Laboratory 6
Single DOF Spring/Mass Response

MECH324
Dynamics of Machines

OBJECTIVES:

BACKGROUND:
As in Lab 2, the vibrating cart tables will be used in combination with LabVIEW, only this time to observe displacement amplitude and output phase with respect to the driving frequency of a single degree of freedom spring/mass system.  It is often necessary to record these responses for a given system because the final driving frequency may be unknown at the time of design.  For example, if General Motors designs a new engine to be used in conjunction with an existing chassis, it would be helpful to know which frequencies to avoid in order to keep the chassis from vibrating at a harmonic of its natural frequency.  Likewise, an amplitude plot is often made for a range of driving frequencies in order to ensure the magnitude of vibration does not exceed a given tolerance.  If you have this amplitude plot while designing the driving system, you can try to avoid frequencies resulting in too large of amplitude.

 

   
LAB SETUP

Position sensors are located on all four carts.  For this lab, the first cart has been fixed to the driving linkage by a rigid metal connection while the second cart is connected to the first cart by a spring.  When the system is driven, the first cart/sensor will track the driving function while the second cart will track the response.

For the second portion of the lab, you are asked to find the mass of one of the carts as well as the spring constant.

The equation of motion for a single degree of freedom spring mass system is given by:

         

For the purpose of this lab, assume the system is undamped, so the equation is reduced to:

        

The general solution and natural frequency of this system can be shown to be:

        

        

Armed with this knowledge, a simple test can be performed to find the mass of the cart and the spring constant.  Use LabVIEW while the driving motor is at rest to measure the natural frequency of the spring/cart system.  (Simply pull the cart back an inch or so, start LabVIEW, and let go.)  Now, add a known mass to the top of the cart and repeat the test.  You now have the following system of two equations and two unknowns:

        

        

MATERIAL AND METHODS:
The lab contains two setups, each with a slider-crank and a scotch-yoke. For this Lab, we will use only the scotch-yoke mechanism because it provides a pure harmonic (sinusoidal) input to the spring-mass system. A computer records data from a data acquisition card gathering position and angular velocity information of the carts. The TAs should already have the lab set up. Be sure to use a relatively flexible spring (for a lower natural frequency and smaller required RPM range) and a light moving mass (for lower inertial forces) so the apparatus won't be over-stressed.

EXPERIMENTAL DATA
 

RESETTING THE SYSTEM
  1. Go to C:\ME 324 Programs\Pacific Scientific SC750 Controller\
  2. Ensure the E-Stop button has been released.
  3. Launch "750.exe"
  4. Open the program "Analog.BAS"
  5. Press Control+R to run the program

MASS AND

SPRING

CONSTANT
  1. Ensure the switch is flipped to DISABLE so that the carts are not being driven.
  2. Open the LabVIEW program labeled "Cart Time Based (Main)."
  3. Click on the white arrow at the top-left of the toolbar to run the program.  The screen should then display the cart motion.
  4. Add <filename>.xls after c:\temp in the box at the bottom of the screen.
  5. Pull the second cart back an inch or so. 
  6. Let go of the cart, and press and hold (for ~1 second) the "Press to START Saving Data" button while the cart is in motion.
  7. As the cart oscillates and comes to rest, the software stores 1000 points of data over 1 second of motion.
  8. Plot the data in Excel and record the frequency.  (Remember, each data point is a thousandth of a second.)
  9. Add a known mass to the cart and repeat steps 4-8, using a different file name.

FREQUENCY

RESPONSE
  1. Ensure that the safety button is not depressed.  If it is, see the RESETTING THE SYSTEM directions above.
  2. Turn the motor speed knob to the OFF position and flip the motor power switch to ENABLE.
  3. Turn the knob to set the speed to 30 RPM (using the tachometer for feedback).
  4. Open the LabVIEW program labeled "Cart Data-Based (Main)."
  5. Delete the text from the FILE PATH box.
  6. Click on the white arrow at the top-left of the toolbar to run the program.  The screen should then display the cart motion.
  7. Record the amplitude of cart 2 and the phase difference between carts 1 and 2 for 30 RPM. Move one of the orange horizontal lines on the LabView plot just below the first positive amplitude peak. Then the vertical lines can then be moved to the indicated peak points to help you measure the phase shift.
  8. Click and hold the STOP button until the arrow at the top of the screen turns white.
  9. Increase the speed by 30 RPM and repeat steps 6-9 until reaching a maximum of 180 RPM.

NOTE:  The natural frequency of this system was calculated in the first portion of the lab above.  As you approach this frequency, the entire system will begin to shake violently as one would expect!  However, you can ramp up the driving frequency (i.e. turn dial really fast) through this frequency to observe the -180 phase shift. As a secondary precaution (to protect the equipment), you can use your hand to dampen the cart motion as you go through resonance. The TA will demonstrate this by using a lower stiffness spring which will create a resonant frequency within the speed range of the motor.

ADDITIONAL RESOURCES: