Optimization and Simulation for Ceramic Injection Mould of ZrO2 Fiber Ferrule

Fiber ferrule is a crucial part for manufacturing fiber connectors. It is fairly difficult to produce fiber ferrule because that it requires high dimension accuracy. Currently, YTZ ceramic powder is the main material used to produce fiber ferrule and Ceramic Injection Molding (CIM) is a new fabricating method capable of producing ZrO2 fiber ferrule (Fig. 1(a), Fig. 1(b)) with complex geometry and high accuracy. ZrO2 fiber ferrule quality is significantly influenced by the process conditions of CIM. Therefore, the main focus of this paper is to optimize mould structure and processing parameters based on the simulation of CIM, which promotes solid load of ceramic powder and product quality. Optimal process conditions of Ceramic Injection Molding could be determined by analyzing the simulation results. It has been found that runner cross-section shape and runner system contribute to the efficiency and filling process significantly. Hence, optimal runner cross-section shape and runner system are proposed. Reducing the gravity influence on CIM is also suggested. Moreover, optimization of cooling system could be considered an effective way to improve the dimensional precision and surface quality of ZrO2 fiber ferrule.


Introduction
Fiber ferrule is a crucial part for manufacturing fiber connectors. It is fairly difficult to produce fiber ferrule because that it requires high dimension accuracy. Currently, YTZ ceramic powder is the main material used to produce fiber ferrule and Ceramic Injection Molding (CIM) is a new fabricating method capable of producing ZrO 2 fiber ferrule ( Fig.  1(a), Fig. 1(b)) with complex geometry and high accuracy. ZrO 2 fiber ferrule quality is significantly influenced by the process conditions of CIM. Therefore, the main focus of this paper is to optimize mould structure and processing parameters based on the simulation of CIM, which promotes solid load of ceramic powder and product quality. Optimal process conditions of Ceramic Injection Molding could be determined by analyzing the simulation results. It has been found that runner cross-section shape and runner system contribute to the efficiency and filling process significantly. Hence, optimal runner cross-section shape and runner system are proposed. Reducing the gravity influence on CIM is also suggested. Moreover, optimization of cooling system could be considered an effective way to improve the dimensional precision and surface quality of ZrO 2 fiber ferrule.

Optimization of runner cross-section shape
During filling stage, the melt is firstly injected into mould cavity and this stage is accomplished as the mould cavity is fully filled by melt. Therefore, it is of great importance to control melt flow pattern within mould cavity, which could promote the solid load of ceramic powder. Cooling time and many product defects like cavitations, weld line, short shot and product deformation are related to the melt flow pattern. The melt flow pattern is influenced by many factors like the dimension of runner cross-section shape and runner system arrangement. Hence, optimized runner cross-section shape and well-designed runner system would be beneficial to the Ceramic Injection Molding. In order to investigate the melt flow pattern, pressure changes, temperature, cavitations etc., we use Moldflow Plastic Insight (MPI) to simulate the melt flow pattern within the mould cavity. Also, potential defects would be predicted during this simulation. The optimal runner crosssection shape could be determined though analyzing simulation results of different runner cross-section shapes.
Runners should ensure that the melt ejected from injection machine can smoothly flow through runners and fully fill mould cavity. What is more, runners should adequately transfer pressure to all the positions of mould cavity to obtain high quality products during filling process.
Common runner cross-section shapes ( Fig. 2) are circular, ladder, U-shape (combination of circular and ladder), semicircular and rectangular. It usually is recommended to use the first three runner cross-section shapes. Considering the ratio of volume to its surface area, circular cross-section shape is most suitable, with minimal pressure drop and heat loss. However, templates on both sides of circular runners need to be processed, which causes much higher cost. Furthermore, semicircles on both surfaces of those two templates of circular runners have to be aligned accurately.
Circular Ladder U-shape Semicircular Rectangular Ladder runner cross-section shape requires one processed template only, which still works well. Ladder runner is commonly used in three-plate mould. Circular runner cross-section shape is rarely adopted in three-plate mould for it may be difficult to demould and cause interference between runner and sliding part of templates. Different runner cross-section shapes could be compared by hydraulic diameter (Table 1) which is the index of flow resistance. The larger the hydraulic diameter is, the lower the flow resistance is. The definition of hydraulic diameter is described as equation 1.
Where h D is the hydraulic diameter, A is the section area and P is the perimeter.
Equivalent hydraulic diameters of various runner cross-section shapes are compared in Table 2. www.intechopen.com

Optimization and Simulation for Ceramic Injection Mould of ZrO 2 Fiber Ferrule 151
Crosssection

Crosssection
2 (a r c t a n ( ) ) HH WH W   Table 2. Comparison between equivalent diameters of various runner cross-section shapes.

Analytical solutions of various runner cross-section shapes
The main factors influencing melt flow are injection pressure, melt temperature and viscosity, mould temperature, runner cross-section area and geometric cross-section shape. The geometric cross-section shape determines runner efficiency.
It requires the following conditions to improve runner efficiency (Pan et al., 1995). Runner resistance to the melt flow, which is normally caused by the friction between melt and inner runner surface, should be as low as possible to ensure that the melt can fully fill the mould cavity before solidifying.
The heat loss should be minimal as the melt flows through runner. When the melt with high temperature flows through runner with comparatively lower temperature, melt would transfer its heat to the mould, which increases mould temperature. On the other hand, the melt temperature decreases. Also, melt viscosity increases when melt temperature becomes lower, which makes melt fluidity worse. When the temperature decreases to a certain degree, temperature distribution within inner side of melt becomes significantly inhomogeneous that causes many defects in the products. In this case, we can improve the www.intechopen.com Some Critical Issues for Injection Molding 152 injection pressure moderately. However, it would affect clamp if injection pressure becomes too high.
For improving runner efficiency, many measurements could be adopted during designing and manufacturing stages. Firstly, the area of runner cross-section shape can be increased, which decreases the resistance to melt flow. However, it would waste energy and raw materials if the area of runner cross-section shape becomes oversize. Secondly, the contact area between runner and melt could be diminished by decreasing periphery length of runner cross-section shape. Thirdly, runner layout should be simple and its length should be minimal. Finally, the runner surface roughness can be decreased. Normally, R a is between 0.8 and 1.8 m  . Also, mould temperature needs to be controlled within certain range.
Projected area of runner on the parting surface should be minimal. The injection area actually is decreased if we decrease projected area, which diminishes the opening force of mould. In this way, we can adequately use the clamp force of injection machine to clamp the mould.
The smaller the runner volume is the better. This would improve utilization ratio of raw materials and save energy. The runner volume with fixed length would become smaller as the runner cross-section shape area decreases. Hence, the runner cross-section shape area should not be oversize.
Runners with advantages mentioned above can be considered to have high efficiency. And runner efficiency is expressed by equation 2.

S Ll
where  is runner efficiency, S is runner cross-section shape area, L is peripheral length of runner cross-section shape, l is runner length and Ll  is runner lateral area.
Equation 2 illustrates that runner efficiency is equal to the ratio of runner cross-section shape area to its lateral area. Also, the runner lateral area is equal to the peripheral length of runner cross-section shape multiplied by runner length. Therefore, increasing the runner cross-section shape area, decreasing the peripheral length of runner cross-section shape and reducing the runner length all can improve runner efficiency. In this paper, runner efficiency refers to the runner efficiency when runner length is unit length ( 1 l  ). Its value is equal to the ratio of runner cross-section shape area to its peripheral length (equation 3).

 
(3) Runner efficiency is influenced by its cross-section shape area and peripheral length. Therefore, runner efficiency is related to its geometric parameters of cross-section shape.
We compare various runners under the same conditions (Table 3). In the Table 3,  is runner efficiency and D is runner width. Cross-section shape areas of different runners are the same ( 2 1 sm m  ) when calculating  and D. V is the runner volume when runner length is unit length and efficiency is 1 ( 1   ). According to Table 3, the width of rectangular runner is minimal. Dimension of runner projection on the parting surface would be decreased if we reduce the width, which improves the mode-locking of the injection machine. This is the main advantage of rectangular runner. However, it is rather difficult to demould for rectangular runner without demoulding inclination. Therefore, we usually use gate with rectangular cross-section in practice.  Table 3. Comparison between the analytical solutions of various runners.

Runners
The efficiency of circular runner is highest and its runner volume to its unit length is minimal. Decreasing runner volume can promote the utilization of raw materials and save energy. However, if the circular runner is used in the cold-runner mould, circular runner needs to be divided into two semicircular runners on the parting surfaces of cover half and moving half respectively. These two semicircular runners have to be exactly the same. Therefore, it would be very difficult to manufacture mould with circular runners. Usually, the circular runners are used in the hot-runner mould rather than in the cool-runner mould.
Apparently, with the same cross-section shape area, efficiency of U-shape runner is highest compared with that of semicircular and ladder runners. The width of U-shape runner is smaller than that of circular runner. With the same efficiency and length (unit length), the volume of U-shape is minimal among the semicircular, ladder and U-shape runners and next to that of circular runner. Therefore, U-shape is most suitable in the cool-runner mould. Semicircular runner is not the perfect approach for its minimal efficiency and largest width and volume.

Feedstock rheology
Compositions of ZrO 2 feedstock are filler (solid paraffin), adhesive (vinyl acetate polymer) and lubricant (stearic acid). These compositions are shown as Table 5 ( Wenjea et al., 1999) and the relationship between viscosity and shear rate is shown as Fig. 3

Simulation outcomes
Pressure drop, filling time, temperature difference and clamp force determines the product quality and these are important parameters of injection machine. In this paper, we use the parameters mentioned above to discuss simulation outcomes of various cross-section shapes (   During these simulations, injection temperature is 140  C and mould temperature is 60  C. Injection time, pressure and velocity are controlled by program. The simulation outcomes of various runner cross-section shapes are shown as  Table 6. Analytical parameters of various runner cross-section shapes.

Circular Semicircular Rectangular Ladder U-shape
Injection pressure is an important, technical parameter of injection molding. It should not be too high or it may be hard to demould and cause raw edges on the product surface. What is more, the melt would not be able to fully fill mould cavity if the injection pressure is too high. Therefore, a suitable injection pressure is very necessary. Improving the injection pressure can improve the melt compression ratio and dimension accuracy . Runners with different cross-section shapes are compared under the same conditions (Table 7). According to Table 7, circular runner has minimal pressure drop, shortest filling time and smallest temperature difference, which means that it has the highest efficiency. On the other hand, rectangular runner has the smallest clamp force.

Runner
Compared with semicircular and ladder runners, U-shape runner has smallest pressure drop, shortest filling time, minimal temperature difference and highest efficiency. Therefore, runner with U-shape cross-section shape is the best choice.

Layout of runner system and optimization of technical parameters
During Ceramic Injection Molding stage, raw materials within staff canister firstly are heated to become melt which is driven quickly by the piston or screw into the closed cavity. Then, the melt within mould cavity compressed by mould and cools down to become product. The main concern of Ceramic Injection Molding is that the products should meet the quality requirement. Also, the solid load of ceramic powder, which is related to the product quality, should be as high as possible.
The conventional methodology optimizing process parameters requires experts use the trial and error method basing on their experience and professional knowledge. As the development of CAE technology, it becomes increasingly important to industry, especially to improve product quality and decrease cost etc. We combine CAE experiment and DOE methodology to get the best parameter combination based on the range analysis of orthogonal experiment. Also, the conclusion could be tested by the CAE comparison experiments.

Layout of runner system
The mould is composed of two templates with six cavities and common arrangement of multi-cavity system is radiated runner system. Melt can only be poured into the cavity through gates on both sides of mould for there is a fairly small hole in the axial center of products. Runner systems with rectangular and circular shunt are showed as Fig. 8 (Zhang, 2005(Zhang, , 2007.

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 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).

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. 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. 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(Zhang, , 2007. 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   Table 9. Orthogonal table.

Experimental number
www.intechopen.com    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.

Simulation results
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. 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.

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(Zhang, , 2007.

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.

Cooling simulations
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 time etc.

Summary of cooling simulation
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 stress within product.
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 given parameters (Chen et al., 2002).

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Some Critical Issues for Injection Molding 162 5.2 Establishing the mathematical model

Basic assumption and controlling equation
Physical process of cooling stage is fairly complex and we need simplify physical process before constructing controlling equation. Firstly, we assume that the mould work state is stable without considering periodic temperature changes of die well. Secondly, we assume that the heat flow only propagates along the normal direction of inner cavity surface. Thirdly, we assume that the product surfaces and die well have the same temperature and the product contacts cavity surface completely.
Based on the assumption mentioned above, we consider the injection molding cooling to be steady heat conduction without heat source. And controlling equation is equation 4 (Li et al., 2001).
Where V is the region enclosed by outer surface of mould, inner surface of cavity and surface of cooling gates.

Boundary conditions
Boundary condition on the cavity surface is equation 5 (Li et al., 2001).
where u is out normal direction of cavity surface, w K is thermal conductivity of mould and q  is average heat flux which is defined by equation 6.
where t is the time, T is the melt temperature,  , K p and C p are the density, heat conductivity and equivalent specific heat respectively and s is local coordinate along the product thickness direction. When analyzing one dimension transient heat conduction of injection mould, we consider the injection temperature or melt temperature distribution at the end of filling stage to be the initial condition. Also, we select the cavity surface temperature as the boundary condition.

Optimization and Simulation for Ceramic Injection Mould of ZrO 2 Fiber Ferrule 163
The boundary condition of gate surface is defined as equation 8 (Li et al., 2001).
where u is outer normal direction of gate surface, c T is cooling medium temperature, h is heat transfer coefficient between mould and coolant (equation 9). The outer surface heat exchange of mould normally does not have much effect on the temperature distribution of cavity surface, which means that it is unnecessary to calculate outer surface temperature distribution of mould. Therefore, we can consider the outer surface of mould to be an infinite, adiabatic sphere.

Cooling analysis and moldflow software application
Regulating and keeping the mould temperature could decrease product deformation and improve mechanical properties and dimension accuracy. Therefore, it is necessary to design the cooling system perfectly for injection molding. Researchers have done a lot of research related to the cooling system and got many simplified and empirical formula. MPI/Cool can analyze the effect of cooling system on the mould and optimize arrangement of cooling system.

Summary of MPI/cool software
Many factors affecting the injection molding cooling are product shape, cooling medium type, temperature, velocity, geometric parameters and arrangement of cooling pipe, mould material, melt temperature, ejected temperature, mould temperature and thermal cycling interaction between production and mould etc. These factors interact and relate with each other, which means that the best methodology is to combine these parameters. Yet, it only can be achieved by CAE analysis rather than by conventional simplified and empirical formula.
MPI/Cool software simulates this three dimension temperature field by boundary element method. Analytical solution could be used to calculate temperature field along the product thickness direction. What is more, MPI/Cool can obtain the interactive solution between mould temperature field and temperature field along the product thickness direction. Also, MPI/Cool can calculate the interface temperature between product and mould by the simultaneous energy equation of mould temperature field. Furthermore, we consider the influence of cavity and core asymmetry along the thickness direction on the product temperature distribution.
MPI/Cool can simulate the cooling pipe (separator pipe, jet pipe and connecting hose), insert, various mould materials, cool runner and hot runner, parting surface and product temperature. This can provide information for optimizing the cooling system.
MPI/Cool can not only analyze the neutral plane and fusion mould but also analyze 3D mould. Also, the dynamic analysis of injection process could be obtained by combining MPI/Cool and MPI/Flow.

Cooling simulation
Product mould could be constructed by Pro/E and UG etc. which can be read into MPI by STL file format. Then, cooling system and gating system are built in MPI. Three different cooling systems are shown Table 11 (Liu et al., 2010).
Cooling system one Cooling system two Cooling system three Table 11. Arrangement of cooling systems.

Input the process parameters
We set the melt temperature, cavity temperature and cooling pipe diameter to be 150  C, 40  C and 8mm respectively. The coolant is water ( 25  C) and Reynolds number is 10000. Finally, we use t software to calculate cooling time.

Simulation results of cooling time
We obtain coolant temperature, coolant velocity, cooling pipe temperature and Reynolds number of coolant (Fig. 13, Fig. 14, Fig. 15) after analyzing cooling process.
According to Fig. 13, Fig. 14, Fig. 15, we find that pipe and coolant temperature distribution in the third cooling system is much more homogeneous than that in the former two. In order to compare the cooling efficiency of three different cooling systems, we can calculate the cooling time of three cooling system by software. The calculated cooling time is shown as Table. 12. According to Table. 12, the first cooling system has longest cooling system, next is the second cooling system and the third cooling system has shortest cooling time.
Therefore, the third cooling system has best heat balance and cooling efficiency.
www.intechopen.com  Table 12. Cycle time of different cooling system.

Comparison between simulation results of these three cooling system
There are two kinds of cooling analysis, namely manual and automatic cooling analysis. We need to set the cooling time when using manual cooling analysis. Cooling time is calculated by software in the automatic cooling analysis. We use the automatic approach to analyze the cooling efficiency of three different cooling systems in the former chapter. In order to compare their cooling efficiency with given cooling time, we use the manual cooling analysis and set the cycle period to be 35s, 30s, 25s respectively.
During cooling process, six cavities are cooled unevenly for the different arrangement of cooling pipes. We number the six cavities according to clockwise direction ( Fig. 16 (a)) and select the top, middle and bottom parts of every cavity ( Fig. 16(b)) to analyze the temperature distribution of each cavity with different cooling condition.  Table 13 demonstrates the general temperature difference of product in three cooling systems respectively when cycle period is 35s. According to Table 13, product temperature difference in the first cooling system is similar to that in the second cooling system. Also, temperature difference in the third cooling system is comparatively higher for it cools much faster, which causes local parts cool significantly. However, product temperature differences in these cooling systems all are acceptable.  Table 13. General temperature difference of product when cycle period is 35s (  C). Table 14 illustrates the temperature simulation of three different parts in the cavity axis in different cooling systems when the cycle period is 35s. According to Table 14, the given part temperature in certain cavity in the first cooling system is the highest. Next is the second cooling system. The given part temperature in certain cavity in the third cooling system is the lowest. The cooling effect of given position varies in different cavities. In the first cooling system, Cavity one and two near the coolant inlet have better cooling effect compared with cavity three and four. In the second cooling system, cavity one and six have better cooling effect compared with cavity four and five. In the third cooling system, Cavity one has the lowest temperature. However, the general temperature of six cavities is approximately the same.

Simulation outcomes with 35s cycle period
In these cooling systems, the extreme value of temperature difference of each cavity is shown as Fig. 17. It demonstrates that the extreme value of temperature difference of top, middle and bottom parts in the third cooling system is much lower than that in the former two, which means that the third cooling system has the best cooling efficiency. Fig. 17. Extreme values of temperature difference of various positions in each cavity when cycle period is 35s (  C). Table 15 demonstrates the general temperature difference of product in these three cooling systems when the cycle period is 30s.

Simulation result with 30s cycle period
According to Table 15, product temperature difference in the first cooling system is similar to that in the second cooling system. On the other hand, product temperature in the third cooling system is comparatively higher. Therefore, simulation results are similar to that in three cooling systems when the cycle period is 35s.  In the second cooling system, product temperature in the cavity one and six is much lower than that in the cavity three and five. In the third cooling system, cavity one and six have much lower temperature. However, temperature distribution in six cavities is even. Extreme values of temperature difference of various positions in each cavity when cycle period is 30s are shown as Fig. 18. The extreme values of temperature difference of top, middle and bottom part in each cavity in the third cooling system are smaller than that in the former two. Fig. 18. Extreme values of temperature difference of various positions in each cavity when cycle period is 30s (  C).

Simulation outcomes when cycle period is 25s
Table 17 demonstrates the temperature difference of product with three cooling system when cycle period 25s. According to Table 17, temperature difference of product in the first cooling system is similar to that in the second cooling system. The general temperature difference of product in the third cooling system is the highest. Simulation results are similar to the outcomes obtained above.
Cooling system one  Table 17. General temperature difference of product when cycle period is 25s (°C). Table 18 shows the temperature simulation of three different positions in different cooling system when the cycle period is 25s. Apparently, cooling efficiency of third cooling system is the best and temperature distribution of each cavity is even in the third cooling system.  Table 18. Temperature simulation of three different positions with different cooling system when cycle period is 25s (  C).
Extreme values of temperature difference of various positions in each cavity are shown as Fig. 19 when cycle period is 25s. The extreme values of temperature difference of top, middle and bottom parts in each cavity in the third cooling system are smaller than that in the former two. Fig. 19. Extreme values of temperature difference of various positions in each cavity when cycle period is 25s (  C).
Cooling system one

Conclusion
Firstly, we used Moldflow to calculate pressure drop, filling time, temperature difference and clamp force of five different cross-section shapes. Outcomes demonstrate that U-shape runner has smallest pressure drop, shortest filling time, minimal temperature difference and highest efficiency. Therefore, U-shape runner is most suitable for cool-runner mould rather than circular or other kinds of runners.
Secondly, we investigated runner systems with rectangular and circular shunt respectively by orthogonal table. Also, we researched influence of mould temperature, injection temperature, screw velocity and gate dimension on products. Results show that runner system with circular shunt is most suitable for Ceramic Injection Molding. Furthermore, we considered the gravity influence on Ceramic Injection Molding and found that short shot tends to happen on the top cavity when runner diameter is 4mm. All six cavities are filled well after increasing runner diameter to 4.17 mm.
Finally, we simulated cooling efficiency of three cooling systems and results show that the third cooling system has shortest cooling cycle and best cooling efficiency, which can cool product as fast as possible. Cooling efficiency in six cavities is not the same for the cooling system arrangement and for the inlet and outlet location. Temperature extreme values of top, middle and bottom positions in each cavity in the third cooling system are smaller than that in former two cooling system.