Full Factorial DOE to determine and optimize [624079]

Full Factorial DOE to determine and optimize
the equation of impact forces produced by water jet used in sewer cleaning
Nicolae Medan1,*, Mihai Banica1, and Sandor Ravai-Nagy1
1Technical University of Cluj-Napoca, Department of Engineering and Management of Technology,
Victor Babes 62A, Baia Mare, Romania
Abstract. The functioning of the equipment to cleaning sewer is
dependent on certain process para meters, which can vary, causin g
variations of the impact forces. The purpose of this paper is t o determine
and optimise the equation of the impact forces produced by wate r jets used
in sewer cleaning. The research method to measure the impact fo rces is the
experiment using full factorial design of experiment. To can ma de the
experiments was used a stand to g enerate the water jets and a d evice to
measurement the impact forces. In the first part of paper was d etermine the
equation of impact forces produced by water jet and then was re alised a
multiple linear regression model in three different ways to opt imised the
prediction of the proposed equation.
1 introduction
I n d u s t r y w a t e r j e t t e c h n o l o g y i s f r e q u e n t l y u s e d i n a l o t o f a r eas such: concrete
hydrodemolition, jet cutting for different type of materials, m echanical processing of
minerals, medical applications, rock fragmentation, surface pre paration for protective
coatings [1]. Industrial cleaning is a classic application of w ater jets technology. In the late
1950s, when reliable high pressure pumps were built, the usage of water jets spread widely
in the field of pipes and sewerage cleaning.
Phenomena that occur in the clean ing water jets are complex. Ad ler [2] describes
mechanisms occurring at the imp act of a jet with a surface. Lea ch et al [3], Leu et al [4] and
Guha et al [5] analysed pressure distribution along centreline of the water jet.
The regular cleaning of the mater ials deposed in sewer networks is realized, especially
with equipment that uses high pressure water jets. The function ing of this equipment is
dependent on certain process para meters [1] that can vary, caus ing variations of the impact
forces. The impact for ces directly affect t he cleaning of sewer systems.
To determine an equation who described the values of impact for ces in concordance
with the process parameters is necessary to realised practical experiments to determine the
values of impact forces for diffe rent set-up values of process parameters [6,7].

* Corresponding author: [anonimizat]

2 Apparatus used and met hodology of the measurements
To measure the impact forces produ ced by water jet, were used a nd built a stand for
generating pressure jets, as we ll as a device to measure the im pact force [6].
2.1 Stand to generate pressure water jets
Schematic diagram of the stand to generate pressure jet is show n in figure 1.

Fig. 1. Schematic diagram of the stand to generate pressure jet
Component parts of stand: (1) electric motor (2) flexible coupl i n g ; ( 3 ) h i g h p r e s s u r e
pump, 4) pressure regulator, 5) pressure gauge, 6) nozzle, 7) t ap water, 8) water tank, 9)
chassis. Water coming out of the high-pressure pump (3) goes in to the pressure regulator
(4). Through it adjusts the pressure and flow of water in the p ath of the high-pressure water.
This pressure corresponds to the one at the outlet of nozzle.
2.2 Stand to generate pressure water jets
In figure 2 is represented the principle diagram of the device for measurement the impact
force of the water jet produced when the w ater jet hit a flat a nd rigid surface.

Fig. 2. Diagram of the device for measurement the impact force of the w ater jet
Main component parts of the device are: 1) high-pressure water hose, 2) support nozzle,
3) nozzle block, 4) nozzle, 5) wa ter jet, 6) flat and rigid tar get plate, 7) collection path
water, 8) scaled container for measurement of the flow of water jet, 9) piezoelectric sensor
mounting, 10) piezoelectric sensor, 11) data acquisition Person al Daq/3000, 12) computer
for the processing of data; 13) support plate, 14) acrylic tube , 15) rods for adjusting

distance x. From high pressure wat er hose (1) come water at a c ertain pressure p desired. At
the outlet of nozzle is generated a water jet (5) that striking target plate (6), who is located
at a certain distance x in front of the nozzle. The jet (5) gen erates an impact force at a time
when he meets target plate (6). This force produces axial movem ent of target plate. This
movement is converted into an electric signal by the piezoelect ric sensor (10). Electrical
signal is collected by data acquisition Personal Daq/3000 (11), w h i c h f o r w a r d d a t a t o a
computer (12) using DaqView soft processes data actually obtain ed.
2.3 Methodology of the measurements
The research method of this study is the experiment. To determi ne the values of impact
forces produced by water jets is used the full factorial method . To determine the impact
forces, it is necessary to set up the experimental domain.
In the water jet cleaning proces s, a series of parameters are i nvolved [1]. These
parameters can be divided into two major groups, namely: 1) tar get parameters which shall
be defined according to the contact area between the water jet and the surface to be cleaned
and 2) process parameters. In the measurement of the impact for ces of a stationary water jet
and flat and rigid surface the pr ocess parameters are involved.
2.4 Setting up the experimental domain.
The process parameters that influence the impact force are: 1) D nozzle diameter, [mm]; 2)
P water pressure, [bars]; 3) x d istance between the nozzle and impact surface, [mm]; 4) α
impact angle (angle formed by th e jet and impact surface), [0].
The value of diameter of nozzle are D=1mm, 1.5mm and 2mm. These are common
values used in equipment to mai ntenance and clean ing of sewers.
The pressures used to perform th e measurements have the values p=100 bars, 120bars,
140bars, 160bars, 180bars and 200bars. For the maintenance sewe rs, are used high pressure
water pumps which generate a maximum pressure of 200 bars.
To perform the measurements distance x has been fixed at the va lues x=25 mm, 50 mm,
75 mm, 100 mm, 125 mm, 150 mm, 175 mm and 200 mm.
The impact angle α has values 600, 750 and 900. For cleaning heads, usual value of the
angle of impact α is 750. If impact angle α decrease below 600 leads to a drop in of the
impact forces. In table 1 are presented the process parameters and levels values according
with full factorial method.
Table 1 . The values of the parameters for full factorial method.
Abbreviation Parameter Values
A Nozzle diameter D [mm] 1, 1.5, 2
B Pressure p [bar] 100, 120,140,160,180,200
C Impact angle α [0] 60, 75, 90
D Distance x [mm] 25, 50, 75,100,125,150,175,200
Corresponding to the 4 parameters and second-degree interaction s of the parameters, for
full factorial method result a plan of experiments who contain a number of 144
experiments.
Based on the parameters established in accordance with Table 1 the impact forces were
determined. For each experiment was performed three measures of impact force and still it
has worked with F med, representing the arithmetic average of the three forces measu red.
Results a total of 432 measurements.
For brief of this paper, we dare not to present the table with the values of F med obtained.

3 Results
For determine the equation of impact forces, in the first step it is necessary to determine the
contribution of each parameter and their interactions.
3.1 Determining the contributions of the parameters and their i nteractions
To calculate the contributions of parameters and their interact ions was used the values of
Fmed obtained in concordance with design of experiments. Using the full factorial method
has conducted an analysis of the variance to determine the infl uence of each parameter and
their interactions on the impact force. In table 2 is presented the analysis of the variance,
using Minitab 17.
Table 2 . Analysis of Variance (Minitab 17).
Source DF
(degree of freedom) SS
(sum of square) Contribution
Regression 10 162559 99.14%
Diamete r 1 116939 71.32%
Pressure 1 29592 18.05%
Angle 1 5959 3.63%
Distance 1 389 0.24%
Diameter*Pressure 1 7596 4.63%
Diameter*Angle 1 1523 0.93%
Diameter*Distance 1 148 0.09%
Pressure*Angle 1 385 0.24%
Pressure*Distance 1 20 0.01%
Angle*Distance 1 5 0.00%
Error 421 1406 0.86%
Total 431 163965 100%
3.2 Determining the regression equations of impact forces
According to the results obtain in table 2, the next step is to determine the equation of the
impact forces using only the para meters and interactions previo usly set.
Using Minitab 17, the multiple linear regression model of impac t forces was determined
(equation 1):
22.91 32.97 0.2088 0.26 0.30072 0.3755         medF AB C A BA C ( 1 )
This multiple linear regression m odel was obtaining without Box -Cox transformation.
In table 3 is presented the analysis of variance of equation (1 ).
Table 3 . Analysis of Varian ce for equation 1.
Source DF
(degree of freedom) SS
(sum of square) Contribution
Regression 5 161610 98.56%
Diamete r 1 116939 71.32%
Pressure 1 29592 18.05%
Angle 1 5959 3.63%
Diameter*Pressure 1 7596 4.63%
Diameter*An gle 1 1523 0.93%
Error 426 2355 1.44%
Total 431 163965 100%

The regression statistics of equation (1) are: R squared: 98.56 % , R s q u a r e d a d j u s t e d :
98.55% and R squared predicted: 98.52%.
To optimise the equation (1), the next step is to be made a reg ression using Box-Cox
transformation with rounded λ . Result the equation (2):
 ln 0.618 1.3611 0.007137 0.00969     medF AB C ( 2 )
In table 4 is presented the analysis of variance of equation (2 ).
Table 4 . Analysis of Varian ce for equation 2.
Source DF
(degree of freedom) SS
(sum of square) Contribution
Regression 5 178.455 97.56%
Diamete r 1 143.163 78.27%
Pressure 1 29.325 16.03%
Angle 1 5.959 3.26%
Diameter*Pressure 1 0.009 0.00%
Diameter*An gle 1 0.00 0.00%
Error 426 4.462 2.44%
Total 431 182.917 100%
The regression statistics of equation (2) are: R squared: 97.56 % , R s q u a r e d a d j u s t e d :
97.53% and R squared predicted: 97.50%.
Another possible optimisation of equation (1) is realised made a regression using Box-
Cox transformation with λ=0.5. Result the equation (3):
0.50.097 0.216 0.00082 0.0002 0.01428 0.0173         medF AB C A B A C ( 3 )
In table 5 is presented the analysis of variance of equation (3 ).
Table 5 . Analysis of Varian ce for equation 3.
Source DF
(degree of freedom) SS
(sum of square) Contribution
Regression 5 1240.51 98.98%
Diamete r 1 963.07 76.84%
Pressure 1 214.07 17.08%
Angle 1 42.99 3.43%
Diameter*Pressure 1 17.15 1.37%
Diameter*Angle 1 3.23 0.26%
Error 426 12.79 1.02%
Total 431 1253.30 100%
The regression statistics of equation (3) are: R squared: 98.98 % , R s q u a r e d a d j u s t e d :
98.97% and R squared predicted: 98.95%.
In table 6 are presented the regression statistics for all of t hree equations determined.
Table 6 . Regression statistics for all 3 equations.
Type of regression Equation no. R squared R squared adjusted R squared
predicted
without transformation (1) 98.56% 98.55% 98.52%
rounded λ transformation (2) 97.56% 97.53% 97.50%
λ=0.5 transformation (3) 98.98% 98.97% 98.95%

4 Conclusions
1) In this work, it is presented a methodology to determine the impact forces produced
by water jets used in sewer cleaning. The impact forces depende nt on certain process
parameters.
2) The research method used is full factorial design of experim ent. After applying full
factorial itinerary for calculating the percentage of influence o f p a r a m e t e r s a n d t h e i r
interactions of the impact force s, it is found: nozzle diameter D is the largest influence, with
a percentage of 71.32%. In the s econd place is pressure P with a value of 18.05%, follow by
interaction between nozzle diamet er D and pressure p with a val ue of 4.63% and the impact
angle α with a value of 3.63%. The lowest value is given by int eraction between nozzle
diameter D and impact angle α with a value of 0.93%.
3) For the experimental domain, the parameter distance x has a percentage of influence
of only 0.24% for impact force s, practically insignificant.
4) According with the influence of parameters and their interac tions, was realised a
multiple linear regression model in three different ways to opt imised the prediction of the
proposed equation:
– first type regression without transformation, with R squared predicted 98.52%;
– second type regression using rounded λ transformation, with R squared predicted
97.50%;
– third type regression using λ=0.5 transformation, with R squa red predicted 98.95%.
5) The best prediction is given by the regression using λ=0.5 t ransformation, followed
by the regression without transformation. The lowest degree of prediction is given by the
regression using rounded λ transformation.
6) It is possible to improve the prediction of the equation who describe the impact
forces only using different type of regression and the same mea sured values of the impact
forces.
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