**5. Cooling simulations**

160 Some Critical Issues for Injection Molding

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.

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

Injection time (s) Injection pressure(MPa) Temperature difference (°C)

Also, gates with too small dimension require comparatively large injection pressure.

shunt 0.195 108 9.1 Circular shunt 0.182 95.1 6.9

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.

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

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,

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

contribute to decrease product surface temperature difference.

Table 10. Simulation outcomes of best parameter combination.

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

into consideration for large runner length, zirconia density and viscosity.

bottom die quality is better than that of top die (Zhang, 2005, 2007).

Rectangular

**4.1 Improvement** 

runner system have same quality.

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.

#### **5.1 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).

Optimization and Simulation for Ceramic Injection Mould of ZrO2 Fiber Ferrule 163

*m c* ( ) *<sup>T</sup> K hT T u*

where u is outer normal direction of gate surface, *Tc* is cooling medium temperature, *h* is

0.8 0.4 0.23 *e r kc h RP*

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

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

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

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

(8)

*<sup>D</sup>* (9)

, *a* and *kc* are the kinematic viscosity, thermal

/ is Prandtl number, Q is the coolant

The boundary condition of gate surface is defined as equation 8 (Li et al., 2001).

is Reynolds number, *P a <sup>r</sup>*

heat transfer coefficient between mould and coolant (equation 9).

Where *R QD <sup>e</sup>* 4 /

system.

formula.

temperature distribution.

 

volume, D is the cooling hole diameter,

**5.3.1 Summary of MPI/cool software** 

diffusivity and heat conductivity respectively.

surface of mould to be an infinite, adiabatic sphere.

**5.3 Cooling analysis and moldflow software application** 

#### **5.2 Establishing the mathematical model**

#### **5.2.1 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).

$$\frac{\partial^2 T}{\partial \mathbf{x}^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\partial^2 T}{\partial z^2} = 0 \quad \text{(x, y, z)}\\ \in V \tag{4}$$

Where V is the region enclosed by outer surface of mould, inner surface of cavity and surface of cooling gates.

#### **5.2.2 Boundary conditions**

Boundary condition on the cavity surface is equation 5 (Li et al., 2001).

$$-K\_w \frac{\partial T}{\partial u} = \bar{q} \tag{5}$$

where *u* is out normal direction of cavity surface, *Kw* is thermal conductivity of mould and *q* is average heat flux which is defined by equation 6.

$$\bar{q} = \frac{1}{t\_c + t\_p} \left( \int\_0^{t\_c} q\_1(t)dt + \int\_0^{t\_c + t\_p} q\_2(t)dt \right) \tag{6}$$

where *ct* and *pt* are cooling and demoulding time respectively, 1 *q t*( ) and 2 *q t*( ) are the instantaneous heat flux during cooling and demoulding stage. The cooling time *ct* and <sup>2</sup> *q t*( ) could be obtained by solving the one dimension transient heat conduction equation (equation 7).

$$
\rho \mathbf{C}\_p \frac{\partial T}{\partial t} = \frac{\partial}{\partial \mathbf{s}} (\mathbf{K}\_p \frac{\partial T}{\partial \mathbf{s}}) \tag{7}
$$

where t is the time, T is the melt temperature, , Kp and Cp 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.

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

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.,

Where V is the region enclosed by outer surface of mould, inner surface of cavity and

*w <sup>T</sup> K q u*

where *u* is out normal direction of cavity surface, *Kw* is thermal conductivity of mould and

*q q t dt q t dt*

where *ct* and *pt* are cooling and demoulding time respectively, 1 *q t*( ) and 2 *q t*( ) are the instantaneous heat flux during cooling and demoulding stage. The cooling time *ct* and <sup>2</sup> *q t*( ) could be obtained by solving the one dimension transient heat conduction equation

> ( ) *p p T T C K ts s*

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

 

0 0 1 2 <sup>1</sup> () () *<sup>c</sup> c p <sup>t</sup> t t*

(,,) *xyz V* (4)

(5)

(6)

(7)

, Kp and Cp are the density, heat

222 <sup>222</sup> <sup>0</sup> *TTT xyz* 

Boundary condition on the cavity surface is equation 5 (Li et al., 2001).

*c p*

*t t*

is average heat flux which is defined by equation 6.

where t is the time, T is the melt temperature,

temperature as the boundary condition.

**5.2 Establishing the mathematical model** 

the product contacts cavity surface completely.

2001).

*q* 

(equation 7).

surface of cooling gates.

**5.2.2 Boundary conditions** 

**5.2.1 Basic assumption and controlling equation** 

The boundary condition of gate surface is defined as equation 8 (Li et al., 2001).

$$-K\_m \frac{\partial T}{\partial \mu} = h(T - T\_c) \tag{8}$$

where u is outer normal direction of gate surface, *Tc* is cooling medium temperature, *h* is heat transfer coefficient between mould and coolant (equation 9).

$$h = 0.23 \frac{kc}{D} R\_e^{0.8} P\_r^{0.4} \tag{9}$$

Where *R QD <sup>e</sup>* 4 / is Reynolds number, *P a <sup>r</sup>* / is Prandtl number, Q is the coolant volume, D is the cooling hole diameter, , *a* and *kc* are the kinematic viscosity, thermal diffusivity and heat conductivity respectively.

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.

#### **5.3 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.

#### **5.3.1 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.

Optimization and Simulation for Ceramic Injection Mould of ZrO2 Fiber Ferrule 165

Circuit coolant temperature=26.60[C] Circuit flow rate=3.387[lit/min]

Circuit metal temperature=31.44[C] Circuit Reynolds number=10001

Circuit coolant temperature=26.18[C] Circuit flow rate=3.387[lit/min]

Circuit metal temperature=31.21[C] Circuit Reynolds number=10001

Fig. 13. Simulation outcomes of first cooling system.

Fig. 14. Simulation outcomes of second cooling system.

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.
