Skip to main content
SpringerLink
Log in

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

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Abbreviations

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

d m1 :

Mean diameter of worm

d f1 :

Tooth bottom diameter of worm

R m :

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

y g :

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

z g :

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

X g :

Position vector of curved surface in Og-xgygzg

N g :

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

θ 0, θ 0’:

Initial value of θ and θ ’

X r :

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

N r :

Unit surface normal of Xr

E :

Offset distance between worm and worm wheel

w :

Relative velocity between worm and worm wheel in O-xyz

X w :

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

N w :

Unit surface normal of Xw

Q :

Contact point between end mill and worm tooth surface

x r :

x component of Xr

n x :

x component of Nr

n y :

y component of Nr

n z :

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

X cr :

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

X cl :

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

References

  1. Townsend DP (1991) Dudley’s gear handbook, The design, manufacture, and application of gears, 2nd edn. McGraw-Hill, New York, pp 2.40–2.46

    Google Scholar 

  2. Davis JR (2005) Gear materials, properties, and manufacture. ASM International Technical Books Committee, USA, pp 8–9

    Google Scholar 

  3. Radzeevich SP (2012) Handbook of practical gear design and manufacture, 2nd edn. CRC Press, Taylor & Francis Group, Boca Raton, pp 34–39

  4. South DW, Ewert RH (1995) Encyclopedic dictionary of gears and gearing. McGraw-Hill, New York, pp 345–349

    Google Scholar 

  5. Simon V (2005) Computer-aided loaded tooth contact analysis in cylindrical worm gears. ASME J Mech Des 127:973–981

    Article  Google Scholar 

  6. Shreehah T, Abdullah R (2006) Modification of geometry and technology of cylindrical worms. Mach Sci Technol 10:539–547

    Article  Google Scholar 

  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 42:940–959

    Article  Google Scholar 

  8. Sohn J, Park N (2017) Modified worm gear hobbing for symmetric longitudinal crowning in high lead cylindrical worm gear drives. Mech Mach Theory 117:132–147

    Article  Google Scholar 

  9. Dudas I (2000) The theory & practice of worm gear drives. Penton Press, London, pp 16–26

  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 1:78–86

    Article  Google Scholar 

  11. Moriwaki T (2008) Multi-functional machine tool. CIRP Ann 57:736–749

    Article  Google Scholar 

  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 135:024502

    Article  Google Scholar 

  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 2014:257581

    Article  Google Scholar 

  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, 1:337-348

  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 135:034504

    Article  Google Scholar 

  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 23:1149–1156

    Article  Google Scholar 

  17. Sakai T (1955) A study on the tooth profile of hypoid gears. Trans JSME 21:164–170 (in Japanese)

    Article  Google Scholar 

  18. Litvin FL, Fuentes A (2004) Gear geometry and applied theory, 2nd edn. Cambridge University Press, UK, pp 98–101

    Book  Google Scholar 

  19. Litvin FL (1989) Theory of gearing, NASA reference publication, Technical report 88-C-035, pp 385-389

  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 132:041004

    Article  Google Scholar 

  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 92:213–229

    Article  Google Scholar 

  22. Okuma Corporation (2017) Intelligent multitasking machines multus bseries. Aichi, pp 1-26

Download references

Author information

Authors and Affiliations

  1. Faculty of Engineering, Niigata University, 8050 Ikarashi 2-nocho, Nishi-ku, Niigata, 950-2181, Japan

    Kazumasa Kawasaki

  2. Iwasa Tech Co., Ltd., Takase-cho 64-2, Funabashi, 273-0014, Japan

    Isamu Tsuji

Authors
  1. Kazumasa Kawasaki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Isamu Tsuji
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kazumasa Kawasaki.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kawasaki, K., Tsuji, I. Machining method of large-sized cylindrical worm gears with Niemann profiles using CNC machining center. Int J Adv Manuf Technol 104, 3717–3729 (2019). https://doi.org/10.1007/s00170-019-04076-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-019-04076-4

Keywords

Search

Navigation