A predictive simulation technique of optimal cutting modes in turning of workpieces made of nickelbased heat-resistant alloys, different from the wellknown ones, is proposed. The impact of various factors on the cutting process with the purpose of determining optimal parameters of machining in concordance with certain effectiveness criteria is analyzed in the paper. Mathematical model of optimization, algorithms and computer programmes, visual graphical forms reflecting dependences of the effectiveness criteria- productivity, net cost, and tool life on parameters of the technological process have been worked out

Afonasov, Aleksey Ivanovich

Bogoljubova (Bogolyubova), Mariya Nikitichna

Shavdurov, D. E.

Electronic archive of Tomsk Polytechnic University

XIV Международная научно-практическая конференция студентов аспирантов и молодых учёных «Молодёжь и современные информационные технологии» 359  MATHEMATICAL SIMULATION AND OPTIMIZATION OF CUTTING MODE IN TURNING OF WORKPIECES MADE OF NICKEL-BASED HEAT-RESISTANT ALLOY  Bogoljubova M. N., Afonasov A.I., Shavdurov D. E. Tomsk Polytechnic University e-mail: mabogol@mail.ruAbstract A predictive simulation technique of optimal cutting modes in turning of workpieces made of nickel-based heat-resistant alloys, different from the well-known ones, is proposed.  The impact of various factors on the cutting process with the purpose of determining optimal parameters of machining in concordance with certain effectiveness criteria is analyzed in the paper. Mathematical model of optimization, algorithms and computer programmes, visual graphical forms reflecting dependences of the effectiveness criteria– productivity, net cost, and tool life on parameters of the technological process have been worked out. 1. Introduction Up-to-date machinery production is impossible without data support of production planning and engineering. Parameters of the manufacturing process should be calculated as well as optimized in order to increase effectiveness and competitiveness. One of the ways of productivity enhancement refers to the application of intensive operating modes. Meanwhile the relevance of these operating modes should be confirmed by a physical experiment or simulation modelling.  2. Materials and methods Nickel-based heat-resistant alloys such as AISI N07263 are widely used in manufacturing of components of machines and devices operating at high temperatures approximately 700 - 950○С. The peculiarity of such alloys is concerned with their complex chemical composition, which defines a specific character of their properties and characteristics.  One of the versions of chemical composition of the alloy AISI N07263 is presented in Table 1. The alloy possesses high specific strength, corrosion resistance, low plasticity and heat conductivity, a tendency to sticking and strain that determines the increased labour intensity and specific features of its machining.  Research conducted by many authors [1, 2] has shown that cutting modes and resistance data of tools in machining of heat-resistant alloys do not always correspond to optimum values and require to examine this issue in details. Table 1. Chemical composition of the alloy AISI N07263 C Si Mn Cr Ti Al W Mo Fe P S (Al+T) % Amount of γ-phase % 0.07 0.5 0.4 14.5 2.75 1.8 6.0 3.2 1.03 0.015 0.007 4.56 22 The objective of the present research is to define the cutting mode parameters optimizing the values of certain effectiveness criteria such as productivity, net cost, and tool life at different options of initial technological parameters. The research method involves mathematical simulation and optimization of the cutting mode of heat-resistant alloy workpieces; development of computer software; use of numerical computation for solving the optimization problem in machining of workpieces made of heat-resistant alloys AISI N07263. The research method also includes experimental check of the obtained research results.   3. Development of Mathematical Model The mathematical model of the optimization has been developed including the following component:  development of the information model;  formalized presentation of input, output and internal parameters;  setting the type and the variation range of running variables;  choice and justification of optimization criteria;  mathematical descriptions of the objective function;  definition of the constraint system; The information model defines a set of initial parameters: cutting modes, the work material, tool geometry, and the processing type on the basis of which a mathematical model for solving a specific problem is constructed. Mathematical models and optimization algorithms reflect the interrelation of cutting mode parameters with such quality criteria as productivity, net cost and etc. A formalized presentation of input and output information with a visual display of the research results is carried out by means of software in Delphi environment [3]. XIV Международная научно-практическая конференция студентов аспирантов и молодых учёных «Молодёжь и современные информационные технологии» 360  Output data include: calculation data of P, T, C criteria; tables of dependences P=f(v), T= f(v),  C= f(v); characteristic curves; optimal values of parameters. Dependences of criteria P, T, C on the parameters of cutting modes are calculated according to formulas worked out by Makarov A.D. [4] and represented as follows: TstnDPсм1 , (1). Where: D – diameter of a workpiece, mm; n - speed of rotation (number of revolutions per minute), r/min; s - feed rate, mm/rev; τсh - tool change rate of a cutting tool, min; T – cutting tool life, min. Cutting tool life is determined according to the following dependence: yxvvstvkCT ,   (2). Where: v –  cutting speed, m/s;  Cv – a constant value for defining a group of the work material; kv – coefficient, depending on properties of materials being machined and a cutting tool, its geometry, wear as well as lubricating-cooling fluid; x, y – exponent quantities, depending on the tool properties and the cutting conditions.  Putting (2) into (1) and taking the change of allowance value z at constant t for a disturbance effect, we obtain the objective function: vvyxсмkCstvstnDP1 , (3). Net cost of manufacturing of a workpiece is defined in accordance with the following formula: ( ) ( ) ,ñìm ðàá ñò ðàá ñmt eA t a a a aQ Q     (4). Where: tm – operating time for machining of a workpiece (min,);  tсm – tool change time for the period of its lifetime (min);  as - salary of a machine worker per minute, (kopeck);  am - operating costs of a machine tool for a minute of its operation, (kopeck); e – operating costs of a tool during tool life, (kopeck); Q – quantity of the machined workpieces during a tool life. Q=f(v); Figure 1 shows characteristic curves reflecting the influence of cutting speed v on basic characteristics of the cutting process.    Figure 1. The influence of cutting speed v on basic characteristics of the cuttingprocess in turning of workpieces made of alloy AISI N07263 at s = 0.26 mm/rev.  XIV Международная научно-практическая конференция студентов аспирантов и молодых учёных «Молодёжь и современные информационные технологии» 361  Analysis of characteristic curves, introduced in Figure 1, demonstrates that there are extreme values – net cost minimum (C) and productivity maximum (P) in a wide range of variation of cutting speed v. In such a case, the impact of cutting speed v on these results is not uniquely defined. Cutting speed v significantly differs with regard to the extreme values - C min and P max. Consequently, it is necessary to examine a variation interval of cutting speed within the range from Vcmin to Vpmax for optimization of the cutting mode.  The mathematical models under study are represented in view of the set of multiparameter nonlinear dependences and functions. These functions are stored on a database and used for the optimization model formation and as well as the presentation in a required format. A nonlinear model for multidimensional functions, “solution of the equation with multiple unknowns”, “coordinate descent method” and heuristic algorithms are accepted to solve the problem of optimization of cutting mode parameters [5]. Allowed values of the parameters are considered as limitations. Optimization is performed owing to the variation of these parameters within the given limited ranges. The optimal solution is presented in view of the adjusted values of the parameters at which the objective function assumes extreme value Fmin (or Fmax) for the specified criterion of effectiveness.   4. Research results Calculations are performed and dependences of productivity, net cost and tool life on cutting speed v and feed rate s are determined. Optimal parameters for various cutting modes for specified effectiveness criteria are defined including restrictions to the variation range of data under research. Thus, in machining of workpieces made of heat-resistant alloy AISI N07263, the highest possible productivity will be achieved at the following parameters: cutting speed v=22.1 m/min., feed rate s=0,26 mm/rev; tool life - 18 min.; net cost - 142 roubles per hour. Cutting speed v has changed in a range of 10-40 m/min. Feed rate has changed in a range of 0,14 -0,4 mm/rev.  5. Conclusion The influence of mechanical properties of the heat-resistant alloy AISI N07263 on characteristics of turning process mode was analyzed in the present paper. For the purpose of reducing labour intensity and expensive full level test, forecasting effort was carried out by means of electronic computing machine and mathematical simulation of the cutting process with the following verification in a view of the experiment in laboratory and working conditions.  We have developed the graphical interface of computational modeling for the optimization of parameters of the cutting process in turning, which allows to predict the cutting modes in accordance with the given optimization criteria on basis of the particular range of initial parameters. The current model can be applied for the other processing types: milling, drilling and etc. with some amendments and modifications determined by the characteristics of the processing type.   With reference to the present research, the guidelines for optimizing the cutting process of heat-resistant alloys AISI N07263 taking into consideration the restrictions imposed on the parameters of cutting systems in conformity with the appropriate effectiveness criteria have been worked out.  References  1. Vereshhaka A.S., Anikeev A.I., Dacheva A.V. Increasing of the effectiveness of cutting difficult-to-machining materials. // Mechanical engineering technology. 2010. № 3. pp. 17-22. 2. Afonasov A.I., Lasukov A.A. Elementary Chip in Metal Cutting.//Vestnik Mashinostrjeniya. 2013. № 12. pp. 69-72. 3. Information on Embarcadero Delphi XE2 Lite-http://www.embarcadero.com/ 4. Makarov A.D. Optimization of cutting processes DJVU. Moscow: Mechanical engineering, 2011, 278 p. 5. Bogoljubova M. N., Sumtsova O. V., Doschinsky D. V. Development of Graphical Interface for Determination of Optimal Cutting Parameters in Turning Operations // Key Engineering Materials : Scientific Journal. — 2016. — Vol. 685: High Technology: Research and Applications 2015 (HTRA 2015). — [P. 948-951].                             

Mathematical simulation and optimization of cutting mode in turning of workpieces made of nickel-based heat-resistant alloy

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