International Journal of Applied Physics and Mathematics, Vol. 2, No. 2, March 2012
Computer –Aided Design of Helical Cutting Tools
Ngoc–Thiem Vu, Shinn–Liang Chang, Jackson Hu, and Tacker Wang
left cutting face, (II) the right cutting face, (III and IV) the
fillet cutting faces, (V) the top land cutting face, and (VI)
the chamfering cutting face. The equations of designed rack
profiles of the hob cutter, and the theory of gearing are
applied, so the mathematical model of the helical cutting
tool can be derived.
is the origin of the coordinate system
In Fig.1,
, ,
, it located at the middle of the rack cutter body.
The equations of the six regions of the rack cutter in the
, ,
can be obtained but only
coordinate system
the equation of left cutting face is shown here as example.
The geometrical properties and theory of gearing can be
applied to find the equations of other regions.
Abstract—The helical cutting tools have complex geometries. A rack
cutter is the most economical tool that has been used for
manufacturing helical cutting tool. In this paper, the computer
program has been designed to evaluate the manufacture abilities
following design concept and analyze the technical parameters of
helical cutting tool. The program can simulate the sections of helical
cutting tool and the rack cutter, analyze the clearance angle, relief
angle, width top of the helical cutting tool, and modify the rack cutter
profile to show the helical cutting tool profile suitably. This program
can predict the differences during manufacture process and offer the
best solution for economical consideration.
Index Terms—Computer aided design, helical cutting tool, rack
cutter, theory of gearing.
I.
INTRODUCTION
The development of information technology supports the
process of mechanical manufacture to very high level and
makes good profit on mechanical industry. Computer
programs have been developed rapidly in the mechanical
process, especially for the manufacture of cutters and design
of cutters [1], [2]. Helical cutting tools have the important
role in the manufacture of machine parts. Rack cutter has
been designed for manufacturing helical cutting tool. The
personal computer is applied to design the cutter and show
the profile of cutters [3]-[5]. Before the manufacture of
helical cutting tool, we can simulate the section of helical
cutting tool that is cut by rack cutter. Therefore, we can
avoid unpredicted errors after manufacturing.
In this study, the computer program has been designed for
general purpose, the helical cutter applied for the resharpening of pencils is investigated. Some important
functions are included in this program. The user inputs
parameters, then the program will calculate automatically to
show results and analysis. It’s convenient and reliable for
the customer.
II.
Fig.1. Normal section tooth profile of hob cutter.
The equation of left cutting face I is presented in the
coordinate system as:
. sin
. cos
. tan
=
DESIGN OF RACK CUTTER
The phenomenon of undercutting has been applied by a
straight-sided hob cutter to generate the profile of the helical
cutting tool [4]. Fig.1 shows an example of normal tooth
section of hob cutter.
The cutting face can be divided into six regions: (I) the
. cos
0
1
. sin
(1)
: Parameter indicates the position on the left cutting face.
III.
EQUATION OF THE HELICAL RACK CUTTER
The normal section of rack cutter is transferred along the
direction of the lead that is shown in Fig.2. We transform
the equations of the cutting face from the rack cutter
coordinate system to the helical rack cutter coordinate
system, we can obtain the equation of the helical rack cutter.
indicates the
The transformation matrix M
transformation of the rack cutter coordinate system to the
helical coordinate system
that is shown in Fig.2 .
Manuscript received February 09, 2012; revised March 30, 2012.
Ngoc–Thiem Vu, Shinn–Liang Chang are with Department of
Mechanical and Electro-Mechanical Engineering, National Formosa
University, 64 WunHua Road, Huwei, 632 Yunlin, Taiwan(a
[email protected] (graduate student), b [email protected]
(professor, corresponding author).
Jackson Hu, and Tacker Wang are with AMAX MFG. CO., LTD.68,
Kuang-Cheng Road, TaliCity, Taichung Hsien 41278, Taiwan
( [email protected], [email protected]).
93
International Journal of Applied Physics and Mathematics, Vol. 2, No. 2, March 2012
M
1
0
=
0
0
0
sin
cos
0
0
cos
sin
0
0
u. cos
u. sin
1
where
is shown in equation (3).
Applying the same method for other regions (region IIVI), the locus equation of the full profile can be obtained.
(2)
B.
Equations of Meshing
In Fig. 3, the helical cutting tool is generated by the rack
cutter. Using the theory of gearing, the relative velocity of
) and the unit normal vectors of the
the contact point (
helical rack cutter ( ) are obtained. Then, the equation of
meshing .
=0 can be obtained.
The equation of meshing of the left cutting face is derived
as below:
indicates the right-hand helix of
The upper sign of M
the helical rack cutter and the lower sign of M
indicates
the left-hand helix.
The equation of left cutting face of the helical rack cutter
coordinate system (region I)
showed in the
.
(3)
. cos
tan 45
. sin
. tan . cos
. tan
2
. tan
.
(6)
Solving equation (6) and equation (5) simultaneously, the
generated tooth profile by region I can be obtained.
Applying the same method for other regions (region IIVI), the generated tooth profile of the other regions can be
obtained.
Fig. 2. The coordinate system of the right-hand helix of the
rack cutter.
V.
The development of this program can automatically
analyze some technical characteristics and simulate sections
of rack cutter and helical cutting tool. The different profiles
and optimal design can be predicted. We can estimate the
manufacture abilities to save time and money for
manufacturers, and enhance the manufacturing efficiency.
The parameters of helical cutting tool and rack cutter can
be modified for finding optimal cases. Finally, we can save
the modified data in text file or multiple points of section to
import into AutoCAD for checking profile again. The
computer program is a window application program which
works on Window 7 or Window XP using Visual Basic
language.
Applying the same method for other regions (region IIVI), the equation of helical rack cutter of 5 regions can be
obtained.
IV.
EQUATION OF THE HELICAL CUTTING TOOL
A.
Flow Chart of the Program
A flow chart of the program for designing the rack cutter
is shown in Fig.4. Input parameters are filled firstly. Then,
the sections of helical cutting tool and helical rack cutter can
be displayed. If we accept those sections, we can continue
for analyzing clearance angle, relief angle, and top land
width of the helical cutting tool. The technical parameters of
cutters can be checked. Then, we can modify input
parameters to show new sections of helical cutting tool and
helical rack cutter. Finally, we can choose the best solution
and save data for manufacturing.
Fig. 3. Coordinate system relationship of the rack cutter and
generated gear.
A.
Locus Equations
Transforming the equation of the cutting face from the
of the helical rack cutter to the
coordinate system
coordinate system of the helical cutting tool is shown in
is shown below.
Fig.3. The transformation matrix M
The locus equation of the helical cutting tool can be
obtained.
M
M
M
B.
Computer Program
The main menu of the program is shown in Fig.5
consisting of File, Edit, and Examples modes, and three tabs.
In the tab “Section of the Cutting Tools”, we can input
parameters of the helical cutting tool then click on the
functions to display the helical cutting tool section or one
tooth section. Then, we can evaluate the left cutting face,
right cutting face, fillet cutting face, top land cutting face,
and chamfering cutting face to choose the compatible rack
(4)
The locus equation of the rack cutter for region I, left
cutting face, is shown below:
.
PROGRAM SUPPORTS DESIGNING RACK CUTTER
(5)
94
International Journal of Applied Physics and Mathematics, Vol. 2, No. 2, March 2012
cutter in the next tab named “Technical Analysis Graphs”.
The second tab is shown in Fig.6 consisting of displaying
rack cutter profile function, analyzing clearance angle, relief
angle, and top land width. In addition, this tab contains
special functions such as parameters of helical cutting tools
and rack cutter that can be exported and saved in the text
files. And, the multiple points in the 2D coordinate of the
helical cutting tool section can also selected to save in the
other text file.
The third tab “Checking Rack Cutter” is shown in Fig.7,
we can modify the parameters to show new section of rack
cutter and helical cutting tool. We can evaluate the new
sections and compare with the old sections for choosing the
best choices for manufacturing.
Clearance angle (90 Pressure angle of chamfering)
=
30
Radius of helical rack cutter, r = 0.15 (mm)
Addendum, HKW=1.24 (mm)
Dedendum, HFW=0.24 (mm)
Tooth thickness of rack cutter, 2 = 5.4 (mm)
Focusing in the third tab in Fig.7, if we want to modify
the profile of rack cutter and helical cutting tool, we can
change the parameters in each data box. In this example the
parameters are modified in Fig.8 shown below:
=45
Pressure angle of left cutting face,
=5
Pressure angle of right cutting face,
Radius of helical rack cutter, r = 0.4 (mm)
Pressure angle of chamfering = 65
Fig. 5. Input parameters and the section of the cutting tools.
Fig. 4. Flow chart of the program.
C.
Example
If the data is inputted as shown in Fig.5, we obtain the
sections and technical parameters of helical cutting tool and
rack cutter shown in Fig.5, Fig.6, and Fig.7. In addition, we
can use those sections as original sections to compare with
modified sections of helical cutting tool and helical rack
cutter.
1)
Parameters of Helical Cutting Tool
Number of teeth, T =12
Outside diameter, D=15.37(mm)
Root diameter, d=12.4(mm)
Rake angle, α =29
Helical angle, deg =60
Module, m= 1.28
2) Parameters of Rack Cutter
=40
Pressure angle of left cutting face,
=4
Pressure angle of right cutting face,
Fig. 6. Properties of helical cutting tool and profile of rack cutter.
Fig. 7. The modifying field of HCTA program.
95
International Journal of Applied Physics and Mathematics, Vol. 2, No. 2, March 2012
We can obtain the results in Fig.8, Fig. 9, and Fig. 10.
input parameters to get the better profile of the cutter as the
mentioned example in the previous section. The new profile
of rack cutter and helical cutting tool can be obtained in
Fig.8, Fig.9 and Fig.10. Although, the two sets of input
parameter both can be accepted. When we input the
improper parameters as in Fig. 11, Fig.11 and Fig.12 show
the improper profiles of helical cutting tool. The crossing
section of the left cutting face and the top land cutting face
are intersected on the smaller circle than the required circle.
D.
Choosing Improper Parameters Causes the Wrong
Result
The fail section of helical cutting tool is shown in the
Fig.11 and Fig.12 when the input parameters are improper.
Fig.11 shows the failure of section when increase number of
teeth of cutter from 12 teeth to 14 teeth. Intersection of left
cutting face and right cutting face is on a circle with smaller
diameter than standard circle. It can’t be accepted. Fig.12
shows another improper input parameters when we decrease
the helical angle of cutter from 60 degrees to 45 degrees. On
the other hand, if the other parameters are changed to be
unsuitable values, the HCTA program can predict and
evaluate the unable ability for manufacturing.
Fig. 11. Wrong section when entering parameter is improper.
Fig. 8. Modified profile of rack cutter and helical cutting tool.
Fig. 12. Wrong section when entering parameter is improper.
Fig. 9. Rack cutter is modified and before.
VII.
Fig. 10. Helical cutting tool is modified and before.
VI.
CONCLUSION
In this study, the computer program has been designed to
simulate and modify the sections of helical cutting tool and
helical rack cutter. Before we manufacture the cutters, we
can simulate the profiles of cutters using this program to
display the sections and technical characteristics. Then, we
evaluate the producing abilities and predict the differences
of cutters after manufacturing. This program is written by
Visual Basic language with simple interface helping users
use easily.
This program design not only supporting for manufacture
but also helping learners to study this field easily.
DISCUSSION
When the helical cutting tool is designed, designers can
check the profile of cutter by using HCTA program. When
the result is proper as Fig.5, Fig.6, and Fig.7 shown, we
accept the input parameters and save them for
manufacturing the cutter. In addition, we can modify some
APPENDIX
2
C
D
96
Tooth thickness of the rack cutter
Shifted amount
Outside diameter of the helical
International Journal of Applied Physics and Mathematics, Vol. 2, No. 2, March 2012
cutting tool
e
Height of chamfering from point q to the
root of tooth of the rack cutter
HKW :Addendum of the rack cutter
HFW: Dedendum of the rack cutter
,
,
:
Parameter of vector
,
,
respectively
Origin of coordinate system
Circular pitch of the rack cutter
r
Outside radius of the helical cutting tool
Radius of pitch circle of the helical
cutting tool
,
μ:
Parameters of
,
,
,
R
Radius of the rack cutter fillet
Fixed coordinate system
Coordinate system of helical rack cutter
Coordinate system of helical cutting tool
and
u
Distance between origins
λ
Lead angle of the helical cutting tool
Angular displacement of the helical
cutting tool while hobbing
, ,
: Pressure angle of cutting edge I, II,
and VI respectively.
ACKNOWLEDGMENT
The work outline in this paper was supported by APEX
MFG. CO., LTD and the National Science Council under
grants NSC91-2212-E-150-022 and NSC92-2212-E-150033.
REFERENCES
[1]
[2]
[3]
[4]
[5]
97
J. Argyris, M. D. Donno, and F. L. Litvin, “Computer program in
Visual Basic language for simulation of meshing and contact of gear
drives and its application for design of worm gear drive,” Computer
Methods in Applied Mechanics and Engineering, vol. 189, pp. 595612, 2000.
J. D. Kim and D. S. Kim, “The development of software for shaving
cutter design,” Journal of materials processing technology, vol. 59,
pp. 359-366, 1996.
F. L. Litvin, “Gear geometry and applied theory, second edition,”
Published by Cambridge University press, September 2004.
S. L. Chang and H. C. Tseng, “Design of a novel cutter for
manufacturing helical cutting tools,” Proceeding of the institution of
mechanical engineers, Journal of Mechanical Engineering Science
vol. 219, pp.395-408, 2005.
J. K. Hsieh, H. C. Tseng, and S. L.Chang, “Novel hob cutter design
for the manufacture of spur-typed cutters,” Journal of materials
processing technology, vol. 209, pp. 847-855, 2009.