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Int J Adv Manuf Technol (2001) 17:4714762001 Springer-Verlag London LimitedComparative Analysis of Conventional and Non-ConventionalOptimisation Techniques for CNC Turning ProcessR. Saravanan1, P. Asokan2and M. Sachithanandam21Department of Mechanical Engineering, Shanmugha College of Engineering, Thanjavur, India; and2Department of ProductionEngineering and Management Studies, Regional Engineering College, Tirchirapalli, IndiaThis paper describes various optimisation procedures forsolving the CNC turning problem to find the optimum operatingparameters such as cutting speed and feedrate. Total pro-duction time is considered as the objective function, subject toconstraints such as cutting force, power, toolchip interfacetemperature and surface roughness of the product. Conven-tional optimisation techniques such as the Nelder Meadsimplex method and the boundary search procedure, andnon-conventional techniques such as genetic algorithms andsimulated annealing are employed in this work. An example isgiven to illustrate the working procedures for determining theoptimum operating parameters. Results are compared and theirperformances are analysed.Keywords: Boundary search procedure; Genetic algorithm;Nelder Mead simplex method; Optimisation; Simulatedannealing1. IntroductionOptimisation of operating parameters is an important step inmachining optimisation, particularly for operating CNCmachine tools. With the general use of sophisticated and high-cost CNC machines coupled with higher labour costs, optimumoperating parameters are desirable for producing the parteconomically. Although there are handbooks that provide rec-ommended cutting conditions, they do not consider the econ-omic aspect of machining and also are not suitable for CNCmachining. The operating parameters in this context are cuttingspeed, feedrate, depth of cut, etc., that do not violate any ofthe constraints that may apply to the process and satisfyobjective criteria such as minimum machining time or minimummachining cost or the combined objective function of machin-ing time and cost.Correspondence and offprint requests to: R. Saravanan, Departmentof Mechanical Engineering, Shanmugha College of Engineering, Than-javur 613402, Tamilnadu, India. E-mail: saradharaniKMachining optimisation problems have been investigated bymany researchers. Gilbert 18 presented a theoretical analysisof optimisation of the process by using two criteria: maximumproduction rate and minimum machining cost. Since the resultsobtained by using these two different criteria are always differ-ent, a maximum profit rate, which yields a compromise resulthas been used in subsequent investigations. These early studieswere, however, limited to single-pass operations without con-sideration of any constraints. Subsequent studies included vari-ous operating constraints in the optimisation models and severaltechniques have been tried for optimisation 17. In order toaccount for the stochastic nature of tool use, various probabilis-tic approaches have also been proposed. Since multipass oper-ation is often preferred to single-pass operation for economicreasons, efforts have been made to determine optimal machin-ing conditions for multipass operations 2,8,9.So far, machining optimisation problems have been investi-gated by many researchers using conventional techniques suchas geometric programming 3,4, convex programming 10,and the Nelder Mead simplex search method 1,2. Ruy Mes-quita et al. 7 have also used a conventional technique (directsearch method combination of Hook and Jeeves and randomsearch) for optimisation of multipass turning. A mathematicalmodel proposed by S. J. Chen was used in this work. It isobserved that the conventional methods are not robust because:1. The convergence to an optimal solution depends on thechosen initial solution.2. Most algorithms tend to become stuck on a suboptimal sol-ution.3. An algorithm efficient in solving one machining optimisationproblem may not be efficient in solving a different machin-ing optimisation problem.4. Computational difficulties in solving multivariable problems(more than four variables).5. Algorithms are not efficient in handling multiobjective func-tions.6. Algorithms cannot be used on a parallel machine.To overcome the above problems, non-conventional tech-niques are used in this work for solving the optimisation of472 R. Saravanan et al.the turning process. In earlier work, a standard optimisationprocedure using a genetic algorithm 11 was developed tosolve different machining optimisation problems such as turn-ing, face milling and surface grinding 12. In this work,in addition to a GA, the simulated annealing technique hasbeen tried.In this work, the mathematical model proposed by Agapiou1,2 is adopted for finding the optimum operating parametersfor CNC turning operations. Total production time is consideredas the objective function, subject to constraints such as cuttingforce, power, toolchip interface temperature, and surfaceroughness of the product. Conventional optimisation techniquessuch as the Nelder Mead simplex method and the boundarysearch procedure, and non-conventional techniques such asgenetic algorithms and simulated annealing are used in thiswork. An example is given to illustrate how these proceduresare used to determine the optimum operating parameters.Results are compared and their performances are analysed.2. The Optimisation Problem 12.1 Objective FunctionThe total time required to machine a part is the sum of thetimes necessary for machining, tool changing, tool quick return,and workpiece handling:Tu= tm+ tcs(tm/T)+tR+ thThe cutting time per pass (tm) = PDL/1000 V f. Taylors toollife equation is:Vfa1doca2Ta3= KThis Eq. is valid over a region of speed and feed for whichthe tool life (T) is obtained.2.2 Operating Parameters2.2.1 FeedrateThe maximum allowable feed has a pronounced effect on boththe optimum spindle speed and production rate. Feed changeshave a more significant impact on tool life than depth of cutchanges. The system energy requirement reduces with feed,since the optimum speed becomes lower. Therefore, the largestpossible feed consistent with the allowable machine power andsurface finish is desirable, in order for a machine to be fullyused. It is often possible to obtain much higher metal removalrates without reducing tool life by increasing the feed anddecreasing the speed. In general, the maximum feed in aroughing operation is limited by the force that the cutting tool,machine tool, workpiece and fixture are able to withstand. Themaximum feed in a finish operation is limited by the surfacefinish requirement and can often be predicted to a certaindegree, based on the surface finish and tool nose radius.2.2.2 Cutting SpeedCutting speed has a greater effect on tool life than either depthof cut (or) feed. When compared with depth of cut and feed,the cutting speed has only a secondary effect on chip breaking,when it varies in the conventional speed range. There arecertain combinations of speed, feed, and depth of cut whichare preferred for easy chip removal which are mainly dependenton the type of tool and workpiece material. Charts providingthe feasible region for chip breaking as a function of feedversus depth of cut are sometimes available from the toolmanufacturers for a specific insert (or) tool, and can be incor-porated in the optimisation systems.2.3 Constraints1. Maximum and minimum permissible feed rates, cuttingspeed, and depth of cut:fmin# f # fmaxVmin# V # Vmaxdocmin# doc # docmax2. Power limitation:0.0373 V0.91f0.78doc0.75# Pmax3. Surface roughness limitations especially for finish pass:14 785 V- 1.52f1.004doc0.25# Ramax4. Temperature constraint:74.96 V0.4f0.2doc0.105#umax5. Cutting force constraint:844 V- 0.1013f0.725doc0.75# Fmax3. Conventional Optimisation Techniques3.1 Boundary Search Procedure (BSP)To start with, the depth of cut (doc) is fixed and the feedrate(f) is assumed to be at the maximum allowable limit. Thevalues of “doc” and “f” are substituted in power and tempera-ture constraint equations and the corresponding cutting speeds(Vpand Vt) are calculated. Further the obtained values “f” and“V” are accepted or modified according to constraint violationand objective function minimisation using the bounding phaseand interval halving method the flowchart of which is givenin Fig. 1.3.2 Nelder Mead Simplex Method (NMS) 13In this method, three points are used in the initial simplex. Ateach iteration, the worst point (Xh) in the simplex is found. Atfirst, the centroid (Xo) of all but the worst point is determined.Thereafter, the worst point in the simplex is reflected aboutthe centroid and the new point (Xr) is found. If the constraintsare not violated at this point the reflection is considered tohave taken the simplex to a good region in the search space.Thus, an expansion (Xe) along the direction from the centroidto the reflected point is performed. On the other hand, if theconstraints are violated at the reflected point, a contraction(Xcont) in the direction from the centroid is made. The procedureConventional and Non-Conventional Optimisation Techniques 473Fig. 1. Flowchart of “boundary search procedure”.Table 1. By boundary search procedure.Number doc Vf TU1 2.0 119.77 0.762 2.842 2.5 112.95 0.762 2.933 3.0 114.02 0.680 3.114 3.5 118.28 0.582 3.345 4.0 122.13 0.509 3.596 4.5 124.45 0.452 3.847 5.0 125.10 0.406 4.10is repeated until the termination criteria are met. The followingequations are used in the method:Xo= (Xl+ Xg)/2Xr= 2Xo- XhXe= (1 + g) Xo- g XhXcont= (1 + b) Xo- b XhTable 2. By Nelder Mead simplex method.Number doc Vf TU1 2.0 118.32 0.750 2.872 2.5 113.13 0.738 2.973 3.0 108.67 0.660 3.154 3.5 117.50 0.546 3.445 4.0 126.25 0.473 3.696 4.5 125.42 0.463 3.847 5.0 126.35 0.420 4.10Where, g = expansion coefficient (2.0); b = contraction coef-ficient (0.5).The flowchart is given in Fig. 2.4. Non-Conventional OptimisationTechniques4.1 Genetic Algorithms (GA) 1417GAs form a class of adaptive heuristics based on principlesderived from the dynamics of natural population genetics. Thesearching process simulates the natural evaluation of biologicalcreatures and turns out to be an intelligent exploitation of arandom search. A candidate solution (chromosomes) is rep-resented by an appropriate sequence of numbers. In manyapplications the chromosome is simply a binary string of 0and 1. The quality is the fitness function which evaluates achromosome with respect to the objective function of theoptimisation problem. A selected population of solution(chromosome) initially evolves by employing mechanismsmodelled after those currently believed to apply in genetics.Generally, the GA mechanism consists of three fundamentaloperations: reproduction, crossover and mutation. Reproductionis the random selection of copies of solutions from the popu-lation according to their fitness value, to create one or moreoffspring. Crossover defines how the selected chromosomes(parents) are recombined to create new structures (offspring)for possible inclusion in the population. Mutation is a randommodification of a randomly selected chromosome. Its functionis to guarantee the possibility of exploring the space of sol-utions for any initial population and to permit the escape froma zone of local minimum. Generally, the decision of thepossible inclusion of crossover/mutation offspring is governedby an appropriate filtering system. Both crossover and mutationoccur at every cycle, according to an assigned probability. Theaim of the three operations is to produce a sequence ofpopulations that, on average, tends to improve.4.1.1 The Optimisation Procedure Using GAStep 1. Choose a coding to represent problem parameters, aselection operator, a crossover operator and a mutation operator.Choose a population size n, crossover probability pc, andmutation probability pm. Initialise a random population ofstrings of size l. Choose a maximum allowable generationnumber tmax. Set t = 0.474 R. Saravanan et al.Fig. 2. Flowchart of “Nelder Mead simplex method”.Step 2. Evaluate each string in the population.Step 3.Ift . tmax(or) other termination criteria is satisfied,terminate.Step 4. Perform reproduction on the population.Step 5. Perform crossover on random pairs of strings.Step 6. Perform bitwise mutation.Step 7. Evaluate strings in the new population. Set t = t+1and go to step 3.End4.1.2 GA ParametersSample size = 20Crossover probability = 0.8Mutation probability = 0.05Number of generations = 1004.2 Simulated Annealing (SA) 16The simulated annealing procedure simulates the annealingprocess to achieve the minimum function value in a minimis-ation problem. The slow cooling phenomenon of the annealingprocess is simulated by controlling a temperature-like parameterintroduced using the concept of the Boltzmann probabilitydistribution. According to the Boltzmann probability distri-bution, a system at thermal equilibrium at a temperature T hasits energy distributed probabilistically according to P(E) =exponent of (- DE/kT), where k is the Boltzmann constant. Thisexpression suggests that a system at a high temperature hasan almost uniform probability of being at any energy state,but at a low temperature it has a small probability of beingat a high energy state. Therefore, by controlling the temperatureT and assuming that the search process follows the Boltzmannprobability distribution, the convergence of an algorithm canbe controlled.Conventional and Non-Conventional Optimisation Techniques 475Table 3. By genetic algorithm.Number doc Vf TU1 2.0 118.91 0.764 2.852 2.5 114.15 0.644 3.123 3.0 114.49 0.665 3.134 3.5 120.61 0.531 3.465 4.0 106.16 0.565 3.516 4.5 104.80 0.454 3.967 5.0 110.58 0.435 4.14Table 4. By simulated annealing.Number doc Vf TU1 2.0 120.39 0.753 2.852 2.5 112.57 0.761 2.933 3.0 116.68 0.648 3.154 3.5 118.21 0.582 3.345 4.0 122.05 0.507 3.596 4.5 125.41 0.448 3.857 5.0 126.28 0.400 4.12The above procedure can be used in the function minimis-ation of the total production time in the CNC turning optimis-ation problem. The algorithm begins with an initial point x1(V1, f1) and a high temperature T. A second point x2(V2, f2)is created at random in the vicinity of the initial point and thedifference in the function values (DE) at these two points iscalculated. If the second point has a smaller function value,the point is accepted; otherwise the point is accepted with aprobability exp (- DE/T). This completes one iteration of thesimulated annealing procedure. In the next generation, anotherpoint is created at random in the neighbourhood of the currentpoint and the Metropolis algorithm is used to accept or rejectthe point. In order to simulate the thermal equilibrium at everytemperature, a number of points are usually tested at a parti-cular temperature, before reducing the temperature. The algor-ithm is terminated when a sufficiently small temperature isobtained or a small enough change in function values is found.4.2.1 The Optimisation Procedure Using SAStep 1. Choose an initial point x1(V1, f1), a terminationcriteria e.Table 5. The total production time obtained from different techniques and percentage deviation of time with reference to BSP methods.NMS GA SABSPNumber doc TUTU% dev TU% dev TU% dev1 2.0 2.84 2.87 +1.0 2.85 +0.4 2.85 +0.42 2.5 2.93 2.97 +1.0 3.12 +1.0 2.93 03 3.0 3.11 3.15 +1.0 3.13 +1.0 3.15 +1.04 3.5 3.34 3.44 +3.0 3.46 +3.0 3.34 05 4.0 3.59 3.69 +3.0 3.51 +3.0 3.59 06 4.5 3.84 3.88 +1.0 3.96 +1.0 3.85 +0.37 5.0 4.10 4.23 +3.0 4.14 +3.0 4.12 +0.5Set T a sufficiently high value, number of iterations to beperformed at a particular temperature n, and set t = 0.Step 2. Calculate a neighbouring point x2. Usually, a randompoint in the neighbourhood is created.Step 3.IfDE = E(x2) - E(x1) , 0, set t = t +1;Else create a random number r in the range (0,1). Ifr # exp (- DE/T) set t = t+1;Else go to step 2.Step 4. If ux2- x1u ,eand T is small, terminate.Else if (t mod n) = 0 then lower T according to acooling schedule.Goto step 2;Else goto step 2.5. Data of the Problem 1L = 203 mm D = 152 mm Vmin= 30 m min- 1Vmax= 200 m min- 1fmin= 0.254 mm rev- 1fmax= 0.762 mm rev- 1Ramax(rough) = 50 mm Ramax(finish) = 20 mm Pmax= 5kWFmax= 900 N umax= 500 Cdocmin(r)= 2.0 mmdocmax(r)= 5.0 mm docmin(f)= 0.6 mm docmax(f)= 1.5 mma1 = 0.29 a2 = 0.35 a3 = 0.25K = 193.3 tcs= 0.5 min/edge tR= 0.13 min/passth= 1.5 min/piece Co= Rs3.50/min Ct= Rs17.50/edge6. Optimisation ResultsTables 1 to 4 show the operating parameters such as cuttingspeed, feed rate and total production time obtained usingconventional and non-conventional techniques.Table 5 shows the total production time obtained fromdifferent techniques and percentage deviation of time withreference to BSP method.7. ConclusionIn this work, optimisation of the CNC turning process issolved using conventional and non-conventional optimisationtechniques. An example is given to illustrate the workingprocedures of these techniques in solving the above problem.It is observed that a boundary search procedure is able to findthe exact answer, but it is not flexible enough to include more476 R. Saravanan et al.variables and equations. The results obtained by simulatedannealing are comparable with the boundary search procedureand the flexibility of the method needs further investigation.The Nelder Mead simplex method deviates from the boundarysearch method by 1%3%, but with simple modification it canbe extended to other machining problems by including onemore variable. The genetic Algorithm method also deviatesfrom boundary search method by 1%3%, but by adopting asuitable coding system, this can be used to solve any type ofmachining optimisation problem such as milling, cylindricalgrinding, surface grinding, etc., by including any number ofvariables.References1. J. S. Agapiou, “The optimization of machining operations basedon a combined criterion, Part 1: The use of co