# Resonant Frequency of a spring

1. Aug 3, 2009

### kieren12345

Hi all,

I have a problem at work, I have been asked to work out the resonant frequency of an assembly within our mechanical face seal.

We have a mass (the face) attached to springs that are preloaded. The springs are fixed at the other end and the face is also pressed up against the seat.

The seal works by maintaning a force between the seat and face so liquid cannot escape, but allows the two face to rotate against each other. The springs provide a constant load under dynamic conditions.

The problem I am having is that I have no experience within resonant frequencies and the formula I keep finding does not account for preload or the boundary conditions.

f=1/(2*PI)*SQRT(k/M)

2. Aug 3, 2009

### Nick Bruno

Hi, I really dont understand your configuration, but I can tell you that a system reaches resonance when it oscillates at its natural frequency, or fundamental frequency.

for mechanical systems natural frequency = wn = sqrt(k/m) or as you said f = 1/2pi*sqrt(k/m) for units of hertz.

M stands for the mass of the object being held by the spring. K stands for the spring stiffness in N/m or force/ distance.

Possibly your mass is that of the plate, and you have to find an equivalent spring constant value for your system. Springs can either be modeled in series or parallel.

If memory serves me right, I think springs are in parallel if they deflect the same and they are in series if they see the same force load.. I may be wrong about this.

3. Aug 3, 2009

### Mike_In_Plano

Hello, Mike here.

Given the case that your preload force is sufficient to mate the face and seat, there won't be any motion between them, and the resulting resonance will be determined by the accumulated mass (face and seat) and accumulated stiffness (face loading springs and the seat to it's mounts).

I suspect your seat is a stiff and mounted firmly, so this resonance would be quite high. You'd likely need to use an FEA solver to get at that one. That, or measure it with an accelerometer & something to hit it with.

When performing resonance tests, there are analyzers available with a "calibrated" hammer (it has an accelerometer in it) and accelerometer inputs. The guys that design cars go to town with this equipment, since everything in a car is subject to resonance.

Something different happens if you experience a shock sufficient to lift the face off of the seat. In that case, force = mass x acceleration becomes sufficient to counter the preload force. Then, the natural reaction of the face is to lift off, and assuming the acceleration must die down, the face will eventually crash back into the seat. For an acceleration impulse, the face will lift away and fall back following a half sine wave curve. The frequency of that sine wave will be determined by the mass of the face and stiffness of the springs. If the face crashes to the seat without rebounding, the assembly will then resonate based on the accumulated mass and stiffness of the two parts.