Equiv. stiffness matrix (Mech. circuit) for hydraulic flow circuit?

[reach_spk]

Dear All,

I need to represent a hydraulic system into an equivalent mechanical (spring-mass-damper) system.

But actually, they have reverse analogy in terms of flow resistance and stiffness..
meaning, Force=stiffness(k)*displacement; but Flowrate=(Pressure drop)/Flow resistance
i.e., for series and parallel combinations, k and flow resistances will have reverse analogy additions..

I formed a stiffness matrix using concept of FE global elemental matrices assembly.. (1 dof @ each element nodes) - by considering the flow resistances of hydraulic circuit as spring stiffness directly...

Similarly, i used the same matrix assembly process to determine flow coefficients matrix for hyd. circuit - but ending up with FLowrate = Pressure drop * Flow resistance (wrong relation)
ie. Ab=X instead of AX=b

So, how can i represent my flow matrix now?? Only after achieving this, I can proceed forward..
Also let me know that whether I can replace all co-efficients of stiffness matrix with 1/R terms..
Or should I have to take inverse of that matrix and perform the calculations..

Help me out in reaching the soln..
Ur ideas/suggestions r most welcome…

Thanks in advance!

 

[Achy47]

Thank you for your question. Representing a hydraulic system into an equivalent mechanical system can be a challenging task, but it is definitely achievable. The key to understanding the reverse analogy between stiffness and flow resistance is to think about the physical properties that they represent.

In a hydraulic system, stiffness represents the resistance to deformation or displacement of the system. This is similar to a spring in a mechanical system, where the stiffness of the spring determines how much force is required to compress or stretch it. On the other hand, flow resistance in a hydraulic system represents the resistance to flow of the fluid. This is similar to a damper in a mechanical system, where the flow of the fluid is controlled by the resistance offered by the damper.

To represent a hydraulic system into an equivalent mechanical system, you can use the equations you have mentioned: Force=stiffness(k)*displacement and Flowrate=(Pressure drop)/Flow resistance. However, as you have correctly pointed out, the flow coefficients matrix will have a different relation than the stiffness matrix.

To overcome this issue, you can use the concept of inverse matrices. The inverse of a matrix is a matrix that, when multiplied by the original matrix, gives the identity matrix (a square matrix with 1s on the main diagonal and 0s everywhere else). In your case, you can take the inverse of the stiffness matrix to get the flow coefficients matrix, or vice versa.

Alternatively, you can also replace all coefficients of the stiffness matrix with 1/R terms, where R represents the flow resistance. This will result in a flow coefficients matrix that gives the correct relation between flow rate and pressure drop.

I hope this helps in solving your problem. If you have any further questions or need clarification, please do not hesitate to ask. Good luck with your research!