Updated 5-27-08

Vibrating Table Procedure

The purpose of this experiment is to study the response of a damped system to an external load. The experimental apparatus, shown in Figure 1 (schematic in Figure 2) can be mathematically modeled as a mass attached to a spring (the four vertical leaf springs at the base of the table) and a viscous damper which works as a break on the system (the oil-filled dashpot on the base of the table). The electric motor and belt driven wheel are used to apply a sinusoidal force for steady state analysis.

Figure 1: Vibrating Table

Transient Response

First, the transient response of the table will be investigated. An impulse force is applied to the table by hitting it with a hammer and the acceleration of the table will be recorded as a function of time. You will be able to see the table oscillate until it converges to zero and will determine the values of the damped natural frequency wd and damping coefficient C.

Steady State Response

In the steady state analysis, an oscillatory force will be applied to the same table by attaching a disc to a motor with a weighted blot mounted eccentrically away from the center of the wheel. This is analogous to continuously applying a sinusoidal force on the table and investigating its response. By varying the motor speed the frequency of the forcing function is varied.

Figure 2: Schematic Diagram of the Vibrating Table Apparatus

Experimental Equipment

Table

v  Models a mass attached to a spring and damper

v  Four vertical leaf springs attach the table to the base

v  Oil-filled dashpot on the base of the table works as a damper

v  Mass : 62.72 kg (including the safety cover)

Figure 2: Vibrating Table Components

Motor

v  Used to apply a sinusoidal force for steady state analysis

v  Controlled using the blue Motor controller

v  Attached to disc with 74.20 g bolt mounted eccentrically 82.6 mm away from the center of the wheel in order to apply the sinusoidal force

Accelerometer

v  Measures the acceleration of the table

v  Manufacturer: Analog Devices

v  Model: ADXL50EM-1 +4g

Tachometer

v  Measures the frequency of the force (or the rate of the rotating wheel)

v  Displays the motor revolutions per minute (RPM) on The SPU

Proximeter/Linear Displacement Sensor

v  Omega LD701-2/5

v  Non-contact transducer that measures distance based on inductive technology

v  Located adjacent to a cam mounted on the shaft that drives the wheel and unbalanced mass. As the shaft rotates the distance between the cam and the proximeter varies and the proximeter gives a sinusoidal electrical signal which is linearly converted to the angular position of the mass. This can then be related to the forcing function.

Signal-processing Unit (SPU)

v  Signal-conditioning for the Proximeter and Tachometer

Figure 3: Signal Processing Chassis

Procedure

Set Up

  1. The module is located downstairs at lab station 17B. It is best if the module is set up so that the Vibrating Table is to the right of the cart with the SPU and motor control. The cart should be placed so that it is at the end of the lab station so the power cords do not have to stretch.
  2. Connect the marked, matching cable ends for the accelerometer, tachometer and proximeter between the vibrating table and the signal processing unit (SPU). Note where the sensors are mounted on the table.
  3. Connect the military connector exiting the SPU to P3B on the lab station base next to the computer tower. Turn ON the SCXI chassis found directly above the computer tower on the B side of the lab station.
  4. Connect the large black power cable between the motor and the blue switch box. Make sure you twist the connector to lock it in place.
  5. Connect power to the accelerometer. Connect the +5V terminal of the power supply (mounted on the side of the lab-station panel near the computer monitor) to + XTRA6 terminal on the lab station panel using a red banana cable and connect the GND of the power supply to -XTRA6 terminal using the black banana cable.

CAUTION: Ensure you have NOT reversed the polarity before turning the power supply on. Reversing the polarity will damage the accelerometer!

  1. Finally, plug the power cable from the motor power switch into circuit #7 (power outlet opposite the military connector) and the power to the spu into circuit #6 (below circuit #7). If both plugs are plugged into the same circuit, there is a chance of blowing a fuse or worse!!! Note: both plugs must use the sockets on the same Labstation in order to use a common ground. Do not turn on the motor or SPU yet.
  2. Turn on the +5V power supply on the side of the breakout panel of the LabStation.

Transient Response

  1. Open the Vibrating Table Transient Response.vi, located under Vibrating Table in the Modules folder on the desktop.

2.  Run the VI by clicking on the run arrow on the upper left hand corner of the VI.

3.  Begin data acquisition by clicking on “Start Acquisition” and then hitting the SIDE of the table near the black power cable where it says “hit here” with the rubber mallet. Do not hit the accelerometer side of the table. If you fail to trigger the VI (within approximately ten seconds) check that your equipment is set up correctly.

  1. A “good” data set center around a constant line, have clear peaks and valleys (no double-peaks and no clipping) and show a smooth exponential decay. Change the VI settings so that there is enough data to show the end of the vibration. This will show if there is any offset in the data collection (i.e. does the vibration center around zero?). .
  2. When you produce a “good” set of data, save it and record the sample rate and the number of samples acquired. It should be noted that you have to hit the “Start Acquisition” button each time before you hit the table.
  3. Repeat this procedure two more times, saving the data each time. You will use this data to estimate uncertainty in your calculations.
  4. Exit the VI.

Steady-State Response

  1. Open Vibrating Table Steady State with Lissajous.vi found in the Module Folder on the desktop under vibrating table.
  2. Turn on the SPU by flipping the switch.
  3. Turn on the power to the motor by flipping the black circuit breaker to the right of the SPU. A red light will be illuminated when the power supply is on.
  4. Turn the motor speed knob on the blue controller fully Counter-clock-wise and press the start button in the upper left corner of the blue motor controller.
  5. Run the VI. Note where all the sensors are located and what information they are giving you. The time-base scope is visible so that you can more easily understand what is happening with the Lissajous display. The table vibrations are shown in green, and the phase of the forcing function (the angle of the heavy, off-set mass) is shown in red. Adjust the motor speed until you find the resonant frequency (how do you tell that you have found the resonant frequency?). Save your data and record the RPM.
  6. To ensure that you have selected an appropriate resonance frequency, take data (as above) for several motor speeds very close to your suspected resonance and save your data for each trial. Be sure to record which file corresponds to which motor frequency (RPM).
  7. Repeat data collection for at least eight more motor speeds, four below and four above the resonant frequency in 25 RPM increments. The speeds should be within ±100 RPM range of the resonant frequency. Your goal is to produce data for a system frequency response plot with good resolution near the resonant frequency. Be sure to record which file corresponds to which motor frequency (RPM).
  8. When finished, press “stop” on the VI and quit LabView. Also, press “stop” on the blue motor controller and close the VI. Turn off the SPU, motor power circuit breaker, 5 V power supply, and SCXI chassis. Carefully unplug all cables, return checked out items and clean up.

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