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<p>The equivalent curvature radius and entrainment velocity are essential parameters for lubricating modified face gear pairs and require further investigation. An analytical model for the equivalent curvature radius and entrainment velocity of an orthogonal face gear pair with tooth profile and axial modifications on the spur gear is proposed in this paper. Quadratic parabolas are used to modify the tooth tip and root of the spur gear while retaining the involute profile in the middle; the axial modification also employs quadratic parabolas. Using the coordinate system of the shaper cutter, the tooth surface equations of the modified orthogonal face gear pair are established. Applying the theory of differential geometry, the equivalent curvature radius of point contact is derived. Considering the relative motion of the gear pair, the entrainment velocity is obtained. The equivalent curvature radius and entrainment velocity with and without modifications are compared, and the effects of modification parameters on them are analyzed. The results indicate that in the modified region, the equivalent curvature radius is smaller than that of the unmodified tooth surface, exhibiting a gradual decrease with a discontinuity at the junction point; here, the entrainment velocity <i>v</i><sub>x</sub> is discontinuous at the connection, while <i>v</i><sub>y</sub> decreases gradually. Additionally, the optimal modification parameters ensuring continuity of both the equivalent curvature radius and entrainment velocity are determined as ∆<sub>1</sub> = 0.06&#xa0;mm, <i>L</i><sub>1</sub> = 2.44&#xa0;mm, and <i>a</i><sub>m</sub> = 0.0003.</p>

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Analytical modeling and analysis of the equivalent curvature radius and entrainment velocity in orthogonal face gear drives with modified spur gears

  • 期刊论文

  • 发表日期：

    2025年6月6日

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  • Wenguang Zhou,
  • Hongmei Wu,
  • Fengxia Lu,
  • Rupeng Zhu,
  • Wenzheng Liu,
  • Jingjing Wang

摘要

The equivalent curvature radius and entrainment velocity are essential parameters for lubricating modified face gear pairs and require further investigation. An analytical model for the equivalent curvature radius and entrainment velocity of an orthogonal face gear pair with tooth profile and axial modifications on the spur gear is proposed in this paper. Quadratic parabolas are used to modify the tooth tip and root of the spur gear while retaining the involute profile in the middle; the axial modification also employs quadratic parabolas. Using the coordinate system of the shaper cutter, the tooth surface equations of the modified orthogonal face gear pair are established. Applying the theory of differential geometry, the equivalent curvature radius of point contact is derived. Considering the relative motion of the gear pair, the entrainment velocity is obtained. The equivalent curvature radius and entrainment velocity with and without modifications are compared, and the effects of modification parameters on them are analyzed. The results indicate that in the modified region, the equivalent curvature radius is smaller than that of the unmodified tooth surface, exhibiting a gradual decrease with a discontinuity at the junction point; here, the entrainment velocity vx is discontinuous at the connection, while vy decreases gradually. Additionally, the optimal modification parameters ensuring continuity of both the equivalent curvature radius and entrainment velocity are determined as ∆1 = 0.06 mm, L1 = 2.44 mm, and am = 0.0003.