2016 3rd International Conference on Mechanical, Industrial, and Manufacturing Engineering (MIME 2016)

ISBN: 978-1-60595-313-7

1 INTRODUCTION

The Low Speed Research Compressor (LSRC) is used to test large-scale models of smaller high-speed compressors in an environment where very detailed measurements of the flowfield can be made. LSRC has some advantages such as low mechanical stress, low cost et.al (Wisler D C et al., 1999).

Injection molding is the most widely used processing technique for polymers. In the process of compressor experimental blade, the melted polymer is injected into a mold cavity with a desired shape and then cooled down under a high packing pressure. It offers several advantages over other processing conditions such as good surface finish, the ability to process complex parts without the need of secondary operations, and low cost for mass production. However, residual stress is often found in the compressor experimental blade due to the high temperature and pressure in the injection process. And it may shorten the blade service life and lead to dimensional instability and so on.

Residual stresses are the stresses left inside the molding product under the condition of no external loads. In the molding process, internal stresses are frozen inside the mold cavity. After demolding, the residual stresses will redistribute and cause the part shrinkage and warpage. Possible thermal stresses may still be introduced into the part after demolding because of further cooling to the room temperature. The residual stresses may include the flow-induced

residual stress and thermal induced residual stress. The flow-induced residual stresses include those caused by polymer chain preferential orientations and freeze-off packing pressure, and the thermal induced residual stress is caused by non-uniform cooling of the molding part.

Several researchers have proposed different methods to investigate the residual stresses induced during the injection molding process. Azaman, MD et al. (Azaman, MD et al., 2015) investigated the optimal parameter selection, the significant parameters, and the effect of the injection-molding parameters during the post-filling stage with respect to in-cavity residual stresses, volumetric shrinkage and warpage properties. The research results showed that the packing pressure and mold temperature have important influence on residual stresses and volumetric shrinkage, while the packing pressure, packing time, and cooling time are the dominant factors to control the warpage for molded thin-walled parts fabricated using lignocellulosic polymer composites. Jin, K et al. (Jin, K et al., 2014) reported that the residual stresses were formed due to different temperature gradient, which uneven distribution of the thermal stresses. Yu, H et al. (Yu, H et al., 2014) investigated the effect of molded-in residual stress on microchannel deformation during the subsequent thermal bonding process. The dominant molding parameters with positive effects were found to be melt temperature, mold temperature as well as cooling time after packing.

Effect of Injection Processing Parameters on Residual Stress for Compressor Experimental Blade Using FEM and RSM

Dezhong Zhao, Wenhu Wang, Ruisong Jiang, Kang Cui, Qichao Jin Key laboratory of ministry of educational for contemporary design and integrated manufacturing technology, Northwestern Polytechnical University, Xi’an 710072 China

ABSTRACT: Injection molding-induced residual stresses have strong influence on molding precision for compressor experimental blade used on LSRC (Low Speed Research Compressor). In this paper, finite element model (FEM) and response surface methodology (RSM) are employed to reveal the effect of processing parameters on residual stress for injection molding of compressor experimental blade. First, the influence of processing parameters such as melt temperature, mold temperature on the residual stress of blade was studied based on factorial experiment. Then, the rules of influence of the main processing parameters and their interactions on injection residual stress of blade was analyed based on RSM．The results show that the packing time and melt temperature are the principle factors for controlling injection residual stress of compressor experimental blade．In addition, the packing time and melt temperature has strong interaction effect on the residual stress of blade.

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Xie, PC et al. (Xie, PC et al., 2014) studied the effects of gate size on the cavity filling pattern and residual stress of injection molded parts. A total of three rectangular gates with different sizes were used. Experiments were carried out by using a dynamic visualization system. It was found that the undersized gate has many adverse effects on the filling behavior and residual stress of molded parts. With a larger gate, the cavity will be filled faster and residual stress of parts may be smaller. Azaman, MD et al. (Azaman, MD et al., 2013) showed that the shallow thin-walled part is preferable in molding lignocellulosic polymer composite material due to the low residual stress and warpage. The shallow thin-walled part is structurally rigid, such that it can be used in applications involving small shell parts, and can be processed more economically using less material than that of the flat thin-walled part. Liu, F et al. (Liu, F et al., 2012) found that the effect of processing conditions on shrinkage is different from that on warpage during injection molding. Specifically, packing pressure affects shrinkage most while packing time is the dominant factor in determining warpage. The reaction of shrinkage to packing pressure is monotonic, whereas the plot of warpage shows a U-shaped variation. Weng, C et al. (Weng, C et al., 2010) investigated the effects of aperture shape on the value of maximum residual stress by both the numerical simulation and experimental methods. The results indicate that the geometrical configuration of the aperture can profoundly influence the levels of residual stresses in precision injection-molded microlens arrays. The values of maximum residual stresses are found to decrease with the increase of the melt temperature, the mold temperature, and to increase with the increase of the packing pressure for all shapes of the lens arrays, but there is no regular correlation with the flow rate and the packing time over the range of processing parameters used.

These previous investigations on injection molding residual stress usually focused on analyzing the profile of residual stress by considering different injection processing parameters or other factors. But the interactions among these factors on injection molding induced residual stress needs further especial focus. Therefore, the main objective of this research work is to analyze the influence of processing parameters and their interaction on the residual stress of experimental blade.

2 FLOW FORMULATION

In injection molding, plastic parts are assumed to be three-dimensional with thin-walled geometry. The polymer melt flow is assumed to be a quasi-steady flow of generalized-Newtonian compressible fluid under nonisothermal conditions. The governing

equations, describing the continuity, momentum, and energy of the flow field are as follows (Azdast, T et al., 2008), respectively (R. Y. Chang et al., 1996).

( ) ( )0

0

0

0

u v

t x y

p u

x z z

p v

y z z

p

z

ρ ρ ρ

η

η

∂ ∂ ∂+ + = ∂ ∂ ∂

∂ ∂ ∂

− + = ∂ ∂ ∂

∂ ∂ ∂ − + = ∂ ∂ ∂

∂ =∂

(1)

p

T T T T pc u v k T

t x y z z tρ β η

∂ ∂ ∂ ∂ ∂ ∂ + + = + + Θ

∂ ∂ ∂ ∂ ∂ ∂ (2)

where: p -pressure, T -temperature, u and v -planar velocity components, ρ -polymer density, β -coefficient of thermal expansion, η -viscosity, Θ -dissipation function, k -thermal conductivity, pc -specific heat.

Temperature and pressure histories of mold cavity can be determined using the above equations.

The cross-WLF model that found by Williams et al. ( Williams et al.,1955) is use to model the viscosity.

0

1

01n

ηη

η γ τ−

∗=

+ �

(3)

Where: 0η -zero shear rate viscosity, γ� -shear rate, n -power-law index, τ ∗ -metarial constant.

Zero shear rate viscosity can be represented by a WLF-type equation as follows：

10 1

2

( )= exp -

( )

A T TD

A T Tη

∗

∗

−

+ − (4)

in which

*

2 3

2 2 3

T D D p

A A D p

= +

= +�

(5)

Where: 1 2 3 1, , ,D D D A and

2A� - material constants.

For polymer density calculation a modified two-domain Tait model is used as follow:

0( , ) ( ) 1 ln(1 ) ( , )( )

t

PV T P V T C V T P

B T

= − + +

(6)

Where: ( , )V T P -specific volume at temperature T and pressure P , V0-specific volume at zero gauge pressure, T -temperature (in K), P -pressure(in Pa), C -constant(0.0894), ( )B T -accounts for the pressure sensitivity of the material,

( , )tV T P -an additional transition function required for non-amorphous (crystalline) materials.

In this paper, the FE software Moldflow is utilized to simulate the blade injection molding process. This commercial software has two core

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products. Moldflow Adviser and Moldflow Insight which provides definitive results for flow, cooling, and warpage along with support for specialized molding processes. It can calculate residual stress automatically after injection. The effect of processing parameters is determined with the Factoral experiment and RSM， and the processing parameters include mold temperature, melt temperature, injection time, packing pressure, packing time, and cooling time.

3 FACTORIAL EXPERIMENT

3.1 Method of factorial experiment

Factorial design is an effective method to determine the effects of multiple variables on a response. Traditionally, experiments are designed to determine the effect of one variable upon one response. R.A. Fisher showed that there are advantages by combining the study of multiple variables in the same factorial experiment. Factorial design can reduce the number of experiments by studying multiple factors simultaneously. Additionally, it can be used to find both main effects (from each independent factor) and interaction effects (when both factors must be used to explain the outcome). However, the factorial design can only give relative values, and to achieve actual numerical values the math becomes difficult, as regressions (which require minimizing a sum of values) need to be performed. The factorial design is a useful method to design experiments in both laboratory and industrial settings.

The theoretical formula of factorial experiment is as follows:

=1

=1

=

1

1

=1

= =1,2 ; =1 2

(= =1,2

0 ( 1,

1 2

2, )

;

,

=

n

ij iij n

ii

n

ij ik ii

jk n

ii

n

ij

i

l RE i n j m

R

l l RI i n k m

R

l j n=

× × ×

= =

∑∑

∑∑

∑

� �

�

�

�

（ ）（ ， ，， ）） （ ， ，， ） (7)

where, jE -the main effect of the j factor to the

observation target. ijl -the level of the j factor for

the i test, iR - the response to the i test; N-the

test times; m -the number of test factors; jkI -the

interaction between factor j and k ; The main

factor of two levels, 1 represents high level and -1

represents low level.

3.2 Finite element model for blade injection

In this paper, resign blade that used on LSRC was taken as the research object. The overall dimention of the blade is 70mm×30mm×100mm. Blade material is PA66 that produced by DuPont Co. and the material trademark is Zytel 101 NC010. The material has excellent abrasion performance, self-lubricating ability, high strength and stiffness at higher temperatures.

Fig.1 shows the FE model of tne blade consists of 3783 grid units, and the grid is of “Double layer grid” type. And the injection system, cooling system and the surface of the mold are established in Moldflow software with reference to the mold design.

1 mold system 2 inserts 3 cooling water channel 4 blade

5 sprue and runners

Figure 1. Finite element model of blade injection process.

3.3 Factorial experiment

The mold temperature (A), melt temperature (B), injection time (C), packing time (D), packing pressure (E), cooling time (F) and their interaction were studied. Table 1 shows the processing parameters and their levels.

Table 1. Experimental factor level.

Factor

name

Low

level

High

level

A:Mold temperature (°C) 70 110

B:Melt temperature (°C) 260 320

C:Injection time (s) 0.5 2.5

D:Packing time (s) 10 50

E:Packing pressure (MPa) 5 25

F:Cooling time (s) 15 75

3.4 Results and discussion

There are six factors need to be studied in this paper. Considering the high order interaction can be neglected, the paper uses the partial factor test with the resolution of VI, which can realize the interaction of the three order without confounding. The experimental design scheme and the experimental results are shown in Table 2. In this table, 1 represents the high level of each factor, and -1 represents the low level of each factor.

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Table 2. Fractional factorial experiment scheme and results.

Run A (°C)

B (°C)

C (s)

D (MPa)

E (s)

F (s)

Stress (MPa)

1 1 -1 1 1 1 -1 140.3 2 -1 1 -1 1 1 1 140.3 3 -1 1 -1 1 -1 -1 141.7 4 1 -1 -1 1 1 1 125.6 5 1 1 -1 -1 1 1 120.3 6 1 -1 1 1 -1 1 142.3 7 -1 -1 -1 1 -1 1 120.3 8 -1 -1 -1 -1 1 1 142.7 9 -1 -1 1 -1 -1 1 122.4 10 -1 1 1 -1 -1 -1 141.8 11 1 -1 -1 -1 1 -1 140 12 1 1 1 -1 1 -1 140.1 13 -1 -1 -1 1 1 -1 159.3 14 -1 -1 -1 -1 -1 -1 158.1 15 -1 1 1 1 -1 1 142 16 1 1 -1 1 1 -1 158.9 17 1 1 1 1 1 1 124.2 18 -1 1 -1 -1 -1 1 117.3 19 1 1 1 1 -1 -1 158.1 20 1 1 -1 -1 -1 -1 157.4 21 1 -1 -1 1 -1 -1 139.9 22 -1 -1 1 1 -1 -1 140.1 23 -1 1 1 1 1 -1 142.1 24 -1 -1 1 -1 1 -1 157.4 25 1 1 1 -1 -1 1 142.6 26 1 -1 1 -1 -1 -1 160.2 27 -1 1 1 -1 1 1 139.8 28 -1 -1 1 1 1 1 142.4 29 1 1 -1 1 -1 1 121.6 30 1 -1 1 -1 1 1 140 31 1 -1 -1 -1 -1 1 159.9 32 -1 1 -1 -1 1 -1 117.3

The experimental results were analyzed by factor analysis. Figure 2 shows the Pareto chart of residual stress. The figure shows that packing time, melt temperature are the significant factors to the residual stress of blade, packing time and melt temperature has strong interaction effect on the residual stress of blade. Cooling time and injection time had no significant effect on the residual stress of blade.

Figure 2. Pareto chart of effects for residual stress.

4 ANALYSIS OF THE MAIN FACTORS AND INTERACTION

The main factors and their interaction effect on the blade residual stress has been obtained from the factorial experiment. Then, the RSM approach is applied to determine the effect level of the factors and interaction in blade injection molding. The response surface experimental factors and their levels are Shown in table 3. The experimental scheme and results are shown in Table 4.

Table 3. Processing parameters and their level.

Factor name

Low level

High level

A:Mold temperature (°C) 70 110 B:Melt temperature (°C) 260 320 D:Packing time (s) 10 50 E:Packing pressure (MPa) 5 25

Table 4. RSM experiment scheme and results.

Run A (°C)

B (°C)

D (MPa)

E (s)

Stress (MPa)

1 90 290 15 30 148.7 2 70 320 15 30 140.6 3 110 290 15 50 149.6 4 90 290 15 30 148.7 5 70 290 5 30 148 6 90 260 25 30 143.9 7 110 290 15 10 149.5 8 110 320 15 30 141.1 9 90 320 5 30 139.9 10 90 290 25 50 149.5 11 90 290 15 30 148.7 12 90 320 15 10 141.1 13 70 290 15 50 138 14 70 290 15 10 149.1 15 90 320 25 30 141.7 16 70 260 15 30 130.2 17 90 290 25 10 150.3 18 90 320 15 50 140.9 19 90 290 15 30 148.7 20 90 260 15 50 122.9 21 110 260 15 30 149.9 22 90 290 15 30 148.7 23 110 290 5 30 148 24 90 260 5 30 135.2 25 90 290 5 10 148.1 26 90 290 5 50 144.7 27 110 290 25 30 149.6 28 70 290 25 30 149.5 29 90 260 15 10 158.5 Compared to conventional methods, RSM has

many advantages including the provision of rapid and reliable experimental data, a consideration of the effects and interactions between factors, reduction in the number of experiments and minimizing experimental costs and time consumption. Second-order polynomial Equation which includes all interaction terms is employed to calculate the predicted residual stress.

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2 2 2

0

1 1 1

( )k j j ij i j

j i j

X c c x c x xσ= = =

= + +∑ ∑∑ (8)

Where the kσ is residual stress, the

1 2( , , , )nX x x x= � is the processing parameters, and

0c , jc and

ijc are the undetermined coefficient.

Through the regression analysis of experimental

data, the final empirical model for residual stress of

blade is as follows.

1 2 3

4 1 2 2 3

=253.097+0.3257 0.3534 4.9766

+0.0944 0.00102 +0.01553

kx x x

x x x x x

σ − −

− (9)

where, 1x- the mold temperature, 2x

- the melt

temperature, 3x- the packing pressure, 4x

- the

packing time.

The model and factor significance is investigated

using the ANOVA to the 95% of confidence from

the F test of distribution and P values.

4.1 Main factors analysis

Figure 3 shows the relationship between the residual stress of the blade and packing time when the mold temperature maintains at 90°C, the melt temperature maintains at 290°C, and the packing pressure is fixed at 15MPa. From Fig. 5 it can be seen that the residual stress in the blade decreases with the increase of the packing time.

Figure 3. Effect of packing time on residual stress.

Figure 4 reveals the effect of the packing pressure

on the residual stress of the blade for the mold temperature of 90°C, the melt temperature of 290°C, and the pressure time of 30s. From Fig. 5 it can be seen that the value of the residual stress in the blade

become bigger when increasing the packing pressure.

Figure 4. Effect of packing pressure on residual stress.

Figure 5 displays the relationship between the

residual stress of the blade and mold temperature when the melt temperature is 290°C, packing pressure is 15MPa, and the packing time is 90 s. From Fig. 5 it can be seen that the residual stress in the blade is bigger at high mold temperature than that at low mold temperature.

Figure 5. Effect of mold temperature on residual stress.

Figure 6 describes that the changes of residual

stress for the blade with the melt temperature when the mold temperature, packing pressure, and the packing time is fixed at 90°C, 15MPa, 90 s, respectively. From Fig. 5 it can be observed that the residual stress in the blade increases with the increase of the melt temperature.

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Figure 6. Effect of melt temperature on residual stress.

4.2 Interaction analysis

Figure 7 shows the interaction effects of the packing time and melt temperature on the residual stress induced by injection operation under the condition with the mold temperature of 90°C, and packing pressure of 15MPa. From Fig. 5. It can be obviously observed that packing time and melt temperature has strong interaction effect on the residual stress. Residual stress decreased sharply with the increase of the melt temperature and the decrease of the packing time, or the decrease of the melt temperature and the increase of the packing time. Blade residual stress achieve the maximum value while the mold temperature and packing time reduce to 260°C, 10s, respectively. This phenomenon may be understood by low temperature leading to poor melt liquidity.

Figure 7. Effects of the packing time and melt temperature on the residual stress.

Figure 8 displays the 3D graphic of response surface for injection induced residual stress with the interaction effects of mold temperature and melt temperature when the packing time and packing pressure maintains at 30s,15MPa, respectively. It can be observed that increasing mold temperature a significant increase in the residual stress. This may because the increase of the mold temperature will lead to the increase of the blade shrinkage, and then cause the larger residual stress. The change of the residual stress caused by the melt temperature is the result of the coupling effect of the shrinkage rate and the melt liquidity.

Figure 8. Effects of the mold temperature and melt temperature

on the residual stress.

5 CONCLUSION

The effect of the processing parameters on residual stress of blade during injection operation is investigated using FEM and RSM. Some conclusions are summarized as follows.

(1) The main factors that influence the residual stress of the blade during injection molding are packing time, packing pressure, mold temperature and melt temperature. Packing time has a significant effect on the residual stress of blade. With the increase of the packing time, the residual stress of the blade was significantly decreased.

(2)The interaction item of packing time and melt temperature has significant effect on the residual stress of the blade. Lower blade residual stress can be obtained under condition of Low melt temperature and long packing time, or high melt temperature and short packing time. There is also a certain interaction between the melt temperature and mold temperature on the residual stress of injection blade.

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FUNDING

This work is supported by the National Natural Science Foundation of China (No.51475374), the Fundamental Research Funds for the Central Universities of China (No.3102015ZY087).

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