ME4440 Vibration Project Solved

Goal:

Develop, model, analyze, design, and build a mechanical vibration test setup and investigate one DOF, two DOF vibration as well as vibration absorber designs.

Introduction:

Consider a one DOF linear vibration test set up, as depicted in Figure 1 a):

b)

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x1

Figure 1: a) Picture of 1 DOF prototype, b) schematic of 2DOF system including vibration absorber.

X2

ME 4440/5540 Project Fall Semester 2018 Page 1

The linear vibrational system is composed of a slider and a track, where the slider is fixed by elastic elements (the figure shows springs, however you will be using rubber bands). The system shown in Figure 1a) is a one degree of freedom system with an eccentricity driven by a DC motor. The motor’s speed is controlled by a voltage regulator. You will be mathematically modelling this system, simulate the resulting model, construct the system based on the simulation parameters and compare the response of the constructed system with the simulation results. Following the successful construction and operation of your 1DOF system, you will design a vibration absorber that mitigates the vibration of the original sliding mass (m1) by adding a second 1 DOF system to it.

The itemized steps and due dates for your semester project are as follows:

1. Develop the governing equation of motion in parametric form.
2. Find the closed form solution of the governing differential equation in

   parametric form.

3. Using MatlabTM simulate the dynamics as described in step 2 and generate plots

   that show the system behaves as desired. To find the desired response, vary the parameters of the system. Have a draft report (technical memo) ready on Monday October 22nd, and turn in a final technical memo, October 24th, 2018, class time.

4. Generate a complete frequency response plot (magnitude and phase).
5. Using the extracted parameters of the system, construct a physical system using

   the parts provided as well as any additional parts you may find helpful.

6. Wire the system to provide a variable speed drive and test the system. Finalize your system construction by November 2nd, 2018, class time (demo in class by

   your group).

7. Calibrate the speed control for RPM and corresponding voltage (potentiometer

   position). Record the response of the system and compare this response with

   the simulation results. Make comments on the outcome and the comparison.

8. Generate a complete frequency response plot of the physical system (magnitude and phase). Turn in a short memo detailing the system and its corresponding

   frequency response, November 9th, 2018, class time.

9. Design a vibration absorber.
10. Simulate the vibration absorber using MatlabTM and change any parameters in

    order to obtain a zero amplitude for resonance frequency of the one DOF system. Complete the simulation and hand in your simulation notes and graphs on November 16, class time.

11. Build the vibration absorber and incorporate this into the vibration system.
12. Test the resulting two DOF system by recording the amplitudes of the different

    masses. Demonstrate your system in class on November 30th.

13.Comment on the outcomes, the comparisons, the improvements or

modifications, etc.

ME 4440/5540 Project Fall Semester 2018 Page 2

14. Develop a full technical memorandum for this project, using project format as outlined in class. Submit your completed technical memorandum by December 7th, 5:00 PM