PlatinumZealot wrote: ↑14 Jan 2018, 14:52
Three layers might have to be used then to effectivley lengthen the bar. Takes up more space though.
You don't have to lengthen the bar..
Let's assume that mass doubles and lift halves when moving to a double valve.
In order to maintain the same natural frequency you need to preserve the stiffness to mass ratio. Effectively you need to double the stiffness of the 2 valve bar.
Torque is stiffness (torsional) x angular displacement. Since you've doubled the stiffness but halved the lift (angular displacement) the torque has not changed. The radius of the shaft can remain the same as the shear stress in the bar is not a function of length. You still have to achieve the increase in stiffness which you do by
decreasing the shaft length.
The other thing to consider is the change in angular acceleration. For a simple harmonic cam profile the max acceleration is given by lift x w^2. Halving the lift would halve the angular acceleration. Since the mass has doubled and T=I*a , the torque requirement can again be shown to remain constant. Of course cams use significantly more complex profiles and peak accelerations occur on the flanks rather than at max lift but I think this is a reasonable assumption.