Patent ID: 11859686
Assignee: HARBIN ENGINEERING UNIVERSITY
Field: Mechanical elements (Mechanical engineering)
Classification: CPC F | IPC F

Claim 2:
3. The method according to claim 2, wherein the step 3 comprises: according to a structure that the negative stiffness electromagnetic actuator is symmetrical up and down, establishing an electromagnetic force-displacement expression of the negative stiffness electromagnetic actuator under the condition of magnetic unsaturation, determining a magnitude of an electromagnetic attraction force of the negative stiffness electromagnetic actuator under ideal conditions, and representing an electromagnetic attraction force Fmag under ideal conditions by the following formulas:, F
       
        m
        ⁢
        a
        ⁢
        g
       
      
      =
      
       
        
         F
         
          mag
          ⁢
          1
         
        
        -
        
         F
         
          mag
          ⁢
          2
         
        
       
       =
       
        2
        ⁢
        
         N
         1
         2
        
        ⁢
        
         I
         
          c
          ⁢
          1
         
         2
        
        ⁢
        
         μ
         0
        
        ⁢
        
         S
         
          i
          ⁢
          n
         
        
        ⁢
        
         
          
           S
           out
          
          (
          
           
            S
            
             i
             ⁢
             n
            
           
           +
           
            S
            out
           
          
          )
         
         [
         
          
           1
           
            
             (
             
              
               a
               ⁢
               x
              
              +
              b
             
             )
            
            2
           
          
          -
          
           1
           
            
             (
             
              
               a
               ⁢
               x
              
              -
              b
             
             )
            
            2
           
          
         
         ]
        
       
      
     
     ,
    
   
  
  
   
    
     
      
       F
       
        mag
        ⁢
        2
       
      
      =
      
       
        
         1
         2
        
        ⁢
        
         
          Φ
          2
          2
         
         
          
           μ
           0
          
          ⁢
          
           S
           
            i
            ⁢
            n
           
          
         
        
       
       +
       
        
         1
         2
        
        ⁢
        
         
          Φ
          2
          2
         
         
          
           μ
           0
          
          ⁢
          
           S
           
            o
            ⁢
            u
            ⁢
            t
           
          
         
        
       
      
     
     ,
    
   
  
  
   
    
     
      a
      =
      
       2
       ⁢
       
        (
        
         
          S
          
           i
           ⁢
           n
          
         
         +
         
          S
          out
         
        
        )
       
      
     
     ,
    
   
  
  
   
    
     
      b
      =
      
       
        
         (
         
          
           
            l
            8
           
           
            μ
            r
           
          
          +
          
           
            2
            ⁢
            
             l
             b
            
           
           
            μ
            r
           
          
          +
          
           2
           ⁢
           g
          
         
         )
        
        ⁢
        
         (
         
          
           S
           
            i
            ⁢
            n
           
          
          +
          
           S
           out
          
         
         )
        
       
       +
       
        
         
          2
          ⁢
          
           l
           a
          
         
         
          μ
          r
         
        
        ⁢
        
         S
         
          i
          ⁢
          n
         
        
        ⁢
        
         S
         out
        
        ⁢
        
         (
         
          
           1
           
            S
            1
           
          
          +
          
           1
           
            S
            2
           
          
         
         )
        
       
      
     
     ,
    
   
  
 

wherein Fmag2 represents an electromagnetic attraction force of second electromagnet; Φ2 represents a magnetic flux of the second electromagnet; x represents a displacement of a negative stiffness spring; Ic1 represents a current passing through the first coil, and a current Ic2 passing through the second coil is equal to the current Ic1; μr represents a magnitude of a relative magnetic conductivity of materials of the first iron core, the second iron core, the first armature and the second armature; g represents a maximum value of a unilateral air gap; a represents an intermediate calculation variable about Sin and Sout; and b represents an intermediate calculation variable about l8, la, lb, Sin, Sout, S1, S2 and μr; and
according to the number of turns of the coil and the current of the second electromagnet and the total reluctance of the second electromagnet, determining the magnetic flux of the second electromagnet, and representing the magnetic flux of the second electromagnet by the following formulas:, Φ
       2
      
      =
      
       
        
         N
         2
        
        ⁢
        
         I
         2
        
       
       
        R
        
         t
         ⁢
         o
         ⁢
         t
         ⁢
         a
         ⁢
         l
         ⁢
         2
        
       
      
     
     ,
    
   
  
  
   
    
     
      
       R
       
        total
        ⁢
        2
       
      
      =
      
       
        R
        
         gap
         ⁢
         21
        
       
       +
       
        R
        
         gap
         ⁢
         22
        
       
       +
       
        R
        arm
       
       +
       
        R
        
         i
         ⁢
         r
         ⁢
         o
         ⁢
         n
        
       
      
     
     ,
    
   
  
  
   
    
     
      
       R
       
        gap
        ⁢
        21
       
      
      =
      
       
        x
        2
       
       
        
         μ
         0
        
        ⁢
        
         S
         
          i
          ⁢
          n
         
        
       
      
     
     ,
    
   
  
  
   
    
     
      
       R
       
        gap
        ⁢
        22
       
      
      =
      
       
        x
        2
       
       
        
         μ
         0
        
        ⁢
        
         S
         
          o
          ⁢
          u
          ⁢
          t
         
        
       
      
     
     ,
    
   
  
 

wherein x2 represents an air gap of the second electromagnet; N2 represents the number of turns of the second coil of the second electromagnet; Rtotal2 represents a total reluctance of the second electromagnet; Rgap21 represents an air gap reluctance corresponding to an inner magnetic pole of the second armature, and Rgap22 represents an air gap reluctance corresponding to an outer magnetic pole of the second armature.