Improvements in the micro tooth surface topography of hobbed spur and helical gears

  • Vilmos V. Simon
Technical Paper


A new model of the gear hobbing process is presented in this paper to determine the micro tooth surface topography in spur and helical gears. The model is based on the generation of tooth surfaces by successive cuts of the finite number of hob teeth, as they come into interaction with the gear tooth. For every relative position of the hob and the gear, an analysis is carried out to find the active cutting edge points which generate the gear tooth surface. Repeating this procedure for all the selected gear tooth surface points, the micro topography of the gear tooth surface is determined. Therefore, the developed method determines the deviations of the manufactured tooth surface from the theoretical tooth surface of spur and helical gears. The method is applied to improve the micro tooth surface topography of spur and helical gears, namely to reduce the deviations of the hobbed tooth surface. Spur and helical gear examples are used to demonstrate the effectiveness of the method.


Spur and helical gears Hobbing Tooth surface topography Improvements 

List of symbols


Deviation of the hobbed tooth surface


Ratio of the angular velocities of the hob and the gear


Normal module (mm)


Number of hob cutting edges


Gear tooth number


Hob tooth number


Hob thread number


Roughness height (μm)

\(R_{ \hbox{max} }\)

Maximum roughness height (μm)

\(r_{\text{f}}^{{\left( {{\text{c}} . {\text{e}} .} \right)}}\)

Cutting edge variable (mm)

\(r_{\text{o}}\), \(r_{\text{og}}\), \(r_{\text{oh}}\)

Pitch cylinder radii of the involute helical surface, gear, and hob, respectively (mm)

\(r_{\text{b}}\), \(r_{\text{bg}}\), \(r_{\text{bh}}\)

Base cylinder radii of the involute helical surface, gear, and hob, respectively (mm)


Axial feed of the gear per gear revolution (mm/rev)

u, \(u_{\text{g}}\), \(u_{\text{h}}\)

Surface variables (mm)

\(\alpha_{ 0}\)

Pressure angle on the pitch cylinder (°)


Pressure angle in an arbitrary chosen tooth surface point (°)


Normal pressure angle (°)


Transverse pressure angle (°)

\(\beta_{ 0}\)

Helix angle of the helical gear on the pitch cylinder (°)


Helix angle of the helical gear on the base cylinder (°)

\(\omega_{0}\), \(\omega_{{0{\text{h}}}}\)

Lead angles on the pitch cylinder (°)

\(\omega_{\text{b}}\), \(\omega_{\text{bh}}\)

Lead angles on the base cylinder (°)

\(\omega^{{\left( {\text{g}} \right)}}\), \(\omega^{{\left( {\text{h}} \right)}}\)

Angular velocities of the gear and the hob, respectively (sec−1)

\(\theta\), \(\theta_{\text{h}}\)

Surface variables (°)

\(\theta_{i}^{{\left( {{\text{c}} . {\text{e}} .} \right)}}\)

Parameter of the cutting edge (°)


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Department for Machine and Product Design, Faculty of Mechanical EngineeringBudapest University of Technology and EconomicsBudapestHungary

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