Patent Publication Number: US-9421592-B2

Title: Asymmetric rolling device, asymmetric rolling method and rolled material manufactured using same

Description:
TECHNICAL FIELD 
     The present invention relates to a rolling technology used to form a metal into a rolled material, and more particularly, to a rolling technology for improving formability or other physical properties of a rolled material by controlling texture of the rolled material. 
     BACKGROUND ART 
     In general, rolling is performed to process a metal into a sheet having a certain size. When rolling is performed, the volume of a rolling material changes and thus microstructures of the rolling material also change. When microstructures of a rolling material change, the rolling material has texture in which crystals are oriented in a particular direction. Texture formed due to rolling is closely related to formability of a rolling material. Accordingly, by controlling texture of a rolling material in a rolling process, formability of the rolling material after being rolled may be improved. 
     DETAILED DESCRIPTION OF THE INVENTION 
     Technical Problem 
     The present invention provides a rolling method capable of providing a high formability to a rolled material by controlling texture of the rolled material. 
     The present invention also provides a rolled material having a formability improved by performing the rolling method. 
     The present invention also provides a rolling apparatus for performing the rolling method. 
     Additional aspects and/or advantages of the invention will be set forth in part in the description which follows and, in part, will be apparent from the description, or may be learned by practice of the invention. 
     Technical Solution 
     According to an aspect of the present invention, there is provided an asymmetric rolling method including disposing a rolling material having first and second surfaces between a first roll and a second roll having a diameter greater than that of the first roll; and rolling the rolling material by adjusting power provided from a power providing unit to each of the first and second rolls to control angular velocities of the first and second rolls to be different from each other such that a shear strain applied by the first roll to one of the first and second surfaces of the rolling material is different from that applied by the second roll to the other of the first and second surfaces. 
     The rolling material may be rolled by maintaining linear velocities of the first and second rolls to be the same. 
     A linear velocity difference between the first and second rolls, which is defined by Equation 1, may be equal to or less than 10%. 
     
       
         
           
             
               
                 
                   
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                   [ 
                   
                     Equation 
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     υ 1 : a linear velocity of the first roll 
     υ 2 : a linear velocity of the second roll 
     The rolling material may be rolled two or more times by allowing the first roll to apply a shear strain to the first surface and allowing the second roll to apply a shear strain to the second surface. 
     The rolling material may be rolled two or more times by switching surfaces of the rolling material, which receive shear strains from the first and second rolls, at least once. 
     The rolling material may be rolled two or more times in the same rolling direction. 
     The rolling material may be rolled two or more times by changing rolling directions of the rolling material at least once. 
     A third roll having a diameter greater than that of the first roll may be coupled to the first roll to support the first roll at a side opposite to the second roll. 
     According to another aspect of the present invention, there is provided an asymmetric rolling method for rolling a rolling material by using at least one pair of working rolls with different diameters and controlled to rotate at the same linear velocity by power provided by a power providing unit. 
     An asymmetric rolling method may be performed a plurality of times, and the plurality of times may include turning the rolling material upside down at least once between passes. 
     An asymmetric rolling method may be performed a plurality of times, and the plurality of times may include changing rolling directions of the rolling material at least once between passes. 
     A backup roll for supporting one of the working rolls, which has a relatively small diameter, may be coupled to the one of the working rolls at a side opposite to the other of the working rolls, which has a relatively large diameter. 
     According to another aspect of the present invention, there is provided a rolled material manufactured by using the above asymmetric rolling method. 
     The rolled material may have a hexagonal close-packed (HCP) crystal structure. Also, the rolled material may include magnesium (Mg), an Mg alloy, titanium (Ti), or a Ti alloy. Alternatively, the rolled material may include aluminum (Al), an Al alloy, or an iron-silicon (Fe—Si) alloy. 
     According to another aspect of the present invention, there is provided an asymmetric rolling apparatus including a first roll contacting a first surface of a rolling material; a second roll having a diameter different from that of the first roll and contacting a second surface of the rolling material opposite to the first surface; and a power providing unit for providing power to each of the first and second rolls so as to adjust linear velocities of the first and second rolls to be the same. 
     The power providing unit may control linear velocities of the first and second rolls to be the same. 
     The power providing unit may include first and second motors for respectively driving the first and second rolls; and a motor control unit for controlling angular velocities of the first and second motors. 
     The asymmetric rolling apparatus may further include a first gear coupled to the first roll and a second gear coupled to the second roll, wherein the second gear is coupled to the first gear with a gear ratio different from that of the first gear, and the power providing unit may include a motor for providing driving power to the first or second gear. 
     The asymmetric rolling apparatus may further include a third roll having a diameter greater than that of the first roll and coupled to the first roll to support the first roll at a side opposite to the second roll. 
     The power providing unit may include a first motor for driving the first or third roll, a second motor for driving the second roll, and a motor control unit for controlling angular velocities of the first and second motors. 
     The asymmetric rolling apparatus may further include a first gear coupled to the first or third roll and a second gear coupled to the second roll, wherein the second gear is coupled to the first gear with a gear ratio different from that of the first gear, and the power providing unit may include a motor for providing driving power to the first or second gear. 
     The first or second gear may be a variable gear for changing at least one gear ratio, and the asymmetric rolling apparatus may further include a gear control unit for controlling the gear ratio. 
     Advantageous Effects 
     A rolling method and apparatus according to embodiments of the present invention may produce rolled material with improved formability compared to conventional systems. In particular, if a metallic material having a poor formability at room temperature such as a magnesium (Mg) alloy is rolled according to an embodiment of the present invention, slip systems may be oriented in such a way that shear strains are easily received even at room temperature. Thus, an excellent formability at room temperature may be achieved. 
     The effects of the present invention are not limited to the above-mentioned advantages, and may be applied to all materials of which formability is improvable through rolling. Additional effects of the present invention will be apparent to one of ordinary skill in the art from the following description. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
         FIGS. 1A and 1B  are a front view of and a perspective view of a rolling apparatus according to an embodiment of the present invention. 
         FIGS. 2A and 2B  are a front view of and a perspective view of a rolling apparatus according to another embodiment of the present invention. 
         FIG. 3  is a front view of a rolling apparatus according to another embodiment of the present invention. 
         FIG. 4  shows slip systems of magnesium (Mg) having a hexagonal close-packed (HCP) crystal structure. 
         FIG. 5  shows orientations of HCP crystals of a rolling material. 
         FIG. 6  shows poles of crystals A, B, C, and D illustrated in  FIG. 5 , on the (0001) pole figure. 
         FIG. 7  shows the (0001) pole figures of an AZ31 alloy rolled by using a rolling method according to an embodiment of the present invention. 
         FIGS. 8 through 10  show the (0001) pole figures of an AZ31 alloy rolled by using rolling methods according to comparative examples. 
         FIG. 11  is a diagram for describing a rolling method according to another embodiment of the present invention. 
         FIG. 12  shows the (0001) pole figure of an AZ31 alloy rolled by using the rolling method illustrated in  FIG. 11 . 
         FIG. 13  is a diagram for describing a rolling method according to another embodiment of the present invention. 
         FIG. 14  shows the (0001) pole figures of an AZ31 alloy rolled by using the rolling method illustrated in  FIG. 13 . 
     
    
    
     BEST MODE 
     Hereinafter, the present invention will be described in detail by explaining embodiments of the invention with reference to the attached drawings. In the following description of the present invention, a detailed description of known functions and configurations incorporated herein will be omitted when it may make the subject matter of the present invention unclear. 
     A rolling apparatus and a rolling method, according to embodiments of the present invention, may be applied to any rolling material in order to improve formability of the rolling material, and the following embodiments exemplarily show the concept of the present invention. 
     The invention may, however, be embodied in many different forms and should not be construed as being limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of the invention to one of ordinary skill in the art. In the drawings, the sizes of elements may be exaggerated for convenience of explanation. 
     In the following description, the term “texture” may refer to the crystalline orientation of a polycrystalline material. The term “texture” does not limit the scope of the present invention. The texture of a material is used as a relative concept rather than an absolute concept. That is, if a material has texture in a predetermined direction, it means that most, not all, of crystalline grains of the material have texture in the mentioned direction. 
     A pole figure may be a figure showing a distribution of the direction of crystallographic lattice planes in the form of stereographic projection to show the orientation or texture of crystals of a material. The pole figure may be created by using X-ray diffraction (XRD). 
     Furthermore, as used herein, a rolling material refers to a target material to be rolled, and a rolled material refers to a resultant material obtained by rolling the rolling material. 
       FIGS. 1A and 1B  illustrate a rolling apparatus  100  according to an embodiment of the present invention. In more detail,  FIG. 1A  is a front view of the rolling apparatus  100 , and  FIG. 1B  is a perspective view of first and second rolls  101  and  102 , and a rolling material  104  of the rolling apparatus  100  illustrated in  FIG. 1A . As illustrated in  FIGS. 1A and 1B , the rolling apparatus  100  is an asymmetric rolling apparatus in which the first and second rolls  101  and  102  have different diameters. The exemplary rolling apparatus  100  includes the first roll  101  contacting a first surface  104   a  of the rolling material  104 , the second roll  102  having a diameter greater than that of the first roll  101  and contacting a second surface  104   b  of the rolling material  104  opposite to the first surface  104   a , and a power providing unit  105  for providing power to each of the first and second rolls  101  and  102  to separately adjust angular velocities of the first and second rolls  101  and  102 . 
     Although, as working rolls, the first and second rolls  101  and  102  are oriented as upper and lower rolls in the embodiment shown in  FIGS. 1A and 1B , other embodiments are also available. Also, for convenience of explanation, a surface contacting the first roll  101  that is the upper roll is shown as the first surface  104   a , and a surface contacting the second roll  102  that is the lower roll is shown as the second surface  104   b . Accordingly, if the rolling material  104  is turned upside down, the first roll  101  contacts the second surface  104   b  of the rolling material  104 , and the second roll  102  contacts the first surface  104   a  of the rolling material  104 . 
     The first and second rolls  101  and  102  are oriented in parallel and are spaced apart from a supporting plate  110 , and are mounted between frames  111  fixed by a coupling member  112  such as a screw. 
     In an embodiment, as illustrated in  FIG. 1A , the power providing unit  105  may include first and second motors  106  and  107  for respectively driving the first and second rolls  101  and  102 , and a motor control unit  108  for controlling angular velocities of the first and second motors  106  and  107 . 
     In this embodiment, the first and second motors  106  and  107  transfer rotatory power to the first and second rolls  101  and  102  via connection members  109 . 
     The motor control unit  108  may control the angular velocities of the first and second rolls  101  and  102  connected to or coupled to the first and second motors  106  and  107  by controlling the angular velocities of the first and second motors  106  and  107 , and thus may control linear velocities of the first and second rolls  101  and  102 . The relationship between angular velocity and linear velocity can be represented by multiplying angular velocities of the first and second rolls  101  and  102  by radiuses of the first and second rolls  101  and  102 . 
     By controlling the linear velocities of the first and second rolls  101  and  102  as described above, a first shear strain applied by the first roll  101  to the first surface  104   a  of the rolling material  104  may be controlled to be different from a second shear strain applied by the second roll  102  to the second surface  104   b  of the rolling material  104 . 
     For example, the motor control unit  108  may control the first and second rolls  101  and  102  to roll the rolling material  104  by rotating the first and second rolls  101  and  102  to have the same linear velocity. That is, the linear velocities of the first and second rolls  101  and  102  may be the same by controlling a ratio between the angular velocities of the first and second rolls  101  and  102  to be the same as the inverse of the ratio between the radiuses of the first and second rolls  101  and  102 . Although linear velocities have been described as being the same, the term “the same” should be regarded as substantial sameness including complete sameness and sameness within a process margin caused by an error that occurs due to process variations even when a user controls signals of the motor control unit  108  with an intention of controlling the angular velocities of the first and second rolls  101  and  102  to be the same. The “sameness” between the linear velocities of the first and second rolls  101  and  102  is also applied to the following descriptions. 
     Meanwhile, according to another embodiment of the present invention, as illustrated in  FIGS. 2A and 2B , a third roll  103  having a diameter greater than that of the first roll  101 , and coupled to the first roll  101  to support the first roll  101  at a side opposite to the second roll  102  may be further included. In an embodiment, the first and second rolls  101  and  102  may function as working rolls that contact and directly apply shear strains to the first and second surfaces  104   a  and  104   b  of the rolling material  104 , and the third roll  103  may function as a backup roll that helps the first roll  101  to be balanced against an external force applied in a rolling process from the second roll  102  having a diameter greater than that of the first roll  101 . 
     A power providing unit  105  may include the first motor  106  for driving the first or third roll  101  or  103 , the second motor  107  for driving the second roll  102 , and the motor control unit  108  for controlling the angular velocities of the first and second motors  106  and  107 . 
     For example, as illustrated in  FIG. 2A , the first motor  106  is coupled to the third roll  103  and transfers driving power to the third roll  103 . If the third roll  103  rotates, the first roll  101  contacting the third roll  103  may also rotate due to friction. Although not shown in  FIGS. 2A and 2B , the first motor  106  may be connected to or coupled to the first roll  101  to allow the first roll  101  to rotate, and the third roll  103  may rotate due to friction according to the above-described principle. 
     Meanwhile, according to another embodiment of the present invention, power provided by the power providing unit  105  may be transferred to the working rolls via gears. For example, as illustrated in  FIG. 3 , the rolling apparatus  100  including the first through third rolls  101  through  103  may include a first gear  114  coupled to the first or third roll  101  or  103 , and a second gear  115  coupled to the second roll  102 , wherein the second gear  115  is coupled to the first gear  114  with a predetermined gear ratio, and the power providing unit  105  may include a motor  113  for transferring driving power to the first or second gear  114  or  115 . 
     Although power of the motor  113  may be transferred to the second gear  115  via a driving gear  116  as shown in  FIG. 3 , embodiments of a rolling apparatus  100  are not limited thereto, and a motor  113  may be directly connected to and may directly transfer power to the first or second gear  114  or  115  without using the driving gear  116 . 
     Also, although the embodiment of the rolling apparatus  100  shown in  FIG. 3  includes the third roll  103  as a support roll, in embodiments where only the first and second rolls  101  and  102  are included without including the third roll  103 , the first and second gears  114  and  115  may be respectively connected to the first and second rolls  101  and  102  as described above. 
     Meanwhile, the first or second gear  114  or  115  may be a geared for variably changing at least one gear ratio, and a gear control unit  117  coupled to the first or second gear  114  or  115  which may be configured for controlling the gear ratio may be further included. 
     In an embodiment of the rolling apparatus  100 , the linear velocities of the first and second rolls  101  and  102  may be controlled by adjusting the gear ratios of the first and second gears  114  and  115  in consideration of the diameters of the first and second rolls  101  and  102 . For example, power generated by the motor  113  may be transferred so that the first and second rolls  101  and  102  have the same linear velocity according to the gear configurations described above. Also, if the first and second gears  114  and  115  are variable gears, the gear ratios of the first and second gears  114  and  115  may be variably controlled by using the gear control unit  117  in consideration of the diameter of the first or second roll  101  or  102 , and thus the linear velocities of the first and second rolls  101  and  102  may be controlled to be the same. 
     Meanwhile, although the first and second rolls  101  and  102  having different diameters form a pair of working rolls in  FIGS. 1 and 3 , the present invention is not limited thereto, and a plurality of pairs of working rolls may be formed adjacent to each other. Accordingly, a rolling method according to an embodiment of the present invention may include rolling a rolling material by using at least one pair of working rolls including rolling rolls having different diameters. 
     The rolling material  104  to be rolled by the above-described asymmetric rolling apparatus  100  may include magnesium (Mg) or a Mg alloy having a hexagonal close-packed (HCP) crystal structure. Research is being currently conducted on Mg as a next-generation lightweight material. Mg, which typically has a density of 1.74 g/cm 3  has a low weight and excellent specific strength and specific modulus in comparison to iron (Fe) which typically has a density of 7.90 g/cm 3  or aluminum (Al) which typically a density of 2.7 g/cm 3 . Also, due to high absorption of vibration, impact, electromagnetic waves, etc. and excellent electric and thermal conductivities, Mg is used as a lightweight material in motor vehicles, aircraft, etc. and is also used in electronic fields of mobile phones, laptop computers, etc. 
     However, Mg having a HCP crystal structure has poor slip systems and thus has a low formability at room temperature. That is, as illustrated in  FIG. 4 , during formation, a basal plane slip system of {0001}&lt;1120&gt;, a prismatic slip system of {1010}&lt;1120&gt;, a pyramidal slip system of {1011}&lt;1120&gt;, etc. are mainly used as deformation mechanisms of Mg. However, since critical resolved shear stress values of the basal plane slip system are substantially lower than values for other mechanisms at room temperature, the orientation of the basal plane slip system within the rolling material has a great influence on room temperature formability. 
     When the basal plane slip system is parallel to rolling surfaces of the rolling material  104 , i.e., perpendicular to a normal direction ND, as represented by crystal A in  FIG. 5 , when the basal plane slip system is perpendicular to a transverse direction TD as represented by crystal B in  FIG. 5 , or when the basal plane slip system is perpendicular to a rolling direction RD as represented by crystal C in  FIG. 5 , formability at room temperature is poor. This is because, when rolled Mg is formed, if a main deformation direction (i.e., ND, RD, or TD in  FIG. 5 ) is perpendicular or parallel to the basal plane slip system, the orientation of the basal slip plane is not configured to facilitate deformation caused by the forming process. 
     However, if the basal plane slip system is tilted by a certain angle with respect to a main deformation direction as represented by crystal D in  FIG. 5 , the basal slip plane is oriented to facilitate deformation, and an excellent formability at room temperature is achieved. 
     The orientation and distribution of the basal plane slip systems in a material may be characterized as illustrated in the (0001) pole figure of  FIG. 6 .  FIG. 6  shows how poles of the crystals A, B, C, and D illustrated in  FIG. 5  would appear on an (0001) pole figure. 
     If a rolling process is performed by using the asymmetric rolling apparatus  100  illustrated in  FIGS. 1 through 3 , crystals of Mg or an Mg alloy may have an orientation that is advantageous for formability. In more detail, an asymmetric rolling method according to an embodiment of the present invention may include disposing the rolling material  104  having the first and second surfaces  104   a  and  104   b  between the first and second rolls  101  and  102 , and rolling the rolling material  104  by adjusting angular velocities of the first and second rolls  101  and  102  to be different from each other such that a shear strain applied by the first roll  101  to one of the first and second surfaces  104   a  and  104   b  of the rolling material  104 , for example, the first surface  104   a , is different from that applied by the second roll  102  to the other of the first and second surfaces  104   a  and  104   b , for example, the second surface  104   b.    
     In this case, the rolling material  104  may be rolled by maintaining, for example, linear velocities of the first and second rolls  101  and  102  to be the same. 
     The rolling material  104  may include an AZ31 alloy as an Mg alloy. Although embodiments are not limited thereto, in the following description, the rolling material  104  is assumed as an AZ31 alloy. 
     Meanwhile, an asymmetric rolling method according to an embodiment of the present invention includes a method of rolling the rolling material a plurality of times. The above rolling method may be used to prevent a problem caused when a large reduction ratio is applied to a rolling material, by repeatedly applying appropriately predetermined reduction ratios to the rolling material. 
     In an embodiment, the plurality of times refers to a total number of times that a rolling material is rolled by working rolls. In embodiments, a rolling material may be rolled a plurality of times by reinserting the material through the same set of working rolls, or by inserting the rolling material into a plurality of pairs of working rolls arranged in series in a continuous process. Embodiments of the present invention include continuous insertion and intermittent insertion of the rolling material between the working rolls. 
     A method of rolling a plurality of times may include reinsertion of the rolling material after being physically released from the working rolls, and reinsertion of the rolling material between the working rolls by allowing the working rolls to rotate in reverse while the rolling material is still disposed between the working rolls. 
     In some cases, each of the plurality of times that rolling is performed may be referred to as a “pass”. 
       FIG. 7  shows the (0001) pole figures of an AZ31 alloy rolled five times by using the rolling apparatus  100  illustrated in  FIGS. 2A and 2B  and by controlling the first and second rolls  101  and  102  to have the same linear velocity. In this case, a reduction ratio of the AZ31 alloy was 75%, and a rolling temperature was 300° C. Rolling was performed in the same rolling direction by allowing the first and second surfaces  104   a  and  104   b  of the rolling material  104 , i.e., the AZ31 alloy, to respectively contact and receive shear strains from the first and second rolls  101  and  102 . In  FIG. 7 , a lower figure is the (0001) pole figure of the first surface  104   a  that received a shear strain from is the first roll  101 , and an upper figure is the (0001) pole figure of the second surface  104   b  that received a shear strain from the second roll  102 . 
     As illustrated in  FIG. 7 , in an asymmetric rolling method according to an embodiment of the present invention, an orientation of a basal plane, i.e., the (0001) plane, of HCP crystal is out of center. In more detail, a rotation angle (i.e., an angle from the center) of a pole point of the basal plane with respect to the first surface  104   a  that received a shear strain from the first roll  101  was about 15°, and a rotation angle of a pole point of the basal plane with respect to the second surface  104   b  that received a shear strain from the second roll  102  was about 6°. 
     As comparative examples,  FIGS. 8 through 10  show the (0001) pole figures of an AZ31 alloy rolled by using a conventional rolling apparatus including working rolls having the same diameter. 
       FIGS. 8A through 8C  show the (0001) pole figures of the AZ31 alloy rolled a plural number of times to a reduction ratio of 75% at a rolling temperature of 300° C. by allowing first and second surfaces of a rolling material, i.e., the AZ31 alloy, to respectively contact and receive shear strains from first and second rolls. In more detail,  FIG. 8A  shows the (0001) pole figure obtained when rolling with a reduction ratio of 10% was performed twelve times,  FIG. 8B  shows the (0001) pole figure obtained when rolling with a reduction ratio of 20% was performed six times, and  FIG. 8C  shows the (0001) pole figure obtained when rolling with a reduction ratio of 30% was performed four times. As illustrated in  FIGS. 8A through 8C , in all conditions, pole points have maximum polar strengths equal to greater than 10% and are all centered. 
       FIGS. 9A through 9C  show the (0001) pole figures of the AZ31 alloy rolled at a rolling temperature of 200° C. In this case, reduction ratios were 50%, 30%, and 15% respectively. As illustrated in  FIGS. 9A through 9C , pole points of a basal plane have maximum polar strengths equal to greater than 12% and are all centered. 
     Based on the above results, if rolling is performed by using the conventional rolling apparatus including the first and second rolls having the same size, even when a reduction ratio or a rolling temperature is changed, the pole points of the basal plane are centered. Therefore, in comparison to an AZ31 alloy rolled using conventional rolling rolls having the same diameter, a texture of an AZ31 alloy rolled according to an embodiment of the present invention may have an orientation capable of greatly improving formability. 
     Meanwhile,  FIGS. 10A through 10C  show the (0001) pole figures of the AZ31 alloy rolled by using a conventional differential speed rolling method performed by rotating one of working rolls having the same diameter at a linear velocity greater than that of the other of the working rolls. In this case, a ratio between linear velocities of the working rolls was maintained as 3:1, a rolling temperature was 200° C., and reduction ratios were 70%, 30%, and 15% respectively in  FIGS. 10A through 10C . In  FIGS. 10A through 10C , lower figures are the (0001) pole figures of a surface that receives a shear strain from the fast roll, and upper figures are the (0001) pole figures of a surface that receives a shear strain from the slow roll. 
     If differential speed rolling is performed as described above, regardless of reduction ratios and a linear velocity difference between the two rolls, orientations of crystals are centered in comparison to the embodiments shown in  FIG. 7 , and a characteristic of having pole points of a basal plane out of center in the embodiment illustrated in  FIG. 7 , is not present in the pole figures of  FIGS. 8 through 10 . 
     As described above, in comparison to an AZ31 alloy rolled by using rolling rolls having the same diameter, an AZ31 alloy rolled by using an asymmetric rolling method according to an embodiment of the present invention may have an orientation of crystals on a basal plane which is capable of greatly improving formability. 
     In addition, if differential speed rolling is performed by using working rolls having the same diameter, since a rolling material slips due to a linear velocity difference between two rolls, shear strains may not be actually applied from rolling rolls to the rolling material. Also, the rolling material released out of the rolling rolls may be bent or may have rough surfaces. 
     However, if an asymmetric rolling method according to an embodiment of the present invention is used, since asymmetric shear strains due to different diameters of working rolls are applied using the same linear velocities, even though asymmetric rolling is performed, the rolling material may not slip. Also, defects such as bending or increased surface roughness of the rolling material, which occur in differential speed rolling, are not caused. 
     Meanwhile, if an asymmetric rolling method according to an embodiment of the present invention is used, angular velocities of the first and second rolls  101  and  102  may be controlled with in a range in which a linear velocity difference defined by Equation 1 is equal to or less than 10%. 
     
       
         
           
             
               
                 
                   
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     υ 1 : a linear velocity of the first roll  101   
     υ 2 : a linear velocity of the second roll  102   
     In an embodiment, if the linear velocity difference between the first and second rolls  101  and  102  having different diameters, which is defined by Equation 1, is greater than 10%, the rolling material released from the two rolling rolls may be bent due to, for example, an imbalance in stress. 
     Another embodiment of an asymmetric rolling method performed a plurality of times includes switching surfaces of the rolling material  104 , which receive shear strains from the first and second rolls  101  and  102 , at least once between passes. 
     For example, in an embodiment illustrated in  FIG. 11 , the rolling material  104  is rolled in a first pass where the first and second surfaces  104   a  and  104   b  of the rolling material  104  to contact the first and second rolls  101  and  102  respectively. Subsequently, the rolling material  104  is turned upside down and is rolled in a second pass where the first and second surfaces  104   a  and  104   b  of the rolling material  104  contact the second and first rolls  102  and  101 , respectively. In other words, in an embodiment, upper and lower surfaces of rolling material  104  may be inverted in separate passes of a plurality of passes performed on the same rolling material. 
     In an embodiment, two or more passes may be performed between the same pair of rolling rolls in a batch process, or may be performed between different pairs of rolling rolls corresponding to the passes. 
     Thus, the asymmetric shear strains due to different diameters of the first and second rolls  101  and  102  may be alternately applied to the first and second surfaces  104   a  and  104   b , so that shear strains applied to each surface in the first and second passes may be normalized to a certain degree. The number of times that rolling is performed may be two or more according to a desired reduction ratio. Embodiments of the present invention are not limited by the particular number of times that the first and second surfaces  104   a  and  104   b  of the rolling material  104  are switched, or the number or order of passes that may be performed between switching 
       FIG. 12  shows an (0001) pole figure of an AZ31 alloy rolled at a rolling temperature of 300° C. in a total of five passes by switching rolling surfaces between each pass (a rolling reduction ratio was 75%). A rotation angle of a basal plane is about 17°, which is greater than those of the (0001) pole figures illustrated in  FIGS. 8 through 10 . 
     Meanwhile, a rolling method according to another embodiment of the present invention includes rolling a plurality of times while changing rolling directions between passes. 
     For example, as illustrated in  FIG. 13 , a rolling direction of the rolling material  104  is set in such a way that the rolling material  104  is inserted between the first and second rolls  101  and  102  in direction A in a first pass. In a second pass, the rolling direction of the rolling material  104  is turned by 180° so that the rolling direction is direction B while the first and second surfaces  104   a  and  104   b  are in the same orientation as the first pass. 
       FIG. 14  shows the (0001) pole figures of an AZ31 alloy rolled at a rolling temperature of 300° C. in a total of five passes while changing rolling directions between each pass (a rolling reduction ratio was 75%). In  FIG. 14 , a lower figure is the (0001) pole figure of the first surface  104   a  that received a shear strain from the first roll  101 , and an upper figure is the (0001) pole figure of the second surface  104   b  that received a shear strain from the second roll  102 . As illustrated in  FIG. 14 , a rotation angle on the first surface  104   a  that received a shear strain from the first roll  101  was about 5°, and a rotation angle on the second surface  104   b  that received a shear strain from the second roll  102  was about 17°. The rotation angles are greater than those of the (0001) pole figures illustrated in  FIGS. 8 through 10 . 
     In addition to reinserting a rolling material after being physically released from working rolls of a rolling apparatus as illustrated in  FIG. 13 , embodiments of a method of performing rolling a plurality of times by changing rolling directions include reinserting the rolling material between the working rolls by allowing the working rolls to rotate in reverse while the rolling material is still disposed between the working rolls. 
     In addition to Mg or an Mg alloy, the above-described rolling apparatuses and rolling methods may be applied to any material for controlling texture of a rolled material. For example, a metallic material containing titanium (Ti) or a Ti alloy and having a HCP crystal structure, a metallic material containing Al or an Al alloy, or an iron-silicon (Fe—Si) alloy having magnetic properties influenced by an orientation of crystals of a rolled material may be used as a rolling material. 
     While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it will be understood by one of ordinary skill in the art that various changes in form and details may be made therein without departing from the spirit and scope of the present invention as defined by the following claims.