NORMALLY CLOSED VALVE
OPTIMIZATION

WITH APPLICATION TO POLYNOMIAL MODELS

Roman N. Tunkel,

Ingersoll-Rand Co.,
Waterjet System Division,

Farmington Hills, MI 48335, U.S.A.

ABSTRACT

Most high pressure waterjet cutting systems use normally closed pneumatic valves (NCV). These valves are designed and used only as nozzle valves to control and operate flow. While the characteristics and performance of a simple NCV are well known, the influence of
these parameters on the time response is not so clear. This paper presents an experimental approach for the solution of this problem.

An experimental approach (investigation) was conducted to investigate the influence of NCV parameters on the time response in
abrasive waterjet cutting. High water pressure, air pressure and orifice diameter were the principal variables that were investigated. Using the multifactor method of experiment, four polynomial equations for geometrical and mechanical parameters of the normally closed valve were created. Closure speed function of actual pressure and orifice size were used. Comparison of two
different polynomial models such as linear and mixed for NCV were
made.

The experimental data was compared with the results of a polynomial model and good correlation was found. The result of these equations also suggests a potential for optimizing the design of the NCV and
orifice tube composition.

NOMENCLATURE

Fhwp

- a water force (N);

Fair

- a air force (N);

Fsprng

- a spring force (N);

Fdrag

- a drag force (N);

Ffriction

- a total friction force between movement components inside NCV (N);

Ftotal

- a total closing force (N);

Pw

- a water static pressure due the movementt of the stem (MPa);

Pair

- an air pressure due the movement of the steam (MPa);

x

- a deflection of the spring (m);

s

- a travel of the stem
(m);

k

- a rate of the spring
(N/m);

Sp

- the cross section of the
piston (m2);

St

- the cross section of the
stem (m2);

Stn

- a cross-sectional stem area relevant to the drag force
(m2);

fk

- a friction coefficients;

ro

- a density of the water
(kg/m3);

W

- an approximattely weight of moved parts (N);

g

- a specific gravity
(m/sec2
);

T

- an estimation of closing
time (msec);

d Yi

- a sum of the squared
deviation from the mean;

Yi

- a current response for
each experiment;<

Yav

- an arithmetic average - mean;

- a standdard
deviation;

- a standard error of
estimate;

- a confidence
interval;

1. INTRODUCTION

The Normally Closed Valve (NCV) is being designed and used only as a nozzle valve [ 5 ]. It is a very sophisticated device, which works in a wide range of pneumatic and high water pressures. The NCV is used mostly for waterjet abrasive cutting systems and is intended for controlling high pressure water flow. Fast response for this type of control device is extremely important - stop / start operation has strong impact on quality of cutting. Instantaneous opening / closing should be possible at all pressures. The existing NCV is a very safe, fast responding and reliable valve. However, the main goal of this investigation is to overlook the existing design of the NCV and show ways to improve its characteristics.

The most important characteristic of the valve is its reaction speed [4]. This is especially important in numerous
piercing
operations. In turn, the speed of reaction is determined by the forces applied to the movable parts of the valve.

Theoretical calculations of the closing time for the NCV as a hydromechanical system are possible, but several unknown parameters, mostly internal friction, make results unstable or even unpredictable.

An experimental approach is preferable for a case like this. The multifactor method of experiment, suits this investigation better.
Results of the analytic investigation would be
compared with polynomial models such as linear and mixed.

2. DESCRIPTION.

The standard NCV [3] is a pneumatically actuated, normally closed, on/off valve with an integral nozzle. The NCV is designed to accept a wide variety of orifice mount assemblies and nozzle nuts to accommodate specific cutting or trimming applications. For safety
reasons it should be closed by spring force without any certain air pressure for the entire range of high water pressure.

Although serving the purpose, these valves have seat in high-cycling applications due to the constant pounding between the two
components. NCV is called the normally closed valve because the valve port is closed by the valve stem through spring force exerting on the actuator piston.

To open the outlet port of such valves, compressed air is introduced into the actuator chamber below the piston to lift the piston against the spring, thus releasing the downward force acting on the valve stem. Venting the compressed air will again close the outlet
port. Since the spring force is directly transmitted to the valve seat through the valve stem, a striking force of significant magnitude is produced during the time that the outlet port is opened and closed. The exact magnitude of this force is a function of the spring involved and the fluid-induced force on the valve stem.

The design of the NCV are shown in
Fig.1
, where
Body (1), Cylinder (2), Nut (3), Seat (4), Stem (5),
Back-up (6), Ring-b/u (7), Seal (8), O-ring (9), Cap (10), Piston (11), Springs (12), O-ring (13), O-ring (14), Seal (15), Plastic cap(16) are parts of the valve.

The NCV principles of operation are depicted in the figure shown. As the steam (5) moves through seals (6), (7), (8), (9) and finally departs from the seat (4) surface, the high-pressure water flows through channel (19), seat (4) channel (20) and the orifice (not shown) in the form of a dense high-energy jet.

In the static state, the steam is seated against the nozzle due to the spring (12) force which exceeds the force generated by water pressure at the inlet port (19). When the shop air is applied and fills the chambers
(17), (18)
, the air pressure acting on the
piston (11) will result in an opposing force to the spring force.

3. THEORETICAL FORCE ANALYSIS.

The Normally Closed Valve is a hydro-pneumo- mechanical system which works under the balance of mechanical (spring), hydraulic (high water pressure) and pneumatic (air pressure) forces. The fourth component of force is friction, because several parts in the NCV move during the open / close procedure.

In turn, the high pressure water force contains two components. The first is a static pressure force which is applied to the cross section of the stem against the spring force. The second is a dynamic component, which is developed by a flow of liquid (drag force) and is also applied to the stem in the nose area in the opposite direction. The air pressure force is a force developed by the static air pressure and applied to the piston. The spring force is a force which is developed by springs and is also applied to the piston but in a direction opposite of the air pressure force.

Let's take a closer look at these forces, which are responsible for the closing time value.

There are a five forces (components of the total force which is applied to the stem and piston inside NCV) responsible for the movement and closing/opening procedure:

1. The high water pressure force is calculated by using a formula:

2. The air pressure force is calculated by using a formula:

3. The spring force is calculated by using a formula:

4. The drag force is calculated by using a formula:

5. The friction force is calculated by using a formula:

Where:

CD
- the coefficient of drag for the nose of the stem, approximately equal to 1, if the Re number stays in the range of 10 to 500,000;

V
- the speed of water flow (m/sec). The speed which is calculated by fluid flow finite element analysis will not exceed 40 m/sec in the minimum cross section of the flow (around nose of the stem).

F
nk
- the radial component of forces such ass weight or other forces (N).

Finally, the total force which is

applied to the stem and piston is:

For the first calculation let's assume that - the total force is a constant during the closing / opening of the valve.

This assumption will give us the minimum possible value for the closing time.

By using Newton's equation, in this case of constant

forces, we can define closing time by the formula:

Note that the closing time is calculated from the moment of time when the stem / piston system began movement until the moment when the stem contacted the seat.
For the practical range of changes in these parameters of the real NCV we will receive the value for the closing time as represent on Fig.2.

According to this calculations and Fig.2 notes:

1. The distance of travel is approximately less then 0.005 m (0.2 inch) f
or the existing design
of the NCV.

2. The total internal force of the NCV does not exceed 3000 N for investigated design, the maximum water and

air pressure, and for the highest friction coefficient .

air pressure, and for the highest friction coefficient .

3. According to the result of this calculation, the closing time for the total force of 1500 N is less than 1.25 msec

for a full 0.005 m stroke.

for a full 0.005 m stroke.

4. Definitely more accurate results for the closing time could be obtained if all of the forces influencing the

movement of the piston /stem system were accounted.

movement of the piston /stem system were accounted.

Actually, the internal forces are changed in time and the real dependence on these forces has a very complicated character. The real diagram for the real water, air, spring, drag and friction forces, measured inside the NCV, is shown in Fig.3.

From the diagram in Fig.3, we can see that the total force during opening / closing is changed by linear law. That means the total force is a time proportional. Now, let's do some more accurate calculation of the closing time in an assumption that the closing force changed in a time by known law.

Assume that in general

and for a different "n"
overview of three different models
for

the
Ftotal
,
which is
dependent
on the time by linear, by quadratic or by square
:

Model #1:

Model #2:

Model #3:

The Fig.4 represents the difference between those models, and we can see behavior of the total force for both nonlinear models. Practically it is very unlikely that friction force disaccelerate stem/piston a
very significant in initial study of movement, as model #3 shown. The linear model seems to be more realistic.

The well known Newton's equation
was used
to

computing the closing time for these models:

After some transformation, the expression for closing time was
received
:

Considering the equations (8), (9) a result for variable closing
time,
T, is obtained:

Substituting in equation (10) all "n" for the different models, was received:

Model#1 :

Model#2 :

Model#3 :

Fig.5 represents the result of the calculation of closing
time by these equations, which more
or less considers the real characters of the internal forces of the NCV.
Note that this analysis was done
without the calculation of deformations
of the walls and seals, without the calculation of the friction forces.

A couple of words about the
friction forces. There are at least two wear couples where friction has a place
and has a substantial level. These are a piston / cylinder pair and a stem /
seal pair. Behavior of the forces is practically unpredictable, because the friction force depends on the condition of the O-ring,temperature,oilability, from the relative speed of wear parts, geometrical parameters (concentricity, misalignment, clearance etc.) and materials, i.e. from the coefficient of friction. The magnitude of these friction forces has a very strong dependence on the performance of each valve
individually, but for all tested NCV's never exceed 250 N.

As a result of friction force action, the moment of time when the valve should be closed was changed significantly and the closing times were substantially increased. We can prove this by result of experiment.

4. DESIGN OF EXPERIMENT

Theoretical calculations of closing time for the NCV as a hydromechanical system are possible, but several unknown parameters, mostly the internal frictions, could bring the different results. Because it is a very complicated problem, and the behavior of some parameters is unpredictable, a n experimental approach is preferable for this
particular case.

The multifactor method of
experiment (design of experiment), is better for this investigation. The result of this experimental investigation could be polynomial models (for closing time, for example)
such as linear or mixed.

During the
multifactor method of experiment (design of experiment)the next procedure is followed:

Select the most important factors and the range of their variation.

Select the effects or responses, which is most important, for an understanding of the process.

Select the plan (matrix) of the experiment (full, part, type-latin, square, star, etc.).

Make the right selection of the type of the model (linear, nonlinear, etc.).

Make a statistical analysis of the results of the experiment and receiving polynomial equations.

Check the adequation of the model for the F-criterion and check coefficients for the t-criterion.

Analyze the final system of equation with coefficients above the significance level and look over the model.

Select the most important factors and the range of their variation.

Select the effects or responses, which is most important, for an understanding of the process.

Select the plan (matrix) of the experiment (full, part, type-latin, square, star, etc.).

Make the right selection of the type of the model (linear, nonlinear, etc.).

Make a statistical analysis of the results of the experiment and receiving polynomial equations.

Check the adequation of the model for the F-criterion and check coefficients for the t-criterion.

Analyze the final system of equation with coefficients above the significance level and look over the model.

Select the most important factors and select the range of their variation.

Three factors were chosen for the process variables, in the factorial experiment plan, which influent the closing time:

Three factors were chosen for the process variables, in the factorial experiment plan, which influent the closing time:

X1
- is High Water Pressure (HWP) and represents the water force;

X2
- is Diameter of the Water Orifice (DWO) and represents the flow and indirectly the drag force;

X3
- is Air Pressure (AP) and represents the air force and indirectly the friction forces.

The spring force is not included because it is a constant.

The spring force is not included because it is a constant.

All the other variable parameters, such as orifice tube size and length, jet inclination angle, fluid type, orifice material, crystal structure and shape were maintained constant during the experiments.

Let's select all effects or responses, which are most important for understanding of this process. Because we are looking for a dependence between time of response (closing time - CT) and our variables, which are described
above, it is better to select the following responses:

Y1
- Closing Time (CT),

Y2
- Air pressure after Closing (AC),

Y3 -
Air pressure after Opening (AO),

Y4
- Friction air Pressure (FP).

These variables (factors) in original units and

in coded units are represented in the matrix:

VARIABLES IN ORIGINAL UNITS

We have selected the friction air pressure, because the opening or closing speed and closing time is a function of actual air pressure, water pressure, orifice size and internal friction. In turn, the internal friction is defined by excessive air pressure necessary to overcome the friction force.
Coded units are connected with the original by these equations (11):

X1
=(Pw
-284.1)/71;

X2
=(Do
-0.254)/0.1016;

X3
=(Pa
-0.5327)/0.0355

Selection of the plan of the experiment.

For this investigation, the Box-Benken plan of experiment [ 1 ] with 3 factors and 2 level for variation of their parameters was selected. The factors HWP , DWO, AP had two level of value: +1 and -1 are represented in the matrix below:

Two levels were selected for these variables and each point was replicated three times.

In order to reduce the influence of a possible uncontrolled systematic error in the exp., the cuts were performed on a random sequence with the only constraint that two replicated cuts could not be performed on the same speciment.

This Box-Benken plan is full, including a combination of 8 experiments, symmetrical relatively to the center of experimental field and allows us to obtain a model with liner and interactive effects. It provides a readily generalized method for direct and exact calculation.

In order to reduce the influence of a possible uncontrolled systematic error in the exp., the cuts were performed on a random sequence with the only constraint that two replicated cuts could not be performed on the same speciment.

This Box-Benken plan is full, including a combination of 8 experiments, symmetrical relatively to the center of experimental field and allows us to obtain a model with liner and interactive effects. It provides a readily generalized method for direct and exact calculation.

Selection of the type of model.

We are looking for a dependence between Response
Time (RT), Air Pressure after closing (AC), Air Pressure after Opening (AO) and
Friction Air Pressure (FP) and our variables, which are described
above.

First of all, let's assume
that function has a normal distribution.

Then we can assume that this
dependence is a polynomial function of the kind :

1. Linear
model:

(simple linear model of the
factors)

2. Mixed non-quadratic
model:

(linear model with effect of
interaction)

Where:

u,j=1,2, ... ,k - numbers of
the factors,

Experimental apparatus.

The normally closed valve
used for experiments was a conventional valve, after 50000 opening / closing cycles under a certain amount of pressure. High water pressure came from a high pressure pump made by Ingersoll-Rand Inc. Air pressure used by conventional air supply line. High water pressure and air pressure was measured by pressure sensors made by Autoclave Inc.
Response time was calculated as the difference between relay signal and jet impact time. Impact time was registered by a strain gage lever with stand by distance of about 0.0125 m. Friction
force was registered by a load cell with a special stem end. All sensors
were connected by Keithley Metrabyte DAS K-500 data acquisition system and recorded with a frequency of
100 Hz. Result of the experiments are represented in matrixes R1, R2, R3 (see applications).

Linear model.

For s tatistical analysis of the result of the experiment were calculated coefficients

of the polynomial equations, of linear model, using formula (12) and the

r esults of these calculations are shown in the matrix B.

In order to check the model adequation, the experiment #R2-2 was repeated 3 times and standard deviation was found. Results of experiment #R2-2 and calculations of the deviation are shown in matrix
R4.

After that, the model was checked for adequation for the F-criterion (Fisher Criteria) and a value of coefficients for the t-criterion was found.

In our case, F=0.5 and from [ 2 ] we have F(2;4)=6.9 .

In our case, F=0.5 and from [ 2 ] we have F(2;4)=6.9 .

This means that the calculated F is significantly smaller than the F-criterion form the table, and it means that the model is adequate.

After the confidential interval was built and, using the t-criterion (from Student's distribution),all coefficients were checked for a significance, a final system of equations of four
linear polynomial equations (13) for responses (linear model ,all factors coded, dimensionless) was received:

For Closing Time (CT)

For Air pressure after Closing (AC)

For Air pressure after Opening (AO)

For Friction Pressure (FP)

Linear with effect of interaction model.

Same results of the experiment were used and same procedure was repeated for the other model - linear with effect of interaction. Results of these calculations are represented in matrix B2.

This model also was checked for the F-criterion (Fisher Criteria) and a value of coefficients for the t-criterion was found.

In this case F=0.5 and from [ 1 ] we have F(2;4)=6.9.

This means that model 2 is adequate.

After the confidential interval was built and all coefficients were checked for a significance, a final system of equations of four linear polynomial equations for responses (linear model with effect of interaction, all factors coded) was received:

For CT

For AC

For AO

For FP

5. ANALYSIS OF RESULTS

Now let's look over the results and influence of each factor on the effects starting with the Linear model.

First of all, the system of equations (13) or (14) is 3-dimentional and difficult to reflect on 2-dimentional pages.

This means we will try to keep one (or two) factors constant in order to investigate the influence others on effects. Let's start with the internal Friction force and recalculate last equation for system (13) for worse friction conditions when X1=1, X2 =1 (Pw=355 MPa , D= 0.3556 mm) and Air Pressure varial from 0.4972 to 0.5682 MPa . After some transformations of the system (13) we obtain:

Friction Pressure, kPa

Equivalent Static Friction Force, N

We can see (Fig.6 ) a linear dependence between friction air pressure,or static friction force,and air pressure, with a full range of about 125 N. We selected friction air
pressure, because the opening or closing speed and closing time is a function of actual air pressure, water pressure, orifice size and internal friction. In turn, the internal friction is defined by excessive air pressure is necessary to overcome the friction force. Notice, that force decrease with increasing of the air pressure.

Now, look over the other responses. Since, we can look over the influence of just 2 parameters, we can assume that X3=0 (Pa=0.5327 MPa ) and recalculate the system of equations (13) to create a group of plots.

Finally, we get charts Fig.7a, 7b, 7c , which represent the dependencies of these parameters on water orifice size (flow) and high water pressure. As we can see the closing time by experiment and first of polynomial
equation from system (13) approximately 10 times bigger then calculated by formulas (7) - (10), which not include friction as significant force.

The next step is to look over the more complicated model - the linear with an effect of interaction (mixed non-quadratic). We will follow the same procedure, and first of all look over the worst case for Friction force when X1=1 and X2=1 (Pw=355 MPa , D= 0.3556 mm) and recalculate the system of equations (14) for these conditions:

Friction Pressure, kPa

Equivalent Static Friction Force, N

For this model we can also see (Fig.8 ) a linear dependence between friction air pressure,or static friction force,and air pressure, with a full range of about the same 125 N. Notice, that in this case the force also decreases with an increase of the air pressure. For the other equations from (14), we will review
the influence of just 2 parameters, in assuming that X3 =0 (Pa=0.5327 MPa).

Finally we get charts Fig.9a, 9b, 9c , which represent dependencies of these parameters on orifice diameter and high water pressure. Notice, that the s econd model brings more accurate results and in investigated area of changes of the factors, the dependence of air pressure (when NCV is open) vs. water pressure and flow has almost a linear character.

The dependence for Closing Time and air pressure (when NCV is closed) vs. high water pressure and water flow shows as non-linear.

For the most farthest point of investigated factors (1,1,1) and (-1,-1,-1) the difference in results of calculation for the system of equations (13) and (14) could reach 10% for CT, 5% for AO, 10% for AC, and 30% for FP.

According to a simple linear model the closing time changed between 30.5 - 77.75 msec, according to the linear model with an effect of interaction between 37.87 - 85.12 msec.

As a first investigation, however, the equations (14) had demonstrated to be a fairly good approximation.

According to a simple linear model the closing time changed between 30.5 - 77.75 msec, according to the linear model with an effect of interaction between 37.87 - 85.12 msec.

As a first investigation, however, the equations (14) had demonstrated to be a fairly good approximation.

6. CONCLUSIONS

1. Two systems of polynomial equations for two different models, which define the closing time and other parameters of NCV were received.

2. The system of equations (14) gives us a possibility to estimate the closing time and other parameters of NCV with higher accuracy than the simple model, if water pressure does not exceed 213...355 MPa, air pressure 0.49...0.57 MPa and orifice size 0.1524...0.3556 mm ranges.

3. Inside the area of the multifactor experiment (-1,-1,-1)...(1,1,1) the closing time is changed from 38 to 85 milli seconds and has a maximum for (-1,-1,-1) and minimum for (1,1,1).

4. Inside the area of the multifactor experiment (-1,-1,-1)...(1,1,1) the air pressure after opening is changed from 312500 to 419100 Pa and has a maximum for (-1,1,1) and minimum for (1,1,1).

5. Inside the area of the multifactor experiment (-1,-1,-1)...(1,1,1) the air pressure after closing is changed from 120750 to 312500 Pa and has a maximum for (-1,1,1) and minimum for (1,-1,-1).

6. Inside the area of the multifactor experiment (-1,-1,-1)...(1,1,1) the friction pressure is changed from 850 to 29300 Pa and has a maximum for (1,-1,-1) and minimum for (-1,1,1). The static
friction force is changed from 3 to 110 N.

7. The closing time is mainly caused by the high water and air pressure load. The effect of the orifice size load becomes significant, while the air pressure grows.

ACKNOWLEDGMENTS

The author gratefully acknowledge significant contributions of Jose Munoz for actively supporting the research and development over many years.

REFERENCES

1. Box, G.E.P.,
Hunter, W.G., Hunter, J.S., "
Statistics for experimenters,"1978, by
John Wiley & Sons, Inc.

2. Jaccard,
J., Becker, M.A., " Statistics for the behavioral sciences,"1990,
by Wadsworth Publishing
Company.

3. Miller, J., " High Pressure Valve Assembly, Service Maintenance
and Repair," Ingersoll-Rand
Waterjet Cutting Systems , Rev.3,
1993.

4. Yie,
G.G., " High Pressure Flow Control
Valves," Proceeding of the 6th American
Water Jet conference , pp.575-589, Water Jet Technology Association,
Houston, Texas, 1991

5. Zaring,K., " Advanced abrasive-waterjet hardware and cutting
performance," Proceeding of the 5th American
Water Jet conference ,
pp.473-483, Water Jet Technology
Association, Canada, 1989.

TABLES, FIGURES, AND ILLUSTRATIONS

X1 X2 X3
Y1 Y2 Y3
Y4

X1 X2 X3
Y1 Y2 Y3
Y4

X1 X2 X3
Y1 Y2 Y3
Y4

Where:

X1 - HWP (kpsi) , Y 1 - CT
( msec)

X2 - DWO (mills of inch) , Y2 - AC
( psi),

X3 - AP (psi) , Y3
- AO ( psi)

Y4 - FP (psi)

Force, N

Stroke, mm

Water

Air

Friction

Drag

Total

Spring

For CLOSING TIME
(msec):

For AC (kPa):

For AO (kPa):

For FRICTION PRESSURE
(kPa):

Mathcad
file developed by Dr. Roman N Tunkel,

Advance
Development Center, Waterjet System Division, Ingersoll-Rand
Co.

tunkelr@juno.com,
02/12/1996