mass clamped to the end of the beam (a mass is clamped to the end of the beam and the beam, in turn, is clamped to the table, so two clamps are in use). L=______________  

2. Use a BNC-BNC cable to connect the appropriate signal conditioner output to Channel 1 on the Analog Discovery Kit 2. Run the Waveforms software on your lab PC and set the oscilloscope to run continuously. Gently pluck the end of the beam and observe the resulting acceleration signal on the oscilloscope. Select the appropriate V/div vertical setting so that you will be able to see all of the acceleration signal (you will be able to see all of the peaks and valleys in the response). Select the appropriate s/div time setting so that you can see at least eight periods of the signal.

3. Pluck the beam again and, at the same time, record a single trace of the oscilloscope data. Save that data in a .csv file. Open that file in Excel and verify that you can observe at least eight periods of the signal with sufficient time and voltage resolution so as to get a good idea of each period’s peak value and the time that it occurs.

4. Remove the mass from the end of the beam. Use the scale at your lab station to measure the mass of the end-mass (include the clamp used to hold the end-mass on the end of the beam).

Mend-mass=_____________

5. Apply a different mass (say twice or half the original amount) to the end of the beam. Repeat steps 3 and 4.

 
Outside of Lab:  

6. Estimate the two different natural frequencies measured in the lab (in steps 3 and 5).

7. Use the two different natural frequencies and the two different known masses to obtain the approximate stiffness of the beam. In your calculations, you should consider the mass of the beam; you can estimate that value if you know the cantilevered length of the beam, its cross-sectional area, and the density of aluminum.

8. Compare the measured stiffness of the beam to the theoretical stiffness listed in the equation on the previous page. How do the two compare? You do NOT need to include uncertainty in your analysis.

9. For each of the two tests, estimate the damping ratio of the beam using the log-decrement method outlined in the class notes. Use the damping ratio and the theoretical natural frequency as listed on the previous page to estimate the theoretical damped natural frequency. Compare that value to the measured natural frequencies as estimated in (6) above.