**3.2 Orthogonal experiment methodology**

Injection molding CAE technology uses finite element methodology, finite difference methodology and boundary element methodology to analyze the flow, dwell and cooling stage. It can calculate stress distribution within product and mould to predict product quality. Also, it can analyze the influences of process conditions, material parameters and mould structure on the products for the purpose of optimizing mould structure and process parameters.

Experiment design method (DOE) is mainly used to acquire the experimental data and analyze the experimental data and results scientifically. The main DOE application is the orthogonal experiment which designs the experiment based on data orthogonality (Yang et al., 2004). There are many distinct advantages of orthogonal experiment. Firstly, it can select a small number of experimental conditions, which are representative, from a large number of experimental conditions. Secondly, the best experimental conditions and manufacture process could be determined by analyzing experimental outcomes with those representative conditions. Finally, it would be much easier to process the data based on the orthogonal experiment.

Orthogonal table is the most important, basic tool and orthogonal experiments can easily calculate the effect of each condition on the results and display them by tables. Then, we can determine the best parameters after range analysis and comparison. All the calculations are done by tables and the whole processes are rather easy. Therefore, DOE is able to shorten the cycle of developing and designing new products, which is necessary to the manufacture and

Optimization and Simulation for Ceramic Injection Mould of ZrO2 Fiber Ferrule 159

Fig. 9. Relationships between filling time and each factor.

Fig. 10. Relationship between injection pressure and each factor.

Fig. 11. Relationship between temperature difference and each factor.

Fig. 9 illustrates that screw velocity has largest influence on filling time. Therefore, increasing screw velocity can shorten filling time. Other factors influence filling time

**3.4 Simulation results** 

slightly.

research. During injection molding, injection process parameters directly affect the product quality. Many researchers have designed experiments to research the relationship between them and got some useful conclusions (Skourlis et al., 1997; Jansen et al., 1998). However, conventional methodology requires a large number of experiments to research that relationship. Yet, research demonstrates that an economic method is to use the orthogonal experiment which in turn can instruct the injection molding process (Jin & Zhu., 2000).

### **3.3 Arrangement of orthogonal experiment**

In this paper, we focus on these two runner systems mentioned above and use orthogonal experiment method to study the influence of two runner systems on products.

Mould temperature, injection temperature, screw velocity and gate dimension all are important parameters influencing product quality. Mould temperature A, injection temperature B, screw velocity C and gate dimension D all have three different values, namely A1, A2, A3, B1, B2, B3, C1,C2, C3, D1, D2, D3. We use L9 ( <sup>4</sup> 3 ) orthogonal table to design experiments and use Moldflow software to investigate the influence of those parameters on product quality.


Table 8. Arrangement of factors and levels.

Finally, we can obtain the best parameter combination. Values of four parameters mentioned are shown as Table 8 and orthogonal table L9 is shown as Table 9. We consider the actual filling time, maximal injection pressure and temperature difference at the end of filling stage as the main parameters. By orthogonal experiment, we can know that when we just consider one condition with different values, this condition would have much more effect on the result if it has a larger range (Shen et al., 2001, 2002). In order to demonstrate the influence of each condition on the injection flow, we draw the relation graphs between them as Fig. 9, Fig. 10 and Fig. 11 (Zhang, 2005, 2007).


Table 9. Orthogonal table.

research. During injection molding, injection process parameters directly affect the product quality. Many researchers have designed experiments to research the relationship between them and got some useful conclusions (Skourlis et al., 1997; Jansen et al., 1998). However, conventional methodology requires a large number of experiments to research that relationship. Yet, research demonstrates that an economic method is to use the orthogonal

In this paper, we focus on these two runner systems mentioned above and use orthogonal

Mould temperature, injection temperature, screw velocity and gate dimension all are important parameters influencing product quality. Mould temperature A, injection temperature B, screw velocity C and gate dimension D all have three different values, namely A1, A2, A3, B1, B2, B3, C1,C2, C3, D1, D2, D3. We use L9 ( <sup>4</sup> 3 ) orthogonal table to design experiments and use Moldflow software to investigate the influence of those

A Temperature of mould (oC) 35/40 45/50 60/65 B Injection temperature(oC) 130/135 145/150 160/165 C Screw velocity (%) 75 60 50 D Width and length of the gates(mm) 1, 0.5 1.2, 0.6 1.5, 0.8

Finally, we can obtain the best parameter combination. Values of four parameters mentioned are shown as Table 8 and orthogonal table L9 is shown as Table 9. We consider the actual filling time, maximal injection pressure and temperature difference at the end of filling stage as the main parameters. By orthogonal experiment, we can know that when we just consider one condition with different values, this condition would have much more effect on the result if it has a larger range (Shen et al., 2001, 2002). In order to demonstrate the influence of each condition on the injection flow, we draw the relation graphs between

Experimental number A B C D

1 1 1 1 1 2 1 2 2 2 3 1 3 3 3 4 2 1 2 3 5 2 2 3 1 6 2 3 1 2 7 3 1 3 2 8 3 2 1 3 9 3 3 2 1

factor Level 1 Level 2 Level 3

experiment which in turn can instruct the injection molding process (Jin & Zhu., 2000).

experiment method to study the influence of two runner systems on products.

**3.3 Arrangement of orthogonal experiment** 

parameters on product quality.

Table 9. Orthogonal table.

Table 8. Arrangement of factors and levels.

them as Fig. 9, Fig. 10 and Fig. 11 (Zhang, 2005, 2007).

Fig. 9. Relationships between filling time and each factor.

Fig. 10. Relationship between injection pressure and each factor.

Fig. 11. Relationship between temperature difference and each factor.

#### **3.4 Simulation results**

Fig. 9 illustrates that screw velocity has largest influence on filling time. Therefore, increasing screw velocity can shorten filling time. Other factors influence filling time slightly.

Optimization and Simulation for Ceramic Injection Mould of ZrO2 Fiber Ferrule 161

(a) (b)

Fig. 12. Simulation of gravity effect on ceramic injection molding; (a) runner diameter is 4mm;

Injection molding cooling refers to the stage after solidification to demould products from mould which occupies 3/4 of product cycle. Cavity temperature and uniformity directly influences product efficiency and quality. Injection molding temperature can be affected by various factors. Temperature control and regulation are mainly accomplished by cooling system. Cooling process parameters are composed of cooling pipeline dimension, connection and location etc. Physical parameters include cooling medium flow and gate temperature etc. The most important process parameter during cooling stage is cooling time and an efficient and balance cooling system could improve cooling efficiency and decrease residual stress. The purpose of cooling analysis is to determine cooling system though simulating the cooling process which predicts the surface temperature of mould and cooling

The main stages of injection molding cycle are filling, dwell and cooling stages. The heat transfer process of injection molding shows that inner part of melt with high temperature transfers heat to the mould and the heat is taken by cooling medium. Therefore, balance cooling could prevent hot streak on product surface and decrease warpage and residual

Injection molding cooling is mainly controlled and regulated by cooling system. The main purpose of cooling system is to cool the product fast and evenly. Cooling system parameters are composed of geometric and process parameters like cooling hole location, dimension, cooling medium flow and gate temperature. Cooling stage simulation could predict the cavity and core temperature, temperature difference distribution and cooling time with

(b) runner diameter is 4.17mm.

**5.1 Summary of cooling simulation** 

given parameters (Chen et al., 2002).

stress within product.

**5. Cooling simulations** 

time etc.

Product quality could be improved by decreasing injection pressure. According to Fig. 10, we can see that injection temperature and gate dimension have largest effect on injection pressure. Therefore, improving injection temperature could decrease the injection pressure. Also, gates with too small dimension require comparatively large injection pressure.

Comparatively small temperature difference could be beneficial to the homogenous filling of powder and adhesive, which can prevent temperature gradient and density gradient caused by two-phase separation. Fig. 11 demonstrates that injection temperature and screw velocity have largest effect on temperature difference and next is the gate dimension and mould temperature. Hence, lower injection temperature and higher screw velocity contribute to decrease product surface temperature difference.


Table 10. Simulation outcomes of best parameter combination.

Considering all the factors, we can conclude that the best parameter combination of runner system with rectangular shunt is A2B2C2D3 and best parameter combination of runner system with circular shunt is A3B2C1D2. Simulation outcomes of two runner system are shown as Table 10. What is more, filling quality of runner system with circular shunt is much better than that of runner system with rectangular shunt and injection pressure the former runner system requires is 15MPa, less than that of the latter. Filling time and surface temperature difference of the former one are much smaller compared that of the latter one. Therefore, runner system with circular shunt is most suitable for ceramic injection molding.

#### **4. Gravity influence on the ceramic injection mould**

The melt fills five of six cavities well except the one on the top of mould where short shop happens. However, mould with six cavities is designed to have balance runner system, which means that the six cavities should all be filled well. Therefore, gravity should be taken into consideration for large runner length, zirconia density and viscosity.

In order to simplify the calculation and analysis, we select two cavities on the top and bottom parts of mould respectively as research objects. Fig. 12(a) demonstrates the simulation outcomes with conditions namely mould temperature ( 60 C), injection temperature ( 145 C), screw velocity (75%) and gate dimension (1.2mm and 0.6mm) when considering gravity influence. According to Fig. 12(a), we can see that cavities show difference in filling stage. Filling time of bottom die is much less than that of top die where the short shot happens. Also, bottom die quality is better than that of top die (Zhang, 2005, 2007).

#### **4.1 Improvement**

Two cavities on the top and bottom parts of mould show difference on the filling stage and short shot happens on the top cavity. Therefore, we increase runner diameter from 4mm to 4.17 mm. Fig. 12(b) illustrates that both the top and bottom dies with optimized balance runner system have same quality.

Fig. 12. Simulation of gravity effect on ceramic injection molding; (a) runner diameter is 4mm; (b) runner diameter is 4.17mm.
