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Experimental and numerical analysis of helical-wedge rolling process for producing steel balls
International Journal of Machine Tools & Manufacture 67 (2013) 1–7
Contents lists available at SciVerse ScienceDirect
International Journal of Machine Tools & Manufacture journal homepage: www.elsevier.com/locate/ijmactool
Experimental and numerical analysis of helical-wedge rolling process for producing steel balls Zbigniew Pater a,n, Janusz Tomczak a, Jaros"aw Bartnicki a, Michael R. Lovell b, Pradeep L. Menezes b a b
Lublin University of Technology, Nadbystrzycka 36, Lublin 20-618, Poland Department of Industrial Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA
a r t i c l e i n f o
abstract
Article history: Received 9 May 2012 Received in revised form 21 December 2012 Accepted 21 December 2012 Available online 31 December 2012
The helical-wedge rolling (HWR) process is a new metal forming technique for producing spherical parts of various dimensions. In this paper, the overall details of the HWR process are described and the important process parameters that control the HWR process are systematically discussed. A new experimental method, developed under laboratory conditions, showed that the HWR process can produce spherical steel parts (balls) with high manufacturing quality. Numerical simulations of the HWR process were carried out using a commercially available FEM software (Simufact) to show the stress, strain, and temperature distributions in the rolled balls. In addition, the variation of forces and rolling moments during the process are analyzed. Based on the experimental and numerical investigations, the HWR technique has been found to be a viable process for enhancing the quality and productivity of formed spherical products. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Helical wedge rolling FEM Steel balls
1. Introduction Steel balls are employed on a mass scale as grinding media in ball mills. They are used for grinding metal ores, coal, and used-up molding sands through an abrasive wear process. The effectiveness of the grinding media is dictated by the surface-to-weight ratio of the balls. At present, steel balls used for grinding media are mainly produced by casting, die forging, and an efficient helical rolling process. In helical rolling, two skewly positioned rolls with helical grooves (roll passes) on their circumference rotate in the same direction to form steel balls [1,2]. The helical rolling process was first implemented in early 1950s in the USSR [3]. More recently, investigations have been conducted to design roll passes with variable pitch and depth [4]. In Bourkine et al.’s investigation [3], it was found that the following three conditions need to be satisfied in order to obtain semi-finished steel balls with optimum shape: 1. The volume of the material confined in the roll pass should be constant throughout the forming process. 2. The change in the profile and dimensions of the roll pass prongs should entail elongation in the semi-finished product which is confined in the roll pass, and 3. Confining the metal in the roll pass should be performed on relatively short sections of the roll to prevent cracking that occurs in the axial zone of the semi-finished product.
n
Corresponding author. Tel.: þ048815384242; fax: þ 048815384241. E-mail address: [email protected] (Z. Pater).
0890-6955/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijmachtools.2012.12.006
Taking the above three points into consideration, a methodology for designing roll passes used in the skew rolling of semifinished balls has been developed as documented in the literature. [5–7]. The helical rolling process of steel balls is difficult to analyze theoretically due to its complexity. Advancements in the process have primarily been made using trial and error experimental techniques. Recently, Shi and Wang [8] numerically modeled the skew rolling process and determined a number of simplifications for the production of steel parts. In the present investigation, new tools for producing spherical parts with helical rolling have been designed. The roll passes of the tools are constructed using an innovative technology that utilizes a helical roller wedge which produces necking between adjacent steel balls. Under such conditions, it is possible to take advantage of knowledge that pertains to better-known processes, such as cross-wedge rolling [9–10].
2. Design of the helical-wedge rolling process The design of the HWR process used for producing spherical parts is shown in Fig. 1. It is assumed that the parts are formed between two rolls as the roll passes. The axes of the rolls are turned relative to the billet axis by an angle, ‘g’’. The value of ‘g’’ should be taken from the equality condition of a projection of the roll circumferential velocity in the axial direction and of the billet pitch per one rotation. This ensures that the volume of the material confined in the roll pass will be the same as the volume of the ball being formed. During the rolling process, the semifinished product is held in the appropriate position using guiding
2
Z. Pater et al. / International Journal of Machine Tools & Manufacture 67 (2013) 1–7
blades (see Fig. 1). The surface of the semi-finished product corresponds to the surface profile of the guiding blades. This design is currently used in the helical rolling process for producing steel balls. The rolls (with the nominal diameter D) used in the HWR process are comprised of two basic parts: (a) the input (conical) part and (b) the forming (cylindrical) part where the wedge is wound up on a barrel of the roll. The process is used to roll semifinished balls that are either connected to one another by connectors (the situation is shown in Fig. 1) or are separated with an additional cutting coil. The role of the input part is to size the billet diameter, which is significant if the billets with low production accuracy are used. The key parameters of the HWR process include wedge angles (the forming angle a and the spreading angle b) as well as the cross-sectional reduction Rp. The Rp can be determined using the following formula: Rp ¼ 100%
S0 S , S0
ð1Þ
Billet
Guide 2 Guide 1
d0
a=D
Roll 1
2β
Roll 2
where S0 denotes the cross-sectional area of the billet and S denotes the cross-sectional area of the necking connection of the balls. Based on previous analysis [11], it was recommended that the tools with ‘a’ of 451 and ‘b’ of 21 should be used in the HWR process. In addition, the maximum cross-sectional reduction Rp obtained during one rotation of the rolls should not be greater than 85%.
3. Experimental details 3.1. Experimental tests Experimental tests of the HWR process were conducted using a two-roll skew rolling mill available at the Akademia Gorniczo Hutnicza (AGH) University of Science and Technology in Krakow, Poland. Due to the overall dimensions of the rolling mill, it was determined that the balls with a diameter of 33 mm would be formed during experiments. Fig. 2(a) depicts the rolls with helical wedges which were used in the experimental trials. Table 1 shows the design parameters of the rolls, all of which were chosen in accordance with Fig. 1. To ensure process stability, two guiding blades, as shown in Fig. 2(b), were additionally incorporated. The guiding blades were attached to the body of the rolling mill by means of a connector in the form of a dovetail. The position of the tools in the rolling mill is illustrated in Fig. 3, where semi-finished balls are shown departing from the mill. The billets for the rolling were made of 100Cr6 steel rods and were 350 mm in length and had a constant diameter of 33 mm. They were heated in an electric furnace to a temperature of 1150 1C for approximately 20 min. The billets were then inserted into the working space of the rolling mill. Once they were contacted by the rollers, they were automatically pulled in between the rollers, and formed into balls, which were then ejected from the rolling mill as shown in Fig. 3. 3.2. Finite element modeling
α γ γ
L Fig. 1. Design of the HWR process for producing balls.
Finite element modeling of HWR process was performed using FEM-based Simufact software. A geometrical model of the analyzed process is illustrated in Fig. 4. As illustrated in the figure, the model comprises of two identical helical rolls, two guides, and one billet in the form of a cylindrical rod. In the numerical simulation, a rigid plastic material model was employed. For the billet, material properties of 100Cr6 steel were assigned. The material model and parameters were obtained from the database library of the Simufact software. The plastic material behavior of the billet is specified with a material flow stress function
Fig. 2. Photograph of the (a) rolls with helical wedges and (b) guiding blades that were used in experimental tests of the HWR process for producing steel balls.
Z. Pater et al. / International Journal of Machine Tools & Manufacture 67 (2013) 1–7
3
Table 1 Design parameters of the rolls. Parameters
Values
Forming angle (a) Spreading angle (b) Feed angle (g) Nominal roll diameter (D) Roll length (L)
451 21 31 215 mm 205 mm
Fig. 3. Photograph shows the arrangement of tools in HWR process.
Fig. 5. Flow curves of 100Cr6 steel at strain rates of (a) 1.5 s 1 and (b) 100 s 1.
Fig. 4. Simufact designed geometrical model of HWR process.
or flow stress data. The flow stress equation is dependent on the strain, strain rate, and temperature. Fig. 5(a) and (b) present the flow curves of 100Cr6 steel material, which depicts the variation of flow stress as a function of strain for different billet temperatures, at strain rates of 1.5 s 1 and 100 s 1, respectively. The operating parameters assumed in the calculations corresponded to the parameters used in the rolling experimental tests. More specifically, the material before the forming process was heated over its whole volume to a
temperature of 1150 1C and the tools were maintained at a constant temperature of 150 1C. The rolls were turned relative to the billet axis by an angle, g, of 31. The rolls were rotated in the same direction at a velocity of 60 rotations per minute. The friction on the material-tool contact surface has the boundary value determined by the friction factor m that was set equal to 1. The material-tool heat exchange coefficient was set to 10 kW/m2 K. It was assumed in the process simulation that the rolls would make at least four rotations, as this number of rotations is sufficient to form the ball. Each roll rotation was modeled with 1000 calculation time steps.
4. Results and discussion 4.1. Experimental results The experimental results showed that the balls formed with the HWR process could be accurately separated. The photograph
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Z. Pater et al. / International Journal of Machine Tools & Manufacture 67 (2013) 1–7
Fig. 8. Numerical simulation of HWR process showing necking of steel balls.
45 40 Fig. 6. Photograph of the steel ball obtained in the HWR process. In the figure, the diameter of the steel ball was 33 mm.
Load,kN
35 30 25 20 15
FEM
10
Experiment
5 1.8
2
2.2
2.4 2.6 Time,s
2.8
3
3.2
Fig. 9. Comparison between the experimental and simulation forces obtained in the HWR process of producing steel balls during one rotation of rolls.
Fig. 7. Photograph recorded using the infrared camera shows the temperature distribution during the HWR process.
of the ball produced in the HWR process is shown in Fig. 6. The obtained balls had the desired spherical shape with a diameter of 33 mm; the overall dimensional accuracy of the balls was approximately7500 mm. The surface of the balls was free from burrs and remnants of the necking process. The only defect encountered in the process was scratches on the surface of the balls. This is most likely due to the very small rounding radii of the roll pass edges. During the rolling experiments, it was observed that the material did not undergo significant chilling despite a relatively long forming time (which is approximately 20 s). Fig. 7 shows the photograph of the temperature distributions, which is recorded using infrared camera during the experimental tests. This photograph verifies that the temperature of billet and rolls during the process of producing the steel balls is still above 1000 1C. The reason for this stems from the fact that the heat losses (resulting from the heat being carried away by the tools) are compensated by the heat being generated when the deformation work changes into friction work. The amount of work done is depending on the load parameters. The high temperature also leads to decrease of risk of the cracks within the work material. 4.2. FEM results In the simulation, the rolls were designed with the cutting tools for the purpose of separating the steel balls. It was observed
that the numerical simulation was automatically stopped once the material is being formed and separated into two parts. This step was encountered at the beginning of the fourth rotation of the rolls, as shown in Fig. 8. Hence, in the simulation, a complete separation of steel ball could not be obtained. Minor changes in the shape of the tools were made to carry out the numerical analysis to the next level. The force affecting the roll, calculated during the simulation, was then used to verify the designed FEM model of the HWR process. Fig. 9 presents a comparison between the forces that were measured in the experiments and calculated in the simulation during one rotation of the rolls. As shown in the figure, the force was varied during the forming process and reached its maximum value after approximately 0.4 rotation of the roll when the wedge drove the material into its maximum depth. Then, the force decreased and reached its initial value. A comparison between the distributions and values of the measured and calculated forces demonstrates that the forces are compatible in terms of both quality and quantity. This validates the use of numerical modeling of the HWR process as a means for optimizing the HWR process parameters. The analysis of the HWR process consisted of rolling the spherical parts without incorporating cutting tools for ball separation. Hence, at the initial stage, the analysis was focused on rolling balls with a ball diameter (d0) of 50 mm by means of rolls with the diameter D equal to 300 mm. It was assumed that the semi-finished balls were connected to one another by means of cylindrical connectors whose diameter equals to 0.2d0 (i.e., 10 mm). Fig. 10 presents the variations in the contact regions between the upper roll and the materials that undergo forming. It can be observed that a necking with the target diameter, 0.2d0, is
Z. Pater et al. / International Journal of Machine Tools & Manufacture 67 (2013) 1–7
5
Fig. 10. Material-roll contact region in HWR process.
Fig. 12. Distribution of principal stresses (in MPa) during the HWR process of balls with diameter of 50 mm at t¼ 5 s.
Fig. 11. Effective strain distribution during the HWR process of balls with diameter of 50 mm at t ¼5 s.
completed after three rotations of the rolls. During the first halfturn of the rolls, a ring-shaped groove, in the shape of the letter ‘V’ is formed. Subsequently, during the remaining half-turn, this groove is transformed into a groove with concave walls with a depth equal to a diameter of 0.5d0. During the second rotation of the rolls, the shape of the obtained groove does not change significantly; however, deeper necking is being created as the rolls proceed. In this respect, a ball starts to form from the rest of the billet by means of necking with a diameter equal to a half of the billet diameter. During the third roll turn, the value of the connector diameter gets reduced to the assumed value of 0.2d0. As the semi-finished product enters between the rolls, a considerable decrease in width of the contact region can be formed as shown in Fig. 10. This occurs when material undergoes significant ovalisation during the forming process which is the characteristic of cross and helical rolling processes. Such ovalisation is effectively removed after three rotations of the rolls. During the helical rolling of steel balls, the material is intensively worked over its entire volume, which is demonstrated by the distribution of effective strain as shown in Fig. 11. The highest strain occurs in the connectors between the balls, which is due to the largest reduction of the cross section of the billet. The strain reaches moderate values inside the steel ball as well as at some other places where the cross-sectional reduction is low. This means that the dominant direction of material flow is circumferential caused by the friction forces, as a result of which considerable redundant strains occur in the product during the HWR process. The state of stress in the semi-finished material during the HWR process was also analyzed. Fig. 12 illustrates principal stress distributions in the longitudinal direction of the product after five roll turns. As shown in the figure, the greatest variations in
Fig. 13. The distribution of temperature (in 1C) during the HWR process of steel balls with diameter of 50 mm (at t ¼5 s).
stresses were registered during the first three turns of the rolls when the connector is being formed. At this point, the material at the surface layers is subject to tri-axial compression due to the roll thrust. Conversely, in the axial (central) areas, stretching stresses occur. It is also possible to distinguish areas where a state of tri-axial stretching occurs in the material, such stresses may negatively affect the material cohesion. Nevertheless, it must be emphasized that the stretching stresses in the analyzed case reach the values that are lower than the materials’ ultimate tensile strength values. As regards to the separated balls, they are characterized by a nearly homogenous state of stress, the components of which take insignificant values. Fig. 13 reveals the temperature distribution in the semifinished balls after five turns of the rolls. As expected, the lowest temperature can be observed on the surface of the formed balls where its value is about 50–100 1C lower than the temperature of the billet. A similar temperature difference was also observed using infrared camera in the experimental tests. This result demonstrates that the heat is carried away from the deforming material to the tools which is maintained at a lower temperature. At the same time, it can be observed during the rolling process that the material temperature in the connectors between the balls increases, which is caused by the generation of heat owing to deformation and friction. The application of the FEM allows a systematic analysis of forces during the HWR process. Figs. 14 and 15 show the variation
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Z. Pater et al. / International Journal of Machine Tools & Manufacture 67 (2013) 1–7
140
onRoll 1 onRoll 2 onGuide 1 onGuide 2
120
Load,kN
100 80 60 40 20 0 0
1
2
3
4
5
Time,s Fig. 14. Forces affecting tools during the HWR process of steel balls with diameter of 50 mm. The variations is shown in accordance with Fig. 1.
4500
Roll 1 4000
Roll 2
Tuningmoment,Nm
3500 3000 2500 2000 1500 1000 500 0 0
1
2
3
4
5
Time,s Fig. 15. Turning moment distribution in the HWR process of balls with diameter of 50 mm.
in the forces and moments during the HWR process. It should be noted that the tools indicated in these figures are in accordance with Fig. 1. It is observed that the forces and moments vary in the HWR process in the form of oscillations which are typical during a metal forming process. Additionally, it can be observed that the roll load is almost identical, and the small differences have been observed due to a variation in the location of the billet between the guides during the rolling process. In accordance with the guidelines presented in the literature [4], the helical rolling processes of the steel balls are most effective when the roll diameter is approximately six times larger than the ball diameter. The feed angle g is then approximately 31. This approach, however, results in the reduction of the quantity of the balls which can be produced in a particular rolling mill. A solution to this problem could be to employ helical rolling using multi-coil rolls in which the multiplication factor of ball diameters produced within one rotation of the rolls is equal to the diameter of balls produced in the process of standard helical rolling. Fig. 16 illustrates three models of the HWR process for producing balls with different dimensions and quantities that would be produced per one turn of the rolls. For example, the model shown in Fig. 16(a) can be used to produce 1 ball with a diameter of 60 mm, whereas model Fig. 16(b) can be used to produce 2 balls with a diameter of 30 mm, and finally the model Fig. 16(c) can be used to produce 3 balls with a diameter of 20 mm. A key characteristic of all the rolls shown in Fig. 16 is that they all have the identical nominal diameter D of 300 mm. Additionally, the rolls used to form the balls of 30 mm in diameter have two-coil roll passes, while the rolls which form the balls of 20 mm in diameter have three-coil roll passes. In the figure, the effective strain distribution is presented for the comparison. As expected, it is shown that the highest amount of strain was observed for the balls having the smallest diameter, owing to largest reduction in the cross sectional area. As mentioned previously, a HWR process with multi-coil rolls could be beneficial for optimizing spherical part production. For this purpose, numerical simulations were performed to analyze the feasibility of such a process. Fig. 17 shows the distribution of effective strain when semi-finished balls are formed in a multiwedge helical process after 4 turns of the forming rolls. In the
Fig. 16. HWR processes when (a) 1 ball with diameter of 60 mm, (b) 2 balls with diameter of 30 mm, and (c) 3 balls with diameter of 20 mm are formed. The effective strain distribution is also presented in the figure.
Z. Pater et al. / International Journal of Machine Tools & Manufacture 67 (2013) 1–7
7
of the rolls because of the smaller volume of the material which undergoes forming during one rotation of the rolls.
5. Summary and conclusions The conducted experiments and numerical analyses have led to the following conclusions:
The HWR process can be successfully employed to form spherical parts, such as steel balls used for grinding media.
Steel balls produced using the HWR process are deformed over Fig. 17. Distribution of effective strain when semi-finished balls are formed in multi-wedge helical rolling after 4 roll turns.
6000
1 x 60 mm ball
Turning moment, Nm
2 x 30 mm balls
5000
3 x 20 mm balls
their whole volume owing to an intensive material flow in the circumferential (tangential) direction. During the rolling process, unfavorable stretching stresses would occur in the axial zone, which could lead to material cracking. The forces and turning moments affecting the helical rolls vary oscillatory, which is typical variation of the analyzed HWR process. The application of helical rolling for producing steel balls using multi-coil rolls makes the machines employed in the HWR process more versatile.
4000
Acknowledgements 3000
This research work was financed by funds from the Ministry of Science and Higher Education of Poland over years 2009–2012, as a project for development no. 0457/R/T02/2009/06.
2000 1000
References
0 0
1
2
3
4
5
Time, s Fig. 18. Turning moment in helical rolling processes performed in specified configurations.
simulation, the parameters were identical to the ones that were incorporated in the previous HWR process for a ball with a diameter of 50 mm. As demonstrated in Fig. 17, the proposed multi-coil HWR process makes it possible to produce balls with a desired shape. In addition, this process increases the range of balls which can be produced using the rolling mills characterized by the nominal diameter of their rolls. It has been hypothesized that a decrease in the diameter of the steel balls would ultimately increase the quantity of the balls during one roll turn while significantly decreasing the rolling mill load. This theory is verified by the distributions of the turning moments as shown in Fig. 18 which was simulated for the HWR processes shown in Fig. 16. It can be inferred that the decrease in the diameter of the rolled balls is accompanied by a decrease in the turning moment
[1] K. Lange, et al., Handbook of Metal Forming, McGraw-Hill Book Company, 1985. [2] S. Ji Ch., Study of a new type ductile iron for rolling: deformation tests (2), Materials Science and Engineering A 419 (2006) 326–330. [3] E.R. Shor., New Processes of Rolling. Moscow 1960 (in Russian). [4] S.P. Bourkine, E.A. Korshunov, N. Loginov, N.A. Babailov, V.A. Tchestnov, New industrial technology for producing mill balls in a continuous-casting deformation complex, Journal of Materials Processing Technology 92–93 (1999) 316–322. [5] Q. Wang, Q. Wang, J. Xiao, Study on the method for groove design in the helical rolling of steel balls, Journal of Materials Processing Technology 55 (1995) 340–344. [6] S.C. Yang, C.K. Chen, The surface geometry of rollers with skew rolling of steel balls, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 215 (2001) 523–532. [7] X.M. Shi, B.Y. Wang, Z.H. Li, Optimization of pass parameters on two-grooves skew rolling for Al ball, Key Engineering Materials 419–420 (2010) 3313–3316. [8] X.M. Shi, B.Y. Wang, Numerical simulation of Al ball forming process in skew rolling, Materials Science Forum 704–705 (2012) 151–154. [9] X.P. Fu, T.A. Dean, Past developments, current applications and trends in the cross wedge rolling process, International Journal of Machinery Tools Manufacture 33 (1993) 367–400. [10] Z. Pater, Development of cross-wedge rolling theory and technology, Steel Research International. Special Edition: Metal Forming 2010 81 (2010) 25–32. [11] Z. Pater, J. Kazanecki, J. Tomczak, Helical—wedge rolling of steel balls, Steel Research International. Special Edition: Metal Forming (2012) 79–83.
Contents lists available at SciVerse ScienceDirect
International Journal of Machine Tools & Manufacture journal homepage: www.elsevier.com/locate/ijmactool
Experimental and numerical analysis of helical-wedge rolling process for producing steel balls Zbigniew Pater a,n, Janusz Tomczak a, Jaros"aw Bartnicki a, Michael R. Lovell b, Pradeep L. Menezes b a b
Lublin University of Technology, Nadbystrzycka 36, Lublin 20-618, Poland Department of Industrial Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA
a r t i c l e i n f o
abstract
Article history: Received 9 May 2012 Received in revised form 21 December 2012 Accepted 21 December 2012 Available online 31 December 2012
The helical-wedge rolling (HWR) process is a new metal forming technique for producing spherical parts of various dimensions. In this paper, the overall details of the HWR process are described and the important process parameters that control the HWR process are systematically discussed. A new experimental method, developed under laboratory conditions, showed that the HWR process can produce spherical steel parts (balls) with high manufacturing quality. Numerical simulations of the HWR process were carried out using a commercially available FEM software (Simufact) to show the stress, strain, and temperature distributions in the rolled balls. In addition, the variation of forces and rolling moments during the process are analyzed. Based on the experimental and numerical investigations, the HWR technique has been found to be a viable process for enhancing the quality and productivity of formed spherical products. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Helical wedge rolling FEM Steel balls
1. Introduction Steel balls are employed on a mass scale as grinding media in ball mills. They are used for grinding metal ores, coal, and used-up molding sands through an abrasive wear process. The effectiveness of the grinding media is dictated by the surface-to-weight ratio of the balls. At present, steel balls used for grinding media are mainly produced by casting, die forging, and an efficient helical rolling process. In helical rolling, two skewly positioned rolls with helical grooves (roll passes) on their circumference rotate in the same direction to form steel balls [1,2]. The helical rolling process was first implemented in early 1950s in the USSR [3]. More recently, investigations have been conducted to design roll passes with variable pitch and depth [4]. In Bourkine et al.’s investigation [3], it was found that the following three conditions need to be satisfied in order to obtain semi-finished steel balls with optimum shape: 1. The volume of the material confined in the roll pass should be constant throughout the forming process. 2. The change in the profile and dimensions of the roll pass prongs should entail elongation in the semi-finished product which is confined in the roll pass, and 3. Confining the metal in the roll pass should be performed on relatively short sections of the roll to prevent cracking that occurs in the axial zone of the semi-finished product.
n
Corresponding author. Tel.: þ048815384242; fax: þ 048815384241. E-mail address: [email protected] (Z. Pater).
0890-6955/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijmachtools.2012.12.006
Taking the above three points into consideration, a methodology for designing roll passes used in the skew rolling of semifinished balls has been developed as documented in the literature. [5–7]. The helical rolling process of steel balls is difficult to analyze theoretically due to its complexity. Advancements in the process have primarily been made using trial and error experimental techniques. Recently, Shi and Wang [8] numerically modeled the skew rolling process and determined a number of simplifications for the production of steel parts. In the present investigation, new tools for producing spherical parts with helical rolling have been designed. The roll passes of the tools are constructed using an innovative technology that utilizes a helical roller wedge which produces necking between adjacent steel balls. Under such conditions, it is possible to take advantage of knowledge that pertains to better-known processes, such as cross-wedge rolling [9–10].
2. Design of the helical-wedge rolling process The design of the HWR process used for producing spherical parts is shown in Fig. 1. It is assumed that the parts are formed between two rolls as the roll passes. The axes of the rolls are turned relative to the billet axis by an angle, ‘g’’. The value of ‘g’’ should be taken from the equality condition of a projection of the roll circumferential velocity in the axial direction and of the billet pitch per one rotation. This ensures that the volume of the material confined in the roll pass will be the same as the volume of the ball being formed. During the rolling process, the semifinished product is held in the appropriate position using guiding
2
Z. Pater et al. / International Journal of Machine Tools & Manufacture 67 (2013) 1–7
blades (see Fig. 1). The surface of the semi-finished product corresponds to the surface profile of the guiding blades. This design is currently used in the helical rolling process for producing steel balls. The rolls (with the nominal diameter D) used in the HWR process are comprised of two basic parts: (a) the input (conical) part and (b) the forming (cylindrical) part where the wedge is wound up on a barrel of the roll. The process is used to roll semifinished balls that are either connected to one another by connectors (the situation is shown in Fig. 1) or are separated with an additional cutting coil. The role of the input part is to size the billet diameter, which is significant if the billets with low production accuracy are used. The key parameters of the HWR process include wedge angles (the forming angle a and the spreading angle b) as well as the cross-sectional reduction Rp. The Rp can be determined using the following formula: Rp ¼ 100%
S0 S , S0
ð1Þ
Billet
Guide 2 Guide 1
d0
a=D
Roll 1
2β
Roll 2
where S0 denotes the cross-sectional area of the billet and S denotes the cross-sectional area of the necking connection of the balls. Based on previous analysis [11], it was recommended that the tools with ‘a’ of 451 and ‘b’ of 21 should be used in the HWR process. In addition, the maximum cross-sectional reduction Rp obtained during one rotation of the rolls should not be greater than 85%.
3. Experimental details 3.1. Experimental tests Experimental tests of the HWR process were conducted using a two-roll skew rolling mill available at the Akademia Gorniczo Hutnicza (AGH) University of Science and Technology in Krakow, Poland. Due to the overall dimensions of the rolling mill, it was determined that the balls with a diameter of 33 mm would be formed during experiments. Fig. 2(a) depicts the rolls with helical wedges which were used in the experimental trials. Table 1 shows the design parameters of the rolls, all of which were chosen in accordance with Fig. 1. To ensure process stability, two guiding blades, as shown in Fig. 2(b), were additionally incorporated. The guiding blades were attached to the body of the rolling mill by means of a connector in the form of a dovetail. The position of the tools in the rolling mill is illustrated in Fig. 3, where semi-finished balls are shown departing from the mill. The billets for the rolling were made of 100Cr6 steel rods and were 350 mm in length and had a constant diameter of 33 mm. They were heated in an electric furnace to a temperature of 1150 1C for approximately 20 min. The billets were then inserted into the working space of the rolling mill. Once they were contacted by the rollers, they were automatically pulled in between the rollers, and formed into balls, which were then ejected from the rolling mill as shown in Fig. 3. 3.2. Finite element modeling
α γ γ
L Fig. 1. Design of the HWR process for producing balls.
Finite element modeling of HWR process was performed using FEM-based Simufact software. A geometrical model of the analyzed process is illustrated in Fig. 4. As illustrated in the figure, the model comprises of two identical helical rolls, two guides, and one billet in the form of a cylindrical rod. In the numerical simulation, a rigid plastic material model was employed. For the billet, material properties of 100Cr6 steel were assigned. The material model and parameters were obtained from the database library of the Simufact software. The plastic material behavior of the billet is specified with a material flow stress function
Fig. 2. Photograph of the (a) rolls with helical wedges and (b) guiding blades that were used in experimental tests of the HWR process for producing steel balls.
Z. Pater et al. / International Journal of Machine Tools & Manufacture 67 (2013) 1–7
3
Table 1 Design parameters of the rolls. Parameters
Values
Forming angle (a) Spreading angle (b) Feed angle (g) Nominal roll diameter (D) Roll length (L)
451 21 31 215 mm 205 mm
Fig. 3. Photograph shows the arrangement of tools in HWR process.
Fig. 5. Flow curves of 100Cr6 steel at strain rates of (a) 1.5 s 1 and (b) 100 s 1.
Fig. 4. Simufact designed geometrical model of HWR process.
or flow stress data. The flow stress equation is dependent on the strain, strain rate, and temperature. Fig. 5(a) and (b) present the flow curves of 100Cr6 steel material, which depicts the variation of flow stress as a function of strain for different billet temperatures, at strain rates of 1.5 s 1 and 100 s 1, respectively. The operating parameters assumed in the calculations corresponded to the parameters used in the rolling experimental tests. More specifically, the material before the forming process was heated over its whole volume to a
temperature of 1150 1C and the tools were maintained at a constant temperature of 150 1C. The rolls were turned relative to the billet axis by an angle, g, of 31. The rolls were rotated in the same direction at a velocity of 60 rotations per minute. The friction on the material-tool contact surface has the boundary value determined by the friction factor m that was set equal to 1. The material-tool heat exchange coefficient was set to 10 kW/m2 K. It was assumed in the process simulation that the rolls would make at least four rotations, as this number of rotations is sufficient to form the ball. Each roll rotation was modeled with 1000 calculation time steps.
4. Results and discussion 4.1. Experimental results The experimental results showed that the balls formed with the HWR process could be accurately separated. The photograph
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Fig. 8. Numerical simulation of HWR process showing necking of steel balls.
45 40 Fig. 6. Photograph of the steel ball obtained in the HWR process. In the figure, the diameter of the steel ball was 33 mm.
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2.4 2.6 Time,s
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Fig. 9. Comparison between the experimental and simulation forces obtained in the HWR process of producing steel balls during one rotation of rolls.
Fig. 7. Photograph recorded using the infrared camera shows the temperature distribution during the HWR process.
of the ball produced in the HWR process is shown in Fig. 6. The obtained balls had the desired spherical shape with a diameter of 33 mm; the overall dimensional accuracy of the balls was approximately7500 mm. The surface of the balls was free from burrs and remnants of the necking process. The only defect encountered in the process was scratches on the surface of the balls. This is most likely due to the very small rounding radii of the roll pass edges. During the rolling experiments, it was observed that the material did not undergo significant chilling despite a relatively long forming time (which is approximately 20 s). Fig. 7 shows the photograph of the temperature distributions, which is recorded using infrared camera during the experimental tests. This photograph verifies that the temperature of billet and rolls during the process of producing the steel balls is still above 1000 1C. The reason for this stems from the fact that the heat losses (resulting from the heat being carried away by the tools) are compensated by the heat being generated when the deformation work changes into friction work. The amount of work done is depending on the load parameters. The high temperature also leads to decrease of risk of the cracks within the work material. 4.2. FEM results In the simulation, the rolls were designed with the cutting tools for the purpose of separating the steel balls. It was observed
that the numerical simulation was automatically stopped once the material is being formed and separated into two parts. This step was encountered at the beginning of the fourth rotation of the rolls, as shown in Fig. 8. Hence, in the simulation, a complete separation of steel ball could not be obtained. Minor changes in the shape of the tools were made to carry out the numerical analysis to the next level. The force affecting the roll, calculated during the simulation, was then used to verify the designed FEM model of the HWR process. Fig. 9 presents a comparison between the forces that were measured in the experiments and calculated in the simulation during one rotation of the rolls. As shown in the figure, the force was varied during the forming process and reached its maximum value after approximately 0.4 rotation of the roll when the wedge drove the material into its maximum depth. Then, the force decreased and reached its initial value. A comparison between the distributions and values of the measured and calculated forces demonstrates that the forces are compatible in terms of both quality and quantity. This validates the use of numerical modeling of the HWR process as a means for optimizing the HWR process parameters. The analysis of the HWR process consisted of rolling the spherical parts without incorporating cutting tools for ball separation. Hence, at the initial stage, the analysis was focused on rolling balls with a ball diameter (d0) of 50 mm by means of rolls with the diameter D equal to 300 mm. It was assumed that the semi-finished balls were connected to one another by means of cylindrical connectors whose diameter equals to 0.2d0 (i.e., 10 mm). Fig. 10 presents the variations in the contact regions between the upper roll and the materials that undergo forming. It can be observed that a necking with the target diameter, 0.2d0, is
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Fig. 10. Material-roll contact region in HWR process.
Fig. 12. Distribution of principal stresses (in MPa) during the HWR process of balls with diameter of 50 mm at t¼ 5 s.
Fig. 11. Effective strain distribution during the HWR process of balls with diameter of 50 mm at t ¼5 s.
completed after three rotations of the rolls. During the first halfturn of the rolls, a ring-shaped groove, in the shape of the letter ‘V’ is formed. Subsequently, during the remaining half-turn, this groove is transformed into a groove with concave walls with a depth equal to a diameter of 0.5d0. During the second rotation of the rolls, the shape of the obtained groove does not change significantly; however, deeper necking is being created as the rolls proceed. In this respect, a ball starts to form from the rest of the billet by means of necking with a diameter equal to a half of the billet diameter. During the third roll turn, the value of the connector diameter gets reduced to the assumed value of 0.2d0. As the semi-finished product enters between the rolls, a considerable decrease in width of the contact region can be formed as shown in Fig. 10. This occurs when material undergoes significant ovalisation during the forming process which is the characteristic of cross and helical rolling processes. Such ovalisation is effectively removed after three rotations of the rolls. During the helical rolling of steel balls, the material is intensively worked over its entire volume, which is demonstrated by the distribution of effective strain as shown in Fig. 11. The highest strain occurs in the connectors between the balls, which is due to the largest reduction of the cross section of the billet. The strain reaches moderate values inside the steel ball as well as at some other places where the cross-sectional reduction is low. This means that the dominant direction of material flow is circumferential caused by the friction forces, as a result of which considerable redundant strains occur in the product during the HWR process. The state of stress in the semi-finished material during the HWR process was also analyzed. Fig. 12 illustrates principal stress distributions in the longitudinal direction of the product after five roll turns. As shown in the figure, the greatest variations in
Fig. 13. The distribution of temperature (in 1C) during the HWR process of steel balls with diameter of 50 mm (at t ¼5 s).
stresses were registered during the first three turns of the rolls when the connector is being formed. At this point, the material at the surface layers is subject to tri-axial compression due to the roll thrust. Conversely, in the axial (central) areas, stretching stresses occur. It is also possible to distinguish areas where a state of tri-axial stretching occurs in the material, such stresses may negatively affect the material cohesion. Nevertheless, it must be emphasized that the stretching stresses in the analyzed case reach the values that are lower than the materials’ ultimate tensile strength values. As regards to the separated balls, they are characterized by a nearly homogenous state of stress, the components of which take insignificant values. Fig. 13 reveals the temperature distribution in the semifinished balls after five turns of the rolls. As expected, the lowest temperature can be observed on the surface of the formed balls where its value is about 50–100 1C lower than the temperature of the billet. A similar temperature difference was also observed using infrared camera in the experimental tests. This result demonstrates that the heat is carried away from the deforming material to the tools which is maintained at a lower temperature. At the same time, it can be observed during the rolling process that the material temperature in the connectors between the balls increases, which is caused by the generation of heat owing to deformation and friction. The application of the FEM allows a systematic analysis of forces during the HWR process. Figs. 14 and 15 show the variation
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140
onRoll 1 onRoll 2 onGuide 1 onGuide 2
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Time,s Fig. 14. Forces affecting tools during the HWR process of steel balls with diameter of 50 mm. The variations is shown in accordance with Fig. 1.
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Time,s Fig. 15. Turning moment distribution in the HWR process of balls with diameter of 50 mm.
in the forces and moments during the HWR process. It should be noted that the tools indicated in these figures are in accordance with Fig. 1. It is observed that the forces and moments vary in the HWR process in the form of oscillations which are typical during a metal forming process. Additionally, it can be observed that the roll load is almost identical, and the small differences have been observed due to a variation in the location of the billet between the guides during the rolling process. In accordance with the guidelines presented in the literature [4], the helical rolling processes of the steel balls are most effective when the roll diameter is approximately six times larger than the ball diameter. The feed angle g is then approximately 31. This approach, however, results in the reduction of the quantity of the balls which can be produced in a particular rolling mill. A solution to this problem could be to employ helical rolling using multi-coil rolls in which the multiplication factor of ball diameters produced within one rotation of the rolls is equal to the diameter of balls produced in the process of standard helical rolling. Fig. 16 illustrates three models of the HWR process for producing balls with different dimensions and quantities that would be produced per one turn of the rolls. For example, the model shown in Fig. 16(a) can be used to produce 1 ball with a diameter of 60 mm, whereas model Fig. 16(b) can be used to produce 2 balls with a diameter of 30 mm, and finally the model Fig. 16(c) can be used to produce 3 balls with a diameter of 20 mm. A key characteristic of all the rolls shown in Fig. 16 is that they all have the identical nominal diameter D of 300 mm. Additionally, the rolls used to form the balls of 30 mm in diameter have two-coil roll passes, while the rolls which form the balls of 20 mm in diameter have three-coil roll passes. In the figure, the effective strain distribution is presented for the comparison. As expected, it is shown that the highest amount of strain was observed for the balls having the smallest diameter, owing to largest reduction in the cross sectional area. As mentioned previously, a HWR process with multi-coil rolls could be beneficial for optimizing spherical part production. For this purpose, numerical simulations were performed to analyze the feasibility of such a process. Fig. 17 shows the distribution of effective strain when semi-finished balls are formed in a multiwedge helical process after 4 turns of the forming rolls. In the
Fig. 16. HWR processes when (a) 1 ball with diameter of 60 mm, (b) 2 balls with diameter of 30 mm, and (c) 3 balls with diameter of 20 mm are formed. The effective strain distribution is also presented in the figure.
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of the rolls because of the smaller volume of the material which undergoes forming during one rotation of the rolls.
5. Summary and conclusions The conducted experiments and numerical analyses have led to the following conclusions:
The HWR process can be successfully employed to form spherical parts, such as steel balls used for grinding media.
Steel balls produced using the HWR process are deformed over Fig. 17. Distribution of effective strain when semi-finished balls are formed in multi-wedge helical rolling after 4 roll turns.
6000
1 x 60 mm ball
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2 x 30 mm balls
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3 x 20 mm balls
their whole volume owing to an intensive material flow in the circumferential (tangential) direction. During the rolling process, unfavorable stretching stresses would occur in the axial zone, which could lead to material cracking. The forces and turning moments affecting the helical rolls vary oscillatory, which is typical variation of the analyzed HWR process. The application of helical rolling for producing steel balls using multi-coil rolls makes the machines employed in the HWR process more versatile.
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This research work was financed by funds from the Ministry of Science and Higher Education of Poland over years 2009–2012, as a project for development no. 0457/R/T02/2009/06.
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References
0 0
1
2
3
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Time, s Fig. 18. Turning moment in helical rolling processes performed in specified configurations.
simulation, the parameters were identical to the ones that were incorporated in the previous HWR process for a ball with a diameter of 50 mm. As demonstrated in Fig. 17, the proposed multi-coil HWR process makes it possible to produce balls with a desired shape. In addition, this process increases the range of balls which can be produced using the rolling mills characterized by the nominal diameter of their rolls. It has been hypothesized that a decrease in the diameter of the steel balls would ultimately increase the quantity of the balls during one roll turn while significantly decreasing the rolling mill load. This theory is verified by the distributions of the turning moments as shown in Fig. 18 which was simulated for the HWR processes shown in Fig. 16. It can be inferred that the decrease in the diameter of the rolled balls is accompanied by a decrease in the turning moment
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