MACHINABILITY OF MATERIALS AND THEIR MATHEMATICAL MODELS FROM AN ECONOMIC POINT OF VIEW OF MATERIALS AND THEIR MATHEMATICAL MODELS

: This article is about the economics aspects on optimization of components production are nowadays very current issue. Article is about the criteria of economic efficiency of production of mechanical components for machine tools and CNC machines. The machinability of materials is considered to be a parameter which characterizes the machined material in the process of cutting and expresses the degree of machining effectivity in terms of material of a product and is expressed by mathematical model .


Introduction
Cutting speed when considering certain cutting edge durability, surface roughness, degree of splinter deformation and resultant splinter shape and its proportions are utilitised as evaluation of machinability indexes. Confrontation with the reference material enables to determine the rated machinability as one of the basic characteristics of machined material used when cutting conditions are optimized. The simple solution is not to divide general expenses into two parts i.e. joint expenses of a department and costs of a workplace but leave it as the average value of hourly overhead lump sum designed on the basis of share of total of all overhead costs within a department and total department capacity. It is a simple solution that can be appropriate as the first stage of transition from a calculation through an extra charge to a calculation with the usage of the hourly overhead lump sum method. By this simplification the influence of individual factors is covered and their impact is not clear in the total calculation.

Optimal Serviceability of a Machine from The Point of Production Costs
Essential matters for the working process optimization are a solid analysis of on what the value of expense units depends. It is determining just because the information enables to manage the working process effectively. [155] First of all, we are going to define the terms "decision" and "strategy". Under the term "decision" we are going to understand the determination of values of input parameters in the given stage of controlled process. Under the term "strategy of decision" we are going to understand the sequence of the step-by-step decisions. Strategy which satisfies the conditions of the preset defined criterion of optimization will be defined as the optimal strategy. [4] It is possible to present the relation for optimal durability as Where: Determination of optimal serviceability does not depend on cutting conditions, but leads to simplification of cutting conditions optimization. After that, it relates usage of gradual way of optimal cutting conditions setting. The procedure does not lead to optimal values.
Optimization of cutting conditions is always realized according to a optimization criterion within a restriction (restrictive conditions given by production conditions).
Working process is always limited by a certain group of restrictive conditions. It is possible to formulate these conditions mathematically as in equations. The exception is the complex Taylor´s relation that is an equation.
Using more expensive production installation the costs raise more rapidly. They reach minimum at higher cutting speed than when utilizing usual machines. Disobedience to this relation leads to sharp rise of production costs when machining using the CNC machines. The basic cost development scheme is in the figure 2.
In market mechanism it is required to produce a product in such economic conditions so that its sale price be acceptable and attractive. To start thinking about a production process it is necessary to get an idea about its cost structure.

Mathematical Formulation of Production Costs
We attempt to describe the criteria for minimum production costs. We shall consider only the costs items that are dependent on cutting conditions. Consequently, total costs may be given by the relation [8,9]: Where: Optimization of cutting conditions is convenient to realize by a complex calculation whose outputs are optimal values of cutting conditions and durability of a cutting wedge. According to complexity it is necessary to use a computer with appropriate software.
Restrictive conditions are given by a working machine (its performance, cut-off twisting moment of retentive unit, cut-off size of cutting power elements, range of twists and offsets), a device (cutting material, geometry, surface roughness), material of a work-piece, cutting environment, requested qualitative parameters. [7,8,9] For complex optimization calculation of cutting conditions mostly linear parametric programming was used. The mathematical apparatus comes out of linear or linearized restricting conditions. In connection with the development of production technology the utilization of non-linearized restricting conditions arose. It related for example continuous, non-linearized restricting conditions from the point of twisting moment (twist of a work-piece in a chucking device) and a bending moment (extraction of a work-piece one-sidely attached in a chucking device) by machines with high rotational frequency.
Apart from the continuous non-linearized restricting conditions more and more non-continuous restricting conditions occur. Before all, it relates different characteristic of working machines performance. Mathematical methods of cutting conditions optimization with these restricting conditions lead to interval optimization tasks.
For example, two restricting non-linearized conditions are mentioned.
For linear process of performance characteristic for performance holds the following line-equation: Where: 1 k and q are constants.
For the process of performance it is possible to derive for example for turning operation a restricting condition as follows: At chucking devices at high rotational frequency under influence of centrifugal force opening of jaws and lowering of chucking power occurs. Even if the chucking devices are constructed specially to restrict the occurrence, at these devices it is possible to come out of the assumption that the decrease of chucking power is given by centrifugal power on jaws, at one jaw it is possible to think about dependence of chucking power Fu on rotational frequency n as follows: The n k constant can be drawn from the details of a manufacturer as the decrease of chucking power at maximum rotational frequency of a spindle. From the point of maximum acceptable rotational moment for 3-jaw chucking device is applicable: Where: It is clear that for general optimization of cutting conditions it is important to use different mathematical apparatus from linear programming or linear parametric programming. It mainly relates the analytic methods implicit in the analysis of possible solutions; the gradient method, geometric modeling or it is also possible to use suitable optimizing software.
It is important to emphasize on the fact that concrete data that relate given company must be brought into the optimizing software as results from preceding analysis. The results of optimizing procedures at production of the same component in various companies lead to different values of cutting conditions and to different production costs. [3,4,9] The important part from the point of reliability of working process presents it monitoring. The table no. 1. introduces main subjects of eventual monitoring.

Conclusion
Win present, with regard to stochastics of cutting process it is possible to deal with optimization with the output of machine serviceability with confidence interval. The input then does not have to be the Taylor´s complex relation but the table of combinations: serviceability, cutting speed, displacement, depth of cut. [11] From the point of optimization of machine serviceability and cutting conditions, the most important part is machine monitoring. It means the monitoring of serviceability that has certain dispersion for concrete working conditions. Afterwards, the optimization performs for center of dispersion and exchange of individual machines is determined by the monitoring device. In the case of working without work-monitoring of a cutting machine the constant v c is determined with high level of security. Next, it is possible to monitor total deterioration of a machine or of parts of a cutting edge as well. Monitoring of cutting process is realized by appropriate sensors whose outputs are processed using appropriate logic.