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This is called as local grey relation measurement.Hence, the grey relation coefficient ji ðkÞ for kth performancecharacteristics in the ith experiment can be expressed as: ji ðkÞ¼ Dmin þ 6DmaxD0i ðkÞþ Dmaxð5Þwhere D0i is the deviation of reference sequence and thecomparability sequence:D0i ¼ x*0ðkÞ 2 x*iðkÞ ð6ÞDmin ¼ ;j[imin;kmin x*0ðkÞ 2 x*jðkÞ ð7ÞDmax ¼ ;j[imax;kmax x*0ðkÞ 2 x*jðkÞ ð8Þx*0ðkÞ denotes the ideal (reference) values and x*jðkÞdenotes thecomparability value. 6 is distinguishing or identificationcoefficient. As the value of this factor is smaller, thedistinguishability is larger. In these calculations, 6 ¼ 0.5 wasused.The grey relation coefficientswere calculated by consideringthe ideal condition (reference sequence) x*0ðkÞ¼ 1:0and 6 ¼ 0.5.Then the grey relation grades were computed by equation (9):gi ¼ 1nX nk¼1ji ðkÞð9ÞThe grey relation coefficients and the grades calculated fromequations (5) and (9) for all nine sets of experiments are shown inTabl e VI .In Table VI, the experiment No. 3 has the highest greyrelational grade, which indicates that the injection moldingparameters used in this set (that is, injection pressure:30MPa, melt temperature: 3008C, injection speed: 60mm/s,injection time: 3 s) gives better performance in terms of partshrinkage (dimensional error) and weight.5. Influence of molding parametersTo assess the importance of molding process variable on thetargeted multiple quality factors, grey relational analysis hasbeen further extended by calculating the average grey relationalcoefficients at each level. The steps involve grouping the greyrelational grades by process parameters level for each column inthe orthogonal array, and calculating the average.The level that has highest average grey relation gradesindicates the optimal value of a specific parameter for better molding performance. As listed in the response table(Table VII), the difference between the maximum andminimum value of the grey relational grade of injectionmolding process variables represents the significance ofcorresponding variable. It has been found that injectionspeed and melt temperature are the most significant variablesfor the desired part quality. Another key observation noted inthis analysis is that all the four process variables arecontributing best at their third level (highest). This indicatesthat DMLS molds need a higher range of process variablesthan the variables suggested in material data sheet.The final experiment was conducted using optimized processparameters (all four parameters at third level). Theimprovements in two quality factors were confirmed withincrease in grey relation grades (0.8126, 0.8302 and 0.8188) inall three test runs conducted. The average shrinkage errormeasured with this confirmation tests was 1.64 percent, whichis slightly more than its normal shrinkage, with marginalimprovement in weight of molded part, which was 70.408 g.Although DMLSmold dimensions were varying in the range of0.3-0.6mmfromtheCADmodel,majority of the dimensions ofthe molded part were within the range of 30-100mm from themold dimensions. Therefore, the desired tolerance ^20 mmoncentral hole diameter has been achieved on molded part bymachining ofDMLS core pin beforemold assembly.Thismoldwas further used to produce 5,000 components, and to confirmits suitability further for rapid manufacturing, mold surfaceswere tested for surface finish, wear, scratch, and corrosionresistance. These results are discussed next.6. Mold surface characterizationIn post-molding stage, the DMLS mold surface was studiedunder SEM to check the surface degradation or surface cracksformed after producing 5,000 molding. Figure 5 shows thatmold surface does not undergo any severe damage even afterproducing 5,000 moldings (Figure 5(a)); however, few sub-surface micro cracks were observed after machining the moldsurface to a depth of 0.5mm. This implies that DMLS moldscan easily produce few thousands of moldings with acceptablequality level using optimized parameters. The surfacehardness measured was 62 HRB. The scratch testconducted using pointed diamond needle in a Scratch Tester100 showed the minimum variation of traction force variedbetween 1 and 2.5Nm. Similarly, the reciprocating wear testconducted on DMLS samples estimated the specific wear rateas 3.81 £ 10211m3/Nm, which is significantly less than steelmold surface (1.3 £ 10215m3/Nm). However, the corrosiontest based on weight loss method using spray technique,shows good corrosion resistance of 1.2 £ 1024mil per year(one mil equals one thousandth of an inch).7. ConclusionsThis investigation was focused on understanding the effect offour important injection molding process variables onshrinkage and weight of the moldings produced in DMLSmolds.
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