An Optimization Approach to Valve Train Design

Flexible cam profile synthesis method using smoothing spline curves

“…Because of the physical essence of cam mechanisms, the curve needs continuity up to second order derivatives only (continuity up to the acceleration). Sometimes, for cam mechanisms with very high operative speeds, continuity up to the third order is required (jerk continuity) [12,20]. Because the degree of the smoothing spline in Eq.…”

“…If the Lagrange multipliers are determined, the set of piecewise polynomials in Eq. (12), which represents a desired cam profile, is determined.…”

“…Some cam profiles used at high operating speeds require not only a low peak value but also a continuous jerk curve [12,20]. Because the jerk continuity cannot be achieved by the cubic spline curve, it necessitates the use of a quintic spline curve.…”

“…The magnitude of change in each curve totally depends on the weighting factors assigned to each control points and the redundant constants. The local modifications of acceleration curves can be used in many applications [5,12,22,23]. Fig.…”

“…By adjusting the weighting factors and the redundant constants, designers can tighten or loosen the local constraints in the designed cam profiles [15]. On the other hand, smoothness of the designed cam profile is also important for better performance in highspeed cam follower systems [12,14]. The roughness penalty function, which is defined in Eq.…”