All of the cutting edges on an hourglass worm gear hob have different shapes and spiral angles. If the spiral angles are small, straight flutes are typically adopted. However, for hobs with multiple threads, the absolute values of the negative rake angles on one side of the cutting teeth will greatly affect the cutting performance of the hob if straight flutes are still used. Therefore, spiral flutes are typically adopted to solve this problem. However, no method to determine the spiral flute of an hourglass worm gear hob has been proposed until now. Based on the curved surface generating theory and the hourglass worm forming principle, a method for generating the spiral flute of the planar double enveloping hourglass worm gear hob is proposed in this paper. A mathematical model was built to generate the spiral flute. The rake angles of all cutting teeth of the hob are calculated. The laws of the rake angles of the cutting teeth for four hobs with different threads from one to four threads were analyzed when straight flutes and spiral flutes are adopted. The laws between the value of the negative rake angles of the hob with four threads and the transmission ratio were studied. The most appropriate transmission ratio for generating the spiral flute was obtained. The machining of the spiral flutes was simulated using a virtual manufacturing system, and the results verify the correctness of the method.

References

References
1.
Dong
,
X.
,
2004
,
Design and Modification of Enveloping Worm Gearing
,
China Mechanical Industry Press
, Beijing, China.
2.
Pavlov
,
A.
, and
Bogatsky, M.
,
1975
, “
Method of Forming Globoid Worm Thread and Worm Wheel Teeth
,” U.S. Patent No.
3875635
.
3.
Sakai
,
T.
, and
Maki
,
M.
,
1980
, “
Globoid Worm Gear Generating Method
,” U.S. Patent No.
4184796
.
4.
Simon
,
V.
,
1988
, “
Computer Aided Manufacturing of High Precision Hobs
,”
Int. J. Mach. Tools Manuf.
,
28
(
4
), pp.
443
452
.
5.
Simon
,
V.
,
1993
, “
Hob for Worm Gear Manufacturing With Circular Profile
,”
Int. J. Mach. Tools Manuf.
,
33
(
4
), pp.
615
625
.
6.
Dong
,
L.
,
2013
, “
Research on NC Machining Technology of Enveloping Worm Gear Hob
,” Ph.D. thesis, China Agricultural University, Beijing, China.
7.
Liu
,
G.
,
2016
, “
Research on CNC Relief Grinding Technology of Enveloping Worm Gear Hob
,” Ph.D. thesis, China Agricultural University, Beijing, China.
8.
Liu
,
G.
,
Wei
,
W.
,
Dong
,
X.
,
Rui
,
C.
,
Liu
,
P.
, and
Li
,
H.
,
2016
, “
Relief Grinding of Planar Double-Enveloping Worm Gear Hob Using a Four-Axis CNC Grinding Machine
,”
Int. J. Adv. Manuf. Technol.
,
89
(9–12), pp.
3631
3640
.
9.
Zhou
,
L.
,
2005
,
The Modification Principle and Manufacturing Technology of Hourglass Worm
,
China National University of Defense Technology Press
, Changsha, China.
10.
Simon
,
V.
,
1982
, “
Grinding Wheel Profile for Hob Relief Grinding
,”
ASME J. Mech. Des.
,
104
(
4
), pp.
731
742
.
11.
Simon
,
V.
,
1985
, “
The Influence of Hob Diameter on Worm Gear Mesh
,”
Symposium on Machine Design
, pp.
49
64
.
12.
Günay
,
M.
,
Aslan, E.
,
Korkut, Ï
., and
Seker, U.
,
2004
, “
Investigation of the Effect of Rake Angle on Main Cutting Force
,”
Int. J. Mach. Tools Manuf.
,
44
(
9
), pp.
953
959
.
13.
Saglam
,
H.
,
Unsacar
,
F.
, and
Yaldiz
,
S.
,
2006
, “
Investigation of the Effect of Rake Angle and Approaching Angle on Main Cutting Force and Tool Tip Temperature
,”
Int. J. Mach. Tools Manuf.
,
46
(
2
), pp.
132
141
.
14.
Altintas
,
Y.
,
2000
,
Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations and CNC Design
,
Cambridge University Press
, Cambridge, UK.
15.
Liu
,
J.
,
1996
, “
Dressing Calculation of the Profile of the Grinding Wheel on the Rake Face of the Hob With Zero Rake Angle
,”
Grinding Mach. Grinding
,
4
, pp.
25
26
.
16.
Chang
,
S. L.
,
2003
, “
Helix Gash of Hob Cutter Manufactured by Milling
,”
J. Mater. Process. Technol.
,
142
(
2
), pp.
569
575
.
17.
Sheth
,
D. S.
, and
Malkin
,
S.
,
1990
, “
CAD/CAM for Geometry and Process Analysis of Helical Groove Machining
,”
Ann. CIRP
,
39
(
1
), pp.
129
132
.
18.
Kang
,
S. K.
,
Ehmann
,
K. F.
, and
Lin
,
C.
,
1996
, “
A CAD Approach to Helical Groove Machining
,”
Int. J. Mach. Tools Manuf.
,
36
(
1
), pp.
141
153
.
19.
Sakai
,
T.
, and
Maki
,
M.
,
1978
, “
A Study on Hourglass Worm Gearing With Developable Tooth Surfaces
,”
ASME J. Mech. Des.
,
100
(3), pp.
451
459
.
20.
Rababah
,
M.
,
Almagableh
,
A.
, and
Aljarrah
,
M.
,
2013
, “
Five-Axis Rake Face Grinding of End-Mills With Circular-Arc Generators
,”
Int. J. Interact. Des. Manuf.
,
11
(1), pp.
93
101
.
21.
Liu
,
G.
,
1999
, “
Study on the Basic Worm Gear Tooth Surface of General Equation of Worm Gear Hob
,”
Mech. Design Manuf. Eng.
,
28
(
6
), pp.
30
32
.
22.
Litvin
,
F. L.
, and
Seol
,
I. H.
,
1996
, “
Kinematic and Geometric Models of Gear Drives
,”
ASME J. Mech. Des.
,
118
(4), pp.
544
550
.
23.
Litvin
,
F. L.
, and
Fuentes
,
A.
,
2004
,
Gear Geometry and Applied Theory
,
Cambridge University Press
, Cambridge, UK.
24.
Berbinschi
,
S.
,
Teodor
,
V.
, and
Oancea
,
N.
,
2013
, “
3D Graphical Method for Profiling Gear Hob Tools
,”
Int. J. Adv. Manuf. Technol.
,
64
(
1–4
), pp.
291
304
.
25.
Lu
,
H.
,
Liu, Z.
, and
Wang, S.
,
2014
, “
Digitization Modeling and CNC Machining for Enveloping Surface Parts
,”
Int. J. Adv. Manuf. Technol.
,
73
(
1–4
), pp.
209
227
.
26.
Litvin
,
F. L.
,
1989
,
Theory of Gearing
,
NASA Reference Publication
, Washington DC.
27.
Dong
,
X.
,
1989
,
Gear Meshing Theory
,
China Machine Press
, Beijing, China.
28.
Wu
,
X.
,
2009
,
Gear Meshing Theory
,
2nd ed.
,
China Xi'an Jiao Tong University Press
, Xian, China.
29.
Jiang
,
Z.
,
Zhang
,
W.
, and
Li
,
Z.
,
2011
, “
Calculation of the Rake Angle of Micro Drill and Drilling Test
,”
J. Dalian Inst. Light Ind.
,
30
(2), pp. 145–147.
30.
Li
,
Y.
, and
Cao
,
Y.
,
2005
,
NC Machining Simulation System VERICUT
,
China Xi'an Jiao Tong University Press
, Xian, China.
31.
Yang
,
S.
, and
Tang
,
X.
,
2010
,
VERICUT NC Machining Simulation Technology
,
China Tsinghua University Press
, Beijing, China.
You do not currently have access to this content.