Machining is one of the jobs that are widespread due to a number of advantages. The goal of each company, whose activity is associated with t machining, is separation of particles adopt in optimum working conditions. In doing so it implies the largest number of production of the product in the quickest time with minimal production costs, along with the required quality of products. Many studies have been carried out in order to understand the physics of the process of processing the separation of the particles. Research has been carried out experimentally which caused a large consumption of time and money. To avoid this, computer programs based on numerical methods are used, saving time and money. An example of one of such programs is DEFORM 2D, from the company Scientific Forming Technologies Corporation. In order to make a numerical simulation in the computer program DEFORM 2D, which is contained in this graduate work, to resemble more to the actual process of the separation of particles, basic concepts have been adopted and parameters related to the area of machining, which are listed in the first two chapters of this work. In addition to the basic concepts, it is important to specify the physical processes that take place in the contact area during machining, such as: heat in the tools system – the work item, tool wear, the emergence of the cutting, friction, etc. To control the processes in the contact zone, it is necessary to notice the importance of a single change on an individual processing parameter on the output data, which is described in detail in the third chapter of the thesis. Then follows the development of the numerical simulation of orthogonal turning in DEFORM 2D. DEFORM 2D is a computer program based on the finite element method, whose features are described in the fourth chapter. The goal of making the numerical simulation of machining is to calculate the optimal conditions of processing with a minimum temperature of the cutting part of the tool. Special attention was paid to the definition of the boundary conditions of the tool and the work items. For the defined input parameters, the calculated output data are the following: the accumulation of damage, temperatures, stress and pressure that occurs in a contact zone when processing, they are described in detail in the fourth chapter of this thesis. On the basis of input and output data, the Taguchi plan experiment is defined. A total of 27 numerical simulations were carried out with different combinations of the input parameters, where it was defined what numerical simulation provides the optimal conditions of processing with regard to the observed output value. With regard to the Taguchi plan experiment, statistical analysis was carried out of the output data "the temperature of the cutting parts of the tool" by using analysis of variance. Based on the regression equation it was concluded what parameter has the biggest impact on the observed output value.