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LINIER HYDRAULIC ACTUATORSMeasurement and Control TechnologyBY:Agus Dwy Bramastha4214101005Rika Citra4214101006Rizal Saputra4214101007Desta Rifqi Aldara4214101008M. Amin Sentosa4214101009Rivaldi Clarence Tjoa4214101010FLOW CHARTLinier Hydraulic ActuatorMathematic Modeling for find the Xo/Xv equationSpool-valve AnalysisForce to accelerate the mass AnalysisAnalysisActuator Analysis4.534.55Xo/Xv equationAnalysis to mathematic models

Equation (4.56) may be re-arranged to give the transfer function relating xo(s)and xv(s)

Actuator analysis

Analysis to mathematic models1SPOOL-VALVE CONTROLLED LINIER ACTUATORThe continuity equation for the chamber may be written

Hence

Analysis to mathematic models

Giving,when differentiated with respect to time Then the equation :

Analysis to mathematic models

1SPOOL-VALVE CONTROLLED LINIER ACTUATORFor chamber (1) ,the equation may be express as And for the chamber (2)

Analysis to mathematic models1SPOOL-VALVE CONTROLLED LINIER ACTUATOR

Analysis to mathematic models

Analysis to mathematic models1SPOOL-VALVE CONTROLLED LINIER ACTUATOR

Where Then the equation is

Linearized spool-valve analysis

Analysis to mathematic models2SPOOL-VALVE CONTROLLED LINIER ACTUATORAssume that spool-valve ports are rectangular in from ,and have areaWhere W is the width of the port,the from orifice theory

And

Where Cd is coefficient of discharge and is the fluid density

Analysis to mathematic models2

SPOOL-VALVE CONTROLLED LINIER ACTUATOR

Analysis to mathematic models

Analysis to mathematic models

Analysis to mathematic models

(4.45)(4.46)Analysis to mathematic models3SPOOL-VALVE CONTROLLED LINIER ACTUATOREquation (4.45 ) can be linearized using Linearization of nonlinear function for small perturbation.If qL,xV,and pL are small pertubartions of parameters QL,XV, and PL about some point a,then from equation(4.46) .Example :

Analysis to mathematic models

Then at

The linier equation ( tangential ) is

Analysis to mathematic models

Then the value of m and n is

Analysis to mathematic models

Then

Analysis to mathematic models

then the equation of qL is

Analysis to mathematic models

Note that and are the values of and at the operating point a. The relationship between , and , from equation (4.45), together with the linearized relations , and are shown in Figure 4.20.Equation (4.39) is true for both large and small perturbations, and so can be written

Equating (4.48) and (4.51) gives

Analysis to mathematic models

(4.53)Taking Laplace transforms (zero initial conditions), but retaining the lower-case small perturbation notation givesAnalysis to mathematic models3

SPOOL-VALVE CONTROLLED LINIER ACTUATORThe force to accelerate the mass m is shown inFrom FigureTake Laplace transforms with zero initial conditions and using lower-case notation

4EXAMPLESPOOL-VALVE CONTROLLED LINIER ACTUATOR4EXAMPLE

SPOOL-VALVE CONTROLLED LINIER ACTUATOR4SOLUTIONSPOOL-VALVE CONTROLLED LINIER ACTUATOR

If and

Then the equation is :

The value of xo is

4SOLUTIONSPOOL-VALVE CONTROLLED LINIER ACTUATOR

POWER STEERINGPump is moved by engine or electrical motor. Both of them have same purpose to increase the hydraulic pressure which use to move piston on cylinder.Some car has power steering with special equipment installed in the gear housing. The sensor used is a vehicle speed sensor, where vehicle speed detected by speed sensor and fluid pressure acting on the pump will be changed based on speed sensor.Power steering which uses a sensor attached to a vane pump is a type of power steering with engine rotation (RPM) sensor. In this type of engine rpm sensing, at above certain speed the volume of fluid flow will be lowered so that the pressure acting on the pump will be reduced.5

The input or command signal is the turning of the steering wheel.This moves the valve sleeve, which ports oil to the actuator (steering cylinder).The piston rod moves the wheels via the steering linkage.The valve spool is attached to the linkage and thus move with it.When the valve pool has moved far enough, it cuts off the oil flow to the cylinder. This stops the motion of this actuator.Mechanical feedback recenter (nulls) the valve to stop motion at the desired point as determined by the position of the steering wheel. Additional motion of the steering wheel is required to cause further motion of the output wheelsPOWER STEERING5

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