Higher-Order Sensitivity Minimization Applied to the Design of Dwell-Rise-Dwell Cams

In many dwell-rise-dwell (D-R-D) cam-follower systems the angular velocity of the cam may undergo large variations from the nominal. Thus, to preserve optimal performance of the system it is desirable to have D-R-D cams that are speed insensitive. The paper formulates and solves this cam design problem as a linear quadeatic (LQ) optimal control problem. Speed insensitivity is accomplished by minimizing the higher-order trajectory sensitivities; i.e., second-order, third-order, etc., partial derivatives of the system response with respect to the angular velocity of the cam. The results indicate that, when compared to other cam designs, higher-order sensitivity minimization is most effective at reducing the residual vibration response at high speeds. However, cams designed using this approach may require larger preloads to ensure that the cam and follower do not separate at low speeds.