Re: Wire Rope Isolator -> Low pass filter??

Thanks!

If this tool is analog to RLC network and can act as low pass filter at certain direction, what parameters are needed to calculate its cutoff frequency?

-nick

tadchem wrote:
On Mar 29, 9:26 pm, Nick <tk...@xxxxxxxxxxx> wrote:
Thanks!

I see, so its lateral dynamics can be generally modeled as?
c*dot_x+k*x-mg=ma

The dynamics of an oscillator are described by a second order
differential equation.

m*x" + a*x' + k*x = 0

The usual treatment in undergraduate physics classes (for mathematical
and pedagogical reasons) is to assume a linear oscillator, meaning
that the coefficients m, a, and k in the differential equation are
constants.

In an oscillatory system with an externally applied force F (generally
a function of time), this becomes

m*x" + a*x' + k*x = F(t)

This case is covered in more advanced classes in physics and
engineering mechanics.

In a non-linear oscillator the coefficients themselves may be
functions of the displacement or its derivatives, and in the "real
world" there are three orthogonal dimensions to consider, so there are
a set of *six* coupled equations - three each for displacement waves
and for torques. This feature assures that the resonant frequencies
for each mode of motion will be quite different from that for any of
the other modes, regardless of the mass. The value of this feature is
that the isolator has no single frequency to which it is essentially
transparent.

The design of the isolators you have referenced insures different
damping behavior (the a constant) and different feedback behavior (the
k constant) for each direction of thrust and each axis of rotation.

The equation must be expressed in terms of tensors with applicable
tensors for the damping and feedback, and then any given externally
applied force tensor can be tested against the equation to estimate
the system response.

Except lateral movement, I see that there is some effects for shearing.
Is it analog to RLC network's characteristics as well?

This is a three-dimensional system, with X-Y-Z axes along which motion
may occur, and around which rotation can occur. The RLC network
analogy works best for one-dimensional systems, and somewhat
satisfactorily (when properly designed) for two-dimensional networks.
I have never heard of a three-axis system like this being successfully
modeled with an RLC analog computer. The possibility of torsion
(rotation) coupling two axes together in a mechanical system is
difficult to model electronically.

Tom Davidson
Richmond, VA
.