CC BY
46
3d model of cutting by rolling cut type shears
Fig. 6. Effect of knife curve radius to cutting force: a - specific dependences of cutting force in increasing knife curve radius; b dependence of maximum cutting force on knife curve radius
According to the results of the work one can summa- 6.
rize:
- technological opportunities of rolling cut type shears are not always used in full volume due to large 7. (about 60%) divergence between maximum cutting force and its steady value;
- increasing the knife curve radius to certain value provides more even distribution of force during cutting process and then its visible growth on knife coming out of cut;
- applied to the given shears design at cutting the sheets with maximum depth 50 mm knife curve radius 80...200 meters allows to obtain more stable force distribution during the cutting process;
- in given conditions maximum cutting force relatively to curve radius of 47 m reduces for 25.30 %, that indicates to real opportunity to increase the range of cut sheets.
The results of the work can be used for practical application and during research and development of cutting process for rolling cut type shears.
References
1.
Korolev A.A. Konstrukcija i raschet mashin i mehanizmov prokatnyh stanov. [Design and calculation of rolling mill machinery]. Moscow : Metallurgija, 1985. 376 p. Ivanchenko F.K., Grebenik V.M., Shirjaev V.I. Rozrahunok mashin i mehanizmivprokatnih cehiv. [Machinery calculating for rolling mills]. Kiev: Vishha shk., 1995. 455 p. Adamovich R.A., Rudel'son L.M., Rogoza A.M., Pal'min A.D. Nozh dlja listovyh nozhnic s katjashhimsja rezom. [Knife with rolling cutter for sheet shears]. A.s. USSR, no. 810403, 1981.
Adamovich R.A., Rudel'son L.M., Rogoza A.M., Pal'min A.D. Nozh dlja nozhnic s katjashhimsja rezom. [Knife shears with rolling cutter]. A.s. USSR, no. 902989, 1982. Liu G.R., Quek S.S. The Finite Element Method: A Practical Course, 2003, 348 p. Borovik P.V., Usatjuk D.A. Novye podhody k matematicheskomu mod-elirovanju tehnologicheskih processov obrabotki davleniem. [New approaches to the mathematical modeling of pressure treatment processing]. Alchevsk : DonGTU, 2011. 299 p.
Notchenko V.D, Bojdenko A.N., Emchenko E.A., Cherkasov N.D., Zozulja E.S., Poslushnjak A.V. Chislennoe matematicheskoe modelirovanie processa rezanija listovogo metalloprokata na nozhnicah s dugoobraznym nozhom. [Numerical mathematic process simulation of sheet metal cutting with shears with embowed knife]. Udoskonalennja procesiv i obladnannja obrobki tiskom v mashinobuduvanni i metalurgii : temat. zb. nauk.. pr. [Pressure treatment processing and machinery improving in machine building and metallurgy: Col.of Scient Papers]. Kramators'k, 2001. pp. 454-457.
3.
4.
5.
Gribkov E.P., Danilyuk V.A.
MATHEMATICAL MODELLING OF SRTESS-STRAIN BEHAVOIR IN ROLLING OF THE COMPOSITIONS INCLUDING POWDER MATERIALS
Abstract. The developed mathematical model of rolling of two-layer powder materials allows to determine the rational technological parameters of process excluding deformation of a substrate and raising an exit of suitable by production of inserts of sliding bearings. It is established that the less thickness of a metal substrate, the more subjects is deformed, and respectively, powder is less deformed. In increasing the layers ratio the force and the rolling moment growing and the increasing of final relative density of powder composition are observed.
Keywords: mathematical model, rolling, powder materials, substrate, relative density, deformation center.
One of the perspective directions in the field of composite hardware production is rolling of compositions with using the powder materials, allowing to receive wide assortment of production with simultaneous ensuring specific operational properties and simultaneous economy of extremely scarce and expensive materials. The most widespread ways of rolling of such type production is rolling of compositions powder-powder and powder-monometal.
The mathematical model of rolling single-layer pow-
der materials [1] was taken as a principle of numerical mathematical model of rolling of two-layer powder materials. The settlement scheme of the integrated deformation center used in this case is submitted in figures 1 and 2.
Splitting of a consolidation zone into a final set of elementary volumes and definition of geometrical characteristics, and also tensions Ox, Tx and px in a final and differential form (Fig. 2) was carried out by analogy to a technique stated in work [1].
Gribkov E.P., Danilyuk V.A.
Fig. 1. The settlement scheme of the integrated deformation center in realization of rolling of composition powder (m) - powder (l)
Fig. 2. The settlement scheme of allocated i-th of elementary volume of the deformation center in realization of rolling of composition powder (m) - powder (l)
At the same time it should be noted that friction existence between layers alters a condition of static balance of the allocated elementary volume of the deformation center, having the following appearance: for less plastic component:
S Fxil = CTx2ilhx2il -CTrfAltf - °-5AX(PxliJx2li + + Px2Ufx 22, ) + °.5(pxi¡I + px2il )kxfci + (1)
°-25( Pxll + Px 2 il) X( Kxli " K 2, )± °-5( Pxll + Px 2 il ) X hxiil - hx2il -(hxU - hx2i ) /2) = for more plastic component:
ZF. =ct .. h .. -a i h*. - °.5Ax x
xi m x21 m x 21 m xl i m xl i m
X( Pxlimfxlli + Px2 imfxl2i) ~ °.5( Pxlim + Px 2im ) X (2) xAxfci + °.25(Pxlm + Px2im ) (Kxli " Kx2 i ) = °
where hxlil(m), hx2il(m) are the current thickness less (more) strong components at the entrance and at the exit from the allocated elementary volume, respectively; hxli, hx2i are the current thickness of all compositions at the entrance and at the exit from the allocated elementary volume, respectively; Ax is the extent of the allocated elementary volume of the deformation center; fxll(2)i, fx2l(2)i are the current values
of friction coefficients at the entrance and at the exit from the allocated elementary volume, respectively; fci is the current value of friction coefficient between composition layers; pxiil(m), px2il(m) are the current values of normal contact tension at the entrance and at the exit from the allocated elementary volume, respectively; ax1il(m), ax2il(m) are the current values of normal tension at the entrance and at the exit from the allocated elementary volume, respectively.
Substituting in the equation of static balance a condition of plasticity for loose environments [2]:
1-2a
=-Px
1 + 4a
f 1-2ax ^2 1+4a
-1
4 1+a 2 +--- , (3)
31+4a
it is possible to determine normal contact tension:
p2 f^ " t3 )+ 2Px2^2 + ^ - h = 0, for less plastic component:
ti = 1 2a'21 hx2l +1 (Ahxl - fx22 Ax + fc Ar),
1 + 4«x 21 2
12 = 05 Pxl (Ahxl -Arfx2i + fc Ax)-^xUhxll ;
(4)
t = h
l3 nx2l
1-2«x
1 + 4a,
Y
-1
t - 4h2 1 + "x2l
1 A
^x2l /
for more plastic component 1 - 2a
3 x2/1 + 4«
Px2ial
t =
1 + 4a x lm x2 m 2
hx2m + 1 faxm ~ fx12 ^ ~ fc ^),
x1mhx1m ;
12 = 0-5Px1 {Ahxm -teffxu - fc AT t3 = hx22m [((1 - 2a x 2m )/(1 + 4«x 2 m ))2 " 1JI
14 = 4 hx22m K1 + «x2m M1 + 4«x2m )R2m^2
where ax, Px are the coefficients characterizing mechanical properties of powder materials of various structure depending on value of relative density; asx is a limit of fluidity of a firm phase of powder composition.
As entry conditions, that is geometrical characteristics for the first elementary volume, accepted the following:
h^ = h, h,, / h • h= h,, - h.,,; x 2m x1m x 2 x1 ' x 2l x 2 x 2/'
hx1m |I=1 _ hx0m ; hx1l |I=1 _ hx0/-
(5)
Final thickness of the first layer hx2m determined from a condition of equality of normal contact tension between layers:
hx2m = hx2im + As Si§n{Px2lm ~ Px2U } , (6)
where As is a step of change of the layer thickness, which size to dependences on extent of approach to initial result was accepted by a variable; sign{px2im-px2il} is a gradient assessment of the direction of the increment.
As a whole, the considered analytical decisions along with iterative procedure of extent deformation center determination, the accounting of elastic flattening of working rolls surface, procedure of numerical integration of the main indicators of process made full algorithm on numerical one-dimensional mathematical modeling stress-strain behavior when rolling two-layer powder materials. As an example of result of numerical realization of the received mathematical model in figure 3 settlement distributions of local and integrated characteristics of process are presented.
Integrated characteristics of process, namely, settlement distributions of force P and the moment M of rolling, indicators of final relative density y2m, y2l and the relation of final thickness of layers h2m/h2l of dependence on the size of relative reduction e are submitted in figure 1a. Local characteristics, that are distributions of the current thickness hx2m, hx2l and relative density of each composition yx2l, yx2m, are submitted in figure 1b. From the analysis of the presented settlement distributions it is visible that with increase in relative reduction the intensive growth of the moment and rolling force, and also final relative density takes place.
P,kH
1500
1125
750
375
Til
72m P v
M
MJcH m
40 T1
30
20
10
0
0.9
O.S
0.7
O.S
0.75 0.75
0.50 0.50
0.25 0.25
h^im Kil A
hf=2 TT1TT1 hpâmii
s NN.
0.25 0.375
0.5
0.S25 0.75 S
11» mm
4
25
50
0
75 100 x/1
a b
Fig. 3. Settlement distributions integrated (a) and local (b) characteristics of rolling of two-layer powder preparation depending on reduction: m - Cu; l - Fe
Gribkov E.P., Danilyuk VA.
Besides, results from numerical realization established that increasing in coefficient of external friction of more intensive deformation are observed from a firm component, growth of normal contact tensions, force and the total moment of rolling.
In increasing the ratio of thickness of soft component to thickness firm to hlm/hil=1.75 some decreasing in the total moment and increasing in force of rolling are observed. However, in case of further increasing in this ratio there is a boomerang effect. Change of the relation of thickness does not practically influence on the final relative density.
Comparison of the received settlement distributions with experimental [3] showed that the error of determination of final relative density was made by about 8%, rolling forces - about 5%, the rolling moment - about 10%. It confirms sufficient degree of reliability of the received mathematical model and legitimacy of its use for design of the mechanical equipment of specialized camps and calculation of technological modes of rolling powder compositions.
The other perspective direction in the field of production of composite hardware is rolling of powder materials on a metal substrate. Features of this process at half-devout rolling are a bend of the rolled leaf towards a steel substrate and the existence of cross cracks in a layer of the rolled powder material. These defects are caused mainly by deformation of a metal substrate, which leads to different longitudinal deformations of layers of composition, and respectively to above-mentioned defects. One of ways of this problem solution is the choice of such mode of reduction at which powder would be only deformed, that can be possible with using of mathematical model, which would predict substrate deformation.
Considered earlier mathematical model of rolling of composition powder- powder was put in the basis of considered numerical one-dimensional mathematical model of rolling of two-layer composition powder-monometal. The problem definition and character of assumptions were similar to the previous case.
Full calculation stress-strain behavior for separately allocated elementary volume is also reduced to definition of normal ctx1, ctx2 and normal contact tensions px on the basis of the directed search of thickness hx1, hx2 by criterion of section balance at the exit from elementary volume in the vertical plane:
h^mm
7.0
5.6 4.2 2.8 1.4 0
Pxlm ~ Pxll ~ Px2>
(7)
h*
Km^,
where «l» and «m» are indexes determine accessory by a tear of monometal and a tear of a powder material, respectively.
Having substituted in the equation (1) condition of plasticity for continuous environments:
= p - 2K
-ix X
(8)
where 2KX is a coefficient of the doubled resistance of deformation of shift which can be determined by [4] :
2Kx = 1-155 ( ao + a8* + a2sl + a3sl );
(9)
a0, a1; a2, a3 are the coefficients of regression characterizing intensity of deformation hardening of metal.
The normal contact tension operating at the exit from elementary volume of the deformation center:
Px2l ~
2Kx 2lKx2l +
(10)
+ 1 P*f Ax " 1 Pxll (hx1l - K2l )
Kx2l " 2 Zx2AX " 2 fc AX + 2 (Kx1l - Kx2l )
The further solution of the task (definition of entry conditions, conditions transition to the following section, iterative procedure by definition of the current geometrical characteristics of composition components) is similar to the previous case, the case of rolling of powder-powder composition.
As an example of numerical realization of the developed mathematical model of rolling of powder-monometal composition in figure 4, settlement distributions of local characteristics of rolling of powder bronze-graphite (79% Cu; 15% Sn; 4% Pb; 2% C) under following conditions: radius of rolls - R=125 mm; substrate material - steel DC 01; initial thickness of a powder layer - 5 mm; the initial relative density of a powder material - y0=0.27; final thickness of all composition - 4 mm; strip width - 100 mm; initial thickness of a substrate - 4 mm are presented.
Px.C^H/mm2
700
560
420
280
140
0 0.25 0.50 0.75 1.0
yJ.I 0
Ckitl X j>x
/ c^l V
\
0 0.25 0.50 0.75 1.0 b
x/I
Fig. 4. Settlement distributions of local characteristics of rolling of composition the powder M1 - steel DC 01
From the analysis of the presented settlement distributions it is possible to draw a conclusion that deformation of a metal substrate begins near the neutral line of rolling. As well as at the time of the beginning of its deformation intensity of growth of normal contact tensions px sharply decreases, and is observed and with intensity of growth of normal tensions ctx, the difference in the size of normal tension of a powder material and a metal substrate is also visible.
In figure 5 settlement distributions of integrated characteristics of process depending on a ratio of powder layers and steel are presented. That is at a fixed thickness of
7 1.0
0.9 0.8 0.7 0.6 0.5
■J
hm/^
jt
/ / -Ji!
/
0
0.74
0.68
0.62
0.56 0.5
0.75 1.50 2.25 3hm/hl
powder - hpol=4 mm and the variable thickness of a metal substrate is hpll=1.2...12 mm. Apparently from the presented settlement distributions than less thickness of a metal substrate of subjects it is more deformed, and powder respectively is less deformed. Also in increasing of a ratio of layers growth of force and the rolling moment, increasing in final relative density of powder composition is observed.
The developed mathematical model allows to determine the rational technological parameters of process excluding deformation of a substrate and raising at the exit of suitable by production of bearings sliding inserts.
0.8 20
1000
P,kH
M.kHm
16 940
12 880
8 820
4 760
0 700
P _- ^
15
13.6
12.2
10.8
9.4
0 .75 1.5 2.25 3 hWhl
a b
Fig. 5. Settlement distributions of integrated characteristics of rolling of composition powder-steel
References
Levkin A.N., Gribkov E.P., Vorobyev Yu.A. Mathematical modeling stressstrain behavior and geometrical characteristics at realization of rolling of bimetallic powder compositions. Kramatorsk, 2000. pp. 360-363. Volkogon G.M., Dmitriev A.M., Dobryakov E.P. etc. Progressive technological processes of stamping of details of powders and equipment. Mos-
cow : Mechanical engineering. 1991, 320 p.
3. Tselikov A.I., Nikitin G.S., Rokotyan S.E. Theory of longitudinal rolling. Moscow : Metallurgy, 1980, 320 p.
4. Potapkin V.F. Levkin A.N., Satonin A.V., Romanov S.M., Vorobyev Yu.A., Gribkov E.P. Stressed state and kinematics in the rolling of powder materials on a metal substrate. Powder Metallurgy and Metal Ceramics, 2000, vol. 39, no. 1-2, pp. 11-17. ISSN 0032-4795.
Tulupov O.N., Moller A.B., Kinzin D.I., Levandovskiy S.A., Ruchinskaya N.A., Nalivaiko A.V., Rychkov S.S., Ishmetyev E.N.
STRUCTURAL-MATRIX MODELS FOR LONG PRODUCT ROLLING PROCESSES: MODELING PRODUCTION TRACEABILITY AND FORMING CONSUMER PROPERTIES OF PRODUCTS
Abstract. The development of rolling production processes towards flexible manufacturing schemes in tightening quality factors makes the search of methods of effective influence on the process, labor management and personnel competence relevant.
To resolve the problems it is expedient to utilise structural matrix of mathematical models based on matrix presentation of long product rolling processes, and on a body of structural matrixes. In order to create mathematical apparatus we proposed to assign a sophisticated structure matrix consisting of units (cells) to each process operation and operation result. These results are identified with a rolling phase, while the process operation - with transformation of the product.
Structural matrix description of a process phase includes blocks that contain data of rolling process factors and parameters. To describe the dynamics of rolling process was presented the relationships between separate process states in a matrix form, e.g. as matrices of technological transformations.
Keywords: long products, rolling processes, structural-matrix models, computer simulation, consumer properties.
