metals Article
Physical Modelling of the Ball-Rolling Processes Zbigniew Pater * , Janusz Tomczak , Łukasz Wójcik
and Tomasz Bulzak
Mechanical Faculty, Lublin University of Technology, 36 Nadbystrzycka Str., 20-618 Lublin, Poland;
[email protected] (J.T.);
[email protected] (Ł.W.);
[email protected] (T.B.) * Correspondence:
[email protected]; Tel.: +48-81-538-4242 Received: 22 November 2018; Accepted: 27 December 2018; Published: 4 January 2019
Abstract: The objective of the article was to present the state of the problem of physical modelling of the hot-working processes with plasticine as the model material. It was stated that the aforementioned method can prove helpful in analyzing complex plastic forming processes such as cross rolling and helical rolling of balls. In order to confirm this hypothesis, an attempt at forming steel balls with diameters of 40 mm (cross rolling) and 57 mm (helical rolling) under laboratory conditions was made. Further on, these processes were conducted in model form using special model rolling mills and 3D printed acrylonitrile butadiene styrene (ABS) tools. The comparison of the test results regarding shape and manufacturing accuracy, as well as force parameters, confirmed the validity of using physical modelling in the investigation of the process of cross rolling and helical rolling of balls. Keywords: cross rolling; helical rolling; balls; tools; forces; physical modelling
1. Introduction Steel balls are widely used as grinding medium in mills for grinding materials such as metallic ores, coal, gravel, or used molding sand. Hot-working and, above all, die forging and rolling are used in their production. Ball rolling appears to be the most effective method and can be performed as helical rolling (HR) or cross rolling (CR), although the former is used more frequently in industrial practice. It is claimed that the most problematic aspect of implementing the processes of ball rolling is designing the proper shape of tools (rolls or flat jaws). The basic recommendations concerning this issue were presented in specialist literature a long time ago, for example, in the works of Wang et al. [1] or Yang & Chen [2]. The process of cross rolling of balls, however, was discussed just recently, with its bases introduced by Pater [3]. Further development of the ball-rolling processes is linked to the possibility of using Finite Element Method (FEM)-based numerical modelling in their analysis. Recently, several works on this subject were published. Thus, Pater et al. [4] introduced a new variant of the HR process based on the numerical simulations. In this process, balls are hot formed by rolls with helically wound wedges. Cao et al. [5] conducted an analysis of the stress and strain state in small diameter balls, cold formed in the process of helical rolling. Furthermore, Pater et al. [6] introduced an innovative technology of cross rolling balls with a diameter of 70 mm, manufactured from heads of scrapped rails. In the above-mentioned works, the commercial programme Simufact Forming was used. The software did not, however, allow for the simulation of the separation of balls and, therefore, a simplification in the form of leaving a small-diameter connector between adjacent balls was made. In order to remove the occurring limitation, it was necessary to determine how helpful physical modelling is with plasticine as the model material in an analysis of ball rolling. The results of the research on this subject are presented in this article. Physical modelling with plasticine as model material was widely used in analyses of the processes of plastic forming in the late 20th century, that is, in the period during which numerical modelling of Metals 2019, 9, 35; doi:10.3390/met9010035
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complex cases of forming was not yet possible. This phenomenon can be observed in the works of Japanese researchers in the 1980s. Chijiwa et al. [7] conducted extensive plastometric tests in which plasticine was deformed statically and dynamically in temperatures ranging between −20 ◦ C and 50 ◦ C. On the basis of the test results, it was stated that plasticine is suitable for simulating hot-working behavior, not only in terms of strain state, but also stress state. For the reasons presented above, this material was widely used by Japanese researchers in the analysis of rolling processes. Yazawa et al. [8] used plasticine in the research of plate rolling in order to determine such parameters of the process that guarantee even melt flow not only in longitudinal, but also transverse directions. Chijiwa et al. [9] conducted an analysis of the force parameters in the process of longitudinal rolling on a two-roll mill, focusing on determining the stress distribution on the material-roll surface, internal stress distribution in the material, as well as force distribution and torque. Yazawa et al. [10] used plasticine in the research of an innovative grooveless rolling process, in which flat rolls for rod rolling were used. Furthermore, Chijiwa et al. [11] conducted research on double-stand longitudinal rolling in terms of strip geometry, force parameters in rolling, and stress state of the material. In the 1990s, the possibilities offered by numerical modelling, still limited mostly to forming processes occurring in plane or axially-symmetric state of strain, were more widely used. Still, such research was often supplemented by physical modelling in which plasticine was used. The work of Segawa and Kawanami [12] on asymmetric rolling of a bimetal strip can serve as an example of this situation. Physical modelling was still most frequently used in processes of plastic forming in the 3D deformation state. Thus, Takemasu et al. [13] used plasticine in the research on the process of flashless forging of connecting rods. This resulted in designing forging preform in a shape that allows for obtaining a forging of anticipated geometry. Dutta and Rao [14], on the other hand, used plasticine to attain such parameters of the forging process that guarantee the right shape of the forging of a compressor disc. After the year 2000, numerical modelling became a widely recognized standard. It enables one to analyze the cases of forming conducted in both the plane and 3D deformation state, which was used by Miñano et al. [15] in research on anisotropy of sheets. In many cases, however, physical modelling is still used, with plasticine as model material. Such hybrid modelling was used mostly in analyses of forging. Thus, Vazquez and Altan [16] analyzed the processes of flashless forging of the connecting rod and cross groove inner race. In turn, Fujikawa [17] examined the process of crankshaft forging in terms of minimalizing the amount of charge material. Park et al. [18] used this method for analyzing the rotational upset forging process, where very high shear strain occurs. Zhan et al. [19] examined the kinematics of melt flow in the process of turbine blade forging. In their tests, forging preforms made of several layers of plasticine in various colors were used. Similarly, Yang et al. [20] used this method while analyzing the influence of the billet shape on the filling of the impression during the forming process of the spider and two-rib wheel forgings. Fereshteh-Saniee and Hosseni [21] used plasticine to determine the influence of the amount of flash on force parameters in the process of die forging. Multi-layer samples made from plasticine in various colors were also used by Buteler et al. [22] in their research on the open die forging process, where the influence of the anvil shape on the elongating of the formed parts was examined. Hosseini-Ara and Yavari [23] used plasticine while establishing a new criterion applied for designing forging preforms utilized in forging H-shaped parts. In recent years, plasticine was used in analyses of extrusion processes. In this area, the work of Kim and Park [24] on the torsional backward extrusion process is worth mentioning. Using multi-layer plasticine billets allowed for examining melt flow in this process. Kazanowski et al. [25] utilized plasticine in analyzing bi-material rod extrusion. In order to examine different extrusion settings focusing on the thickness of each surface, two types of plasticine were used. Sofuoglu and Gedikli [26] used plasticine in analyzing the process of forward extrusion in order to examine the influence of
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the parameters on extrusion force. Moreover, Zhou et al. [27] used plasticine for examining a new extrusion process called differential velocity sideways extrusion (DVSE). Plasticine is also currently used as a model material for examining different rolling processes. Shih and Hung [28] utilized commercial plasticine in their research on the process of three-roll planetary rolling. Using a special model rolling-mill and plasticine samples allowed for verifying the results obtained from numerical analysis. The same procedure was adopted by Hwang et al. [29], who focused on determining the influence of the billet shape on manufacturing accuracy of rods. In turn, Stanistreet et al. [30] built a rolling-mill for plasticine rings, which they used for examining material flow. Plasticine was also used by Jeon et al. [31] in the analysis of cold rolling of Al–Cu double layered sheet by physical modelling and finite element method, and by Lee et al. [32] in the research on design of roll profile for complex door hinge in shape rolling. Furthermore, Wójcik and Pater [33] conducted a process of cross-wedge rolling of a stepped shaft in a 1:4 scale model. The comparison of the results of the model rolling and the real process showed a high convergence not only in the manufacturing accuracy, but also in the force parameters. The analysis of works on physical modelling of the hot forming processes, especially rolling processes, shows that this method should prove beneficial in researching ball-rolling processes. 2. Materials and Methods The model material used in this research was black and white commercial plasticine “Primo”. The plastometric tests of the aforementioned plasticine (in temperatures of 0–20 ◦ C) consisted of the compression test, conducted on Instron 3369 universal testing machine (Instron, Norwood, MA, USA). As a result of said tests, the following constitutive equations describing flow stress were obtained [34]: . (m+bT ) aT
σF = Cεn1 en2 ε ε
e
(1)
.
where σF —flow stress, MPa; ε—effective strain; ε—strain rate, s−1 ; T—temperature, ◦ C; C, n1 , n2 , m, b, a—constants presented in Table 1. Table 1. Constant of the white and black plasticine material models. Material
C
n1
n2
m
b
a
White plasticine Black plasticine
0.48057 0.6817
−0.0313 −0.0711
0.08705 0.07203
0.2451 0.2701
−0.0026 −0.0037
−0.03283 −0.07358
The model material was also tested in order to determine the critical value of the Cockroft–Latham integral at which beam cracking occurs. In order to achieve this, axially symmetrical samples with an undercut in the center were stretched in the universal testing machine (in temperatures between 0 and 20 ◦ C) until failure. Further on, this process was numerically simulated in order to acquire the parameters of the damage function. As a result of the research [35], it was established that at the temperature of 5 ◦ C, the limit value of the Cockroft–Latham integral equals 0.786 for white plasticine and 1.134 for black plasticine. The obtained results proved close to the critical value of the damage function of hot-formed steel. For example, in the case of C45 grade steel, the critical value equals 0.756, whereas for R200 rail steel grade, it is 1.05. That being said, plasticine in 5 ◦ C is expected to crack similarly to hot-formed steel. On this account, it was decided that model testing was to be performed on samples cooled to 5 ◦ C. An important parameter in the rolling process is coefficient of friction. As no lubricants are applied during cross-rolling and hot skew-rolling, friction values are very high, close to critical. It was presumed that during cross-rolling of steel elements, the coefficient of friction equaled 0.8 [36]. In order to attain a similar friction value in plasticine forming, the use of lubricant is required. Teflon oil proved to be suitable as lubricant for the pair plasticine—ABS (acrylonitrile butadiene styrene). The tests
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proved that the friction value after using lubricant in the rolling process (conducted in temperature ◦ C) equaled 0.82 for white plasticine and 0.73 for black plasticine. 5Metals 2018, 8, x FOR PEER REVIEW 4 of 14 The research consisted of rolling balls of the real material, that is, C45 and C60 grade steel. The constitutive wereofgiven byballs the following The researchmodels consisted rolling of the realequations: material, that is, C45 and C60 grade steel. The
constitutive models were given by the following equations: I1 T + I2 . ( m T + m ) 2 (2) σF = C1 e(C2 T ) ε(n1 T +n2 ) e( ε ) ε 1 (2) 𝜎 =𝐶 𝑒 𝜀 𝑒 𝜀 . where σF —flow stress, MPa; ε—effective strain; ε—strain rate, s−1−1; T—temperature, ◦ C; C1 , C2 , n1 , n2 , where σF—flow stress, MPa; ε—effective strain; 𝜀—strain rate, s ; T—temperature, °C; C1, C2, n1, n2, I1 , I2 , m1 , m2 —constants presented in Table 2. I1, I2, m1, m2—constants presented in Table 2. Table 2. Constant of the C45 and C60 grade steel material models. Table 2. Constant of the C45 and C60 grade steel material models. Material
Material C45 C45 C60 C60
CC11 4105 4105 4857 4857
C2C2 nn1 1 n2n2 II1 1 II22 −0.00354 −0.00013 −0.00013 −0.0051 −0.0051 −0.000023 −0.000023 −0.0281 −0.0281 −0.00354 −0.00374 −0.00022 0.07908 −0.000026 −0.0149 −0.00374 −0.00022 0.07908 −0.000026 −0.0149
2 mm1 1 mm 2 0.00018 −0.0241 −0.0241 0.00018 0.00016 −0.00965 0.00016 −0.00965
3. Test Stand 3. Test Stand Used Used in in Research Research During the research research of of cross-rolling of steel balls, aa laboratory cross-rolling mill mill (Sigma, (Sigma, Barak, Barak, During the cross-rolling of steel balls, laboratory cross-rolling Poland), shown in Figure 1, was used. The aforementioned machine operates in a circuit in which Poland), shown in Figure 1, was used. The aforementioned machine operates in a circuit in which the the upper (hydraulically driven) makes a reciprocatingmotion, motion,whereas whereasthe thelower lower tool tool remains upper tooltool (hydraulically driven) makes a reciprocating remains static. Moreover, the machine is equipped with a measurement system that allowed for registering static. Moreover, the machine is equipped with a measurement system that allowed for registering the of the the pressure pressure force force of of the the hydraulic hydraulic cylinder. cylinder. The The technical technical specifications specifications of the cross-rolling cross-rolling mill mill are are presented in Table 3. presented in Table 3.
Figure 1. Laboratory stand for cross rolling—flat wedge rolling mill. Table 3. Technical specification of the cross rolling mill located in the Lublin University of Technology. Table 3. Technical specification of the cross rolling mill located in the Lublin University of Technology. Parameter Value Speed of the Parameter main cylinder’s piston Nominal force of the cylinder’s piston’s pressure Speed of the main piston Working stroke of the main cylinder Nominal force of the piston’s pressure Engine power of the main drive Working diameter stroke ofofthe Maximum themain rolledcylinder product Maximum length of Engine power ofthe therolled mainproduct drive Dimensions: lengthof × the width × height Maximum diameter rolled product Weight of the machine without the hydraulic power unit
300Value mm/s 105 300 kN mm/s 2000 mm 105 kN 55 kW 2000mm mm Ø70 320 55mm kW 6000 mm × 1350 Ø70mm mm× 2000 mm 10,500 kg
Maximum length of the rolled product 320 mm Dimensions: length × width × height 6000 mm × 1350 mm × 2000 mm The model tests of cross-rolling conducted in a test the basis Weight of the machine without were the hydraulic power unitstand created on 10,500 kg of a laboratory chain drawing machine CGD-E 2000 (Figure 2, Rodent, Pruszków, Poland). The test stand consists of The model tests of cross-rolling were conducted in a test stand created on the basis of a four main sets containing a drawing machine; a module of the model rolling mill; a measuring circuit; laboratory chain drawing machine CGD-E 2000 (Figure 2, Rodent, Pruszków, Poland). The test stand and a computer with software allowing for importing the test result data and, further on, its processing consists of four main sets containing a drawing machine; a module of the model rolling mill; a measuring circuit; and a computer with software allowing for importing the test result data and, further on, its processing via the Internet. The linear velocity of the chain in the laboratory drawing machine can be regulated, which allows for the regulation of the displacement of the upper tool ranging from 0 to 136 mm/s. The module of the rolling mill enables the use of flat tools of a maximum of 140 mm × 400 mm overall dimensions.
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Metals 2018, 8, x FORThe PEER REVIEW 5 of 14 via the Internet. linear velocity of the chain in the laboratory drawing machine can be regulated, which allows for the regulation of the displacement of the upper tool ranging from 0 to 136 mm/s. A laboratory mill (Sigma, Barak, Poland) shown 3a was of used the research of The module of therolling rolling mill enables the use of flat toolsin ofFigure a maximum 140inmm × 400 mm helical rolling of steel balls. The rolls of the machine are driven by an electric motor through belt overall dimensions. Metals 2018, toothed 8, x FOR PEER 5 ofa 14 transmission, beltREVIEW transmission, and Cardan Thein rolling mill equipped circuit A laboratory rolling mill (Sigma, Barak, Poland)joint. shown Figure 3a is was used inwith the research measuring the torque and the pressure force on the roll. The data specifications of this machine are of helical A rolling of steel balls. rollsBarak, of thePoland) machine are driven by3aan electric through laboratory rolling millThe (Sigma, shown in Figure was used inmotor the research of belt shown in Table 4. transmission, toothed beltballs. transmission, and The rolling is equipped with belt a circuit helical rolling of steel The rolls of theCardan machinejoint. are driven by an mill electric motor through The model tests of helical rolling of balls were conducted in a model skew-rolling mill (Sigma, transmission, toothed and on Cardan joint.The The data rolling mill is equipped a circuit measuring the torque andbelt thetransmission, pressure force the roll. specifications of with this machine are Barak, Poland), shown in Figure 3b. The drive unit of the machine consists of a 0.25 kW electric motor measuring shown in Table the 4. torque and the pressure force on the roll. The data specifications of this machine are that The allows forming samples withof the reaching 99 (for skew-rolling each roll). The shown infor Table 4. of helical model tests rolling ballstorque were conducted in Nm a model millnominal (Sigma, The model tests of helical rolling of balls were conducted in a model skew-rolling mill (Sigma, rotational speed of the rolls equals 12 rpm, whereas their overall dimensions are Ø150 mm × 200 mm. Barak, Poland), shown in Figure 3b. The drive unit of the machine consists of a 0.25 kW electric motor
Barak, Poland), shown in Figure 3b. The drive unit of the machine consists of a 0.25 kW electric motor
that allows for forming samples with the torque reaching 99 Nm (for each roll). The nominal rotational that allows for forming samples with the torque reaching 99 Nm (for each roll). The nominal speed of the rolls equals 12 rpm, whereas their overall dimensions are Ø150 mm × 200 mm. rotational speed of the rolls equals 12 rpm, whereas their overall dimensions are Ø150 mm × 200 mm.
Figure 2. Laboratory stand for cross rolling of model material with an emphasized rolling module. Figure 2. Laboratory stand crossrolling rollingof of model model material emphasized rolling module. Figure 2. Laboratory stand forfor cross materialwith withanan emphasized rolling module.
(a)
(a)
(b)
(b)
Figure 3. Laboratory stand for helical rolling of (a) real material—steel; (b) model material— Laboratorystand stand helical rolling real material—steel; (b)material—plasticine. model material— Figure 3.3.Laboratory forfor helical rolling of (a)of real(a)material—steel; (b) model plasticine.
plasticine.
4. Tools for Rolling Steel Balls 4. Tools for Rolling Steel Balls
4. Tools for Rolling Balls Cross rolling ofSteel 40 mm diameter usingtwo two tools, which enabled Cross rolling of 40 mm diameterballs ballswas was performed performed using tools, which enabled eveneven forming of six of these tools is balls shown schematically Figure 4. In In thetool, tool, twozones zones can be forming ofballs. six balls. of diameter these tools is shown schematically in Figure the two can Cross rolling ofOne 40One mm was performedin using two tools, which enabled even be distinguished; namely forming (635 mm long) and sizing (300 mm long). In the forming zone, the distinguished; namely forming (635 mm long) and sizing (300 mm long). In the forming zone, the billet forming of six balls. One of these tools is shown schematically in Figure 4. In the tool, two zones can billet of the initial dimensions Ø36 ×mm 220 is mm is divided parts, the volumeof of which which equals of initial dimensions mm × mm 220 intointo parts, the volume equals be the distinguished; namely Ø36 forming (635 mm long)divided and sizing (300 mm long). In the forming zone, the the the volume of the formed balls. Apart from being divided, the balls in the forming zone are volume of the formed balls. Apart from being divided, the balls in the forming zone are compressed billet of the initial dimensions Ø36 mm × 220 mm is divided into parts, the volume of which equals compressed as well, which allows for reaching the assumed diameter. In the sizing zone, the
the volume of formed the formed balls. Apart from being divided, therolling balls direction in the forming previously balls are rolling in impressions inclined from the by 2.5° to zone 3.5°. are compressed as well, which allows for reaching the assumed diameter. In the sizing zone, the previously formed balls are rolling in impressions inclined from the rolling direction by 2.5° to 3.5°.
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asMetals well,2018, which allows reaching the assumed diameter. In the sizing zone, the previously formed 8, x FOR PEERfor REVIEW 6 of 14 balls are rolling in impressions inclined from the rolling direction by 2.5◦ to 3.5◦ . The inflection of The inflection of the impressions forces thetoball rotation change and thus helps to remove the the impressions forces the ball rotation axis change andaxis thustohelps to remove the remainder of the Metals 2018, 8, x FOR PEER REVIEW 6 of 14 remainderbetween of the connectors between balls. connectors balls. The inflection of the impressions forces the ball rotation axis to change and thus helps to remove the remainder of the connectors between balls.
Figure 4. Flat tool for cross rolling of Ø40 mm diameter balls, with the chosen dimensions in mm given. Figure 4. Flat tool for cross rolling of Ø40 mm diameter balls, with the chosen dimensions in mm Figure 4. Flat tool for cross rolling of Ø40 mm diameter balls, with the chosen dimensions in mm given. 5a shows the tools used for forming steel balls, manufactured in a Computerized Figure given.
Numerical Control (CNC) machine (Feeler, Taichung, Taiwan) and heat treated to 44–46 HRC hardness Figure 5a 5ashows the used for forming formingsteel steelballs, balls, manufactured a Computerized the tools tools used for manufactured in a in Computerized accordingFigure Rockwellshows (Innovatest, Wiry, Poland). The tools were manufactured from hot work tool steel. Numerical Control (CNC) machine (Feeler, Taichung, Taiwan) and heat treated to 44–46 Numerical Control (CNC) machine (Feeler, Taichung, Taiwan) and heat treated to 44–46 HRC HRC Additionally, Figure 5b shows 1:2.5 scale model tools, 3D printed from ABS. hardness according Rockwell (Innovatest, Wiry,Poland). Poland). The tools were manufactured from hot hardness according Rockwell (Innovatest, tools were manufactured from hot In the process of rolling 57 mm diameterWiry, steel balls, twoThe identical helical rolls were used. Figure 6 work steel. Additionally,Figure Figure 5b model tools, 3D printed from from ABS. ABS. work tooltool steel. Additionally, 5b shows shows1:2.5 1:2.5scale scale model tools, 3D printed schematically shows one of these rolls. Each roll has a helically wound wedge defined by the side In the process rolling57 57mm mm diameter two identical helical rolls rolls were were used. used. FigureFigure In the process ofofrolling diametersteel steelballs, balls, two identical helical wall’s angle of inclination equal to 45◦ . The wedge cyclically (once each turn) cuts into the billet, 6 schematically shows one of these rolls. Each roll has a helically wound wedge defined by the side 6 schematically shows one of these rolls. Each roll has a helically wound wedge defined by the side closing the angle volume of the material equal to The the volume of the formed ball in the cuts impression. As a result wall’s of inclination equal to 45°. wedge cyclically (once each turn) into the billet, wall’s angle of inclination equal to 45°. The wedge cyclically (once each turn) cuts into the billet, of theclosing impactthe ofvolume the collar, thematerial height of which gradually the ball is separated fromAs thea billet. of the equal to the volume increases, of the formed ball in the impression. closing the volume of the material equal to the volume of the formed ball in the impression. As a In theresult finalofphase of theofprocess, the is sized in the impression in order to remove the occurring the impact the collar, theball height of which gradually increases, the ball is separated from result of the impact of the collar, the height of which gradually increases, the ball is separated from billet. In the final phase of the process, the ball is sized in the impression in order to remove the shapethe deviations. the occurring billet. In the final phase of the process, the ball is sized in the impression in order to remove the shape deviations. Figure 7 shows one of the helical tools, manufactured using the CNC method and heat treated to occurring shape deviations. Figure 7 shows onetool of the helical tools, manufactured CNC to method and 44–46 HRC hardness. The consists of three parts fixedusing withthe screws the roll inheat the treated rolling mill. Figure 7 shows one ofThe thetool helical tools, manufactured using the CNC method and heat treated to 44–46 HRC hardness. consists of three parts fixed with screws to the roll in the rolling A key joint is used to distribute the drive from the roll to the working segment. One of two guiding mill. A key joint is used to distribute the drive from the roll to the working segment. One of tworolling to 44–46 HRC hardness. The tool consists of three parts fixed with screws to the roll in the devices was placed next to the elements of the rolling mill. The aim of the guiding device was to keep placed next to thethe elements the the rolling Theworking aim of thesegment. guiding device mill.guiding A keydevices joint iswas used to distribute drive of from rollmill. to the One of two the material in the material working segment during theduring rolling process. In theIn case of the 1:2 1:2 scale model was todevices keep thewas in the working therolling rolling process. the scaledevice guiding placed next to thesegment elements of the mill. The aimcase of of thetheguiding mademodel of ABS, the rolls divideddivided into two These elements were with screws screws to the made ABS, were theinrolls intoparts. two parts. These elements werefixed fixed was to keep theof material the were working segment during the rolling process. In thewith case of the to 1:2 scale aluminum shafts. the aluminum shafts. model made of ABS, the rolls were divided into two parts. These elements were fixed with screws to the aluminum shafts.
(a)
(b)
Figure 5. Flat tools forming sixballs: balls: (a) (a) 40 mm balls; (b) (b) 1:2.5 scalescale model tools tools Figure 5. Flat tools forfor forming ofofsix mmdiameter diametersteel steel balls; 1:2.5 model for plasticine balls. for plasticine balls.
(a)
(b)
Figure 5. Flat tools for forming of six balls: (a) 40 mm diameter steel balls; (b) 1:2.5 scale model tools for plasticine balls.
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Figure 6. Helical roll for rolling Ø57 mm diameter balls, with the selected dimensions in mm given. Figure6.6.Helical Helicalroll rollfor forrolling rollingØ57 Ø57mm mmdiameter diameterballs, balls,with withthe theselected selecteddimensions dimensionsininmm mmgiven. given. Figure
(a) (a)
(b) (b)
Figure Figure7.7.Tools Toolsfor forhelical helicalrolling rollingofof(a)(a)5757mm mmdiameter diametersteel steelballs; balls;(b) (b)1:2 1:2scale scalemodel modeltools toolsfor for Figure balls. 7.balls. Tools for helical rolling of (a) 57 mm diameter steel balls; (b) 1:2 scale model tools for plasticine plasticine plasticine balls. Table 4. Technical specification of the skew rolling mill located in the Lublin University of Technology. Table 4. Technical specification of the skew rolling mill located in the Lublin University of Table 4. Technical specification Lublin University of Technology. Parameter of the skew rolling mill located in the Value Technology. Nominal diameter of rolls 300 mm Parameter Value Working length of roll barrel 400 mm Parameter Nominal diameter of rolls 300Value mm Distance between roll axes: maximum/minimum 350 mm/300 mm Nominal diameter of rolls 300 mm Working length of of roll barrel 400 mm Rotational speed rolls 30/15 rpm Working length of roll barrel 400 Distance between roll axes: maximum/minimum 350 mm/300 mm Engine power of the main drive 60/80mm kW Distance between rollspeed axes: maximum/minimum 350 mm/300 mm Dimensions: length × width × height 3200 mm × 1800 mm × 2100 mm Rotational of rolls 30/15 rpm Weight of the machine 17,500 kg Rotational of rolls 30/15 rpm Engine power of speed the main drive 60/80 kW
Engine power the main drive Dimensions: lengthof × width × height Dimensions: length × width × height Weight of the machine Weight of the machine
60/80 3200 mm × 1800 mmkW × 2100 mm 3200 mm17,500 × 1800kg mm × 2100 mm 17,500 kg
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5. Test Results 5. Test Results Cross rolling of 40 mm diameter balls was performed using Ø36 mm × 220 mm C45 grade steel Cross rolling of 40 mm diameter balls was performed using Ø36 mm × 220 mm C45 grade steel billets. These billets were heated up to 1000 °C in an electric chamber furnace and placed on a lower, billets. These billets were heated up to 1000 ◦ C in an electric chamber furnace and placed on a lower, motionless/static tool. After putting the upper tool in motion, the material rolled on the lower tool motionless/static tool. After putting the upper tool in motion, the material rolled on the lower tool and formed balls rolled down to the container (Figure 8). and formed balls rolled down to the container (Figure 8). In the case of cross-rolling of the 1:2:5 scale model plasticine balls, the dimensions of the billet In the case of cross-rolling of the 1:2:5 scale model plasticine balls, the dimensions of the billet were equal to Ø14.5 mm × 90 mm. The method of manufacturing aforementioned billets was that of were equal to Ø14.5 mm × 90 mm. The method of manufacturing aforementioned billets was that of direct extrusion. They were also cooled for 24 h at 5 °C prior to rolling. The model rolling process was direct extrusion. They were also cooled for 24 h at 5 ◦ C prior to rolling. The model rolling process was conducted similarly to the real process. It was assumed that the displacement speed of the upper tool conducted similarly to the real process. It was assumed that the displacement speed of the upper tool was 122 mm/s (in the process of forming steel balls, the displacement speed was equal to 300 mm/s). was 122 mm/s (in the process of forming steel balls, the displacement speed was equal to 300 mm/s). The tools were lubricated with teflon oil. The tools were lubricated with teflon oil.
(a)
(b)
Cross rolling of six balls in (a) the model rolling mill; (b) a flat wedge rolling Figure 8. Cross rolling mill. mill.
The in the The balls balls manufactured manufactured in the process process of of cross-rolling cross-rolling are are presented presented in in Figure Figure 9. 9. An An analysis analysis of of the shape of balls showed that the side balls contain a ring-shaped underfill, most likely the result of the shape of balls showed that the side balls contain a ring-shaped underfill, most likely the result of excessive waste. This This defect defect occurs occurs in in both both steel steel and and plasticine plasticine balls. balls. Moreover, Moreover, excessive material material flow flow into into side side waste. the remainders of the connectors could be noticed in some of the steel balls. This defect occurred most the remainders of the connectors could be noticed in some of the steel balls. This defect occurred most frequently in balls made of black plasticine. frequently in balls made of black plasticine. As as the the manufacturing manufacturing accuracy As far far as accuracy is is concerned, concerned, it it is is to to be be stated stated that that the the diameter diameter of of the the steel steel balls was Ø39.7 mm ± 0.6 mm, that of the balls made of white plasticine was Ø16.4 mm ± 0.4 mm, mm, balls was Ø39.7 mm ± 0.6 mm, that of the balls made of white plasticine was Ø16.4 mm ± 0.4 and and that that of of the the balls balls made made of of black black plasticine plasticine was was Ø16.3 Ø16.3 mm mm± ± 0.3 0.3 mm. mm. As As the the producing producing tolerance tolerance for grinding medium equals ± 3 mm, it is to be noted that the steel balls manufactured using for grinding medium equals ±3 mm, it is to be noted that the steel balls manufactured using the crossthe cross-rolling technique meet this requirement and can thus be manufactured in such a way. rolling technique meet this requirement and can thus be manufactured in such a way. A comparison A of the shapes and dimensions of steelballs and shows plasticine ballslevel shows a high leveland of of comparison the shapes and dimensions of steel and plasticine a high of compliance compliance and validates the use of physical modelling in the analysis of the cross-rolling process. validates the use of physical modelling in the analysis of the cross-rolling process. During the process processofofcross-rolling, cross-rolling,the the displacement force of the upper registered. During the displacement force of the upper tooltool was was registered. The The attained parameters are presented in Figure 10.analysis An analysis of these parameters in attained parameters are presented in Figure 10. An of these parameters showsshows that inthat terms terms of quality, the force parameters concerning the forming of white and black plasticine balls are of quality, the force parameters concerning the forming of white and black plasticine balls are identical, plasticine are higher. The force parameters parameters for identical, although although the the forces forces required required to to deform deform black black plasticine are higher. The force for C45 grade steel, however, differ somewhat from the ones registered in the model testing. During the C45 grade steel, however, differ somewhat from the ones registered in the model testing. During the rolling forming zone, which can partially be be justified by rolling of of the thesteel steelballs, balls,the theforce forceincreases increasesfaster fasterininthe the forming zone, which can partially justified the cooling of the material. This process leads to the increase in flow stress. TheThe opposite effect cancan be by the cooling of the material. This process leads to the increase in flow stress. opposite effect noticed in model rolling (the temperature of plasticine increases and the flow stress decreases). Further be noticed in model rolling (the temperature of plasticine increases and the flow stress decreases). on, the force reaches maximal in the moment balls separation and decreases Further on, the forceits reaches its value maximal value in theofmoment of balls separation anddrastically decreases only to maintain decreasing (for the model increasing (for steel) trend in the sizing drastically only tothe maintain the decreasing (for material) the modelormaterial) or increasing (for steel) trend in zone. The reason for such a discrepancy is most likely the aforementioned temperature difference of the sizing zone. The reason for such a discrepancy is most likely the aforementioned temperature the formedofmaterial. difference the formed material.
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(a) (a)
(b) (b)
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100 100 90 90 80 80 70 70 60 60 50 50 40 40 30 30 20 20 10 10 0 0
C45 steel C45 steel
100 100 90 90 80 80 70 70 60 60 50 50 40 40 30 30 20 20 10 10 0 0
Black plasticine Black plasticine
White plasticine White plasticine
0 0
1 1
2 2
3 3
Time, s Time, s
4 4
5 5
Formingload loadfor forsteel, steel,kN kN Forming
Formingload loadfor forplasticine, plasticine,NN Forming
Figure 9. Balls manufactured duringthe the research from top to to bottom) white plasticine (a), (a), Figure 9. Balls manufactured during from(from (fromthe the top bottom) white plasticine Figure 9. Balls manufactured during theresearch research from (from the top to bottom) white plasticine (a), black plasticine (b), and C45 grade steel (c). blackblack plasticine (b), (b), andand C45C45 grade steel plasticine grade steel(c). (c).
6 6
Figure 10. Distribution forcemoving moving the wedge tool, during cross rolling of balls. Figure 10. Distribution of of thethe force tool,registered registered during cross rolling of balls. Figure 10. Distribution of the force movingthe the wedge wedge tool, registered during cross rolling of balls.
a quantitative comparison,maximum maximum force, Fmax , was AsAs far as rolling of steel balls balls For aFor quantitative comparison, waschosen. chosen. as rolling of steel max For a quantitative comparison, maximumforce, force, Fmax , ,was chosen. As far far as rolling of steel balls ◦ from a 1000 °C billet is concerned, the maximum force equaled 94.37 kN. In order to estimate the Fmax Fmax from from a 1000 C billet is concerned, the 94.37kN. kN.InIn order to estimate a 1000 °C billet is concerned, themaximum maximumforce force equaled equaled 94.37 order to estimate the Fthe max value, the following relation was applied on the basis of a physical simulation: value,value, the following relation was applied physicalsimulation: simulation: the following relation was appliedon onthe thebasis basis of aa physical 𝐹 𝐹
=𝜆𝐹 =𝜆𝐹
𝑠 𝑠
(3) (3)
Fmax = λand F 0 C45 s2 grade steel flow stress; F’max—maximum where λ—the similarity factor of model material where λ—the similarity factor of model material andmax C45 grade steel flow stress; F’max—maximum force from the model tests, N; s—scale of tools. force from the model tests, N; s—scale of tools.
(3)
where λ—the similarity factor ofsimilarity model material and C45plasticine grade steel stress;steel F’ at —maximum In order to determine the factor λ between andflow C45 grade 1000 °C, In order to determine the similarity factor λ between plasticine and C45 grade steelmax at 1000 °C, following relation was applied: forcethe from the model tests, N; s—scale of tools. the following relation was applied: In order to determine the similarity factor λ between plasticine and C45 grade steel at 1000 ◦ C, the following relation was applied: R1 σF steel dε λ = R1 0 (4) σ dε F plasticine 0
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𝜆=
𝜎
𝑑𝜀 𝑑𝜀
𝜎
10 of (4)14
where to to calculate calculate the the flow flow stress, stress, Equations Equations (1) (1) and and (2) (2) were were applied. applied. The The obtained obtained results results are are shown shown where in Table Table 5. 5. in Table maximum forces occurring in cross rolling of 40 of mm balls, based Table5.5.Extrapolation Extrapolationofofthe the maximum forces occurring in cross rolling 40diameter mm diameter balls, on the on testthe results of the model process. based test results of the model process.
Materials Materials
λ λ
ss
White plasticine215.7 215.7 2.5 2.5 White plasticine Black plasticine Black plasticine 171.8 171.8 2.5 2.5
F’ Fmax F’max Fmax max 63.44 kNkN 63.44N N 85.52 85.52 89.66N N 96.27 96.27 89.66 kNkN
The obtained the value of of maximum force registered in the The obtained results resultsremain remainhighly highlycompliant compliantwith with the value maximum force registered in real process. Higher compliance, however, was achieved for black plasticine. In this case, force the real process. Higher compliance, however, was achieved for black plasticine. In this case, force overestimation equaled equaled 2%, overestimation 2%, whereas whereas the the underestimation underestimation of of force force for for white white plasticine plasticine reached reached 9.4%. 9.4%. Thus, it is to be stated that physical modelling with plasticine as the model material can helpful Thus, it is to be stated that physical modelling with plasticine as the model material can prove prove helpful in estimating estimating the the forces forces occurring occurring in in the the process process of of cross cross rolling. rolling. in In the mm diameter balls were formed using C60 C60 steelsteel grade, Ø55 In the case case of ofhelical helicalrolling, rolling,Ø57 Ø57 mm diameter balls were formed using grade, mm × 600 mm billets. This time, the material was heated to 1050 °C and the rolls were inclined at ◦ Ø55 mm × 600 mm billets. This time, the material was heated to 1050 C and the rolls were inclinedthe at angle of 4° in relation to the centerline of the billet. During the rolling process, the tool was cutting ◦ the angle of 4 in relation to the centerline of the billet. During the rolling process, the tool was cutting into the thebillet billet(once (once each turn) creating a narrowing of a gradually increasing depth. Such into each turn) andand creating a narrowing of a gradually increasing depth. Such forming forming caused the material to lose its structural integrity and thus resulted in separation of balls, caused the material to lose its structural integrity and thus resulted in separation of balls, presented in presented 11.phase In theoffinal of the balland was sized and rotated around various Figure 11. in In Figure the final the phase process, the process, ball was the sized rotated around various axes. axes.
(a)
(b) Figure 11. The rolled item seen during helical rolling of steel (a) and plasticine balls (b). Figure 11. The rolled item seen during helical rolling of steel (a) and plasticine balls (b).
The process of helical rolling of the 1:2 scale model material was similar to the real process. The process of helical rolling of the 1:2 scale model material was similar to the real process. The The only difference was lubricating the surface of the tools with teflon oil before rolling. The process only difference was lubricating the surface of the tools with teflon oil before rolling. The process of of manufacturing the Ø27.5 mm × 200 mm billets was similar to the previously described process of manufacturing the Ø27.5 mm × 200 mm billets was similar to the previously described process of cross rolling. cross rolling. Figure 12 shows the helically rolled balls manufactured both from the model material and C60 Figure 12 shows the helically rolled balls manufactured both from the model material and C60 steel grade. The shape of the balls was perfect and they were essentially free of surface defects. On the steel grade. The shape of the balls was perfect and they were essentially free of surface defects. On basis of the measurements taken, it was stated that the diameter of steel balls and balls made of the the basis of the measurements taken, it was stated that the diameter of steel balls and balls made of model material was equal to Ø57.4 mm ± 0.5 mm and Ø28.4 mm ± 0.3 mm, respectively. The obtained the model material was equal to Ø57.4 mm ± 0.5 mm and Ø28.4 mm ± 0.3 mm, respectively. The manufacturing accuracy meets the requirements of the balls for mills. obtained manufacturing accuracy meets the requirements of the balls for mills.
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12. Helically rolled balls of (a) plasticine with Ø28.5diameter; mm diameter; (b) steel with Figure Figure 12. 12. Helically Helically rolled rolled balls balls of of (a) (a) plasticine plasticine with with Ø28.5 Ø28.5 mm mm diameter; (b) (b) steel steel with with Ø57 Ø57 mm mm Ø57 mm diameter. diameter. diameter.
During helicalrolling rolling ofballs, balls, thetorque torque ofone one roll was registered. The obtained parameters During During helical helical rolling of of balls, the the torque of of one roll roll was was registered. registered. The The obtained obtained parameters parameters for for for the model material are presented in Figure 13a, whereas those for C60 grade steel are shown in the the model model material material are are presented presented in in Figure Figure 13a, 13a, whereas whereas those those for for C60 C60 grade grade steel steel are are shown shown in in Figure Figure Figure 13b. The analysis of these parameters showed a highcompliance. level of compliance. In all ofthe the cases, 13b. 13b. The The analysis analysis of of these these parameters parameters showed showed aa high high level level of of compliance. In In all all of of the the cases, cases, the torque torque the torque changed cyclically, which was caused by the periodical (once each turn) cutting of the tools changed cyclically, which was caused by the periodical (once each turn) cutting of the tools into changed cyclically, which was caused by the periodical (once each turn) cutting of the tools into the the into the formed material. formed formed material. material. For a quantitative comparison, comparison, the maximum maximum torque was was selected. For For C60 grade grade steel balls balls of For For aa quantitative quantitative comparison, the the maximum torque torque was selected. selected. For C60 C60 grade steel steel balls of of Ø57 mm diameter, the torque was equal to M = 7076 Nm (Figure 13b). In order to estimate the max = 7076 Nm (Figure 13b). In order to estimate theM Ø57 Mmax max Ø57 mm mm diameter, diameter, the the torque torque was was equal equal to to M Mmax max = 7076 Nm (Figure 13b). In order to estimate the Mmax value, the following equation was applied: value, value, the the following following equation equation was was applied: applied: 𝑀 = 𝑠𝑠 (5) 𝑀 = λλ 𝑀 𝑀 (5) M = λ M 0 s3 (5) max
max
—maximum torque during the rolling of the model material, Nm; λ and s—as in Equation where max—maximum torque during the rolling of the model material, Nm; λ and s—as in Equation where M′ M′max 0 where M —maximum torque during the rolling of the model material, Nm; λ and s—as in (5), respectively. max (5), respectively. Equation (5), respectively. The factor The similarity similarity factor λ λ was was calculated calculated on on the the basis basis of of the the relation relation (6), (6), assuming assuming that that the the flow flow The similarity factor λ was calculated on the basis of relation (6), assuming that flow stress σ F is defined by Equations (1), (2) and (4). The scale the tools s was assumed to be 2. Because stress σF is defined by Equations (1), (2) and (4). The scale of the tools s was assumed to be 2. the Because stress σ is defined by Equations (1), (2) and (4). The scale of the tools s was assumed to be 2. Because the shaping of steel balls was a rather long process (over 25 s), the estimations were made for F the shaping of steel balls was a rather long process (over 25 s), the estimations were made for two two the shaping of steel balls was a rather long process (over 25 s), the estimations were made for temperatures, namely 1050 °C (temperature of the billet) and 1000 °C (assumes the 50 °C drop in the temperatures, namely 1050 °C (temperature of the billet) and 1000 °C (assumes the 50 °C drop intwo the ◦ C (temperature ◦presented ◦ C drop in the temperatures, namely 1050 billet) and 1000 C (assumes the 50 temperature during the rolling). The results of the calculations are in Table 6. temperature during the rolling). The results of the calculations are presented in Table 6. temperature during the rolling). The results of the calculations are presented in Table 6. 6 6 5 5
6000 6000 5000 5000
4 4
Torque, Torque,Nm Nm
Torque, Torque,Nm Nm
7000 7000
Black Black plasticine plasticine
3 3 2 2 White plasticine White plasticine
1 1
4000 4000 3000 3000 2000 2000 1000 1000
0 0
0 0
0 0
5 5
10 10
15 15
20 20
25 25
30 30
Time, Time, ss
(a) (a)
35 35
40 40
45 45
50 50
0 0
5 5
10 10
15 15
Time, Time, ss
20 20
25 25
30 30
(b) (b)
Figure 13. Torque the roll registered during (a) rolling of from material; (b) Figure 13. 13. Torque Torqueofof ofthe theroll roll registered during (a) helical helical rolling of balls balls from model model material; (b) registered during (a) helical rolling of balls from model material; (b) helical helical rolling of C60 grade steel balls of 57 mm diameter. helical of C60steel grade steel of 57 mm diameter. rolling rolling of C60 grade balls ofballs 57 mm diameter.
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Table 6. Extrapolation of the maximum moments in helical rolling of 57 mm diameter balls, based on test results of the model process. λ
s
M 0 max
Mmax
White plasticine
◦C
1050 1000 ◦ C
180.18 212.24
2 2
3.80 Nm 3.68 Nm
5477 Nm 6452 Nm
Black plasticine
1050 ◦ C 1000 ◦ C
143.48 169.01
2 2
5.53 Nm 5.53 Nm
6347 Nm 7477 Nm
Materials
T
The comparison of the Mmax values obtained in the process of rolling steel balls (7076 Nm) and the estimations based on the model tests (Table 6) shows a high compliance. Better results, however, were achieved for black plasticine. In this case, the moment value of the real process lay within the range defined by the calculations made for 1050 ◦ C and 1000 ◦ C temperatures. Thus, the validity of determining the torque in the process of rolling steel balls based on the model tests using plasticine was confirmed. 6. Conclusions On the basis of the tests conducted, the following conclusions were drawn:
•
•
• •
Using plasticine as the model material allows for effective research on the kinematics of material flow in the processes of cross rolling and helical rolling of balls, as well as to extrapolate the manufacturing accuracy of the product. An indubitable advantage of physical modelling (compared with FEM-based numerical analysis) is the accuracy of illustrating the moment of material division that occurs in the process of ball rolling. Basing on the test results allows for a highly accurate extrapolation of the following force parameters in the ball rolling process: forming force or the torque of the roll. Plasticine-based physical modelling can prove beneficial in analyses of cross rolling and helical rolling of balls, and may thus be used to optimize their manufacturing techniques.
Author Contributions: The research was conceived by Z.P., J.T., Ł.W. and T.B. The methodology was planned by Z.P. and J.T. Experimental tests of steel rolling were performed by J.T. and T.B. Experimental tests of plasticine rolling was performed by Ł.W. The manuscript was written by Z.P. with support from T.B. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest.
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