ROSE-HULMAN INSTITUTE OF TECHNOLOGY

Transcription

1 More Working Model Today we are going to look at even more features of Working Model. Specifically, we are going to 1) Learn how to add ropes and rods. 2) Learn how to connect object using joints and slots. 3) Learn how to apply forces to objects. 4) Learn how to change the effect of gravity 5) Learn how to change the effect of air friction 6) Learn how to change the material properties 7) Learn how to change the starting point of a simulation run. On our way to learning these things we are going to construct models for both a 5 ball pendulum and a Do-Nothing Slider Mechanism. Tutorial 2: Part A: Creating a 5 ball Pendulum Simulation: Step 1: Start up Working Model. Step 2: Set up your working environment: Choose Units in English with Distance in Inches Check to see if the Coordinates, Rulers, Grid Lines, and X-Y Axes are on. Make sure the Snap feature is on. Step 3: Rescale the screen so that workspace field definition is approximately 20 inches high and 30 inches wide. Step 4: Create 5 balls (Circular Bodies) each 1 inch in diameter in contact with each other along a horizontal line. 1 inch dia Step 5: Connect a rod from the top of each ball to a point 6 inches directly above each ball. (Locate the rod button bottom of the contruction bar) A rod will automatically connect to the object or the background with pinned connections when you click on the object or background. Step 6: Before running the simulation, pull the left most ball up and out to the left, so that the rod attached to it makes about a 30 degree angle with the vertical. Now save this as a Working Model file, mypendulum.wm Step 7: Go ahead and Run the simulation. More Working Model Page 1 of 9

2 Explain what happened: Step 8: The behavior was not quite what you had in mind or thought was going to happen was it. That's because there are some properties that are not consistent with the physical example yet. We need to adjust some of these properties to get a more realistic simulation. What are the properties that we can adjust? air friction acceleration of gravity material type bob mass elastic constant pivot friction Step 9: Let's start by changing the material type... to steel Open up the property dialog box and select one of the pendulum bobs. Under material: change from Standard to Steel. How can we change all bob property values at the same time? More Working Model Page 2 of 9

3 Change the material property of all the bobs to Steel. Now Run the simulation again. Explain the behavior you find: Was is closer to the behavior you expected? Step 10: Add the effect of air friction on the simulation. Under World... Air Resistance...select Standard for air resistance and Run the simulation again. Explain the behavior you find. Let's try a lower air resistance coefficient. You can alter the coefficient when either the Standard or High air resistance selection is made. Try a few different ones until you think you have one which gives you one that you feel provide a good system response. Your best choice for friction coefficient: lb/ in-s. Step 11: Restarting from the last simulation state It is very likely that your system is still bouncing around and not settling down like the actual pendulum system. One cause of this is that the original positions of the 5 bobs may not have started at a true equilibrium position. If we let the model run until the model decays, we will have established a stable equilibrium position. Once this has happened, we will change the starting conditions to match those of this decayed systems. One way to do this would be to type the last position and velocity properties back into the Property Dialog Box. Another way to change the starting position is to set it to the very last position of the current simulation run, by use of the Start Here option. Run your current simulation until it is barely moving. Now we will reset the starting positions and velocities as last state of the current simulation run. using World... Start Here... update the initial values of position and velocity. Now Pull the left most bob up and out to the the left. Once again start a simulation Run. More Working Model Page 3 of 9

4 This should improve the settling of your system, since the bobs started from a state very close to equilibrium and in contact with each other. Save this model as MyPendulumWithRods.wm Step 12: Now experiment with your simulation for a couple of minutes. What happens when you increase the elastic coefficient above 1.0? decrease the elastic coefficient to 0.0? What happens when you change the mass of one bob to 2 times the others? give the bobs different masses? What happens when you pull the first bob back up over 90 degrees? What happens when you drop two bobs from the same side? drop two bobs from opposite sides? Part B: Do-Nothing Slider Mechanism: Step 1: Open up a New Working Model document. Step 2: Once again set up the environment: Make sure the Coordinates, Ruler, Grid, and X-Y Axes are on. Make sure the Snap feature is on. This time we'll use Numbers and Units as SI(radians) (the default units) Step 3: Create three rectangular bodies and one circular body as shown below, in your workspace di It will be a really big slider mechanism! Two of the rectangles should be 1 x 2 meters, the circle should be 1 meter in diameter, and there should be a 4 meter space between the objects as shown of 4 m. The other rectangle should be long and thin. (0.3 m high and 11 m wide) Change the color of each object by opening the Appearance Dialog Box. Also turn off the Track Outlines switch in the Appearance Dialog Box. More Working Model Page 4 of 9

5 Step 4: Create a horizontal slot by using the Horizontal Slot button. Select a point on the background approximately in the middle of the workspace and click there Step 5: Create a vertical slot by using the Vertical Slot button. Select a point on the background approximately in the middle of the workspace and click there. Step 6: Create square point elements at the center of the 1 x 2 rectangles and the circle. Create a square point element near the right end of the long slender rectangle. Your model should approximately look like this. Step 7: Make joints by using elements and the Join Button To make a joint, you need to select either two point elements; or else one point element and one slot element. Once two elements are selected, use the Join button to bring them together. Select the point element on the left most rectangle and the horizontal slot...then Join them. Select the point element on the middle rectangle and the vertical slot...then Join them. Select the point element on the circle and the point element on the long slender rectangle...the Join them. More Working Model Page 5 of 9

6 Step 8: Making pinned joints that pivot. We want to connect the long rectangle to the slotted rectangles with pinned joints. Now create point elements (the round one, not the square one) at the center of each of the two 1 x 2 rectangles, and place two point elements on the long slender rectangle, one at its center and one near its left end. Select the point element of the left most rectangle and the point element near the left end of the long rectangle... Join them. Select the point element at the center of the other 1 x 2 rectangle and the point element at the center of the long slender rectangle... Join them. Step 9: Test your linkage model by selecting the circle and dragging it around the workspace. The Smart Editor should allow the linkage should move with it. Zoom out once or twice to give you a field so you can you see the entire motion. Step 10: Adding an output meter. Start by selecting the long slender rectangle. We want to add a meter to show its angular rotation. The to create a meter for this measure.. Measure... Position... Rotation Graph Drag it into the upper right corner of the workspace. More Working Model Page 6 of 9

7 Step 11: Now Run the simulation. Notice how gravity causes the motion of the system. Let's turn gravity off. World... Gravity... None. Step 12: Applying a force. Select the Force button and apply a force to the center of the long slender rectangle. Draw it any size and direction since we will redefine it using the Property Dialog Box. Open up the Property Dialog Box and select the Force[#]. Now locate and change the components of the force to Fx : 0 Fy: 20*sin(.5*time) This will set up a time varying vertical force Run the simulation to see the effect. Step 13: Since we will want to control the force with slider controls, create two controls. Define... New Control...Generic Control and repeat a for a second control. Define the first control as a slider control with min: 0 max: 50 and number of snaps: 50 change its label to: Force Amplitude Define the second control as a slider control with min: 0 and max : 2 and number of snaps: 50 change its label to: Force Frequency Take note of the ID given to each of the Inputs. In my model, they were Input[23] and Input[24]. We will need these numbers for the next step. What are your Input ID numbers? Force Amplitude: Input[ ] Force Frequency: Input[ ] More Working Model Page 7 of 9

8 Step 14: Link the Inputs to the Force Constraint. Open up the Property Dialog Box for the Force and change the definitions of Fx: 0 Fy: Input[23]*cos(2* *Input[24]*time) Close the Property Dialog Box and check to see if the slider controls now control the magnitude and frequency of the force. Try to set the controls that get the mechanism to rotate counter clockwise as quickly as possible. How long many rotations of the rod can you make in 1 minute? Step 15: Since we want to measure revolutions of the rod (not the radians of the rod), we need to scale the output of our meter. Open up both the Appearance and the Property Dialog Box for the output meter. On the Properties Box you should see the y1 variable as Body[4].p.r. The.p.r refers to the rotation value in radians of the position vector that describes Body[4]. (If you have a different number than 4, that's the number you will use in the next equation.) Change the y1 variable line to read: Body[4].p.r/(2* ) so that it will give the output in revolutions instead of radians. On the Appearance Dialog Box of the output meter change the title to Rod Rotation turn of the show units option and type in revs for the label (where rot was was) Now the output will give the units in revolutions and also be labeled correctly. Step 16: Finish up your simulation by adding documentation which gives a title, a short program description, what the input and output are, your name, and the date. More Working Model Page 8 of 9

9 Assignment 8B: Due Thursday, February 5, ) Change the pendulum model so that instead of using rods to connect the bobs, use ropes instead. How does this constraint change the behavior of the system? 2) Complete the Do-Nothing Machine Tutorial and print out a copy of your final documented simulation model. More Working Model Page 9 of 9