**2.3 Bubble growth process**

When the nucleation is completed, bubbles begin to grow up. Because the pressure of the mixer is higher than the pressure inside bubbles, SCF in the mixer diffuses into the bubbles and the bubbles grow up. Until the pressure inside the bubbles equals to the outside one or the melt is frozen, the bubbles will keep growing up.

#### **2.3.1 Classic bubble growth model**

Initially, the growth and collapse of gas bubbles in both viscous Newtonian and viscoelastic non-Newtonian fluids has been investigated to research on the effect of mass transfer, and the hydrodynamic interaction between the bubble and the liquid was neglected. Barlow et al. [21] are the first to study the phenomenon of diffusion-induced bubble growth in a viscous Newtonian fluid with both mass and momentum transfer. To predict the diffusion of the dissolved gas in the viscous liquid, they used a thin shell approximation. It is assumed that the gas concentration outside the shell always remained equal to the initial concentration. The simplified diffusion equation and an analytical solution were obtained to describe the initial stage of the growth at low Reynolds numbers.

Microcellular Foam Injection Molding Process 191

tension at the interface of the melt and the gas, *P* is the pressure of the melt at the outer

Based on the dynamics principle of cell model, the value of *P***<sup>g</sup>** decreases when *R* becomes larger. At the same time, the gas only diffuses into the cell. The gas diffusion is determined by the gas dissolution grads. The diffusion will be going on until the driven power disappears or the melt is frozen. Thus, the relationship between *R* and *P***g** can be governed

> 2 1

where *c* is the concentration of the dissolved gas in the mixer, *<sup>r</sup> v* is the gas diffusion velocity in the radius direction of spherical coordinates, *D* is the diffusion coefficient in the

The left of Equation 2-10 shows the change rate of gas concentration, while the right shows

**d d**

2 *r* 2 *R R*

*cc c D r t r rr r*

single solution, *r* is the radial coordinate, *t* is the time, *S* is the radius of the cell.

*v*

And the gas concentration *c* between *S* and *R t*( ) can be calculated by Henry law:

where **h***k* is the Henry law coefficient. It is determined by the plastics and gas type and

As said above, the gas in the cell is assumed as ideal gas. Thus **g***P t*( ) can be calculated by

where *R***g** is gas constant, **<sup>g</sup>** *R* 8.3145 J/(molK), *T* is the temperature (K), *M***w** is gas

**g <sup>g</sup> g g <sup>w</sup>** <sup>1000</sup> ( ) () () *R T P t t A tT <sup>M</sup>* 

 

*r*

the gas mass diffusion. Where *<sup>r</sup> v* can be estimated by Equation 2-11 [22]:

It assumes that the cell size in the same area is consistent. Thus,

2

R(t)≤r≤S (2-10)

*<sup>r</sup> <sup>t</sup>* (2-11)

**h g** *cRt k P t* ( ,) () , (2-12)

**<sup>h</sup> cr** ln 2.1 0.0074 *k T* , (2-13)

(2-14)

 

**<sup>g</sup>** is the gas density in the cell. Here 1000 / *A RM <sup>g</sup> <sup>W</sup>* , thus *A* is

is the surface

is the melt viscosity, *P***<sup>g</sup>** is the gas pressure in the micro-cell,

where

boundary of the cell. **2.3.1.1 Gas diffusion** 

by Fick´s law of diffusion:

when 0 *t* , 0 *crt c* ( , 0) .

*r* .

governed by Equation 2-13:

where *T***cr** is the critical temperature.

when *r S* : 0 *<sup>c</sup>*

Equation 2-14 [23]:

molecular weight,

constant for a certain gas.

Classic bubble growth model was constructed to illustrate bubble growth in foam processing after bubble nucleation. Considered a bubble concentrically surrounded by a shell of polymer melt with a constant mass, the gas dissolved in the melt shell uniformly distributes in a saturation state at the initial time and only diffuses between the melt shell and the bubble during bubble growth. Figure 2-5 shows the configuration of the bubble and the melt shell surrounding the bubble. The spherical coordinate is selected with the center of the bubble as the origin. In Figure 2-5, *R* is the bubble radius, *S* is the outer radius of the melt shell, and *c* is the concentration of the dissolved gas in the mixer.

Fig. 2-5. Schematic of the unit cell model.

Before analyzing the bubble growth, the following assumptions are made.


At the same time, it is also assumed that the cell shape is spherical, the initial radius is *R*<sup>0</sup> ,the internal gas pressure *P***g**0 equals to the melt plasticization pressure and the gas in the cell is ideal gas. Thus the change rate of the radius of the cell, *R* , is controlled by Equation 2-9 [22]:

$$\frac{\mathbf{d}R}{\mathbf{d}t} = \frac{1}{4\eta} \left[ \left( P\_\mathbf{g} - P \right) \mathbf{R} - 2\sigma \right] \tag{2-9}$$

where is the melt viscosity, *P***<sup>g</sup>** is the gas pressure in the micro-cell, is the surface tension at the interface of the melt and the gas, *P* is the pressure of the melt at the outer boundary of the cell.

#### **2.3.1.1 Gas diffusion**

190 Some Critical Issues for Injection Molding

Classic bubble growth model was constructed to illustrate bubble growth in foam processing after bubble nucleation. Considered a bubble concentrically surrounded by a shell of polymer melt with a constant mass, the gas dissolved in the melt shell uniformly distributes in a saturation state at the initial time and only diffuses between the melt shell and the bubble during bubble growth. Figure 2-5 shows the configuration of the bubble and the melt shell surrounding the bubble. The spherical coordinate is selected with the center of the bubble as the origin. In Figure 2-5, *R* is the bubble radius, *S* is the outer radius of the

melt shell, and *c* is the concentration of the dissolved gas in the mixer.

Before analyzing the bubble growth, the following assumptions are made.

Gas

Envelope

the growth process is considered to be isothermal.

**d d**

*t*

4 *<sup>R</sup> P PR*

1. Bubble and melt shell have the same and fixed sphere center during the bubble growth. 2. The gravity and inertia effects are ignored because of the highly viscous polymer melt. 3. The polymer melt is incompressible. The volume of dissolved gas in the melt is ignored. 4. Because the timescale of the bubble expansion is much shorter than the cooling time,

5. The dissolved gas in the polymer melt is in the uniformly supersaturated state before

6. The dissolved gas does not go in and out at the outer boundary of the analyzed region.

At the same time, it is also assumed that the cell shape is spherical, the initial radius is *R*<sup>0</sup> ,the internal gas pressure *P***g**0 equals to the melt plasticization pressure and the gas in the cell is ideal gas. Thus the change rate of the radius of the cell, *R* , is controlled by Equation 2-9 [22]:

**<sup>g</sup>**

<sup>1</sup> <sup>2</sup>

(2-9)

Fig. 2-5. Schematic of the unit cell model.

bubble growth.

Based on the dynamics principle of cell model, the value of *P***<sup>g</sup>** decreases when *R* becomes larger. At the same time, the gas only diffuses into the cell. The gas diffusion is determined by the gas dissolution grads. The diffusion will be going on until the driven power disappears or the melt is frozen. Thus, the relationship between *R* and *P***g** can be governed by Fick´s law of diffusion:

$$\frac{\partial \mathbf{\hat{c}}}{\partial t} + \nu \underbrace{\frac{\partial \mathbf{c}}{\partial r}}\_{r} = D \left[ \frac{1}{r^2} \frac{\partial}{\partial r} \left( r^2 \frac{\partial \mathbf{c}}{\partial r} \right) \right] \text{ R(t)} \mathbf{\hat{s}} \mathbf{\hat{r}} \mathbf{S} \tag{2-10}$$

where *c* is the concentration of the dissolved gas in the mixer, *<sup>r</sup> v* is the gas diffusion velocity in the radius direction of spherical coordinates, *D* is the diffusion coefficient in the single solution, *r* is the radial coordinate, *t* is the time, *S* is the radius of the cell.

The left of Equation 2-10 shows the change rate of gas concentration, while the right shows the gas mass diffusion. Where *<sup>r</sup> v* can be estimated by Equation 2-11 [22]:

$$
\upsilon v\_r = \frac{R^2}{r^2} \frac{\text{d}R}{\text{d}t} \tag{2-11}
$$

when 0 *t* , 0 *crt c* ( , 0) .

It assumes that the cell size in the same area is consistent. Thus,

when *r S* : 0 *<sup>c</sup> r* .

And the gas concentration *c* between *S* and *R t*( ) can be calculated by Henry law:

**h g** *cRt k P t* ( ,) () , (2-12)

where **h***k* is the Henry law coefficient. It is determined by the plastics and gas type and governed by Equation 2-13:

$$
\ln k\_{\rm h} = -2.1 + 0.0074 T\_{\rm cr\ \ \prime} \tag{2-13}
$$

where *T***cr** is the critical temperature.

As said above, the gas in the cell is assumed as ideal gas. Thus **g***P t*( ) can be calculated by Equation 2-14 [23]:

$$P\_{\mathbf{g}}(t) = \begin{bmatrix} 1000 R\_{\mathbf{g}} T \\\\ \end{bmatrix} \Big\langle \Big. \Big|\_{\mathbf{w}} \Big] \rho\_{\mathbf{g}}(t) = A \rho\_{\mathbf{g}}(t) T \tag{2-14}$$

where *R***g** is gas constant, **<sup>g</sup>** *R* 8.3145 J/(molK), *T* is the temperature (K), *M***w** is gas molecular weight, **<sup>g</sup>** is the gas density in the cell. Here 1000 / *A RM <sup>g</sup> <sup>W</sup>* , thus *A* is constant for a certain gas.

Microcellular Foam Injection Molding Process 193

parameters required by traditional injection process simulation. Finite element method and finite difference method are combined to solve the equations. To ensure the accuracy of simulation results, plastics properties used in the simulation must be recalculated based on

A flat part, with the size of 320mm×280mm×2mm, is selected for simulation. Figure 2-6 shows the part geometries, gate and cooling systems. As known from the former research, the difference of cell size near the gate between the true value and simulation result is smaller. So the characteristic point near the gate is selected to study the effect of process

Polypropylene material is used in the simulation. Its main properties are shown in Table 2-9. Nitrogen is used as blow agent. Its main properties are as follows.

<sup>1</sup> *kh* 1.346 10 , <sup>5</sup>

<sup>2</sup> *kh* 1.709 10 , <sup>7</sup>

<sup>1</sup> *df* 3.819 10 ,

the material model described in the "Material properties" section.

parameters on the cell size. The position is also shown in the Figure 2-6.

**2.3.2.2 Simulation experimental model** 

Fig. 2-6. Experiment model.

*M*w=28, **N/mm** <sup>5</sup>

(298) 5 10 , <sup>9</sup>

<sup>2</sup> *df* 2803.5 [24].

The gas diffusion coefficient *D* in the Equation 2-10 can be calculated by Equation 2-15:

$$D = df\_1 \exp(\frac{df\_2}{T}) \tag{2-15}$$

where *T* is the temperature, 1 *df* and 2 *df* are given coefficients.

#### **2.3.1.2 Material properties**

The melt viscosity can be proposed by Cross-WLF model. Thus the melt viscosity in the Equation 2-9 can be expressed by Equation 2-16 [23]:

$$\eta(T,\dot{\gamma},p) = \eta\_0(T,p)f(\phi)\left[1 + \left(\frac{\eta\_0 \dot{\gamma}}{\tau^\*}\right)^{(1-n)}\right]^{-1} \tag{2-16}$$

where is the viscosity of the polymer-gas single solution, *T* is the temperature, . is the shear rate, *p* is the pressure, *n* is the power coefficient, \* the critical shear stress, 0 (,) *T p* is the viscosity under zero shear rate. Because SCF is added into the melt, the effect of SCF on the plastics viscosity can be expressed by *f* ( ) . The following equation can be used to describe *f* ( ) [23]:

$$f(\phi) = (1 - \phi)^{\alpha} \tag{2-17}$$

where is an empirical constant. here 2 . is the volume fraction of the gas. It can be calculated by Equation 2-18:

$$\phi = \frac{4\mathbf{n}\mathbf{R}^3 \Big/ 3}{\mathbf{1}\Big/ \left(\rho \mathbf{N}\_\mathbf{m}\right)^{+} \mathbf{4}\mathbf{n}\mathbf{R}^3 \Big/ 3} \tag{2-18}$$

where *N***m** is the cell number in unit volume.

The surface tension at the interface between melt and gas in the Equation 2-9 can be calculated by Equation 2-19 [22]:

$$
\sigma(T) = \sigma(298) \left( \frac{\overline{\rho}}{\overline{\rho}(298)} \right)^4 \tag{2-19}
$$

where (298), ( ) *T* are the surface tensions at the room temperature and at process temperature respectively, and (298), are the densities of the single solution at the room temperature and at process temperature respectively.

#### **2.3.2 Effect of process conditions on bubble morphology**

#### **2.3.2.1 Simulation experimental model**

Based on the above mathematic model, the pre-filled volume, initial cell diameter, cell density and SCF concentration are necessary as boundary conditions besides the process

2

can be proposed by Cross-WLF model. Thus the melt viscosity

 

<sup>1</sup> (1 ) . . <sup>0</sup>

 

is the viscosity of the polymer-gas single solution, *T* is the temperature, .

is the viscosity under zero shear rate. Because SCF is added into the melt, the effect of SCF

*f* ( ) (1 )

**m**

( ) (298) (298)

Based on the above mathematic model, the pre-filled volume, initial cell diameter, cell density and SCF concentration are necessary as boundary conditions besides the process

1 4 () 3

*N*

**π**

4

3

*R*

 . 

*T*

 

(298),

**2.3.2 Effect of process conditions on bubble morphology** 

temperature and at process temperature respectively.

**π**

3

3

at the interface between melt and gas in the Equation 2-9 can be

4

*R*

*T* are the surface tensions at the room temperature and at process

<sup>0</sup> \* ( , , ) ( , )()1

*T p Tpf*

 

<sup>1</sup> exp( ) *df D df <sup>T</sup>* (2-15)

*n*

is the

(,) *T p*

(2-16)

the critical shear stress, 0

(2-17)

(2-18)

(2-19)

are the densities of the single solution at the room

is the volume fraction of the gas. It can be

. The following equation can be used to

in the

The gas diffusion coefficient *D* in the Equation 2-10 can be calculated by Equation 2-15:

where *T* is the temperature, 1 *df* and 2 *df* are given coefficients.

**2.3.1.2 Material properties** 

Equation 2-9 can be expressed by Equation 2-16 [23]:

shear rate, *p* is the pressure, *n* is the power coefficient, \*

on the plastics viscosity can be expressed by *f* ( )

is an empirical constant. here 2

where *N***m** is the cell number in unit volume.

The melt viscosity

where 

where 

where

describe *f* ( )

[23]:

calculated by Equation 2-18:

The surface tension

calculated by Equation 2-19 [22]:

(298), ( ) 

temperature respectively, and

**2.3.2.1 Simulation experimental model** 

parameters required by traditional injection process simulation. Finite element method and finite difference method are combined to solve the equations. To ensure the accuracy of simulation results, plastics properties used in the simulation must be recalculated based on the material model described in the "Material properties" section.

#### **2.3.2.2 Simulation experimental model**

A flat part, with the size of 320mm×280mm×2mm, is selected for simulation. Figure 2-6 shows the part geometries, gate and cooling systems. As known from the former research, the difference of cell size near the gate between the true value and simulation result is smaller. So the characteristic point near the gate is selected to study the effect of process parameters on the cell size. The position is also shown in the Figure 2-6.

Fig. 2-6. Experiment model.

Polypropylene material is used in the simulation. Its main properties are shown in Table 2-9. Nitrogen is used as blow agent. Its main properties are as follows. *M*w=28, **N/mm** <sup>5</sup> (298) 5 10 , <sup>9</sup> <sup>1</sup> *kh* 1.346 10 , <sup>5</sup> <sup>2</sup> *kh* 1.709 10 , <sup>7</sup> <sup>1</sup> *df* 3.819 10 , <sup>2</sup> *df* 2803.5 [24].

Microcellular Foam Injection Molding Process 195

According to Table 2-11, the effect of process parameters on the cell size is showed in the

According to the *R*diff values in Table 2-11, the effect order from big to small of each process parameter on the cell size is melt temperature, pre-filled volume, injection time and mold temperature and the optimization parameters combination is mold temperature(10Ԩ), melt temperature(180Ԩ), injection time(1s) and pre-filled volume(95%). Based on the above combination, the cell size distribution is shown in Figure 2-8. The cell radius at the characteristic point is 7 µm and the cell size in whole part is between 5µm and 40µm. The smaller cell size can avoid some part defects such as dimples etc. Obviously this cell size

According to Figure 2-7, appropriately reducing the melt temperature and increasing the pre-filled volume can optimize the cell size. However the effect of injection time and mold temperature on cell size was less significant. In order to further research the effect trend of each process parameters on the cell size. More simulation experiments are done. Because the mutually effect among the selected process parameters is not taken into account, the further research is done by adjusting one of the four parameters and fixing the other parameters.

Fig. 2-7. Effect of each process parameter on cell size.

distribution can be accepted.

Fig. 2-8. Cell size distribution.

Figure 2-7.


Table 2-9. Polypropylene properties.

The effect of mold and melt temperatures, injection time and pre-filled volume on the cell size is studied. Based on the cooling and gate systems, recommended material parameters and the initial simulation results, the selected levels for each process parameter are shown in Table 2-10. Besides the studied four parameters, the initial values of other parameters are set as the following. nucleation density **<sup>3</sup> /m** <sup>11</sup> 2 10 , initial gas concentration 0*c* =0.25%, initial cell radius <sup>6</sup> <sup>0</sup> *<sup>R</sup>* 1.0 10 m [25].

#### **2.3.2.3 Results and discussion**

The <sup>4</sup> <sup>9</sup> *L* (3 ) orthogonal array is used to arrange the simulation experiments. The cell sizes values at the characteristic point are calculated. Table 2-10 shows the experiment arrangement order and the simulation results. Based on the Equation 2-8, the average values of each process parameter at each level are calculated. The *R*diff values are also achieved after the max. and min. average values are gotten. Table 2-11 shows the details.


Table 2-10. <sup>4</sup> <sup>9</sup> *L* (3 ) orthogonal array, experiment arrangement and results.


Table 2-11. Direct analysis of process parameters.

The effect of mold and melt temperatures, injection time and pre-filled volume on the cell size is studied. Based on the cooling and gate systems, recommended material parameters and the initial simulation results, the selected levels for each process parameter are shown in Table 2-10. Besides the studied four parameters, the initial values of other parameters are set

<sup>9</sup> *L* (3 ) orthogonal array is used to arrange the simulation experiments. The cell sizes values at the characteristic point are calculated. Table 2-10 shows the experiment arrangement order and the simulation results. Based on the Equation 2-8, the average values of each process parameter at each level are calculated. The *R*diff values are also achieved after

> Melt temp. (Ԩ)

1 1 1 1 1 10 180 1 85 28 2 1 2 2 2 10 210 1.5 90 43 3 1 3 3 3 10 240 2 95 40 4 2 1 2 3 20 180 1.5 95 25 5 2 2 3 1 20 210 2 85 47 6 2 3 1 2 20 240 1 90 42 7 3 1 3 2 30 180 2 90 34 8 3 2 1 3 30 210 1 95 37 9 3 3 2 1 30 240 1.5 85 47

<sup>9</sup> *L* (3 ) orthogonal array, experiment arrangement and results.

*m*<sup>1</sup> 37.0 29.0 35.7 40.7 *m*<sup>2</sup> 38.0 42.3 38.3 39.7 *m*<sup>3</sup> 39.3 43.0 40.3 34.0 *R*diff 2.3 14.0 4.6 6.7

Melt temp. (Ԩ)

1 2 3 4 (um)

Inj. time (s)

Inj. time (s)

2 10 , initial gas concentration 0*c* =0.25%,

Pre-filled vol. (%)

> Pre-filled vol. (%)

Cell size

the max. and min. average values are gotten. Table 2-11 shows the details.

temp. (Ԩ)

Table 2-9. Polypropylene properties.

initial cell radius <sup>6</sup>

**2.3.2.3 Results and discussion** 

The <sup>4</sup>

No.

Table 2-10. <sup>4</sup>

as the following. nucleation density **<sup>3</sup> /m** <sup>11</sup>

Column Mold

Mold temp. (Ԩ)

Table 2-11. Direct analysis of process parameters.

<sup>0</sup> *<sup>R</sup>* 1.0 10 m [25].

Main properties Value Eject temperature /Ԩ 122 Max. melt temperature /Ԩ 250 Special heat /J/kg•Ԩ 3531 Thermal conductivity /W/m•Ԩ 0.17 Melt density /g/cm3 0.814

According to Table 2-11, the effect of process parameters on the cell size is showed in the Figure 2-7.

Fig. 2-7. Effect of each process parameter on cell size.

According to the *R*diff values in Table 2-11, the effect order from big to small of each process parameter on the cell size is melt temperature, pre-filled volume, injection time and mold temperature and the optimization parameters combination is mold temperature(10Ԩ), melt temperature(180Ԩ), injection time(1s) and pre-filled volume(95%). Based on the above combination, the cell size distribution is shown in Figure 2-8. The cell radius at the characteristic point is 7 µm and the cell size in whole part is between 5µm and 40µm. The smaller cell size can avoid some part defects such as dimples etc. Obviously this cell size distribution can be accepted.

Fig. 2-8. Cell size distribution.

According to Figure 2-7, appropriately reducing the melt temperature and increasing the pre-filled volume can optimize the cell size. However the effect of injection time and mold temperature on cell size was less significant. In order to further research the effect trend of each process parameters on the cell size. More simulation experiments are done. Because the mutually effect among the selected process parameters is not taken into account, the further research is done by adjusting one of the four parameters and fixing the other parameters.

Microcellular Foam Injection Molding Process 197

As said in above chapter, microcellular foam injection molding parts have many advantages such as saving material and energy, reducing cycle time, and parts excellent dimensional stability. Despite these advantages, the low parts' surface quality limits its application scope seriously. Typical defects are swirl marks, silver streak, surface blistering, post-blow, large

Until now, many technologies for improving surface quality have been studied. The typical technologies include Gas Counter Pressure (GCP), Rapid Heating Cycle Molding (RHCM)

When polymer-SCF mixer is injected into the cavity, counter pressure can prevent bubbles growth due to the high cavity pressure. When the injection is completed, the high cavity pressure is released, and then the bubbles begin to grow up. However, the surface melt has solidified at that time. So the parts surface quality can be as satisfied as traditional injection

GCP method can control the bubbles growth and remove the swirl marks. But it is not

Compared with conventional injection molding process, RHCM process is that the mold is rapidly heated before filling stage. The heated mold temperature is higher than the polymer thermal deformation temperature. Then the filling and packing process are going. Afterward, the mold is rapidly cooled. Finally, the products are ejected from the mold. So

RHCM technology is widely used to improve the surface quality of injection molding parts. For example, to improve optical transparence and decrease birefringence of polystyrene, radiation heating on injection mold is proposed to directly control the temperature during the filling stage. A polycarbonate lens with a variation thickness from 1.5 mm to 7 mm can be successfully produced by electric heaters combined with chilly water cooling method.

Previous discussions about microcellular foam injection parts surface defects show that the melt temperature on the cavity surface affects the parts surface quality obviously. RHCM can meet the temperature requirement. On Oct., 2010, Trexel Inc., the supplier of the MuCell microcellular foaming technology, announced to promote MuCell for injection molding parts with Class-A/high-gloss surface finish at a global licensing agreement with Ono Sangyo Co. Ltd.. Chen SC and Li HM has successfully demonstrated the usefulness of a variable mold temperature in improving parts surface quality during microcellular foam

Figure 3-2 shows that the effect of mold temperature on the surface roughness is very insignificant when the mold surface temperature is below 100Ԩ. The surface roughness

injection molding process [14]. Figure 3-1 shows their experimental results.

suitable for mass production due to the complex mold structure and high cost.

**3. Microcellular foam injection molding products surface defects and** 

surface roughness. The details are introduced on above chapter.

**3.1 Technologies to improve surface quality** 

and Film Insulation which is derived from RHCM.

**Gas Counter Pressure (GCP)** 

**Rapid Heating Cycle Molding (RHCM)** 

RHCM process circle is finished [18].

**solutions** 

parts'.

When one of the four parameters is studied, other parameters are set according to the optimization result. Table 2-10 shows the adjusted values of each parameter. So the effect trend of melt temperature, pre-filled volume, injection time and mold temperature on the cell size are achieved. Figure 2-9 shows the effect trend.

Fig. 2-9. Effect trend of each process parameters on cell size (a) melt temperature; (b) pre-filled volume; (c) injection time; (d) mold temperature.

According to Figure 2-9 (A), cell size changes largely along with temperature drop. Because of the lower melt temperature, the cooling time is shorter and the cell growth time also becomes shorter. The cell size becomes smaller. At the same time, due to the shorter cooling time, the cell growth can be controlled easily. Thus the smaller and evener cell size can be produced. With the pre-filling volume increasing, the foaming space becomes smaller. At the same time, the number of nucleation points per volume is certain. So the cell size becomes smaller. However, on the other hand, the more part weight can not be reduced with the pre-filled volume increasing. Figure 2-9 (B) shows the cell size change trend along with the pre-filled volume change. When the injection time is increased, the cell growth time also becomes longer. Thus the cell size becomes bigger. However Figure 2-9(C) shows the effect of injection time on the cell size is inferior to melt temperature and pre-filled volume. At last, according to the mathematic model of cell growth, the effect of mold temperature on the cell size is little. Figure 2-9 (D) also shows that the cell size changes little with mold temperature decreasing.

When one of the four parameters is studied, other parameters are set according to the optimization result. Table 2-10 shows the adjusted values of each parameter. So the effect trend of melt temperature, pre-filled volume, injection time and mold temperature on the

(a) (b)

(c) (d)

According to Figure 2-9 (A), cell size changes largely along with temperature drop. Because of the lower melt temperature, the cooling time is shorter and the cell growth time also becomes shorter. The cell size becomes smaller. At the same time, due to the shorter cooling time, the cell growth can be controlled easily. Thus the smaller and evener cell size can be produced. With the pre-filling volume increasing, the foaming space becomes smaller. At the same time, the number of nucleation points per volume is certain. So the cell size becomes smaller. However, on the other hand, the more part weight can not be reduced with the pre-filled volume increasing. Figure 2-9 (B) shows the cell size change trend along with the pre-filled volume change. When the injection time is increased, the cell growth time also becomes longer. Thus the cell size becomes bigger. However Figure 2-9(C) shows the effect of injection time on the cell size is inferior to melt temperature and pre-filled volume. At last, according to the mathematic model of cell growth, the effect of mold temperature on the cell size is little. Figure 2-9 (D) also shows that the cell size changes little with mold

Fig. 2-9. Effect trend of each process parameters on cell size (a) melt temperature;

(b) pre-filled volume; (c) injection time; (d) mold temperature.

temperature decreasing.

cell size are achieved. Figure 2-9 shows the effect trend.
