Projecting Parameters of a Microprofile for a Surface

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ScienceDirect Procedia Engineering 150 (2016) 1013 – 1019

International Conference on Industrial Engineering, ICIE 2016

Projecting Parameters of a Microprofile for a Surface Obtained as a Result of the Thermofrictional Treatment N. Pokintelitsa*, E. Levchenko Polytechnic Institute, Sevastopol State University,33, Universitetskaya St., Sevastopol, 299053, Russia

Abstract The article presents the results of the studies that allow determining the mechanism of forming macro and micro relief of surfaces taking place at termo frictional treatment of parts and ensuring the acquisition of a given accuracy and quality of treatment. It is established that thermo frictional treatment is characterized by complex temperature-deformation processes in the contact zone of the tool and part that are associated with the formation of treatment zones with heating and melting the material. We present complex methods of surface treatment that implement features of thermo frictional and mechanical treatment processes using machine tools by combining preliminary treatment of parts by a disk tool, which has a circular cutting edge and subsequent milling, or grinding and finishing bilateral operations. Thus, after processing we obtain a wavy surface with a random profile, which has a system of parallel grooves and ridges oriented perpendicular to the feeding direction. Parameters of waviness depend on the dynamic characteristics of the machine tool, on the cutting process, and on the use of additional devices. The developed mathematical model of a microprofile allows for determination of the shape and nature of the surface, obtained as a result of complex processing. ©2016 2016The TheAuthors. Authors. Published by Elsevier © Published by Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the organizing committee of ICIE 2016. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICIE 2016 Keywords: thermo frictional processing; disk, cutting edge; microprofile; correlation function; mean

* Corresponding author. Tel.: +7-978-767-9653. E-mail address: [email protected]

1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICIE 2016

doi:10.1016/j.proeng.2016.07.155

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1. Introduction Industrial use of the method of thermos frictional treatment (TFT) of components allows for obtaining surfaces with selected quality indicators. Therefore, studies aimed at improving the process of TFT, are relevant. TFT of parts leads to the formation of a wavy surface, so the problem in general is to study the causes and consequences of the formation of waviness and its connection to the parameters of the machine system. The problem is also associated with important scientific and practical tasks of the development of progressive technological processes of treating parts on the CNC metal-processing equipment. In recent literature we can see a significant amount of research results on the process of parts’ TFT. The optimum cutting conditions and recommended materials are determined, treatment of which allows for significant decrease in the intensity of setting and built-up edge processes [1, 3, 7-9]. A number of publications are devoted to the study of the characteristics of work processes [4, 5, 12]. In some works they consider the temperature field in the cutting area [10, 11, 19, 21]. A number of materials are dedicated to the development of tools providing advanced treatment methods [2, 13]. We haven’t discovered any works providing results of studies that determine the mechanism of formation of micro- and macro-relief of surfaces that occur during parts TFT and are prerequisites for obtaining a given accuracy and processing quality. The purpose of this article is to determine the mechanism of formation of quality indicators in TFT that will predict the degree of deviation of the actual shape of the processed products from its nominal value, and establish a deterministic and random errors of geometrical parameters of obtained surfaces. The researched complex methods of surface treatment that implement features of termo friction and machining processes, include a preliminary rough TFT of parts by the disk tool, which has a circular cutting edge and subsequent milling, or grinding and finishing bilateral operations. Thus, after processing we obtain a wavy surface with a random profile, which has a system of parallel grooves and ridges oriented perpendicularly to the feeding direction. Parameters of waviness depend on the dynamic characteristics of the machine tool, the cutting process and additional devices that are used. A substantial difference of the method of complex processing is heating the zone by frictional forces, which contributes, along with the design features of the tool used, to the concentration of heat in a small volume of metal, which is then removed from the surface of the part. The processes of complex treatment have a complex stochastic nature, which leads to the spread of product quality indicators and does not allow for the use of all possibilities of the method. Ensuring the quality and efficiency of complex machining operations is only possible based on the development of dynamic models that determine parameters of stochastic processes. The totality of these problems is the unresolved issue to date. 2. Main text TFT is characterized by complex temperature-deformation processes in the contact zone of the tool and the part. At the first step of the process, formation of the treatment zone with heating and melting of the material take place. Treatment processes at this stage are transient in nature. The second stage is characterized by well-established thermodynamic phenomena that are associated with the vibrating processes in the technological system. A stable layer of molten metal, corresponding to the thickness of the shear layer from which a flat drain shaving is formed, is formed between the tool and the part. During the third stage non-stationary processes take place and we observe the increase in the vibration of the machine table [17, 18]. During the TFT machining operation, formation of a wavy surface, caused by the relative vibrating movement between tool and part, takes place. These movements cause pulsating flow of molten metal. The mechanism of formation of the wavy surface is grounded theoretically and confirmed experimentally. The resulting waviness of the microprofile is the result of periodic changes in the thickness of the metal layer due to mutual relative vibrations between the tool and the part (Fig. 1, a). Complete machining of the obtained wavy surface is performed on vertical milling machines, and includes: a grinding operation, in particular, of the edges of flat pads, polishing, and finishing operations (Fig. 1, b).

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Next operation after milling - finishing grinding operation - is carried out taking into account the direction of the grooves created by the system. Movement of the grinding wheel is oriented at the prevailing direction of the grooves and their respective flat sections. The fine grinding operation is carried out taking into account the technological heredity of the previous complex and rough grinding operations.

Fig. 1. Thermal frictional treatment of parts (a); treating surface with the needle mill (b).

Given the technological heredity an operation of the intermediate rough grinding of a wavy surface is performed [22]. This removed the wave crests from a flat surface with intermittent quasi-uniform topography (Fig. 2, a). Depressions between the flat portions have a reflow surface without micro-defects and impurities (Fig. 2, b).

Fig. 2. Part after rough grinding operation (a); appearance of a groove with sites on both sides (b).

A mathematical model of a microprofile makes it possible to determine the shape and nature of the surface obtained as a result of complex processing. Depending on the type of the part as a result of complex processing and subsequent grinding operations we received intermittent flat surfaces with different platforms. Next after grinding is the treatment of the edges of the flat surface portions. The operation is performed by needle mills with various thickness (Fig. 1, b). This rounds areas’ edges (Fig. 3, a, b).

Fig. 3. Change in the appearance of the flat edge of the area after treatment with needle mill: edge before treatment (a); flat platform edge after treatment with needle mill (b).

Finishing operation includes finishing the machined surface. When finishing, abrasive pastes of different grits are used with increasing fineness of paste in the process of performing finishing operations. The final polishing operation is carried out, which is aimed at rounding edges between flat surface portions and depressions [6].

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When grinding and finishing we received the intermittent flat surface. The total length of the flat areas in the section of the microprofile is a base length of a microprofile. For an approximate estimate of the base length we assume that the microprofile corresponds to the Gaussian random process which is stationary and ergodic [14, 15]. The distribution of random values of ordinates of the microprofile defined relative to the midline, is (Fig. 4):

Fig. 4. Determination of random values of the lengths for flat areas of the microprofile

1

Px  y

2SV y



e

y2 2V 2y

(1)

where Px  y is a probability of ordinates of the profile y in the section x; V y is a standard deviation with respect to the midline. Variance of the microprofile ordinates is:

V y2

1 xm

xm

2 ³ y  x dx

(2)

0

where xm is the length of the microprofile. Correlation function of the microprofile as a stationary andergodic process is: Ry (W )

1 xm

xm

³ y  x ˜ y  x  ' x dx

(3)

0

where 'x is the elementary section length reference of the microprofile. The value of the correlation function is the undamped periodic process with cosines components. This description of the process imposes a limitation on the structure [16]. Therefore, to determine the base length we use an assumption of the normal distribution law for microprofile ordinates. The length of the bearing surface of the microprofile is defined as the total length of the random values of flat areas. It depends on the height of platforms above the midline (Fig. 4). Let S(h) be the total length of the flat sections. It depends on the thickness of the shear layer, i.e. value of h. For fixed values of the thickness of the shear layer of h and part length of the value of xm, S(h) is random [20]. We introduce the random function:

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°­1 ɩɪɢ y  x ! h °¯0 ɩɪɢ y  x d h

(4)

K  x ®

Then the total length of the bearing surface is: S h

xm

³ K  x dx

(5)

0

The mean of the random function K  x will be:

M K  x 1˜ P ^ y  x ! h`  0 ˜ P ^ y  x d h`

P ^ y  x ! h`

(6)

where Ɋ is the function of ordinates distribution for the microprofile that by definition is according to the normal law. Density of the distribution is according to the normal law: § h P ^ y  x ! h` 1  ) ¨ ¨Vy ©

· ¸¸ ¹

(7)

where Ɏ is an Laplace function (integral of probability). This given function is defined in the form of special computing procedures of mathematical packages. Thus the mean of the function K  x is defined as: § h M K  x 1  ) ¨ ¨Vy ©

· ¸¸ ¹

(8)

From this formula it follows that the mean doesn’t depent of the length of x. The mean of the length of the support surface S(h) of the microprofile is: M  S  h

xm

³ M ¬ªK  x ¼º dx

(9)

0

Taking into account that according to (8) the integrand in (9) does not depend on x and is given by (8), we obtain:

M  S  h

ª § h «1  ) ¨ ¨Vy © ¬«

·º ¸¸ » xm ¹ ¼»

(10)

From relation (10) it implies that the total length of the support surface is uniquely defined by the standard deviation ıy of the microprofile. Formula (10) is the basis for calculation of the mean for the total length of flat areas for the processed part of length xm with respect to the thickness of the metal removal midline h. The total length of the flat portions is a function of two variables h and ıy. For its calculation the following procedure of the mathematical package is used:

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§ § h MS  h, V y : ¨1  ) ¨ ¨ ¨ ©Vy ©

·· ¸¸ ¸ xm ¸ ¹¹

(11)

The calculated values are verified by comparing the results with experimental data. For the real microprofile of the treated surface we have found the values of mean – Table 1. Table 1. The experimental values of the length of the flat areas h, μm

-60

-30

-10

0

+10

+30

S/xm

0,9

0,77

0,74

0,59

0,32

0,18

The calculated values of the mathematical expectation of the total length of plateaus presented as a percentage. Mean values of in per cent. To calculate the standard deviation of the profile, we use the rule of three sigma:

Vp |

 ymax  6

ymin



(12)

where ymax, ymin are maximal and minimal values of the microprofile in relation to the middle line. As a result of calculations, we found the approximate standard deviation value. For the given value we calculated the total length of the flat sections of the microprofile depending on the thickness of the shear layer. From the comparison of the calculated and experimental data, we infer the presence of qualitative similarity and deviation of random nature. 3. Conclusion

Depending on the type of a part, as a result of thermal frictional treatment and subsequent grinding and milling operations, we obtained intermittent flat surfaces with areas of various configurations. The length of the bearing surface of the microprofile is defined as the total length of random values of flat areas. The mathematical model of the microprofile allows for determination of shape and nature of the surface obtained as a result of complex processing, for prediction of the degree of deviation of the actual shape of the processed products from its nominal value, and for establishing deterministic and random errors of geometrical parameters for obtained surfaces. References [1] E.U. Zarubitskiy, Development and research of process efficiency thermofrictional processing of materials, VIPOL, Kiev, 1993. [2] A.D. Kryskov, The technology of friction formation, RVL KNTU, Kirovograd, 2008. [3] E.U. Zarubitskiy, Low shoot allowance when cutting thermofrictional, Optimization of processes of cutting heat-resistant and high-strength materials, UAI, Ufa, 1986. [4] L.A. Gik, Rotary cutting metals, Bk. Publishing House, Kaliningrad, 1990. [5] T.G. Nasad, A.A. Ignatiev, High-speed processing difficult materials with additional streams of energy in the cutting zone, STSU, Saratov, 2002. [6] V.B. Strutinskiy, N.I. Pokintelitsa, The mechanism of formation of a wavy surface when handling parts thermofrictional, Vestnik SevNTU, Seria: Mashinopriborostroenie i transport. 160 (2014) 161169. [7] B.I. Kostetskiy, M.E. Nathanson, D.I. Bershadskiy, Mechanical and chemical processes in the boundary friction, Science, Moscow, 1972. [8] A.V. Chichinadze, The Basics of tribology (friction, wear, lubrication), Mashinostroenie, Moscow, 2001. [9] N.S. Penkin, A.N. Penkin, V.M. Serbin, Fundamentals of Tribology and tribotechnology, Mashinostroenie, Moscow, 2008. [10] D.N. Garkunov, Tribotechnology, Mashinostroenie, Moscow, 1989. [11] N.V. Talantov, Physical bases of the cutting process, the tool wear and fracture, Mashinostroenie, Moscow, 1992. [12] N.P. Mazur, Basic theory of cutting materials, Novij svit, Lviv, 2010. [13] V.A. Balakin, The friction and wear at high sliding, Mashinostroenie, Moscow, 1980.

N. Pokintelitsa and E. Levchenko / Procedia Engineering 150 (2016) 1013 – 1019 [14] A.V. Khomenko, J.A. Lyashenko, Periodic intermittent boundary friction, Journal of Technical Physics. 1 (2010) 2733. [15] V.B. Strutinskiy, Tensor mathematical models of processes and systems, ZHGTU, Zhitomir, 2005. [16] V.B. Strutinskiy, N.R. Veselovskaya, Simulation technology of dynamic processes and systems, VGTU, 2007. [17] V.B. Strutinskiy, V.M, Drozdenko, Dynamic processes in machine tools, Osnova-Print, Kiev, 2010. [18] V.F. Terentyev, Cyclic strength metallic materials, Mashinostroenie, Moscow, 2001. [19] V.A. Bufeev, Mechanofriktional effect, Journal of Friction and Wear. 3 (2010) 252௅257. [20] S.A. Vasin, A.C. Vereshchaka, V.S. Kushner, Cutting materials: thermomechanical approach to the relationship system in cutting, MSTU, Moscow, 2001. [21] A.M. Rosenberg,The mechanics of plastic deformation in the process of cutting and deforming broaching, Naukova Dumka, 1990. [22] E.R. Clark, Microscopic methods of research materials, Technosphere, Moscow, 2007.

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