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Hydraulic Cylinders

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Hydraulic Cylinders

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    1. Hydraulic Cylinders BAE 515 – Lecture 8

    2. Hydraulic Cylinders By definition hydraulic cylinders are motors Provide linear rather than rotary actuation For variation see text Unbalanced actuator Balanced actuator

    3. Design considerations Stalled (no flow) force, Hydraulic Cylinder Design After selecting the appropriate piston area and choosing a valve, additional specifications for the cylinder can be determined as follows,

    4. Hydraulic Cylinder Design Choose the rod diameter, The fixity coefficient for most cylinders is 2.05 for one fixed end and one pinned end.

    5. Hydraulic Cylinder Design cont.. Some values for typical materials…

    6. Hydraulic Cylinder Design cont.. Second moment of cross-sectional area, After selecting the rod and bore sizes, the cylinder wall thickness is determined using the thick wall pressure vessel formula,

    7. Hydraulic Cylinder Design cont.. After choosing a wall thickness the deflection of the wall should be checked to guard against seal failure. Deflection of inside wall radius is given as,

    8. Hydraulic Cylinder Design cont.. Actuator Sizing Stalled or no-flow force output No-load velocity Schedule of force/velocity requirements Dynamic load analysis

    9. Hydraulic Cylinder Design cont.. The simplest description of the valve flow-pressure coefficient, Kc , is the valve conductance, The load pressure is described by, The load velocity by,

    10. Hydraulic Cylinder Design cont.. The piston force can be written as, Assuming the valve is sized to accommodate highest power requirement (force/velocity) --- 1/3 pressure drop through valve,

    11. Hydraulic Cylinder Design cont.. For laminar flow, For turbulent, If the supply and return losses are equal,

    12. Hydraulic Cylinder Design cont.. Assuming laminar flow as a starting point, From the previous relationships, Rearranging terms,

    13. Hydraulic Cylinder Design cont.. Isolating and multiplying through by , Substituting for in third term and rearranging,

    14. Hydraulic Cylinder Design cont.. If line size is known, a plot of force and velocity can be constructed from this relationship. If a critical combination of force and velocity is known, a quadratic solution for line pressure drop can be found.

    15. Hydraulic Cylinder Design cont.. Assumption – actuator is to be cycled sinusoidally. The actuator piston velocity can be written as, The dynamic load relationship can be written as,

    16. Hydraulic Cylinder Design cont.. Isolating and setting the two previous relationships equal to one another,

    17. Hydraulic Cylinder Design cont..

    18. Hydraulic Cylinder Design cont..

    19. Hydraulic Cylinder Design cont.. To evaluate the relationship at any frequency, s is replaced by The general form of the equation takes the form,

    20. Hydraulic Cylinder Design cont..

    21. Hydraulic Cylinder Design cont.. When choosing cylinders remember … No one technique is sufficient. Final F-V curve must enclose all critical points. Must consider best combination of valve coefficients and actuator working area.

    22. Hydraulic Cylinder Design cont.. Actuator Dynamics - steady-state velocity can be written as, However, instantaneous velocity is affected by valve and load characteristics. A non-linear second order differential equation can be used to describe the motion. Applying the orifice flow equation to the metering ports of the valve,

    23. Hydraulic Cylinder Design cont.. For an unbalanced actuator the flow on either side is, For a supply pressure of and return pressure of zero, the corresponding pressure drops through the metering orifices are,

    24. Hydraulic Cylinder Design cont.. The head end pressure can be written as, The load is assumed to be purely inertial (no spring or damper),

    25. Hydraulic Cylinder Design cont.. Which takes the form, where, The standard form of the equation can be written as,

    26. Hydraulic Cylinder Design cont.. Where and Using the classical solution Since then

    27. Hydraulic Cylinder Design cont.. Maximum velocity is reached when or Optimization- The previously derived relationship can be used to select the optimum piston area for a specified combination of and . From the previous equations or Differentiating with respect to A1,and setting the resultant equal to zero,

    28. Hydraulic Cylinder Design cont.. By substituting and solving equation in conjunction with , at this condition is either max. or min. Substituting these values back into the equation defining Y,

    29. Hydraulic Cylinder Design cont.. Or, For optimum travel time ( ) to position ( ) the optimal piston area becomes, Time ( )can be evaluated as ,

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