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Upper bound analysis for forging of trochoidal gears

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Forging of trochoidal gears has been investigated by means of upper-bound analysis. A kinematically admissible velocity field for forging of a trochoidal gear was proposed. A neutral surface has been used to represent the inward flow of material during forging operation by using a hollow billet with a flat punch. By using the suggested kinematically admissible velocity fields, the applied forces were successfully calculated and compared with experimental inspections. The experimental set-up was installed in a 200-ton hydraulic press for forging. The billets of A1 2218 aluminum alloys were slightly coated with phosphate. It was found that the theoretical solutions were useful to predict the forging load forforging of trochoidal gears.

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x, θ, z :

Cylindrical coordinate system


Fillet radius, tooth radius [mm]

r n :

Neutral surface radius [mm]

r r :

Root circle radius [mm]


Ram speed [mm/s]

\(\mathop {\overline {\varepsilon _i } }\limits^. \) :

Effective strain rate fori zone


Flow stress

Ur, Uθ, Uz :

Velocity component for each direction


Number of teeth

r p :

Pitch circle radius [mm]


Height of workpiece[mm]

α :

Half pitch angle[rad]

V :

Velocity discontinuity


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Correspondence to Jongung-Choi or Hae-Yong Cho or Chang-Yong Jo.

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Jongung-Choi, Cho, H. & Jo, C. Upper bound analysis for forging of trochoidal gears. KSME International Journal 13, 332–338 (1999).

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  • Deformation Zone
  • Energy Dissipation Rate
  • Spur Gear
  • Tooth Profile
  • Helical Gear