Spiral involutes and their application in gear transmission

Liu, L; Huang, Yin

doi:10.1177/0954406211408782

Cited by 4 publications

(5 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…According to the design idea of the tooth surface of pure rolling variable transmission ratio, the mathematical model of the tooth surface of herringbone involute helical gear is established. 28,29 Based on the meshing principle of variable transmission, the tooth face of rack variable transmission ratio with herringbone involute helical gear is established. In coordinate system s 1 , the equation of the left flank of the herringbone involute helical gear is…”

Section: Rack-and-pinion Model With Pure Rolling Variable Transmissio...mentioning

confidence: 99%

Design method of rack-and-pinion pair with pure rolling variable transmission ratio

Ziru,

Shuai,

Fuhui

et al. 2024

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

Rack-and-pinion pair with variable transmission ratio can achieve the unity of vehicle steering portability and sensitivity, and effectively reduce vehicle steering energy consumption. Therefore, they have gradually become the standard core components of steering system. However, the gear surface of rack-and-pinion pair with variable transmission ratio is seriously worn under long-term service, which leads to the degradation of performance and cannot achieve the theoretically variable transmission ratio. To solve these problems, a new configuration of rack-and-pinion pair for commercial vehicle with herringbone pure rolling variable transmission ratio is proposed in this paper. The tooth surface mathematical model of the fully-conjugate variable transmission ratio is established based on the variable speed envelope principle, and the formula for calculating pure rolling point of tooth surface with variable transmission ratio is derived. The tooth point deviation equation of fully-conjugate variable transmission ratio is proposed, and the method of constructing pure rolling variable transmission ratio tooth surface is formed. The finite element analysis shows that the design of the pure rolling rack-and-pinion pair with variable transmission ratio has good tooth surface quality without the phenomenon of contact spot intermittent and edge contact during the meshing process, and the contact ellipse center of the tooth surface is located at the theoretical pure rolling point of the tooth surface. The measured transmission ratio curve of the samples is in good agreement with the theoretical variable transmission ratio curve, and the transmission ratio error is within a reasonable range. The contact strips of tooth surface impression test are consistent with those of finite element analysis, which indicates that the designed rack-and-pinion pair with variable transmission ratio has the characteristics of pure rolling and point contact. The tooth surface wear test shows that the wear of pure rolling gear surface with variable transmission ratio is obviously less than that of traditional gear surface with variable transmission ratio. The above tests and simulation indicate the correctness of the design method.

show abstract

Section: Rack-and-pinion Model With Pure Rolling Variable Transmissio...mentioning

confidence: 99%

Design method of rack-and-pinion pair with pure rolling variable transmission ratio

Ziru,

Shuai,

Fuhui

et al. 2024

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

show abstract

“…Besides, invariables θ1 and θ2 indicate that the contact path is corresponding to the normal profiles with inclined angle θ1 and θ2 on the rack cutter. In this case, the gear pair works on meshing of engaged spatial curves called spiral involutes, 25 which still have the characteristics of involutes, so the transmission error is zero. The torus involute gear set can be regarded as insensitive to misalignment assembly errors.…”

Section: Tooth Contact Analysis Of Torus Involute Gearsmentioning

confidence: 99%

Geometry and contact characteristics of torus involute gears

Liu

Tan

Fang

2016

Proceedings of the Institution of Mechanical Engineers, Part E:

View full text Add to dashboard Cite

Aimed at overcoming high sensitivity to machining or mounting error of line-contact conjugate surfaces, a novel torus involute gear drive is proposed which can compensate large axial misalignments and possess good meshing characteristics without lead correction. The torus involute gear is essentially a special spur gear with continuous shifting in the second order. Based on the processing principle of the torus involute gears, their mathematical models are established according to the corresponding imaginary rack cutter. In order to provide the approach to choose proper designing parameters, geometry characteristics of the torus involute gear are investigated: condition equations of tooth undercutting for a convex torus involute gear and tooth pointing for a concave torus involute gear are formulated utilizing the developed mathematical models, and the approach to checking tooth flank interference is provided. Contact characteristics of the gear set is studied through tooth contact analysis and finite element analysis. The simulated results produce useful information about tooth contact pattern, stress distribution, and transmission errors of the gear set.

show abstract

“…From differential geometry, the term r 1ð1Þ 2 in equation (17), represents the tangent direction of À 1 . Therefore, after equations (16) and (17) are synthesized, it can be concluded that the tangent directions of À 1 and À 2 are not the same at the instantaneous contact point. However, for the spiral bevel gears of continuous pure rolling contact, the relative slide does not exist, which means…”

Section: The Derivatives Of ' and Rmentioning

confidence: 99%

“…16 proposed a new gear generating method for the spiral bevel gear with spherical involutes tooth curves. Liu and Huang 17 proposed so-called spiral involute gears. Wang and Zhang 18 introduced the tensor analysis method to research the curvature relationships of conjugate surfaces and applied it for the face-milled spiral bevel gears of local bearing contact.…”

Section: Introductionmentioning

confidence: 99%

The geometric principles of general spiral bevel gears of local bearing contact from spatial conjugate curves

Tan

Chen

Peng

et al. 2015

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

This paper aims at obtaining the mathematical model of the general spiral bevel gears of local bearing contact from spatial conjugate curve theory. Differential geometry and gearing kinematics are introduced to derive this model. Meshingcorrectly conditions are set in the theoretical derivation process. The final model is represented in the form of equations and inequalities. According to the arguments in this paper, a process of designing the tooth surface of spiral bevel gears of local bearing is proposed. Based on this process, the numerical example of a pair of these gears with specific profiles is represented by applying the finite element analysis. Results show that the magnitudes of the deviations between theoretical contact points and real contact points are small. Therefore, the results agree with the mathematical model of the spiral bevel gears of local bearing contact in this paper.

show abstract

Spiral involutes and their application in gear transmission

Cited by 4 publications

References 7 publications

Design method of rack-and-pinion pair with pure rolling variable transmission ratio

Design method of rack-and-pinion pair with pure rolling variable transmission ratio

Geometry and contact characteristics of torus involute gears

The geometric principles of general spiral bevel gears of local bearing contact from spatial conjugate curves

Contact Info

Product

Resources

About