Pressure angle Linear Cycle guide bearing Follower Cam 90 180 270 Axial cam Radial cam Eccentricity...

Transcribed Image Text:

Pressure angle Linear Cycle guide bearing Follower Cam 90 180 270 Axial cam Radial cam Eccentricity FIGURE 3.9: Rotary to translational motion conversion mechanism: cam mechanism. 7. Consider the cam and follower mechanism shown in Figure 3.9. The follower arm is connected to a spring. The follower is to make an up-down motion once per revolution of the cam. The travel range of the follower is to be 2.0 in in total. 1. Select a modified trapezoidal cam profile for this task. 2. Assume the input shaft to the cam is driven at 1200 rpm constant speed. Calculate the maximum linear speed and linear accelerations experienced at the tool tip. 3. Let the stiffness of the spring be k = 100 lb/in and the mass of the follower and the tool it is connected to m, 10 lb. Assume the input shaft motion is not affected by the dynamics of the follower and tool. The input shaft rotates at constant speed at 1200 rev/min. Determine the net force function at the follower and tool assembly during one cycle of the motion and plot the result. Notice that F(t) = mx(t)+k+x(t) (3.335) and x(t), x(t) are determined by the input shaft motion and cam function. What happens if the net force F(t) becomes negative? One way to assume that F(1) does not become negative is to use a preloaded spring. What is the preloading requirement to ensure F(1) is always positive during the planned motion cycle? The preload spring force can be taken into account in the above equation as follows, F(t) = mx(t)+k+x(t) + Fre (3.336) where Fre=k-x, is a constant force due to the preloading of the spring. This force can be set to a constant value by selection of spring constant and initial compression. Pressure angle Linear Cycle guide bearing Follower Cam 90 180 270 Axial cam Radial cam Eccentricity FIGURE 3.9: Rotary to translational motion conversion mechanism: cam mechanism. 7. Consider the cam and follower mechanism shown in Figure 3.9. The follower arm is connected to a spring. The follower is to make an up-down motion once per revolution of the cam. The travel range of the follower is to be 2.0 in in total. 1. Select a modified trapezoidal cam profile for this task. 2. Assume the input shaft to the cam is driven at 1200 rpm constant speed. Calculate the maximum linear speed and linear accelerations experienced at the tool tip. 3. Let the stiffness of the spring be k = 100 lb/in and the mass of the follower and the tool it is connected to m, 10 lb. Assume the input shaft motion is not affected by the dynamics of the follower and tool. The input shaft rotates at constant speed at 1200 rev/min. Determine the net force function at the follower and tool assembly during one cycle of the motion and plot the result. Notice that F(t) = mx(t)+k+x(t) (3.335) and x(t), x(t) are determined by the input shaft motion and cam function. What happens if the net force F(t) becomes negative? One way to assume that F(1) does not become negative is to use a preloaded spring. What is the preloading requirement to ensure F(1) is always positive during the planned motion cycle? The preload spring force can be taken into account in the above equation as follows, F(t) = mx(t)+k+x(t) + Fre (3.336) where Fre=k-x, is a constant force due to the preloading of the spring. This force can be set to a constant value by selection of spring constant and initial compression.