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

In summary: Your name]In summary, representing a hydraulic system into an equivalent mechanical system requires understanding the reverse analogy between stiffness and flow resistance. This can be achieved by using equations such as Force=stiffness(k)*displacement and Flowrate=(Pressure drop)/Flow resistance. However, the flow coefficients matrix will have a different relation than the stiffness matrix, and this can be solved by using inverse matrices or replacing coefficients with 1/R terms. Further questions or clarifications can be asked for assistance in reaching a solution.
  • #1
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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!
 
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  • #2




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!


 

1. What is an equivalent stiffness matrix in a mechanical circuit?

An equivalent stiffness matrix in a mechanical circuit is a mathematical representation of the stiffness of a hydraulic flow circuit. It takes into account the geometry, material properties, and boundary conditions of the circuit to calculate the overall stiffness.

2. Why is an equivalent stiffness matrix important in hydraulic flow circuits?

An equivalent stiffness matrix is important in hydraulic flow circuits because it helps determine the response of the circuit to external loads. It also allows engineers to optimize the design and performance of the circuit.

3. How is an equivalent stiffness matrix calculated?

An equivalent stiffness matrix is typically calculated using finite element analysis or other numerical methods. It involves breaking down the circuit into smaller elements and then using equations and algorithms to determine the stiffness of each element. These individual stiffness values are then combined to create the overall stiffness matrix.

4. What factors can affect the accuracy of an equivalent stiffness matrix?

Several factors can affect the accuracy of an equivalent stiffness matrix, including the complexity of the circuit, the accuracy of material properties and boundary conditions, and the chosen numerical method. It is important to carefully consider these factors and validate the results to ensure the accuracy of the stiffness matrix.

5. How can an equivalent stiffness matrix be used in practical applications?

An equivalent stiffness matrix can be used in practical applications to predict the behavior of hydraulic flow circuits under different loads and conditions. It can also be used to optimize the design of the circuit and make improvements for better performance and efficiency.

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