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Research Papers

Design and Manufacture of Spiral Bevel Gears With Reduced Transmission Errors

[+] Author and Article Information
Vilmos V. Simon

Department of Machine and Product Design, Faculty of Mechanical Engineering, Budapest University of Technology and Economics, Műegyetem rakpart 3, H-1111 Budapest, Hungarysimon.vilmos@gszi.bme.hu

J. Mech. Des 131(4), 041007 (Mar 23, 2009) (11 pages) doi:10.1115/1.3087540 History: Received September 17, 2008; Revised December 09, 2008; Published March 23, 2009

A method for the determination of the optimal polynomial functions for the conduction of machine-tool setting variations in pinion teeth finishing in order to reduce the transmission errors in spiral bevel gears is presented. Polynomial functions of order up to 5 are applied to conduct the variation in the cradle radial setting and in the cutting ratio in the process for pinion teeth generation. Two cases were investigated: In the first case, the coefficients of the polynomial functions are constant throughout the whole generation process of one pinion tooth-surface; in the second case, the coefficients are different for the generation of the pinion tooth-surface on the two sides of the initial contact point. The obtained results have shown that by the use of two different fifth-order polynomial functions for the variation in the cradle radial setting for the generation of the pinion tooth-surface on the two sides of the initial contact point, the maximum transmission error can be reduced by 81%. By the use of the optimal modified roll, this reduction is 61%. The obtained results have also shown that by the optimal variation in the cradle radial setting, the influence of misalignments inherent in the spiral bevel gear pair and of the transmitted torque on the increase in transmission errors can be considerably reduced.

Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 2

Machine-tool setting for pinion tooth-surface finishing

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Figure 3

Motion graphs for the case when the variation in the radial setting is conducted by the same polynomial functions up to third order throughout the whole generation process

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Figure 4

Motion graphs for the case when the variation in the radial setting is conducted by two different polynomial functions on the two sides of the initial contact point

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Figure 5

Variation in the cradle radial setting for the generation of one pinion tooth conducted by the two fifth-order polynomial functions

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Figure 6

Motion graphs for pinion tooth number N1=9 when the variation in the radial setting is conducted by two different polynomial functions on the two sides of the initial contact point

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Figure 7

Motion graphs for pinion tooth number N1=19 when the variation in the radial setting is conducted by two different polynomial functions on the two sides of the initial contact point

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Figure 8

Motion graphs for the case when the variation in the modified roll for pinion tooth generation is conducted by the same polynomial functions up to third order throughout the whole generation process

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Figure 9

Motion graphs for the case when the variation in the modified roll for pinion tooth flank generation is conducted by two different polynomial functions on the two sides of the initial contact point

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Figure 10

Variation in the modified roll for the generation of one pinion tooth flank conducted by two different fourth-order polynomial functions on the two sides of the initial contact point

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Figure 11

Influence of pinion offset on transmission errors

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Figure 12

Influence of displacements of the pinion along its axis on transmission errors

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Figure 13

Influence of displacements of the pinion along the gear axis on transmission errors

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Figure 14

Influence of the angular misalignment of the pinion axis in the horizontal plane on transmission errors

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Figure 15

Influence of the angular misalignment of the pinion axis in the vertical plane on transmission errors

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Figure 16

Influence of the transmitted torque on transmission errors

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Figure 17

Influence of the transmitted torque on motion graphs for the case when no modifications are introduced into the pinion tooth-surface

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Figure 18

Influence of the transmitted torque on motion graphs when the optimal cradle radial setting variation is applied for pinion teeth finishing

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Figure 19

Influence of the transmitted torque on motion graphs when optimal modified roll variation is applied for pinion teeth finishing

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Figure 20

Tooth contact pressure distribution when the pinion teeth are generated with the basic machine-tool setting

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Figure 21

Tooth contact pressure distribution when the pinion teeth are generated with optimal cradle radial setting variation

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Figure 22

Tooth contact pressure distribution when the pinion teeth are generated with optimal modified roll variation

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Figure 1

Relative position of the pinion and the gear in mesh

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