Patent ID: 11965578
Assignee: DALIAN UNIVERSITY OF TECHNOLOGY
Field: Mechanical elements (Mechanical engineering)
Classification: CPC F  G | IPC F

Claim 0:
1. A design method for a lead screw flywheel the inerter having a flywheel and an adaptively adjusted inertia ratio in order to reduce a basic moment of inertia of the flywheel, the flywheel having a disk with spring-mass block structures; a lead screw that is subjected to an external force load to make the flywheel rotate, the mass blocks are moved along the radial direction of the flywheel under the combined action of a centrifugal force and a spring restore force, and the change of positions of the mass blocks changes the moment of inertia of the flywheel accordingly, so that the inertia ratio of the inerter is adaptively adjusted along with the change of the external force load; the design method comprising steps of:
providing a mass distribution of the flywheel and the spring-mass block structures on the disk such that a relation between positions of the mass blocks in a radial direction of the flywheel and an angular velocity of the flywheel is obtained by a force balance between a centrifugal force on the mass blocks and a spring restore force during rotation of the flywheel, the relation being expressed as:, m
          ⁢
          
            
              
                d
                2
              
              ⁢
              
                R
                ⁡
                
                  (
                  t
                  )
                
              
            
            
              d
              ⁢
              
                t
                2
              
            
          
        
        =
        
          
            m
            ⁢
            
              
                ω
                2
              
              ⁡
              
                (
                t
                )
              
            
            ⁢
            
              R
              ⁡
              
                (
                t
                )
              
            
          
          -
          
            k
            ⁡
            
              [
              
                
                  R
                  ⁡
                  
                    (
                    t
                    )
                  
                
                -
                
                  R
                  0
                
              
              ]
            
          
        
      
    
    
      
        (
        1
        )
      
    
  

wherein the left side of the equal sign is an inertial force on the mass blocks; the first term on the right side of the equal sign is the centrifugal force on the mass blocks, and the second term on the right side of the equal sign is the spring restore force; m is mass of the mass blocks, ω(t) is angular velocity of the flywheel, R(t) is distance between the centroid of the mass blocks and the center of rotation of the flywheel, k is stiffness coefficient of springs, R0 is minimum distance between the centroid of the mass blocks and the center of rotation of the flywheel, and t is a time variable;
providing a lead screw-nut sport pair such that a following movement equation between the angular velocity ω(t) of the flywheel and a load on a lead screw of the lead screw-nut sport pair is obtained as expressed as the following differential equation:, J
            ⁡
            
              (
              t
              )
            
          
          ⁢
          
            
              d
              ⁢
              
                ω
                ⁡
                
                  (
                  t
                  )
                
              
            
            
              d
              ⁢
              t
            
          
        
        =
        
          
            p
            
              2
              ⁢
              π
            
          
          ⁢
          
            
              F
              l
            
            ⁡
            
              (
              t
              )
            
          
        
      
    
    
      
        (
        2
        )
      
    
  

wherein p is a pitch of the lead screw; Fl(t) is a load on the lead screw; and J(t) is a moment of inertia of the flywheel, J(t) being further expressed as:

J(t)=J0+nmR2(t)  (3)

wherein J0 is a fixed moment of inertia of the flywheel; the second term on the right side of the equation represents an adjustable moment of inertia part of the flywheel, n is quantity of the spring-mass block structures, and n is an integral multiple of 2;
providing the inerter such that an adaptive inertia ratio is obtained, the ratio being expressed as:, b
            v
          
          ⁡
          
            (
            t
            )
          
        
        =
        
          
            
              (
              
                
                  2
                  ⁢
                  π
                
                p
              
              )
            
            2
          
          ⁡
          
            [
            
              
                J
                0
              
              +
              
                n
                ⁢
                m
                ⁢
                
                  
                    R
                    2
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
              
            
            ]
          
        
      
    
    
      
        (
        4
        )
      
    
  

providing the flywheel as a homogeneous disc making a fixed axis rotation around the center, the fixed moment of inertia of the flywheel being expressed as:

J0=½ρVr2  (5)

wherein r is the radius of the flywheel, ρ is the density of the flywheel, and V is the total volume of the flywheel;
providing a main body of the flywheel made of aluminum alloy, removing part of the material on the disk of the flywheel so as to further reduce the fixed moment of inertia of the flywheel;
providing the material of mass blocks as copper;
providing
the inerter as further comprising a shell, the lead screw, the flywheel and a nut;
the nut being in solid connection to the flywheel, and the axis of the nut being coaxial with the center of rotation of the flywheel; the top of the lead screw being an inerter endpoint B; the lead screw being connected to the nut, and the lead screw-nut sport pair being composed by the lead screw and the nut to convert the rectilinear motion of the inerter endpoint B into the rotational motion of the flywheel;
the flywheel comprises a flywheel basic part, the springs and the mass blocks; the flywheel basic part being formed by removing part of the material on the disk of the flywheel; the flywheel being provided with a plurality of guide grooves along the radial direction, and the mass blocks being installed in the guide grooves and can make rectilinear motion along the radial direction of the flywheel; one end of each spring being connected to each mass block, and the other end thereof being connected to one side of each guide groove near the center of rotation of the flywheel;
the shell has having a hollow structure in the flywheel, the nut and the lead screw are disposed therein;
providing
a numerical simulation model of the inerter with the adaptively adjusted inertia ratio, and verifying the numerical simulation model of the inerter with numerically simulated load signals.