jadavpur university

CHARECTERIZATION & POSITION TRACKING OF ELECTROHYDRAULIC VLAVE CYLINDER SYSTEM

DIPANJAN BARMANMECHANICAL ENGINEERING

BME-IVROLL– 000811201020

CHARECTERIZATION & POSITION TRACKING OF ELECTROHYDRAULIC VLAVE CYLINDER SYSTEM

INTRODUCTION:

In comparison to electrical systems electrohydraulic systems have higher power to weight ratio. However electrical systems have much higher speed & precision. It is well known that PID control yields poor tracking performance due to friction and flow related nonlinearities in electrohydraulic servo systems. However there is an ever increasing demand on precision and speed of response on machine tool application and motion simulations. Non-linear properties are more significant in proportional valve. A feedback based model has been designed (using 3 way 4 position servo solenoid spool valve) for achieving good tracking performance overcoming severe nonlinearities.

TYPES OF DIRECTION CONTROL VALVES (DCV):

There are several types of DCV depending of the types of the spools, opening of the orifice, number of ports, number of positions etc. –

A. Check valveB. 2 way valveC. 3 way valveD. 4 way valve —

1) 2 position 4 way valve2) 3 position 4 way valve

According to the type of control of the spool 3 position 4 way spool valve can be classified in 4 basic types-

a) Mechanical controlb) Hydraulic controlc) Pneumatic controld) Solenoid control

According to the opening of the spool orifice 3 position 4 way spool valve can be classified in 3 basic types –

a) Overlapped ValveWidth of the spool is greater than the width of the orifice

b) Under lapped ValveWidth of the spool is smaller than the width of the orifice

c) Critically lapped ValveWidth of the spool is equal to the width of the orifice

Y Critically lapped Over lapped Under lapped

X axis: Spool positionY axis: Discharge

-X X

-Y

Spool position vs. Discharge for three different types of spool

Flow pressure relationship with spool position for a 3 way 4 position spool valve:

u= lap of the spool (initially)u is +ve for under lapped u is –ve for overlappedu is zero for critically lapped

x=distance travelled by spoolCr= Radial clearance

Ps= Pressure at the supply portPr= Pressure at the return portP1= Pressure at the port BP2= Pressure at the port A

V1= Velocity of liquid at port BV2= Velocity of liquid at port A

ᵨ= Density of the liquid

Cr

V1V2

B

x

u

Pr Pr Ps

A

A schematic diagram of a spool valve where liquid is entering through Ps flowing from B to A and returning to tank through Pr

Width of flow at P1-

L=√(u+x )2+Cr2

Velocity-

V1=Cv√ 2(Ps−P1)ρ

V2= Cv√ 2(P2−Pr)ρ

θp= Angle of wrapnp= No. of portsd= diameter of the spool

Total width –

w=n p . d . sin (θp2np

)

Area of opening –

A=w√¿¿

∴ A=np . d .sin (θ p2n p

)√¿¿

Volume flow rate through port B –

Q1=Cd . A .V 1

∴Q1=Cd . np . d .sin (θ p2n p

)√¿¿

Q2=Cd . np . d . sin (θp2np

)√¿¿

Considering u=0 and Cr=0, we get –

Q1=Q2=Cd .w . x √ 2(Ps−P1)ρ=Cd .w . x √ 2(P2−Pr)ρ

(θpnp

) d

L

Cr

u+x

So,

Ps−P1=P2−Pr

Defining load pressure, PL=P1−P2 …………………….. ①

Ps+Pr=P1+P2 …………………….. ②

From ① & ②, we get —

P1=(Ps+Pr+PL

2)

P2=(Ps+Pr−PL

2)

When all the pressures are taken gauge pressures then Pr=Patm=0

∴P2=(Ps−PL2

)

QL=Cd .w . x √ (Ps−PL)ρ

=Cd .w .x

∣ xmax ∣.∣ xmax ∣ .√ Psρ √1− x

∣ x ∣.PLPs

xmax=¿ Maximum value of x

N.B.: When x becomes –ve i.e. spool move towards the left then PL will be –ve, it simply indicates that

flow direction is reverse. In this case QL also becomes –ve.

MATHEMATICAL MODELLING (IN SIMHYDRAULICS) & ITS IMPLICATIONS OF A SPOOL TYPE DCV:

A feedback model is developed in simhydraulics in Matlab to check the tracking performance and to characterize the servo valve.

In this model a sinusoidal demand is given as input and it is seen that how well the actuator follows the demand. It is seen that tracking performance decreases with increase in frequency of the demand. Here the spool valve used in the model is critically lapped.

A tracking response is shown below using the following parameters —

Demand: Frequency= 2 rad/s Amplitude= 0.001 m (i.e. full opening of the spool valve)

Pressure: A constant pressure of 107 MPa is applied on the spool valve

Set-up for an Electrohydraulic Actuation System

Water is used as an experimental liquid.

Spool valve: Maximum area of the valve passage = 8x 10-6 m2

Maximum opening of the valve = 0.001 m Discharge co-efficient= 0.7

Double acting cylinder: Area A= 0.005 m2

Area B= 0.003 m2

Spring: Stiffness of the spring= 106 N/m

The following graph shows the demand in yellow line and the movement of the actuator in pink line.

Y axis: Distance travelled by the actuator in m.X axis: Time in seconds

The yellow and pink line superimposed. So we can conclude that the tracking characteristic of the model is good.

In real-time response, the system shows good tracking performance for low frequencies (up to 0.5 Hz) and starts deviating from tracking the actual demand for higher frequencies. This happens for several reasons that have not been countered in this model like several frictional losses, leakage loss, pressure variation etc. The results we get from this model match with the real time data for low frequencies only, but for higher frequencies the results does not match with the real one.

Another model is developed in simhydraulics to characterize the 3 way 4 position spool valve and it has been compared with the real time data. Here the spool valve is overlapped.

Characterization set-up for a servo controlled 3 position 4 way spool valve

The real time values of discharges for fro various voltage inputs have been inserted in the spool valve block parameter. The discharge vs. voltage is plotted.

The pink line is generated by the simhydraulics modelThe black is generated from the real time data

So it is seen that the model shows good result beyond 1.5 volts i.e. beyond 0.15 mm opening of the spool on either side. Within -1.5 to 1.5 volts range the pink line does not match with the black one. This happens because of the leakage at the port. Properties like frictional losses at this zone are not exactly known so the model cannot be configured exactly likewise. But it shows good response beyond this zone.