Advertisement

Machining method of large-sized cylindrical worm gears with Niemann profiles using CNC machining center

  • Kazumasa KawasakiEmail author
  • Isamu Tsuji
ORIGINAL ARTICLE
  • 35 Downloads

Abstract

In this paper, a machining method of large-sized cylindrical worm gears with Niemann profiles using a computer numerical control (CNC) machining center is proposed. For this study, the tooth contact pattern and transmission errors of large-sized worm gear pair with Niemann profiles are analyzed before machining of the worm and worm wheel. Next, the machining conditions of worm are determined calculating each offset distance between the worm axis and the center axis of the end mill, and then the worm is machined by swarf cutting that means machining by the side surface of the end mill. The tooth profiles of worm wheel are modeled using a 3D computer-aided design (3D-CAD) system based on the analyzed results and the worm wheel is machined by swarf cutting through a computer-aided manufacturing (CAM) process. Afterwards, the axial tooth profile of the machined worm, and the tooth surface deviations and surface roughness of the machined worm wheel are measured. Moreover, the experimental tooth contact pattern is compared with analyzed one. As a result, the validity of the proposed machining method of the large-sized worm gears with Niemann profiles using a CNC machining center was confirmed.

Keywords

Machining center Niemann profile Offset machining Swarf cutting Tooth contact analysis Worm gear Worm wheel 

Nomenclature

P

Arbitrary point set on convex circular arc of grinding wheel

u, u

Variable parameter representing position on curved line of grinding wheel corresponding to right and left tooth surfaces

dm1

Mean diameter of worm

df1

Tooth bottom diameter of worm

Rm

Basic radius of grinding wheel

ρ

Radius of curvature of circular arc of grinding wheel

α

Pressure angle

V

V gage for dressing

H

H gage for dressing

yg

y component of position vector of point P in cross section xg = 0 in Og-xgygzg

zg

z component of position vector of point P in cross section xg = 0 in Og-xgygzg

ψ, ψ

Rotation angle of curved line about zg axis corresponding to right and left tooth surfaces

Xg

Position vector of curved surface in Og-xgygzg

Ng

Unit surface normal of Xg

e

Offset distance between grinding wheel and worm

γ

Incline angle of axis of worm wheel

X

Position vector of curved surface in O-xyz

M

4 × 4 matrix of the rotational and translational coordinate transformation from Og-xgygzg to O-xyz

W

Relative velocity between grinding wheel and worm in O-xyz

N

Unit surface normal of X

h, h

Screw parameter of worm corresponding to right and left tooth surfaces

ω

Relative angular velocity

k

Unit vector toward z axis

A, A

x component of coordinates of point P corresponding to right and left tooth surfaces

B, B

y component of coordinates of point P corresponding to right and left tooth surfaces

C, C

z component of coordinates of point P corresponding to right and left tooth surfaces

θ, θ

Rotation angle of screw motion about worm axis corresponding to right and left tooth surfaces

θ0, θ0

Initial value of θ and θ

Xr

Position vector of right tooth surface of worm in O-xyz

Nr

Unit surface normal of Xr

E

Offset distance between worm and worm wheel

w

Relative velocity between worm and worm wheel in O-xyz

Xw

Position vector of left tooth surface of worm wheel in O-xyz

Nw

Unit surface normal of Xw

Q

Contact point between end mill and worm tooth surface

xr

x component of Xr

nx

x component of Nr

ny

y component of Nr

nz

z component of Nr

T

Offset distance between worm and end mill axes

d

Diameter of end mill

S

Point of rotation center of edge of end mill

Xcr

Position vector representing coordinates of point E of right tooth surface in O-xyz

Xcl

Position vector representing coordinates of point E of left tooth surface in O-xyz

Notes

References

  1. 1.
    Townsend DP (1991) Dudley’s gear handbook, The design, manufacture, and application of gears, 2nd edn. McGraw-Hill, New York, pp 2.40–2.46Google Scholar
  2. 2.
    Davis JR (2005) Gear materials, properties, and manufacture. ASM International Technical Books Committee, USA, pp 8–9Google Scholar
  3. 3.
    Radzeevich SP (2012) Handbook of practical gear design and manufacture, 2nd edn. CRC Press, Taylor & Francis Group, Boca Raton, pp 34–39Google Scholar
  4. 4.
    South DW, Ewert RH (1995) Encyclopedic dictionary of gears and gearing. McGraw-Hill, New York, pp 345–349Google Scholar
  5. 5.
    Simon V (2005) Computer-aided loaded tooth contact analysis in cylindrical worm gears. ASME J Mech Des 127:973–981CrossRefGoogle Scholar
  6. 6.
    Shreehah T, Abdullah R (2006) Modification of geometry and technology of cylindrical worms. Mach Sci Technol 10:539–547CrossRefGoogle Scholar
  7. 7.
    Litvin FL, Gonzalez-Perez I, Yukishima K, Fuentes A, Hayasaka K (2007) Design, simulation of meshing, and contact stresses for an improved worm gear drive. Mech Mach Theory 42:940–959CrossRefGoogle Scholar
  8. 8.
    Sohn J, Park N (2017) Modified worm gear hobbing for symmetric longitudinal crowning in high lead cylindrical worm gear drives. Mech Mach Theory 117:132–147CrossRefGoogle Scholar
  9. 9.
    Dudas I (2000) The theory & practice of worm gear drives. Penton Press, London, pp 16–26Google Scholar
  10. 10.
    Nakaminami M, Tokuma T, Moriwaki T, Nakamoto K (2007) Optimal structure design methodology for compound multiaxis machine tools–I (Analysis of requirements and specifications). Int J Autom Technol 1:78–86CrossRefGoogle Scholar
  11. 11.
    Moriwaki T (2008) Multi-functional machine tool. CIRP Ann 57:736–749CrossRefGoogle Scholar
  12. 12.
    Alves JT, Guingand M, Vaujany J (2013) Designing and manufacturing spiral bevel gears using 5-axis computer numerical control (cnc) milling machines. ASME J Mech Des 135:024502CrossRefGoogle Scholar
  13. 13.
    Lei B, Cheng G, Lowe H, Wang X (2014) Remanufacturing the pinion: an application of a new design method for spiral bevel gears. Adv Mech Eng 2014:257581CrossRefGoogle Scholar
  14. 14.
    Kawasaki K, Tsuji I, Abe Y, Gunbara H (2010) Manufacturing method of large-sized spiral bevel gears in cyclo-palloid system using multi-axis control and multi-tasking machine tool. Proc. of International Conference on Gears, Garching, Germany, 1:337-348Google Scholar
  15. 15.
    Tsuji I, Kawasaki K, Gunbara H, Houjoh H, Matsumura S (2013) Tooth contact analysis and manufacture on multitasking machine of large-sized straight bevel gears with equi-depth teeth. ASME J Mech Des 135:034504CrossRefGoogle Scholar
  16. 16.
    Kawasaki K, Tsuji I, Gunbara H (2016) Manufacturing method of double-helical gears using CNC machining center. Proc Inst Mech Eng C J Mech Eng Sci 23:1149–1156CrossRefGoogle Scholar
  17. 17.
    Sakai T (1955) A study on the tooth profile of hypoid gears. Trans JSME 21:164–170 (in Japanese)CrossRefGoogle Scholar
  18. 18.
    Litvin FL, Fuentes A (2004) Gear geometry and applied theory, 2nd edn. Cambridge University Press, UK, pp 98–101CrossRefGoogle Scholar
  19. 19.
    Litvin FL (1989) Theory of gearing, NASA reference publication, Technical report 88-C-035, pp 385-389Google Scholar
  20. 20.
    Kawasaki K, Tsuji I (2010) Analytical and experimental tooth contact pattern of large-sized spiral bevel gears in cyclo-palloid system. ASME J Mech Des 132:041004CrossRefGoogle Scholar
  21. 21.
    Kawasaki K, Tsuji I, Gunbara H, Houjoh H (2015) Method for remanufacturing large-sized skew bevel gears using CNC machining center. Mech Mach Theory 92:213–229CrossRefGoogle Scholar
  22. 22.
    Okuma Corporation (2017) Intelligent multitasking machines multus bseries. Aichi, pp 1-26Google Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of EngineeringNiigata UniversityNiigataJapan
  2. 2.Iwasa Tech Co., Ltd.FunabashiJapan

Personalised recommendations