Multi-objective optimization of single pass turning using performance diagrams

Maximization of productivity and minimization of cost with acceptable quality of the parts are the most important goals of the production. In machining multi-objective optimization is a real problem. For solving this problem modern optimization methods are used. In this paper is presented a multi-objective optimization of single-pass turning of stainless steel with coated carbide tool using performance diagrams.


Introduction
Optimization of cutting performances is one of the most important problems in machining processes.Multi-objective optimization provides optimal or near-optimal solution for two or more objectives in machining process.Number of researchers has studied multiobjective optimization in turning operations.Kubler F. et al. in 1 studied turning of 42CrMo4 using coated carbide cutting tool.They investigated the effect of depth of cut, feed rate and cutting speed on machining time, tool wear and process energy.For solving the multi-objective optimization problem with three objectives they applied GA based non dominated sorting algorithm-II (NSGA-II).Soni V. et al. in 2 studied turning of aluminum using carbide cutting tool.They investigated the effect of depth of cut, feed rate and cutting speed on material removal rate and surface roughness.For solving the multiobjective optimization problem with two objectives they applied Multi Objective Genetic Algorithm (MOGA).Abbas A. et al. in 3 studied turning of J-steel using uncoated carbide cutting tool.They investigated the effect of depth of cut, feed rate and cutting speed on machining time and surface roughness.For solving the multi-objective optimization problem with two objectives they applied Multi-objective Efficient Global Algorithm.Dhandapani K. et al. in 4 studied turning of AISI 4340 using uncoated carbide cutting tool.They investigated the effect of depth of cut, feed rate and cutting speed on material removal rate, flank wear and surface roughness.For solving the multi-objective optimization problem with three objectives they applied GA based non dominated sorting algorithm-II (NSGA-II).Soury E. et al. in 5 studied turning of St 37 using high speed steel cutting tool.They investigated the effect of depth of cut, feed rate, cutting speed, tool rake angle and nose radius on tool life and surface roughness.For solving the multiobjective optimization problem with two objectives they applied the optimization software program based on Visual Basic.
Corresponding author: mirado@masfak.ni.ac.rsIn this paper is presented a multi-objective optimization of single-pass turning of stainless steel with coated carbide tool.For solving the multi-objective optimization problem with two objectives (material removal rate and machining cost), three factors (tool nose radius, feed rate and cutting speed) and nonlinear constraints (surface roughness, tool life and cutting power), performance diagrams are used.

Multi-objective optimization
Procedure of solving the multi-objective optimization problem has four phases.First phase is selecting objectives, factors and constraints.Second phase is determining optimization problem.Third phase is selection of method for solution the optimization problem.Fourth phase is solution the optimization problem.First phase in multi-objective optimization is selection of objectives, factors and constraints.Two objectives, material removal rate and machining cost, and three factors, tool nose radius, feed rate and cutting speed, are selected.For nonlinear constraints, surface roughness, tool life and cutting power are used.
Tool life is performance of the cutting tool from which depends continual work.Relation between the tool life and the cutting factors is expressed with the Taylor's formula.
Where: T (min)tool life, ap (mm) -depth of cut, f (mm/rev) -feed rate, vc (m/min)cutting speed, CT, r, m and pempirical constants relevant to a specific tool-workpiece combination.
Surface roughness is performance of the workpiece which must be satisfy.Ordinarily, average surface roughness is used.
Cutting power is important in view of available machine tool power.
Material removal rate is volume of removed material in unit time.Where: MRR (cm 3 /min) -material removal rate, ap (mm) -depth of cut, f (mm/r) -feed, vc (m/min)cutting speed.
Machining cost for machining working diameter on cutting length is: Where: C (EUR)machining cost per piece, Cr (EUR)labor plus overhead cost, tn (min) nonproductive time, tm (min)machining time, T (min)tool life, td (min)tool changing time, Ca (EUR)tool cost per cutting edge.
Tool life equation for turning stainless steel with coated carbide tool is 6: Mathematical model of multi-objective optimization for this example is: For solving the optimization problem performance diagrams are used.Performance diagrams are drawn for all combinations of tool nose radius, feed rate and spindle speed, with respect to constraints of surface roughness, tool life and machine tool power.In this way 2500 different cutting conditions were obtained.In figure 1 is shown 2D diagram of material removal rate versus cutting conditions, and in figure 2 is shown 2D diagram of machining cost versus cutting conditions.Each point in 2D performance diagrams presents one particular cutting condition, i.e. combination of factor levels (r,f,n).

Fig. 2. Machining cost vs cutting conditions.
Based on the performance diagrams, the effects of factors on the objectives can be analyzed.From Figure 1 it can be seen that the point where the material removal rate has maximal value of 183 cm 3 /min corresponds to combination 1694.From Figure 2 it can see that the point where the machining cost has minimal value of 0.9088 EUR corresponds to the same combination 1694.In Figure 3 is shown the diagram of machining cost versus material removal rate.From Figure 3 it can see global optimum, i.e. the point positioned in the lower right corner, where the material removal rate has maximal value of 183 cm 3 /min and machining cost has minimal value of 0.9088 EUR.This point corresponds to combination of factor levels 1694 with data: r=2.4 mm, f=0.785 mm/rev and n=330 rpm (vc=77.715m/min).For these factor levels material removal rate is maximal MRRmax=183 cm 3 /min, machining cost is minimal Cmin=0.908EUR, machining time is tm=0.772min, tool life is T=63 min, surface roughness is Ra=8.22 m and cutting power is Pc=8.33 kW.

Conclusion
Performance diagrams were used for solving multi-objective optimization in single-pass turning of stainless steel with coated carbide tool.Cutting factors, tool nose radius, feed rate and cutting speed, were selected for maximal material removal rate and minimal machining cost.For factor levels r=2.4 mm, f=0.785 mm/rev, and n=330 rpm (vc=77.715m/min) material removal rate is maximal MRRmax=183 cm 3 /min and machining cost is minimal Cmin=0.908EUR.In this way the performance diagrams can be used as decision making tool in process planning for selection of cutting conditions.
The paper is a result of the technological project TR35034 which is supported by the Ministry of Education, Science and Technological Development of Republic of Serbia.