1 Introduction

The demand for the plastic product is very high in the market as a wide variety of shapes can be produced using the injection moulding process. However, a number of defects usually occur during the process, affecting the quality and cost of the products. The undesirable defects such as weld lines, shrinkages and warpage affect the quality of the moulded parts in terms of their mechanical strength, causing poor overall quality [1,2,3,4,5]. Defects such as weld line occur when plastic melt splits and then recombines at a certain location during the injection moulding process [6]. These defects can be minimised using a good combination of parameters setting during the injection moulding process [7,8,9,10]. Numerous research works regarding this problem have recently been conducted due to the ever-growing technologies for quality improvement of injection moulded parts [11,12,13,14]. In order to increase the mechanical strength at the critical location on the moulded parts, many researchers had used a variety of techniques such as mechanical assistance [15], thermal assistance[16,17,18] and material additives methods such as adding fillers to the parent material or blending two or more materials [19, 20]. On the other hand, parameter’s optimisation methods were widely used as a technique to improve the strength of the moulded part [21, 22].

The process of strengthening the product especially at the location of weld line formation through mechanical assistance had been found in the early 1980s by Tom et al. [23] in his study of VAIM method using polystyrene (PS) as a moulded material. In the VAIM method, the vibrational forces were used to induce flow of the melted polymer during the filling and packing phases of injection moulding process. In recent years, Lu et al. [24] reported using an ultrasonic oscillations technique which was applied to improve the weld line strength of the moulded parts. Ultrasonic signal from the ultrasonic generator was induced to a core side of the mould via the ultrasonic horn. The ultrasonic oscillations were induced into the mould after the filling phase of the injection moulding process was effective to enhance the weld line strength for PS and PS/HDPE blends. In the following year, Lu et al. [25] utilised the same equipment to improve the mechanism of ultrasonic oscillations that increases the molecular diffusion across the weld line formation. These combined methods resulted in an increase in the weld line strength of the moulded parts.

Kikuchi et al. [15] conducted a study on VAIM technique using polystyrene to improve the mechanical behaviour of the moulded part. The result indicated that the improvement of the strength of the moulded part depends on vibration amplitude, frequency, duration and delay time between the injection start and vibration start. The strength was improved as much as 28% compared to the conventional method. Li & Shen [26] also studied the improvement of mechanical properties of the plastic part using VAIM technique and found that the tensile property of the PP part was increased with an increase in vibration pressure amplitude, but the elongation at the break was decreased.

Xie & Ziegmann [20] studied the weld line strength using PP material which was compounded at various weight fractions (10%, 20%, 30%, 35%) of carbon nanofibres (CNFs) and titanium dioxide (TiO2) nanoparticles through co-screws internal mixing in microinjection moulding process. Results showed that the weld line strength of moulded part was lower than the virgin PP when the CNFs is filled higher than 10%.

Mechanical and thermal assistance in injection moulding processes are successful techniques to improve the strength of moulded parts, as well as the strength at the weld line position, but the shrinkage problem is not considered concurrently during the improvement. The disadvantages of these techniques include their lack of practicality due to the higher setup cost, and the complex mould design requires higher knowledge and skill during the operation. Due to these reasons, these techniques are not widely used in the industry.

In addition, one of the well-known improvement methods was parameter optimisation which involves Design of Experiment (DOE) and artificial intelligence techniques such as Taguchi method, artificial neural networks (ANN), genetic algorithm (GA) and response surface methodology (RSM) where some parameters were attuned to the suitable value in order to obtain an optimum value of shrinkage and weld line strength [1, 27,28,29,30]. Some researchers had also combined more than one optimisation methods known as the hybrid optimisation method [31, 32]. The combination of more than one response is becoming more popular among researchers. This technique is called the multi-objective optimisation method [33, 34].

The improvement of weld line strength and shrinkage on the moulded part by optimising the injection moulding parameters is an alternative technique, as well as simpler and easier to implement. There are many optimisation tools that can be used to improve the strength of weld line, as well as shrinkage, in order to optimise the product quality by using single and multiple objectives (responses) method. The improvement of the weld line strength and shrinkage of the moulded parts should be done in parallel, especially for the part which requires the strength for its functionality with precision critical dimensions. It is hard to find studies which consider both elements (shrinkage and weld line strength) as defects. Therefore, this study focuses on improving both shrinkage and weld line strength using a multi-objective optimisation method. This optimisation technique is powered by response surface methodology (RSM) in choosing the best combination and proposing the minimum shrinkage and maximum weld line strength to the parts.

2 Methodology

Autodesk Moldflow Insight (AMI) software was used for simulation to obtain the recommended processing parameters, as well as the range of selected parameters, while Nessei NEX1000 injection moulding machine was employed for the experimental process. The details of mould design were calculated and designed according to the guideline in ISO standard. Design-Expert software was used to generate the list of experiment and analysis of results using RSM technique [35].

2.1 Part and mould design

The design of a thick flat part was based on ISO 3167:2002(E) [36] international standard of multipurpose test specimen for plastic injection moulding as shown in Fig. 1a which includes the feed system design. The mould was designed according to part design of ISO 294-1:1996(E) [37] standard for two-cavity mould. The relative runner diameter used in this study is 8 mm. Tab gate was used in this study as recommended in ISO 294-1:1996(E)[37]. The selected material for mould was P20 steel, and the plastic resin was acrylonitrile butadiene styrene (ABS). The properties of ABS are shown in Table 1.

Fig. 1
figure 1

Thick flat part; a feed system design using tab gate; b cooling channel design

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Table 1 Material properties of a plastic resin [30]
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The pressure drop for each design is estimated to determine the significance of the design [35]. The pressure drop, ∆P, is calculated using Eq. 1 [35],

$$ \Delta P = \frac{2 k L }{R}\left[ {\frac{{\left( {3 +\frac{1}{{\varvec{n}}}} \right)\varvec{dot{V}}_{{{\varvec{melt}}}} }}{{\varvec{\pi}{R}^{3} }}} \right]^{{\varvec{n}}} $$
(1)

where k and n are the reference viscosity (\(Pa.s^{n}\)) and power-law index of the polymer melt at the melt temperature, respectively, L is the length of feed system (m), R is the radius of feed system (m) and \(\dot{V}\) melt is volumetric flow rate at the inlet (m3/s). The acceptable pressure drop is below 30 MPa [35].

The cooling time for the runner is estimated to ensure that the runner size does not affect the cooling time of the moulded part. The cooling time for the runner must be less or slightly more than the cooling time for the moulded part [30]. If not, the size of the runner needs to be changed. The cooling time, tc,runner, for the runner is calculated using Eq. (2) and the cooling time, tc, part, for the moulded part is calculated using Eq. (3) [35],

$$ t_{c, runner} = \frac{{D^{2} }}{23.1\left( \alpha \right)} ln\left[ {0.692\left( {\frac{{T_{melt - } T_{coolant} }}{{T_{eject - } T_{coolant} }}} \right)} \right]{ } $$
(2)
$$ t_{c, part} = \frac{{h^{2} }}{{\pi^{2} \left( \alpha \right)}} ln\left[ {\left( {\frac{4}{\pi }} \right)\left( {\frac{{T_{melt - } T_{coolant} }}{{T_{eject - } T_{coolant} }}} \right)} \right] $$
(3)

where D is the diameter of the runner (m), h is the wall thickness of the moulded part (m), α is the thermal diffusivity of the material (m2/s), Teject is the specified ejection temperature (°C), Tcoolant is the coolant temperature (°C) and Tmeltis the melt temperature of the material (°C). The estimated cooling time for the runner can be calculated using Eq. (2) as follows; Teject, Tcoolant, Tmelt and α are taken from the material properties shown in Table 1.

Apart from the cooling time, shear rate for the gate also needs to be calculated because the gate is the smallest area in the feed system. The shear rate at the gate should not exceed the maximum shear rate allowed as stated for the material properties [35]. The shear rate of this study for dual gate is calculated using Eq. (4) [35],

$$\dot{\gamma }=\frac{2\left(2 + \frac{1}{n}\right)\dot{V}}{W{ h}^{2}}$$
(4)

where n is the power-law index of the polymer melt, \(\dot{V}\) is a volumetric flow rate (m3/s), W is the width of the gate (m) and h is the thickness of the gate (m).

The design of the cooling channel used in this study is illustrated in Fig. 1b according to the requirement proposed in ISO 294-1:1996(E) [37] document. Four channels are needed for each insert to absorb the heat released from the molten plastic as mentioned in ISO 294-1:1996(E) [37]. The size of the cooling channel is estimated by calculating the heat capacity of the moulded part.

The total amount of heat that needs to be removed by the cooling system, \({Q}_{molding}\) (J) can be calculated using Eq. (5) [35],

$${Q}_{molding}={m}_{molding}\left({C}_{p}\right)\left({T}_{melt} - {T}_{eject}\right)$$
(5)

where \({m}_{molding}\) is the mass of the moulded part including feed system (kg), \({C}_{p}\) is the specific heat of material (J/kg.°C), \({T}_{melt}\) is the melt temperature (°C) and \({T}_{eject}\) is the ejection temperature (°C).

With the consideration of the coolant control pressure, \(\Delta P\) (kPa) and the length of cooling channels, the minimum diameter of the cooling channels can be calculated from Eq. (6) with the allowable pressure drop assumed to be 100 kPa which is half of the maximum pressure supplied from the coolant controller [35]. The coolant pressure drop is due to friction of hoses, turns, plugs and connectors.

$${D}_{min}=\sqrt[5]{\frac{{\rho }_{coolant}\left({L}_{line}\right){\left({\dot{V}}_{coolant}\right)}^{2}}{\Delta P\left(10\pi \right)}}$$
(6)

where \({\rho }_{coolant}\) is density of the coolant (kg/m3), \({L}_{line}\) is the total length of the cooling channels at core and cavity sides (m), \({\dot{V}}_{coolant}\) is the coolant flow rate (m3/s) and D is the diameter of cooling channels (m).

After the diameter of cooling channel has been estimated, the distance between mould surface and cooling channel is calculated. The linear distance between the cooling channels and the mould surface, \({H}_{line}\) (m) can be calculated using heat conduction equation state as shown in Eq. (7) [35],

$${h}_{conduction}= \frac{{K}_{mold}}{{H}_{line}}$$
(7)

where \({h}_{conduction}\) is the convection heat transfer coefficient (W/°C), and \({K}_{mold}\) is the thermal conductivity of mould material (W/m°C).

By referring to P20 mould steel properties for endurance limit stress and assuming the nominal compressive stress as 150 MPa [35], the value of stress concentration factor, K, in this study is calculated to be 3.51. Thus, in this study, the diameter of the cooling channel was selected to be 8 mm which complies with the calculated values. The distance of cooling channel is selected to be 12 mm as classified within the calculated range.

2.2 Variable parameter and range

Four independent parameters were selected as the variables in this study namely coolant inlet temperature, melt temperature, packing pressure and cooling time based on the previous results of significant parameters that affect shrinkage and weld line strength [21, 38,39,40,41,42]. Coolant inlet temperature was chosen instead of mould temperature because the mould temperature was controlled by coolant inlet temperature.The range of variable parameters was determined based on the recommended simulation results and material specification as shown in Table 2.

Table 2 Selected process variable range for ABS material
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2.3 Experimental design and analysis of data

The results obtained from the experiment for shrinkage and strength of weld line were analysed using Design-Expert software with RSM method. All the results from the experiments were arranged in a list of experiments and used to generate a relationship between input parameters setting and output responses which are shrinkage and strength of weld line on the specimen. Two levels of full factorial design were selected using four factors which are coolant inlet temperature (°C), melt temperature (°C), packing pressure (MPa) and cooling time (s). Shrinkages in both parallel to and normal to melt flow directions, and weld line strength were selected as the responses. A list of experiments generated in Design-Expert software based on four factors and four centre points is depicted in Table 3 for Run numbers 1–20. Then, the full factorial design was augmented to RSM using centre composite design (CCD) that consists of additional ten runs as shown in Table 3 for Run numbers 21–30. Based on these results, a model was generated for each response based on the required backward model selection (alpha out = 0.05). The insignificant parameters or interaction between parameters were removed and excluded from the generated models for both shrinkage and strength of weld line. These models were used during the optimisation process.

Table 3 List of experiments and results of shrinkage and weld line strength
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2.4 Tensile test

Tensile strength, \({\sigma }_{M}\) (N/m2), was obtained from the maximum tensile stress of the specimen. Universal testing machine (UTM) was used to measure the tensile strength of the moulded part. Extensometer was used as the aid to increase the accuracy of the data collected. The speed of testing used in this study was 50 mm/min according to ISO 527-1:2012 [43]. Five specimens were used for tensile testing for each set of moulding conditions.

2.5 Shrinkage measurement

Shrinkage was measured according to the ISO 294-4:2001 [44] standard to determine the shrinkage of the moulded part. The shrinkage measurement (post-moulding) was measured 48 h after the moulding process.

The specimens were trimmed from the gating system just after the moulding process and stored at room temperature between 16 and 24 h. Five specimens for each of the mouldings were selected for shrinkage measurement. The results of the moulding shrinkage measurement can be calculated for shrinkage in parallel to the melt flow direction, \({S}_{Mp}\) (%) and normal to the melt flow direction, \({S}_{Mn}\) (%).

3 Results and discussion

3.1 Analyses of full factorial experiment

The results of average shrinkage and weld line strength for full factorial experiments are shown in Table 3, row numbers 1 until 20. Average shrinkages were calculated based on the shrinkage values both parallel to and normal to the melt flow direction in both cavities. Besides, weld line strength was obtained from the maximum stress of the thick flat part during the tensile test. The minimum value of shrinkages in both normal to and parallel to the melt flow directions for full factorial experiments is 1.06 mm and 0.46 mm, respectively, and maximum weld line strength is 41.5181 N/mm2. From these results, Analysis of Variance (ANOVA) was conducted for each response in order to analyse the curvature of the model that will be created. The shrinkages and weld line strength can be improved using response surface methodology (RSM) if the curvature is present in the model.

3.2 Significant factors affecting shrinkage and weld line strength

Table 4 shows the percentage contribution of each factor and significant interaction for shrinkage and weld line strength obtained from ANOVA. The most significant factor of shrinkage for both normal to and parallel to the melt flow directions was packing pressure with 85.24% and 90.64% contribution, respectively. Packing pressure influenced the density of the molten plastic during the packing process. Packing pressure plays a vital role to pack the molten plastic until the solid density is achieved, since the density of polymer varies from melt to solid. Change in packing pressure will also affect the density of molten plastic that leads to the shrinkage issue. Results also showed that coolant inlet temperature, melt temperature and cooling time contributed less significantly towards shrinkage in this study.

Table 4 Percentage contribution of factors
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Besides, the highest percentage contribution of parameter for weld line strength is the coolant inlet temperature with 59.37%. Therefore, the coolant inlet temperature was the most significant factor that affected the weld line strength of the moulded part. The coolant inlet temperature significantly affects the mould temperature, where the increase in the mould temperature resulted in diffusion on the molecular chains to a higher degree of bonding at the weld line interface. This molecular chain affects the quality of the bonding and the strength of the moulded part. The mould temperature was also found to be the most significant parameter affecting the weld line strength of the moulded part by Annicchiarico & Alcock [45].

3.3 Analysis results of shrinkage in normal to the melt flow direction

Table 5 shows a statistical analysis of ANOVA for two-level factorial of shrinkage in both normal to and parallel to the material flow directions, and weld line strength. ANOVA results indicated several significant terms to the response, including main factors and interactions. The probability values less than 0.05 (p value < 0.05) were considered to have a significant effect [46]. Meanwhile, insignificant terms (p value > 0.05) have been removed in order to obtain an accurate empirical model based on the backward elimination regression with alpha out to exit being 0.05. The significant terms model was determined with 95% of confidence level that was applied in an ANOVA analysis. From the analysis, the probability values (p value) below 0.05 indicate that analysis of shrinkage in normal to and parallel to the material flow model is significant with p value < 0.0001 [46]. Meanwhile, the curvature is significant because the p value is less than 0.05. Thus, it is possible that a quadratic model is a better fit compared to a linear model [46]. Therefore, the models are best fit with second-order models rather than first-order by augmenting axial runs to allow quadratic terms to be incorporated into the model. Data were augmented using rotatable central composite design (CCD) to produce a quadratic model. The CCD is a very efficient design for fitting the second-order model or response surface [47]. It requires additional 10 axial runs with two replication of centre runs as recommended by the Design-Expert software.

Table 5 Summary of ANOVA results for shrinkage in normal and parallel directions to the melt flow, and weld line strength
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The models of shrinkage in the normal to and parallel to the melt flow directions, as well as weld line strength, are developed based on the CCD results. These models are used to predict the best combination of parameters in order to reduce shrinkages, as well as increase the weld line strength of the moulded part. The results for all responses are shown in Table 3 starting from run 21–30.

3.4 Analysis results of CCD for shrinkage in normal to the melt flow direction

The ANOVA of shrinkage in normal to melt flow direction after augmentation of full factorial experimental design is shown in Table 6. The results showed that the model is significant with several model terms. The block gives the lowest sum of square value compared to other terms which indicated that the variation between block 1 and 2 is not critical. As shown in Table 6, the interaction of AC and the main effects of A, B and C are significant to the model. After fitting the first-order model, the result shows that only packing pressure (C) gives a quadratic effect to the model. Besides, the lack of fit (LOF) value is 0.0932 (p value > 0.05) which satisfies the model to be fitted.

Table 6 ANOVA of CCD for shrinkage in normal direction to the melt flow
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The values of R2 and Adjusted R2 are very high which are close to 1 (≈0.9377 and ≈0.9243) indicating that the model is desirable. The Adjusted R2 has a difference of only 0.0681 with Predicted R2 which implies that it is in reasonable agreement (< 0.2). On the other hand, the value of adequate prediction is above 4 (≈ 28.9702), which indicates that the model is adequate [46].

Furthermore, the main effects plot namely coolant inlet temperature (A), melt temperature (B) and packing pressure (C), on the shrinkage in normal to the melt flow direction, are shown in Fig. 2a–c, respectively. The plot of shrinkage versus coolant inlet temperature shows that an increase in temperature reduces the shrinkage. This result is in line with the documented research works where the shrinkage on the moulded parts was reduced with an increase in mould temperature due to better pressure transmission [48]. The same pattern is shown for melt temperature, while an increase in the melt temperature resulted in a decrease in shrinkage in normal to the melt flow direction [49]. These mould and melt temperatures affected the stress relaxation of the moulded material. High mould and melt temperature will cause the material to be more ‘relaxed’ during the cooling process [50]. Cooling rate has a significant effect on the degree of relaxation [50]. Thus, rising the mould and melt temperature will reduce the shrinkage by allowing the material to ‘relax’. Meanwhile, the shrinkage in the normal to the melt flow direction decreased with the increase in packing pressure which is in agreement with other research works [49, 51, 52]. Increasing the packing pressure resulted in the increase in the density of polymer melt. The shrinkage was reduced when the melt density increased as close as solid density of the moulded material. Therefore, shrinkage was reduced when the packing pressure increased.

Fig. 2
figure 2

Main effect plot for factor, a coolant inlet temperature, b melt temperature, c packing pressure, d contour plot of interaction coolant inlet temperature and packing pressure to the shrinkage

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Figure 2d shows the contour plot of interaction between coolant inlet temperature (A) and packing pressure (C). The response line of both factors tends to crossover, indicating that the interaction is significant. It can be seen that by increasing the coolant inlet temperature with packing pressure at high level (70 MPa), the shrinkage in normal to the melt flow direction was decreased drastically. On the other hand, at the lowest packing pressure setting (50 MPa), increasing the coolant inlet temperature from 50 to 70 °C showed no significant effect on the shrinkage. The contour plots can be used to estimate the effect of the interaction between variables and responses [45]. The contour graph in Fig. 2d reveals that the lowest shrinkage can be achieved when packing pressure is set at a high level (70 MPa) and the coolant inlet temperature is at a high level (70 °C). This finding is in agreement with Altan [49].

The empirical model generated by the Design-Expert software was used to estimate the response of shrinkage in normal to the melt flow direction at a different setting within the range investigated. The empirical models in terms of actual factor are shown in Eq. (8),

$$ \begin{aligned} \left( {Shrinkage_{normal} } \right) & = 0.32456 + 0.016917A - 2.70832 \times 10^{ - 3} B \\ & \quad + 0.07175C - 3.4375 \times 10^{ - 4} AC - 5.92361 \times 10^{ - 4} C^{2} \\ \end{aligned} $$
(8)

where A is the coolant inlet temperature (°C), B is the melt temperature (°C) and C is the packing pressure (MPa).

The experimental and predicted results of shrinkage in the normal to the melt flow direction are illustrated in Fig. 3. Overall, the experimental results are in line with the results from the empirical model. Therefore, the empirical model has a good prediction in predicting the shrinkage values with 9.06% error between average experimental results and predicted results.

Fig. 3
figure 3

Experimental and predicted results of shrinkage in normal direction to the melt flow using CCD

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3.5 Analysis results of CCD for shrinkage in parallel to the melt flow direction

Table 7 shows an ANOVA result of shrinkage in parallel to the melt flow direction after augmentation of full factorial experimental design. The sum of square value for the block is 0.00004 which shows that the variations between blocks are not critical (≈ 0). Besides, the model is significant with p value lower than 0.0001. Coolant inlet temperature (A), melt temperature (B) and packing pressure (C) are significant parameters where the of “Prob > F” is less than 0.05 [45]. No interaction between parameters has been found as significant for shrinkage in parallel to the melt flow direction. Moreover, the lack of fit (LOF) is not significantly (p value > 0.05) relative to the pure error which satisfies the model to be fitted.

Table 7 ANOVA of CCD for shrinkage parallel to melt flow direction
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The R2 and Adjusted R2 have high values which are close to 1 (≈0.9633 and ≈0.9572), hence, are desirable. There is only 0.0467 difference between Adjusted R2 and Predicted R2 which is in a reasonable agreement because the value is below 0.2 [45]. The adequate prediction is above the value of 4 (≈ 436,654), indicating that the model is adequate.

The main effect plot for coolant inlet temperature (A), melt temperature (B) and packing pressure (C) is shown in Fig. 4a–c, respectively. Shrinkage versus coolant inlet temperature plot (Fig. 4a) illustrated that the shrinkage is minimum with the increase in the coolant inlet temperature. This result shows a similar pattern with shrinkage in normal to the melt flow direction and agreed with previous researchers where the shrinkage on the moulded parts was reduced when the mould temperature was increased [42]. The trend for the shrinkage in both (parallel and normal) to the melt flow directions is in line with the finding from previous researcher [42]. Besides, packing pressure showed a quadratic relation towards shrinkage, and the graph shows that the shrinkage was decreased with the increase in packing pressure [49, 51, 52]. The contour plots obtained in this study were used to estimate the effect of the interaction to the response when the parameters are at high and low levels [45]. No interaction was found for the shrinkage parallel to the melt flow direction. The results from the contour plot (Fig. 4d) showed that shrinkage was reduced with the increase in packing pressure, as well as coolant inlet temperature. This finding agreed with that of Chen [53] in the study of reducing shrinkage of the moulded part.

Fig. 4
figure 4

Main effect plot for, a coolant inlet temperature, b melt temperature, c packing pressure and d contour plots of coolant inlet temperature and packing pressure

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The empirical model for the shrinkage parallel to the melt flow direction in terms of actual factors is expressed in Eq. (9),

$$ \begin{aligned} \left( {Shrinkage_{parallel} } \right) & = 0.75694 - 1.775 \times 10^{ - 3} A - 7.5 \times 10^{ - 4} B \\ & \quad + 0.013639{\text{C}} - 1.87435 \times 10^{ - 4} C^{2} \\ \end{aligned} $$
(9)

where A is coolant inlet temperature (°C), B is melt temperature (°C) and C is packing pressure (MPa).

The experimental and predicted results of shrinkage parallel to the melt flow direction are illustrated in Fig. 5. The generated graph of experimental versus shrinkage parallel to the melt flow direction has yielded a good prediction, whereas the pattern shows similarity between the experimental results and empirical model. Error of average value between experiment and predicted model is 1.72%, indicating that the model has a very good relation with the experimental results.

Fig. 5
figure 5

Experimental and predicted results of shrinkage in parallel to the melt flow using CCD

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3.6 Analysis of results of CCD for weld line strength

The analysis of results from CCD for weld line strength of the moulded part implies that the model is significant (p value < 0.05) as shown in Table 8. This means that there is less than 0.0001% chance for F-Value of model occurring due to noise [45]. Coolant inlet temperature (A), packing pressure (C) and cooling time (D) have significant impacts, while AB, AC, BC and CD indicated significant interactions in the model (p value < 0.05). The terms A2, B2 and C2 are also significant (p value < 0.05) in establishing the polynomial model. The lack of fit (LOF) is insignificant (p value > 0.05) which indicates that the quadratic model is fitted.

Table 8 ANOVA of CCD for weld line strength
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From Table 8, the R2 (0.9537) value is acceptable for the model (≈ 1). The predicted R2 is in reasonable agreement with the adjusted R2 where the difference between them is below 0.2, which is only 0.107 in this study. The adequate precision value is above 4 (≈22.1196) which shows that the model is adequate.

Figure 6a–d shows the main effect of weld line strength of the moulded part for terms A, B, C and D, respectively. Terms A, B and C illustrated that the curvature is significant (p value < 0.05) representing the second-order terms in the model. Coolant inlet temperature (A) indicates a positive effect on the weld line strength of the moulded part, where an increase in coolant inlet temperature resulted in an increase in the weld line strength due to the fact that the molecular chains gained higher ability to flow at a higher temperature [45]. On the other hand, with the lower temperature of coolant inlet, the molecular diffusion and subsequent molecular bonding in weld interface are incomplete, so, it weakens the interaction of the molecular chain. Thus, the strength of the weld line area is weak. This result is in line with that of Chen et al. [54] in their study on thin wall part.

Fig. 6
figure 6

Main effect of weld line strength on the moulded part for terms for, a coolant inlet temperature, b melt temperature, c packing pressure and d cooling time, contour plots of e melt temperature and coolant inlet temperature, f packing pressure and coolant inlet temperature, g packing pressure and melt temperature and h cooling time and packing pressure

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The same trend is illustrated for term B (melt temperature) as shown in Fig. 6b, but the line is slightly decreased near the middle and tends to increase subsequently. This term contributes to the increase in the melt temperature resulting in increasing the weld line strength. The molecules carry higher energy at higher melt temperature. This energy decreases when the melt material enters the mould cavities due to lower mould temperature compared to the barrel. Thus, higher melt temperature carries more molecular energy bonding compared to low melt temperature. This result is in line with those of Chen et al. [54] and Ozcelik et al. [41].

The trend of factor C (packing pressure) also illustrated similar trend with A and B as shown in Fig. 6c. Increasing the packing pressure led to an increase in the weld line strength. Low pressure at the flow front of material does not promote molecular chain entanglement, resulting in poor strength of the moulded part. This result agrees with a research by Chen et al. [54] and Ozcelik et al. [41].

In this study, cooling time (D) was found as a significant factor for weld line strength of the moulded part. The graph shown in Fig. 6d indicates that weld line strength decreases with an increase in cooling time. Residual stress on the moulded parts depends on the cooling rate where the cooling rate after the moulded part was ejected from the mould is faster than the cooling stages inside the mould [55]. Thus, shorter cooling time in the mould increases the residual stress of the part. Furthermore, tensile stress on the moulded part is increased with the increase in residual stress [56].

Figure 6e illustrates the contour plots of factors A and B at packing pressure of 50 MPa and cooling time of 10 s. The maximum strength of the moulded part is achieved at high melt temperature (270 °C) and high coolant inlet temperature (70 °C). The contour plot of factors A (coolant inlet temperature) and C (packing pressure) at melt temperature of 260 °C and cooling time of 10 s are shown in Fig. 6f. High packing pressure (70 MPa) and high coolant inlet temperature (70 °C) increase the weld line strength. The contour plots of factors B (melt temperature) and C (packing pressure) at coolant inlet temperature of 60 °C and cooling time of 10 s are shown in Fig. 6g, respectively. The interaction of BC (B is melt temperature; C is packing pressure) showed similar trends with the interaction of AB (A is coolant inlet temperature; B is melt temperature) and AC (A is coolant inlet temperature; C is packing pressure) where the maximum weld line strength can be achieved at high packing pressure (70 MPa) and high coolant inlet temperature (70 °C). Figure 6h illustrates the contour plots of factors C (packing pressure) and D (cooling time) at coolant inlet temperature of 60 °C and melt temperature of 260 °C. Differing from other interactions, the interaction of CD shows that the weld line strength is optimal when the cooling time is at the minimum parameter (8 s) with the maximum packing pressure (70 MPa).

The empirical model of the weld line strength in terms of the actual factors is shown in Eq. (10),

$$ \begin{aligned} Strength_{WL} & = 104.64646 - 0.29657A - 0.36123B - 0.36159C + 0.2659D \\ & \quad + 6.70528 \times 10^{ - 4} AB + 1.54873 \times 10^{ - 3} AC + 8.58055 \times 10^{ - 4} BC \\ & \quad - 50337 \times 10^{ - 3} BC + 5.28646 \times 10^{ - 4} A^{2} + 5.25396 \times 10^{ - 4} B^{2} \\ & \quad + 9.40648 \times 10^{ - 4} C^{2} \\ \end{aligned} $$
(10)

where A is coolant inlet temperature (°C), B is melt temperature (°C), C is packing pressure (MPa) and D is cooling time (s).

The experimental and predicted results of weld line strength are illustrated in Fig. 7. The generated graph of experimental versus predicted results of weld line strength showed a similar pattern. It can be concluded that the predicted value is in a very good agreement with the experimental results because the error between experiment and predicted values is about 0.20%. Based on the predicted model of CCD, the result of optimisation of shrinkages and weld line strength is discussed in the next section.

Fig. 7
figure 7

Experimental and predicted results of the weld line strength using CCD

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3.7 Optimisation result of CCD

The predicted optimal solution of parameters for the shrinkage in both parallel to and normal to the melt flow directions, and the weld line strength of the moulded part using RSM are concluded in Table 9. To obtain the significant result of this study, the optimal solution of the parameters in experimental works was compared to the recommended value obtained from the simulation. Results showed that shrinkage was reduced significantly by 5.969% and 4.375% in normal to and parallel to the melt flow direction, respectively, while the weld line was improved 3.758% compared to the recommended setting from the simulation. Meanwhile, the reduction in shrinkage in parallel to and normal to the melt flow direction using multi-objective optimisation was 5.891% and 4.160%, respectively, and the weld line strength of the moulded part was increased by 3.759%. These improvements are according to the combination of parameters setting used during experimental works to improve the shrinkage and weld line strength on the moulded part.

Table 9 Predictive optimal solution of shrinkage and the weld line strength in multi- and separate objectives
Full size table

The result of shrinkages and weld line strength in multi-objectives is found to be almost similar. Therefore, the multi-objective optimisation using RSM was preferable due to the same parameters that were employed to obtain the minimum shrinkage, as well as the maximum weld line strength conditions.

3.8 Verification test

A series of verification tests were conducted in order to validate the predicted model solutions. Three empirical models had been generated using ANOVA in Design-Expert software, by comparing the results from prediction and confirmation tests using the following equation;

$$Error=\left|\frac{Result\, of\, conformation\, tests-Predicted\, value}{Result\, of\, conformation\, tests}\right|\times 100$$
(11)

The verification results from all experiments are represented in Table 10. The results indicated that the predicted errors ranged from 0.2 to 14.5%. The prediction system is in good agreement with the verification experiments where the errors are below 20% [57].

Table 10 Results of verification test
Full size table

4 Conclusions

Optimisation process using RSM has been applied to find the best parameters setting in order to reduce shrinkage and increase the weld line strength, through injection moulding process. Packing pressure was found to be the most significant factor affecting the shrinkage, while the coolant inlet temperature had the most significant effect on the weld line strength. Final result revealed that the coolant inlet temperature of 69.93 °C, melt temperature of 270 °C, packing pressure of 70 MPa and cooling time of 8 s are the best combination of parameters to reduce the shrinkage up to 5.969% and increase the weld line strength up to 3.758% compared to the values from the recommended setting obtained from the simulation in experimental research. Validation process shows that the prediction system is in good agreement with the verification experiments with an error of less than 14.5%.