Vibration Isolation Damping Coefficient

[p_j_whelan]

Homework Statement

I am trying to solve how to select a vibration isolator for a machine to be mounted on a vibrating surface. I know the disturbance frequency, 22.5Hz and the mass of the machine is 40kg. I have selected some commercially available rubber isolators and subsequently know their stiffness but nothing else. Is there a correlation between the stiffness, natural frequency etc. to the damping coefficient. It is a single degree of freedom system so I know that omega(n) =sqrt(k/m).

Homework Equations

How do I determine the damping coefficient, C, if I want to determine the transmission of energy from one system to the other by as much as possible? Should the selected dashpots have a specified damping coefficient or can it be derived? Does the dampign factor depend on conditions and not a rating?

The Attempt at a Solution

I am led to believe that C^2- 4mk=0 where:
C = damping co-eff
m = mass of machine
k = stiffness of spring from which I can get a value for C, but is that not in units (kg*N/m) not Ns/m?

And from there, if I get value for C, can I just assume Cc is the same even though I would have to select a dashpot with that subsequent damping coefficient? I am really struggling if anybody could help.

 

[anathema]

Thank you for posting your question. It seems like you have a good understanding of the basics of vibration isolation, but you are unsure about how to determine the damping coefficient for your specific system. Let's break down the problem and see what steps we can take to find a solution.

First, let's review the equation you mentioned: C^2- 4mk=0. This is known as the "undamped natural frequency" equation, and it relates the damping coefficient (C), mass (m), and stiffness (k) of a system. However, this equation assumes that there is no damping present, which is not the case in most real-world scenarios. In order to account for damping, we need to modify this equation to include a damping ratio (ζ). The modified equation is:

ωn = √(k/m) * √(1-ζ^2)

Where ωn is the damped natural frequency.

Now, how do we determine the damping ratio (ζ)? This is where things can get a bit tricky. The damping ratio is affected by a variety of factors, such as the material properties of the isolator, the mounting configuration, and the environmental conditions. It is not a fixed value and can vary depending on the specific system.

One way to determine the damping ratio is to perform experiments on the isolator to measure its damping characteristics. This can be done by applying a known force to the isolator and measuring the resulting displacement and velocity. From these measurements, you can calculate the damping ratio using the following equation:

ζ = c/(2√(km))

Where c is the damping coefficient, k is the stiffness, and m is the mass of the isolator.

However, this approach may not be practical for your situation. In that case, you can estimate the damping ratio based on the type of isolator you have selected. Different types of isolators (e.g. rubber, steel, air) have different damping characteristics, and the manufacturer may be able to provide you with an estimated damping ratio for their product.

In summary, the damping coefficient and damping ratio are not fixed values and can vary depending on the specific system and conditions. It is important to consider these factors when selecting an isolator for your machine. I hope this helps you in your research. Good luck with your project!