DESIGNING AND MODELLING OF WORM GEAR HOB Sándor Bodzás 1, Dr. Illés Dudás 2 1 PhD student,
[email protected] 2 DSc professor,
[email protected] 1,2 Department of Production Engineering, University of Miskolc, H-3515 Miskolc, Egyetemváros, Hungary 1,2 Department of Technical Preparatory and Production Engineering, College of Nyíregyháza, H-4400, Nyíregyháza, Sóstói u. 9-11., Hungary ABSTRACT In this article the designing of hob which is needed for production of worm gear is introduced. Based on the designing method we designed, modelled and produced different types of hob. 1. INTRODUCTION Worm gear hobs are often used hobs which are prepared with Archimedean basic worm. These have linear profile in axial section that is why the production of these is simpler than the other types of hob [4]. In Figure 1 a fixed, calibre Archimedean hob can be seen. υ
ϕ
γ
ϕ
α
α
Figure 1 The elements of worm gear hobs For defining of the elements of hob the following data have to be known starting: • max axial module; • z1 number of threads of the worm; • i21 transmission ratio; • d01 pitch diameter of the worm; • α0 axial profile angle; • l1 dedendum of hob; 12
• l2
dedendum of worm gear.
2. THE DESIGNING METHOD 2.1. The pitch cylinder diameter of hob During the resharpenings the changing of the centre distance and the lead of thread have to be corrected so that the profile of the worm gear cannot be changed that is why the hob has to certain resharpening reserve so the ds pitch diameter of hob has to be chosen higher value than the d01 pitch diameter of worm: 0,1~0,05 ·
(1)
Where the 0,1~0,05 · expression means the grinding reserve. The purpose is the many assurance of resharpening of the hob [2]. The profile deformation of hob effects for the profile of the worm gear (Figure 2). If the profile deformation of the worm gear is higher than its permissible tolerance value than the appropriate cog connection does not appear that is why the drive will be waste (the confusion of the connection picture and the efficiency, etc.). Designation
Appellation
Designation
Appellation
Sl
Hob tooth thickness
c1
Bottom clearance
Scs
Worm tooth thickness
c2
Head clearance
Sk
Worm gear tooth thickness
hw
Useful depth of thread
js
Backlash
d1
Worm reference diameter
hcsf
Worm addendum
hk
Worm gear depth of thread
hcs
Worm depth of thread
hkf
Worm gear addendum
hcsl
Worm dedendum
hkl
Worm gear dedendum
hll
Hob dedendum
hlf
Hob addendum
rs
Fillet radius
hl
Hob depth of thread
Figure 2 Basic profile of worm-, worm gear and hob 2.2. The major diameter of hob For defining of the major diameter of hob the duplicate of the hob addendum have to be added to the calculated pitch cylinder diameter of the worm gear hob: 2 ·
(2)
2.3. The number of threads of the hob For defining of the number of thread of the hob (the numbers of flutes) the following empirical formula could be used:
13
, ·
(3)
2.4. The flute angle Based on the experiences the flute angle can be chosen ! 20° " 30° value [1]. α
υ
Figure 3 Defining of the parameters of backward turning 2.5. The backward turning angle The backward turning angle can be chosen $ 8° " 10° value [3]. 2.6. The dimension of the backward turning &
'·( )
· *+$
(4)
If the profile of the hob has to be produced with double backward turning then: & 1,2~1,3 · &
(5)
2.7. Right and left side profile angle The examination of the gear rack profile in axial section it can be seen that the angles are different on the right and left side of the tooth space. This is partially the effect of the backward turning for the profile. In the axial section of worm gear hob the line of intersection with the head ribbon of the hob leans to the axis with φx angle. For defining of the φx it has to be determined how changes are created by the backward turning in axial section during the worm gear cutting. The axial section of the worm gear hob is a linear gear rack profile because the basic worm of hob is an Archimedean worm. However the profile deforms because of the backward turning along Archimedean spiral. In Figure 4.a. is shown the blade is backward turning the cog side of the hob. The form blade starts the backward turning of the I. cog on the D1 point. The working of the form blade has to be concordance with the rotation of the hob and the vertical directional feed of the backward turning slide. After one rotation of the hob the blade is situated on the II. position which is nominated with das hed line (Figure 4.a). During this the DI point is situated on the DII point. In Figure 4.a. the section plane which crosses the hob axis is nominated with das hed line. Every cogs of the worm gear hob have to be 14
backward turned along Archimedean spiral which means the γs angle tending cutting edges are situated such the DII point of the head ribbon is nearer to the hob axis than the DI point. Based on this every cogs of the hob are situated different position because of the backward turning such the head blades connection line tends φx angle to the axis in axial section.
ϕ
α
α α γ
ϕ
ϕ
a)
b)
Figure 4 Backward turning of the cogs of the worm gear hob The following expression can be written for the defining of φx angle: *+,
-. ·)
(6)
/0
Defining of the αj right and αb left angles are shown in Figure 4.b. In this figure the side blade of the α profile angle worm is drown with full line thickness. If the head line of the cogs tends φx angle obvious the full profile is deformed. In Figure 4.b. the A point is situated to AI and the B point is situated to B1 but the axial pitch is equal in both cases. Based on 4.b. the following expressions can be written: a) Right cog side 33333 3333 33333 1 2 24 " 1 4
(7)
3333 567 · 8*+$9 24
(8)
567 313333 · *+, 4
(9)
567 313333 · 8*+$ 2
(10)
The (8), (9) and (10) is replaced to (7) and reducing with
8*+$9 8*+$ " *+, 15
567
: (11)
b) Left cog side analog the previous 8*+$: 8*+$ *+,
(12)
The defined αj and αb angles have to be given the axial section drawing of the backward turned hob cog. 2.8. The depth of hob flute The H depth of hob flute can be defined the following expression based on Figure 3: ; &
-. <-=
" 0,5~1
(13)
2.9. The section conical angle These types of worm gear hobs which creates the worm gear with tangent feed have a conical tip. The surface roughness of the produced worm gear depends of the dimension of the tangent feed. The φ conical angle of the section cone which starts the cutting can be defined by the following expression: 8>?,
= A @A=
= ·C=
(14)
2.10. The section cone length The l section cone length can be calculated from the triangle of Figure 1: D ; · 8*+,
(15)
where the ; 0,8~0,9 · & . 2.11. The length of the working part of hob F G D & · 8*+$ *
(16)
If the tip cylinder diameter is such small so that the hole execution cannot be used then the hob with its adapter has to be produced in one part (Figure 5.a.). In case of the shaft execution the shafts could be prepared from structural steel because of material saving and this time these could be fixed to the hob with flash welding. Because of the centre direction a conical connection element is usually on the one tip of the hob shaft, but on the other tip the cylindrical part connected to the fixture of the machine.
16
3. THE OUR DESIGNED HOBS During our research work we designed and produced many types of worm gear hobs (conical, cylindrical with different profiles) (Figure 5).
α γ
a)
b)
c)
d) Figure 5 The our designed hobs
SUMMARY We introduced the main periods of designing of worm gear hobs. During our research work we designed many different types of cutting tool. It can be seen every gear drives need different tools in function of the module, the basic profile angle and the number of threads. We work our research work in the Difi CAD Mérnökiroda Ltd. The described work was carried out as part of the TÁMOP-4.2.2/B-10/1-2010-0008 project in the framework of the New Hungarian Development Plan. The realization of this project is supported by the European Union, co-financed by the European Social Fund.
REFERENCES [1] [2] [3] [4]
Dr. Bakondi Károly: Hátraesztergált marók és fogazószerszámok tervezése, Tankönyvkiadó, Budapest, 1976. Dr. Dudás Illés: The Theory and Practice of Worm Gear Drives. Penton Press, London, 2000. ( ISBN 1 8571 8027 5) Dr. Dudás Illés – Csóka János: Csigakerék megmunkáló szerszámainak tervezése, gyártása, Oktatási segédlet, Miskolc, 1988. Sasi Nagy István: Fogazószerszámok tervezése, Budapest, Műszaki Könyvkiadó, 1961. 17
TARTALOMJEGYZÉK Antal Dániel EJTÉSI TESZT EGYSZER SÍTETT MODELLEZÉSE A TERVEZÉS FÁZISÁBAN
1
Bodolai Tamás MINTATESZTEL SZOFTVER FEJLESZTÉSE LINE SCAN KAMERÁS ALKALMAZÁSOKHOZ
7
Bodzás Sándor DESIGNING AND MODELLING OF WORM GEAR HOB
12
Burmeister Dániel BUCKLING OF SHELL-STIFFENED AND AXISYMMETRICALLY LOADED ANNULAR PLATES
18
Daróczy Gabriella EMOTION AND THE COMPUTATIONAL MODEL OF METAPHORS
24
Drágár Zsuzsa NEM SZABVÁNYOS SZERSZÁM-ALAPPROFIL KIALAKÍTÁSÁNAK LEHET SÉGEI FOGASKEREKEKHEZ
30
Fekete Tamás MEMBRÁNOK ALKAKMAZÁSA SZINKRON VÁLTAKOZÓ ÁRAMÚ HIDRAULIKUS HAJTÁSOKBAN
35
Ferenczi István MODELING THE BEHAVIOR OF PROFINET IRT IN GIGABIT ETHERNET NETWORK 41 Ficsor Emese AUTOMATIZÁLT AZONOSÍTÁSTECHNIKAI ÉS NYOMONKÖVETÉSI LEHET SÉGEK VIZSGÁLATA INTERMODÁLIS SZÁLLÍTÁS SORÁN
47
Gáspár Marcell Gyula NAGYSZILÁRDSÁGÚ ACÉL HEGESZTÉSTECHNOLÓGIÁJÁNAK FEJLESZTÉSE A H LÉS ID ELEMZÉSÉVEL
54
Hriczó Krisztián NEMNEWTONI FOLYADÉKOK HATÁRRÉTEG ÁRAMLÁSÁNAK HASONLÓSÁGI MEGOLDÁSAI KONVEKTÍV FELÜLETI PEREMFELTÉTELEK MELLETT 60 Kelemen László Attila DOMBORÍTOTT FOGAZAT MATEMATIKAI MODELLEZÉSE FOGASGY R S TENGELYKAPCSOLÓKHOZ 66
Krizsán Zoltán STRUCTURAL IMPROVEMENTS OF THE OPENRTM ROBOT MIDDLEWARE 72 Mándy Zoltán A POSSIBLE NEURAL NETWORK FOR A HOLONIC MANUFACTURING SYSTEM 78 Simon Pál GRAFIKUS PROCESSZOROK ALKALMAZÁSA KÉPFELDOLGOZÁSI FELADATOKRA
84
Skapinyecz Róbert OPTIMALIZÁLÁSI LEHET SÉGEK VIZSGÁLATA EGY E-PIACTÉRREL INTEGRÁLT VIRTUÁLIS SZÁLLÍTÁSI VÁLLALATNÁL 90 Somosk i Gábor COLD METAL TRANSFER – THE CMT PROCESS Szabó Adél Anett A TELJES KÖLTSÉG KONCEPCIÓ BESZERZÉSI GYAKORLATBAN
JELENT SÉGE
96 A
Szamosi Zoltán MEZ GAZDASÁGI HULLADÉKOK VIZSGÁLATA Szilágyiné Biró Andrea BETÉTEDZÉS ACÉLOK KARBONITRIDÁLÁSA
KÜLÖNBÖZ
VÁLLALATI 102 108
H MÉRSÉKLET 114
Tomkovics Tamás DARABÁRU OSZTÁLYOZÓ RENDSZEREK KISZOLGÁLÁSI STRATÉGIÁIT BEFOLYÁSOLÓ JELLEMZ K; A RENDSZEREK MODULJAI KÖZÖTTI ÖSSZEFÜGGÉSEK FELTÁRÁSA 120 Tóth Zsolt EL REDUKCIÓ ALKALMAZÁSA A TBL ALGORITMUS ID KÖLTSÉGÉNEK CSÖKKENTÉSÉRE 126 Varga Zoltán KONKRÉT LOGISZTIKAI MINTARENDSZER MODELLEZÉSE
131
Vincze Dávid MATLAB INTERFACE FOR THE 3D VIRTUAL COLLABORATION ARENA 137 Wagner György INTENZÍTÁS BÁZISÚ OPTIMALIZÁLÁS FORGÁCSOLÁSI PARAMÉTEREK MEGHATÁROZÁSÁHOZ 143
