CHINESE JOURNAL OF MECHANICAL ENGINEERING
Vol. 26, No. 3, 2013
·547·
DOI: 10.3901/CJME.2013.03.547, available online at www.springerlink.com; www.cjmenet.com; www.cjmenet.com.cn
Three-dimensional Tool Radius Compensation for Multi-axis Peripheral Milling
CHEN Youdong* and WANG Tianmiao
School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China
Received October 26, 2012; revised January 24, 2013; accepted March 5, 2013
Abstract: Few function about 3D tool radius compensation is applied to generating executable motion control commands in the existing
computer numerical control (CNC) systems. Once the tool radius is changed, especially in the case of tool size changing with tool wear
in machining, a new NC program has to be recreated. A generic 3D tool radius compensation method for multi-axis peripheral milling in
CNC systems is presented. The offset path is calculated by offsetting the tool path along the direction of the offset vector with a given
distance. The offset vector is perpendicular to both the tangent vector of the tool path and the orientation vector of the tool axis relative
to the workpiece. The orientation vector equations of the tool axis relative to the workpiece are obtained through homogeneous
coordinate transformation matrix and forward kinematics of generalized kinematics model of multi-axis machine tools. To avoid cutting
into the corner formed by the two adjacent tool paths, the coordinates of offset path at the intersection point have been calculated
according to the transition type that is determined by the angle between the two tool path tangent vectors at the corner. Through the
verification by the solid cutting simulation software VERICUT with different tool radiuses on a table-tilting type five-axis machine
tool, and by the real machining experiment of machining a soup spoon on a five-axis machine tool with the developed CNC system, the
effectiveness of the proposed 3D tool radius compensation method is confirmed. The proposed compensation method can be suitable for
all kinds of three- to five-axis machine tools as a general form.
Key words: tool compensation, multi-axis machine tool, offset vector
1
Introduction
∗
Multi-axis peripheral milling is widely used for the
manufacture of profiled components in aerospace,
automotive and mould/die industries. Functions about 3D
tool radius compensation are widely used in CAD/CAM
system, but still few is applied to generating executable
motion control commands in CNC systems. Once the tool
radius is changed, especially in the case of tool size
changing with tool wear in machining, a new NC program
has to be recreated.
HU, et al[1], applied a planar geometry projection method
in tool radius compensation for three-axis NC peripheral
milling, which is similar to standard 2D tool radius
compensation. YANG[2] used space transition to get the
cutter position in three dimension space, but it is just used
for five-axis spindle-tilting machine tools. WANG[3]
presented a movement projection method for 3D tool radius
compensation, which is actually similar to the planar
geometry projection method. MORETON[4] realized 3D
tool compensation by calculating the required position of
* Corresponding author. E-mail: chenyd@buaa.edu.cn
This project is supported by National Major S&T Program of China
(Grant No. 2010zx04008-041), and National Hi-tech Research and
Development Program of China (863 Program, Grant No.
2011AA04A104)
© Chinese Mechanical Engineering Society and Springer-Verlag Berlin Heidelberg 2013
the tool control point relative to the surface of the
workpiece, but it is only used in 3-axis turning. To obtain
3D tool compensation method for five-axis milling in
machine controllers, TUNG, et al[5], defined a relationship
between the workpiece and the cutter to attain the aim of
three-dimensional tool compensation, but it would probably
lead to cutting into the corner formed by the two adjacent
tool paths in peripheral milling. HONG, et al[6], detailed the
algorithm of three-dimensional cutter radius compensation
for 5-axis end milling, but it can’t be used for peripaheral
milling. CHEN, et al[7], presented a 3D cutter radius
compensation method for five-axis peripheral milling, but it
is just used for five-axis peripheral milling.
Some commercially available CNC systems, such as
Sinumerik 840D and Heidenhain iTNC, have provided the
feature of a 3D tool compensation method for five-axis
peripheral milling. However, the related algorithm is
unpublished.
Most approaches used in 3D tool radius compensation
can only be applicable to specific machine tool
configuration. A 3D tool radius compensation algorithm
presented here can be suitable for all kinds of three- to
five-axis peripheral milling in CNC controllers. The
proposed 3D tool radius compensation method can enhance
the facility and flexibility of CNC controllers. The offset
path can be calculated by offsetting the tool path with a
given distance along the direction of the vector that is
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CHEN Youdong, et al: Three-dimensional Tool Radius Compensation for Multi-axis Peripheral Milling
perpendicular to both the tangent vector of the tool path and
the orientation vector of the tool axis relative to the
workpiece. To avoid cutting into the corner formed by the
two adjacent tool paths, the coordinates of offset path at the
intersection point have been calculated according to the
transition type that is determined by the angle between two
tool path tangent vectors at the corner.
2
Calculation of the Orientation Vector of
the Tool Axis Relative to the Workpiece for
Generalized Multi-axis Machine Tools
2.1
Generalized kinematics model of multi-axis
machine tools
Three- to five-axis milling machines have many types of
structural configuration. Four-axis machine centers can be
classified into two categories: table-tilting type with one
rotation on the table, and spindle-tilting type with one
rotation on the spindle. KIRIDENA, et al[8], showed the
structural configuration of five-axis machine centers and
classified them into three categories: table-tilting type with
two rotations on the table, spindle-tilting type with two
rotations on the spindle, and table/spindle-tilting type with
one rotation each on the table and spindle.
Denavit-Hartenberg method[9] was adopted to manipulate
the orientation and position of the tool relative to the
workpiece. RÜEGG, et al[10], presented a generalized
kinematic model for three- to five-axis milling machines.
Recently, SHE, et al[11–13], proposed a generalized
kinematics model of common five-axis machines
constructed by combining two rotational degrees of
freedom on the fixture table and two rotational degrees of
freedom on the spindle. A general kinematic model for
three- to five-axis milling was proposed that comprised 3
linear axes, and 4 rotational ones, of which zero, one or two
are active for the computation[14]. This method is also
applied to calculating the orientation vector of the tool axis
relative to the workpiece of multi-axis machine tools. A
notation based on Schewerd[15] is used to describe the serial
kinematic structure. The general multi-axis machine tools
are specified as follows:
set of Cartesian vectors. They don’t specify the orientation
vector of the tool axis relative to the workpiece. Actually,
the orientation vector of the tool axis relative to the
workpiece is T[0 0 1 0]. The tool orientation along the
X-axis, Y-axis and Z-axis are feasible. The Z-axis is
assumed below.
Take Schwerd’s notation as a starting point, and the
general multi-axis machine tools can be specified as a
sequence of transformations of coordinates. To describe the
relative position and orientation of the cutting tool with
respect to the workpiece, the appropriate coordinate system
should be established, as shown in Fig. 1. The coordinate
systems for the workpiece and the cutting tool are
OwXwYwZw and OTXTYTZT respectively. Coordinate systems
OBX BY BZ B, OL1XL1YL1ZL1, OL2XL2YL2ZL2 and OL3XL3YL3Z L3
are attached to the machine base, and X, Y and Z table,
respectively. The coordinate systems for the primary and
secondary rotations attached to the fixture table are
OR4XR4YR4ZR4 and OR3XR3YR3ZR3, respectively. The
coordinate systems for the primary and secondary rotations
attached to the spindle are OR2XR2YR2ZR2 and OR1XR1YR1ZR1,
respectively. The relative orientation and position of the
coordinate system OTXTYTZT with respect to the coordinate
system OwXwYwZw can be expressed as follows:
W
AT  W AR4 R4 AR3 R3 AL1 L1 AL2 L2 AL3 L3 AR2 R2 AR1 R1 AT AT ,
(1)
where iAj represents the relative transformation matrix of
system OjXjYjZj with respect to system OiXiYiZi.
W-R4-R3-B -L1-L2-L3 -R2-R1-T,
where
W—Workpiece,
T—Tool,
L1, L2, L3—Linear axes,
B—Machine base,
R1, R2—Rotational axes on the spindle,
R3, R4—Rotational axes on the fixture table.
2.2
Calculating the orientation vector of the tool axis
relative to the workpiece
Machining of workpieces requires the generation of tool
paths defined by the motion of the tool with respect to the
workpiece[16]. Three-axis tool paths can be represented by a
Fig. 1.
General multi-axis machine tool with coordinates
The orientation vector of the coordinate system
OTXTYTZT with respect to the coordinate system
OwXwYwZw is just subject to the movement of rotational
axes. Therefore, it can be expressed as
W
OT  Rot(k4 , ΦR 4 )Rot(k3 , ΦR3 ) 
Rot(k2 , ΦR 2 )Rot(k1 , ΦR1 ) AT ,
(2)
where Rot is a 44 homogeneous rotation matrices adopted
from Paul’s notation[17], k4, k3, k2, k1  x, y, z. ΦR 4 , ΦR3 ,
CHINESE JOURNAL OF MECHANICAL ENGINEERING
ΦR 2 , and ΦR1 represent the rotation angles for the fixture
table and the spindle, respectively.
Vector T is the orientation vector of the tool axis relative
to the workpiece. If the kinematics model applied to threeaxis machine, and ΦR 4  ΦR3  ΦR2  ΦR1  0, the vector
T is expressed as
T
T  0 0 1 0 .
(3)
According to the rotational movement characteristics, the
four-axis machine tool can be designated as two types, i.e.,
A and B type. The tool orientation along the X-axis or
Y-axis is feasible. Generally, the tool orientation along the
Z-axis is used in machine tools. The vector T can be
obtained as follows. The A types are chosen as an example.
For the spindle-tilting A type, ΦR 4  ΦR3  ΦR1  0
and ΦR 2  x, and the right-hand side of Eq. (1) for vector
T is
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vector T is
T
T  Rot(k3 , ΦR3 )Rot(k2 , ΦR 2 ) 0 0 1 0 
 SΦy

3
SΦx CΦy
CΦx CΦy
T
0 .
Algorithm of 3D Tool Radius
Compensation
3.1 Basic compensation principle
The 3D tool radius compensation method for peripheral
milling is illustrated as Fig. 2. The offset vector with a
length equal to the tool radius R is perpendicular to the tool
path. The tail of the offset vector is on the workpiece side
and the head positions on the tool center. The offset path l1
can be calculated by offsetting the tool path l with a given
distance R along the direction n (nxinyjnzk) of the offset
vector, as follows:
l1lRn.
T
T  Rot(k2 , ΦR 2 ) 0 0 1 0 
T
0 SΦx CΦx 0 ,
(8)
(9)
(4)
where “C” and “S” refer to cosine and sine functions,
respectively.
For the table-tilting A type, ΦR3  ΦR2  ΦR1  0 and
ΦR4  x, and the right-hand side of Eq. (1) for vector T is
T
T  Rot(k4 , ΦR 4 ) 0 0 1 0 
T
0 SΦx CΦx 0 .
(5)
According to the rotational movement characteristics, the
five-axis machine tool can be designated as six types, i.e.,
AB, AC, BA, BC, CA and CB type. The tool axis vector
along the X-axis and Z-axis are feasible. Ordinarily, the tool
orientation along the Z-axis is used in machine tools. The
vector T can be obtained as follows. The AB types are
chosen as an example.
For the spindle-tilting AB type, ΦR 4  ΦR3  0,
ΦR 2  x, and ΦR1  y, and the right-hand side of Eq. (1)
for vector T is
T
T  Rot(k2 , ΦR 2 )Rot(k1 , ΦR1 ) 0 0 1 0 
S Φ y

SΦx CΦy
CΦx CΦy
T
0 .
(6)
For table-tilting AB type, ΦR2  ΦR1  0, ΦR4  x, and
ΦR3  y, and the right-hand side of Eq. (1) for vector T is
T
T  Rot(k4 , ΦR 4 )Rot(k3 , ΦR3 ) 0 0 1 0 
 SΦy

SΦx CΦy
CΦx CΦy
T
0 .
(7)
For table/spindle tilting AB type, ΦR4  ΦR1  0,
ΦR 2  x, and ΦR3  y, and the right-hand side of Eq. (1) for
Fig. 2.
Three-dimensional cutter radius compensation
for multi-axis peripheral milling
With Eq. (9), the tool will cut into the corner formed by
the two adjacent tool paths, if it doesn’t take the preventive
measures at the corner point. To achieve the accurate
workpiece shape, a 3D tool radius compensation method is
proposed to make the tool move along corners.
Tool radius compensation allows programming of the
workpiece contour to be independent of the geometry of the
tool. When an angle of intersection created by tool paths
specified with movement commands for two blocks is over
180° as shown in Fig. 3(a), it is referred to as the “inner
side”. When the angle is between 0° and 180° as shown in
Fig. 3(b), it is referred to as the “outer side”. In space, the
two straight lines may be coplanar or non-coplanar. When
they are coplanar, Compensate C can be easily used for
cutter radius compensation. The radius compensation for
non-coplanar lines will be discussed here.
When the tool path goes around the inner side corner or
the outer side corner at an obtuse angle as shown in
Fig. 4(a), the transition type is referred to as “Type A”. If
the tool moves around the outer side corner at an acute
angle, as shown in Fig. 4(b), the transition type is referred
to as “Type B”. In Type A, a line that is the common
CHEN Youdong, et al: Three-dimensional Tool Radius Compensation for Multi-axis Peripheral Milling
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perpendicular to the two paths is inserted since the two tool
paths are skew lines which don’t intersect. In Type B, the
inserted block is a straight line Q11Q22, as shown in Fig.
4(b). The point Q11 is the offset R along the line P1Q1 to the
point Q1. The point Q22 is the offset R along the opposite
direction of the line Q2R1 to the point Q2.
The vector τ1 (τ1xiτ1y jτ1zk) is the tangent vector of the
tool path PQ at the point Q. The vector τ2 (τ2xiτ2y jτ2zk)
is the tangent vector of the tool path QR at the point Q.
The coordinate system O1X1Y1Z1 is constructed from
linearly independent vectors τ1 and τ2 by applying the
Gram-Schmidt orthogonalization procedure. It is a
Cartesian coordinate system whose vectors are the unit
vectors e1, e2, and e3.
β1  τ1 , e1 
β2  τ 2 
1
τ1
(τ 2 , β1 ) β1 , e2 
i
e3  e1  e2  e1x
e2x
Fig. 3.
Tool path inner side and outer side
β1
,
β1
j
e1y
e2y
(10)
β2
,
β2
k
e1z .
e2z
(11)
(12)
The coordinate conversion matrix M from the coordinate
system OXYZ to O1X1Y1Z1 is expressed as
 e1 
 
M   e2  .
 
e 
 3
(13)
(2) The vector τ1 and τ2 in the coordinate system OXYZ
are converted to τ1 and τ 2 in the coordinate system
O1X1Y1Z1, respectively, by using the following expressions,
τ1  Mτ1 ,
(14)
τ 2  Mτ 2 .
(15)
(3) Determining the transition type:
Cθ1 
Fig. 4.
Transition type of compensation
3.2 Determining the transition type
The transition type is determined by the offset direction
and the angle between two tangent vectors of tool paths at
the corner. In order to get the transition type, firstly, the
tangent vector of tool paths are projected to the coordinate
system constructed from linearly independent tangent
vectors. Secondly, the transition type can be determined by
the offset direction and the angles between the projected
vectors and the coordinate axis. The transition type is
determined as follows.
(1) Calculating the coordinate conversion matrix
The coordinate system OXYZ is a Cartesian coordinate
system whose fundamental vectors are the unit vectors
along the X-, Y-, and Z-axis.
(τ  , e )
(τ 2 , e1 )
, Cθ 2  2 2 .

τ 2 e2
τ 2 e1
where θ1 is the angle between e 1 and τ 2 , and θ 2 is the
angle between e2 and τ 2 , as shown in Fig. 5.
Fig. 5.
Angle of intersection
CHINESE JOURNAL OF MECHANICAL ENGINEERING
According to C θ1 and C θ 2 , the transition type can be
obtained, as illustrated in Table 1.
Table 1.
Cutter
compensation
Transition type
Cθ1  0
Cθ 2  0
Transition type
–
N
Y
–
Y
N
Y
N
N
N
Y
Y
A
B
A
A
A
B
Left
Right
(16)
3.4 Determining the tool paths at the corner
The point Q1(x1, y1, z1) is an intersection of the tool offset
path and the offset vector at the point Q. The relation
between point Q1 and Q is restricted by
Q1 Q  Rv1,
(17)
where R is the tool radius, and v1 is the unit offset vector at
the point Q.
The offset path r that passes through the point Q1 and
parallels to the tangent vector τ1 of the tool path at the point
Q is
rQ1τ1t.
(18)
The five-axis spindle-tilting AB type and linear
interpolation are chosen as an example. The start and end
points of a block are P(xp, yp, zp, Ap, Bp), and Q(xq, yq, zp, Aq,
Bq) respectively, and the end point of the next block is R(xr,
yr, zr, Ar, Br), as shown in Fig. 4.
The tangent vector τ1 of the point Q in the line PQ is
a
τ1  1 ,
a1
(19)
where a1  ( xq  xp , yq  yp , zq  zp ).
The orientation vector of the tool axis relative to the
workpiece t1 at the point Q is
t1 [SBq
SAqCBq
CAqCBq ].
v1τ1t1.
(21)
The head position Q1 of the offset vector t1 at the point Q
along the straight line PQ can be obtained from Eq. (17).
The straight line r1 on which the start point is Q1 that
parallels to the tangent vector of the point Q along the
straight line PQ is
r1Q1τ1t.
3.3 Calculating the offset vector
In peripheral milling, the tool axis is perpendicular to
both the movement direction and the offset vector.
Consequently, the offset vector is perpendicular to both the
tangent vector of the tool path τ (τxiτyjτzk) and the
orientation vector of the tool axis relative to the workpiece
t (txityjtzk). The tail of the vector is on the workpiece
side and its head on the tool center path. The offset vector
v (vxivyjvzk) is calculated as follows:
vτt.
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(20)
The offset vector v1 at the point Q along the straight line
PQ is
(22)
In the same manner, the head position Q2 (x2, y2, z2) of
the offset vector t2 at point Q can be obtained along the
straight line QR, and the straight line r2 on which the start
point is Q2 that parallels to the tangent vector τ2 of the point
Q can be obtained along the straight line QR.
3.4.1 Type A
In Type A, the inserted block is a straight line Q11Q22 that
is a common perpendicular L of the two line r1 and r2, as
shown in Fig. 4(a). The common perpendicular L can be
described as
x  x0
y  y0
z  z0


,
m
n
l
(23)
where point c( x0 , y0 , z0 ) is an arbitrary point in the L.
Coefficients m , n and l are the direction vector LL of
L, at least one of which is non-zero.
L meets both lines r1 and r2 and is perpendicular to them.
LL is obtained as follows:
LL τ1τ2.
(24)
The connection line between point c and Q1, LL and τ1
are coplanar. Hence, the following equation is valid:
x0  x1
m
y0  y1
n
z0  z1
l
 0.
τ 1x
τ1 y
τ 1z
(25)
The connection line between point c and Q2, LL and τ2
are coplanar. Hence, the following equation is valid:
x0  x2
y0  y2
z0  z 2
m
n
l
τ 2x
τ 2y
τ 2z
 0.
(26)
The point c can be derived as follows from the above
two simultaneous equations:
 x0  0,




(τ n τ 2 y m) A  (τ1x n τ1 y m) B

 y0  2 x
,


C



(τ l τ 2 z m) A  (τ1x l τ1z m) B

z0  2 x
,


C


(27)
CHEN Youdong, et al: Three-dimensional Tool Radius Compensation for Multi-axis Peripheral Milling
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where
A  (τ1y l τ1z n) x1  (τ 1x l τ 1z m) y1  (τ 1x n τ 1 y m) z1 ,
B  (τ 2y l τ 2z n) x2  (τ 2x l τ 2z m) y2  (τ 2x n τ 2 y m) z2 ,
C  (τ 2 x l τ 2z m)(τ1x n τ1 y m)  (τ1x l τ 1z m)(τ 2x n τ 2y m).
The common perpendicular L can be derived from Eqs.
(23), (24) and (27).
The point Q11 is the intersection point of the common
perpendicular L and the straight line r1. The coordinate of
Q11 can be obtained as
Q11Q1t1τ1.
If
If
If
(28)
τ1y
τ
m( z1  z0 )  l ( x0  x1 )
.
τ1x l τ1z m
τ 1x
τ
τ1 y
m( y1  y0 )  n( x0  x1 )
.
τ 1 x n τ 1 y m
τ1 y
τ
τ
m( z1  z0 )  l ( y0  y1 )
.
τ 1y l  τ 1z n
τ1x
m

 1z , then t1 
n
l
 1z 
, then t1 
m
l
n
 1z  1x , then t1 
n
l
m
Similarly, the coordinate of point Q22 can be obtained
which is the intersection point of the common
perpendicular L and the straight line r2.
The tool paths at the corner are Q1  Q11  Q22  Q2 ,
as shown in Fig. 4(a).
3.4.2 Type B
In Type B, the inserted block is a straight line Q11Q22, as
shown in Fig. 4(b). The point Q11 is the offset radius R
along the line P1Q1 to the point Q1. The point Q22 is the
offset radius R along the opposite direction of the line Q2R1
to the point Q2.
The coordinate of point Q11 is expressed as
Q11Q1Rτ1.
(29)
The coordinate of Q22 is obtained as
Q22Q2Rτ2.
(30)
The tool paths at the corner are Q1  Q11  Q22  Q2 ,
as shown in Fig. 4(b)
4
Verification and Experiments
To illustrate the new approach, the presented
compensation method has been applied by the VERICUT
and the tool path of the test workpiece.
4.1 VERICUT verification
To verify the effectiveness of the proposed methodology,
a postprocessor program for multi-axis machine has been
developed to generate the offset path. The user configured
the kinematics model, and entered the NC code and tool
radius. The NC codes with the radius offset were generated
accordingly. In order to verify it, the generated NC codes
are further input into the solid cutting simulation software
VERICUT which can customize or design kinematics of
the machine and simulate the NC codes. The VERICUT
reads the generated NC codes to perform the cutting
actions.
Fig. 6 shows the result for simulating the NC data in a
three-axis machine tool. The finishing part shapes of
simulation are the same with different cutter radiuses as
shown in Fig. 6(a), Fig. 6(b) and Fig. 6(c). Note that the
cutter radius is 15 mm, 10 mm, and 5 mm, respectively.
Fig. 7 shows that a table-tilting type of machine tool is
constructed in the software environment and the final
shapes of the workpiece with different cutter radiuses are
simulated. The cutter radius is 1.5 mm, 1 mm and 0.5 mm
as shown in Fig. 7(a), Fig. 7(b) and Fig. 7(c), respectively.
Fig. 6 and Fig. 7 demonstrate that the developed 3D radius
compensation is highly effective.
4.2 Experimental validation
The effectiveness of the presented 3D tool radius
compensation algorithm was conducted in an experiment to
machine a soup spoon on a spindle-tilting type of
machining centre. The CNC controller reads CL data for
machining the soup spoon generated by the MasterCam,
calculates the cutter compensation, and drives the machine
tools. The part shown in Fig. 8 is machined on a five-axis
machining center controller with an in-house developed
CNC. Fig. 8 shows the machined soup spoon,
demonstrating that the proposed algorithm can be
successfully applied to the practical five-axis machining.
5
Conclusions
(1) A 3D tool radius compensation algorithm is proposed
for various three- to five-axis peripheral milling based on
generalized kinematics model and relations of two lines in
three dimensions. The offset path can be calculated by
offsetting the tool path along the direction of the offset
vector obtained by the orientation vector of the tool axis
relative to the workpiece.
(2) To avoid cutting into the corner formed by the two
adjacent tool paths, the coordinates of the offset path at the
intersection point have been calculated according to the
transition type that is determined by the angle between the
two tool path tangent vectors at the corner.
(3) Although the presented methodology about 3D tool
radius compensation can be used in CNC systems, it is just
for linear or circular tool paths. Therefore, further research
on parametric curves, such as Bezier, B-Spline and NURBS
curves for 3D cutter compensation is needed.
CHINESE JOURNAL OF MECHANICAL ENGINEERING
(a) 15 mm
(b) 10 mm
(c) 5 mm
(d) Screenshot of the VERICUT simulation and verification for the three-axis machine tool
Fig. 6. VERICUT simulation and verification for the three-axis machine tool
(a) 1.5 mm
(b) 1 mm
(c) 0.5 mm
(d) Screenshot of the VERICUT simulation and verification for the table-tilting type five-axis machine tool
Fig. 7. VERICUT simulation and verification for the table-tilting type five-axis machine tool
·553·
·554·
CHEN Youdong, et al: Three-dimensional Tool Radius Compensation for Multi-axis Peripheral Milling
[8]
[9]
[10]
[11]
[12]
[13]
Fig. 8.
Soup spoon machined
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Biographical notes
CHEN Youdong, born in 1973, is currently an associate professor
at Beihang University, China. He took his PhD degree from
Beihang University, China, in 2003. His research interests cover
CNC system, mechachonics control, robotics control system and
embedded system.
Tel: +86-10-82338271; E-mail: chenyd@buaa.edu.cn
WANG Tianmiao, born in 1960, is currently a professor at
Beihang University, China. He took his PhD degree from Xi’an
Jiaotong University, China, in 1990. His research interests include
intelligent robotics and mechachonics engineering.
Tel: +86-10-82338271; E-mail: wtm_itm@263.net