# Construction and Working of a Single Hydraulic Cylinder | Simulink Tutorial

#### Hydraulic Cylinder Introduction

hydraulic cylinder (also called a linear hydraulic motor) is a mechanical actuator that is used to give a unidirectional force through a unidirectional stroke. It has many applications, notably in construction equipment (engineering vehicles), manufacturing machinery, and civil engineering.

##### Operation And diagram

Schematic diagram of a hydraulic cylinder

Hydraulic cylinders get their power from the pressurized hydraulic fluid, which is typically oil. The hydraulic cylinder consists of a cylinder barrel, in which a piston connected to a piston rod moves back and forth. The barrel is closed on one end by the cylinder bottom (also called the cap) and the other end by the cylinder head (also called the gland) where the piston rod comes out of the cylinder. The piston has sliding rings and seals. The piston divides the inside of the cylinder into two chambers, the bottom chamber (cap end) and the piston rod side chamber (rod end/head end).

A hydraulic cylinder is the actuator or “motor” side of this system. The “generator” side of the hydraulic system is the hydraulic pump which delivers a fixed or regulated flow of oil to the hydraulic cylinder, to move the piston. The piston pushes the oil in the other chamber back to the reservoir. If we assume that the oil enters from cap end, during extension stroke, and the oil pressure in the rod end/head end is approximately zero, the force F on the piston rod equals the pressure P in the cylinder times the piston area A:

Let us consider the following diagram:

##### Equations Involved

Equation Block 1

Q=q12 + q1cx

q1ex= C2.p1

p1= (Q-q12)/C2

Where,

Q= pump flow

q12= control valve flow

q1ex= leakage

C2= flow coefficient

p1= pump pressure

Equation Block 2

Where

Cd= orifice discharge coefficient

A= orifice area

p2= pressure downstream of control valve

ρ= fluid density

The fluid within the cylinder pressurizes due to this flow, q12= q23, minus the compliance of the piston motion.

Equation Block 3

Where,

V3= V3o+ Ac*x

p3= piston pressure

β= fluid bulk modulus

V3= fluid volume at p3

V3o= fluid volume in piston for x=0

Ac= cylinder cross-sectional area

##Note##: We neglected the piston and spring masses because of the large hydraulic forces. We completed the system of equations by differentiating this relationship and incorporating the pressure drop between p2 and p3. Equation Block 3 models laminar flow in the line from the valve to the actuator.

Equation Block 4

q23= q12= C1 (p2– p3)

p2= p3 + q12/C1

Where,

K= spring constant

C1= laminar flow constant

Equation block 4 gives the force balance at the piston.

##### Simulation screenshots

The demo model can be opened in MATLAB by typing sldemo_hydcyl

The above diagram shows the Simulink model of the single hydraulic cylinder.

To look inside the components, Just right click on the component, then go to maskà under the mask

The pump subsystem contains the following blocks.

The valve/cylinder/piston/spring system block consists of the following block:

The control valve is made from the following blocks:

The output is obtained as Pressure applied vs piston movement:

##### Application:

A hydraulic jack for vehicles represents a common application of a single-acting, gravity-return cylinder.

Single-acting cylinders can be spring-extend or the more common spring-return type.

It’s used in car servicing & washing shops

The general knowledge about concepts of actuators and cylinders equations is required.

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