Patent ID: 11965445
Assignee: TOYOTA JIDOSHA KABUSHIKI KAISHA
Field: Environmental technology (Chemistry)
Classification: CPC F | IPC F

Claim 0:
1. A fastening structure that fastens an exhaust manifold to a cylinder head of an engine, the fastening structure comprising:
an exhaust port of the cylinder head, the cylinder head including an opening of the exhaust port that is open to outside of the cylinder head;
a flange arranged on an end of a branch pipe of the exhaust manifold, wherein the flange is fastened to a coupling surface that surrounds the opening of the exhaust port to connect an opening of the exhaust manifold to the opening of the exhaust port, and the flange includes a first end portion and a second end portion that contact the coupling surface and are located at opposite sides of the branch pipe;
a fixing member fixing the first end portion of the flange to the cylinder head;
a bolt extending through the second end portion of the flange, the bolt being inserted into and fixed to a bolt hole of the cylinder head; and
a nut fastened to the bolt to fix the second end portion of the flange to the cylinder head, wherein:
a direction orthogonal to the coupling surface that contacts the second end portion of the flange defines a first direction;
a direction in which the first end portion and the second end portion of the flange are located next to each other defines a second direction;
a direction orthogonal to the first direction and the second direction defines a third direction; and
as viewed in the third direction, the second end portion of the flange includes a contact surface that contacts the coupling surface of the cylinder head, and an inclined surface that is inclined with respect to the contact surface such that the inclined surface becomes closer to the contact surface as the inclined surface becomes farther away from the branch pipe;
the nut is fastened to the bolt so that a compression force is applied to the inclined surface; and
when “x0” represents a length of a part of the bolt that is not in contact with a wall of the bolt hole and is from where the nut applies the compression force to the inclined surface to where the bolt contacts the wall of the bolt hole in a cross section taken along a plane extending along the second direction and a center axis of the bolt when the fastening structure is not thermally expanded;
“Δx” represents an amount of deformation of the bolt in an axial direction of the bolt resulting from thermal expansion of the fastening structure;
“ΔF” represents an amount of change in the force of the nut that compresses the second end portion resulting from thermal expansion of the fastening structure in the cross section;
“θ” represents an angle of the inclined surface with respect to the contact surface in the cross section;
“l” represents a distance from a distal end of the first end portion of the contact surface of the flange to a center of the bolt hole in the cross section when the fastening structure is not thermally expanded;
“αh” represents a coefficient of linear expansion of the cylinder head in the cross section;
“αf” represents a coefficient of linear expansion of the flange;
“αb” represents a coefficient of linear expansion of the bolt;
“ΔTh” represents a temperature change of the cylinder head during thermal expansion of the fastening structure;
“ΔTf” represents a temperature change of the flange during thermal expansion of fastening structure;
“ΔTb” represents a temperature change of the bolt during thermal expansion of the fastening structure;
“κf” represents a spring constant of the flange at a part where the flange is held between the cylinder head and the bolt in the cross section when the fastening structure is not thermally expanded;
“Kb” represents a spring constant of the bolt in the axial direction of the bolt;
“FC” represents a limit load at which any of the cylinder head, the flange, or the bolt undergoes plastic deformation;
“Δxc” represents a limit displacement at which any of the flange or the bolt undergoes plastic deformation; and
“εbc” represents a limit strain at which the bolt undergoes plastic deformation in the axial direction of the bolt;, Δ
      ⁢
      F
     
     =
     
      
       
        K
        b
       
       ⁢
       
        K
        f
       
       ⁢
       
        x
        0
       
       ⁢
       
        {
        
         
          l
          ⁢
          sin
          ⁢
          
           θ
           ⁡
           (
           
            
             
              α
              f
             
             ⁢
             Δ
             ⁢
             
              T
              f
             
            
            -
            
             
              α
              h
             
             ⁢
             Δ
             ⁢
             
              T
              h
             
            
           
           )
          
         
         +
         
          
           x
           0
          
          (
          
           
            
             α
             f
            
            ⁢
            Δ
            ⁢
            
             T
             f
            
           
           -
           
            
             α
             b
            
            ⁢
            Δ
            ⁢
            
             T
             b
            
           
          
          )
         
        
        }
       
      
      
       
        
         (
         
          
           K
           b
          
          +
          
           K
           f
          
         
         )
        
        ⁢
        
         x
         0
        
       
       +
       
        
         K
         b
        
        ⁢
        l
        ⁢
        sin
        ⁢
        
         θ
         ⁡
         (
         
          
           
            α
            f
           
           ⁢
           Δ
           ⁢
           
            T
            f
           
          
          -
          
           
            α
            h
           
           ⁢
           Δ
           ⁢
           
            T
            h
           
          
         
         )
        
       
      
     
    
   
  
  
   
    
     
      Δ
      ⁢
      x
     
     =
     
      
       
        x
        0
       
       ⁢
       
        α
        b
       
       ⁢
       Δ
       ⁢
       
        T
        b
       
      
      +
      
       l
       ⁢
       sin
       ⁢
       
        θ
        ·
        
         α
         h
        
       
       ⁢
       Δ
       ⁢
       
        T
        h
       
      
      +
      
       
        
         K
         f
        
        ⁢
        
         x
         0
        
        ⁢
        
         {
         
          
           l
           ⁢
           sin
           ⁢
           
            θ
            ⁡
            (
            
             
              
               α
               f
              
              ⁢
              Δ
              ⁢
              
               T
               f
              
             
             -
             
              
               α
               h
              
              ⁢
              Δ
              ⁢
              
               T
               h
              
             
            
            )
           
          
          +
          
           
            x
            0
           
           (
           
            
             
              α
              f
             
             ⁢
             Δ
             ⁢
             
              T
              f
             
            
            -
            
             
              α
              b
             
             ⁢
             Δ
             ⁢
             
              T
              b
             
            
           
           )
          
         
         }
        
       
       
        
         
          (
          
           
            K
            b
           
           +
           
            K
            f
           
          
          )
         
         ⁢
         
          x
          0
         
        
        +
        
         
          K
          b
         
         ⁢
         l
         ⁢
         sin
         ⁢
         
          θ
          ⁡
          (
          
           
            
             α
             f
            
            ⁢
            Δ
            ⁢
            
             T
             f
            
           
           -
           
            
             α
             h
            
            ⁢
            Δ
            ⁢
            
             T
             h
            
           
          
          )
         
        
       
      
     
    
   
  
  
   
    
     
      Δ
      ⁢
      F
     
     <
     
      F
      c
     
    
   
  
  
   
    
     
      Δ
      ⁢
      x
     
     <
     
      Δ
      ⁢
      
       x
       c
      
     
    
   
  
  
   
    
     ε
     =
     
      
       
        Δ
        ⁢
        x
       
       
        x
        0
       
      
      <
      
       ε
       
        b
        ⁢
        c
       
      
     
    
   
  
 

the above equations are satisfied.