(a) (b)

(c)

Figure 1。 The prototyping mold and plastic car fender: (a) movable die, (b) stationary die, (c) molded part。

ing process parameters which can be changed during the molding process。 The remainder of the paper is organized as follows。 Section 2 introduces a framework to approach and solve multi-objective optimization problem。 Section  3 presents numerical experiments and descriptive data analysis。 Section 4 describes optimization results。 Section 5 gives con- clusions and goes over possible future work。

2。 Optimization framework

2。1 Optimization problem

Figure 2。 Share total energy consumption。

the plasticization and heating process, clamping force can be considered as the great influence factor for energy saving。 In this paper, we focus on the minimizing clamping force which gives rise to clamping energy based on the optimization of process parameters。 Additionally, due to thin-shell characte- ristic, the warpage values that should be minimized to im- prove molded product quality are employed as the optimiza- tion criteria。 To save the time and costs, the simulation-based optimization is employed instead of expensive physical expe- riments。 Because the simulation values correlated sufficiently with the experimental values [7], a FE-based model is devel- oped to obtain desired criteria。 The commercial software, namely Autodesk Molflow Insight 2012 that can guarantee reliable results is used to simulate the molding process。

During the simulation, the maximum value of injection pressure has been set as the fixed value according to real manufacturing conditions。 Based on the molding process conditions and previous studies [2-5], five critical parameters are considered as control factors: mold temperature  (TM), melt temperature (TME), packing time (Pt), packing pressure (PP), and cooling time (tc)。 Multiple-objective optimization functions can be described in the below equation:

shown in Figure 1。 The part's dimension were 650 mm × 1160 mm × 235 mm, and the thickness was fixed at 2。8 mm。 In the injection molding process of car fender, energy is con- sumed by plasticization, heating, molten-plastic injection, clamping forces, auxiliary device-operation, and mold movements  /  part-ejection。  Through  previous  studies   [6],

manufacturing data and the interviews with company experts,

an investigation indicated that the greatest amount of energy was consumed in plasticization, where the energy- consumption rate was 48%。 Barrel heating expenditure was 19%。 Clamp-force use rate was 12%。 Injection force con- sumption-rate was 11%。 Only small amounts of energy (4% per each process) were used by linear movements to open and close molds, and retract barrels for cooling。 The share total energy consumption is shown in Figure 2。

According to the analysis of energy consumption,    except

where F denotes the clamping force, W presents the warpage。

2。2 Optimization strategy

In this section, a multi-objective optimization framework is presented to obtain optimal process parameters。 Figure 3 describes two stages of the multi-objective optimization pro- cedure of the proposed approach。 A systematic methodology based on response surface methodology (RSM) is adopted to establish a relationship between process parameters and the performance of objective functions。 The RSM relates to   re-

Figure 3。 Multi-objective optimization framework。

gression analysis and numerical-experiment statistical design, towards constructing the global optimization。 RSM is a well- known method with higher accuracy and better ease-of use than other popular meta-models, such as radial basis function and kriging model。 The second-order RSM model is suitable for modeling the moderate non-linear behavior with few de- sign variables。 These factors make the RSM model an appro- priate method。