# Fuzzy sets with using full factorial experiment for production optimization.

 Author: Hron, Jan

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1 INTRODUCTION

At present, when machining there are, besides technological considerations, also economic analyses and calculations as an integral part of technical preparation. An economic side of the production process then represents a key aspect in conditions of prevailing difussion competition. Difussion competition is characterized by equal distribution of inner energetic and tangible sources with all competitors of a given industry with the same availability of external sources. It means that no competitor has better access to any of the sources. Under this situation, there is the only one source of competitive advantage more efficient use of technological potential which is at the disposal of a particular company. In effect, this efficiency is carried out through lowering the consumption of material, work, production time and energy in order that production costs are minimalized. This cost minimalization of variable production costs makes the background for the creation of a sufficiently high profit spread, not only for creating reserves of necessary financial sources for the recovery of the production device, but also for creating a means by which we will finance the development and innovation of contemporary technological progress. Nevertheless, it is possible to start from conventional cost itemization when machining, i. e. from the minimalization of partial costs which are as follows:

--Unit (average) costs for machine work (related to one workpiece),

--Unit costs for extra work,

--Unit costs for the exchange / adjustment of a worn-out tool,

--Unit material costs.

The biggest cost item is represented according to [2], [4] by costs for machine work [N.sub.SP], The calculation is based on time costs for machine work [n.sub.t] (for instance in CZK/minute) and from the costs related to one cutting blade life [n.sub.b] (for instance in CZK).:

[N.sub.SP] = [t.sub.A] x [n.sub.t] + z x [n.sub.b] (1)

Where cutting blade life [T.sub.b] is possible to be determined for instance by Tailor relation which expresses this cutting blade life in the dependence on cutting speed [v.sub.c] :

[T.sub.b] = [C.sub.T]/[v.sub.c.sub.m] (2)

Where [c.sub.T], m are constants which are determined experimentally/empirically and are dependent (with certain depth of the cut and feed) on the character of a machined material (especially on its machinability).

The choice of a machine from the point of view of a produced batch size belongs to other conventional procedures contributing to reaching a sufficiently high profit spread during the production. It usually includes a decision-making process which from two and more processing equipments (usually having at disposal various degree of automation) decides the cheapest use in the production. When taking into consideration the batch produced in order to determine the costs, we start from so called marginal batch [d.sub.K]. The marginal batch determines the critical amount of workpieces in a batch, when the total costs [CN.sub.1] for the batch production, with the usage of the first machine equal the total costs for the batch production of the second machine [CN.sub.2]. If the total costs for the production of the batch CN contain q amount of workpieces, we determine the total costs as the sum of variable v and fixed costs FN:

CN - v x q + FN (3)

Then it is possible for the critical amount of workpieces in the produced batch to be determined according to the relation:

[q.sub.KR] = [[FN.sub.2] - [FN.sub.1]]/[[v.sub.1] - [v.sub.2]] (4)

At the same time, fixed costs represent the sum of costs for machine adjustment, machine depreciation (purchasing), costs for managing programme creation, etc. The average variable costs represent the costs for machine work, costs for exchange, and tool adjustment, etc. related to one workpiece. This critical amount of workpieces in a batch then determines from what amount of items it is economically advantageous to substitute a certain machine by the machine with a higher degree of automation (for instance a universal lathe by a turret type semi-automatic lathe, or a turret type semiautomatic lathe by an automatic lathe).

When optimizing cutting conditions, it is possible to use the so-called gradual method, when first of all, according to [2] we determine the cutting depth. When finish machining, the cutting depth [a.sub.p] is equal to the size of the whole machining allowance. Roughing allowance is determined by the size of the whole allowance decreased by finish machining allowances and by allowances for other finishing operations. Then it is possible for chosen [a.sub.p] to determine the optimum size of the feed f from lifting conditions, which are not the function of the cutting speed. One of the limiting conditions can be according to [1], [4] for instance, maximum allowable intensity of tangential force [F.sub.Zmax], which has the form:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

Where [c.sub.Fz], [x.sub.Fz], [y.sub.Fz] are empirical constants. For optimum values T, [a.sub.p], f the optimum cutting speed v is determined from the complex Taylor relation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

Where again [c.sub.v], [h.sub.Xv], [s.sup.Yv], m are empirically determined constants. In the last step, it is necessary to verify that the performance of processing equipment enables the use of optimum cutting conditions.

In the second case, when optimizing cutting conditions, production standards of cutting conditions are ordinarily used. Production standards (they represent tabular processing of the relation (6), start from the tool cutting life. Both mentioned ways prefer the economic nature of a machining process, and surface roughness Ra represents a limiting condition (such as feed size, optimum cutting depth, component of cutting force Fy and cutting speed).

At present, besides the economic nature of a production process, it is necessary to take into consideration resultant characteristics of a product (a workpiece forming part of a resultant product). At the same time, nowadays, there are heavy demands placed on the product in the field of reliability, service life and the efficiency of final assembly. The surface quality is considered to be a decisive factor in achieving the above mentioned characteristics. For instance, one of the main components of the surface quality--its roughness (surface microgeometry) is, according to [8], responsible for the accuracy of a particular mechanism running, size, operational wear, notch impact strength/notch toughness, lubricating conditions, corrosion resistance, noisiness, time of running in, electrical resistance and transfer of heat. From the point of view of constructional demands, surface roughness represents an important condition of the exchangeability of components in mass production [2]. At the same time, a reached value of roughness and its character is the function of a chosen machining procedure, cutting conditions, the state of the tool and workpiece material, tool geometry, effectiveness of heat removal by cooling, toughness of systems: machine--jig or workpiece--tool, etc. During the process of machined component surface creation, the literature [4] recognizes the theoretical and real surface unevenness. The theoretical deviation of the surface is determined in case of the...