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  3. problem 5 fig5 shows a doubleacting pistoncylinder hydraulic servomechanism a...

Question: problem 5 fig5 shows a doubleacting pistoncylinder hydraulic servomechanism a...

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Problem 5. Fig.5. shows a double-acting piston-cylinder hydraulic servomechanism. A posilive spool-valve displacement >0 connects the high-pressure supply Ps with the left oylinder chamber 1 and chamber 2 is connected with the low-low-pressure drain P. Consequently for z> 0, volumetric flow Qi is into chamber 1 and flow 02 is out of chamber 2 to the drain. When z <0 the flow is reversed. The orifice are of the spool valve is Ag 1zh where h is the height of the valve opening. Piston position x is measured from the left side and hence the volume of chamber 1 is VAx and the volume of chamber 2 is V2 A2(L -x) where I. is the total stroke length of the piston. Derive the complete mathematical model of the hydrodynamical system Piston with area Area, A Load mass P.V m -Load Chamber I Chamber force, Fi Cylinder Viscous friction, b 4-way spool valve Drain Supply Drain Ps P, Fig.5. Hydraulic damper system
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