Influence of anodic oxidation factors to layer thickness by means of doe.

Hloch, Sergej ; Gombar, Miroslav

Abstract: The paper deals with mathematical modeling of dependence between anodic oxidation factors in sulfuric acid and thickness of created layer [Al.sub.2][O.sub.3]. By means of full factorial design were studied four independent variables the amount of sulfuric acid, aluminum, time and voltage. Results show the anodic oxidation factors significance and their effect to the layer thickness. It is the first step towards to the optimization of the eloxal process.

Key words: anodic oxidation, aluminum, thickness layer

1. INTRODUCTION

Anodizing is a commonly used method for surface treatment of aluminum. This is due to a number of properties offered by this technique. Depending on the process conditions the following properties can be obtained: corrosion resistance, decorative surfaces, surfaces in almost any color on the palette, except white, hard and wear resistant surfaces, electrical and thermal insulation, the surface can be used as a base for organic finishing and for plating, the anodizing technique is expected to have an increasing advantage over many (Montgomery, 1990).

2. PROBLEM DEFINITION

Technologic process of anodic oxidation in real objects is in the most of cases very dynamic and stochastic process. Analytic process identification seems to be no effective and of low practical use. By its application, it is not possible to achieve the completed model of the process--the influence of certain parameters are neglected (fig. 1), in some of the factors there are not known the exact values, they are variable in time and most often, the intuition is applied to determine them. Their complicacy incomplete knowledge functioning mechanisms and large amount factors entering to the process complicate of mathematical model fitting by theoretical and analytical methods.

[FIGURE 1 OMITTED]

Vice versa a mathematic-statistical method allows fitting of statistical models even from relative large amount input data. The figure 1 shows influence of the operation time on thickness layer (Bekes & Andonov, 1986), (Wernick et al, 1987). The anodic oxidation of process factors optimization has been accelerated because of the need for improvements of process quality. Moreover, the process features change drastically with eloxal process factors entering the anodic oxidation process. For such classic experimental design (fig. 1), some routine is needed and it is not effective from the time point of view. On the other hand, the mathematical statistical methods the statistic model designs outsourcing from the great amount of independent variables (Kreibich, 1990), (Mohyla, 1995).

3. EXPERIMENTAL PROCEDURE

In order to investigate the influence of anodic oxidation process factors on layer thickness full factorial design for four independent variables has been designed. Full factorial analysis was used to obtain the combination of values that can optimize the response, which allows one to design a minimal number of experimental runs. Four factors submitted for the analysis in the factorial design of each constituent at levels [-1; +1] are listed in the table 1.

A tank with dimension 210 x 130 x 100 mm (fig. 2) has been used with volume of electrolyte of 2.2 l. Experiment was realized at constant temperature of 21 [degrees]C, that had been controlled by laboratory thermometer. Samples that have been eloxed was connected to anode and aluminum plates were connected on pole of adjustability unidirectional voltage.

[FIGURE 2 OMITTED]

The experiments were carried out based on the analysis using Statistica 7.0 and Matlab to estimate the responses of the thickness layer h [[micro]m]. A digital thickness gauge MINITEST 400 has been used to calculate the thickness layer with 0.02 [micro]m precision of measurement. The measurement procedure consisted of measure variable dependent h with replicates of 5-times yielding total of 80 measurements.

4. RESULTS AND DISCUSSION

The quantitative description of the conditions effects on thickness layer h [[micro]m] was performed. Response surface methodology is an empirical modeling technique used to evaluate the relationship between a set of controllable experimental factors--independent variables and observed results--dependent variable thickness layer h [[micro]m]. The experiment results were analyzed using the analysis of variance. The regression coefficients and equations obtained after analysis of variance gives the level of significance of variable parameters tested according to Student's t-test. Obtained regression coefficients that show no statistical significance has been reject from the further evaluation. All terms regarding of their significance are included in the following equation (1):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

These results can be further interpreted in the Pareto Chart, which graphically displays the magnitudes of the effects from the results obtained. Fig. 3 graphically displays the influence magnitudes of the effects, which are sorted from largest to smallest, from obtained results.

From the Pareto chart is evident that the significant influence that affect the thickness layer have the interaction [x.sub.1][x.sub.3][x.sub.4] (sulfuric acid, operation time and the voltage) and the main effect [x.sub.2]--the amount of the aluminum. With the raising of the sulphuric acid amount the conditioned value of studied dependent variable--the thickness layer. The figure 4 shows the significance of the factors and their interactions that affects the layer thickness h [[micro]m]. As can be seen the most important factor affecting the thickness layer from controllable factors is the interaction--[x.sub.1][x.sub.3][x.sub.4] (29%). The second most important factor is the amount of the aluminum in the electrolyte that significance in percent proportion is 19 %.

[FIGURE 5 OMITTED]

According to (fig. 5) as the amount of the sulfuric acid and the voltage will be rising in the electrolyte, the thickness of the layer will be raising. The reverse trend has the influence of the aluminum amount in the electrolyte, at which as the amount of the aluminum in electrolyte will be higher the thickness of the deposited layer will decrease.

5. CONCLUSION

Technological process of anodic oxidation of aluminum and its alloys from the point of view of created layer pursuant of realized experiment is mainly affected by interaction of the amount of sulphuric acid and the operation time and by the voltage. With the raising of the sulphuric acid amount the conditioned value of studied dependent variable--the thickness layer. On the contrary with the raising of the aluminum amount in electrolyte the value of the thickness layer decreases. Thickness layer decreasing on operation time can be explained by process of creation and properties of anodic layer, which is none conducted. In the anodic oxidation process of aluminum, is necessary to pay attention to identify the state of the electrolyte, mainly the aluminum amount and the amount of the overall and free sulphuric acid. Relative high influence on thickness created layer has the electrolyte temperature that was constant at the experiment. The total rate evaluated factors and further neglected factors that affect the anodic oxidation process, by means of statistical analysis represent 54%. In further research it will be necessary to study those factors, which affect the created layer.

6. REFERENCES

Montgomery, D. C. (1990). Light Metals Finishing Process Manual, AESF.

Wernick, S., Pinner, R. & Sheasby, P. G. (1987). The Surface Treatment and Finishing of Aluminium and its alloys, 5th edition.

Kreibich, V. (1999). Theory and technology of surface treatment. ES EVUT Praha.

Mohyla, M. (1995). Metal surface treatments technologies. VSB Ostrava.

Bekes, J., Andonov, I. (1986). Analysis and synthesis of the engineering processes and objects. 1.edition., Bratislava: Alfa, pp. 376.

Table 1. Evaluated factors at the anodic oxidation.

 Factors Factor level

Var. Terminology and dimension -1 +1

[x.sub.1] Sulfuric acid [H.sub.2]S[O.sub.4] [l] 0.15 0.25
[x.sub.2] Aluminium Al [g.[l.sup.-1]] 4.5 7.5
[x.sub.3] Time t [min] 7 13
[x.sub.4] Voltage U [V] 9 15

Fig. 3. Significance of evaluated factors and their interactions that
affects the layer thickness h [[micro]m].

[X.sub.1][X.sub.3][X.sub.4] 27,72142
[X.sub.2] -16,201
[X.sub.4] 9,234887
[X.sub.1] 7,028486
[X.sub.3] -6,93394
[X.sub.3][X.sub.4] 5,307518
[X.sub.1][X.sub.2][X.sub.3] 4,505094
[X.sub.1][X.sub.4] 4,450417
[X.sub.2][X.sub.3][X.sub.4] 3,696291
[X.sub.2][X.sub.3] 3,003834
[X.sub.1][X.sub.2][X.sub.4] -2,37959
[X.sub.1][X.sub.3] -2,1129
[X.sub.2][X.sub.4] 1,271136
[X.sub.1][X.sub.2] ,9202527

Independent factors:
([X.sub.1]) Sulfuric acid [H.sub.2]S[O.sub.4] = [0.15; 0.25] l
([X.sub.2]) Aluminum Al = [4.5; 7.5] g.[l.sup.-1]
([X.sub.3]) Time t = [7; 13] min
([X.sub.4]) Voltage U = [9; 15] V
electrolyte temperature 21[degrees]C

Dependent factor:
thickness layer h mm

Note: Table made from bar graph.

Fig. 4. Percent expression of the significance of evaluated factors
and their interactions that affects the layer thickness h [[micro]m].

[X.sub.2.sup.*][X.sub.3.sup.*][X.sub.4] 2%
abs. 10%
[X.sub.1] 11%
[X.sub.2] 1%
[X.sub.3] 11%
[X.sub.4] 9%
[X.sub.1.sup.*][X.sub.2] 1%
[X.sub.1.sup.*][X.sub.3] 14%
[X.sub.1.sup.*][X.sub.4] 11%
[X.sub.2.sup.*][X.sub.3] 0%
[X.sub.2.sup.*][X.sub.4] 2%
[X.sub.3.sup.*][X.sub.4] 11%
[X.sub.1.sup.*][X.sub.2.sup.*][X.sub.3] 2%
[X.sub.1.sup.*][X.sub.2][X.sub.4] 1%
[X.sub.1.sup.*][X.sub.3.sup.*][X.sub.4] 14%

Note: Table made from pie chart.