Geometrical design of variable ratio tooth profile based on Boolean subtraction operation and a novel modification method

Niu, Ziru; Li, Jianlei; Xin, Shuai; Zou, Liangliang; Li, Yuhua; Hou, Jialin; Tu, Ming; Sun, Tao

doi:10.25165/j.ijabe.20201305.4884

Cited by 3 publications

(4 citation statements)

References 23 publications

(26 reference statements)

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“…At present, a universal variable transmission ratio function can be expressed as equation ( 21), 27,28 and the related curve is shown in Figure 9. Equation (21) and Figure 9 show that the variable transmission ratio curve is segmented, symmetrical, and continuous.…”

Section: Kinematic Equations Of Variable Transmission Ratio Gear Pairmentioning

confidence: 99%

Novel generation method of tooth surface points for variable transmission ratio gears

Xin

Niu

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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Variable transmission ratio gears have shown considerable potential as key components of variable speed transmission steering boxes that balance steering portability and sensitivity. The objective of this study is to develop a novel method for designing variable transmission ratio tooth surfaces to circumvent the shortcomings of the meshing theory method. The involute rack of the variable transmission ratio pinion-and-rack pair is considered as a set of countless and infinitely close transverse sections, each of which is referred to as a gear element. Assuming evenly distributed circles in the physical domain of the variable transmission ratio tooth surfaces of the pinion, the problem of generating a tooth surface point is transformed into solving the specific geometric feature intersection point of each circle and corresponding gear element during variable transmission ratio meshing. Thereafter, a mathematical model and algorithm are developed to generate tooth surface points in an approximately even pattern. The normal deviations of the gear-element–generated tooth surface points and the corresponding tooth surface points calculated using meshing theory show that the proposed design method has a sufficiently high accuracy. Finite element models are employed analyzing the contact pattern, contact stress, bending stress, and transmission ratio error. The results indicate that the layout of approximately even tooth surface points using the gear element method is beneficial for improving the fitting precision of tooth surfaces and reducing the contact stress and transmission ratio error. Further, the same derived law of the flank and fillet tooth surfaces is conducive to the continuity of the tooth surfaces, which contributes toward reducing the bending stress. Finally, a prototype is manufactured via CNC end milling. The major contributions lie in a robust and efficient modeling method for variable transmission ratio tooth surfaces, which combined forms a solid foundation for their application.

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Section: Kinematic Equations Of Variable Transmission Ratio Gear Pairmentioning

confidence: 99%

Novel generation method of tooth surface points for variable transmission ratio gears

Xin

Niu

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

show abstract

“…Because Boolean cuts will occur in the model of variable-ratio tooth surfaces acquired by Boolean reduction, the author of this research has proposed a continuous fairing method to modify variable-ratio tooth surfaces in previous studies. 24,25 However, the modeling accuracy of this method is not satisfactory owing to inaccessible precise positions of points in the theoretical tooth surface. High accuracy point cloud of variable-ratio tooth surfaces can be acquired analytically based on the meshing theory.…”

Section: Introductionmentioning

confidence: 99%

“…Hu et al 23 established a macroprogram of Boolean subtraction operation with three-dimensional modelling software and simulated the generating cutting process of the variable transmission ratio tooth surface. Niu et al 24,25 developed a novel fitting algorithm using approximate variable transmission ratio tooth profile points extracted from the Boolean cutting marks to generated a series of smooth tooth surfaces by utilizing B-spline with different orders.…”

Section: Introductionmentioning

confidence: 99%

Investigating tooth surface reconstruction principle of a gear rack and pinion system with variable transmission ratio pinion

Ziru,

Da,

Fuhui

et al. 2024

Proceedings of the Institution of Mechanical Engineers, Part C:

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Rack-and-pinion gear sets with variable transmission ratios have gradually become a standard core component in steering systems, as the harmony between portability and sensitivity in vehicle steering can be achieved with such applications. When the conventional meshing theory is adopted to calculate point clouds of variable-ratio tooth surfaces, drawbacks will occur with respect to unevenness in point cloud density, inaccessible tooth surface boundaries, and point cloud fusion at the interface between the working tooth surface and fillet. Thus, the generated point cloud of variable ratio tooth surfaces is inapplicable for computer-aided engineering (CAE) and plastic forming. In this study, the point cloud reconstruction of pinion tooth surfaces with variable transmission ratio was investigated. Meanwhile, based on the analysis of transient length in contact lines that occur during gear meshing, various criteria were proposed to determine the validity of the variable-ratio rack-and-pinion design in terms of whether continuous and reverse driving can be achieved. By adopting the proposed methods, the designed variable-ratio pinion tooth surfaces demonstrate point clouds with equidistant distributions and clear boundaries. CAE analysis results also indicate a good quality in gear meshing. The real-time gear meshing status of variable-ratio rack-and-pinion sets is characterized by the transient length of contact lines. The measured variation curves for the transmission ratios of a prototype demonstrate significant consistency with the theoretical curves, indicated by attaining transmission ratio errors within a reasonable range. The validity of the design methods proposed in this study has been verified by the aforementioned results.

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“…The third type is double-variable-ratio sector gear and rack pair. 12 The variable transmission ratio rack is formed by variable motion envelope of involute straight cylindrical sector gear, and then the variable transmission ratio sector gear is formed by the variable motion envelope of the shape rack. The shape rack is formed by the envelope of the variable transmission ratio rack.…”

Section: Introductionmentioning

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:

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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.

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Geometrical design of variable ratio tooth profile based on Boolean subtraction operation and a novel modification method

Cited by 3 publications

References 23 publications

Novel generation method of tooth surface points for variable transmission ratio gears

Novel generation method of tooth surface points for variable transmission ratio gears

Investigating tooth surface reconstruction principle of a gear rack and pinion system with variable transmission ratio pinion

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

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