Natural frequency of a spring loaded valve 2

[ivoryhorseman]

Can any one of you please provide help in calculating the natural frequency of a spring loaded valve. The spring which has got a mass in its end(i.e poppet) weighs 40 gms.Rate of the spring is 0.20 N/mm.
the installed lenght of the spring is 40mm. the free lenght is 49mm.

The way i see it , is to calculate force, i.e f=KX
and then pressure= f/a
1) what area should i take, is it the area of the poppet(which is circular)

2) and what is the formuale for calculating the natural frequency of the system.


3) will a kerosene present inside the valve damp the resonance, if it does how will the natural frequency formulae change.

 

[MikeHalloran]

First rough approximation is just a 1DOF system

f = ( 1 / (2*pi) ) * sqrt (k/m)

where m is the mass of the poppet + part of the mass of the spring,
and k is the spring rate of the spring, in consistent units.

That's the natural frequency of the poppet and spring, not including any effects from the seat or the fluid.

Adding kerosene adds a little effective mass to the system, but very little damping.

( Someone will probably come up with a fancier equation that includes flow effects, and more or less models the valve as a relaxation oscillator. I couldn't find one, but I think they exist. )

Pressure control valves of any kind will always 'buzz' unless some additional damping is included. It may be very subtle, but usually involves something like letting the poppet rise into an essentially closed chamber that includes a small leak. The leak may be an orifice, or it may be a very slight, almost unnoticeable, flat ground on the outside cylindrical surface of the poppet.

That describes how typical hydraulic valve poppets (that look like a 'bucket' tappet) are damped. If you've got a plate/stem type poppet as commonly used on engine valves, I have no idea how to damp it.

Ball check valves are worse. E.g.,

http://www.waset.org/journals/waset/v68/v68-218.pdf‎

Mike Halloran
Pembroke Pines, FL, USA

 

[ivoryhorseman]

thanks mike