Curvature interference characteristic of conical worm gear

Meng, Qiaoling; Zhao, Yaping; Yang, Zaiyou

doi:10.1007/s10010-019-00372-3

Cited by 10 publications

(7 citation statements)

References 6 publications

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“…In terms of Equation (10), with the assistance of the circle vector function and the sphere vector function [3], the firstorder partial derivatives of the tooth surface equation r…”

Section: Normal Vector Of the Face Worm Gear Tooth Surfacementioning

confidence: 99%

“…By combining Equation (20) and the face worm gear tooth surface equation in Equation (10), the equation of the singular points trajectory on the face worm gear tooth surface can be expressed as…”

Section: Simplification Of the Coefficient Expressionsmentioning

confidence: 99%

“…Then used this technique to solve the curvature interference problem of the conical worm drive. Meng and Zhao [10] used the same technique to figure out the influences of design parameters on the curvature interference limit line of the conical worm gear. So far, few numerical results can be obtained for the curvature interference problem research of the worm drive, due to the complexity of building and solving the equation of the curvature interference limit line.…”

Section: Introductionmentioning

confidence: 99%

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Curvature interference characteristic analysis of offset involute cylindrical worm drive

Yu,

Zhao,

et al. 2023

Math Methods in App Sciences

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The theory of calculating the curvature interference limit line of the offset involute cylindrical worm drive based on the singular point condition on the enveloping surface is established. The tooth surface equations and the meshing function of the worm drive are derived. Based on the singular point condition that the normal vector of the enveloping surface is zero, the equation of the curvature interference limit line is obtained. By employing the resultant elimination method and the geometric construction, the existence of the solutions of the curvature interference limit line is determined, and the reasonable initial values for the iteration program are afforded. The numerical outcomes show that there is one meaningful curvature interference limit line on each flank of single tooth of the worm gear, which usually does not enter the worm gear tooth surface. Both flanks of the worm gear are all settled in the side of the limit line, the curvature interference does not happen on the worm gear tooth surface. The undercutting of the cutting engagement process generally does not happen. The results also reveal that the curvature interference limit line is closer to the addendum and heel of the face worm gear on the i flank, which has the greatest potential venture inflict the undercutting.

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“…In terms of Equation (10), with the assistance of the circle vector function and the sphere vector function [3], the firstorder partial derivatives of the tooth surface equation r…”

Section: Normal Vector Of the Face Worm Gear Tooth Surfacementioning

confidence: 99%

Section: Simplification Of the Coefficient Expressionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Curvature interference characteristic analysis of offset involute cylindrical worm drive

Yu,

Zhao,

et al. 2023

Math Methods in App Sciences

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“…Chen et al [22] obtained the undercutting line for a novel worm drive consisting of a planar internal gear and a crown worm, and drew it on the worm tooth surface. Zhao et al [23,24] studied the undercutting problems in the conical surface enveloping conical worm drive and supplied detailed numerical results of limit points. While constructing a three-dimensional model for the planar worm wheel, Deng & Feng [25] encountered an interference problem, and this interference was avoided by modifying the tooth profile of the gear.…”

Section: Introductionmentioning

confidence: 99%

Direct method to determine singular point of enveloped surface and its application to worm wheel tooth surface

Cui,

Zhao,

Meng

et al. 2024

Proc. R. Soc. A.

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A novel methodology for determining the singular point of an enveloped surface is put forward. Unlike some existing methods, the presented method starts directly from the equation of the enveloped surface instead of that of the generating surface, and it is thus called a direct method. The calculation for the normal vector of the enveloped surface is well simplified with the help of the moving frame approach, which makes the presented method feasible. The singularity condition equation is extracted by using the theory of linear algebra. For singular points with different properties, proper solving techniques are established, including resultant elimination and simple elimination. Applying the developed method, the undercutting characteristics of the Archimedes worm wheel are investigated from the perspective of spatial meshing. The numerical results demonstrate that the worm wheel generally has one undercutting limit line, whose trend is along the tooth width of the wheel. Locating on one side of the tooth surface and near the tooth root is a dangerous part of the worm wheel undercutting. The proposed method is beneficial for the development of gear meshing science.

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“…Analogously, using the vector equation that the normal vector of the enveloped surface is equal to zero, a similar singularity condition to that in Litvin et al 6 is obtained in Wu and Luo 3 and Litvin et al 12 Dong 4 derived the singularity condition for the enveloped surface in scalar form by associating the equation that the tangent vector of the enveloped surface is equal to zero with the full differentiation of the meshing equation and employing Euler and Bertrand formulas, 1 and then he 13 applied this singularity condition to the study of the curvature interference theory for different types of the toroidal worm pairs. Using Dong's singularity condition, Zhao and Meng [14][15][16] investigated the curvature interference theory of conical surface enveloping the conical worm pair and the ZC1 worm pair. Sohn and Park 17,18 studied the geometric interference problem of mismatched cylindrical worm pairs using the separation topology method.…”

Section: Introductionmentioning

confidence: 99%

New method for determining singularities on enveloped surface and its application to study curvature interference theory of involute worm drive

Zhao

Tian-Feng

et al. 2021

Advances in Mechanical Engineering

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In this paper, a more computationally convenient singularity condition of the enveloped surface is proposed using the theory of linear algebra. Its preconditions are only the tangential vector of the enveloping surface, the relative velocity vector, and the total differential of the meshing function. It avoids calculating the curvature parameters of the enveloping surface. It is proved that the singularity conditions of enveloped surface from different references are equivalent to each other and the relational equations among them are obtained. The curvature interference theory for the involute worm drive is established using the proposed singularity condition. The equation for the singularity trajectory is obtained. The calculation method for the singularity trajectory is proposed and its numerical result is obtained. The influence of the design parameters on the singularity trajectory is studied using the proposed curvature interference theory. The study results show that the risk of curvature interference is high when the transmission ratio is too small, especially in the case of the single-threaded worm and large modulus. The proposed singularity condition can also be applied to study the curvature interference mechanism in other types of the worm drive and to study the undercutting mechanism when machining the worm drive.

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Curvature interference characteristic of conical worm gear

Cited by 10 publications

References 6 publications

Curvature interference characteristic analysis of offset involute cylindrical worm drive

Curvature interference characteristic analysis of offset involute cylindrical worm drive

Direct method to determine singular point of enveloped surface and its application to worm wheel tooth surface

New method for determining singularities on enveloped surface and its application to study curvature interference theory of involute worm drive

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