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A new worm grinding method of face gears based on the optimization of dressing wheel profile

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Abstract

Face gear drives have been well applied in high-speed and heavy load applications. Due to the strict requirements of machining accuracy and quality for those applications, face gears are mainly manufactured by worm grinding method, of which a dressing wheel is applied to generate the worm surface as its enveloped surface. Based on this manufacturing process, the profile of the dressing wheel should be well defined to make sure the final meshing performance of the face gear drives. In this work, we firstly investigate the mathematical model of dressing wheel with a general profile modification. The worm surface is the envelope to the family of dressing wheel surfaces. Specially, the result is obtained as a closed-form. Subsequently, the face gear tooth surface is calculated as the envelope surface of the worm surface. With the tooth surface models of both face gear and pinion, the tooth contact analysis (TCA) can be computed. According to this method, different parameters for the profile modification of the dressing wheel are compared to improve the working performances by finding the minimal transmission error without edge contacts. The proposed method is validated with simulations.

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Abbreviations

γ0 :

Initial installation angle of dressing wheel (Fig. 1)

φg :

An instantaneous position angle of the dressing wheel relative to the worm (Fig. 1)

φw :

Angle of rotation of the worm (Figs. 1 and 6)

E g :

Shortest distance between two axes of the dressing wheel and the shaper (Figs. 1 and 2)

E ws :

Shortest distance between two axes of the worm and the shaper (Figs. 1 and 6)

θ:

Angle of rotation of the dressing wheel (Fig. 2)

s 0 :

The tooth width of the standard rack cutter (Fig. 3)

l d :

The length of oro0 (Fig. 3)

α0 :

Pressure angle of the standard rack cutter (Fig. 3)

f d :

The offset distance between p0 and o0 (Fig. 3)

u r :

Rack cutter profile parameters (Fig. 3)

a r :

Parabolic coefficient of the rack cutter profile (Fig. 3)

p 0 :

The vertex of the parabola (Fig. 3)

p r :

One point on the rack cutter profile (Fig. 3)

N g :

Normal vector of a point on the surface of the dressing wheel (Fig. 4)

T g :

Tangent vector of a point on the surface of the dressing wheel (Fig. 4)

T gx :

The component of tg along the direction of xg (Fig. 4)

T gz :

The component of tg along the direction of zg (Fig. 4)

α:

The angle between tgx and tgz (Fig. 4)

p :

One point on the dressing wheel (Fig. 4)

p h :

The intersection of ng and zg (Fig. 4)

h :

The distance between the points og and ph (Fig. 4)

ρ:

The distance between the points p and ph (Fig. 4)

φs :

Angle of rotation of the shaper (Fig. 6)

φ2 :

Angle of rotation of the face gear (Fig. 6)

E 2s :

The distance between the central points of face gear and shaper (Fig. 6)

λw :

Crossing angle between axes of shaper and worm (Fig. 6)

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Authors and Affiliations

  1. College of Mechanical and Electrical Engineering, Central South University, 410083, Changsha, China

    Xianlin Shi, Yuansheng Zhou, Wuji Zhang & Jinyuan Tang

  2. State Key Laboratory of High Performance Complex Manufacturing, Central South University, 410083, Changsha, Hunan, China

    Xianlin Shi, Yuansheng Zhou, Wuji Zhang & Jinyuan Tang

Authors
  1. Xianlin Shi
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  2. Yuansheng Zhou
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  3. Wuji Zhang
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  4. Jinyuan Tang
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Correspondence to Yuansheng Zhou.

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Shi, X., Zhou, Y., Zhang, W. et al. A new worm grinding method of face gears based on the optimization of dressing wheel profile. Forsch Ingenieurwes 83, 751–757 (2019). https://doi.org/10.1007/s10010-019-00353-6

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  • DOI: https://doi.org/10.1007/s10010-019-00353-6

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