1

Lab 4b: Dynamic Response of a Rotor with Shaft Imbalance OBJECTIVE: • To calibrate an induction position/displacement sensor using a micrometer • To calculate and measure the natural frequency of a simply-supported shaft with a centered

load and compare the two obtained natural frequencies. • To balance an unbalanced rotating shaft using induction position sensors and oscilloscope • To study how the rotor mass position changes the natural frequency • To study how adding a second rotor mass affects the system modes • To perform frequency analysis on accelerometer data using DASYLab’s Fast Fourier

Transform (fft) function

Figure 1: Bently Nevada RK 4 Rotor Kit Experimental Setup PROCEDURE: DAY 1 – Sensor Calibration and Natural Frequency 1) Calibrate the induction sensor using the micrometer mounted to the rotor test stand with a

piece of the shaft material mounted to the end of it. You will position the sensor using the bracket mounted to the lab test stand. The end result is an equation that converts the induction sensor voltage to the distance between the steel and the sensor surface.

a) Unscrew and unplug the sensor from the Probe 1 input on the back of the Rotor Kit

Proximitor Assembly (RKPA).

2

b) Unscrew the Induction Proximity Sensor 1 from the shaft imbalance stand.

***BE CAREFUL NOT TO TWIST THE CORD ATTACHED TO THE INDUCTION SENSOR!!!***

c) Drop the plug-end of the induction sensor through the lower hole of the clamp located

inline with the micrometer. See Figure 2.

d) Carefully screw the induction sensor into the upper bracket hole located directly below the micrometer, and then re-plug and screw the plug-end back into the RKPA. See Figure 3.

e) Position the sensor flush (as close as possible) with the steel shaft piece mounted on the

end of the micrometer by screwing the sensor into the bracket the appropriate distance. The micrometer should be set to 10.0 mm for the first reading, with the sensor flush against the bottom of the shaft piece. Screw the plug end of the induction sensor back into Port 1 of the RKPA. See Figure 3.

f) Connect the output of the induction sensor (from RKPA front panel) to channel 1 of the

oscilloscope using a BNC coaxial cable. Using the remaining 2 ports in the Prox 1 Out of the RKPA, connect the induction sensor to a DMM.

Figure 2: Inserting the induction sensor plug-end into the calibration setup

3

Figure 3: Inserting the induction sensor into the calibration bracket

g) Turn on the shaft imbalance system by flipping the switch on the back of the Rotor Kit

Motor Speed Control (RKMSC).

h) Turn on the oscilloscope, and set up the display so that the signal is visible. In the Channel 1 menu on the oscilloscope, change the coupling to DC coupling. Set the SEC/DIV to 25 ms; adjust the VOLTS/DIV and position for Channel 1 so the signal appears on the screen. The volts/div should be set at approximately 5 V.

i) Look at the signal generated by the induction sensor.

j) Go to the save menu on the oscilloscope, and save the signal. Using the measure menu,

measure the mean voltage produced on channel 1 when the shaft piece is flush with the sensor (micrometer reads 10 mm, but overall displacement will be 0). Record this, along with a reading from the DMM.

k) Calibrate the induction sensor output over the range of the sensor by recording mean

voltages from the OS and the DMM. Report the minimum and maximum displacement the sensor is capable of detecting. Describe what happens to the sensor’s output at these limits in your logbook.

l) Using upscale/downscale progression, repeat the calibration runs so that you have five

sets of data from which you can determine sensor bias and precision errors.

4

m) Carefully unscrew the sensor from the back of the RKPA, and remove it from the calibration bracket. Replace the sensor in the shaft imbalance setup and plug it back into the RKPA

n) With the calipers, measure the length L and diameter d of the shaft. See Figure 4.

Note: the effective rotor length, L, is the distance between the bearing blocks.

o) Measure the distance from the center of the 800-g disc to the left end to ensure that the mass is in the center.

Figure 4: Schematic of simply-supported shaft with centered load. 2) Determine the natural frequency by whirling the shaft.

a) Using a signal splitter and BNC cables, connect Channel 1 of Rotor Kit Proximitor Assembly (RKPA) to Channel 1 of the oscilloscope and Channel 1 of the Wavebook. This channel represents the voltage detected by the induction sensor, which can be used to determine the shaft position relative to the sensor.

b) Turn on Rotor Kit Motor Speed Control (MSC) by flipping the switch located on the back.

c) On the oscilloscope, adjust the positions of Ch. 1 so the signal is in view. Using the Channel 1 menu, ensure that the signal is now set to AC coupling. Press the “measure” button to reveal such values as peak-to-peak voltage for Ch. 1.

d) With the shaft at rest, record the mean voltage to be used later to convert voltage to deflection.

e) Connect the accelerometer to channel 2 of the Wavebook. The accelerometer is connected through the charge amplifier.

f) Ensure that the charge amplifier is plugged in, and flip the power switch (the center toggle) to ON. The charge amplifier toggle for the accelerometer should be set to OPERATE.

g) Open the DASYLab file (D:\Data\Lab4\Lab4b.DSB).

h) Double click on the modules for file output (the icon on the worksheet that looks like a disk), and change the settings to File format=ASCII; File name = Combi; Save to D:\Lab4bTeam**.ASC. Click OK.

i) Press Play, , in DASYLab. Change the zoomed width of x scaling to 0-200 Hz in the FFT spectrum graph.

W L/2

L

d

5

j) The value on the dial on MSC is the actual RPMs divided by 10. Set this dial to some low value (say 50). Make sure the left switch is set to “up” and flip the right switch to “ramp”.

k) Increase the RPMs by turning the dial. Eventually, an RPM value will be reached when the rotation of the shaft matches the natural frequency. This will be evident by a high-amplitude vibration. The first amplitude of the FFT spectrum will be significantly increased in the natural frequency.

l) Record the approximate value of natural frequency. Use the oscilloscope to measure the point where the peak-to-peak amplitude is highest. This can be done using the “measure” function.

m) In DASYLab, save the waveforms for rotation speeds less than, equal to, and greater than the natural frequency for later analysis. Copy the plots into your laboratory notebook.

n) Decrease the RPMs to the value that is half of the natural frequency. Copy the data for this frequency and explain any peculiarities. Copy the plot into your laboratory notebook.

o) On the MSC, flip the left switch to “down” and the right switch to “stopped”.

p) Using an allen wrench loosen the screw on the side of the rotor mass, and slide the mass

approximately 1” from the bracket on the left side of the mass.

q) Turn on Rotor Kit Motor Speed Control and repeat steps k-o to observe the effect on the natural frequency

r) Replace the rotor mass to its original location by using the allen wrench to loosen the

screw and sliding the rotor mass to the 50% mark.

DAY 1 ANALYSIS 1) Create the calibration curve for the induction sensor. Construct a calibration curve with the

induction sensor voltage measurements as “x” and the micrometer measurement as “y”. This curve will be used to convert the voltage to a distance between the shaft and proximity sensor.

2) Determine error in calibration curve using standard error of fit and confidence intervals. 3) Calculate the theoretical natural frequency of the simply-supported shaft with a centered load

(Refer to Appendix A). Compare this with the measured value of natural frequency and discuss possible reasons for the difference.

4) Compare the center-load natural frequency to the frequency obtained when the rotor mass

was shifted to the left. If the natural frequency is different, explain why the frequency differs and why it is either higher or lower.

6

DAY 2 – SHAFT BALANCING, MODES, FREQUENCY ANALYSIS

1) Balancing the shaft. Note: in these steps you will use voltage instead of deflection as a

measure of vibration. This is done to save time by eliminating the need to convert from voltage to deflection. Record all data to a file using the DASYLab Output.

a) Ensure the proximity induction sensor 1 is connected to channel 1 of both the Wavebook and Oscilloscope, as it was on Day 1.

b) Using a BNC coaxial cable, connect the channel labeled Kφ on the RKPA front panel to Channel 2 of the oscilloscope. This channel represents an induction sensor that detects a notch located on the shaft. With this, the rotational speed can be displayed on the oscilloscope.

c) Using the channel 2 menu, set the coupling to AC.

d) Rotate the shaft with a single, centered rotor mass (no weights added) at an RPM setting of 1850. Ch.1 should look like a sine wave, and Ch .2 will be flat except when the induction sensor sees the notch. At that point there will be a large dip in the signal.

e) Use the measure menu to determine the period of the vibration of the shaft (channel 1). Then use the Run/Stop button and cursor menu to determine how many seconds after the notch the maximum vibration in the shaft occurs. This is illustrated in Figure 5.

Figure 5: YT plot showing method of determining location of maximum vibration

f) Determine where on the disk the maximum vibration takes place. This is done with this

equation:

7

i) o360____

0 ×=Period

peaktonotchfromTimeθ

(1) Using the measure menu on the oscilloscope, determine the peak to peak voltage. (2) Then denote the following:

ii) PeaktoPeakZ −−= *5.00

g) Add an arbitrary amount of mass to the disk (say 0.8 or 1.0 g). Add this mass to an

arbitrary location on the disk (say anywhere from 180° to 270° from Θ0).

h) With the mass added, run the shaft again at the same RPM setting, and find the new magnitude and location of maximum vibration. Denote these values as |Z1| and Θ1.

i) Follow the steps in Appendix B to determine the optimal location and weight to balance the shaft. Use an allen wrench to add weights to the rotor mass.

j) The exact values for mnew and φ may not be possible to use, since there are only certain masses that are available, and there are only 16 locations (22.5° intervals) to add the mass to the disk. Chose the best location and weight for what you found for mnew and φ. Note: there are two sides to the disk that mass can be added (so for example if mnew is about 1.2 g, then add 0.8 g to one side and 0.4 g to the other side).

k) Run the shaft again at 1850 RPM, and determine the new maximum vibration (Znew). This value for vibration should be considerably less than Z0.

l) On the MSC, flip the right switch to “stopped”.

2) Observing different modes – adding a second rotor mass to the shaft imbalance setup

a) Open the DASYLab file

b) Using an allen wrench, loosen the screw on the connector for the shaft and the motor, and

then slide the shaft and the mass to the left in order to remove the shaft from the motor.

c) Slide a second rotor mass onto the shaft, and position the rotor masses so they are at locations of 33% and 66% of the effective rotor length (the effective rotor length is the distance between the bearing blocks)

d) Connect the shaft to the motor and tighten the screw on the connector with an allen

wrench. And tighten the rotor masses on the shaft using an allen wrench.

e) Observe the different modes of the shaft and record the data in DASYLab. Copy the plots into your laboratory notebook.

8

f) On the MSC, flip the right switch to “stopped”.

g) Remove the second rotor mass and replace the original rotor mass to its original location by using the allen wrench to loosen the screws.

3) Frequency analysis

a) Open the DASYLab file and press play.

b) Turn on the MSC and run it at 1850 rpm.

c) Record data for 2 minutes

d) The FFT, or fast Fourier transform, is an algorithm that is used in frequency analysis to identify the operational frequencies of the system. Using DASYLab’s FFT output plot, determine which frequencies are present in the system. There may be several frequencies (i.e. the shaft frequency, the motor frequency, the bearing frequency). Copy the plot into your laboratory notebook. The zoomed width of x scaling has to be changed to observe the various frequencies precisely. Using the cursor (right click>survey>cursor), read the accurate frequencies with the peaks.

DAY 2 ANALYSIS 1) Convert the induction sensor voltage into deflection using the calibration curves. (Refer to

the VOLTAGE-TO-DEFLECTION CONVERSION). Plot the data as one smooth signal. (See the presentation on the opposite wall for an example of how to plot this data in Excel.)

2) Convert the voltage values of Z0 and Znew into deflection using the calibration curve.

Comment on how well the mass balancing worked on reducing the vibration. Also, if reduced vibration remained, comment on reasons why and the effect of noise on the results.

3) Note the different modes of vibration when a second rotor mass is added to the assembly.

Record the natural frequencies. 4) Perform frequency analysis on accelerometer data using DASYLab’s Fast Fourier Transform

(fft) function.

9

APPENDIX A: NATURAL FREQUENCY OF A SIMPLY-SUPPORTED SHAFT WITH CENTERED LOAD The natural frequency of a simply-supported shaft with a centered load is

stn x

gω

∆=

where g is the gravitational acceleration (= 9.806 m/s2) and .

EI

WLxst 48

3

=∆

where W is the weight of the centered mass (m = 800 g), L is the length of the shaft, E is the modulus of elasticity (207 GPa), and I is the moment of inertia of the shaft (= πd4/64).

10

APPENDIX B: DETERMINING THE OPTIMAL WEIGHT AND LOCA TION TO BALANCE A SHAFT

|Z0|, Θ0, |Z1|, and Θ1 are found through measurements with the oscilloscope. With these values known, the optimal weight and location of that weight can be determined to balance the shaft. Refer to Figure B.1 when performing these steps.

Figure B.1. Vector diagram for one-plane balancing. 1) First determine |Zv| using the law of cosines:

))(cos(***2 1021

20

2vv ZZZZZZ θ−+=

where Θ(Zv) = Θ1 – Θ0.

2) Next determine Φ using the law of sines:

)sin())(sin(

1

φθZ

Z

Z

v

v =

3) Add Φ to the initial angle of the added mass. This is the optimal location for the added mass.

4) Determine the optimal weight with this equation:

v

oldnew Z

Zmm 0=

11

APPENDIX C: ADDITIONAL INFORMATION AND EXAMPLE ON S HAFT

BALANCING

12