A Comprehensive Laboratory Curriculum In Single Degree Of Freedom (S D F) Vibrations; Phase I – Working Model Experiments

A package of experiments for examination of the Single-Degree-of-Freedom Vibration Systems is proposed for national adoption. The comprehensive and robust package will examine the Dynamic Characteristics of Free and Harmonically Forced Systems with and without Damping. The modes of vibration are linear with Mass, Spring and Damper in a vertical orientation. The capabilities incorporated in the design of the associated apparatuses allow for adjustments of the values of: a) mass, b) damping coefficient, c) spring constant, d) the setting of the Initial Conditions, e) control of the frequency, and f) the amplitude of the driving forces. The apparatus will be interfaced with Matlab and Pcvkqpcn"KpuvtwogpvÓu"NcdXKGY1VernierÓu"NcdSwguv to measure system response and display the results both numerically and graphically. Students in a Vibration, Control Systems, or a measurement related exercise/course may be challenged to generate the mathematical models of the proposed modes of experimentation. In Phase-I of the project; and to insure the high quality and reliability of the potential designs (for the robust and affordable apparatus), Working Model Î 2D software has been employed for the preliminary modeling, simulation and testing of a set of practical systems. The successful implementation of this phase of the project has encouraged the authors to share their practical and cost-effective results with the educational community. This effort should prove valuable to those colleagues who are limited in time (for set up and conducting such valuable experiments and exercises) and also those who struggle with resources (for obtaining the necessary hardware/space). Phase-II of the project will concentrate on the design, fabrication, interfacing, and testing of all the intended modes and will be presented in a future work. I INTRODUCTION Experimentation is one of the most effective means for a student to gain a thorough understanding of the materials taught in class. It provides a means to verify the theories through data collection and interpretation. A single degree of freedom vibrations apparatus can be used for either demonstration or experimentation in such classes as Dynamics, Vibrations, Controls, Differential Equations, and of course, an Engineering Laboratory. Despite the many advantages of using a commercially available single degree of freedom apparatus, they are prohibitively expensive for many institutions, which can cost upwards of $20,000. Commercially available vibration apparatuses are not only expensive but they also tend to be limited. The other apparatuses researched by this group did not provide all the desired modes of operation and modularity of experimentation in Single Degrees of Freedom Modes. It was therefore desirable to design an apparatus that would be able to be replicated by other educational institutions, with a budget of $3,000 in materials and components and about 75 hours of machining. The unit created would incorporate design features that would allow for a reduced cost and increased quantity of features. The design would incorporate a wide variety of modes and experimentation in order to provide the students with a comprehensive understanding of (S-D-F) vibrations. P ge 1.24.2 Proceedings of the 2008 American Society for Engineering Education Annual Conference & Exposition Copyright © 2008, American Society for Engineering Education To develop a better appreciation of the proposed simulated experiment (in Working Model), it is essential to have a preliminary discussion of the features of the physical apparatus. This is important in that all the physical parameters of the intended unit are all incorporated in the simulation process and may prove to be a critical link in visualizing the actual environment and the problem at hand. The authors hope to generate sufficient interest in potential use of such easily simulated experiments considering the degree of difficulty involved in the selection, design, and fabrication of the major components and subsystems of the overall design. II OBJECTIVES OF THE PROJECT The following were the predetermined parameters that needed to be incorporated: 1. To create a set of experiments in Single Degree of Freedom (SDF) Vibrations. 2. To design and fabricate the associated apparatus such that it would be safe, robust, modular, and relatively inexpensive. 3. To design the apparatus so that it would be reproducible by other educational institutions. 4. To utilize Working Model for simulation, testing, and obtaining the practical range of parameters that are both suitable for a laboratory environment and are preferably available stock items 5. To provide a means to collect and interpret data recorded through experimentation. 6. To share the schematics and parts required to fabricate additional units via a website accessible through Vjg"Eqnngig"qh"Pgy"Lgtug{Óu"website. 7. To develop appropriate instruction for experimentation to optimize the function of the apparatus. III BACKGROUND A comprehensive review of literature (1-6) was conducted on Single Degree of Freedom (S-D-F) Vibrations as well as the existing pertinent laboratory apparatuses. Appendix (B) reflects on a collection of the relevant equations for the study of S-D-F Vibrations. After examining what was commercially available, and determining what features were both desirable and undesirable, certain design considerations were made. The final design would be available for other educational institutions to manufacture. As a result, the cost was not to exceed $3,000 and the parts used had to be as commercially available stock parts as possible. An important consideration was that the combined mass of the frame of the apparatus and the added dead mass (at the time of operation) had to be large enough in order to suppress the effects of external vibrations and thereby provide more accurate results. One-page laboratory experiments would be developed with the intention of trying to keep the time to complete different phases of the experiments between 30 to 60 minutes. To review the results of experiments, a data acquisition system would need to be integrated. This would require data acquisition hardware as well as programmed software to record and analyze the measured data. It was decided that either an accelerometer or a linear encoder would be used to measure the motion and LabVIEW / LabQuest would be used to acquire the data and export it to an Excel file. Once exported it would be inputted into Matlab for analysis and comparison with theoretical results.