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This study employs a Grey Relational Analysis (GRA) methodology to optimize the parameters of electromagnetic stir casting for semisolid slurries, specifically focusing on AM60 alloy. By normalizing experimental data and calculating grey relational grades and coefficients, this research aims to identify the optimal casting conditions. The process is divided into several steps, including data normalization, grey relational coefficient calculation, grey relational grade computation, determination of optimum levels, and calculation of grey relational grade for the optimal level. This paper outlines the mathematical models used in the analysis and presents the results of an orthogonal array test, highlighting the effectiveness of GRA in enhancing casting quality.
Electromagnetic stir casting is a critical process in the manufacturing of semisolid metal slurries, where controlling the quality characteristics of the casting is paramount.
This study introduces a systematic approach using Grey Relational Analysis (GRA) to optimize the process parameters, thereby ensuring high-quality casting outcomes. GRA provides a robust framework for handling complex and uncertain systems by simplifying the analysis into comprehensible, actionable insights.
To process all parameter values into a comparable sequence, the experimental data were normalized to the range of 0–1 in the grey relational generating process.
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Three general types of the grey relational generating (z_jk) calculation including the higher the-better, the lower-the-better, and the nominal-the-better depending on the characteristics of the original data. The ‘higher-the-better type’ normalizes can be expressed by Eq(1):
z_(jk )=((z°)_(jk )-min(z°)_k)/max((z°)_k–min((z°)_k ) ) j=1….
n ,k=1…. n (1)
The normalized expression for the lower-the-better type quality characteristic can be expressed by Eq(2):
z_(jk )=(max(z°)_k-(z°)_(jk ))/max((z°)_k–min((z°)_k ) ) j=1…..n ,k=1….n (2)
Where z°jk is the k-th semisolid casting quality index of the j-th experiment of an orthogonal array for casting response, max (z°)_k and min (z°)_k are the maximum and minimum values of the k-th semisolid casting quality characteristic.
The grey relational coefficient for each case was calculated to represent the mutual connection between the desired and actual experimental data. The grey relational coefficient (χjk) can be expressed by Eq (3):
(χjk) = (Δ_(min )+ϰΔ_(max ))/(Δ_(jk )+ϰΔ_(max ) ) j =1…..n (The number of experimental data) (3)
K = 1.2.3…. (The number of responses)
Where,
Δ_(min )=min_jk |z_(o(k) ) ┤-├ z_(jk ) ┤|
Δ_(max )=max_jk |z_(o(k) ) ┤-├ z_(jk ) ┤|
Δ_(ij )=|z_(o(k) ) ┤-├ z_(jk ) ┤|
z_(o(k) )is an ideal normalized value for the k-th electromagnetic stir processing which will always be 1. ‘ϰ’ is the distinguishing coefficient value lie between 0-1. ‘ϰ’ has been assumed 0.2 in this paper since, the shape factor, average particle size, particle density, average aspect ratio and roundness are given equal weightage.
After averaging the grey relational coefficients, the grey relational grade can be calculated as [19]:
Ψ_j=1/n ∑_(k=1 )^5χ_jk j=1…..10 (4)
Where n is the number of process response (in this study is 5) of k-th electromagnetic stir casting quality characteristic for AM60.The grey relational grade represents the degree of proximity between the given sequence and the reference sequence.
Since the experimental design is orthogonal, it is possible to fine out the effect of each level of process by using the grey relational grades of all experiments. For example, in this research, the mean of the multi-response grey relational grades for the temperature at level 1 calculated by averaging the multi response grey relational grades for the experiments1 to 3.
Grey relational grade ( χ ̂) of the optimal level of the electromagnetic stir casting can be expressed as:
χ ̂=χ_m+ ∑_(i=1)^F〖(χ ̅_i-χ_m 〗) (5)
where χ_m is the total mean Grey relational grade, χ ̅_i is the mean Grey relational grade at the optimal factor of A2B1C2, and F is the significant factors (here is 3) that affect the quality characteristics.
This study successfully applied Grey Relational Analysis to optimize the electromagnetic stir casting process for AM60 alloy. Through a systematic approach involving normalization, grey relational coefficient calculation, and determination of optimum levels, the research highlights the potential of GRA in enhancing casting quality. The methodology and findings provide a valuable framework for future research in casting process optimization.
Optimizing Semisolid Casting Processes Using Grey Relational Analysis. (2024, Feb 18). Retrieved from https://studymoose.com/document/optimizing-semisolid-casting-processes-using-grey-relational-analysis
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