Математическая модель рациональных режимов резания токарной обработки в mathcad

Abstract

В статье выполнен анализ существующих рекомендаций по выбору режимов резания для токарной обработки, разработана математическая модель для определения рациональных условий обработки на основе решения линейных целевой функции и ограничений-неравенств. В качестве целевой функции выбран показатель производительности, а в качестве ограничений-неравенств - ограничения, связанные c функциональными параметрами и параметрами, определяющими качество обработки.

Determination of optimal cutting conditions is one of the most important technical and economic tasks of modern machine building, since the correctness of their choice depends on the cost, productivity and accuracy of processing, the quality of the surface layer and the operational properties of individual parts and machines in general. In the current conditions of fierce competition, the enterprise, regardless of the form of ownership, must constantly reduce production costs. For example, the use of modern cutting tools will bring additional profit, only with the use of optimal cutting modes, and reducing the computer time by reducing the main and auxiliary time will lead to a decrease in the consumption of expensive electricity. It should be noted that the solution of the problem of envy from the choice of the objective function and the technical limitations of the controlled parameters. The parametric optimization of blade machining has recently received a lot of attention. So in [1-9] the optimization mathematical models are presented, which are constructed on the basis of simplified functional dependencies and do not take into account all the necessary restrictions, and as a consequence, do not always correspond to the conditions of accuracy and adequacy. The authors of [10-13] considered the processing mode, which ensures the lowest cost of processing, provided all requirements for the quality of the product and the given productivity of the machine are satisfied, with a constant value of tool life. Analysis of literature sources showed that it is difficult to find analytical formulas reflecting the interdependence of all factors affecting the cutting process. The article analyzes the existing recommendations on the choice of cutting modes for turning, a mathematical model is developed to determine the rational processing conditions based on the solution of linear objective function and inequality constraints. The performance indicator is chosen as the objective function, and as constraints-inequalities - the restrictions associated with the functional parameters and parameters that determine the quality of processing. Using the mathematical calculation algorithm developed in the MathCAD, theoretical studies of the dependence of the main parameters of the cutting regimes n, s of the shaft turning from steel 40X, the length of the machined surface is 300 mm, on the lathe 16K20, by cutting tools made of a hard alloy T15K6 with coolant cooling . The radius at the tip of the tool is r = 1 mm.