Volumetric error analysis of a super-size floor type boring machine is conducted through geometric error modeling of the machine tool. Thermal deformation errors of the joint and shape elements are included in the model. Boring and milling errors are estimated through simulation

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GEOMETRIC ERROR MODELING OF A SUPER-SIZE FLOOR TYPE 
BORING MACHINE 
 
Bog-Ki Min1, Hyun-Gwang Cho1 and Sung-Chong Chung1  
1 Hybrid System Design and control LABoratory 
School of Mechanical Engineering 
Hanyang University 
Seoul 133-791, KOREA  
 
INTRODUCTION 
Super-size floor type boring machines are used 
for heavy-metal milling, boring, drilling and 
tapping on mega parts for the construction, oil 
field, wind energy, plant, shipbuilding industries. 
To make big machining volume, they are made 
of boring and milling spindle (Z-axis) assembled 
on the ram (W-axis). Strokes of the X, Y, Z axes 
are over 10m. As the size is too big, machining 
error is bigger than small and medium size 
machine tools. It depends upon deformation of 
the structures, as well as internal and external 
heat sources. In general, geometric errors 
degrade accuracy of machine tools. They are 
generated from joint errors of moving axes and 
shape deformations from the machine tool 
structures. Non-repeatable errors of the joint and 
shape deformation errors are generated from 
internal and external thermal error sources. In 
addition, stiffness variation of the spindle and 
ram assembly with respect to the joint 
movement degrades the geometric error. 
 
In this paper, to identify error behavior of the 
super-size floor type boring machine, 
homogeneous transformation matrix (HTM) and 
kinematic error chain [1] are applied for 
modeling the 3D geometric error including 
thermal and loading effects. Excitation of internal 
and external heat sources are to be applied for 
volumetric thermal behavior analysis. Cutting 
load as well as weight effect of the spindle and 
ram is to be analyzed according to the geometric 
error model as well. In addition, laser tracker is 
to be applied to confirm volumetric errors of the 
derived model. 
 
Volumetric Error Model 
Fig. 1 shows a super-size floor type boring 
machine. There are X, Y, Z, V, W and B axes as 
joint elements. Floor bed, rotary table, column, 
head, ram, spindle, etc. are shape elements.  
 
Geometric error model is composed of several 
shape and joint error elements. The shape error 
is generated from a structure of machine tools It 
is represented as a shape transformation 
element in the error model. The joint error is 
occurred at a moving joint of a machine tool. 
Rack and pinion for the X-axis, ballscrews in Y, 
Z, W and V axes, and B-axis are joint elements. 
Fig. 2 shows the kinematic chain of the machine. 
CS1 is the origin of the machine. CS2 is the 
coordinates at the pinion attached to the column. 
CS1-CS2, CS1-CS4, CS5-CS6, CS7-CS8, CS3-
CS9, CS10-CS11, CS12-CS13, CS14-CS15 are 
shape transformation elements S1-2,S1-4,S5-6, S7-8,  
 
 
 
 
FIGURE 1. SUPER-SIZE FLOOR TYPE BORING 
MACHINE AND COORDINATE SYSTEMS FOR 
MODELING. 
 
 
FIGURE 2. KINEMATIC CHAIN OF THE SUPER-
SIZE FLOOR TYPE BORING MACHINE. 
 
S3-9, S10-11, S12-13, S14-15, and CS2-CS3, CS4-
CS5, CS6-CS7, CS9-CS10, CS11-CS12, CS13-
CS14 are joint transformation elements J2-3, J4-5, 
J6-7, J9-10, J11-12, J13-14, respectively. 
 
Ahn [2] and Kim [3] modeled volumetric errors in 
a three-axis machine tool by homogeneous 
transformation matrices considering geometric 
and thermal deformation errors. Contrary to the 
small machine tools, the super-sized floor type 
boring machine has bigger height. Temperature 
difference between the floor and ceiling 
generates significant thermal deformation of the 
column. In addition cutting load and self-weight 
of the ram and spindle induce deformation. To 
model these effects, shape transformation 
elements and joint transformation elements are 
to be generalized as follows: 
  
1 1 1 1
1 1 1 1
1 2
1 1 1 1
    1       - ( )   ( )   ( )
 ( )       1      - ( )   ( )
[S ]  [
- ( )   ( )       1       ( )
    0           0            0              1
s s
z y
s s
z x
actual s s
y x
T T a a T
T T b b T
T T c c T
 
 
 
           
2 2 2 2
2 2 2 2
1 4
2 2 2 2
    1      - ( )    ( )   ( )
 ( )       1      - ( )   ( )
S ]
- ( )   ( )      1        ( )
    0           0            0               1
s s
z y
s s
z x
actual s s
y x
T T a a T
T T b b T
T T c c T
 
 
 
           
3 3 3 3
3 3 3 3
3 9
3 3 3 3
    1       - ( )   ( )   ( )
 ( )       1      - ( )   ( )
[S ]
- ( )   ( )       1       ( )
    0           0             0               1
s s
z y
s s
z x
actual s s
y x
T T a a T
T T b b T
T T c c T
 
 
 
           
4 4 4
4 4 4 4
5 6
4 4 4
    1       - ( )   ( )     ( )
 ( )       1      - ( )    ( )
 [S ]
- ( )   ( )      1          ( )
    0           0            0                1
s s
z y
s s
z x
actual s s
y x
T T a T
T T b b T
T T c T
 
 
 
         
4 4 4
4 4 4 4
5 6
4 4 4
    1       - ( )   ( )     ( )
 ( )       1      - ( )    ( )
[S ]  
- ( )   ( )      1          ( )
    0           0            0                1
s s
z y
s s
z x
actual s s
y x
T T a T
T T b b T
T T c T
 
 
 
         
5 5 5 5
5 5 5 5
7 8
5 5 5 5
    1         - ( )    ( )   ( )
 ( )        1        - ( )   ( )
 [S ]
- ( )     ( )         1      ( )
    0            0               0              1
s s
z y
s s
z x
actual s s
y x
T T a a T
T T b b T
T T c c T
 
 
 
  
 

     
6 6 6 6
6 6 6 6
10 11
6 6 6 6
    1        - ( )    ( )   ( )
 ( )      1         - ( )   ( )
[S ]
- ( )   ( )         1       ( )
    0          0                0              1
s s
z y
s s
z x
actual s s
y x
T T a a T
T T b b T
T T c c T
 
 
 
    

7 7 7
7 7 7 7
12 13
7 7 7 7
    1        - ( )    ( )     ( )
 ( )      1         - ( )   ( )
 [S ]
- ( )   ( )        1        ( )
    0          0               0            
s s
z y
s s
z x
actual s s
y x
T T a T
T T b b T
T T c c T
 
 
 
            1
       
7 7 7
7 7 7 7
12 13
7 7 7 7
    1        - ( )    ( )     ( )
 ( )      1         - ( )   ( )
[S ]
- ( )   ( )        1        ( )
    0          0               0                 1
s s
z y
s s
z x
actual s s
y x
T T a T
T T b b T
T T c c T
 
 
 
   

8 8 8
8 8 8 8
14 15
8 8 8 8
    1        - ( )    ( )    ( )
 ( )       1        - ( )   ( )
 [S ]
- ( )   ( )        1        ( )
    0           0              0            
s s
z y
s s
z x
actual s s
y x
T T a T
T T b b T
T T c c T
 
 
 
             1
       
1 1
1 1
2 3
1 1
  1          - ( , )    ( , )    ( , ) ( )
 ( , )        1        - ( , )             ( , )
[ ]  
- ( , )   ( , )         1                   ( , )
   0               
z y x x
z x y
actual
y x z
x T x T x x T P T x
x T x T x T
J
x T x T x T
  
  
  
  

 0                 0                          1
       
       
 
2 2
2 2
4 5
2 2
   1          - ( , )     ( , )        ( , )
 ( , )        1         - ( , )              ( , )
[ ]  
- ( , )    ( , )         1          ( , ) ( )
   0          
z y x vx
z x y
actual
y x z z
v T v T v T S v
v T v T v T
J
v T v T v v T P T v
  
  
  
 
   
      0                  0                          1
       
      
3 3
3 3
6 7
3 3
  1       - ( , )    ( , )    ( , )
( , )       1      - ( , )    ( , )  
[ ]  
- ( , )    ( , )        1       ( , )
   0                0                 0            1
z y x
z x y
actual
y x z
r T r T r T
r T r T r T
J
r T r T r T
  
  
  



     
                    
4 4
4 4
9 10
4 4
     1        - ( , )   ( , )       ( , )
 ( , )        1       - ( , )   ( , ) ( )
[ ]  
- ( , )   ( , )        1             ( , )
     0              0 
z y x xy
z x y y
actual
y x z yv
y T y T y T S y
y T y T y y T P T y
J
y T y T y T S y
  
  
  
 
    
                0                      1
       
      
5 5
5 5
11 12
5 5
     1        - ( , )   ( , )             ( , )
 ( , )        1       - ( , )        ( , )
[ ] =
- ( , )    ( , )        1        ( , ) ( )
     0                0      
z y x
z x y wy
actual
y x z z
w T w T w T
w T w T w T S w
J
w T w T w w T P T w
  
  
  
 
  
           0                       1
       
       
6 6
6 6
13 14
6 6
     1       - ( , )     ( , )            ( , )
 ( , )         1       - ( , )         ( , )
[ ] =
- ( , )   ( , )         1           ( , ) ( )
     0             
z y x
z x y zy
actual
y x z z
z T z T z T
z T z T z T S z
J
z T z T z z T P T z
  
  
  
 
  
 0                0                       1
       
         (1) 
 
Where, sxi , syi , szi ( i =1~8) and xi , yi , 
zi ( i =1~6) are rotational errors of shape and 
joint transformation elements. ,  i ia b   and 
ic  ( i =1~8) are translational errors of each 
shape transformation elements by thermal 
deformation and load. ,  ,  ,  xy vx yv wyS S S S  and 
zyS  are squareness errors by thermal 
deformation and load.  ,  x yP P  and zP   are 
linear thermal expansion of feed axes. ,  x y   
and  z  are positioning and straightness errors 
of feed axes.  
 
REFERENCES 
[1] Slocum A H. Precision machine design. 
Englewood Cliffs, N.J. Prentice Hall: 1992. 
[2] Ahn J Y, Chung S C. Identification and 
Compensatory control of time-varying 
Volumetric Errors in Machining Centers. 
Proceedings of the ASPE 1999 Annual 
Meeting. 1999: 248-235. 
[3] Kim K D, Chung S C. On-Machine 
Inspection System Accuracy: Improvement 
using an Artifact. Journal of Manufacturing 
Systems.  2004; 4: 299-308. 


Geometric Error Modeling of a Super-size Floor Type Boring Machine

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Geometric Error Modeling of a Super-size Floor Type Boring Machine

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