MODELING OF CUTTING TOOLS WEAR FOR LATHES

A mathematical model to estimate the average number of parts, processing which is possible to achieve the criterion of maximum allowable wear on the back of the cutter heavy lathe, and the maximum allowable amount of tool material, removed from the front surface of the tool. Experimental equipment for measuring tool wear has been developed. Insert wear curves derived from industrial test results. Confirmation of the adequacy of the models of the instrument gives a possibility of their adjustment to the basic criteria of their dullness.

The tool wear of cutting tools has a very strong impact on the product quality as well as on the efficiency of the machining processes. Despite the current high automation level in the machining industry, a few key issues prevent complete automation of the entire turning process. One of these issues is tool wear, which is usually measured off the machine tool. A well-known model for the tool wear rate was developed by Usui et al (Usui& Shirakashi, 1984), and it is based on the idea of contact mechanics and wear. The most famous tool life model is Taylor's model in which the tool life depends mainly on the cutting speed and a constant determined by materials of the tool and the workpiece, feed rate, etc. (Taylor, 1906). In the past over thirty years, much work has been contributed to the tool wear modeling [1][2][3][4][5][6].
While working on the details of heavy lathes main types of fault-alloy cutters are wearing them on the front and back surfaces, as well as fatigue damage cutting plates. Determination of maximum permissible values of wear on the back surface were carried out based on economic criteria.
For practical use have a value of mathematical models to estimate the average number of parts, which was processed to reaching the criterion of wear.
Evaluation of resistance of cutting tool criterion for maximum allowable wear on the rear surface.
Developing a model to assess the average number of parts, processing, which is possible to achieve the criterion of maximum allowable wear on the rear surface is made to the following basic assumptions: criterion of maximum allowable adhesion wear on the back of the formation of a high wear areas [ ] 1, 2 zp h = mm; 139 basic mechanism of cutting tool wear on the back of the adhesion mechanism is; average temperature of the material the instrument is fixed for the whole region back surface contact with the processed material; stress of the cutting tool is a flat; tool material in contact with the workpiece the tool is characterized by a constant value for the whole region stresses fluidity см R ; number of parts, processing which is possible to achieve the maximum allowable height of platform wear [] zp h is: where zp hincreased wear platform for processing one part. Based on studies of normal contact pressure distribution on the back of the instrument (x) q can be represented by dependence: where zp hwidth areas of physical contact in this casewear areas; xdistance from the cutting edge cutter; max. q zmaximum contact pressure at the back of the: (plus sign corresponds to negative front angles); where  tension changes in a layer that trimmed, with the average temperature at the site contact the back of the instrument with the processed material. To Determine the value used   dependence: where R ultimate strength of the material processed at an average temperature at the site of contact; To determine the average temperature dependence of cutting used by the author, obtained by statistical progressing of experimental data: acalculated ratios determined by the method of least squares.
To determine the number of the parts to achieve the criterion of maximum allowable adhesion wear on the back of the take that amount of material d , removed from the back of the instrument for the elementary time interval d physical contact with the workpiece material back of the cutter, can be estimated from geometrical considerations: where haltitude areas of wear, which corresponds to the moment of time  ; dhincrease in areas of wear during d ;  ,  , under the front corner and rear corner of the main corner in terms of the instrument; tdepth of cut. On the other hand, the volume of material removed from the rear surface during d , measured the expression: where u Pthe likelihood that the zone of adhesion failure of communication is not in the treated material, and material of the instrument; speed cutting;  thickness of which is the destruction of products bearing adhesive ties: where e Rmeaning limits yield of processed materials in accordance with the average temperature in the cutting zone; constant friction.
If the average pressure at the site of contact, the workpiece material with the rear surface instruments such that the value 1   , we adopted 1  = . Size u P can be estimated from the ratio of the critical crack lengths Hryffitsa that triggered the destruction of adhesion due: where the average temperature at the site of contact; 0 e Rthe boundary strength of the material processed at a temperature test 0 700 C = ; bestimated coefficient determined by the method of least squares.
To determine the value of eu R used dependence obtained by statistical processing of experimental data: where 0 e , 0 eintensity of deformation speed and intensity of accumulated strain during mechanical testing instrument; T Rboundary strength of the material instrument at ambient temperature; Sconstant characteristic of the tool material. If the temperature does not exceed  cutting temperature early intensive removed p  , instrumental material, it shall eu T RR = . Comparing expressions (8) and (9) and respect for value 2 dh , as the second largest order little, after the integration date was changing altitude areas of wear from time to time contact: where time of processing one part, nspeed spindle.
After substituting the values of  and u P obtained: Then the number of parts, processing of which is available until a maximum allowable height of areas on the back of the depreciation is: The main mechanism of wear of cutting tools on the front surface are adhesion mechanism.
As a criterion of maximum allowable wear of the front surface is proposed to adopt the appearance of the front surface of the hole cutter wear depth   nn h . Average number of blocks and treatment are possible until a maximum allowable depth of the hole wear, can be evaluated dependence: where   Qthe maximum allowable amount of tool material, removed from the front surface of the tool that meets   nn h ; Qvolume of tool material, removed from the front surface of the tool during the processing of one part.
Value   Q is determined from geometric considerations the following expression: where llength of the hole, bwidth of the contact front surface of cutting tools with workpiece: The volume of material Q  , which is removed by an elementary interval of time of physical contact with the chip front surface of the tool is determined by the equation d : where u Pthe likelihood that the zone of adhesion failure of communication is not in the treated material, and material tools, assessments expression (13); where qthe average pressure at the site of contact; q average pressure required to crumple the full surface microroughness processed material on this site, estimated expression (10).
Based on studies of normal contact pressure distribution on the back of the instrument ( ) qx can be represented by dependence: where k lchip contact length on the front surface: max.n q maximum normal pressure on the front surface: The average value of normal pressure on the site of contact is: The volume of material instrument removed from the front surface of the tool during the processing of one part  , is recognized by dependence: Then, taking into account (23)

Evaluation of resistance of cutting tool criterion for maximum allowable wear size.
For the finishing details stochastic equation has the form of wear: Failure occurs when the details of its size to achieve maximum permissible value max x , which happens after a random interval of tool Processed on a machine part has size, which tolerance is within the boundaries min xmax x . With increasing wear on the back of the instrument the size of parts changed. In average (Fig. 1) size of the parts is beyond the tolerance only after an interval time 4 T . But during work tool in the initial period of operation from 1 T to 2 T there is a danger for details, treated on the upper field tolerance, then the reliability of their increases. Excess of the tolerance field components finished to the lower limit of tolerance is possible at time in this case, the probability density of the coordinates x in equation (30) at the initial time 0 t = is a delta-like function, i.e.

( ) ( )
The probability that a random x coordinate at the time t reaches the limits of the interval (   On the basis of students have developed analytical calculation based cutting tool wear on the front and back surfaces of the parameters of the operation, which averages to estimate the period of stability instrument, proposed method of determining the dimensional stability of the instrument with a given probability (for finding the size of workpieces in a given field admission), which depends on tool wear during the finishing details.