This section will discuss the recommendations concerning the use of the pre- dictive model as a tool-set to support production at the industry partner. Anderson Lid Company (ALC) is concerned with producing gland seals that exceed a tensile strength of 15 MPa. The maximum achievable seal strength can be obtained by optimising the predictive model provided in eq. 4.9. This corresponds to a seal strength of 21.9 MPa, and process variables of tempera- ture = 320◦C, pressure = 4.4 bar and dwell time = 5.5 sec. Since 4.4 bar lies on the lower pressure boundary (see Fig 4.8), additional tests outside the design space were conducted to verify the optimum pressure setting, see Table A.8.
CHAPTER 4. RESULTS AND DISCUSSION 68
(a) Contour Plot: Dwell Time-Pressure (b) Contour Plot: Temperature-Pressure
Figure 4.8: Contour plots are based upon the model equation provided in eq. 4.9, in conjunction with eq. 4.6. Two factors are varied and the third is kept constant, e.g. Fig. 4.8a displays the resulted tensile strength based upon the pressure and dwell time at a constant temperature of 320◦C. Also, Fig. 4.8a displays the tensile strength contours based upon the temperature and pressure effects while the dwell time is constantly at 5.5 sec. High strength seals are obtained at the lower pressure values of the design space.
However, in the industry, the high strength seals are normally associated to be deep which refers to the physical depth of the seal interface into the gland fitment. From a marketing point of view, the deeper seals are less aesthetically attractive than the weaker shallow seals. Therefore it is highly desirable to establish a trade-off between aesthetics and seal strength.
Consider the above as a case study to display the possible uses for the pre- dictive model. Since seal strength is directly proportional to seal depth being an industry rule of thumb, the shallowest seal to pass quality will most likely just exceed a seal strength of 15 MPa. Considering the noise between repli- cates being ± 2 MPa from the mean of the response, then the process variables corresponding to a predicted strength of 17 MPa, are a possible solution.
The lowest pressure setting in the design space will most likely produce the shallowest seal, being 4.4 bar. Then, the response surface and corresponding contour plot of the temperature and dwell time can be plotted for a constant pressure of 4.4 bar; see Fig. 4.9. The optimum conditions are clearly seen at temperature = 320◦
C, dwell time = 5.5 sec and pressure = 4.4 bar, which correspond to a seal strength of 21.9 MPa.
CHAPTER 4. RESULTS AND DISCUSSION 69
The 17 MPa contour is highlighted in red in Fig. 4.9b. This line rep- resents all the possible solutions of temperature and dwell time at constant 4.4bar pressure that will yield to a seal strength of 17 MPa. If production is concerned with limiting cycle time, e.g. at 2.5 sec, then the corresponding re- quired temperature will be 314◦C. Then, by using eq. 3.50 the 95 % confidence interval can be constructed about the 17 MPa prediction, which computes to 15.3MPa - 18.9 MPa suggesting there is 95 % confidence that the actual seal strength will fall well within this region. Also, the lower boundary exceeds the minimum 15 MPa requirement by 0.3 MPa, which provides additional leverage outside the confidence interval in the case of outliers.
The manufacturer might also be interested in saving energy, limiting tem- perature at the expense of increasing the dwell time. Although not shown, a similar approach could be followed to obtain a solution as outlined above. Therefore, the manufacturer can tailor specific solutions that comply with their requirements. As a result, the constructed model is highly beneficial for the industry partner, allowing them to adapt in limited time to manufacture gland seals that comply with specific requirements.
(a) Response Surface (b) Contour Plot
Figure 4.9: The consecutive graphs were produced from the model equation provided in eq. 4.9, in conjunction with eq. 4.6. The pressure is kept constant at 4.4 bar to yield the shallowest seal depth, and the temperature and dwell time effects are captured. The response surface is provided in Fig. 4.9a, and the corresponding contour plot is provided in Fig. 4.9b.
Chapter 5
Conclusions and
Recommendations
5.1
Conclusions
This project set out to obtain a predictive model associated with the seal strength between film to gland fitments. The objectives were to establish the significant variables at play, obtain an adequate model equation, and finally predict the adequate process variables that will result in high strength seals, exceeding 15 MPa.
The project was limited to the most common product layout at Anderson Lid Company, being two plies of 100 µm LDPE film welded on a 2 inch hexagon gland. However, the outlined approach can be expanded to different product layouts if required. The approach followed consisted of constructing the design of experiments (DOE), producing the gland seals accordingly; cutting uniaxial tensile samples, conducting tensile tests, processing data and constructing the statistical model.
During the preliminary phase of the project, it was found that the current sample geometry being used at ALC is inadequate to provide accurate results since most failures occurred in the film rather than at the seal interface, and the uniaxial response curves did not provide clear insight into the uniaxial properties. Therefore a new sample geometry and die were designed and man- ufactured. These results resembled that of literature, where similar uniaxial response curves were obtained.
A data processing algorithm was written during the course of this project. The user provides a directory containing all the folders and consecutive raw uniaxial test data corresponding to the constructed DOE. The algorithm then computes and classifies the uniaxial properties of interest. The processed re- sults are written in a CSV-file, which is later utilised for the statistical mod- elling. Although the tensile strength is the only uniaxial property used during modelling, the proceeding uniaxial properties were included for possible fu-
CHAPTER 5. CONCLUSIONS AND RECOMMENDATIONS 71
ture research projects as the industry partner might be interested in other mechanical properties affected by the process variables.
The response surface methodology approach was followed by statistical modelling. The preliminary model made use of a centre composite design. The significant variables of interest were the process variables of the sealing process. This model accounted for 80 % of the total observed variance, where the least square assumptions were violated at the extreme ends of the model predictions. As a result, the hypothesis test concluded that strong evidence existed for lack of fit.
From the preliminary study, a new DOE was constructed consisting of a central composite design in conjunction with a face-centred composite design. The new DOE which provided higher resolution has led to better approxima- tions of the true response. Initially, an additional variable, the perimeter angle position was added to the model to reduce the unaccounted variance. However, multiple statistics tests concluded that the perimeter position is insignificant suggesting that the variance between samples are not directly related to the perimeter position of the seal interface.
A new model was constructed, which excluded the perimeter position, and only consisted of the process variables. Due to the higher resolution DOE, the accounted variance was increased to 88 % which is an 8 % improvement from the preliminary model. Additionally, a power law transformation was performed on the model equation to reduce the lack of fit. The Box-Cox analysis suggested using the natural logarithmic on the predictor variable. As a result, the transformed model accounted for about 90 % of the variance where 3.6 % of the 10 % unaccounted variance is due to lack of fit, and 6.4 % is due to the variability between replicates. Additionally, robust regression was performed to validate the coefficient estimates.
Independent validation tests were conducted to verify the use of the model. Amongst these was the predicted optimum corresponding to a seal strength of 21.9MPa, at process variables of temperature = 320◦C, pressure = 4.4 bar and dwell time = 5.5 sec. The results obtained were within the constructed 95 % confidence interval, and the mean approximated the true response. The model accounted 89 % of the variance of the validation set. Although the model is only suited for process variables falling inside the design space, it can easily be expanded by additional trial points in the experimental design plan if required. Additionally, the predictive model was applied in a case-study. It consid- ered obtaining the adequate process variables that would result in seal strength exceeding 15 MPa, while limiting the process time and seal depth. The predic- tion quality of the model was considered during the analysis, and as a result, a predicted seal strength of 17 MPa ± 2 MPa was regarded as a possible solu- tion. The solution of the process variables was temperature = 314◦C, dwell time = 2.5 sec and pressure = 4.4 bar. The 95 % confidence interval equated to 15.3 MPa - 18.9 MPa where the lower limit exceeds the 15 MPa requirement by 0.3 MPa, which provides additional leverage for outliers.
CHAPTER 5. CONCLUSIONS AND RECOMMENDATIONS 72
Although not limited to, the case-study has displayed a possible application of the predictive model where the manufacturer can tailor specific solutions to comply with changing requirements. As a result, the outlined approach and constructed model are highly beneficial for the industry partner, allowing them to adapt in limited time to manufacture gland seals that comply with specific requirements.