The valve lift curve is not designed directly but its second derivative is used for this purpose. This method offers a
number of advantages and is the current state of development.
A spline function B(x) is sought for which applies:
S(x) is the desired valve lift curve, and B(x) is its second derivative.
Here x is the angle of rotation of the camshaft.
The desired valve lift curve is obtained by double integration:
S(x)= ∫∫ B(x)dx.
The mathematical relationships will not be discussed further here.
This method produces numerically very high-quality valve lift curves,
resulting in equally high-quality cam profiles.
The freeform design of function B(x), i.e. ultimately of the acceleration function, allows any conceivable curve to be created.
This method is particularly effective for the redevelopment of existing valve lift curves that were not generated with CDS.