High Speed Automotive Cam Design Using Direct Multiple-Shooting Optimal Control Techniques

Prior investigations have presented the use of optimal control theory in the design of high-speed cam follower systems. These investigations were constrained by the difficulty of numerical solutions of optimal control problems, and this limited the types of criteria investigated, the state inequality constraints considered, and the realism of the models used. In recent years numerical solution techniques based on direct multiple shooting and using specially structured sequential quadratic programming have become available. These are capable of handling complex optimization criteria and imposing state and control in-equality constraints. This paper investigates and illustrates the potential of such methods in revolutionizing high speed automotive cam design. Cam design is complicated by the number of partially competing criteria one is interested in. This work synthesizes an optimal cam design approach, considering a range of speeds, the area under the lift curve, Hertzian contact stress, vibrations and residual vibrations, energy loss, cam curvature, follower force, and contact stress. The paper illustrates how all of these criteria can be integrated into the optimization in the design stage. Since the polydyne method is not an optimization procedure, the resulting design is superior to polydyne design in all aspects considered.