MEMS 431 (FL11) Lab 1

Basic Vibration Measurements

Objective

To become familiar with vibration testing tools and methods.

Background

To investigate vibration in physical systems, we need to excite motion at specific frequencies and amplitudes. We are interested particularly in the forces, accelerations, velocities, and displacements that a system experiences. High forces are potentially damaging to structural parts, while large oscillatory motions are associated with noise and discomfort. In simple harmonic motion of a linear system, all these variables are related to one another and to the frequency and amplitude of excitation. A PC-based data acquisition system will be used to record experimental data.

Reading

Review textbook sections on simple harmonic motion, and the instructions below. READ THESE INSTRUCTIONS BEFORE COMING TO THE LAB.

Procedure

Step 1: Identify the equipment

Identify the following devices on the test bench and note the manufacturer and model number of each: (1) Function generator; (2) Digital multimeter; (3) Power amplifier; (4) Electromagnetic shaker; (5) Accelerometer; (6) Force transducer; (The accelerometer and force transducer are mounted on the shaker armature.) (7) Signal amplifiers for the accelerometer and force transducer; (8) PC and data acquisition interface. Check with the instructor to make sure you know which device is which. AFTER THE LAB: Sketch the arrangement of instruments and note the connections (e.g. function generator to power amp, power amp to shaker).

Step 2: Measure wave forms

Turn on the following devices only: PC, function generator, multimeter, signal amplifiers. On the PC, start the data acquisition program. Set the function generator to produce a sine wave with frequency near 100 Hz (cycles/second) and RMS voltage near 1 V. Use the data acquisition system to collect one second of data. Using the markers, determine the amplitude and frequency of the wave form. Verify these results with the multimeter. Now switch the frequency to 15 Hz and maintain the same amplitude.

Step 3: Shaker measurements

Make sure the amplitude of the power amp is at its minimum (inner control knob). Make sure that nothing directly in front of the shaker armature is closer than about six inches to the shaker. Turn the outer control knob to CURRENT (all the way right).

Investigate the relationship between shaker acceleration and frequency: Turn on the power amplifier. Slowly increase amplitude until vibrations are approximately 1/8 inch peak-to-peak amplitude. You should still be at 15 Hz. On the PC, enter the acceleration calibration value (m/s²/mV, including amplifier gains that multiply the signal voltage!). Select Free Run and click Start to acquire data. The analyzer will show two time histories. The top graph is the force transducer, which will be used later. The bottom graph is the acceleration. Using the markers, record the acceleration amplitude and frequency. Increase frequency to near 25 Hz. Record the input voltage (RMS) and output acceleration amplitude, and the frequency. Repeat for four more frequencies, increasing frequency by about 8-10 Hz each time. Return the power amp amplitude to zero and turn the outer control knob one notch to the left (RESET). AFTER THE LAB: you will use these data to estimate and plot the displacement amplitude at each frequency. HINT: If acceleration a=A sin wt, what is displacement?

Step 4: Does F=ma?

Attach the threaded magnetic base to the force transducer and use it to hold a steel mass. Turn the power amp back to CURRENT and increase amplitude until small (~1/8 inch) peak-to-peak vibrations are observed near 20-25 Hz. Using both channels on the data acquisition system, acquire data from the accelerometer and the force transducer. NOTE: You do not know the calibration for the force transducer: leave the calibration value at 1. Record amplitude and frequency for both transducers and note the approximate phase relationship. Repeat twice at higher acceleration amplitudes. Repeat the three measurements with a different mass. After completing measurements weigh the masses. AFTER THE LAB: Use the data to find the calibration constant for the force transducer. Make sure to account for the amplification from the signal amplifier when calculating the calibration constant.

Step 5: Estimate shaker armature mass

Add a relatively heavy mass to the shaker armature using the threaded holes at its end. Enlist the help of the instructor. At a constant amplitude and frequency (leave the controls fixed at values that provide about 1/8 inch displacement at 20-30 Hz) measure the acceleration of the armature with and without the added mass. Estimate the armature mass and the electromagnetic force on the armature.

HINT: If the electromagnetic force on the armature does not change, any change in acceleration must be due to change in mass. Note that the electromagnetic force is not the force measured by the force transducer. Draw a free body diagram.

Report

The format for the report is an extended abstract. An extended abstract is less formal than the full lab report, and may not include all of the sections. The extended abstract should briefly address the background of the experiment, but a step-by-step procedure is not required. The core of the abstract should focus on the key results, analysis, and conclusions. Data should be clearly presented in figures. The following elements should be included in the extended abstract:

a. Schematic showing the equipment used in the experiment.

b. Displacement amplitude of the shaker versus frequency.

c. Calibration constant for the force transducer.

d. Estimation of the shaker armature mass.