Lab2	First-Order Mass Damper
Figure 1: First-order rotary system with damping supplied by cup filled with honey, video image shown on screen Figure 2: Drawing of the first-order rotary system The dynamics of a spinning shaft and the effects of adding inertia and viscous fluid damping are examined in this lab. Figure 1 shows the actual apparatus. The drawing in figure 2 depicts the most important parts. The shaft and flywheel are modeled as an equivalent rotary inertia. A brass ring can be added to increase the inertia, as shown in figure 3. The axial position constraint is provided by a ball bearing. This ball bearing is attached to the end of the shaft and rotates on a fixed hardened flat (figure 4). Damping is created by filling with honey the annular space between the end of the shaft and a clear tube. The height of the honey can be changed via the syringe shown in figure 1. The fluid damping can be modeled as an equivalent rotary damper that is linearly proportional to the height L of the viscous fluid. Figure 5 shows the idealization of this first-order system. We have chosen honey as the viscous fluid to attain time constants on the order of 1 second with relatively loose geometric constraints. Furthermore, honey is environmentally safe and can be cleaned up with water. Figure 3: A brass ring can be added to increase the inertia. Figure 4: The end of the shaft is supported by a ball bearing riding on a hardened flat. Honey filling an annular space provides the damping. Figure 5: Idealization: rotary damping and inertia Figure 6: Data readible with transparent angle sheet Figure 7: Plot of angle versus time Figure 6 shows how the animation is being read from the screen. The data can be read by sticking a transparent angle sheet on the screen. By reading every frame and processing the data (with for example MATLAB) a plot of the angle versus time can be constructed (figure 7). Clearly, we could automate this data collection by using for example an optical encoder or a tachometer. The reason for using a camera is to make the data acquisition more intuitive for the students in the early labs. To see an example of such a video capture click on the video button: See below for examples of prelab and lab assignments: Prelab2.pdf Lab2.pdf