Hydraulic and Pneumatic System With Transfer Function

Pneumatic systemIn pneumatic devices, the power is transmitted through the action of air flow under pressure.

Pneumatic actuating valve

The air at pressure Pi is injected through the input manifold. As the plunger is attached to the diaphragm, the pressurized air pushes the plunger as well as the diaphragm and thus the plunger is displaced through a distance dy.

Let the plunger attatchment has a mass “M”.The co-effiecient of viscous friction and spring

deflection coefficient are “B” and “K”.If the area of diaphragm is “A”Then the force exerted on the system is is opposed by inertia force is

Into Laplace Transform;

In hydraulic devices,the power is transmitted through the action of fluid

flow under pressure and the fliud is incompressible.

Input power requirement is provided by the displacement of the valve piston.i.e.(x).The linear motion of the valve piston controls the flow of oils to either side of the main piston.The output is the displacement y of the main piston.

When the input force through the displacement x is applied to the valve piston,the valve piston moves to the right.The piston valve ports (2) and (3) are thus uncovered and oiled higher pressure from port (2) enters into the left side of main piston through main port A.At the same time,the main port B is connected to the sump through port (3).The pressure P1 on the left side of the main piston is higher than the pressure P2 on the right side.The pressure difference (P1-P2) causes the main piston to move from left to right and resulting displacement of mass attached to main piston is y.

Oil flow ‘q’ is a function of valve displacement ‘x’ and pressure difference PL.

i.e. q=f(x , PL)

By partial differentiation:

Measuring q , PL , x from initial zero value and Partial derivatives as constant

By Integration

If the main piston displacement is dy in time it .i.e. assume oil to be incompressible and neglecting leakage, then the rate of flow of oil into main cylinder is,

A=Area of the piston

Multiplied by A,

i.e. =

By Applying Laplace transform,

Sulthan