Finding Transfer Functions for Mechanical Systems

In summary, the speaker is an electrical engineer struggling with a two body problem involving mechanical systems. They understand how to create equations of motion but are unsure how to get the transfer function. They mention attempting to rearrange the equations but finding it too difficult and not understanding the method used in their reference book. They are seeking help and advice on how to approach this problem.
  • #1
jrand26
11
0
Hi guys

I'm an electrical engineer and we're currently doing some control stuff which involves mechanical systems. I'm having particular trouble with a two body problem, I understand how to do the free body diagram and get the equations of motion, but I'm not sure how to get the transfer function. E.g I have, letting ' and '' be the first and second derivatives,

m1x1'' = Fapplied - k2(x1-x2) - k1x1 - c1x1'
m2x2'' = k2(x1-x2) - k3x2 - c2x2'

So now I want to get X1/Fapplied and X2/Fapplied. I'm assuming I want two equations, F = f(x1(t)) and F = f(x2(t)) so I can do the Laplace etc. My first thought was to rearrange the second equation in terms of x1 and then sub into the first equation, but the algebra seemed pretty ridiculous. Is there an easier way? I have Nise but I don't understand the method it uses, it doesn't really explain how it goes from equations of motion to transfer function (or I don't understand the method it uses). Any help is appreciated.
 
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  • #2
It sounds like you were on the right track but simply gave up because you did not want to do the algebra. There is definitely some algebra involved, so go ahead and work it through. It may be easiest if you set this up as a system of two equations in two unknowns in matrix form. It will fall right out that way.
 

1. What is a mechanical transfer function?

A mechanical transfer function is a mathematical representation of the relationship between the input and output of a mechanical system. It describes how the system responds to a given input, taking into account factors such as mass, damping, and stiffness.

2. What are the applications of mechanical transfer functions?

Mechanical transfer functions are commonly used in engineering and physics to analyze and design mechanical systems, such as robots, vehicles, and machines. They are also used in fields such as control systems and vibrations to model and predict the behavior of mechanical systems.

3. How is a mechanical transfer function determined?

A mechanical transfer function can be determined through experimental testing or mathematical modeling. In experimental testing, the input and output of the system are measured and used to calculate the transfer function. In mathematical modeling, the physical properties of the system are used to develop a mathematical equation that represents the transfer function.

4. What are the components of a mechanical transfer function?

The three main components of a mechanical transfer function are the input, output, and transfer function itself. The input is the force or displacement applied to the system, the output is the resulting force or displacement of the system, and the transfer function is the mathematical relationship between the input and output.

5. How is a mechanical transfer function useful in system analysis?

A mechanical transfer function is useful in system analysis because it allows engineers and scientists to predict the behavior of a system without having to physically test it. It can also be used to identify the critical parameters that affect the performance of a system, making it easier to optimize and improve the design.

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