1. Introduction

In Textile processes, it is often of primary interest to develop the relationships between the key process variables and the performance characteristics. MathematicalModelling play an important role in developing, analysing and predictingthe relationship from experiments with certain level of confidence[1-6].When several variables influence a certain characteristic of a product, the best strategy is then to design an experiment(DOE) so that objective conclusions can be drawn rather than judgemental. In the context of DOE in Textiletwo types of process variables: qualitative and quantitative factors[7-12]. The aim of this work was to develop the mathematical model of crease recovery angle for single step fixation process of reactive printing and crease resistance finishing process.The significant factors for the single step fixation of reactive printing and crease resistance finishing process had been reviewed previously [13-16].

In the current studyof single step fixation process of reactive printing and crease resistance finishing chroma, concentration of crease resistant and fixation temperature are quantitative factors. However fixation method is the qualitative factor.

2. Experimental

2.1. Process Route

The singlestep fixation of reactive printing and crease resistance finishing is carried outas follows: Crease Resistant Finish-Dry-Reactive Print-Fix-Wash-Dry-Conditioned.

In the first step ready to print fabric was padded with thecrease resistant finish liquor, and then squeezed to obtain a 70% wet pickup. The fabric was then dried at 100°C for 1 min. The dried fabric was printed by lab scale Rotary Printing machine. The finish-print fabric was concurrently fixed using Econtrol method at 135°C for 5 minutes. The fixed samples were finally washed, dried and conditioned.

2.2. Evaluation of Dry Crease Recovery Angle (DCRA)

The crease resistant properties were evaluated by measuring the dry crease recovery angles (DCRA). The print-finish fabrics were conditioned (at temperature 25±1^oC and relative humidity 65 ±1%) before the measurement of DCRA values. The dry crease recovery angle (DCRA) of the fabric was measured using AATCC test method 66-1990. The wider the DCRA is, the higher the crease recovery. The samples processed with single step fixation were compared with those produced from a conventional two-step process of reactive printing and Crease resistance finishing.The experiment data is shown in Table 1 and 2.

2.3. Statistical Analysis of the Data

After processing the experimental trials, DCRAvalues were measured using crease recovery tester.The results obtained from the different experimental sets are presented in Table 2. The DCR Avalues were statistically analysed. Residual analysis and model adequacy checking were performed. The experiments have been conducted in random order. The results were analysed using software Design Expert 8.0.

2.4. Model Adequacy Checking

2.4.1. The Normality Assumption

The normal probability plot of the residual for dry crease recovery angles has been shown in Figure 1. There is no severe indication of non-normality, nor is there any evidence pointing to possible outliers and the equality of variance assumption does not seem to be violated.

Figure 1. Normal plot of residuals for DCRA

2.4.2. Residual Analysis

Rresidualversus run number and residual versus predicted plots of dry crease recovery angle have been shown from Figure 2and 3. The pattern of the residualsshowed that they are normally distributed and the equality of variance does not seem to be violated.

Figure 2. Residual vs. run number for DCRA

Figure 3. Residual vs. predicted plot for DCRA

Figure 4. The predicted vs. actual plot for DCRA

2.5. Analysis of Variances (ANOVA)

Table 1 shows the summary of ANOVA results ofdry crease recovery angle for single step fixation process of reactive printing and crease resistance finishing. The model p-value implied that the respective model is significant for dry crease recovery angle.As can be seen in Table 1,

The "Lack of Fit p-value" of 0.9998 implies the Lack of Fit is not significant relative to the pure error representing that the suggested models are well-fitted to the observed response.. The "Pred R-Squared" of 0.8630 is in reasonable agreement with the "Adj R-Squared" of 0.9189 specifying the respective model is adequate.

The actual and predicted plot of dry crease recovery angle has been shown in Figure 4. The actual values are the measured response data for particular run and the predicted values are theresults generated using the approximate functions. It is found that the adequate precision of

Dry crease recovery angle is found to be 20.27, which measured the signal to noise ratio is much greater than 4, (Table 1). This indicates the modelis adequate to be used to navigate the design space. Focusing on the model maximizing the “Adjusted R-squared” and the “Predicted R-squared” different process order selection has been made for dry crease recovery angle. The alias structures of the dry crease recovery angle are shown in Table 3.

Table 1. Summary of ANOVA results of dry crease recovery angle (DCRA)

Table 2. ANOVA for DCRA warp

Table 3. Alias structures for DCRA

3. Results and Discussion

3.1. Analysis of Dry Crease Recovery Angle (DCRA)

The sixth order model has been selected for the response variable DCRA Warp. The detail of ANOVA of DCRA Warp is shown in Table 2. The Model p-value less than 0.05 implies the model is significant. In this case B, C, D, AC, AD, BC, B2, ABC, ABD, ACD, BCD, A2B, A2C, AD2, B2C, B2D, BD2, CD2, ABCD, A2B2, A2BC, A2BD, A2CD, A2D2, AB2C, AB2D, ACD2, B2D2, BCD2, A2B2C, A2B2D, A2BD2, A2CD2, AB2CD, AB2D2, ABCD2, B2CD2, A2B2D2, A2BCD2, AB2CD2are significant model terms.

The graphs of significant model terms for DCRA have been shown from Figure 5 to 15.The graphs of significant model terms revealed that the dry crease revovery angle of the single step fixation process of reactive printing and crease resistance finishing is dependent on the interaction and curvature effect of concentration of crease resistant, fixation mode and fixation temperature.Figure 8 and 9 indicated that the Econtrol process supersedes the conventional curing process for fixation and gives a higher dry crease recovery angle in the single step fixation process. Figure 16illustrates the interaction plot of fixation mode and fixation temperature. The graph clearly shown that the Econtrol process at 130°C gives a higher dry crease recovery angle in the CPF process. The reduced regression equation of dry crease recovery angle has been shown in Equation (1).Whereas, the fitted regression equation has been presented in Equation (2). The alias structures are shown in Table 3.

3.2. Mathematical Model with Significant Variables at α = 0.05

(1)

3.3. Fitted Regression Equation of DCRA

(2)

Figure 5. Effect of B on DCRA warp

Figure 6. Effect of C on DCRA warp

Figure 7. Effect of D on DCRA warp

Figure 8. Interaction plot of AC with respect to DCRA warp

Figure 10. Contour plot representing DCRA warp versus chroma and fixation temperature

Figure 11. Interaction plot of BC with respect to DCRA warp

Figure 12. Interaction plot of AB with respect to DCRA warp

Figure 13. Interaction plot of BD with respect to DCRA warp

Figure 14. Contour plot representing DCRA warp versus concentration of CR and fixation temperature

Figure 15. Interaction plot of CD with respect to DCRA warp

4. Conclusions

The factorial design of experiments for single step fixation process of reactive printing and crease resistance finishing was studied. The quadratic effect of three factors namely, concentration of crease resistant, fixation method and fixation temperature on dry crease recovery angle were identified. The statistical analysis gave a reasonably good fit with an F-value of 24.10 and an R2-value of 0.9587. According to the significance effect obtained in variance analysis, the concentration of crease resistant was the most significant factor for the dry crease recovery angle under the conditions investigated.The information obtained from the mathematical model has been used to create optimal parameters of single step fixation process of reactive printing and crease resistance finishing process.

ACKNOWLEDGEMENTS

The authors wish to express their gratitude to Gul Ahmed Textile Mills Ltd and Clariant Pakistan Ltd, for carrying out the necessary experimental work.