0162-A2
Maria PENTILESCU 1
The work presents the preliminary results of the maximizing for the plywood pressing process through experimental-statistic methods.
One system can be represented in two ways in order to be maximized:
The plywood pressing process may be considered as being a system which can_t be represented; but working, and its maximizing can be estimated in an experimental way, and the black-box principle.
According to this principle the variables, which have to be maximized, are modified under control according to an experimental plan and the value of the maximizing criteria is evaluated for each state of the system.
From the multitude of the experimental data which includes the variables values and the adequate answers, an estimating value is evaluated for the objective function; this local evaluation of the objective function allows the orientation and moving of the answer_s surface for maximizing and finally to reach the maximum.
The experimental-statistic scientific researching has three steps, as follows:
The first stage in a maximizing process is choosing the performance of the specific feature (objective function) and its evaluation in order to make the decisions.
The magnitudes, which characterize the plywood pressing process can be found in the special literature and the actual standards and show much more specific features as follows: the cutting strength of the glued plywood_s, the traction strength, the resilience modulus, etc.
The industrial usage endorsed as a performant specific feature for the plywood gluing cutting strength (tmin=1,8 MN/m2 for dried test-pieces).
The variables for maximize (independent) are representing some magnitudes in the maximizing process. These are chosen according to the theoretical studies.
The most important factors were chosen after the analysis of the antecedent information and were proposed by the technologists to be the possible factors, which have the influence and the plywood strength. After the analysis, seven factors were chosen in order to be put in the process model.
For the right choosing of the factors variables, the way in which they have an influence in plywood_s strength has to be known [3].
The factors which have influence in the pressing process.
Table 1
The choosing of the mathematical model allows the option for one kind of function and degree, which will be finally, as a mathematical model, the researched process.
If the answer function can be written as follows: y = f(x1, x2,_xk) (1) in which: y-the dependent variable (the objective function);
x1,x2,_xk - maximizing variables (the process_ factors)
By developing the answer function in Taylor series, around one point, results that any function can be approximated like this:
In our case, a first-degree polynomial was chosen, in order to determine only the direction for the maximizing.
The type of experiment is chosen so as number of the experiments to be higher than the equation coefficients, which are determined. Because for the first stages of the researching, we want to get same information about the answering surface shape and the approximate positioning of the maximizing, we had to choose a factorial fractionate experiment as 27-4 .This experiment gives us less information than the factorial experiment 27, but has more experiences, and allows us to calculate an approximate straight model:
Y=b0 + b 1x1 +b 2x2 +_+b 7x7 (5)
The fractionnel experiment matrix.
in which was codified with +1 the maximum value, which the factor can have and with _1 the minimum value.
After programming the experiment, we put it in practice. In this case a stand was designed for the interior plywood, of beech, with g=3mm, with a 3 layers structure with gveneer=1,1mm, for measuring and verifying the independent variables values and another stand, for the measuring of the breaking forces (the dependent variable) of gluing through netting process for plywood. In order to respect the right values of the independent variables some technical and organizational measures were taken. The uniformity of the thickness and humidity of the veneer, the viscosity of the solution and the specific consumption using adequate devices and instruments. The maintenance of the package before it was introduced in the press was no more than 3 minutes. The glue was formaldehyde, type PN and was prepared according to the following recipe:
The conditions for the plywood pressing experiment.
Table 3
The plywood pressing was realized with a small multitiers press.
After a conditioning of 24 h a t=200C and the relative humidity of 55%, the same test-pieces were cut from the plywood in order to determine the shearing resistance of the gluing (in conformity with
STAS 1809/87). A testing device MTT Timisoara was used. The value of the shearing resistance for the gluing was evaluated with the formula: [N/mm2] (6)
In which: Pr-the breaking loading, in N;
b-the real breadth of the shearing surface, in mm;
l-the real length of the shearing surface, in mm.
The 8 experiments had 3 testings and the results are in the table 4.
In this stage the statistic analysis of the results obtained by the determination of the experimental error was done (the dispersion of the reproducible results) and also the checking of the dispersions_ homogeneousness.
Experimental results. Table 4
The dispersion was done by the following formula from the results of the concomitant determinations:
(7)
where:Su2 =the dispersion of the data series;
u = the number of the determinations;
n = the number of the concomitant experiences;
= the arithmetic average of the results from the concomitant experiments.
The homogeneousness of the dispersions was verified by the Cochran criteria:
(8)
Comparing Gcalc to Gtab for the trusting level =0,05 and the liberty degree =n-1=2, Gcalc =0,296<Gtab=0,516 so as the dispersions are homogeneous.
The dispersion of the reproducible results came from the formula:
(9)
N- the number of experimental points.
After the statistic analysis of the results, the mathematical model is followed by the calculation of the regression equation coefficient and their statistic checking.
The experimental data for the calculation of the bi coefficients, and the necessary data to verify the straight model are in table 5. The programming matrix and the experimental result Table 5
For the calculation of the bi coefficients from the regression equation, which realizes the concordance between model and data the following formula, was used:
and the deviation square average in determining the coefficients is:
The trusting interval in which the coefficients were calculated is:
(12)
CT = represents the Student criteria which for a=0,05 and N=8, CT=2,3
The statistic verifying of the regression coefficients values is made by the condition in which the absolute value of the bi coefficient has to be higher than the trusting interval Dbi.
From this analysis can be nattier that the 2 coefficients b1 and b4 are insignificant; the x1 and x4 factors have a small influence on the process, and they can be excluded from the regression equation, by fixing them at the same levels.
After excluding the two factors, the straight model of the process is:
]=3,26+ o,63x2 _0,54x3 +0,47x5 + 0,46x6 _0,41x7 (13)
In this equation x2,x3,_x7 are representing the code values of the factors.
The concordance of the model for the maximizing was realized by the Fischer criteria, which value can be determined by the formula:
(14)
In which Scon= the dispersion made by the calculated model.
S0=the dispersion of the reproductive results.
(15)
Yu-the calculated values by the help of the regression equation;
- the experimental values.
- the number for the liberty degrees.
Comparing Fcalc and Ftab for a trusting level a=o,o5 and the liberty degrees n1=N-K_=8-6=2,n2=n-1=3-1=2, Fcalc=2,84<F0,05;2;2=19, that means the model_s concordance is verified and this can be used for maximizing the process.
Coming back to the determined equation we can appreciate, in variation intervals chosen for the factors, which is their influence and the maximizing parameter. The most powerful influence has the x2(b2=0,63) factor representing the glue viscosity.
Analyzing the coefficients_ signs we can notice that when the values of the factors are increasing x3 (the veneer humidity), x7 (the time after the glue preparing) the quality of the plywood is lower (the gluing resistance of the veneers).
We can notice that from the first experiments important information were obtained about the analyzed process.
Interpreting the results is graphic presented by using a three-dimensional coordinate system as in fig.1; fig.2; fig.3; fig.4.
Fig.1. Plywood resistance as a function of pressing time and pressure
Fig.2. Plywood resistance as a function of veneer humidity and glue viscosity
Fig.3. Plywood resistance as a function of pressing time and glue viscosity
Fig.4. Plywood resistance as a function of pressure and glue viscosity.
Dancea, I., Methods of Optimisation. Ed. Dacia, Cluj - Napoca, 1976.
Maiorescu, V.D., Laurenzi, V., Bases of experimental research in wood industry. Rep. of University -
Brasov, 1994. Mitisor, Al., Istrate, V., Technology of veneers, plywood and fibreboard, Ed. Technique, Bucharest, 1976.
Stanea, V., Wood - working machines, EDP, Bucharest, 1996.
Taloi, D., Maximizing the metallurgy process, Ed. Of Academy, Bucharest, 1976.
1 Diplomat engineer
Suceava, Romania