Proceedings VCM 2012 47 tính toán các tọa độ máy và hậu xử lý

350 Tran Duc Tang

VCM2012
Tính toán các tọa độ máy và hậu xử lý
cho máy phay CNC 5 trục
Calculation of machine coordinates and postprocessor
for 5-Axis CNC milling machine
Tran Duc Tang
Military Technical Academy, e-Mail:
Tóm tắt
Chức năng chính của bộ hậu xử lý cho máy CNC 5 trục là đọc dữ liệu đường chạy dao (các vị trí dao cắt)-
được tạo bởi các hệ thống CAD/CAM và chuyển dữ liệu này sang hệ thống tọa độ của máy. Bài báo này trình
bày một phương pháp tính toán các tọa độ của máy từ hệ thống tọa độ của phôi và xây dựng bộ hậu xử lý cho
máy phay CNC 5 trục. Dựa trên phương pháp tính toán đã đề xuất, tác giả đã xây dựng một mô đun phần mềm
hậu xử lý trên nền windows bằng ngôn ngữ lập trình Visual Basic. Lấy mô hình máy phay CNC 5 trục kiểu hai
trục quay trên bàn gá phôi làm ví dụ để mô phỏng và kiểm tra tính đúng đắn của phương pháp tính toán bằng
phần mềm VERICUT
®
. Kết quả kiểm tra chỉ ra rằng phần mềm hậu xử lý đáng tin cậy và phương pháp tính
toán đã đề xuất có thể áp dụng cho các kiểu cấu hình máy CNC khác nhau.
Abstract:
The main function of the 5-axis CNC machine postprocessor is reading data from cutter location data
prepared by general purpose CAD/CAM systems and converting these data to machine coordinate system.
This paper presents a method of calculation of the machine coordinate system (from the workpiece coordinate
system) and a postprocessor for 5-axis CNC milling machine. A windows-based postprocessor module written
by Visual Basic was developed according to the presented calculation method. A 5-axis CNC milling machine
tool with two rotary axes on the table is constructed and vefified by VERICUT
®
software to demonstrate and
validate the proposed method. The result shows that the software is reliable and the proposed method can be
applied to any types of 5-axis CNC machine configuration.

Keywords: Postprocessor, 5-axis CNC machine, Inverse Kinematics, NC Simulation, CAD/CAM.

Abbreviations
CAD Computer-Aided Design
CAM Computer-Aided Manufacturing
NC Numerical Control
CNC Computer Numerical Control
CL Cutter Location
MCS Machine Coordinate System
WCS Workpiece Coordinate System

1. Introduction
A 5-axis machine means a machine with five
degrees of freedom: three translatory movements
(X, Y, Z) and two rotational movements AB, AC,
or BC. The 5-axis machine is similar to two
cooperating robots, one robot carrying the
workpiece and one robot carrying the tool. The 5-
axis CNC machines have proved their advantages
in the accurate and fast machining of complex
parts such as impellers, mold/die, and others.
However, the generation of an NC program for 5-
axis machine needs a postprocessor. The
postprocessor is the interface that links the CAM
systems and CNC machines. It converts CL data to
machine code. Concretely, NC postprocessor
converts the machine independent CL data (x, y, z,
i, j, k) into a machine specific NC program (X, Y,
Z, A, B) or (X, Y, Z, A, C) or (X, Y, Z, B, C)
depending on the machine configuration.

The toolpath which is generated by the CAD/CAM
system is provided in a machine independent
format (called the CL data). The CL data gives the
successive tool positions in a coordinate system
fixed to the workpiece. The workpiece is fixed and
the tool does all movements. This CL data
approximates the workpiece geometry with a
certain tolerance which has to be provided to the
CAD/CAM system by the part programmer before
the generation of the CL data. This CL data must
be transformed to the machine coordinates. In 5-
axis machine tool the postprocessor is highly
Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 351

Mã bài: 78
complex because the simultaneous linear and
rotary motions occur.
Various studies have address the issue of
developing postprocessor for 5-axis machine tools.
Bohez [1] classified the CNC machines into three
main types based on the location of the rotary
axes: (i) 5-axis machine tool with two rotary axes
on the machine table; (ii) 5-axis machine tool with
two rotary axes on the tool spindle; and (iii) 5-
axis machine tool with a rotary table and a rotary
tool spindle. Kruth et al. [2] developed an
integration of NC-postprocessor and NC-
simulation. This intergration makes it possible to
exploit fully the capacibilities of the NC-
postprocessor, the NC-simulation package and the

5-axis milling machine. Lee and She [4] presented
an analytical methodology to develop a
postprocessor for three typical 5-axis machine
tools. Jung et al. [5] proposed algorithm for NC-
postprocessing for 5-axis milling machine of table-
rotating/tilting type. The spindle-tilting type 5-axis
machine tool with a nutating head has developed
by She and Chang [6]. The table-tilting type 5-axis
machine tool with nutating table has presented by
Sorby [7]. In [7] Sorby presented an algorithm for
calculating the inverse kinematics of 5-axis
machines close to singular configurations. A
postprocessor for 5-axis machine tool with
nutating head and table configuration has also
developed by She and Huang [9].
This paper presents a method of calculation of
machine coordinates based on the coordinate
transformation to yield the analytical equation of
NC data, and a postprocessor for 5-aixs CNC
machine. A postprocessor software for 5-axis
machine DMU 70eVolution is also developed to
validate the NC data generated by proposed
method. In addition, the generated NC data are
verified using the solid cutting software
VERICUT
®
[10].

2. Calculation of machine coordiantes
The CAD/CAM system normally calculates the

tool coordinates in a reference system attached to
the workpiece (WCS), these are cutter location (x,
y, z) and orienation (i, j, k). The machine however
needs to be programmed in a reference system
fixed to the machine (MCS), these are three linear
motions (X, Y, Z) and two rotary motions (A, B)
or (A, C) or (B, C). Therefore, the machine
coordinates need to be calculated based on the
input data of the workpiece coordate (CL data).
This can be done by the geometry transformation
from the WCS to the MCS.
In this paper, to demonstrate for the proposed
method, a 5-axis with two rotary axes on the table
- DMU 70 eVolution (Fig.1) is used. In order to
calculate the coordinate (X, Y, Z, B, C) of the
machine from the CL data (x, y, z, i, j, k) we have
defined additional coordinate systems at some
joints. These reference systems are defined in such
away that the transformation from workpiece
coordinates to machine coordinates can be done in
simple steps. These intermediate reference systems
are shown as in Fig.2 and the transformation
matrices are calculated as follows:
O
0
(x
0
y
0
z

0
) is located in the center of the table
surface C, when B = C = 0
0
. z
0
-axis coincides with
the C-axis centerline.
O
1
(x
1
y
1
z
1
) is obtained by rotating (x
0
y
0
z
0
) around
z
0
at an angle C. The transformation matrix is
written as:
1
0
cos sin 0 0

sin cos 0 0
0 0 1 0
0 0 0 1
C C
C C
T
 
 

 

 
 
 
(1)
O
2
(x
2
y
2
z
2
) is obtained by translating (x
1
y
1
z
1
) at a

distance d along z
0
. The transformation matrix is
written as:
2
1
1 0 0 0
0 1 0 0
0 0 1
0 0 0 1
T
d
 
 
 

 
 
 
(2)


Fig. 1 5-axis machine tool-DMU 70 eVolution [1]
352 Tran Duc Tang

VCM2012
Z
T
45
°

C
B
d
t
z
t
y
t
O
3, 4
z
3, 4
y
2, 5
y
2, 5
z
2, 3, 4, 5
O
0, 1, 6
O
y
0, 6
0, 6
z

Fig. 2 Intermediate reference coordinate systems

O
3

(x
3
y
3
z
3
) is obtained by rotating (x
2
y
2
z
2
) around
x
2
at an angle +45
0
. The transformation matrix is
written as:
0 0
3
2
0 0
1 0 0 0
0 cos45 sin 45 0
0 sin 45 cos45 0
0 0 0 1
T
 
 


 

 
 
 
(3)
O
4
(x
4
y
4
z
4
) is obtained by rotating (x
3
y
3
z
3
) around
z
3
at an angle B. The transformation matrix is
written as:
4
3
cos sin 0 0
sin cos 0 0

0 0 1 0
0 0 0 1
B B
B B
T

 
 
 

 
 
 
(4)
O
5
(x
5
y
5
z
5
) is obtained by rotating (x
4
y
4
z
4
) around
x

4
at an angle -45
0
. The transformation matrix is
written as:
0 0
5
4
0 0
1 0 0 0
0 cos45 sin 45 0
0 sin 45 cos45 0
0 0 0 1
T
 
 
 

 

 
 
(5)
O
6
(x
6
y
6
z

6
) is obtained by translating (x
5
y
5
z
5
) at a
distance -d along z
5
. The transformation matrix is
written as:
6
5
1 0 0 0
0 1 0 0
0 0 1
0 0 0 1
T
d
 
 
 

 

 
 
(6)
O

w
(x
w
y
w
z
w
) is obtained by translating (x
6
y
6
z
6
)
along the offset vector
x y z
L i L j L k
  from the
workpiece origin O
w
to the rotary C-axis. The
transformation matrix is written as:














10
1
0
0
0
0
1
0
0
0
0
1
6
z
y
x
w
L
L
L
T
(7)
O
t
(x

t
y
t
z
t
) is machine coordinate system fixed to
the tool spindle tip. The transformation matrix is
written as:
0
1 0 0
0 1 0
0 0 1
0 0 0 1
t
X
Y
T
Z
 
 
 

 
 
 
(8)
The coordinate tranformation matrix from WCS to
the MCS (tool’s coordinates: X, Y, Z, B, C) is:
t
TTTTTTT

w
T
t
w
T
0
0
1
1
2
2
3
3
4
4
5
5
6
6

(9)
Because


1
n m
m n
T T

 , therefore, equation (9) can

be expressed as:
t
TTTTTTT
w
T
t
w
T
0
1
0
2
1
3
2
4
3
5
4
6
56
1111111 













































(10)
Use of equations (1)-(8) and substitute into (10),
the solution for
t
w
T
can be found.
The CL data generated by CAM system are the
cutter location (x, y, z) and orientation (i, j, k)
defined in WCS. The CL vector (E) can be
expressed as:
1 0
0 1
0 0
0 0 0 1
i x
j y
E
k z
 
 
 

 
 

 
(11)
And the machine coordinates for a given CL data
can be found with the equation:
t
w
E T

(12)
or
0 0
0 0
1 0
0 1 0 1
t
w
i x
j y
T
k z
   
   
   

   
   
   
(13)
Solving equations (1) - (13), the solutions for X,
Y, Z, B, C can found:

arccos(2 1)
B k
 
(14)
2
2
( 1) 2( )
tan
2( ) ( 1)
k i k k j
C a
k k i k j
 
   
 

 
  
 
(15)
Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 353

Mã bài: 78
)( ) (sin cos )( )
2
( )
2
2 2
(cos cos sin sin cos sin

2 2
2
sin sin
2
x L C B y L
x y
z L
z
X C B C B C B
B d B
   
 
 

(16)
)
2 1 2 1
[ cos sin sin (1 cos )]( ) [ sin sinh cos (1 cos )](
2 2 2 2
1
(cos 1)( ) (cos 1)
2
X
z
y
Y C B C B x L C B C B y L
B z L B d
      
    
(17)

) )
2 1 2 1
[ cos sin sin (cos 1)]( [ sin sin cos (cos 1)](
2 2 2 2
1
(cos 1)( )
2
z T T
x y
Z C B C B x L C B C B y L
B z L d d Z WhereZ isthetoollength


      
    
(18)

Based on the above calculation method the
equations to generate NC data for other types of 5-
axis machine tools can be determined also.

3. Software implementation and
verification
To confirm the feasibility of the presented
machine coordinates calculation method, a
window-based postprocessor for 5-axis with two
rotary axes on the table has been developed under
the Windows XP environment in Visual Basic
programming language. A solid cutting simulation
is also performed by VERICUT

®
software to
validate the correctness of the proposed method.
The user interface of the developed postprocessor
is shown in Fig.3. The user can enter relevant
parameters, e.g. tool length, the distance (d) from
the C table to the intersection of B and C-axis, the
offset vector (L
x
, L
y
, L
z
) from the workpiece origin
to the C-axis. The CL file is opened by selecting
the "File\Open" menu or clicking the Open icon
on the toolbar and the CL data is displayed in
the left below window corner. The NC data are
generated by selecting the "Run\Start" menu or
clicking the Run icon on the toolbar and the
NC data is displayed in the right below window
corner. The generated NC file is saved by selecting
“File\Save” menu or clicking the Save icon
(Fig.3).
To demonstrate and confirm the correctness of the
NC data generated by the proposed postprocessor,
an air-compressor turbine blade (Fig.4) was used.
The CL data are firstly generated by the
commercial CAD/CAM system (Pro/engineer).
These CL data are then inputed into the proposed

postprocessor to generate NC data. Finally, the
generated NC data are verified by VERICUT
©

software with the model of 5-axis machine DMU
70 eVolution is constructed in the software
enviroment (Fig.5).
The results shows that the cutting simulation of the
CL data (Fig.6) and generated NC data (Fig.7) are
the same. Therefore, the calculated machine
coordiantes from the CL data by the proposed
method and postprocessor is correct.

354 Tran Duc Tang

VCM2012

Fig.3 Interactive user interface of the proposed postprocessor


Fig.4 Air-compressor turbine blade and 3D model


Fig.5 Setting simulation and verification in VERICUT® with DMU 70 eVolution 5-axis machine
Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 355

Mã bài: 78

Fig.6 Cutting result by CL data



Fig.7 Cutting result by generated NC data
4. Conclusion
This paper has presented a postprocessor
methodology for 5-axis machine tool with two
rotary axes on the table. The calculation of the
machine coordinates is determined by the
homogeneous coordinate transformation matrix,
forward and inverse kinematics. The generated
NC data are verified using the solid cutting
software VERICUT
®
. The result confirms the
correctness of the proposed method and
postprocessor. The proposed methodology can
be applied to other types of 5-axis machine.

Acknowledgement
This research is funded by Vietnam National
Foundation for Science and Technology
Development (NAFOSTED) under grant No.
107.04.2011.09. The author would like to thank
for their support for this research.
References
[1] Bohez, E. L. J.: Five-axis milling machine
tool kinematics chain design and analysis.
International Journal of Machine Tools &

Manufacture 42 (2002), p505-520.
[2] Kruth, J.P. and Kelwais, P.: NC-Processing
and NC-Simulation for Five-Axis Milling
Operations with Automatic Collision
Avoidance. Proceeding of the International
Manufacturing Engineering Conference,
1996.
[3] Nagasaka, M.; Takeuchi, Y.: Generalized
postprocessor for five-axis control
machining based on form shape function.
Journal of the Japan Society for Precision
Engineering 62 (11), 1996, p1607-1611.
[4] Lee, R S. and She, S H.: Developing a
Postprocessor for Three Types of Five-Axis
Machine Tool. International Journal of
Advanced Manufacturing Technology 13,
1997, p658-665
[5] Jung, Y.H.; Lee, D.W.; Kim, J.S.; Mok,
H.S.: NC Postprocessor for 5-axis milling
machine of table-rotating/tilting type.
Journal of Materials Processing
Technology 130-131, 2002, p641-646
[6] She, C H.; Chang, C C.: Development of
a Five-Axis Post-processor System with A
Nutating Head. Journal of Materials
Processing Technology 187-188, 2007,
p60-64
[7] Knut Sorby: Inverse Kinematics of Five-
Axis Machines Near Singular
Configurations. International Journal of

Machine Tools & Manufacture 47, 2007,
p299-306
[8] She, C.H.; Le, R.S.: A postprocessor based
on the kinematics model for general five-
axis mahine tools. SME Journal of
Manufacturing Process 2 (2), 2000, p131-
141.
[9] She, C H.; Huang, Z T.: Postprocessor
Development of A Five-Axis Machine Tool
with Nutating Head and Table
Configuration. International Journal of
Advanced Manufacturing Technology 38,
2008, p728-740.
[10] VERICUT
®
V6.2 User manual, URL:


356 Tran Duc Tang

VCM2012
Tran Duc Tang is
currently an
Assistant Professor
in the Aerospace
Technology and
Equipments at the
Militaty Technical
Academy, Hanoi,
Vietnam. He

received his PhD
and M.Eng in
Design and
Manufacturing Engineering from Asian Institute
of Technology (AIT) - Thailand in 2007 and
2002, respectively. He is teaching the courses of
advanced manufacturing processes,
CAD/CAM/CAE, FMS, multi-axis machine
tools. His research interests are five-axis
machining, CAD/CAE/CAM/CNC, modeling of
FMS by PetriNet, reverse engineering, rapid
prototyping, NC simulation & programming,
and Computer Graphics. His email address is:
or