With the preliminaries out of the way, now comes the stuff from
Star Trek. Mr. Spock would raise an eyebrow.
I have added several additional points in the range where the dynamic amplitude is a little less, equal to and greater than that of the static pressure loading.
... and what to my wondering eyes should appear, but ...
- not only is the angular velocity decreasing as you decrease the dfr from 0.59 to 0.43, but
- the angular velocity reaches a GLOBAL MINIMUM of almost zero!
I call this phenomenum 'valve gliding'.
At the end of the -tive portion of the cycle, the valve just
glides in for a soft landing at a slow, ever decreasing velocity. Not only is the tip velocity zero, but the whole valve just touches the seat with a velocity of zero.
To support this idea, here is a plot of angular velocity wrtdt (and theta) vs. dimensionless time at this dfr. Note how smoothly theta 'glides' in for a 'soft landing' against the seat. Note too, how the angular velocity smoothly decelerates at the same time.
Both simultaneously and smoothly approach the value of zero at the end of the half cycle!
Here is a plot of the valve box pressures at this dfr.
Note how smooth and symmetrical
p12 (pressure drop across the orifice) and
p23 (pressure drop across the valve opening) are.
Of course, this needs to be verified by the experimental method ... but it appears ... through a judicious choice of dfr, strip valve
damage due to impact loading can be
reduced if not virtually
eliminated !