CC BY
38
Секция 4. Машиностроение
Section 4. Mechanical engineering Секция 4. Машиностроение
Stupnytskyy Vadym Vladimirovich, National University "Lviv Polytechnic", Lviv, Ukraine
PhD, the Institute of Mechanical Engineering and Transport
E-mail: stupn@i.ua
Kuk Andrij Mihaylovich, National University "Lviv Polytechnic", Lviv, Ukraine PhD, the Institute of Mechanical Engineering and Transport
E-mail: andrij.kuk@gmail.com
Determination of deformation component roughness parameters using the methods of rheological simulation modeling of the cutting process
Abstract: Worked out methodology of mathematical modeling of deformation component roughness as a result edge cutting machining. The offered methodology is based on the rheological modeling of cutting process in the in the software system Deform. The brought results over of researches of modeling of deformation constituent of surface pattern at treatment of steel AISI 1045.
Keywords: surface roughness, Prandtl’s problem, technological factors, rheological modeling.
Problem. The roughness of machined surfaces is defined as the mechanical process of interaction between two surfaces — machined tool and frictional contact deformation processes and transformations cutaway layers in chips. The first part can be represented as the estimated height, determined by geometric constructions [1], and its growth is due to the cutting process with regard to vibration phenomena, including regenerative. It can be designed to perform the operation. Second — is formed in the course of operations is the integration — dependent functioning of cutting and is mainly determined by the processes of interaction frictional contact ending in the formation of secondary transition plastically deformed zone. Quasi-stable surface area of partially or completely replace the front and rear surface of the tool and, as a result, alter the geometry and microgeometry shapegenerating blades. The degree of influence frictional contacts on surface roughness in machining metal processing depending on the selected mode processing and geometry of the cutting wedge. When finishing technology transitions, this factor makes the prevailing value [2].
If the calculation of the residual scallop height calculation of the geometric component represents solved problem [1], the analytical component of the deformation is a particularly complicated task because this problem is related to bulk plastic deformation. The complexity of the analytical formalization is
connected with the use of the theory of plasticity and nonlinear thermodynamics, which requires a number of assumptions that severely reduce the reliability of the results obtained [1]. Development of methods for the simulation of dynamic interpretation of nonlinear processes cutting research based on the results of rheological modeling of the cutting process has opened additional opportunities to study the deformed state chip forming area with access to the roughness of the machined surface. This determined the feasibility and validity of the following studies.
Research Methodology. The relief of the treated solid surface as a result of plastic deformation withstand fluctuations at nanometer level, and these fluctuations relief is, in fact, a manifestation of fluctuations in heat. But we should recognize that these fluctuations of thermal energy in this case are such that do not destroy, but rather lead to the formation of stable spatial structures in the structure of the surface. The formation of surface roughness and layer superimposed result of kinematic and power conversion truncated aftereffect allowance in chips, which leads to the formation of secondary transition plastically-deformed zone (so-called secondary contact zones of plastic). To identify patterns of residual comb is necessary to establish the magnitude of the plastic displacement of metal that is deformed in the process of cutting along the cutting blade support.
33
Section 4. Mechanical engineering
In this case, consider the phenomenon of plastic displacement as a particular case of Prandtl problem [3,4]. This kind of deformation of surfaces occurs when the contact stress reaches the yield strength and the material flows counterbody entered in the contact zone ofthe friction pair «tool — workpiece», depending on the strain state. Physically, this phenomenon during cutting may be caused by longitudinal and transverse plastic deformation with respect to the geometry (the ratio of the main and auxiliary ф and ф1 in terms of the angle, radius r at the top of the tool) and the kinematics of the cutting edge of the tool.
Solving the problem of forming deformation component prof. A. Suslov cutting methodology [1], we obtain:
ф < arcsin
on condition that ф < arcsin
\ 2r j
(' S} V 2r j
0,5-r
1 -
A3 =-
4
T +a
1 1
+
(1)
- on condition that ф > arcsin
г s /
ф > arcsin — :
V 2r J
f с Л
V 2r
T
1____ ХУ
\ f ( r
T
V \T*y + CT у
2S. +-
T
1 _ xy
Л =
ф1 < arcsin I —
. 2r j
T
V +a jj
64
on condition that ф < arcsin
(2)
( с Л
V 2r
f
0,5 • r
\
T
1 _ _
A3 =■
V \Txy у
1 2r
Ы + S
- on condition that ф < arcsin
, .Г
ф1 > arcsin
(3)
f с Л
V 2^ У
V 2r у
0,5 • r
T
1 — -
A3 =-
T
V vT +g у
1 2r
Щф + 5,
(4)
where ту — dynamic shear stress, МРа;
о — effective mean stress, МРа;
r — the radius of curvature of the cutting blade, mm.
а)
b)l
Fig. 1. Painting rheological forming input data for the calculation of the deformation component of microscopic
profile: а) тху — dynamic shear stress, MPa; b) о — effective mean stress, MPa (as example ot turning workpiece from AISI 45; P=120 m/min; S=0,2 mm; t=1 mm)
1
1
1
T
ХУ
1
Microscopic deformation component profile Д3 at any time of chip-formation process can be calculated if the use of rheological simulation of the cutting process according to the methodology.
Initial data for calculation of the microscopic deformation component, in addition to the set of geometric
parameters of the instrument (r, ф, ф1) is the dynamic shear stress т and normal stresses о (e. g. formation of
ху ''О
such data is shown in Fig. 1 for the lathe processing, steel AISI 45; V = 120 m/min; S = 0,2 mm, t = 1 mm). Figure 2 shows the results of modeling the deformation component of microscopic Д3 profile for cutting steel AISI
34
Секция 4. Машиностроение
45 depending on the radius r at the top of the tool and the tool feed S. In this case, the conditions were accepted: ф = ф1 = 45°, and therefore Д3 calculated by formula (3). The analysis above allows graphical dependencies conclude that the magnitude of the deformation increases as the microscopic component with increasing radius r at the top of the tool and the tool feed S. Moreover,
the increase in S just feed more significant impact on the result of the formation of deformation component Д3 Thus, the increase in the radius of the top 10 times (from
0.1 to 1.0 mm) caused an increase in the value Д3 only 2.2 times — from 5 to 11 microns. At the same time, increasing the feed from 0.05 to 0.8 mm boosted Д3 to 7 times (from 2 to 14 microns).
a)
b)
Fig. 2. Simulation results constituent microscopic deformation profile in steel AISI45 processing (a) — dependence A3 from the radius at the top of the instrument; (b) — the dependence A3 from the tool feed
To analyze the influence of different mechanical tion study of the rheological steel AISI 45 processing, properties of the materials for the formation of micro- aluminum alloy AL6061, and stainless steel 4340 (Fig.3).
scopic deformation component, a comparative simula- Cutting for all experiments: feed S = 0,25 mm; cutting
35
Section 4. Mechanical engineering
depth t = 1 mm; cutting speed V = 120 mm/min; radius at the top of the instrument r = 0,25 mm.
Simulation results confirm the adequacy of the calculated data in the real cutting process: the largest deformation changes in surface roughness characteristic of soft plastic material — aluminum alloy AL6061, which is 1.8 times higher than the roughness component in steel AISI 45 processing and 2.6 times — when cutting corrosion-resistant stainless steel 4340 (the average value of Д3-9.2 microns, 5.1 microns and 3.5 microns, respectively). This confirms Meyer formula, according to which a spherical indenter cave at the surface of the material acting force P is associated with deep imprint ДН by the formula [1]:
( 4-Ah Y2 (5)
P = m ------- (5)
V n J
where m and n — coefficients, dependent on the properties of the material.
On the other hand, the efforts of strain, according to the theory of contact interaction [5], depending on the hardness of the material being treated and is determined from the formula:
P = HB -u-Ah (6)
where u — the degree of permanent deformation of the part’s material.
For example, structural steel during hardness indentation with radius 0,794 (which roughly corresponds to the range of curvature radius of the cutting blade), the depth of plastic deformation is the linear dependence of hardness is determined by the formula [6]:
Ah = P -(130 - HRC) • 0,002 (7)
where HRC — Rockwell hardness of the material.
If the measured hardness from Brinel or Vickers, the microhardness is approximating a linear dependence of hardness. When measuring the hardness of Rockwell — a stepped dependence. Numerous experiments have shown that when measuring hardness Brinel tension described by the equation [7]:
a0 = (0,32 0,37) • HB (8)
Thus, the magnitude of the deformation component of roughness is directly connected with the hardness of the material, as confirmed by rheological modeling (Fig. 3).
Fig. 3. Graphical interpretation of simulation deformation component of surface roughness in turning cutting piece of steel 45 aluminum alloy AD33 and corrosion-resistant stainless steel 34H2N2M (feed S = 0,25 mm; cutting depth t = 1 mm, cutting speed V = 120 m/min)
Conclusions. Research roughness of machined surfaces suggesting and get confirmation that the process of forming a surface layer of microgeometry defined and accompanied by intense deformations on the scheme of
compression and shear. They apply to the area and chip formation zone and frictional contact front and rear surfaces of the chip and the workpiece. Deformations reach depths of 2 to 5 mm ... 15 ... 25 mm, and the roughness becomes
36
Секция 4. Машиностроение
dependent on the stress- strain state, kinematics deformed zones, as well as nucleation, growth and destruction of the stepping stones to the frictional contact zone. The result is a deformation component of roughness, resulting from the interaction frictional contact surfaces that are formed during the cutting process and is dependent on the mode of treatment. Formation of the analytical model for calculating this component is virtually impossible without the use of the rheological simulation results.
Using the capabilities of the rheological modeling can be at a significant degree of reliability predict all the important components of microscopic profile, taking into account not only the kinematics of geometrical parameters of the technological system, but also such important factors as the dynamic change of the stress-strain state of the workpiece and vibration (including regenerative) tool during cutting.
References:
1. Суслов А. Г. Качество поверхностного слоя деталей машин - М.: Машиностроение, 2000. - 320 с.
2. Свинин В. М. Фрезерование с модулированной скоростью резания. - Иркутск: Изд.-во ИрГТУ, 2007. - 302 с.
3. Ишлинский А. Ю., Ивлев Д. Д. Матетатическая теория пластичности. М.: Физматлит. 2001. - 702 с.
4. Колмогоров В. Л. Теория обработки материалов давлением. Екатеринбург: УрГТУ-УПИ, 2001. - 377 с.
5. Котенева Н. В. Упругопластический контакт гладкой сферы с плоской поверхностью при динамическом нагружении.- Известия Томского политехнического университета. - 2005. Т. 308. № 2, С. 114-116
6. Дрозд М. С., Матлин М. М., Сидяхин Ю. И. Инженерные расчеты упругопластической контактной деформации. - М.: Машиностроение, 1986. - 220 с.
7. Дель Г. Д. Технологическая механика. М., «Машиностроение», 1978. - 174 с.
37
