


ARTICLE 

Year : 2014  Volume
: 4
 Issue : 2  Page : 8794 

Modeling and Optimization of Die Casting Process for ZAMAK Alloy
Satpal Sharma
Mechanical Engineering School of Engineering, Gautam Buddha University, Greater Noida, Uttar Pradesh, India
Date of Web Publication  19Sep2014 
Correspondence Address: Satpal Sharma Mechanical Engineering School of Engineering, Gautam Buddha University, Greater Noida, Uttar Pradesh India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09768580.141176
Abstract   
The objective of the following study was to evaluate the effect of injection pressure of the molten metal, hydraulic pressure, temperature of the molten metal and the cooling time on the dimensional stability of the lock assembly of two wheelers. The material of the lock assembly was ZAMAK 3 (zinc, aluminum, magnesium, and copper) alloy. The lock assembly was produced by die casting process. In order to study the effect the process parameters such as injection pressure of the molten metal, hydraulic pressure, temperature of the molten metal and the cooling time, RSM (response surface methodology) with face center design was used. The experiments were carried out randomly according to design matrix. Three responses (shutter width, shutter thickness and shutter hinge length) were used for study. The RSM model was developed for each response. Analysis of variance for each response was also carried out to find out the significant factors and their interactions. Finally, optimization was carried out and the optimized input parameters were validated by conducting experiments at the optimum input parameters. The modeled and experimental results were compared and an error of 28% was observed. Keywords: Die casting, response surface methodology, zinc alloy
How to cite this article: Sharma S. Modeling and Optimization of Die Casting Process for ZAMAK Alloy. J Eng Technol 2014;4:8794 
1. Introduction   
Die casting is a manufacturing process for producing metal parts by forcing molten metal under high pressure into a die cavity. To ascertain consistent good quality of the end product in die casting, a proper monitoring of the raw materials and process parameters used in die casting is essential. From literature review, it has been found that most of the researchers over the years, have dealt with various process parameters such as metal temperature, piston velocity, filling time, hydraulic pressure etc., for optimization of the objectives such as maximum casting density, minimum porosity, minimum flashes, sufficient spread of molten material etc. Kumar et al. ^{[1]} analyze different parameters of pressure die casting to minimize the casting defects such as porosity. It was reported that good surface finish with required tolerances and dimensional accuracy can be achieved by optimization of controllable process parameters such as solidification time, molten temperature, filling time, injection pressure and plunger velocity. Moreover, by selection of optimum process parameters the die casting defects such as porosity, insufficient spread of molten material, flash etc., were also minimized. Zhang et al. ^{[2]} present a hybrid strategy in a soft computing paradigm for the optimization of the lowpressure die casting process. Casting process parameters, such as temperatures of die, pouring temperature were considered. The hybrid strategy combines numerical simulation software, a genetic algorithm and a multilayer neural network to optimize the process parameters. An approximate analysis model was developed using a back propagation neural network in order to avoid the expensive computation resulting from the numerical simulation software. According to the characteristic of the optimization problem, a realcode genetic algorithm was applied to solve the optimization model.
Chiang et al. ^{[3]} proposed an algorithm, by combining the grey relational analysis with the fuzzy logic, obtains a greyfuzzy reasoning grade to evaluate the multiple performance characteristics according to the grey relational coefficient of each performance characteristic. One of the real case studies performed in the die casting process, thinwalled cover components of liquid crystal display panel, verifies that the proposed optimum procedure was feasible and effective. Zheng et al. ^{[4]} in this work, an evaluation system for the surface defect of casting has been established to quantify surface defects and artificial neural network was introduced to generalize the correlation between surface defects and diecasting parameters, such as mold temperature, pouring temperature and injection velocity. It was found that the trained network has great forecast ability.
Zhu et al. ^{[5]} developed a numerical model for predicting micro porosity formation in aluminum casting, the redistribution of hydrogen between solid and liquid phases, the transport of hydrogen in liquid by diffusion and Darcy flow in the mushy zone. One of the key features of the model was that a twostage approach for porosity prediction was used. In the first stage, the volume fraction of porosity was calculated based on the reduced pressure, whereas the second stage, at fractions solid greater than the liquid encapsulation point. Kumar et al. ^{[6]} proposed a model to identify the influencing factors, causing casting defects and determination of optimum value of factors to minimize these defects in a melt shop industry, situated in north India. Percentage contribution of these factors was also estimated to develop an empirical expression between process performance and independent input variables. The outcome of this case study was to optimize the process parameters of the melt shop process, which led to minimize the casting defects.
Similarly, process parameter like plunger velocity and die temperature were optimized to improve quality and to reduce cost using Taguchi method by Tsoukalas et al. ^{[7]} , Guharaja et al. ^{[8]} , accomplished optimal settings of various significant process parameters such as green strength, moisture content, permeability and mold hardness for minimizing green sand casting defects using Taguchi's parameter design approach. Anastasiou ^{[9]} investigated the effects of process parameters on porosity formation in the pressure die casting process to improve casting quality using Taguchi method. Oktem et al. ^{[10]} , developed a Taguchi optimization method for low surface roughness for milling an aluminum alloy. Kittur et al. ^{[11]} demonstrated the effect of die casting machine parameters (fast shot velocity, slow shot to fast shot change over point, intensification pressure and holding time) on the performance characteristics of die casting process using response surface methodology (RSM).
On reviewing the literature, it has been found that most of the researchers over the years, have dealt with various process parameters such as metal temperature, piston velocity, filling time, hydraulic pressure etc., for optimization of the objectives such as maximum casting density, minimum porosity, minimum flashes, sufficient spread of molten material etc. Based on the literature survey and the subsequent analysis of gaps, the present work aims to investigate the effect of various process parameters in a die casting process (used for production of lock assembly of a two wheeler) and optimize the parameters using RSM. The experiments have been conducted using zinc alloy zinc, aluminum, magnesium and copper (ZAMAK 3). The process parameters varied were the injection pressure, hydraulic pressure, pot temperature and cooling time. This research study has been carried out on the existing die casting machine in the industry located in National Capital Region, Greater Noida.
2. Experimental Methods   
2.1 Material selection
The raw material here used was ZAMAK 3, which is an alloy with base metal of zinc and alloying elements of aluminum, copper, magnesium, lead, cadmium, tin, nickel, indium, thallium and iron. This is the mostly used general purpose zinc die casting alloy, providing an excellent combination of strength, ductility and impact strength. It also provides excellent plating and finishing characteristics. The chemical compositions of the raw material are shown in [Table 1]. To ensure that the raw material is according to the specifications it is tested in the spectroscopy labs whenever the new lot comes.
2.2 Research methodology
For efficient experimentation a systematic scientific approach is necessary to design and carry out the experimentation properly. A properly planned experimentation is of utmost importance for deriving clear and accurate conclusion/inferences from the experimental observations. RSM is considered to be a very useful strategy for accomplishing these tasks. In general, RSM establishes the methods for drawing inferences from observations when these are not exact but subject to variation.
The RSM is a collection of mathematical and statistical techniques for analyzing problems in which several independent variables influence a dependent variable or response. RSM has been developed by Box and Wilson (1951) to explore the potential of statistical design in industrial experiments. In many industrial situations, it is possible to represent independent input parameter in quantitative form and establish a functional relationship with the response as given below:
Where Y is the response and x _{1} , x _{2} , x _{k} are the number of input parameters. The function Φ is called the response surface or response function and ε_{R} is the residual sum of errors.
In the present work, RSM was applied for developing the mathematical models in the form of multiple regression equations for the various responses. In applying the RSM, the dependent variable is viewed as a surface to which the model is fitted. Parametric effects on the response were evaluated by considering a polynomial response surface mathematical model given by:
This assumed surface Y contains linear, squared and cross product terms of variable x _{i} 's. Where,
 b _{0} is the mean response over all the test conditions (intercept),
 b _{i} is the slope or linear effect of the input variable x _{i} (the firstorder model coefficients),
 b _{ii} the quadratic coefficients for the variable i (linear by linear interaction effect between the input factor x _{i} and x _{i} ) and
 b _{ij} is the linear model coefficient for the interaction between factor i and j.
To estimate the regression coefficients, a number of experimental design techniques are available. In this study, a fourfactor, threelevel face centered design (FCD) was used. The FCD was used for study of three responses namely shutter width, shutter thickness and shutter hinge length. The process parameters and their range are shown in [Table 2]. The corresponding design matrix is shown in [Table 3] along with response values. The tests were conducted randomly according to design matrix [Table 3]. The regression coefficients were calculated with the help of Design Expert V6 statistical software. After determining significance of the coefficients at a 95% of confidence level, the final relationships for shutter width, shutter thickness and shutter hinge length in terms of the process parameters were developed.  Table 3: Face centered composite design matrix for 4 variables in actual and coded form
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3. Result and Discussions   
3.1 Model development
Results and analysis of the responses are presented in this section. The appropriate selection of RSM model was carried out on the basis of sequential model sum of squares, lack of fit and model summary statistics tests. The analysis of variance (ANOVA) was also carried out to find the significant factors and interactions. The ANOVA for shutter width is shown in [Table 4]. The ANOVA shows the significance of various factors and their interactions at 95% confidence level. ANOVA [Table 4] shows the "model" as "significant" while the "lack of fit" is "not significant" which are desirable for model adequacy. The P < 0.05 in the "P > F" column indicates the significant factors and interactions. The ANOVA for other responses (shutter thickness and shutter hinge length) were also carried out in the same way and are not shown here for brevity. All the main factors and their significant interactions are included in the final model while the insignificant interactions are excluded from the model. Injection pressure (A), hydraulic pressure (B), pot temperature (C) and cooling time (D) were the significant factors while interactions between hydraulic pressure and pot temperature (BC), hydraulic pressure and cooling time (BD) were found as the significant interactions. Thus, finally quadratic model with main factors (A, B, C and D) and their significant interactions was selected. The final selected model for shutter width in terms of coded and actual forms are shown in [Table 5] and [Table 6] respectively. Similarly the final models for shutter thickness and shutter hinge length were carried out in the same way [Table 5] and [Table 6]. [Table 5] (Eq. 35) shows the response models in terms of coded form while [Table 6] (Eq. 68) shows the response models in terms of actual factor levels ^{[12],[13],[14],[15]} .  Table 5: Response surface models in terms of coded form for various responses
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 Table 6: Response surface models in terms of actual form for various responses
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The single factor effects on various responses were also discussed along with 3D plots of various responses. Finally, the optimum conditions for various responses were determined. To validate the optimum condition, the confirmation tests were also carried out.
3.2 Single factor effects on shutter width, shutter thickness and shutter hinge length
The single factor effect of factors on the responses can be explained with either Eq. 35 (coded formsince all the factors in coded form are at the same levels of +1, 0, −1) or with the help of single factor graphs. As the injection pressure increases the shutter width also increases, but after a certain limit of injection pressure, shutter width decrease with increase in injection pressure as shown in [Figure 1]a. With increase in hydraulic pressure, shutter width also increases as shown in [Figure 1]b; since coefficient of factor B is positive (Eq. 3). With increase in pot temperature, shutter width also increases as shown in [Figure 1]c; it is so because coefficient of factor C is positive. With increase in cooling time, shutter width also increases as shown in [Figure 1]d; because coefficient of factor D is positive (Eq. 3). The single factor effects on shutter thickness and shutter hinge length can be explained in the same way by considering [Figure 2] and [Figure 3] respectively.  Figure 1: Single factor effect on shutter width (a) injection pressure, (b) hydraulic pressure, (c) pot temperature and (d) cooling time
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 Figure 2: Single factor effect on shutter thickness (a) injection pressure, (b) hydraulic pressure, (c) pot temperature and (d) cooling time
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 Figure 3: Single factor effect on shutter hinge Length (a) injection pressure, (b) hydraulic pressure, (c) pot temperature and (d) cooling time
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3.3 Interaction effects on shutter width, shutter thickness and shutter hinge length
The interaction 3 D graphs are shown in [Figure 4], [Figure 5], [Figure 6] for shutter width, shutter thickness and shutter hinge length respectively. The interaction graphs (interaction BC) [Figure 4]a show that with the increase in hydraulic pressure (B) and pot temperature (C) the shutter width increases. Similarly other interactions BD (hydraulic pressure and cooling time) can be explained on similar lines [Figure 4]b. Interactions for shutter thickness and shutter hinge length [Figure 5] and [Figure 6] can be explained on similar lines.  Figure 4: 3D plot showing the effect of (a) hydraulic pressure  pot temperature (BC) and (b) hydraulic pressure  cooling time (BD) on shutter width
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 Figure 5: 3D plot showing the effect of (a) injection pressure  pot temperature (AC) (b) hydraulic pressure  cooling time (BD) and (c) pot temperature  cooling time (CD) on shutter thickness
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 Figure 6: 3D plot showing the effect of (a) hydraulic pressure – pot temperature (BC) and (b) hydraulic pressure  cooling time (BD) on shutter hinge length
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3.4 Process optimization
To investigate the influencing tendency of the process parameters on the responses, 3D graphs were plotted under certain processing conditions. The 3D response surface and 2D plots are the graphical representations of the regression equations used to determine the optimum values of the variables within the ranges considered. Eq. 3 (shutter width) was used to plot the [Figure 1]ad (one factor plot) and [Figure 4]ab (surface plot). Eq. 4 (shutter thickness) was used to plot the [Figure 2]ad (one factor plot) and [Figure 5] ac (surface plot). Eq. 5 (shutter hinge length) was used to plot the [Figure 3] ad (one factor plot) and [Figure 6]ab (surface plot). The optimization module in designexpert searches for a combination of factor levels, which simultaneously satisfy the requirements placed (i.e., optimization criteria) on each of the responses and process factors (i.e., multi response optimization) ^{[12],[13],[14],[15]} . Numerical and graphical optimization methods were used in this study by choosing the desired goals for each factor and response. The optimization process aims to combine the goals into an overall desirability function. The numerical optimization finds a point or more that maximize this function.
In the case of dealing with many responses, it is recommended to perform numerical optimization first; otherwise, one may find it impossible to uncover a feasible region. The graphical optimization displays the area of feasible response values in the factor space. In the numerical optimization part, a criterion was adopted. The criterion is to optimize shutter width, shutter thickness and shutter hinge length, which produces the target value. The target value for these responses were 55, 1.5 and 25 mm respectively. Equal weightage was given to each response for finding the optimum solution. The optimum conditions are shown in [Table 7] having a desirability of 0.966.
3.5 Validity of the response models under different operating conditions
The validity of various models such as shutter width, shutter thickness and shutter hinge length was evaluated by conducting tests at optimum conditions [Table 7] of various experimental factors such as applied injection pressure, hydraulic pressure, pot temperature and cooling time. The optimum conditions correspond to the obtained from design expert software. However it was not possible to set the machine at these conditions. Hence the confirmation tests were conducted at conditions are shown in [Table 7]. The variations between the experimental and the calculated values are of the order of 28% [Table 8].  Table 8: Comparison of modeled and experimental results of various responses
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4. Conclusions   
In the die casting process of ZAMAK 3 alloy, the mathematical models of the various responses have been carried out to correlate the dominant process parameters, including the injection pressure, hydraulic pressure, pot temperature and cooling time. The FCD was employed to carry out the experimental study. The conclusions of research are as follows:
RSM is an effective tool used for modeling and multiresponse optimization in die casting process:
 The shutter width, shutter thickness and shutter hinge length were modeled in terms of die casting process parameters. The confirmation tests results an error of 38%.
 Shutter width is generally increases with increase in the process parameters (injection pressure, hydraulic pressure, pot temperature and cooling time), but in case of injection pressure it decreases with increase in injection pressure after some limit.
 Shutter thickness increases with increase in injection pressure, hydraulic pressure, and pot temperature. With increase in cooling time, shutter thickness gets reduced.
 Shutter hinge length is generally increases with increase in injection pressure, hydraulic pressure, pot temperature and cooling time, but in case of injection pressure when it cross a limit shutter hinge length is reduced.
References   
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15.  W. W. Hines and D. C. Montogomery, "Probability and Statistics in Engineering and Management Sciences," 3 ^{rd} ed. New York, John Willey & Sons 1990. 
Authors   
Dr. Satpal Sharma received his B. E. and M. Tech. from NIT, Kurukshetra. He did his Ph.D. from IIT, Roorkee, Uttrakhand, India. He has a teaching experience of more than 15 years plus 1.25 years of industrial experience. Presently he is with the Department of Mechanical Engineering in School of Engineering, Gautam Buddha University, Greater Noida, U. P., India as an Assistant Professor. His area of research is tribological properties of coatings, weld surfacing and thermal spraying, welding, composite materials and machining. He has published more than 21 research papers in refereed international journals and 05 papers in national journals. Besides this 08 papers were published in international conferences and 01 paper in national conference.Supervised 13 M. Tech. students for dissertation. Presently 06 reaserch scholars (Ph. D. students) are working under my supervision.
Email: satpal78sharma@gmail.com
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5], [Table 6], [Table 7], [Table 8]
