Abstract:
A secondary battery includes a case, the case including a first side having a bead thereon, the bead having a height h and a width w, a ratio of the height h to the width w satisfying 
     
       
         
           
             
               
                 2 
                  
                 % 
               
               ≤ 
               
                 ( 
                 
                   
                     h 
                     w 
                   
                   × 
                   100 
                 
                 ) 
               
               ≤ 
               
                 50 
                  
                 % 
               
             
             , 
           
         
       
     
     h and w being in a same unit of measure, and an electrode assembly in the case, the electrode assembly including a first electrode, a second electrode, and a separator disposed between the first and second electrodes.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims priority to pending U.S. Provisional Application No. 61/282,279, filed in the U.S. Patent and Trademark Office on Jan. 13, 2010, and entitled “SECONDARY BATTERY,” which is incorporated by reference herein in its entirety and for all purposes. 
     
    
     BACKGROUND 
       [0002]    1. Field 
         [0003]    Embodiments relate to a secondary battery. 
         [0004]    2. Description of the Related Art 
         [0005]    Currently, compact and light electric/electronic devices such as cellular phones, laptop computers, and camcorders are being actively developed and produced. These portable electric/electronic devices include a battery pack so as to operate at places where no power source is provided. The battery pack may include a secondary battery that is rechargeable and dischargeable, and may output a certain level of voltage to drive a portable electric/electronic device for a certain period of time. A battery pack may also be used to power a motive power source, such as in an electric or hybrid vehicle. 
         [0006]    Secondary batteries include, for example, nickel (Ni)-cadmium (Cd) batteries, Ni-hydrogen (H) batteries, and lithium (Li) batteries. Li secondary batteries may have a operation voltage of about 3.6V, which is about three times higher than that of Ni—Cd batteries or Ni—H batteries, and may have a high energy density for unit weight. Thus, Li secondary batteries are increasing in popularity. 
         [0007]    Li secondary batteries may use a Li-based oxide as a positive electrode active material and a carbon material as a negative electrode active material. In general, according to the type of electrolyte, Li secondary batteries may be classified as liquid electrolyte batteries and polymer electrolyte batteries. Li secondary batteries using a liquid electrolyte may be referred to as Li ion batteries, and Li secondary batteries using a polymer electrolyte may be referred to as Li polymer batteries. Li secondary batteries are manufactured in various shapes such as a cylinder shape, a rectangular shape, and a pouch shape. 
         [0008]    A Li ion secondary battery may include an electrode assembly in which a positive electrode plate (on which a positive electrode active material is coated), a negative electrode plate (on which a negative electrode active material is coated), and a separator (disposed between the positive and negative electrode plates so as to prevent a short and to allow movement of Li ions) are wound or stacked. The Li ion secondary battery may also include a case for accommodating the electrode assembly, and an electrolyte injected into the case so as to allow movement of Li ions. 
         [0009]    In a Li ion secondary battery, the electrode assembly may be formed by winding or stacking the positive electrode plate (on which the positive electrode active material is coated and to which a positive electrode tab may be connected), the negative electrode plate (on which the negative electrode active material is coated and to which a negative electrode tab is connected), and the separator. The positive electrode active material may contain a complex Li oxide as a main component, e.g., LiCoO 2 , which may be formed by mixing carbonic acid, Li, and cobalt (Co) oxide in a ratio of 1.2:1 and baking the mixture at a temperature of about 400° C. to about 1000° C. The Li secondary battery may be completed by accommodating the electrode assembly into the case, injecting the electrolyte into the case, and then sealing the case. 
         [0010]    When the Li secondary battery is repeatedly recharged, the electrode assembly may repeatedly expand and contract. The expansion and contraction of the electrode assembly may cause a swelling phenomenon such that the case may expand. 
       SUMMARY 
       [0011]    It is a feature of an embodiment to provide a secondary battery capable of efficiently distributing internal pressure and increasing rigidity. 
         [0012]    It is a feature of an embodiment to provide a secondary battery that may compensate or prevent volume expansion during recharge and discharge, and may prevent displacement of an electrode assembly caused by increase of internal pressure. 
         [0013]    At least one of the above and other features and advantages may be realized by providing a secondary battery, including a case, the case including a first side having a bead thereon, the bead having a height h and a width w, a ratio of the height h to the width w satisfying 
         [0000]    
       
         
           
             
               
                 2 
                  
                 % 
               
               ≤ 
               
                 ( 
                 
                   
                     h 
                     w 
                   
                   × 
                   100 
                 
                 ) 
               
               ≤ 
               
                 50 
                  
                 % 
               
             
             , 
           
         
       
     
         [0000]    h and w being in a same unit of measure, and an electrode assembly in the case, the electrode assembly including a first electrode, a second electrode, and a separator disposed between the first and second electrodes. 
         [0014]    The ratio of the height h to the width w may satisfy 
         [0000]    
       
         
           
             
               2 
                
               % 
             
             ≤ 
             
               ( 
               
                 
                   h 
                   w 
                 
                 × 
                 100 
               
               ) 
             
             ≤ 
             
               33 
                
               
                 % 
                 . 
               
             
           
         
       
     
         [0015]    The ratio of the height h to the width w may satisfy 
         [0000]    
       
         
           
             
               2.6 
                
               % 
             
             ≤ 
             
               ( 
               
                 
                   h 
                   w 
                 
                 × 
                 100 
               
               ) 
             
             ≤ 
             
               18.8 
                
               
                 % 
                 . 
               
             
           
         
       
     
         [0016]    N beads may be on the first side, N being one or more, the first side may have a first length A, A being in millimeters, the N beads extending orthogonal to the first length A, and a ratio of N to the first length A may satisfy 
         [0000]    
       
         
           
             
               2 
                
               % 
             
             ≤ 
             
               ( 
               
                 
                   N 
                   
                     A 
                      
                     
                       ( 
                       mm 
                       ) 
                     
                   
                 
                 × 
                 100 
               
               ) 
             
             ≤ 
             
               24 
                
               
                 % 
                 . 
               
             
           
         
       
     
         [0017]    Each of the N beads may be a member of a first set of linear beads, the first side may also have a second set of N′ beads, the beads of the second set being orthogonal to the beads of the first set, the first side may have a second length B, B being in millimeters, the N′ beads extending orthogonal to the second length B, and a ratio of N′ to the second length B may satisfy 
         [0000]    
       
         
           
             
               2 
                
               % 
             
             ≤ 
             
               ( 
               
                 
                   
                     N 
                     ′ 
                   
                   
                     B 
                      
                     
                       ( 
                       mm 
                       ) 
                     
                   
                 
                 × 
                 100 
               
               ) 
             
             ≤ 
             
               24 
                
               
                 % 
                 . 
               
             
           
         
       
     
         [0018]    Respective beads may be disposed between the opposing edges of the first side and the center of the first side, the beads being symmetric about an imaginary line orthogonal to the opposing edges and intersecting the center. 
         [0019]    The beads may convolute the battery case so as to increase a surface area of the battery case. 
         [0020]    At least one of the above and other features and advantages may also be realized by providing a secondary battery, including a case, the case including a first side, the first side having a first edge and a second edge opposite the first edge, and an electrode assembly in the case, the electrode assembly including a first electrode, a second electrode, and a separator disposed between the first and second electrodes. The first side may have a bead disposed thereon symmetrically with respect to an imaginary line orthogonal to the first edge and the second edge, the imaginary line intersecting centers of the first and second edges. 
         [0021]    The bead may be a first linear bead extending between the first and second edges, the bead having a height h and a width w, a ratio of the height h to the width w satisfying 
         [0000]    
       
         
           
             
               
                 2 
                  
                 % 
               
               ≤ 
               
                 ( 
                 
                   
                     h 
                     w 
                   
                   × 
                   100 
                 
                 ) 
               
               ≤ 
               
                 50 
                  
                 % 
               
             
             , 
           
         
       
     
         [0000]    h and w being in a same unit of measure. 
         [0022]    The secondary battery may further include a second linear bead extending orthogonal to the first linear bead. 
         [0023]    The second linear bead may intersect the first linear bead. 
         [0024]    The bead may encircle the center of the first side. 
         [0025]    The bead may be a closed curve. 
         [0026]    The secondary battery may include at least one additional bead encircling and concentric with the bead. 
         [0027]    The battery case may further include at least two discontinuous bead sections disposed symmetrically with respect to the center of the first side, the discontinuous bead sections being disposed outside the bead such that the bead is between the center of the first side and the discontinuous bead sections. 
         [0028]    The first side may have opposing semicircular beads disposed symmetrically with respect to the imaginary line. 
         [0029]    At least one of the above and other features and advantages may also be realized by providing a method of forming a secondary battery, the method including providing a case, the case including a first side having a bead thereon, the bead having a height h and a width w, a ratio of the height h to the width w satisfying 
         [0000]    
       
         
           
             
               
                 2 
                  
                 % 
               
               ≤ 
               
                 ( 
                 
                   
                     h 
                     w 
                   
                   × 
                   100 
                 
                 ) 
               
               ≤ 
               
                 50 
                  
                 % 
               
             
             , 
           
         
       
     
         [0000]    h and w being in a same unit of measure, and disposing an electrode assembly in the case, the electrode assembly including a first electrode, a second electrode, and a separator disposed between the first and second electrodes. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0030]    The above and other features and advantages will become more apparent to those of skill in the art by describing in detail example embodiments with reference to the attached drawings, in which: 
           [0031]      FIG. 1  illustrates a schematic perspective view of a secondary battery; 
           [0032]      FIG. 2  illustrates a cross-sectional view cut along a line II-II of  FIG. 1 ; 
           [0033]      FIG. 3  illustrates a schematic perspective view of a case including different-length sides; 
           [0034]      FIG. 4A  illustrates a schematic perspective view of a case on which beads are formed so as to increase a unit area of the case, according to an embodiment; 
           [0035]      FIG. 4B  illustrates a schematic conceptual view of a portion IVb of  FIG. 4A ; 
           [0036]      FIG. 5  illustrates a schematic conceptual view for describing a principal of pressure distribution; 
           [0037]      FIG. 6A  illustrates side and front views of a plate for describing a principal of bending stress; 
           [0038]      FIG. 6B  illustrates side and front views of a structure on which a bead is formed; 
           [0039]      FIG. 7  illustrates a schematic conceptual view of a bead having a width, a height, an angle, and a curvature; 
           [0040]      FIG. 8A  illustrates a schematic perspective view showing stress when internal pressure is applied to a rectangular case; 
           [0041]      FIG. 8B  illustrates a schematic perspective view showing a displacement amount of the case of  FIG. 8A ; 
           [0042]      FIG. 8C  illustrates a front view of the case of  FIG. 8A ; 
           [0043]      FIG. 9A  illustrates a schematic perspective view of a case on which concentric beads are formed from the center of a surface of the case in correspondence with variations in displacement amount, according to another embodiment; 
           [0044]      FIG. 9B  illustrates a cross-sectional view cut along a line IXb-IXb of  FIG. 9A ; 
           [0045]      FIG. 10A  illustrates a schematic perspective view of a case on which beads are formed on a surface of the case in correspondence with stress-concentrated portions, according to another embodiment; 
           [0046]      FIG. 10B  illustrates a cross-sectional view cut along a line Xb-Xb of  FIG. 10A ; 
           [0047]      FIG. 11A  illustrates a schematic perspective view of a case on which concentric beads and linear beads are formed on a surface of the case in correspondence with variations in displacement amount and stress-concentrated portions, according to another embodiment; 
           [0048]      FIG. 11B  illustrates a cross-sectional view cut along a line XIb-XIb of  FIG. 11A ; 
           [0049]      FIG. 12A  illustrates a schematic perspective view of a case on which concentric beads, linear beads, and radial beads are formed on a surface of the case in correspondence with variations in displacement amount and stress-concentrated portions, according to another embodiment; 
           [0050]      FIG. 12B  illustrates a cross-sectional view cut along a line XIIb-XIIb of  FIG. 12A ; 
           [0051]      FIG. 13A  illustrates a schematic perspective view showing stress distribution when one bead is formed on a case, according to another embodiment; 
           [0052]      FIG. 13B  illustrates a schematic perspective view showing a displacement amount of the case illustrated in  FIG. 13A ; 
           [0053]      FIG. 13C  illustrates a front view of the case of  FIG. 13A ; 
           [0054]      FIG. 14A  illustrates a schematic perspective view showing stress distribution when two beads are formed on a case, according to another embodiment; 
           [0055]      FIG. 14B  illustrates a schematic perspective view showing a displacement amount of the case of  FIG. 14A ; 
           [0056]      FIG. 14C  illustrates a front view of the case of  FIG. 14A ; 
           [0057]      FIG. 15A  illustrates a schematic perspective view showing stress distribution when eight beads are formed on four sides of a case, according to another embodiment; 
           [0058]      FIG. 15B  illustrates a schematic perspective view showing a displacement amount of the case of  FIG. 15A ; 
           [0059]      FIG. 15C  illustrates a front view of the case of  FIG. 15A ; and 
           [0060]      FIG. 15D  illustrates a side view of the case of  FIG. 15A . 
       
    
    
     DETAILED DESCRIPTION 
       [0061]    Example embodiments will now be described more fully hereinafter with reference to the accompanying drawings; however, they may be embodied in different forms and should not be construed as 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 scope of the invention to those skilled in the art. 
         [0062]    In the drawing figures, the dimensions of layers and regions may be exaggerated for clarity of illustration. It will also be understood that when a layer or element is referred to as being “on” another layer or substrate, it can be directly on the other layer or substrate, or intervening layers may also be present. Further, it will be understood that when a layer is referred to as being “under” another layer, it can be directly under, and one or more intervening layers may also be present. In addition, it will also be understood that when a layer is referred to as being “between” two layers, it can be the only layer between the two layers, or one or more intervening layers may also be present. Like reference numerals refer to like elements throughout. 
         [0063]    The structure of a secondary battery  1  will now be described with reference to  FIGS. 1 and 2 , after which the structure of a case  34  capable of efficiently withstanding internal pressure will be described.  FIG. 1  illustrates a schematic perspective view of a secondary battery.  FIG. 2  illustrates a cross-sectional view cut along a line II-II of  FIG. 1 . 
         [0064]    Referring to  FIGS. 1 and 2 , the secondary battery  1  may include an electrode assembly  10 , positive and negative terminals  21  and  22 , and the case  34 . The case  34  may accommodate the electrode assembly  10 , and the electrode assembly  10  may be electrically connected to an external device via the positive and negative terminals  21  and  22 . 
         [0065]    The electrode assembly  10  may include a positive electrode  11 , a negative electrode  12 , and a separator  13 . The positive and negative electrodes  11  and  12  may be wound with the separator  13 , i.e., an insulator, interposed therebetween so as to form the electrode assembly  10 . A center pin (not shown) may be disposed in the electrode assembly  10 , and the positive and negative electrodes  11  and  12  may be wound around the center pin. In another implementation, the positive electrode  11 , the separator  13 , and the negative electrode  12  may be stacked. The positive and negative electrodes  11  and  12  may respectively include positive and negative uncoated parts  11   a  and  12   a  and positive and negative coated parts  11   b  and  12   b.    
         [0066]    Each of the positive and negative uncoated parts  11   a  and  12   a  may be a region of a current collector formed of thin metal foil on which an active material is not coated, while each of the positive and negative coated parts  11   b  and  12   b  may be a region of a current collector formed of thin metal foil on which an active material is coated. 
         [0067]    A positive current collecting unit  40   a  may be welded to the positive uncoated part  11   a  of the electrode assembly  10 . The positive current collecting unit  40   a  may be electrically connected to the positive terminal  21  via a lead member  28 . As such, the positive terminal  21  may be connected to the positive electrode  11  of the electrode assembly  10  via the lead member  28  and the positive current collecting unit  40   a . A negative current collecting unit  40   b  may be electrically connected to the negative terminal  22  via the lead member  28 . As such, the negative terminal  22  may be connected to the negative electrode  12  of the electrode assembly  10  via the lead member  28  and the negative current collecting unit  40   b.    
         [0068]    An insulating member  26  may be formed between the lead member  28  and a cap plate  30 . The lead member  28  may include a current collecting lead unit  28   b  bonded to the positive and negative current collecting units  40   a  and  40   b , and a terminal lead unit  28   a  bonded to the positive and negative terminals  21  and  22 . The positive and negative terminals  21  and  22  may be respectively and electrically connected to the positive and negative electrodes  11  and  12  of the electrode assembly  10 , and may protrude out of the case  34 . 
         [0069]    The case  34  may include the cap plate  30  on one side. The case  34  may have a rectangular can shape of which one side is open, and the open side of the case  34  may be sealed by using the cap plate  30 . The cap plate  30  may cover the case  34  while allowing the positive and negative terminals  21  and  22  to protrude out of the case  34 . When the electrode assembly  10  and an electrolyte are accommodated in the case  34 , the case  34  and the cap plate  30  may be laser-welded to each other so as to seal the electrode assembly  10  and the electrolyte in the case  34 . The cap plate  30  may be a thin plate. 
         [0070]    The cap plate  30  may include a vent member  39  on which grooves are formed, the grooves to be broken when the internal pressure of the case  34  reaches a predetermined value. An electrolyte inlet  38   a , through which the electrolyte is injected into the case  34 , may be formed in the cap plate  30 . A sealing plug  38  may fit in and seal the electrolyte inlet  38   a.    
         [0071]    The secondary battery  1  may have various shapes besides the rectangular shape shown in  FIGS. 1 and 2 . For example, the secondary battery  1  may be a cylinder-type secondary battery or a polymer-type secondary battery. Further, the electrode assembly  10  may be formed as a winding type with a center pin, as a stacking type, etc. 
         [0072]    In the secondary battery  1 , the electrode assembly  10  may expand or contract due to recharge and discharge. The expansion and contraction of the electrode assembly  10  may act as a physical force on the case  34 . Thus, the case  34  may expand or contract accordingly. As such, the expansion and contraction of the electrode assembly  10  may displace the case  34 . Also, repeated expansion and contraction of the electrode assembly  10  may fix the displacement of the case  34 . If the case  34  is displaced due to the electrode assembly  10  being expanded, the efficiency of the secondary battery  1  may be reduced. Also, when recharge and discharge are repeated, an active material coated on the positive and negative coated parts  11   b  and  12   b  may be removed or may deteriorate. 
         [0073]    Embodiments provide structures of the case  34  that are configured to distribute internal pressure and increase rigidity by modifying the case  34 . This may be achieved without having any further components. In order to lower stress on the case  34  and to reduce a displacement amount of the case  34  when the electrode assembly  10  expands, the case  34  may satisfy one or more of the following three conditions. First, a surface area of the case  34  may be increased. Second, the internal pressure in the case  34  may be distributed. Third, the rigidity of the case  34  may be increased. The three conditions with respect to the case  34  will now be described in detail. 
         [0074]    First, referring  FIG. 3 , increasing the surface area of the case  34  to suppress displacement of the case  34  will be described.  FIG. 3  illustrates a schematic perspective view of a case  34  including different-length sides A, B, and C. Stress a will be described with reference to  FIG. 3 . The stress σ refers to a force F that acts on a unit area S. The unit area S refers to a surface area of the case  34  on which the force F acts. The stress σ is defined as represented in Equation 1. 
         [0000]    
       
         
           
             
               
                 
                   σ 
                   = 
                   
                     
                       
                         Force 
                          
                         
                           ( 
                           F 
                           ) 
                         
                       
                       
                         UnitArea 
                          
                         
                           ( 
                           S 
                           ) 
                         
                       
                     
                     ∝ 
                     
                       1 
                       S 
                     
                   
                 
               
               
                 
                   〈 
                   
                     Equation 
                      
                     
                         
                     
                      
                     1 
                   
                   〉 
                 
               
             
           
         
       
     
         [0075]    For example, the force F may be generated due to internal pressure in the case  34  caused by expansion or contraction of the electrode assembly  10  illustrated in  FIG. 2 . However, the cause of the force F is not limited thereto, and the force F may be generated due to various causes such as an increase in the internal pressure due to a gas being generated in the case  34 . 
         [0076]    According to Equation 1, the stress σ is inversely proportional to the unit area S. Accordingly, when the force F is constant, if the unit area S increases, the stress σ decreases. In this case, the decreasing of the stress σ means that the force F on the unit area S (i.e., F/S) to displace the case  34  in a region of the case  34  decreases. Accordingly, in order to withstand the internal pressure of the case  34  and to efficiently suppress displacement of the case  34 , the case  34 ′ may have a structure for increasing the unit area S. In this case, displacement of the case  34  may be suppressed by distributing a direction of the force F, as well as by increasing the unit area S of the case  34 . 
         [0077]    A case  34 ′ having a surface configured to increase the unit area S will now be described with reference to  FIGS. 4A and 4B . As illustrated in  FIGS. 4A and 4B , in order to increase the unit area S of the case  34 ′, beads b having the same ratio of a width w to a peak height h may be formed on surfaces of the case  34 ′. For a projecting bead b, the width w may be measured from peak to peak, and for a recessed bead b, the width w may be measured from edge to edge. The beads b are not restricted to having the same size. The beads b may have different sizes in the same ratio of the width w to the peak height h. 
         [0078]    When one side of the case  34 ′ has a length (A) and a number (N) of beads b are formed on the side having the length (A), the width w of the beads b is A/N In this case, as illustrated in  FIG. 4B , a length x of a hypotenuse of the beads b may be calculated as represented in Equation 2 by using the Pythagorean theorem. 
         [0000]    
       
         
           
             
               
                 
                   x 
                   = 
                   
                     2 
                      
                     A 
                      
                     
                       
                         
                           1 
                           
                             4 
                              
                             
                               N 
                               2 
                             
                           
                         
                         + 
                         
                           
                             ( 
                             
                               h 
                               A 
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   〈 
                   
                     Equation 
                      
                     
                         
                     
                      
                     2 
                   
                   〉 
                 
               
             
           
         
       
     
         [0079]    Here, since N beads b are formed on the case  34 ′, the unit area S′ satisfies Equation 3. 
         [0000]        S″=x·N·B=B √{square root over (A 2 +4 N   2   h   2 )}  &lt;Equation 3&gt;
 
         [0080]    Ideally, in order to maximize the unit area S′, the number N and the peak height h of the beads b would be infinite. However, since an infinite number N and the peak height h of the beads b is not practical, ranges of the number N and the peak height h of the beads b may be determined by distributing pressure and increasing rigidity. 
         [0081]    The principal of pressure distribution will now be described with reference to  FIG. 5 . Referring to  FIG. 5 , in comparison to a bottle having a flat bottom surface BF, a bottle having an internally protruding bottom surface BR may distribute pressure applied onto the bottom surface so as to withstand high pressure. Internal pressure distribution may differ according to a width w and a peak height h of a round bead formed in the bottom surface. In this case, when an angle θ of the bead is equal to 45°, force distribution is maximized. Accordingly, the angle θ of the bead may be equal to or less than 45°. Here, when the angle θ of the bead is 45°, h/w is ½ and thus 
         [0000]    
       
         
           
             
               h 
               w 
             
             × 
             100 
           
         
       
     
         [0000]    may be equal to or less than 50%, h and w being measured in the same units, e.g., millimeters (mm). 
         [0082]    The bottle having the internally protruding bottom surface BR may also compensate with respect to volume expansion of the bottle. In more detail, the bottle may be formed of a bendable material, and when the bottle expands due to an increase in internal pressure, the internally protruding bottom surface may move so as to increase the internal volume of the bottle, thereby preventing the bottle from breaking or exploding. The same principal may also be considered with respect to the case  34 ′ illustrated in  FIG. 4A . When the internal pressure in the case  34 ′ increases, the beads b protruding into the case  34 ′ may protrude out of the case  34 ′ so as to compensate for the increase in the internal pressure, and thus the case  34 ′ may be prevented from breaking or exploding. 
         [0083]      FIG. 6A  illustrates side and front views of a plate for describing a principal of bending stress.  FIG. 6B  illustrates side and front views of a structure on which a bead is formed.  FIG. 7  illustrates a schematic conceptual view of a bead having a width w, a height h, an angle θ, and a curvature r of a bead b. In  FIGS. 6A and 6B , thin arrows represent the bending stress and large arrows represent a bending moment M. 
         [0084]    The bending stress may be represented by Equation 4. 
         [0000]    
       
         
           
             
               
                 
                   σ 
                   = 
                   
                     
                       M 
                       × 
                       c 
                     
                     I 
                   
                 
               
               
                 
                   〈 
                   
                     Equation 
                      
                     
                         
                     
                      
                     4 
                   
                   〉 
                 
               
             
           
         
       
     
         [0085]    In Equation 4, a represents the bending stress, M represents the bending moment, c represents a distance from a central axis to an outer surface, on which the maximum stress occurs, and I represents a moment of inertia. 
         [0086]    As represented in Equation 4, the bending stress σ is inversely proportional to the moment of inertia I. Thus, the bending stress σ may be reduced by increasing the moment of inertia I. If a bead b is formed on the plane in order to increase the moment of inertia I, the bending stress σ may be reduced. Thus, the bead b may be formed on a surface of the case  34  illustrated in  FIG. 3  in order to increase the bending stress σ. 
         [0087]    Referring to  FIG. 7 , parameters that determine the bending stress σ are a width w, a peak height h, an angle θ, and a curvature r of the bead b. Where and in which direction the bead b is formed on the case  34 ′ also influence the bending stress σ. Here, an angle θ of the bead b is equal to or less than 45°. Also, force distribution is maximized when the shape of the bead b is a semicircle. Thus, a curvature r has a maximum value when a diameter of the bead b is equal to a width w of the bead b (2r≦w). 
         [0088]    When the parameters satisfy ranges listed in Table 1, the case  34 ′ may withstand internal pressure more efficiently. That is, the case  34 ′ may efficiently distribute internal pressure and may increase rigidity according to the ranges listed in Table 1. 
         [0000]    
       
         
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 Parameter 
                 Range 
               
               
                   
               
             
             
               
                 Ratio of Peak Height to Width of Bead 
                    0~50% 
               
               
                 Ratio of Number of Beads (N) to Length (A) of One Side 
                 2%~24% 
               
               
                 Number of Beads (N) 
                    1~10 
               
               
                 Angle of Bead (θ) 
                 0 &lt; θ ≦ 45° 
               
               
                 Curvature of Bead (r) 
                 
                   
                     
                       
                         0 
                         &lt; 
                         r 
                         ≤ 
                         
                           w 
                           2 
                         
                       
                     
                   
                 
               
               
                   
               
             
          
         
       
     
         [0089]    The ratio of the peak height to the width of the bead may be about 0% to about 50% and, more particularly, about 2% to about 33%. The number of beads may be about 1 to about 10, or more. 
         [0090]    Where and in which direction the beads b are formed on the case  134  will now be described with reference to  FIGS. 8A through 8C .  FIG. 8A  illustrates a schematic perspective view showing stress when internal pressure is applied to a rectangular case  134 .  FIG. 8B  illustrates a schematic perspective view showing a displacement amount of the case  134  of  FIG. 8A .  FIG. 8C  illustrates a front view of the case  134  of  FIG. 8A . 
         [0091]    Referring to  FIG. 8A , S 1 , S 2 , S 3 , and S 4  indicate stress-concentrated portions on the case  134 , and are symmetrical with respect to x and y axes. Accordingly, in order to distribute stress on the case  134 , the beads b may be formed on the case  134  symmetrically with respect to the x axis, the y axis, or both the x and y axes. Also, the beads b do not need to be sequentially formed, and may be partially formed in correspondence with displacement or stress-concentrated portions so as to distribute displacement or stress. Referring to  FIG. 8B , the amount of displacement may be concentrated concentrically from the intersection of the x and y axes of the case  134 , i.e., displacement may be greatest at the center or origin of the x-y axes. Thus, in order to suppress the displacement, beads b may be formed concentrically from the intersection of the x and y axes of the case  134 . 
         [0092]    Hereinafter, shapes and arrangements of the beads b according to embodiments will be described with reference to  FIGS. 9A and 9B ,  10 A and  10 B,  11 A and  11 B, and  12 A and  12 B, and variations in displacement amount according to the number N and the ratio of the peak height h to the width 
         [0000]    
       
         
           
             w 
              
             
               ( 
               
                 
                   h 
                   w 
                 
                 × 
                 100 
               
               ) 
             
           
         
       
     
         [0000]    of the beads b will be described with reference to  FIGS. 13A through 13C ,  14 A through  14 C, and  15 A through  15 D. 
         [0093]    The shapes and arrangements of the beads b formed on the case  134  will be described with reference to  FIGS. 9A and 9B ,  10 A and  10 B,  11 A and  11 B, and  12 A and  12 B. 
         [0094]    As described above with reference to  FIG. 8A , a displacement amount may vary concentrically from the center of a surface of the rectangular case  134  (an origin of x and y coordinates). Also, the portions S 1 , S 2 , S 3 , and S 4  corresponding to four sides from the center of the surface may be stress-concentrated portions. Accordingly, the beads b may be formed concentrically from the center of the surface, may be formed in correspondence with the stress-concentrated portions, or may be formed both concentrically from the center of the surface and in correspondence with the stress-concentrated portions. 
         [0095]      FIG. 9A  illustrates a schematic perspective view of a case  234  on which concentric beads ccb are formed from the center of a surface of the case  234  in correspondence with variations in displacement amount, according to another embodiment.  FIG. 9B  illustrates a cross-sectional view cut along a line IXb-IXb of  FIG. 9A . In this case, the beads b may include the concentric beads ccb, linear beads lb, and radial beads rb formed in correspondence with stress-concentrated portions or variations in displacement amount, and may also include corner beads cb and assistant beads ab formed in correspondence with the arrangement and functions of the beads b. 
         [0096]    Referring to  FIGS. 9A and 9B , the concentric beads ccb may be formed around the center of the surface of the case  234 . In this case, the corner beads cb may be additionally formed at corners of the case  234 . Also, if the surface of the case  234  on which the beads b are formed is not square, the assistant beads ab may also be formed in correspondence with the shape of remaining portions where the concentric beads ccb are not formed. In another implementation, the beads b may be formed in correspondence with the portions S 1 , S 2 , S 3 , and S 4  illustrated in  FIG. 8A , where stress is concentrated, as illustrated in  FIGS. 10A and 10B . 
         [0097]      FIG. 10A  illustrates a schematic perspective view of a case  234  on which beads b are formed on a surface of the case  334  in correspondence with stress-concentrated portions, according to another embodiment.  FIG. 10B  illustrates a cross-sectional view cut along a line Xb-Xb of  FIG. 10A . 
         [0098]    Referring to  FIGS. 10A and 10B , the beads b may be formed in correspondence with portions of the case  334  where stress is concentrated, i.e., on perpendicular lines from the center of the surface to four sides of the case  334 . The stress-concentrated portions may be located on the x or y axis of the rectangular case  334 . Thus, the beads b may be formed such that the centers of the beads b are disposed on the x or y axis. The beads b are not limited to the shape illustrated in  FIGS. 10A and 10B , and may be various shapes such as linear and non-linear shapes. 
         [0099]    In another embodiment, the beads b may be formed in correspondence with variations in displacement amount and stress-concentrated portions, as illustrated in  FIGS. 11A and 11B .  FIG. 11A  illustrates a schematic perspective view of a case  434  on which concentric beads ccb and linear beads lb are formed on a surface of the case  434  in correspondence with variations in displacement amount and stress-concentrated portions, according to another embodiment.  FIG. 11B  illustrates a cross-sectional view cut along a line XIb-XIb of  FIG. 11A . 
         [0100]    Referring to  FIGS. 11A and 11B , the concentric beads ccb may be formed near the center and sides of the case  434 , and the linear beads lb may be formed at the stress-concentrated portions between the concentric beads ccb. Also, the corner beads cb may be formed at corners of the case  434 . The beads are not limited to the shapes illustrated in  FIGS. 11A and 11B , and may have various shapes as illustrated in  FIGS. 12A and 12B . 
         [0101]      FIG. 12A  illustrates a schematic perspective view of a case  534  on which concentric beads ccb, linear beads lb, and radial beads rb are formed on a surface of the case  534  in correspondence with variations in displacement amount and stress-concentrated portions, according to another embodiment.  FIG. 12B  illustrates a cross-sectional view cut along a line XIIb-XIIb of  FIG. 12A . 
         [0102]    Referring to  FIGS. 12A and 12B , the radial beads rb may be formed in addition to the concentric beads ccb and the linear beads lb. The beads b may be formed having x-axis symmetry, y-axis symmetry, or origin symmetry with respect to the intersection of the x and y axes of a surface of the case  534  in order to distribute stress. 
         [0103]    Table 2 illustrates the stress amounts and displacement amounts of the cases of  FIG. 3 ,  FIGS. 9A through 9B , and  FIGS. 12A through 12B . 
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                   
                 FIGS. 9A 
                 FIGS. 12A 
               
               
                   
                 FIG. 3 
                 through 9B 
                 through 12B 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 Stress Amount (MPa) 
                 22.98 
                 0.07 
                 0.84 
               
               
                 Stress Amount 
                 — 
                 99% 
                 96% 
               
               
                 Reduction (%) 
               
               
                 Displacement 
                 2.9 
                 0.495 
                 1.909 
               
               
                 Amount(mm) 
               
               
                 Displacement Amount 
                 — 
                 83% 
                 34% 
               
               
                 Reduction (%) 
               
               
                   
               
             
          
         
       
     
         [0104]    As shown in Table 2, the stress amounts and displacement amounts of the embodiments of  FIGS. 9A through 9B  and  FIGS. 12A through 12B  are significantly reduced relative to that shown in  FIG. 3 , in which no beads are formed. Also, with respect to the embodiments of  FIGS. 9A through 9B , and  FIGS. 12A through 12B , the embodiment of  FIGS. 9A through 9B  has less strain amount and displacement amount. Here, even though at least one concentric bead ccb having 2 mm width and 0.8 mm depth is formed on the embodiments of  FIGS. 9A through 9B , and  FIGS. 12A through 12B , the amounts of strain and displacement may vary. Without being bound by theory, one of the possible reasons for such is that the additional concentric beads ccb are formed on the embodiment of  FIGS. 9A through 9B , whereas further radial beads rb are formed on the embodiments of  FIGS. 12A through 12B . Thus, it can also be inferred that one or more concentric beads ccb may be efficient in reducing the amounts of stress and displacement. 
         [0105]    Hereinabove, the shapes and arrangements of the beads b formed on the cases  234 ,  334 , and  434  against stress concentration and displacement are described with reference to  FIGS. 9A and 9B ,  10 A and  10 B,  11 A and  11 B, and  12 A and  12 B. Variations in displacement amount according to the number N and the ratio of the peak height h to the width 
         [0000]    
       
         
           
             w 
              
             
               ( 
               
                 
                   h 
                   w 
                 
                 × 
                 100 
               
               ) 
             
           
         
       
     
         [0000]    of the beads b will now be described with reference to  FIGS. 13A through 13C ,  14 A through  14 C, and  15 A through  15 D. Here,  FIGS. 9A and 9B ,  10 A and  10 B,  11 A and  11 B, and  12 A and  12 B may be related to  FIGS. 13A through 13C ,  14 A through  14 C, and  15 A through  15 D. That is, although not described below, the battery case may have any of the shapes and arrangements of the beads b illustrated in  FIGS. 9A and 9B ,  10 A and  10 B,  11 A and  11 B, and  12 A and  12 B, and may also have the numbers N and the ratios of the peak height h to the width 
         [0000]    
       
         
           
             w 
              
             
               ( 
               
                 
                   h 
                   w 
                 
                 × 
                 100 
               
               ) 
             
           
         
       
     
         [0000]    of the beads b to be described with reference to any of  FIGS. 13A through 13C ,  14 A through  14 C, and  15 A through  15 D, at the same time. 
         [0106]      FIG. 13A  illustrates a schematic perspective view showing stress distribution when one bead b is formed on a case  634 , according to another embodiment.  FIG. 13B  illustrates a schematic perspective view showing a displacement amount of the case  634  illustrated in  FIG. 13A .  FIG. 13C  illustrates a front view of the case  634  of  FIG. 13A .  FIG. 14A  illustrates a schematic perspective view showing stress distribution when two beads b are formed on a case  734 , according to another embodiment.  FIG. 14B  illustrates a schematic perspective view showing a displacement amount of the case  734  of  FIG. 14A .  FIG. 14C  illustrates a front view of the case  734  of  FIG. 14A .  FIG. 15A  illustrates a schematic perspective view showing stress distribution when eight beads b are formed on four sides of a case  834 , according to another embodiment.  FIG. 15B  illustrates a schematic perspective view showing a displacement amount of the case  834  of  FIG. 15A .  FIG. 15C  illustrates a front view of the case  834  of  FIG. 15A .  FIG. 15D  is a side view of the case  834  illustrated in  FIG. 15A . 
         [0107]    Table 3 shows parameters for simulations of the embodiments of  FIGS. 13A through 13C ,  14 A through  14 C, and  15 A through  15 D. Here, the case of  FIGS. 8A through 8C  uses the rectangular case  34  on which the beads b are not formed and, in Table 3, the embodiments of  FIGS. 13A through 13C ,  14 A through  14 C, and  15 A through  15 D are compared to that of  FIGS. 8A through 8C  with respect to variation in displacement amount. 
         [0000]    
       
         
               
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                   
                 FIGS. 8A 
                 FIGS. 13A 
                 FIGS. 14A 
                 FIGS. 15A 
               
               
                   
                 through  
                 through  
                 through  
                 through  
               
               
                   
                 8C 
                 13C 
                 14C 
                 15D 
               
               
                   
               
             
             
               
                 Length of Side (A) 
                 34 
                 34 
                 34 
                 34 
               
               
                 Number of Beads (N) of 
                  0 
                  1 
                  2 
                  8 
               
               
                 Side A 
                   
                   
                   
                   
               
               
                 Peak Height of Bead (h) 
                  0 
                  0.8 
                  0.8 
                  0.8 
               
               
                 of Side A (mm) 
                   
                   
                   
                   
               
               
                 Width of Bead (w) of 
                 34 
                 34 
                 17 
                  4.25 
               
               
                 Side A (mm) 
                   
                   
                   
                   
               
               
                 
                   
                     
                       
                         
                           h 
                           w 
                         
                         × 
                         100 
                          
                         
                             
                         
                          
                         of 
                          
                         
                             
                         
                          
                         Side 
                          
                         
                             
                         
                          
                         A 
                       
                     
                   
                 
                  0% 
                  2.6% 
                  4.7% 
                 18.8% 
               
               
                 
                   
                     
                       
                         
                           N 
                           
                             A 
                              
                             
                               ( 
                               mm 
                               ) 
                             
                           
                         
                         × 
                         100 
                          
                         
                             
                         
                          
                         of 
                          
                         
                             
                         
                          
                         Side 
                          
                         
                             
                         
                          
                         A 
                       
                     
                   
                 
                  0% 
                  2.9% 
                  5.9% 
                 23.5% 
               
               
                 Length of Side (B) (mm) 
                 42 
                 42 
                 42 
                 42 
               
               
                 Number of Beads (N) of 
                  0 
                  0 
                  0 
                  8 
               
               
                 Side B 
                   
                   
                   
                   
               
               
                 Peak Height of Bead (h) 
                  0 
                  0 
                  0 
                  0.8 
               
               
                 of Side B (mm) 
                   
                   
                   
                   
               
               
                 Width of Bead (w) of 
                 42 
                 42 
                 42 
                  5.25 
               
               
                 Side B (mm) 
                   
                   
                   
                   
               
               
                 
                   
                     
                       
                         
                           h 
                           w 
                         
                         × 
                         100 
                          
                         
                             
                         
                          
                         of 
                          
                         
                             
                         
                          
                         Side 
                          
                         
                             
                         
                          
                         B 
                       
                     
                   
                 
                  0% 
                  0% 
                  0% 
                 15.2% 
               
               
                 
                   
                     
                       
                         
                           N 
                           
                             B 
                              
                             
                               ( 
                               mm 
                               ) 
                             
                           
                         
                         × 
                         100 
                          
                         
                             
                         
                          
                         of 
                          
                         
                             
                         
                          
                         Side 
                          
                         
                             
                         
                          
                         B 
                       
                     
                   
                 
                  0% 
                  0% 
                  0% 
                 19% 
               
               
                 Displacement Amount 
                  2.9 
                  2.8 
                  2.5 
                  2.1 
               
               
                 (mm) 
                   
                   
                   
                   
               
               
                 Displacement Amount 
                 — 
                  5% 
                 13% 
                 27% 
               
               
                 Reduction (%) 
               
               
                   
               
             
          
         
       
     
         [0108]    As shown in Table 3, in comparison to the case of  FIGS. 8A through 8C , the displacement amount is reduced by about 5% in the embodiment of  FIGS. 13A through 13C , is reduced by about 13% in the embodiment of  FIGS. 14A through 14C , and is reduced by about 27% in the embodiment of  FIGS. 15A through 15D . Thus, according to Table 3, as the number N of the beads b increases, and as the ratio of the peak height h to the width 
         [0000]    
       
         
           
             w 
              
             
               ( 
               
                 
                   h 
                   w 
                 
                 × 
                 100 
               
               ) 
             
           
         
       
     
         [0000]    of the beads b increases, there is a greater reduction in the amount of displacement. In this case, the ratio of the peak height h to the width 
         [0000]    
       
         
           
             w 
              
             
               ( 
               
                 
                   h 
                   w 
                 
                 × 
                 100 
               
               ) 
             
           
         
       
     
         [0000]    of the beads b may be about 0% to about 50%, and more particularly, about 2% to about 33%. In Table 3, the ratio of the peak height h to the width 
         [0000]    
       
         
           
             w 
              
             
               ( 
               
                 
                   h 
                   w 
                 
                 × 
                 100 
               
               ) 
             
           
         
       
     
         [0000]    of the beads b is from about 2.6% to about 18.8%, which is included in the range of about 2% to about 33%. 
         [0109]    The number N of the beads b with respect to one side having a length may be determined by using two methods described below. First, the number N of the beads b may be determined in a range from about 1 to about 10, regardless of the length of one side. In this case, the beads b may have a shape that satisfies the ratio of the peak height h to the width 
         [0000]    
       
         
           
             w 
              
             
               ( 
               
                 
                   h 
                   w 
                 
                 × 
                 100 
               
               ) 
             
           
         
       
     
         [0000]    of the beads, which is indicated in Table 1. Second, the number N of the beads b may be determined as an integer close to a value obtained by multiplying the length A of one side by a ratio of the number N of the beads b to a length of one side 
         [0000]    
       
         
           
             
               ( 
               
                 
                   N 
                   
                     A 
                      
                     
                       ( 
                       mm 
                       ) 
                     
                   
                 
                 × 
                 100 
               
               ) 
             
             . 
           
         
       
     
         [0000]    In this case, referring to Table 1, the ratio of the number N of the beads b to the length A of one side 
         [0000]    
       
         
           
             ( 
             
               
                 N 
                 
                   A 
                    
                   
                     ( 
                     mm 
                     ) 
                   
                 
               
               × 
               100 
             
             ) 
           
         
       
     
         [0000]    may be in a range from about 2% to about 24%. 
         [0110]    As described above, a case configured to efficiently distribute internal pressure of, and increase rigidity of, a secondary battery according to embodiments may be formed by forming beads b by controlling locations, a width w, a peak height h, an angle θ, a curvature r, the number N, and a ratio of the peak height h to the width 
         [0000]    
       
         
           
             w 
              
             
               ( 
               
                 
                   h 
                   w 
                 
                 × 
                 100 
               
               ) 
             
           
         
       
     
         [0000]    of the beads b. 
         [0111]    Example embodiments have been disclosed herein, and although specific terms are employed, they are used and are to be interpreted in a generic and descriptive sense only and not for purpose of limitation. Accordingly, it will be understood by those of skill in the art that various changes in form and details may be made without departing from the spirit and scope of the present invention as set forth in the following claims.