AUTOMATIC PREFORM SHAPE OPTIMIZATION FOR THE STRETCH BLOW MOLDING PROCESS

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1 AUTOMATIC PREFORM SHAPE OPTIMIZATION FOR THE STRETCH BLOW MOLDING PROCESS F. Thibault, B. Lanctot, A. Malo and R. DiRaddo Industrial Materials Institute Boucherville, Quebec Abstract In this work, we develop a new numerical optimization strategy that targets a container thickness distribution by manipulating the preform geometry (thickness and shape) subject to process constraints (injection molding and stretch-blow molding). The proposed optimization strategy is combined with a sequential quadratic programming (SQP) method of the design optimization tools (DOT- Vanderplaats Reseacrh & Development Inc) to update the preform design variables while iterating over the stretch blow molding (SBM) process. The algorithm has been tested successfully on industrial parts. Introduction Stretch blow molding (SBM) is the process of choice for the production of PET containers, for the food and beverage industry as well as the pharmaceutical sector. The stretch blow molding process involves three stages, the reheat stage where previously injection molded preforms are heated to the desired forming temperature distribution, followed by the forming and the solidification stages. During the forming or blowing stage, the preform is stretched with a cylindrical rod. For the duration of stretching, a pre-blow is applied to prevent the stretching rod contacting the inside preform wall, which can lead to container defects. When the rod reaches the mould container bottom wall, a high blow pressure is applied inside the preform to reach the final container shape. The high pressure is held for approximately a second to cool the container down and exhaust is finally performed to get the final product. The SBM process is a high volume process with costly tooling for both the preform and the container. An injection molding machine can have a maximum of 144- cavity preforms. The design of the tooling, via virtual technologies is preferable so as to minimize costly tooling reworks. Industry has readily accepted the use of finite element technologies in the prediction of the stretch blow molding process. In this work, the BlowView software technology from National Research Council is used to model the process [1-3]. The aim of this work is to develop, by iterating over the simulation technology, an optimization strategy that automatically manipulates the preform geometry (shape and thickness) that targets a container thickness distribution taking into account the process constraints for given processing parameters. The software will assist and facilitate the task for designers to minimize preform design time and retoolings for both preform and container moulds. Preform Design and Parameterization Since preforms are injection molded, their geometry has to take into account the process constraints such as the core rod demouldability from the inside preform and the preform demouldability from its cavity. Different types of preform are used in the industry to satisfy those constraints (Fig. 1). In this work, we focus on the first two-preform types (outside and inside taper preforms) that represent around 85% of all the preforms designed in industry. The preform is usually divided into four sections: finish, taper, body and end-cap sections. These sections have been efficiently parameterized to allow us to reconstruct the whole preform geometry by changing one of these parameters (Fig. 2). The variables l, ID, Z, T and OR represent respectively the length, the inside diameter, the finish outside support ledge, the thickness and the outside radius. The indices f, tp, c, TB, BB, EC represent the finish, the total preform, the conveying zone, the top body, the bottom body and the end-cap respectively. The geometric relationship between container and preform is illustrated in Figure 3. From a design point of view [4], three different types of stretch ratios are usually considered in the preform design: axial stretch ratio ( ax ), hoop stretch ratio ( h ) and end-cap thickness ratio (). The axial stretch ratio is the ratio of the bottle length (L b ) to the preform length (l p ), without taking into account the finish length that is not considered to be an active stretched region. The hoop ratio is defined as the ratio of the outside diameter of the container (D b ) to the outside diameter of the preform (d b ). For example, for a typical 2L carbonated soft drink (CSD) bottle, these stretch ratios range in the preform design window: 2.2 < ax < 2.8, 4.4 < h < 5.4 and < < [4]. The product of axial and hoop ratios gives the total blow up ratio (BUR) which is an indication of the

2 total stretch ratio undergone by the PET material during the forming process. Depending on the bottle types (hot fill, CSD or water), the BUR could vary significantly. Industry is constantly pushing the BUR value up in order to improve PET bottle mechanical properties. However, care has to be taken to avoid polymer overstretching or polymer delaminating during the forming process. Optimization Strategy The first step in numerical design stage is the mathematical formulation of the objective function. The purpose of the objective function is to numerically describe in one expression, the part specifications, the design variables and the costs associated with processing and part quality. It consists of the minimization of a cost function, subject to a series of inequality, equality and bound constraints that limit the design space, by automatic manipulation of a series of design variables (X). The problem definition can be expressed as the following: Minimize: F(X) objective function (1) subject to inequality constraints or specifications g j (X) 0, j = 1, m (2) equality constraints or specifications h k (X) = 0, k = 1, n (3) side constraints or design variable limits X i,min < X i < X i,max (4) by manipulating the design variables X = {X 1, X 2,, X p }. Once the objective function is defined, a numerical optimization can be performed using a variety of available techniques such as traditional gradient techniques of zero, first and second order or soft computing methods [5]. In this work, a second order method (sequential quadratic programming (SQP)) of the design optimization tools (DOT) has been used [5]. The numerical optimization iterates over a simulation tool as it moves towards the optimal condition. Starting from a given preform geometry, each objective function evaluation requires the creation of a finite element mesh of the preform and consequently performing a nonlinear finite element analysis of the SBM process. The following objective function is evaluated N 2 e i ( X ) Ti Tt ( y) (5) i1 which represents the container thickness variance around thickness targets (T t ) defined by the designer along the container. N e and T i correspond respectively to the number of finite elements in the preform mesh and the nodal finite element thickness. The variance is weighted by the ratio of the local element surface ( i ) to the total container surface (), which will not be affected by the mesh topology. The process constraints can be expressed as the following: a. Injection molding demouldability constraints: ID BB < ID TB (6) ID BB < ID F (7) ID TB < ID F (8) OD BB < OD TB (9) OD TB < Z (10) b. The stretching rod constraints: D rod + R Cl < ID BB (11) D rod + R Cl < ID TB (12) where R Cl represents the rod clearance (2 mm). For the sake of clarity, only six (6) preform design variables will be manipulated to define the preform geometry as shown on Figure 4. From design rules, the ratio of the preform transition length (l T ) to the active preform length (l p =l tp -l f ) is proportional to the ratio of the bottle transition length (L b_trans ) to the bottle length (L b ). Based on the definition of these preform design variables, the constrained optimization problem can be reformulated as: Minimize the design objective function N 2 i ( X ) Ti Tt ( y) i1 (13) by manipulating the preform design variables X 1,min < X 1 < X 1,max X 2,min < X 2 < X 2,max D rod + R Cl < X 3 < ID F (14) X 4,min < X 4 < X 4,max D rod + R Cl < X 5 < ID F X 6,min < X 6 < X 6,max subject to process constraints X 5 < X 3 (2X 4 +X 5 ) < (2X 2 +X 3 ) (15) (2X 2 +X 3 ) < Z Instead of manipulating the total preform length (X 1 ), it is more appropriate to manipulate the axial stretch ratio (X 1 = ax ) that is related to the total preform length using the next relation X 1 = l p + l f = L b / ax + l f = L b / X 1 + l f (16)

3 Finally, one can notice that the choice of proper design variable limits allows satisfying some of the process constraints (7-8,11-12). Case Study The optimization of a Husky PET preform is investigated to produce an 8oz Mayonnaise container using a stretch blow molding process. The PET material used was a CB12 from Eastman Company and the stretching rod is a 16 mm diameter mushroom type. The objective is to manipulate the preform geometry to target a uniform container thickness of 7 mm. For this case, the reheat stage was not part of the simulation process since the preform temperature profile was known and measured from an infrared camera just before entering the blowing station. Table I illustrates the initial preform design variables and the preform design variable limits (lower bounds and upper bounds) for the case studied. The initial preform body thickness has been decreased in order to test the optimization algorithm. The results are shown in Table II and Figures 5 to 8. The proposed optimization algorithm is able to decrease rapidly the objective function (Fig. 5) from 2 =0.028 mm 2 (=0.167 mm) down to 2 = mm 2 (=0.02 mm) after 5 optimization iterations. At the same time, the preform weight increases from 14.9 g up to 18 g since the preform body thickness has to be increased to satisfy the container thickness targets. During the optimization process, a total of 71 process simulations have been run in order to evaluate gradients of the objective function respect to each preform design variable by using a finite difference technique. These gradients have been passed to DOT to evaluate the search direction to get to the optimal design by using a SQP method. As shown in Figures 6 and 7, the initial preform design was under design since the container thickness profile is much lower than the container thickness target. As the optimization progresses, the container thickness profile increases and gets closer to the thickness target after 5 optimization iterations. The optimal preform geometry obtained satisfies all the process constraints. In Figure 8, the optimal preform geometry obtained in this work gives thickness distribution along the container that is very close to the experimental preform geometry designed by Husky Company. Conclusion In this work, first, we had to parameterize the preform geometry based on design mathematical rules used by Amcor Company. In the second part, we proposed a new optimization methodology, based on DOT technology, to manipulate the preform geometry (shape and thickness) in order to target a container thickness distribution along the container. The algorithm has been tested on industrial case of Husky Company and gave very interesting results. Acknowledgement The authors would like to acknowledge Amcor PetPackaging Company for its financial support and Husky Company for the CAD information and operating conditions of the manufacturing of 8oz mayonnaise container used for the case study. References 1. T. Pham, F. Thibault & L.-T. Lim, August Injection Stretch Blow Moulding of PET: Modelling, Characterization and Simulation, Poly. Eng. Sci., 44 (8), D. Diraddo, D. Laroche and B Brace, Thermomechanical Modelling Microstructure Development and Part Performance in Stretch Blow Moulding, SPE ANTEC Tech. Paper, Dallas, USA. 3. M. Yousefi, D. Diraddo and A. Bendada, Simulation of the Mobile Preform Reheat in Injection Stretch Blow Moulding Process, Polymer Processing Society 17, Montreal, Canada. 4. G.A. Giles and D.R. Bain, Technology of Plastics Packaging for the Consumer Market, Sheffield Academic Press, CRC Press, p G.N. VanderPlaats, Numerical Optimization Techniques for Engineering Design, VanderPlaats Research & Development Inc, Finally, we tried several preform shape optimizations without taking into account the process constraints. As expected, the preform geometry obtained was not satisfying some of the injection molding or the SBM process constraints. Nevertheless, the unconstrained optimization is much more faster and the optimal preform geometry obtained can be used as an initial guess to get better convergence during the constrained optimization.

4 Table I. Definition of initial preform design variables and design variable limits. Design Variable Name Lower Initial Upper Bound Value Bound Axial stretch ratio (X 1 ) Top body thickness (X 2 ) Inside top body diameter (X 3 ) Bottom body thickness (X 4 ) Inside bottom body diameter (X 5 ) End-cap thickness ratio (X 6 ) Table II. Comparison between initial and optimal preform geometries. Design Variable Name Initial Optimal Design Design Axial stretch ratio (X 1 ) Top body thickness (X 2 ) Inside top body diameter (X 3 ) Bottom body thickness (X 4 ) Inside bottom body diameter (X 5 ) End-cap thickness ratio (X 6 ) 67 8 Figure 2. Parameterization of preform into four sections: finish, taper, body and end-cap. l p d p T end-cap T body L b_trans L b axial hoop = L b /l p = D b /d p = T end-cap /T body D b Figure 3. Relationship between container and preform in term of stretch ratios. Figure 1. Different types of preform geometry used in the industry (Courtesy of CRC Press). Figure 4. Preform design variables (X 1 to X 6 ).

5 Bottle Thickness (mm) Bottle Thickness (mm Objective Function - 2 (mm 2 ) Preform Weight (g) Bottle Thickness (mm) 3.0E Objective Function Preform Weight E E Uniform Target = 7 mm Optimal Design Husky Design E E E E Optimization Iteration Figure 5. Objective function and preform weight evolution in function of optimization iterations mm 14 Figure 8. Comparison between container thickness distribution with the optimal preform geometry and the experimental Husky preform design mm 2 Figure 6. Optimization results: initial preform-container thickness profiles (left) and optimal preform-container design (right). Initial Design Uniform Target = 66 mm Initial Iteration Design #1 Iteration #3 Uniform Target = 7 mm Iteration #5 Iteration Husky Design #1 Iteration #3 Iteration #5 Figure 7. Evolution of container thickness distribution in function of optimization iteration.