The design of valve lift curves for valve train cam systems is formulated as an optimization problem, in which the maximum principle is applied. The solution is obtained by utilizing the maximum principle approach for an equivalent linear quadratic optimal control problem. The outcome of the design shows trade-offs between several design criteria. The method is applied to the specification of the lift curve for a finger-follower cam system, and design charts are developed for different choices of design parameters. The method presented in this study provides a unified way of valve lift curve design for those cam systems where the objective functions can be clearly defined.

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