A Thermomechanical Modeling and Experimental Validation of the Gear Finish Hobbing Process

  • Naoual Sabkhi
  • Abdelhadi Moufki
  • Mohammed NouariEmail author
  • Armansyah Ginting
Regular Paper


The current research work aims at developing an analytical modelling of the gear finish hobbing process when the uncut chip thickness may be very small. Numerical models and particularly finite element simulations of this complex material removal process are often limited to one tooth because of the high required computational time. To analyze the performance characteristics of this process, a predictive approach for finish gear hobbing based on an analytical model of orthogonal cutting operation is proposed. To reduce the computational time, a new calculation strategy has been developed. This allows to examine the local parameters which change significantly for each tooth. During the finishing hobbing process of large gears (6 m < diameter < 16 m), the industrial conditions require low cutting speeds (less than 1 m/s) with lubrication. Therefore, in order to consider the effect of lubrication, cutting speed and uncut thickness on the friction coefficient, an appropriate friction law was identified from orthogonal cutting tests. The cutting model has been experimentally validated for different cutting conditions. Finally, the effects of hobbing process on the cutting forces and the tool-chip contact parameters (contact length, pressure, frictional stress and temperature) have been investigated and deeply analyzed using the developed model. The distributions of these local parameters, at each tooth rake face, may be used as a process signature for the resulting condition of the machined surface and subsurface layers.


Gear finish hobbing CAD model Analytical approach Cutting forces Temperature 

List of Symbols


Depth of cut


Axial feed


Setting angle of the hob relative to the workgear


Gear width


Helix angle of the hob


Axial pitch of the hob


Outside diameter of the hob


Outside diameter of the workgear

\(\text{X}_{\text{i}} ,\;\text{Y}_{\text{i}} ,\;Z_{\text{i}}\)

Coordinate system associated to the workgear (i = 1, 2) and to the hob (i = 0, 4)


Cutting speed


Chip velocity


Uncut chip thickness


Length of a cutting edge element


Normal rake angle

\(K_{cv}\), \(K_{cf}\)

Cutting force coefficients

\(K_{ev}\), \(K_{ef}\)

Edge force coefficients

\(dF_{v}\), \(dF_{f}\)

Elementary cutting and feed forces


Total force exerted on a tooth


Angular position of a given tooth


Primary shear zone thickness


Normal shear angle

\(\bar{\mu }\)

Friction coefficient


Mean friction angle


Shear stress


Shear strain


Total shear strain

\(\dot{\gamma }\)

Shear strain rate


Portion of heat source (primary shear zone) going to the workpiece


Tool-chip contact length


Mean pressure along the tool-chip contact




Workpiece temperature


Temperature at the exit of the primary shear zone


Average temperature at the tool-chip interface


Reference temperature


Melting temperature


Hardening exponent


Thermal softening coefficient


Strain rate sensitivity

\(A,\,B,\,\dot{\gamma }_{0}\)

Constant material characteristics (Johnson–Cook law)

\(\rho ,\;c,\,k\)

Material density, heat capacity and heat conductivity coefficient


Taylor-Quinney coefficient


Effusivity ratio



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Copyright information

© Korean Society for Precision Engineering 2019

Authors and Affiliations

  1. 1.Altran France – Région EstBelfortFrance
  2. 2.Laboratoire d’Etude des Microstructures et de Mécanique des Matériaux, LEM3Université de LorraineMetz CedexFrance
  3. 3.Laboratory of Machining Processes, Department of Mechanical Engineering, Faculty of EngineeringUniversitas Sumatera UtaraMedanIndonesia

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