9.6 KINETOSTATICCAMSHAFT TORQUE

A kinetostatic analysis assumes that the camshaft will operate at some constant speed . The input torque must vary over the cycle if the shaft velocity is to remain constant. The torque can be easily calculated from the power relationship, ignoring losses. Power in = Power out

Once the cam force has been calculated from either equation 9.10 or 9.11, the camshaft torque Tc is easily found since the follower velocity v and camshaft ù are both known. Figure 9-17a shows the camshaft input torque needed to drive the force-closed cam designed in Example 9-2 (p. 234). Figure 9-17b shows the camshaft input torque needed to drive the form-closed cam designed in Example 9-3. Note that the torque required to drive the force-closed (spring-loaded) system is significantly higher than that needed to drive the form-closed (track) cam. The spring force is also extracting a penalty here as energy must be stored in the spring during the rise portions that will tend to slow the camshaft. This stored energy is then returned to the camshaft during the fall

portions, tending to speed it up. The spring loading causes larger oscillations in the torque. Section 9.8 (p. 251) discusses the use of flywheels to reduce torque oscillation.

One useful way to compare alternate cam designs is to look at the torque function as well as at the dynamic force. A smaller torque variation will require a smaller motor and/or flywheel and will run more smoothly. Three different designs for a symmetrical single- dwell cam were explored in Chapter 4. (See Examples 4-1, p. 58; 4-2, p. 60; and 4-3, p. 61.) All had the same lift and duration but used different cam functions. One was a double harmonic, one cycloidal, and one a sixth-degree polynomial. On the basis of their kinematic results, principally acceleration magnitude, we found that the polynomial design was superior. We will now revisit this cam as an example and compare its dynamic force and torque among the same three programs.