Patent ID: 11945070
Assignee: DALIAN UNIVERSITY OF TECHNOLOGY
Field: Machine tools (Mechanical engineering)
Classification: CPC B | IPC B

Claim 2:
3. A rocker polishing method for full-aperture deterministic polishing of a planar part, using a rocker polishing apparatus for the full-aperture deterministic polishing of the planar part, comprises the following steps:
step A. measuring original surface profiles of a polishing pad (81) and a planar part (88)
adjusting a rocker (31) to a position where a measuring head of a laser displacement sensor (21) moves radially along the polishing pad (81), collecting an original surface profile of the polishing pad (81) by moving a laser displacement sensor (21) along a linear guide rail (22); and feeding the planar part (88) to a measuring station (51) with the mechanical arm (4) to obtain an original surface profile of the planar part (88);
step B. obtaining a material removal rate distribution of the planar part when a leveled polishing pad is used
starting the linear guide rail and the laser displacement sensor (21) such that a slider of the linear guide rail drives the laser displacement sensor (21) to move radially along the polishing pad (81), thereby measuring the original surface profile of the polishing pad (81); starting the rocker and a motor (71) connected to a diamond dresser (74) such that the diamond dresser (74) dresses the polishing pad (81) at a constant speed along a radial direction of the polishing pad (81), thereby remeasuring a surface profile data of the polishing pad (81); and
according to a difference between surface profiles before and after the polishing pad (81) is dressed and a dressing time, obtaining a dressing removal rate distribution of the polishing pad (81) as follows:, MRR
       pi
      
      =
      
       
        
         
          u
          pi
          0
         
         -
         
          u
          pi
          1
         
        
        
         t
         p
        
       
       ⁢
       n
      
     
     ,
     
      i
      =
      1
     
     ,
     2
     ,
     
      3
      ⁢
        
      …
      ⁢
        
      n
     
    
   
   
    
     (
     1
     )
    
   
  
 

wherein, the MRRpi represents a dressing removal rate of the polishing pad (81) at the ith discrete point, the pi0 represents an original surface profile of the polishing pad (81) at the ith discrete point, the pi1 represents a dressed surface profile of the polishing pad (81) at the ith discrete point, the tp represents dressing time of the polishing pad (81), and n represents the number of radial discrete points of the polishing pad (81); the surface profile is the height data of all discrete points on the surface of the polishing pad (81);
differencing the original surface profile of the polishing pad (81) with a horizontal plane to determine a removal amount distribution of the surface of the polishing pad (81); keeping a dressing pressure constant in a dressing process, the dressing removal rate distribution of the polishing pad being known, and determining the dressing time of the diamond dresser (74) at each radial position of the polishing pad (81), polishing the planar part (88) on the leveled polishing pad (81) after dressing, and obtaining the material removal rate distribution MRRc (r,θ) of the planar part through a difference between surface profiles before and after the planar part (88) is polished:, MRR
       c
      
      (
      
       r
       ,
       θ
      
      )
     
     =
     
      
       
        
         u
         c
        
        (
        
         r
         ,
         θ
        
        )
       
       -
       
        
         u
         c
         ′
        
        (
        
         r
         ,
         θ
        
        )
       
      
      
       t
       c
      
     
    
   
   
    
     (
     2
     )
    
   
  
 

wherein, the MRRc (r,θ) represents the material removal rate distribution of the planar part, the uc(r,θ) represents a surface profile of the planar part (88) before polishing, the uc′(r,θ) represents a surface profile of the planar part (88) after polishing, the r represents a distance from a point on the planar part (88) to a center of the planar part (88), the θ represents an angle of a point on the planar part (88) in a coordinate system with the center of the planar part (88) as an origin, and the tc represents a polishing time;
step C. determining an ideal surface profile of the polishing pad (81) that makes the surface profile of the planar part (88) converged fast and dressing parameters thereof
determining, according to the surface profile of each of the planar part (88) and the leveled polishing pad as well as the removal rate distribution of the planar part (88) when it is polished by the leveled polishing pad, by using a polishing pad surface profile design method, the ideal surface profile of the polishing pad that makes the surface profile of the planar part (88) converged fast and the dressing parameters thereof, comprising the following steps:
step C1. obtaining a Preston coefficient K(r,θ): the material removal rate distribution of the planar part meeting a Preston equation:

MRRc(r,θ)=K(r,θ)P(r,θ)V(r,θ)  (3)

wherein, the K(r,θ) represents the Preston coefficient, the P(r,θ) represents a contact pressure during polishing processing, and the V(r,θ) represents a rotational velocity of the planar part (88) relative to the polishing pad (81);
converting the Preston equation (3) into equation (4) to obtain the Preston coefficient K(r,θ):, K
      ⁡
      (
      
       r
       ,
       θ
      
      )
     
     =
     
      
       
        MRR
        c
       
       (
       
        r
        ,
        θ
       
       )
      
      
       
        P
        ⁡
        (
        
         r
         ,
         θ
        
        )
       
       ⁢
       
        V
        ⁡
        (
        
         r
         ,
         θ
        
        )
       
      
     
    
   
   
    
     (
     4
     )
    
   
  
 

calculating the material removal rate distribution MRRc (r,θ) of the planar part (88) according to equation (2) when polished with the polishing pad (81);
obtaining, according to a rotational velocity parameter used in the polishing process, relative velocity V(r,θ) of the planar part (88) and the polishing pad (81) at each position by kinematics analysis as follows:, {
     
      
       
        
         
          V
          ⁡
          (
          
           r
           ,
           θ
          
          )
         
         =
         
          
           
            
             
              υ
              x
             
             (
             
              r
              ,
              θ
             
             )
            
            2
           
           +
           
            
             
              υ
              z
             
             (
             
              r
              ,
              θ
             
             )
            
            2
           
          
         
        
       
      
      
       
        
         
          
           υ
           x
          
          (
          
           r
           ,
           θ
          
          )
         
         =
         
          
           
            -
            
             ω
             c
            
           
           ⁢
           r
           ⁢
           sin
           ⁢
           θ
          
          +
          
           
            ω
            p
           
           ⁢
           r
           ⁢
           sin
           ⁢
           θ
          
         
        
       
      
      
       
        
         
          
           υ
           y
          
          (
          
           r
           ,
           θ
          
          )
         
         =
         
          
           
            ω
            c
           
           ⁢
           r
           ⁢
           cos
           ⁢
           θ
          
          -
          
           
            ω
            p
           
           (
           
            e
            +
            
             r
             ⁢
             cos
             ⁢
             θ
            
           
           )
          
         
        
       
      
     
    
   
   
    
     (
     5
     )
    
   
  
 

wherein, the vz (r,θ) represents velocity components of relative velocity of the planar part (88) and the polishing pad (81) on an x axis of the planar part (88), the vy(r,θ) represents velocity components of relative velocity of the planar part (88) and the polishing pad (81) on a y axis of the planar part (88), the ωp represents a revolution velocity of the polishing pad (81), and the ωc represents a rotation velocity of the planar part (88);
calculating a contact pressure distribution model based on a Winkler elastic foundation model:, P
      ⁡
      (
      
       r
       ,
       θ
      
      )
     
     =
     
      {
      
       
        
         
          
           K
           [
           
            δ
            -
            
             u
             ⁡
             (
             
              r
              ,
              θ
             
             )
            
           
           ]
          
          ,
         
        
        
         
          δ
          >
          
           u
           ⁡
           (
           
            r
            ,
            θ
           
           )
          
         
        
       
       
        
         
          0
          ,
         
        
        
         
          δ
          ⩽
          
           u
           ⁡
           (
           
            r
            ,
            θ
           
           )
          
         
        
       
      
     
    
   
   
    
     (
     6
     )
    
   
  
 

 
  K
  =
  
   
    
     (
     
      1
      -
      v
     
     )
    
    ⁢
    E
   
   
    
     (
     
      1
      +
      v
     
     )
    
    ⁢
    
     (
     
      1
      -
      
       2
       ⁢
       v
      
     
     )
    
    ⁢
    L
   
  
 

 
  
   u
   ⁡
   (
   
    r
    ,
    θ
   
   )
  
  =
  
   
    
     u
     c
    
    (
    
     r
     ,
     θ
    
    )
   
   -
   
    
     u
     p
    
    (
    
     r
     ,
     θ
    
    )
   
  
 

 
  
   F
   K
  
  =
  
   ∑
   
    A
    [
    
     δ
     -
     
      u
      ⁡
      (
      
       r
       ,
       θ
      
      )
     
    
    ]
   
  
 

wherein, the K represents a stiffness coefficient, the δ represents contact deformation, the (r,θ) represents a thickness of an elastic layer, the v represents a Poisson ratio, the E represents an elasticity modulus, the L represents a thickness of the polishing pad (81), the p (r,θ) represents a circumferentially homogenized surface profile of the polishing pad (81) within a range of the polishing processing, the F represents a positive pressure, and the A represents an area of a region represented by a discrete point of the planar part (88);
obtaining, based on the Winkler elastic foundation model, a polishing pressure P(r,θ) of each point by mechanical analysis in a condition where the surface profile of the planar part (88) and the surface profile of the leveled polishing pad are known; and
therefore, obtaining the Preston coefficient K(r,θ) of the planar part (88) according to the equation (4) due to the MRRc(r,θ), the V(r,θ) and the P(r,θ) are obtained;
step C2. obtaining the ideal surface profile of the polishing pad
based on a hypothesis that the Preston coefficient in the polishing process is unchanged and the Winkler elastic foundation model, performing normalization and mirror symmetry treatment on the surface profile of the planar part (88) obtained in step B, which is taken as a normalization result of the material removal rate distribution MRRc′(r,θ) of the planar part corresponding to an ideal polishing pad, and making an analysis in combination with a model for calculating the material removal rate distribution of the planar part to obtain the ideal surface profile of the polishing pad required by the full-aperture deterministic polishing;
a method for obtaining the ideal surface profile of the polishing pad comprising:
performing the normalization and mirror symmetry treatment on the surface profile of the planar part (88) obtained in step B, which is taken as the normalization result of the material removal rate distribution MRRc′(r,θ) of the planar part corresponding to the ideal polishing pad, with a equation as follows:, MRR
         c
         ′
        
        (
        
         r
         ,
         θ
        
        )
       
       -
       
        min
        [
        
         
          MRR
          c
          ′
         
         (
         
          r
          ,
          θ
         
         )
        
        ]
       
      
      
       max
       [
       
        
         MRR
         c
         ′
        
        (
        
         r
         ,
         θ
        
        )
       
       ]
      
     
     =
     
      
       
        -
        
         
          u
          c
          ′
         
         (
         
          r
          ,
          θ
         
         )
        
       
       -
       
        min
        [
        
         -
         
          
           u
           c
           ′
          
          (
          
           r
           ,
           θ
          
          )
         
        
        ]
       
      
      
       max
       [
       
        -
        
         
          u
          c
          ′
         
         (
         
          r
          ,
          θ
         
         )
        
       
       ]
      
     
    
   
   
    
     (
     7
     )
    
   
  
 

 
  
   
    
     
      MRR
      c
      ′
     
     (
     
      r
      ,
      θ
     
     )
    
    -
    
     min
     [
     
      
       MRR
       c
       ′
      
      (
      
       r
       ,
       θ
      
      )
     
     ]
    
   
   
    max
    [
    
     
      MRR
      c
      ′
     
     (
     
      r
      ,
      θ
     
     )
    
    ]
   
  
  =
  
   
    
     
      u
      c
      ′
     
     (
     
      r
      ,
      θ
     
     )
    
    -
    
     max
     [
     
      
       u
       c
       ′
      
      (
      
       r
       ,
       θ
      
      )
     
     ]
    
   
   
    min
    [
    
     
      u
      c
      ′
     
     (
     
      r
      ,
      θ
     
     )
    
    ]
   
  
 

based on the hypothesis that the Preston coefficient K(r,θ) in the polishing process is unchanged, in view of an actual condition where the V(r,θ) is unchanged due to the rotational velocity process parameter used in the polishing process is unchanged, making the analysis in combination with the model for calculating the material removal rate distribution of the planar part to obtain a normalization result of an ideal contact pressure distribution P′(r,θ) on the surface of the planar part; and
based on the Winkler elastic foundation model, in a condition where the surface profile of the planar part (88) obtained in step B is known, obtaining a contact pressure corresponding to any surface profile of the polishing pad (81), taking the normalization result of the ideal contact pressure distribution P′(r,θ) as an optimization goal to obtain the corresponding ideal surface profile of the polishing pad required by the full-aperture deterministic polishing, and obtaining the ideal contact pressure distribution P′(r,θ) on the surface of the planar part (88);
step C3. determining the dressing parameters of the polishing pad (81)
determining, as the ideal surface profile of the polishing pad and the surface profile of the leveled polishing pad are respectively measured, keeping the dressing pressure constant in the dressing process, and the dressing removal rate distribution of the polishing pad is known according to step B, a dressing time of the diamond dresser (74) at the radial position of the polishing pad (81) as follows:, T
       pi
      
      =
      
       
        
         u
         pi
        
        -
        
         u
         pi
         ′
        
       
       
        MMR
        pi
       
      
     
     ,
     
      i
      =
      1
     
     ,
     2
     ,
     
      3
      ⁢
      …
      ⁢
        
      n
     
    
   
   
    
     (
     8
     )
    
   
  
 

wherein, the Tpi represents dressing time of the diamond dresser (74) at the ith discrete point of the polishing pad (81), the pi represents a surface profile of the leveled polishing pad at the ith discrete point, and the pi′ represents an ideal surface profile of the polishing pad (81) at the ith discrete point; and
step C4. predicting the polishing time obtaining the material removal rate distribution MRRc′(r,θ) of the planar part corresponding to the ideal polishing pad as follows:, MRR
       pi
      
      =
      
       
        
         
          u
          pi
          0
         
         -
         
          u
          pi
          1
         
        
        
         t
         p
        
       
       ⁢
       n
      
     
     ,
     
      i
      =
      1
     
     ,
     2
     ,
     
      3
      ⁢
        
      …
      ⁢
        
      n
     
    
   
   
    
     (
     1
     )
    
   
  
 

deducing an evolution of the surface profile of the planar part (88) in the polishing process in combination with the surface profile of the planar part (88) and the material removal rate distribution MRRc′(r,θ) of the planar part corresponding to the ideal polishing pad obtained in step B, and selecting a maximum peak valley (PV) value of the surface profile of the planar part (88), i.e., corresponding polishing time when the PV value is minimum, as the predicted polishing time;
step D. dressing the polishing pad (81)
controlling a polishing pad surface dressing mechanism (7) to dress the surface profile of the polishing pad (81) as the calculated ideal surface profile of the polishing pad;
step E. polishing the planar part (88)
polishing the planar part (88) with the parameters same as those when the material removal rate distribution of the planar part is obtained with the leveled polishing pad in step B, the parameters comprising a rotation velocity of each of the planar part (88) and the polishing pad (81), a component of a polishing slurry, a supply position of the polishing slurry, a flow velocity of the polishing slurry and a polishing load; and
step F. measuring the surface profile of the planar part (88)
feeding, by the mechanical arm (4), the polished planar part (88) to a washing station (53), and washing to remove the polishing slurry and rest impurities on the surface of the planar part (88) with deionized water at 20-26° C.; then feeding the planar part (88) to a drying station (52) to clamp, and quickly drying the planar part (88) with a strong blower that outputs room temperature air at 20-26° C.; and after the surface of the planar part (88) is clean, transferring the planar part to the measuring station (51) to measure the surface profile of the planar part (88), determining whether a polishing result meets a requirement; and if no, performing step A till a surface of a high-precision planar part (88) meeting the requirement is obtained.