Advanced Materials Research Vols. 488-489 (2012) pp 813-818
© (2012) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMR.488-489.813
Online: 2012-03-15
Computer Program in Visual Basic Language for Manufacture of Helical
Cutting Tools
Ngoc-Thiem Vu1,a, Shinn-Liang Chang2,b, Jackson Hu3,c, Tacker Wang4,d
1, 2
Department of Mechanical and Electro-Mechanical Engineering, National Formosa University, 64
WunHua Road, Huwei, 632 Yunlin, Taiwan.
3, 4
a
AMAX MFG. CO., LTD.68, Kuang-Cheng Road, TaliCity, Taichung Hsien 41278, Taiwan
[email protected] (graduate student), b [email protected] (professor, corresponding
author), c [email protected] (general manager), d [email protected] (manager)
Keywords: helical cutting tool, rack cutter, theory of gearing, computer assisted design, visual basic
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, and 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 give the best solution for economical
consideration.
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 [3,4,5]. 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 re-sharpening 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.
Fig.1. Normal section tooth profile of hob cutter
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Key Engineering Materials II
Fig.2. The coordinate system of the right-hand helix of the rack cutter.
Design of Rack Cutter Profile
The phenomenon of undercutting has been applied by a straight-sided hob cutter to generate the
profile of the helical cutting tool. Fig.1 shows an example of normal tooth section of hob cutter. The
cutting face can be divided into six regions: (I) the left cutting face, (II) the right cutting face, (III and
IV) the fillet cutting faces, (V) the top land cutting face, (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.
In Fig.1, is the origin of the coordinate system , , . The equation of left cutting face
of the rack cutter in the coordinate system , , is shown as example. The geometrical
properties and theory of gearing can be applied to find equations of 5 other regions.
ra( I )
 R − HKW − R.sinψ L + l ( I ) .cosψ L



R
(I )
b −
− HKW .tanψ L + R.cosψ L + l .sinψ L 

=  0 tan(45 +ψ L / 2)


0

1



(1)
The equation of left cutting face I is presented in the coordinate system is ra( I ) :
: Parameter
indicates the position on the left cutting face.
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
and Fig.3. 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.
1
0
[ M wa ] = 0

0
0
sin λ
−
+
cos λ
0
−
+
0
cos λ
sin λ
0
0

u.cos λ 
u.cos λ 

1

+
−
(2)
The transformation matrix M presents the transformation of the rack cutter coordinate system
to the helical coordinate system that is shown in Fig.2
The upper sign of M indicates the right hand helix of 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 in the coordinate system.(region I):
rw( I ) = [ M wa ] .ra( I )
(3)
Advanced Materials Research Vols. 488-489
815
Applying the same method for 5 other regions (region II-VI), the equation of helical rack cutter of
5 regions can be obtained.
Equation of the Helical Cutting Tool
Locus Equations
Transforming the equation of the cutting face from the coordinate system of the helical rack
cutter to the coordinate system of the helical cutting tool using the transformation matrix
M that is shown below, the locus equation of the helical cutting tool can be obtained.
[ M 1w ] = [ M 1h ].[ M hw ]
(4)
The locus equation of the rack cutter for region I, left cutting face is shown below:
rI( I ) = [ M 1w ] .rw( I )
(5)
Where is shown in Eq. 3. Applying the same method for 5 other regions (region II-VI), the
locus equation of the full profile can be obtained.
Equations of Meshing
In the Fig.3, the helical cutting tool is generated by the rack cutter. Using the theory of gearing,
the relative velocity of the contact point ( ) and the unit normal vectors of the helical rack cutter
() are obtained. Then, the equation of meshing . =0 can be obtained. Using the theory of
gearing, the equation of meshing of the left cutting face is generated as below:
u = +− (R − HKW + l ( I ) .cosψ L − c).tan λ.cosψ L +− (b0 −
r .φ
R
I
− HKW.tanψ L + l ( ) .sinψ L ).tan λ +− ( 1 1 )
tan ( 45 +ψ L / 2)
cos λ
(6)
Solving Eq. 6 and Eq. 5 simultaneously, the generated tooth profile by region I can be obtained.
Applying the same method for 5 other regions (region II-VI), the generated tooth profile of the
other regions can be obtained.
Fig.3. Coordinate system relationship of the rack cutter and generated gear
Program Supports Designing Rack Cutter
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.
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Key Engineering Materials II
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.
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 decide choosing the compatible rack 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 can be exported and saved in the text files, and
the multiple point in the 2D coordinate of the helical cutting tool section are 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.
Example
If the data are inputted as shown in Fig.5, we obtain the sections and technical parameters of
helical cutting tool and rack cutter are 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.
Fig.4. Flow chart of the program
Advanced Materials Research Vols. 488-489
817
Fig.5. Input parameters and the section of the cutting tools
Table1: Parameters of rack cutter and helical cutting tool
Parameters of helical cutting tool:
Number of teeth
T
12[teeth]
Outside diameter
D
15[mm]
Parameters of rack cutter:
Pressure angle of left cutting face
Pressure angle of right cutting face
Root diameter
Rake angle
Helical angle
Module
Clearance angle = 90 - !
Radius of helical rack cutter
Addendum
Dedendum
Tooth thickness of rack cutter
d
α
λ
m
11.6[mm)
20
60
1.25
"
R
HKW
HFW
2.%
30
2
35
0.35[mm]
1.42[mm)
0.28[mm]
5.2[mm]
Focusing in the third tab in Fig.7, when we want to modify the profile of rack cutter and helical
cutting tool, we can change the parameters in each data box. The parameters are modified as below:
Table2: Parameters of rack cutter are modified
Pressure angle of left cutting face
Pressure angle of right cutting face
35
2.5
Radius of helical rack cutter
Pressure angle of chamfering
r
!
0.5[mm]
60
We can obtain the results in Fig.7, Fig.8, and Fig.9.
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.
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Key Engineering Materials II
Fig.6. Properties of helical cutting tool and
profile of rack cutter.
Fig.7. Modifying the profile of rack cutter
and helical cutting tool.
Fig.9. Helical cutting tool is modified and
before
Fig.8. Rack cutter is modified and before
Acknowledgement
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-150-033.
References
[1] 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”, Comput. Methods Appl. Mech. Engrg. 189 (2000) 595-612.
[2] J.D.Kim and D.S.Kim, “The development of software for shaving cutter design”, Journal of
materials processing technology 59(1996) 359-366.
[3] F.L.Litvin,“Gear geometry and applied theory, second edition”. Published by Cambridge
University press, September 2004.
[4] S.L.Chang and H.C.Tseng, “Design of a novel cutter for manufacturing helical cutting tools”,
Proceeding of the institution of mechanical engineers, 2005.
[5] 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 209(2009) 847-855.
Key Engineering Materials II
10.4028/www.scientific.net/AMR.488-489
Computer Program in Visual Basic Language for Manufacture of Helical Cutting Tools
10.4028/www.scientific.net/AMR.488-489.813
DOI References
[1] 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, Comput. Methods Appl.
Mech. Engrg. 189 (2000) 595-612.
http://dx.doi.org/10.1016/S0045-7825(99)00313-8