# Patent

## Title
Electronic system and method for compensating the dimensional accuracy of a 4-axis CNC machining system using global offsets

## Abstract

An electronic system for compensating the dimensional accuracy of a 4-axis CNC machining system includes a CNC machining system configured to machine a feature into a part, a dimensional measuring device configured to measure a dimension of the part, and to provide an output corresponding to the measured dimension, and a compensation processor in communication with the CNC machining system and dimensional measuring device. The compensation processor is configured to receive the output from the dimensional measuring device, to calculate a plurality of CNC offsets, and to provide the offsets to the CNC machining system.

## Background
TECHNICAL FIELD
The present invention relates generally to a system and method for computing global offsets for a 4-axis CNC machine.
BACKGROUND
Computer numerical controlled (CNC) machining systems are typically used in industrial settings to accurately machine parts according to previously defined plans. Often these plans are developed in a computer aided design package, and may be represented in the form of engineering drawings. A CNC machining system may operate according to an assembled sequence of commands (e.g., G code) that instruct the system to machine a part by moving a controllable cutting tool. During the operation, the system may monitor the position of the tool, and may control its position relative to the part via precise servomotor control. The part may be held or clamped within a fixture, which is in-turn positioned on a machine table.
SUMMARY
An electronic system for compensating the dimensional accuracy of a CNC machining system includes a CNC machining system configured to machine a feature into a part, a dimensional measuring device configured to measure a dimension of the part, and to provide an output corresponding to the measured dimension, and a compensation processor in communication with the CNC machining system and dimensional measuring device. The compensation processor is configured to receive the output from the dimensional measuring device, to calculate a plurality of CNC offsets, and to provide the offsets to the CNC machining system. The CNC machining system may include a 4-axis CNC mill, and the dimensional measuring device may include a coordinate measuring machine.
In an embodiment, calculating a plurality of CNC offsets may include computing a deviation between the measured dimension of the part and a corresponding nominal dimension; translating the deviation from the CMM coordinate systems to a coordinate system of the CNC machining system; and computing a plurality of CNC offsets that minimize future deviations. The compensation processor may further weight a deviation according to a weighting algorithm, such as by dividing the deviation by a provided tolerance. In an embodiment, the compensation processor may compute a plurality of CNC offsets that minimize future deviations by optimizing a plurality of offset variables within a set of simultaneous equations, such as through a least-square fit. The plurality of CNC offsets may include global CNC offsets, such as, for example, table offsets, fixture offsets, or angular offsets.
An electronic method for compensating the dimensional accuracy of a CNC machining system includes receiving setup information through an interface, receiving measurement data from a coordinate measuring machine through an interface, calculating a plurality of CNC offsets from the setup information and measurement data, and outputting the plurality of CNC offsets. In an embodiment, the setup information may include feature descriptive information and part information, and the measurement data may relate to one or more measured dimensions of a machined part. The feature descriptive information may likewise include a plurality of feature records, where each feature record corresponds to a respective feature machined by a CNC machining system.
Calculating a plurality of CNC offsets may include computing one or more feature deviations from the measurement data and the feature descriptive information, translating the measurement data from the CMM coordinate systems to a plurality of CNC offset variables within a coordinate system of a CNC machining system, and optimizing the CNC offset variables to minimize the feature deviations. In an embodiment, optimizing the CNC offset variables may include performing a least-square fit.
The method may further include applying a weighting algorithm to the one or more feature deviations. The weighting algorithm may be configured to modify the influence of a dimension when optimizing the CNC offset variables, such as by dividing the feature deviation by a tolerance received in the feature descriptive setup information. The method may also include outputting performance data.
The above features and advantages and other features and advantages of the present invention are readily apparent from the following detailed description of the best modes for carrying out the invention when taken in connection with the accompanying drawings.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic diagram of a system for compensating the dimensional accuracy of a machined part.
FIG. 2 is a schematic top view of a part having a plurality of features.
FIG. 3A is a schematic perspective view of a 4-axis CNC mill with an A-table.
FIG. 3B is a schematic perspective view of a 4-axis CNC mill with a B-table.
FIG. 3C is a schematic perspective view of a 4-axis CNC mill with a C-table.
FIG. 4 is a schematic perspective view of a coordinate measuring machine.
FIG. 5 is a flow diagram of an embodiment of a computerized method for calculating CNC calibration offsets from CMM measurement data.
FIG. 6 is a diagram of setup information and CMM data being provided to an interface of a compensation processor.
FIG. 7 is a flow diagram of an embodiment of a computerized method for calculating CNC calibration offsets.
FIG. 8 is a schematic diagram of a plurality of reference coordinate systems within a CNC machining system.
FIG. 9 is a schematic diagram of a reference coordinate system within a coordinate measuring machine.
FIG. 10 is a flow diagram of output data being provided by a compensation processor.



DETAILED DESCRIPTION
Referring to the drawings, wherein like reference numerals are used to identify like or identical components in the various views, FIG. 1 illustrates an exemplary system 10 for compensating the dimensional accuracy of a machined part 12. As shown, the system 10 may include a computer numerical controlled (CNC) machining system 14 that may create one or more features on a part (e.g., hole 16) through one or more machining processes. In an embodiment, the CNC machining system 14 may include a CNC mill, such as, for example, a 4-axis mill, and may perform processes such as cutting, face milling, boring, honing, and/or drilling.
Once the one or more features are machined into the part 12, a dimensional measuring device, such as a coordinate measuring machine (CMM) 18, may measure one or more dimensions of the part 12. Each measured dimension may be taken with respect to an established datum or control surface that may be specified in a corresponding engineering drawing of the part 12. The engineering drawing may specify a nominal dimension for each measurement, and may further provide acceptable tolerances.
The system 10 may further include a compensation processor 20 that may receive part measurement data 22 from the CMM 18, and compute one or more CNC offsets 24. The compensation processor 20 may include, for example and without limitation, a COMP (Capability Optimization for Machining Process) software package that may aid in computing the one or more CNC offsets 24. Once computed, the CNC offsets 24 may be loaded into the CNC machining system 14 to enhance the dimensional accuracy of the machining process.
As generally illustrated in FIG. 2, a part 12 may include a plurality of features 26, 28, 30. Each feature may be machined by a CNC machining system 14 according to an engineering drawing. Exemplary features may include, without limitation, holes, bores, channels, and/or machined faces. Each machined feature may be positioned with respect to one or more datum or control surfaces. For example, the distance between feature 26 and an edge 32 may define a first dimension 34. Similarly, the distance between feature 28 and the edge 32 may define a second dimension 36.
When a dimension of one or more machined features (e.g., dimensions 34, 36) deviates from the nominal dimensions provided in the drawing, a global offset may be provided to the CNC machining system 14 by the compensation processor 20 to modify the machining process and attempt to reduce the deviation.
A global offset may adjust the origin and/or orientation of a machine workpiece coordinate system 38. This type of offset may affect the dimensions or positioning of all features 26, 28, 30 in the part 12. In this regard, the global offset may be similar to a rigid body shift or rotation of the part 12.
Even though the global offset is a rigid body motion, it can adjust the workpiece coordinate system 38 to an optimal place so that the feature deviations are minimized. One type of deviation that may require correction may result from elastic deformation during the machining process. For example, if the part 12 is not sufficiently rigid, clamping forces and/or cutting tool pressure during the machining process may elastically deform the part 12. Once the forces are removed, the part 12 may return to an undeformed state and shift any feature that was machined while the part was deformed. The global offset calculated by the compensation processor 20 may provide a median correction so that the total part deviations are minimized. An exemplary metric representing the total part deviation may include the standard deviation of the difference between each measured dimension and its respective provided nominal dimension.
As illustrated in FIGS. 3A-3C, in some industrial settings, CNC machines may be configured to provide four or more axes of control. For example, FIG. 3A generally illustrates a 4-axis “A” CNC machine, FIG. 3B generally illustrates a 4-axis “B” CNC machine, and FIG. 3C generally illustrates a 4-axis “C” CNC machine. In each illustrated embodiment, the cutting spindle 44 may be capable of three degrees of translation, and the table 46 may be capable of one degree of rotation. As may be appreciated, the control of additional table axes may complicate the computation of the global offsets.
FIG. 4 illustrates an embodiment of a CMM 18. As known in the art, a CMM 18 may include a probe 50 that may be numerically located in three dimensional space 52 by a measurement processor 54. The probe 50 may be moved into physical contact with the part 12, at which time the measurement processor 54 may record a three-dimensional position. By comparing multiple recorded positions, the measurement processor 54 may report one or more distances or dimensions of the part 12.
FIG. 5 illustrates an embodiment of a computerized method 60 for calculating CNC calibration offsets 24 from CMM measurement data 22. The computerized method 60 may be performed in conjunction with or by a compensation processor 20, such as illustrated in FIG. 1. In an embodiment, the computerized method 60 may include providing setup information (Step 62), loading CMM measurement data (Step 64), calculating offsets (Step 66), and outputting offsets and/or performance data (Step 68).
In Step 62, as illustrated in FIG. 6, the setup information 70 may be provided to the compensation processor 20 via an interface 72. Exemplary types of setup information 70 may include feature descriptive information 74 and part information 76. The interface 72 may include a computer terminal configured to receive entry of the setup information 70 from an operator. In another embodiment, the interface 72 may be an electronic interface where the setup information 70 may be uploaded directly to the processor 20.
In an embodiment, feature descriptive information 74 may include a plurality of feature records 78 that each correspond to a respective feature machined by the CNC machining system 14. Each feature record 78 may include, for example, feature identifying information 80, dimensioning information 82, and/or feature orienting information 84. Exemplary feature identifying information 80 may include a descriptive title for each feature 86 and/or a CMM identifier code 88. Exemplary dimensioning information 82 may include a nominal dimensional value 90 that may be specified for the feature 86 and/or a dimensional tolerance 92. Exemplary orienting information 84 may include the orientation 94 of the CNC table 46 when the respective feature is machined and/or the orientation 96 of the part 12 within the CMM 18 when the dimensional measurement is taken.
Part information 76 may include information that may locate the part within the machine coordinate space. Exemplary part information may include table position information 98 and/or fixture position information 100.
Referring again to FIG. 5, once the setup information is provided to the compensation processor 20 in Step 62, measurement data 22 from the CMM 18 may be loaded into the processor 20 (Step 64). In an embodiment, the measurement data 22 may include raw measurements acquired by the CMM 18 that correspond to nominal dimensions 90 provided for the feature in the feature descriptive setup information 74. The measurement data 22 may be loaded via the interface 72 by manually entering it into a computer terminal. Alternatively, the measurement data 22 may be electronically uploaded to the compensation processor 20.
In an embodiment, the measurement data 22 may represent measurements taken from a statistical sample of multiple parts 12. While data 22 from only one part 12 may allow the compensation processor 20 to properly calculate CNC offsets 24, data 22 obtained from a sample of multiple parts 12 may allow the compensation processor 20 to more completely account for statistical deviations attributable to the machining process.
Once the setup information and CMM data are loaded into the compensation processor 20 (i.e., Steps 62, 64), the processor may compute one or more CNC offsets (Step 66) that may be used by the CNC machining system 14 to reduce any deviation between the actual feature positions (as measured by the CMM 18) and the nominal dimensional value 90 provided in the feature descriptive information 74. As illustrated in FIG. 7, in an exemplary embodiment, the step of computing one or more CNC offsets (Step 66) may include: translating the CMM measurement data 22 from the CMM coordinate systems to a coordinate system of the CNC machining system (Step 102); developing a set of equations that relate feature deviations and available offsets (Step 104); weighting the one or more features of the part 12 according to a degree of significance (Step 106); and optimizing offset variables to minimize total feature deviations from the nominally specified dimensions (Step 108).
As illustrated in FIGS. 8-9, the CNC machining system 14 and CMM 18 may each have native, independent coordinate systems (i.e., coordinate systems 110, 126 respectively). As illustrated in FIG. 8, the absolute machine coordinate system “M” 110 of the CNC machining system 14 may be a stationary coordinate system with its origin as the machine home and its positive directions set as the machine way directions. In an embodiment, the CMM 18 may record each measurement as GD&T (geometric dimensioning and tolerancing) value aligned with the arbitrary CMM coordinate system 126.
Referring again to FIG. 8, the origin of a table coordinate system “T” 112 may be aligned on the rotational center of the machine table 46 (as shown in FIGS. 3A-3C). The origin of the T system 112 may be translated a distance from the origin of the M system 110, though may be orientated in a similar manner as the M system 110. Additionally, the table 46 may be capable of rotating about the table center (e.g., the origin of the T system 112) through a variable angle “B” 114.
In an embodiment, a fixture may be positioned on the table 46 and used to locate and restrain a part 12. The fixture may have a corresponding fixture coordinate system “F” 116 that is located at the center of the fixture. The F system 116 may be translated a distance from the table center, though may also be oriented in a similar manner as the M system 110 and the T system 112.
A part 12 may be clamped to the fixture. The part 12 may have a corresponding part coordinate system “P” 118 that is located at the center of the part 12, and aligned with the M system 110. In an embodiment, the origin of the P system 118 may be translated a distance from the origin of the F system 116. As the table 46 rotates about its center through an angle B 114, the fixture and part 12 will similarly rotate about the table center. As illustrated, following a rotation, the origin of the F system 116 (i.e., the fixture center) will assume a new position 120, within the M system 110, and, similarly, the origin of the P system 118 (i.e., the part center) will assume a new position 122. By definition, however, the orientation of the P, F, and T systems 118, 116, 112 may remain aligned with the orientation of the M system 110. The F system 116 may also be referred to as the global coordate system. Using these exemplary relationships, Equation 1 may be used to define the part center (i.e., origin of the P system 118) within the machine system “M” 110, where the table is oriented on the X-Z plane (i.e., a “B” table).




  
    
      
        
          
            M
            ->
          
          global_B
        
        =
        
          {
          
            
              
                
                  Wx
                  =
                  
                    
                      (
                      
                        Tx
                        B
                      
                      )
                    
                    +
                    
                      
                        (
                        
                          
                            Fx
                            0
                          
                          +
                          
                            Px
                            0
                          
                        
                        )
                      
                      ⁢
                      cos
                      ⁢
                      
                        
                      
                      ⁢
                      B
                    
                    -
                    
                      
                        (
                        
                          
                            Fz
                            0
                          
                          +
                          
                            Pz
                            0
                          
                        
                        )
                      
                      ⁢
                      sin
                      ⁢
                      
                        
                      
                      ⁢
                      B
                    
                  
                
              
            
            
              
                
                  Wy
                  =
                  
                    
                      Ty
                      B
                    
                    +
                    
                      Fy
                      0
                    
                    +
                    
                      Py
                      0
                    
                  
                
              
            
            
              
                
                  Wz
                  =
                  
                    
                      (
                      
                        Tz
                        B
                      
                      )
                    
                    +
                    
                      
                        (
                        
                          
                            Fx
                            0
                          
                          +
                          
                            Px
                            0
                          
                        
                        )
                      
                      ⁢
                      sin
                      ⁢
                      
                        
                      
                      ⁢
                      B
                    
                    +
                    
                      
                        (
                        
                          
                            Fz
                            0
                          
                          +
                          
                            Pz
                            0
                          
                        
                        )
                      
                      ⁢
                      cos
                      ⁢
                      
                        
                      
                      ⁢
                      B
                    
                  
                
              
            
            
              
                
                  Wb
                  =
                  B
                
              
            
          
        
      
    
    
      
        Equation
        ⁢
        
          
        
        ⁢
        1
      
    
  




As used in Equation 1, the point (TxB,TyB,TzB) represents the nominal center of the B-Table (i.e. the origin of the T system 112), as measured from the machine zero (i.e., the origin of the M system 110). Similarly, the point (Fx0,Fy0,Fz0) represents the distance between the fixture center (i.e., origin of the F system 116) and the table center when table angle B=0; and, (Px0,Py0,Pz0) represents the distance between the part center (i.e., origin of the P system 118) and the fixture center when table angle B=0.

As illustrated in FIGS. 8-9, a feature 124 may be machined into the part 12 by a tool. As illustrated in FIG. 8, as the part 12 moves through an angle “B” 114, the feature 124 may move within the P, F, and T systems 118, 116, 112, though is inherently fixed on the part 12.
As illustrated in FIG. 9, the CMM coordinate system 126 may be defined on the part 12 and may maintain a constant orientation with respect to the part. Therefore, as the part 12 rotates through an angle B 114, the CMM coordinate system 126 may likewise rotate. In this manner, the position of the feature 124 within the CMM coordinate system 126 may remain constant. In an embodiment, the CMM coordinate system 126 may be positioned on the part center, and may be aligned with the machine coordinate system 110 when B=0. Given this exemplary coordinate definition, Equation 2 may represent the location of the feature 124 within the machine coordinate system 110, where (Xcmm, Ycmm, Zcmm) may represent the position of the feature 124 within the CMM coordinate system 126.



  
    
      
    
    ⁢
    
      Equation
      ⁢
      
        
      
      ⁢
      2
    
  




  
    
      
        M
        ->
      
      
        global_B
        ⁢
        _feature
      
    
    =
    
      {
      
        
          
            
              Wx
              =
              
                
                  (
                  
                    Tx
                    B
                  
                  )
                
                +
                
                  
                    (
                    
                      
                        Fx
                        0
                      
                      +
                      
                        Px
                        0
                      
                      +
                      
                        X
                        cmm
                      
                    
                    )
                  
                  ⁢
                  cos
                  ⁢
                  
                    
                  
                  ⁢
                  B
                
                -
                
                  
                    (
                    
                      
                        Fz
                        0
                      
                      +
                      
                        Pz
                        0
                      
                      +
                      
                        Z
                        cmm
                      
                    
                    )
                  
                  ⁢
                  sin
                  ⁢
                  
                    
                  
                  ⁢
                  B
                
              
            
          
        
        
          
            
              Wy
              =
              
                
                  Ty
                  B
                
                +
                
                  Py
                  0
                
                +
                
                  Y
                  cmm
                
              
            
          
        
        
          
            
              Wz
              =
              
                
                  (
                  
                    Tz
                    B
                  
                  )
                
                +
                
                  
                    (
                    
                      
                        Fx
                        0
                      
                      +
                      
                        Px
                        0
                      
                      +
                      
                        X
                        cmm
                      
                    
                    )
                  
                  ⁢
                  sin
                  ⁢
                  
                    
                  
                  ⁢
                  B
                
                +
                
                  
                    (
                    
                      
                        Fz
                        0
                      
                      +
                      
                        Pz
                        0
                      
                      +
                      
                        Z
                        cmm
                      
                    
                    )
                  
                  ⁢
                  cos
                  ⁢
                  
                    
                  
                  ⁢
                  B
                
              
            
          
        
        
          
            
              Wb
              =
              B
            
          
        
      
    
  



In an embodiment, the location of the table 46 (TxB,TyB,TzB) and/or the part 12 (Px0,Py0,Pz0) may be offset within the machine coordinate system 110 to correct deviations between the CMM measured location of a feature 124, and the nominal location of the feature specified by an engineering drawing. Similarly, the angular rotation of the table B may offset to correct deviations. Equation 3 represents the position of a feature 124 within the machine coordinate system 110 (as identified in Equation 2), though including offsets (ΔTxB,ΔTzB), (ΔPx0,ΔPy0,ΔPz0), and ΔB.



  
    
      
    
    ⁢
    
      Equation
      ⁢
      
        
      
      ⁢
      3
    
  




  
    
      
        M
        ->
      
      
        global_B
        ⁢
        _feature
      
    
    =
    
      {
      
        
          
            
              x
              =
              
                
                  (
                  
                    
                      Tx
                      B
                    
                    +
                    
                      Δ
                      ⁢
                      
                        
                      
                      ⁢
                      
                        Tx
                        B
                      
                    
                  
                  )
                
                +
                
                  
                    (
                    
                      
                        Fx
                        0
                      
                      +
                      
                        Px
                        0
                      
                      +
                      
                        
                          X
                          cmm
                        
                        ⁢
                        Δ
                        ⁢
                        
                          
                        
                        ⁢
                        
                          Px
                          0
                        
                      
                    
                    )
                  
                  ⁢
                  cos
                  ⁢
                  
                    
                  
                  ⁢
                  B
                
                -
                
                  
                    (
                    
                      
                        Fz
                        0
                      
                      +
                      
                        Pz
                        0
                      
                      +
                      
                        Z
                        cmm
                      
                      +
                      
                        Δ
                        ⁢
                        
                          
                        
                        ⁢
                        Pz
                      
                    
                    )
                  
                  ⁢
                  sin
                  ⁢
                  
                    
                  
                  ⁢
                  B
                
              
            
          
        
        
          
            
              Wy
              =
              
                
                  Ty
                  B
                
                +
                
                  Py
                  0
                
                +
                
                  Y
                  cmm
                
                +
                
                  Δ
                  ⁢
                  
                    
                  
                  ⁢
                  
                    Py
                    0
                  
                
              
            
          
        
        
          
            
              Wz
              =
              
                
                  (
                  
                    
                      Tz
                      B
                    
                    +
                    
                      Δ
                      ⁢
                      
                        
                      
                      ⁢
                      
                        Tz
                        B
                      
                    
                  
                  )
                
                +
                
                  
                    (
                    
                      
                        Fx
                        0
                      
                      +
                      
                        Px
                        0
                      
                      +
                      
                        X
                        cmm
                      
                      +
                      
                        Δ
                        ⁢
                        
                          
                        
                        ⁢
                        
                          Px
                          0
                        
                      
                    
                    )
                  
                  ⁢
                  sin
                  ⁢
                  
                    
                  
                  ⁢
                  B
                
                +
                
                  
                    (
                    
                      
                        Fz
                        0
                      
                      +
                      
                        Pz
                        0
                      
                      +
                      
                        Z
                        cmm
                      
                      +
                      
                        Δ
                        ⁢
                        
                          
                        
                        ⁢
                        
                          Pz
                          0
                        
                      
                    
                    )
                  
                  ⁢
                  cos
                  ⁢
                  
                    
                  
                  ⁢
                  B
                
              
            
          
        
        
          
            
              Wb
              =
              
                B
                +
                
                  Δ
                  ⁢
                  
                    
                  
                  ⁢
                  B
                
              
            
          
        
      
    
  



Partial derivatives may be used to solve for the linear and/or angular offsets, as demonstrated in Equations 4-5.




  
    
      
        
          Δ
          ⁢
          
            
          
          ⁢
          
            
              M
              ->
            
            
              global_B
              ⁢
              _feature
              ⁢
              _linear
            
          
        
        =
        
          
            
              
                ∂
                
                  
                    M
                    ->
                  
                  
                    global_B
                    ⁢
                    _feature
                  
                
              
              
                ∂
                T
              
            
            ⁢
            Δ
            ⁢
            
              
            
            ⁢
            T
          
          +
          
            
              
                ∂
                
                  
                    M
                    ->
                  
                  
                    global_B
                    ⁢
                    _feature
                  
                
              
              
                ∂
                
                  P
                  0
                
              
            
            ⁢
            Δ
            ⁢
            
              
            
            ⁢
            
              P
              0
            
          
        
      
    
    
      
        Equation
        ⁢
        
          
        
        ⁢
        4
      
    
  
  
    
      
        
          
        
        ⁢
        
          
            Δ
            ⁢
            
              
            
            ⁢
            
              
                M
                ->
              
              
                global_B
                ⁢
                _feature
                ⁢
                _angular
              
            
          
          =
          
            
              
                ∂
                
                  
                    M
                    ->
                  
                  global_feature
                
              
              
                ∂
                B
              
            
            ⁢
            Δ
            ⁢
            
              
            
            ⁢
            B
          
        
      
    
    
      
        Equation
        ⁢
        
          
        
        ⁢
        5
      
    
  




As can be seen in Equation 6, CNC convention may define the linear adjustment in an opposite direction as the CMM deviation, where the angular adjustment may be in the same direction as the CMM deviation. As shown in Equation 7, the total feature deviation, as expressed in the machine coordinate system “M” 110, may be the sum of the linear and angular deviations.

Δ{right arrow over (M)}=−Δ{right arrow over (M)}global—feature—linear+Δ{right arrow over (M)}global—feature—angular  Equation 6

Combining Equations 3-6 may result in Equation 7:



  
    
      
    
    ⁢
    
      Equation
      ⁢
      
        
      
      ⁢
      7
    
  




  
    
      Δ
      ⁢
      
        
      
      ⁢
      
        M
        ->
      
    
    =
    
      {
      
        
          
            
              
                Δ
                ⁢
                
                  
                
                ⁢
                
                  X
                  global
                
              
              =
              
                
                  
                    -
                    Δ
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    Tx
                    B
                  
                
                -
                
                  Δ
                  ⁢
                  
                    
                  
                  ⁢
                  
                    Px
                    0
                  
                  ⁢
                  cos
                  ⁢
                  
                    
                  
                  ⁢
                  B
                
                +
                
                  Δ
                  ⁢
                  
                    
                  
                  ⁢
                  
                    Pz
                    0
                  
                  ⁢
                  sin
                  ⁢
                  
                    
                  
                  ⁢
                  B
                
                -
                
                  
                    (
                    
                      
                        Fx
                        0
                      
                      +
                      
                        Px
                        0
                      
                      +
                      
                        X
                        cmm
                      
                    
                    )
                  
                  ⁢
                  sin
                  ⁢
                  
                    
                  
                  ⁢
                  B
                  ⁢
                  
                    
                  
                  ⁢
                  Δ
                  ⁢
                  
                    
                  
                  ⁢
                  B
                
              
            
          
        
        
          
            
              
                Δ
                ⁢
                
                  
                
                ⁢
                
                  Y
                  global
                
              
              =
              
                
                  -
                  Δ
                
                ⁢
                
                  
                
                ⁢
                
                  Py
                  0
                
              
            
          
        
        
          
            
              
                Δ
                ⁢
                
                  
                
                ⁢
                
                  Z
                  global
                
              
              =
              
                
                  
                    -
                    Δ
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    Tz
                    B
                  
                
                -
                
                  Δ
                  ⁢
                  
                    
                  
                  ⁢
                  
                    Px
                    0
                  
                  ⁢
                  sin
                  ⁢
                  
                    
                  
                  ⁢
                  B
                
                -
                
                  Δ
                  ⁢
                  
                    
                  
                  ⁢
                  
                    Pz
                    0
                  
                  ⁢
                  cos
                  ⁢
                  
                    
                  
                  ⁢
                  B
                
                +
                
                  
                    (
                    
                      
                        Fx
                        0
                      
                      +
                      
                        Px
                        0
                      
                      +
                      
                        X
                        cmm
                      
                    
                    )
                  
                  ⁢
                  cos
                  ⁢
                  
                    
                  
                  ⁢
                  B
                  ⁢
                  
                    
                  
                  ⁢
                  Δ
                  ⁢
                  
                    
                  
                  ⁢
                  B
                
                -
                
                  
                    (
                    
                      
                        Fz
                        0
                      
                      +
                      
                        Pz
                        0
                      
                      +
                      
                        Z
                        cmm
                      
                    
                    )
                  
                  ⁢
                  sin
                  ⁢
                  
                    
                  
                  ⁢
                  B
                  ⁢
                  
                    
                  
                  ⁢
                  Δ
                  ⁢
                  
                    
                  
                  ⁢
                  B
                
              
            
          
        
      
    
  



While Equation 7 is helpful in describing feature deviation in a global, machine coordinate system “M” 110, measurement of the feature deviation occurs in the CMM coordinate system 126. Therefore, through a coordinate transformation, Equation 7 may be written in CMM space as shown in Equations 8-10, where Equation 10 is the compensation formula for an embodiment of a 4-axis B machine global offset.




  
    
      
        
          (
          
            
              
                
                  Δ
                  ⁢
                  
                    
                  
                  ⁢
                  
                    X
                    cmm
                  
                
              
            
            
              
                
                  Δ
                  ⁢
                  
                    
                  
                  ⁢
                  
                    Y
                    cmm
                  
                
              
            
            
              
                
                  Δ
                  ⁢
                  
                    
                  
                  ⁢
                  
                    Z
                    cmm
                  
                
              
            
          
          )
        
        =
        
          
            (
            
              
                
                  
                    
                      
                        i
                        ->
                      
                      cmm
                    
                    ·
                    
                      
                        i
                        ->
                      
                      global
                    
                  
                
                
                  
                    
                      
                        i
                        ->
                      
                      cmm
                    
                    ·
                    
                      
                        j
                        ->
                      
                      globalc
                    
                  
                
                
                  
                    
                      
                        i
                        ->
                      
                      cmm
                    
                    ·
                    
                      
                        k
                        ->
                      
                      global
                    
                  
                
              
              
                
                  
                    
                      
                        j
                        ->
                      
                      cmm
                    
                    ·
                    
                      
                        i
                        ->
                      
                      global
                    
                  
                
                
                  
                    
                      
                        j
                        ->
                      
                      cmm
                    
                    ·
                    
                      
                        j
                        ->
                      
                      global
                    
                  
                
                
                  
                    
                      
                        j
                        ->
                      
                      cmm
                    
                    ·
                    
                      
                        k
                        ->
                      
                      global
                    
                  
                
              
              
                
                  
                    
                      
                        k
                        ->
                      
                      cmm
                    
                    ·
                    
                      
                        i
                        ->
                      
                      global
                    
                  
                
                
                  
                    
                      
                        k
                        ->
                      
                      cmm
                    
                    ·
                    
                      
                        j
                        ->
                      
                      global
                    
                  
                
                
                  
                    
                      
                        k
                        ->
                      
                      cmm
                    
                    ·
                    
                      
                        k
                        ->
                      
                      global
                    
                  
                
              
            
            )
          
          ⁢
          
            (
            
              
                
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    
                      X
                      global
                    
                  
                
              
              
                
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    
                      Y
                      global
                    
                  
                
              
              
                
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    
                      Z
                      global
                    
                  
                
              
            
            )
          
        
      
    
    
      
        Equation
        ⁢
        
          
        
        ⁢
        8
      
    
  
  
    
      
        
          (
          
            
              
                
                  Δ
                  ⁢
                  
                    
                  
                  ⁢
                  
                    X
                    cmm
                  
                
              
            
            
              
                
                  Δ
                  ⁢
                  
                    
                  
                  ⁢
                  
                    Y
                    cmm
                  
                
              
            
            
              
                
                  Δ
                  ⁢
                  
                    
                  
                  ⁢
                  
                    Z
                    cmm
                  
                
              
            
          
          )
        
        =
        
          
            (
            
              
                
                  
                    cos
                    ⁢
                    
                      
                    
                    ⁢
                    B
                  
                
                
                  0
                
                
                  
                    sin
                    ⁢
                    
                      
                    
                    ⁢
                    B
                  
                
              
              
                
                  0
                
                
                  1
                
                
                  0
                
              
              
                
                  
                    
                      -
                      sin
                    
                    ⁢
                    
                      
                    
                    ⁢
                    B
                  
                
                
                  0
                
                
                  
                    cos
                    ⁢
                    
                      
                    
                    ⁢
                    B
                  
                
              
            
            )
          
          ⁢
          
            (
            
              
                
                  
                    [
                    
                      
                        
                          
                            
                              
                                -
                                Δ
                              
                              ⁢
                              
                                
                              
                              ⁢
                              
                                Tx
                                B
                              
                            
                            -
                            
                              Δ
                              ⁢
                              
                                
                              
                              ⁢
                              
                                Px
                                0
                              
                              ⁢
                              cos
                              ⁢
                              
                                
                              
                              ⁢
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                            +
                            
                              Δ
                              ⁢
                              
                                
                              
                              ⁢
                              
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                                0
                              
                              ⁢
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                              ⁢
                              
                                
                              
                              ⁢
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                            -
                          
                        
                      
                      
                        
                          
                            
                              
                                (
                                
                                  
                                    Fx
                                    0
                                  
                                  +
                                  
                                    Px
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                                  +
                                  
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                                    cmm
                                  
                                
                                )
                              
                              ⁢
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                              ⁢
                              
                                
                              
                              ⁢
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                              ⁢
                              
                                
                              
                              ⁢
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                              ⁢
                              
                                
                              
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                            -
                          
                        
                      
                      
                        
                          
                            
                              (
                              
                                
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                              )
                            
                            ⁢
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                            ⁢
                            
                              
                            
                            ⁢
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                            ⁢
                            
                              
                            
                            ⁢
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                            ⁢
                            
                              
                            
                            ⁢
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                    ]
                  
                
              
              
                
                  
                    
                      -
                      Δ
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
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                      0
                    
                  
                
              
              
                
                  
                    [
                    
                      
                        
                          
                            
                              
                                -
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                              ⁢
                              
                                
                              
                              ⁢
                              
                                Tz
                                B
                              
                            
                            -
                            
                              Δ
                              ⁢
                              
                                
                              
                              ⁢
                              
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                              ⁢
                              
                                
                              
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                            -
                            
                              Δ
                              ⁢
                              
                                
                              
                              ⁢
                              
                                Pz
                                0
                              
                              ⁢
                              cos
                              ⁢
                              
                                
                              
                              ⁢
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                            +
                          
                        
                      
                      
                        
                          
                            
                              
                                (
                                
                                  
                                    Fx
                                    0
                                  
                                  +
                                  
                                    Px
                                    0
                                  
                                  +
                                  
                                    X
                                    cmm
                                  
                                
                                )
                              
                              ⁢
                              cos
                              ⁢
                              
                                
                              
                              ⁢
                              B
                              ⁢
                              
                                
                              
                              ⁢
                              Δ
                              ⁢
                              
                                
                              
                              ⁢
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                            -
                          
                        
                      
                      
                        
                          
                            
                              (
                              
                                
                                  Fz
                                  0
                                
                                +
                                
                                  Pz
                                  0
                                
                                +
                                
                                  Z
                                  cmm
                                
                              
                              )
                            
                            ⁢
                            sin
                            ⁢
                            
                              
                            
                            ⁢
                            B
                            ⁢
                            
                              
                            
                            ⁢
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                            ⁢
                            
                              
                            
                            ⁢
                            B
                          
                        
                      
                    
                    ]
                  
                
              
            
            )
          
        
      
    
    
      
        Equation
        ⁢
        
          
        
        ⁢
        9
      
    
  
  
    
      
        
          (
          
            
              
                
                  
                    -
                    Δ
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    X
                    cmm
                  
                
              
            
            
              
                
                  
                    -
                    Δ
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    Y
                    cmm
                  
                
              
            
            
              
                
                  
                    -
                    Δ
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    Z
                    cmm
                  
                
              
            
          
          )
        
        =
        
          (
          
            
              
                
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    
                      Tx
                      B
                    
                    ⁢
                    cos
                    ⁢
                    
                      
                    
                    ⁢
                    B
                  
                  +
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    
                      Tz
                      B
                    
                    ⁢
                    sin
                    ⁢
                    
                      
                    
                    ⁢
                    B
                  
                  +
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    
                      Px
                      0
                    
                  
                  +
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    
                      B
                      ⁡
                      
                        (
                        
                          
                            Fz
                            0
                          
                          +
                          
                            Pz
                            0
                          
                          +
                          
                            Z
                            cmm
                          
                        
                        )
                      
                    
                  
                
              
            
            
              
                
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                  ⁢
                  
                    
                  
                  ⁢
                  
                    Py
                    0
                  
                
              
            
            
              
                
                  
                    
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                    ⁢
                    
                      
                    
                    ⁢
                    
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                    ⁢
                    
                      
                    
                    ⁢
                    B
                  
                  +
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    
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                      B
                    
                    ⁢
                    cos
                    ⁢
                    
                      
                    
                    ⁢
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                  +
                  
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                    ⁢
                    
                      
                    
                    ⁢
                    
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                      ⁡
                      
                        (
                        
                          
                            Fx
                            0
                          
                          +
                          
                            Px
                            0
                          
                          +
                          
                            X
                            cmm
                          
                        
                        )
                      
                    
                  
                
              
            
          
          ⁢
          
            
          
          )
        
      
    
    
      
        Equation
        ⁢
        
          
        
        ⁢
        10
      
    
  




Equation 10 may be re-written as a linear matrix, as shown in Equation 11.





  
    
      
        
          -
          
            (
            
              
                
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    
                      X
                      cmm
                    
                  
                
              
              
                
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    
                      Y
                      cmm
                    
                  
                
              
              
                
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    
                      Z
                      cmm
                    
                  
                
              
            
            )
          
        
        =
        
          
            (
            
              
                
                  
                    cos
                    ⁢
                    
                      
                    
                    ⁢
                    B
                  
                
                
                  
                    sin
                    ⁢
                    
                      
                    
                    ⁢
                    B
                  
                
                
                  1
                
                
                  0
                
                
                  0
                
                
                  
                    
                      Fz
                      0
                    
                    +
                    
                      Pz
                      0
                    
                    +
                    
                      Z
                      cmm
                    
                  
                
              
              
                
                  0
                
                
                  0
                
                
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                  1
                
                
                  0
                
                
                  0
                
              
              
                
                  
                    
                      -
                      sin
                    
                    ⁢
                    
                      
                    
                    ⁢
                    B
                  
                
                
                  
                    cos
                    ⁢
                    
                      
                    
                    ⁢
                    B
                  
                
                
                  0
                
                
                  0
                
                
                  1
                
                
                  
                    
                      -
                      
                        Fx
                        0
                      
                    
                    -
                    
                      Px
                      0
                    
                    -
                    
                      X
                      cmm
                    
                  
                
              
            
            )
          
          ⁢
          
            (
            
              
                
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    
                      Tx
                      B
                    
                  
                
              
              
                
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    
                      Tz
                      B
                    
                  
                
              
              
                
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    
                      Px
                      0
                    
                  
                
              
              
                
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    
                      Py
                      0
                    
                  
                
              
              
                
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    
                      Pz
                      0
                    
                  
                
              
              
                
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    B
                  
                
              
            
            )
          
        
      
    
    
      
        Equation
        ⁢
        
          
        
        ⁢
        11
      
    
  




As used in Equation 11, each element within the coefficient matrix on the right side of the equation may be determined from the setup information 70 (illustrated in FIG. 6) provided to the compensation processor 20 in Step 62. The left side of Equation 11 represents the difference between a CMM measured dimension for a particular feature and the nominal dimension specified in an engineering drawing. In this exemplary embodiment, the feature deviations are represented in a CMM coordinate system 126 that is aligned with the machine coordinate system 110 when B=0.
As may be appreciated, Equations 1-11 are shown for exemplary purposes. While these equations represent global offsets for a 4-axis CNC machining system 14 with a B-table, one skilled in the art may similarly develop equations that represent offsets for other table configurations (e.g., 4-axis A-tables and/or C-tables).
The part 12 may include one or more features that do not lend themselves to be easily measured with reference to the CMM coordinate system 126. For example, the part 12 may include several features that are dimensioned from various datum. Due to operator or machine convenience and/or accessibility, the part 12 may need to be physically manipulated to obtain the corresponding CMM measurements. In such a case, the compensation processor 20 may need to translate all measurements back into the common CMM coordinate system 126 (which may also be aligned with the global, machine coordinate system 110 when B=0). In an embodiment, the translation from a measurement in an independently oriented coordinate system to a measurement in the CMM reference frame may require a rotational transformation. As known in the art such a rotational transformation may be assembled through a series of 1-3 discrete rotations about one or more axes of the initial coordinate system. Exemplary rotational transforms may include ZYZ or ZYX rotations.
While Equation 11 may describe the global correction/offset for a single feature, in practice a part 12 may include a plurality of features that may each require varying degrees of correction. The compensation processor 20 may use Equation 11 a plurality of times to describe each measured dimension for each respective feature. Referring again to FIG. 7, in Step 104, the processor may assemble all generated equations into a redundant set of simultaneous equations. This set may relate all measured feature deviations back to the six available offsets. This set of equations may likewise account for measurements from more than one part 12 (i.e., from a statistical sample of parts).
Once the set of simultaneous equations is assembled, the compensation processor 20 may subsequently eliminate, or “blank,” any equations that may not bear on the final solution. For example, if the data of one of the plurality of features is incomplete or undefined, the equations describing that particular feature may be eliminated from the set.
Once a corresponding set of simultaneous equations is developed that describes all of the intended features, the compensation processor 20 may apply a weighting algorithm to the various equations and/or features (Step 106). The weighting algorithm may increase the influence of more critical features when solving for the global offsets. For example, a feature with a tighter tolerance may be weighted higher than a feature with a more generous tolerance. In an embodiment, the weighting algorithm may operate by dividing both sides of Equation 11 by that particular feature's dimensional tolerance 92. As such, features with a smaller tolerance will be weighted more significantly
In Step 108 the compensation processor 20 may determine values for the six offset variables that minimize the feature deviations described in the set of redundant equations. Such a determination may occur via an optimization routine that may choose offset variables which may minimize the expressed deviations. Exemplary optimization routines may include a least square fit solver, a linear programming optimization routine, or other numerical optimization methods.
In an embodiment, prior to performing any optimization, the solver may check the system for the existence of singularities. If the solver detects that a singularity is likely to exist, the processor 20 may alert the user and/or modify the equation set to eliminate or “blank” additional problematic equations.
Referring back to FIG. 5, once the offsets are calculated (Step 66), the compensation processor 20 may output them to the CNC machining system 14, and may further output various forms of performance data to the user. Depending on the level of integration between the compensation processor 20 and the CNC machining system 14, the offsets 24 may be either directly provided to the CNC machining system 14, or may be displayed for a technician to enter them manually. In either embodiment, the offsets 24 may serve to adjust one or more coordinate systems 38 defined within the CNC code. As described above, the global offsets that may be derived from, for example, an optimization routine, and may serve to may manipulate the perceived position and/or orientation of the part 12 as a whole.
As illustrated in FIG. 10, in addition to outputting the offset calibration information 24, the compensation processor 20 may also compute and provide performance data 130 to the user. The performance data 130 may summarize and/or compare the deviations before and after the corrections, and may be summarized in tabular form 132 and/or graph form 134. In an embodiment, the performance data 130 may analyze the changes in feature deviations as a percent of the provided tolerance for that feature. The performance data 130 may report the changes on a feature-by-feature basis and/or as an average deviation for the part 12.
While the best modes for carrying out the invention have been described in detail, those familiar with the art to which this invention relates will recognize various alternative designs and embodiments for practicing the invention within the scope of the appended claims.
All directional references (e.g., upper, lower, upward, downward, left, right, leftward, rightward, above, below, vertical, and horizontal) are only used for identification purposes to aid the reader's understanding of the present invention, and do not create limitations, particularly as to the position, orientation, or use of the invention. It is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative only and not as limiting.

## Claims

1. An electronic system for compensating the dimensional accuracy of a CNC machining system comprising:
a CNC machining system including a rotatable table disposed within a machine coordinate system and configured to restrain a part, the CNC machining system configured to machine plurality of features into the part;
a dimensional measuring device configured to measure a dimension corresponding to each of the plurality of features, and to provide an output corresponding to the measured dimensions; and
a compensation processor in communication with the CNC machining system and dimensional measuring device, the compensation processor configured to receive the output from the dimensional measuring device, to calculate a plurality of CNC offsets to minimize future deviations, and to provide the offsets to the CNC machining system; and
wherein the compensation processor is configured to calculate a plurality of CNC offsets to minimize future deviations by:
computing a deviation between each of the measured dimensions and a respective nominal dimension;
determining a planar table offset within the machine coordinate system using the computed deviations;
determining a three-dimensional part offset within the machine coordinate system using the computed deviations;
determining a table rotation offset using the computed deviations; and
wherein the planar table offset, the three-dimensional part offset, and the table rotation offset are determined to minimize the computed deviations.

2. The electronic system of claim 1, wherein the dimensional measuring device is a coordinate measuring machine.

3. The electronic system of claim 1, wherein calculating a plurality of CNC offsets further includes weighting each respective measured deviation according to a weighting algorithm.

4. The electronic system of claim 3, wherein the weighting algorithm includes dividing the respective deviation by a provided tolerance for a corresponding nominal dimension.

5. The electronic system of claim 1, wherein computing a plurality of CNC offsets that minimize future deviations includes optimizing a plurality of variables within a set of simultaneous equations.

6. The electronic system of claim 5, wherein optimizing a plurality of variables includes performing a least-square fit.

7. The electronic system of claim 1, wherein the plurality of CNC offsets comprise global CNC offsets.

8. The electronic system of claim 7, wherein the global CNC offsets include the planar table offset, the three-dimensional part offset, and the table rotation offset.

9. The electronic system of claim 1, wherein the CNC machining system comprises a 4-axis CNC mill.

10. The electronic system of claim 9, wherein the plurality of CNC offsets comprise global CNC offsets.

11. An electronic method for compensating the dimensional accuracy of a CNC machining system comprising:
receiving setup information through an interface, the setup information including feature descriptive information and part information the feature descriptive information including one or more nominal dimensions for each of a plurality of features to be machined into a part;
receiving measurement data from a coordinate measuring machine and through the interface, the measurement data relating to one or more measured dimensions of a machined part;
calculating a plurality of CNC offsets from the setup information and measurement data; and
outputting the plurality of CNC offsets; and
wherein calculating a plurality of CNC offsets from the setup information and measurement data includes:
computing a deviation between each of the measured dimensions and a respective nominal dimension;
determining a planar table offset for a rotatable machining table using the computed deviations;
determining a three-dimensional part offset for a part secured to the rotatable machining table using the computed deviations;
determining a table rotation offset for the rotatable machining table using the computed deviations;
wherein the planar table offset, the three-dimensional part offset, and the table rotation offset are determined to minimize the computed deviations; and
wherein the plurality of CNC offsets include the planar table offset, the three-dimensional part offset, and the table rotation offset.

12. The electronic method of claim 11, wherein the feature descriptive information includes a plurality of feature records, each feature record corresponding to a respective feature machined by a CNC machining system.

13. The electronic method of claim 11, wherein calculating a plurality of CNC offsets further includes applying a weighting algorithm to the one or more deviations, the weighting algorithm configured to modify the influence of a dimension when determining the plurality of CNC offsets.

14. The electronic method of claim 13, wherein the weighting algorithm divides a deviation by a tolerance received in the feature descriptive setup information.

15. The electronic method of claim 11, wherein determining each of the plurality of CNC offsets to minimize the computed deviations includes performing a least-square fit.

16. The electronic method of claim 11, further comprising outputting performance data.