Simulation Lab Group #5 Dynamic Systems 1, ME3211 David Cramer Percentage of Work_______________________________________ Cory Spelman Percentage of Work_______________________________________ Table of Contents Objective Calculations Experimentation Results Appendices Objective The objective of this lab was to understand how to use the Working Model 2D software and to apply this knowledge to create a vibration absorber. Part 1 was to open up a demo file and analyze the force vs. time of the piston. Part 2 was to create a vibration absorber.
The reason for creating the vibration absorber was to limit the motion of a punch press. This press causes unwanted vibrations that affect nearby equipment during operation. The vibration of this press was to be dissipated using a mass and spring sized appropriately for the size of the press and its motion. Calculations The reciprocal motion of the press was given by Equation 1: RPM=440+5*group number? (1) where group number was 5 and RPM is the reciprocal motion of the press in revolutions per minute. This motion was converted to radians per second by using Equation 2: ? RPM*2? 60 (2) where (2? )/(60) was used to convert the revolutions per minute to radians per second. The mass of the press and table top was given as 320kg. The mass for the vibration absorber, ma, was calculated using Equation 3: kama=? 2 (3) where ? was found based on Equation 2 and ka was found using Equation 4: ka=(4450+50*group number) (4) where group number was 5 and ka was found in units of Newtons per meter.
These values were used to construct a mass spring system suspended from the table top with mass ma and spring ka. Another mass spring system was created with a mass five times larger than the previous mass and an equivalent spring necessary to satisfy Equation 3. The values found from the calculations are summarized below in Table 1 and the calculations are attached in Appendix A. | Table 1: Calculations| | ? (rad/s)| ka (N/m)| ma (kg)| 1| 15. 5| 4700| 19. 6| 2| 15. 5| 23545| 98| Experimentation For Part 1 the demo file Piston2. m2d was used to analyze the forces on a piston on a crank moving at 500 and 6500 RPM. The animation step was changed from the default value to 0. 001 seconds to allow more data points to be plotted. The plot displayed force in X-direction vs. time that was provided by the Working Model simulation and also a second set of data points for the theoretical force that was calculated using the mass of the piston and its X-acceleration. The objective of Part 2 of this lab was to create a mass spring element to dampen the vibrations of a punch press.
For this part the gravity was turned off so that the displacement of the press table caused by the forcing function could be analyzed without the effect of gravity. The punch press table was modeled in Working Model as a rectangle with a mass of 320kg which was given. The two legs were each modeled as a spring damper system with stiffness and damping given as 15N/mm and 500kg/s respectively. The sinusoidal motion of the press was modeled as a force in the Y-direction with the value given by Equation 5: F=-150sin(? t) (5) where F was the force in Newtons and ? was the value found using Equation 2. The force was applied to the center of the press table. The simulation was run on the system and a plot of the displacement of the table vs. time was created. A spring with stiffness ka found using Equation 4 was attached to the bottom of the center of the table and mass ma found using Equation 3 was attached to the other end of the spring to act as a vibration damper. The displacement of the table top vs. ime was again plotted as well as the displacement of ma vs. time. The test procedure was repeated using a ma value 5 times larger than the previous ma value and a different ka value sized accordingly. The values for displacement for this setup were also plotted. All data series for the displacement of ma were imposed on the same chart to allow comparison between the three tests. The model used for this simulation can be seen below in Figure 1: Figure 1, [ ] Results Using demo file Piston2. wm2d a crank with a running speed of 500 RPM, was analyzed in the program for three seconds.
After looking at the calculations, calculate the theoretical force by taking the mass multiplied by the acceleration. Figure 2 below shows the theoretical force compared to the actual force. Figure 1 The calculated theoretical force is similar to the actual force relative to time but differs in the directional force by being less than what the actual value really is. Changing the engine speed to 6500 RPM and repeating the process as mentioned above is the next part. Figure 3 shows the theoretical force compared to the actual force with an engine speed of 6500 RPM. Figure 3
The difference between the theoretical and actual force for 6500 RPM is the same as for the speed of 500 RPM. The theoretical force doesn’t have as much directional force as the actual. As predicted, the 6500 RPM engine moved at a much faster rate than the 500 RPM for the three seconds tested. It created many more data points and more values to compare. For part two of the experiment, a mass spring element to dampen the vibrations of a punch press was created. After calculating the ka and ma values as shown in Table 1,the mass was to be multiplied by five and the spring constant must represent the ass calculated which is also shown in Table 1. A plot was created to show the displacement of the table and displacement of ma after the addition of the absorber for both sets of masses.. Figure 4 below shows the top without dampering, the top with a damper of 19. 6 kg , and a top with a damper of 98 kg. Figure 4 Comparing the three different table top displacements, the second absorber clearly works the best. Based on figure 4, it shows to be more constant and steadily goes towards zero at a faster rate than the top without dampering and the top with a damper of 19. 6 kg.
The displacement of the top with the damper of 19. 6 kg and the top with the damper of 98 kg was plotted based on its displacement of ma. Figure 5 below shows the comparison between the two table tops with different dampering. Figure 5 Based on the given information from the graph, the second absorber works better yet again. The ma of the 19. 6 absorber isn’t as constant and dispersed everywhere while the ma of the 98 absorber is more constant and has a steady range for the seconds that it was tested. References 1 Design Simulation Technologies. (2007). Working Model 2D [Computer program]