smd writeup - Matthew Callesen Daniel Roberts MAE 3183...

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Matthew Callesen Daniel Roberts MAE 3183 Wednesday Section Experiment #3 Frequency Response of a Physical System Date Performed: 10/5/06 Date Due: 10/12/06
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Abstract In this experiment, and system composed of a spring, mass and damper (SMD) was utilized, with numerous variables available for adjustment. A total of three different springs were used, each possessing a different spring constant. A viscous damper was added to one spring component to observe the effects of damping on the response of the system. The damper utilized a variable damping system, which allowed for incremental reductions of damping to be tested for an individual spring. The objective of the experiment was to calculate the spring constant for the three springs, and compare the experimental frequency and undamped natural frequency versus the theoretical values. By testing the responses of the different components, and recording the system displacement with a DAQ, students were able to derive the spring constants and damping ratios of the individual systems. Using the accumulated data, it was also possible to determine the internal damping of the system. It was found that there was significant damping in the mechanical system due to friction in the components. It was also found that springs with higher spring constants resulted in higher natural frequencies. These results agreed with relevant published data for comparable SMD systems. It was also determined that the experiment could be improved by implementing several changes. First, the damper utilized in the system was open to the atmosphere, and fluid was visible around the testing apparatus. A closed system would be more sanitary, as well as minimize changes from experiment to experiment that could result from extensive fluid loss. A second improvement could be the elongation of the test apparatus. The travel of the system was sometimes insufficient, and required adjustment of the fixed parameters. Finally it was found that the DAQ system should be periodically inspected to ascertain of noise is recorded instead of the LVDT displacement. Some of the accumulated data was deemed as unsatisfactory, and was not beneficial to the analysis of the system. Introduction The simulation of physical system is an integral part of mechanical engineering. Understanding and applying the concepts of force, weight to a physical system which 2
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contains springs, masses and dampers (figure 1) is a widespread technique to determine the physical response of dynamic systems. Figure 1: Typical spring mass damper system In this experiment, a SMD system is used to observe these behaviors, where each component has a different effect on the total response of the system. The spring is an energy storage device, and it typically provides an opposing force to the mass in the system. The relationship between the elongation (or compression) of the spring and the resulting force is given in equation one, where k is the spring constant expressed in force/ distance, x is the displacement, and F is the resulting force.
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