Multi objective prediction and optimization of control parameters of Friction stir welding on Casted AlSi10Mg plates with Taguchi – Gray Relational Analysis

In this study, a 3 mm thickness of AlSi10Mg Casted alloy plates was used in the friction stir welding process. The experimentations were conducted Using design of experiment to shorten the number of experiments and to get optimal friction stir welding parameters by utilizing Gray relational analysis based on the ultimate tensile and hardness test results. Orthogonal array of L9 (33) was used based on three main parameters and three stages for each parameter, where tool velocity of three stages are 800, 900 and 1000 Rpm, tool feed of 30,40,50 mm/min, plus axial load of 300,400 and 500 Kg. Using Minitab 17 software. Gray Relational analysis is used to explore the optimal set of process variables and their effects on the ultimate tensile strength and hardness of weld plates. The plates are effectively welded, tensile test and hardness is measured at room temperature. The end result shows that the tool velocity 1000 rpm, feed 50 mm / min, then axial load of 400 kg are dominant process parameters to join AlSi10Mg Casted alloy plates.


Introduction
The need for high strength to weight ratio is continuously growing especially in automobiles and aviation sector in improving fuel efficiency and reducing harmful emissions [1]. AlSi10Mg alloy belongs to hypoeutectic aluminum alloys group. It is frequently used in automotive, aircraft and armed applications because of superior mechanical properties combined with low strength to weight ratio, corrosion resistance and quite decent castability [2]. The presence of Eutectic Al+Si phase in this alloy has greatly effects ductility and strength, and also effects machinability. One of the significant characteristics of AlSi10Mg alloy are low shrinkage and melting point, hence this alloy is highly suitable candidate for casting. FSW (friction stir welding) is solid state joining technique. Especially well-suited to aluminum alloys, even though much care is taken in welding, these are difficult to fusion weld without experiencing hot cracking, porosity, or distortion. The rotating tool's Frictional heat and plastic flow cause major microstructure changes, resulting in variations in the weld's quality on mechanical properties [3]. A nugget or a stir region, a thermo-mechanically affected zone (TMAZ), and a heat affected zone make up the FSW zone (HAZ). The stir zone's grain structure is exceptionally equiaxed and extremely fine, resulting in improved ductility and mechanical endurance [4]. In FSW, the plates are heated to a temperature of one third of its melting point of metal hence the mechanical properties of the welded region, such as ductility and strength, are much higher than in conventional techniques [5][6][7]. Here, welding process optimization is the primary concern in order to achieve an improved weld joint, as incorrect chosen parameter leads to tool failure and lower weld efficiency. Researchers use a number of optimization methods, such as Taguchi, Grey relation analysis, and ANN, to arrive at the best solution for industrial problems [8,9].

Experimental Work
In this work, AlSi10Mg casted alloy manufactured through casting process is used for experimentation work. 100 mm long 50mm width and 3mm thick Plates are obtained by wire EDM and Spectrometric analysis of chemical composition (Table 1) was also included. In this work, FSW is used to join AlSi10Mg alloy plates using R.V. Machine tools make with 3 ton capacity equipped with CNC control. The tool used to join AlSi10Mg plates fabricated by using H13 grade tool steel with 12 mm diameter shoulder and straight cylindrical pin with 4 mm diameter and 2.8mm length, shown in fig.1. Prior to welding, edges were thoroughly cleaned by mechanical method and applied ethanol solution, to make sure edges are free from any contamination. Then the plates are rigidly clamped on to the FSW machine table using clamps and T-bolts. Three FSW parameters were selected with three levels shown in table.2. Friction stir welding carried out using 9 different parameter combinations that were derived using Taguchi's DOE concept. Gray relational method is used to study the response of output parameters over input parameters [5].

Gray Relational Analysis
Grey relational analysis technique has been used where n = number of trails, yij = detected response significance where i=1, 2, ....n; j=1, 2...k This is used to solve problems where the goal is to increase the quality of a desired characteristic. This is known as the larger-is-better scenario, and to be an important method for optimizing multiple responses. To find the optimum value in GRA, the sequence of steps are: Step I S/N Ratios are determined by below equations i) Higher is the better S/N ratio( ) = (This is known as the Higher -is -better scenario, in which the aim is to maximization of response.) 5 where n= the number of replicas, xij=observed responses, where i=1, 2, ....n; j=1, 2...k This is useful for situations where the objective is to increase the quality parameter of interest. This is referred to as the "higher is better" situation.
ii) The lower the better.
(This is known as the smaller-is-better scenario, in which the aim is to minimization of response.) Step II xij is normalize as Zij (0≤Zij≤1) using the formula to minimize uncertainty and elude the impact of using diverse units Before using the grey relation theory or some other methodology to analyze the original data, it is important to normalize it. To make the sum of this array approximate to 1, an equivalent value subtracted from the same list of values. We investigated the normalization process's sensitivity to the sequencing results, because the normalization process affects the rank. As a result, when using grey relation analysis to normalize data, we suggest using S/N ratio value.

(applied for S/N ratio with Lower the better scenario)
Step III Using the S/N ratio values that have been normalized, evaluate the grey relational co-efficient  x k x k    is The distinction between x0(k) and xi(k) in absolute terms.
  is the distinguishing coefficient,  , is within the given range 01   (the coefficient may be modified depending on the system's practical needs).
Step IV obtain the Gray Relational Grade 6 where j  is grey relational rating for j th trail, and number of output features are k.
Step V Determine the best factor to use and the best degree combination for it.
Good product quality needs The greater the grey relational grade(GRG), as a consequence, the factor effect can be assessed using the GRG., similarly for each controllable factor, the optimal degree should be calculated.
For instance, to assess the impact of a factor i, we determine the average grade value(AGV) for each level j, and indicated as AGVj , the effect, Ei, can be defined as once we control factor i, Finest value of J* is obtained by j*=maxj (AGVij)

Implementation of the GRA
Step I Using one of the Eqs (1), (2), compute S/N ratios of the initial conditions and the S/N ratios for a given response.
Depending on what kind of quality characteristics you're looking for. Table 3 shows the computed S/N ratios related to each quality characteristic.
Step III The grey relational analysis should be carried out. using the information in Table 3, Using Eq, (6) compute the grey relational co-efficient using normalized S/N ratio values.  can be assumed as 0.5 in Eq. (6) for this run. Since all process parameters are equally weighted, [10]. Table 4 summarizes the results.
Step IV The GRG can then be calculated using Eq. (7). then, grades are taken into account when attempting to solve the multiple-response parameter problem. Table 5 summarizes the findings.
Step V Maximum of grade values is taken into consideration (Table 5),,we can obtain optimal parameter conditions Ts3 Fw3 Al 2.   Table 5 was used to compute the GRG means to each degree of controllable parameters, which were then summarized in Table 6. Highlighted values in Table 6 indicates larger GRG, the superior the compound performance characteristics. So, the controllable parameters' and their optimal values are: Tool velocity of 1000 rpm (stage 3), feed rate of 50 mm/min (stage 3), axil load of 400 kg (stage 2).  Table 6 shows the responses for Gray relational grade, Rotational speed has given rank 1, hence it has more influence on the tensile strength and hardness among three input parameters, as it causes more frictional heat input during welding. Large heat input causes grain refinement and leads to better Ultimate tensile strength and micro hardness. Next influential parameter among three is the Axial load raked 2, and the least influential parameter is the Feed Rate ranked 3.

Results and discussion
In this article, Using Taguchi's experimental design process, the parameters influencing the multiple performance characteristics of Friction stir welding of AlSi10Mg Casted alloy were investigated. For better multiple performance characteristics, the optimum Friction stir welding parameters were established. (Ultimate Tensile strength, Micro hardness) in the FSW process with the aid of grey relational analysis. Where three separate controllable parameters are used, this study suggests using an orthogonal array in conjunction with GRA to optimize multiple performances of the FSW process: Tool velocity, Feed rate, and Axial Load. Since tool velocity is a major factor in heat generation near the weld zone, tool velocity was considered a sensitive parameter in the FSW phase. At low tool velocity, heat generation is limited, resulting in poorer plastic deformations and weld region is sufferers with insufficient material flow, lowering hardness. However, with greater tool velocity, the heat produced increases, causing turbulence to form coarse grains. As a result, the hardness of the material is reduced. As welding speed increases, the hardness values decreases. [11].

Conclusion
 Looking at GRG values and table 6 reveals that higher GRG aims better multiple response. As a result, ideal levels in FSW of AlSi10Mg casted alloy for the combination of desired output characteristics Ts3 Fw3 Al 2 parameters. With this combination it is possible to get more Ultimate tensile strength and reasonable Micro hardness in the heat effected zone of FSWed joint.  2 According to the GRG findings, tool velocity, axial load, and Axial load have a significant impact on different responses.  This work can be considered as reference to establish the optimized process parameters for joining Additive Manufactured AlSi10Mg.