3.2. Quantitative Analysis of Data
Analysis of variance (ANOVA) was carried out to study the effects of each test parameter/factor and their interactions on the response variable, i.e., weight loss rate, in order to find out the significance of each factor and their interactions on the erosion wear performance. First of all, we need to calculate the average impact of the factors for each level. For instance, the low level of the temperature factor is at the test conditions 1, 2, 5, 6, while the high level at 3, 4, 7, 8, as shown in
Table 3. Therefore, the average effect of low and high levels for temperature can be calculated as follows:
where
W1,
W2,
W5,
W6 are weight loss rates in low level corresponding to test conditions 1, 2, 5, 6, while
W3,
W4,
W7,
W8 are weight loss rates in high level corresponding to test conditions 3, 4, 7, 8 shown in
Table 3, respectively. Similarly, the others including all interactions could be computed as
WlS,
WhS,
WlA,
WhA in the same manner. Thus, the computed results are shown in
Table 5.
Defining the sum of squares (SS) was the next step of the ANOVA method. The sum of squares could be obtained according to the following formula:
where
Wln and
Whn are the average impact corresponding to the factor n viz. speed, temperature, and acid concentration, as well as their interactions for high and low levels and
WG is the average total weight loss rate for eight trial conditions, which is 67 g⋅m
−2⋅h
−1 according to
Table 3. All the sums of square
SSn for each factor and their interactions are gathered in
Table 6.
The final step of ANOVA was defined as the percentage contribution by using the following equation [
27]:
K represents the factor whose effect can be calculated.
Table 7 is the result for the percentage contributions of all factors and their interactions. From
Table 7, we can easily find that the percentage contributions of four factors are higher than 20%, they are speed-temperature-acid concentration (
STA, its
K value reached 25%), temperature-acid concentration (
TA, its
K value reached 25%), speed-temperature (
ST, its
K value reached 20%), and temperature (
T, its
K value reached 20%). This indicated that the prominent contribution of the total erosion wear rate is due to temperature
T and its interactions, i.e.,
STA.,
TA, and
ST. At the same time, contribution percentages of the interactions for the factors are higher than single-acting ones, and synergistic action is significant. It was followed by speed-acid concentration, acid concentration, and velocity, respectively. It is obvious that temperature has the largest contribution percentage of more than 20% in the range of three considered factors, i.e., temperature, speed, and acid concentration, and temperature plays a remarkable role on erosion wear rate variation of 304 stainless steel in this study. This is a good agreement with the experimental result conducted by Hu and Neville [
33], etc. The second is acid, concentration with contribution percentage of 5%. The smallest is speed only contribution percentage of 0.4%, such trend could be due to so-called speed threshold effect [
34,
35,
36,
37,
38,
39]. Only when impact speed is higher than threshold value will it cause wear rate transition of the test material [
34]. Although many investigations have indicated that impact velocity is a critical test variable on erosion wear rate [
40], in this research the rotational speed of 1200 rpm, i.e., high level, could still not be high enough to reach the threshold velocity. Therefore, rotational speed has the smallest effect on erosion wear rate of 304 stainless steel in the range of considered factors in our research.
3.3. Qualitative Analysis of Data
Although quantitative analysis can provide statistical analysis of data [
27] and objective and precise merits [
41], it is difficult in description and justification of variation direction. Qualitative analysis is versatile/ubiquitous and easy to apply [
42,
43]. Moreover, it can predict variation direction of test result and obtain overwhelming parameter [
27], as well as offer evaluative general information [
44], suit most practical conditions, and simplify experimental and measurement procedures [
45]. Whereas qualitative analysis is open to error and can be subjective [
46]. Therefore, in general, two kinds of analysis approaches are combined to use [
41,
45].
In this study, as the first step for qualitative analysis, a symmetric 8 × 8 matrix was designed according to previous reference [
27]. Each array represents the result that was obtained by comparing the erosion wear rates corresponding to the trial numbers shown in
Table 3 and
Table 4. For example, the array A
2,1 represents (A > 0) the result comparing the erosion wear rate of trials 2 and 1. From
Table 3, we can easily see that these two trials (2 and 1) only differed in acid concentration factor. Acid concentration factor of trial 2 has a high level while trial 1 has a low level. From
Table 4, it can be seen that erosion wear rate of trial 2, i.e.,
W2, is larger than
W1 of trial 1 (
W2 >
W1), this indicates that erosion wear rate increases with the rise of acid concentration value while the other factor values are fixed. Acid concentration factor has an accelerating effect on erosion wear rate. Similarly, the other arrays (A
3,1, A
4,1, A
5,1, A
6,1 A
7,1, A
8,1) of the first column can be obtained by comparing the corresponding erosion wear rate with that of the first trial. The comparison result is shown in
Table 8. If the value of A
3,1, and so on, is “> 0”, it shows having an accelerating effect on erosion wear rate, and if the value is “< 0”, it has an inhibitory effect. For example, the array A
6,1 > 0 (
W6 >
W1) means SA > 0, which indicates that the synergistic action of speed and acid concentration has the accelerating effect on erosion wear rate. According to
Table 8, all the arrays (A
2,1, A
3,1, A
4,1, A
5,1, A
6,1 A
7,1, A
8,1) of the first column are greater than zero, and from
Table 3 compared with trial 1, trials 2, 3, 5 have only the difference in high level of acid concentration, temperature, speed factor, respectively. This shows that regardless of acid concentration, speed, and temperature, every factor has an accelerating effect on erosion wear rate of 304 stainless steel (304 SS) materials. However, from the values of three arrays in the first column of
Table 8 (A
2,1, A
3,1, and A
5,1), we can clearly find that the rank of effect on erosion wear rate is temperature > acid concentration > speed. That is, among three factors, influence of temperature factor was the most significant followed by acid concentration, and with the above quantitative analysis this is in good agreement that speed has the smallest effect. It can be observed with other arrays in the first column, which correspond to the interaction factors, that A
4,1, A
7,1, and A
8,1 of the combining action of temperature with other factors are much greater than the combining action value of acid concentration and speed factor without temperature factor, i.e., A
6,1. This further illustrates that the effect of temperature factor is the strongest.
As for other arrays of matrix
Ax,y (x represents rank while y represents column), the values of |
Wx −
W1| and |
Wy −
W1| need be calculated and compared, where
Wx,
Wy, and
W1 are erosion wear rates of trial condition x, y, and 1, respectively, which are shown in
Table 3 and
Table 4. For example,
A3,2 can be obtained by calculating |
W3 −
W1| and |
W2 −
W1|. The value |
W3 −
W1| represents
A3,1, it is an array of the first column as mentioned above; the array shows the effect of temperature. While |
W2 −
W1| means
A2,1, it is also an array of the first column, which indicates the effect of acid concentration. The result of |
W3 −
W1| > |
W2 −
W1| was obtained by calculating, and the conclusion of T > A can be inferred, i.e., temperature factor has a higher effect than acid concentration factor. Similarly, other arrays can be obtained as shown in
Table 8. The greater difference value of |
Wx −
W1| and |
Wy −
W1|, the more significant the effect for the corresponding factor of trial condition x comparing with trial condition.
In
Table 8, besides the arrays of the first column, for convenient comparison purposes, the significant comparisons of the other arrays are divided into three grades. The difference of two absolute value equal or less than 20 is considered to be insignificant (marked as ≈) with 20 to 50 generally significant (marked as >) and more than 50 be highly significant (marked as »). At the same time, increasing effect of combining action is shown as “↑”, decreasing effect of combining action as “↓”, and insignificant effect of combining action as “°”. Thus, obtained results are shown in
Table 8. For three single factors corresponding to the arrays, i.e., A
3,2, A
5,2, and A
5,3, according to the above method, e.g., A
3,2, forA
5,2,|
W5 −
W1| < |
W2 −
W1|, are easily drawn, since |
W5 −
W1| represents the effect of speed, |
W2 −
W1| represents the effect of acid concentration, and |
W5 −
W1| < |
W2 −
W1| the conclusion S < A can be drawn. Nevertheless, the difference value of |
W5 −
W1| and |
W2 −
W1| has only −4.35. Therefore, the effects of speed and acid concentration could be considered as S ≈ A, which have insignificant effect of speed compared with acid concentration. Finally, we can obtain these results: T > A, S ≈ A and S < T. As discussed above, temperature factor has the remarked effect on erosion wear rate.
To further analyze the synergistic effect of factors, three groups of arrays can be divided as follows [
27].
The first group of arrays exhibits the increasing effect of factors combination compared with individual ones on erosion wear rate. For example, the array A4,3 presents the result of TA > T, which can be derived by means of the above mentioned method. To analyze A4,3, we need to study A4,1 and A3,1, respectively, that is compared with the two values |W4 − W1| and |W3 − W1|. As mentioned above, |W4 − W1| corresponds to the array A4,1 and shows the combining effect of temperature and acid concentration (TA). |W3 − W1| represents the arrayA3,1 and shows the effect of temperature (T). Due to |W4 − W1| > |W3 − W1|, the conclusion TA > T is obtained. This result shows the cooperation effect of temperature and acid concentration is greater than temperature alone on increasing the erosion wear rate. After adding acid concentration to temperature factor, it promotes the effect of temperature, i.e., TA > T. The arrays that belong to this group are shown by using the arrow pointing up in the cell. It should be pointed out that, for example, the array A4,2 shows the result of TA » A. This is since the difference values of |W4 − W1| and |W2 − W1| corresponding to the two arrays, i.e., A4,1 and A2,1, are larger than 50. It indicates that the cooperation effect of temperature and acid concentration is far greater than acid concentration alone on increasing the erosion wear rate. After adding temperature to acid concentration factor, it strongly promotes the effect of acid concentration, i.e., TA » A. Such situation also contains STA » A of A8,2, STA » T of A8,3, STA » S of A8,5, STA » SA of A8,6.
The second group of arrays displays the decreasing effect of factors combination in comparison with single ones on erosion wear rate. Such arrays are shown by using the arrow pointing down in the cell. In
Table 8, these arrays can not be seen. All the effects of the combining actions of two and/or more than two factors are greater than one factor alone in a different degree.
The third group of arrays defines the insignificant effect of factors combination compared with individual ones on erosion wear rate. For example, A6,2 exhibits the effect of acid concentration nearly as much as combining action of acid concentration and speed (SA ≈ A). This shows to some extent (as mentioned above) nearly negligible effect of speed while acting with acid concentration. These arrays are marked with a circle sign in the cell.
The above analysis shows that three groups (there are not the second groups with decreasing effect) exhibit obvious differences in combining action of factors selected. Qualitative analysis can clearly display effect of factors and their combinations on variation direction of erosion wear rate.