Mechanical Engineering Lab “Vibration Measurement And Analysis”

This lab used numerous strategies to examine the vibrations within the structures. Through these techniques, certain properties could be discovered and contemplated. These properties include: damping coefficient, regular frequencies, decay envelope, and resonance. These properties are critical and should be considered when assembling any sort of gadget or structure. An accelerometer (sensor) was used to measure the acceleration in terms of frequency and time. The accelerometer measurement would be related to the beam displacement measurement. Theoretical and experimental values for the natural frequencies of the beam are likened to determine the accuracy of the results. Theoretical and experimental frequencies at location one were 15.23 Hz and 14.77 Hz, respectively whereas at location two were 98.265 Hz and 86.82 Hz respectively.

Introduction

In this part of the experiment, we are going to study the frequency spectrum of certain measured variables and actual response data. We will achieve the following by controlling the frequency and damping analysis. The way vibrations can be monitored is by investigating the types of loads that act on a given structure and its components. To measure the vibrations, sensors can be used to measure displacements, accelerations, angles, angular velocities, velocities, strain levels, temperatures as well as, many other quantities. In this lab, the sensor that we will use is accelerometer as mentioned before. This lab is isolated into three sections and each part accomplishes a different standpoint however they are altogether related. The vibrating beam test comprises of two situations, one for a free vibrating cantilever beam. The free vibrating cantilever beam is solidly braced to the table at two different positions. By holding the edge of the bar toward the end and redirecting it towards the table, the accelerometer will transmit a flag to the voltmeter. This voltmeter is connected to a computer and with the aid of LabVIEW, the spectra waveforms are noted down. This oscillation of beam is called natural frequency as not outside force was involved to help vibrate the beam.

The next part of the experiment uses a beam with an external force applied on one end. As we increase the frequency with the increments of 2.5Hz from 2.5Hz to 20Hz and then with increments of 10Hz from 20Hz to 50Hz, the amplitude would vary and would be recorded. The information from the free vibrating shaft with the accelerometer at the hub of the second mode can be utilized to evaluate the damping properties of the beam. A condition is determined where the commitments of modes higher than the second hub are overlooked. Therefore, the main commitment to the beam amplitude is the amplitude of the principal mode making this a one mode reaction equation.

The last piece of the experiment is engaged at finding the natural frequency and the damping coefficients of the first mode when beam is exposed to an external force at the fixed end. For each node, the amplitude s reliant on on the driving frequency as well as the natural frequency. To dig the resonance facts, we could plot the ratio of natural frequency and force frequency which also yields important characteristics of the system.

Results and discussion

There were a few contrasts when examining the Spectral Frequency of the sinusoidal and square waves. The most noticeable contrast between the two data is the highpoints of the amplitude. The sinusoidal wave has one highpoint at around 0.063. However, as we can see that the square wave has multiple peaks at different frequencies. Although the maximum peaks of both waves are obtained at the same frequency. This graph also shows that as the frequency is increased, the amplitude is decreasing hence we can see that frequency and amplitude are inversely proportional to one another

When comparing the experimental data with the actual or the calculated data, there may be slight difference in results. This might be due to some errors when doing the experiment. This part of experiment uses a freely vibrating cantilever beam and we could figure out the theoretical natural frequency of it by using the equation.

As the frequency increases, the vibration of the beam decreases which causes the amplitude to decrease. For the amplitude spectra at both positions, notice that we got one peak at position 1 whereas 2 peak at position 2. The peak for position 1 was approximately at 14.42 Hz. For position 2, the peaks were at 14.21 Hz and 87.59 Hz.

Now since we have found the natural frequency, we could calculate the damping ration along with the logarithmic decrement using equation (5) and equation (6). The damping factor gradually diminishes as the peak increases because of the amplitude diminishing after some time. However, the log decrement doesn't relentlessly diminish because of the manner in which the value is computed utilizing the characteristic log of the two peaks.

For this part of the lab, we had an external force applied to the beam. By dissecting the outcomes, it is discovered that the natural frequency of the beam doesn't change when it is under external force. It fluctuates a bit for every single relating frequency however a critical ascent in amplitude is noted in the region of the beam's natural frequency. We could plot the amplitude ratio. This ratio is is calculated by input frequencies divided by the natural frequencies. The cantilever beam responded in a movement like a sine wave, as the input function escalated up, the accelerometer position went downward. The output frequencies are perceptibly higher than the input frequencies, however the peaks for both functions reached simultaneously which implies there was no delay.

Conclusion

This lab was effectively performed and permitted a top to bottom inquiry to the vibration of a cantilever beam. The lab was distributed in three sections which showed distinctive properties of vibrations. The initial segment clarified the significance between the sinusoidal and square graphs. In the second piece of the lab there was significantly more usage of the data picked up from the initial segment of the test. In this area, diverse properties could be figured and concentrated, for example, the damping co-efficient, the damping factor and the rot envelope. The last piece of the test revealed more wisdom to the subject. The output and input frequencies at resonance were explored to observe how the output frequencies were extensively more striking than the input frequencies. Error analysis was done and the outcomes verified that the theoretical and experimental numbers were very close. These errors might have occurred because of human, systematic and machinery errors. I would say that this experiment went successful since we got an idyllic data if not accurate.