Third order curvature analysis of conjugate surfaces

Wang, Peng; Zhang, Yidu; Wan, Min

doi:10.1016/j.mechmachtheory.2016.09.008

Cited by 3 publications

(17 citation statements)

References 31 publications

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“…Based on the extremum condition of a continuous function, taking the first-order derivation of k (12) with respect to C (qp) , we obtain…”

Section: Relative Normal Curvatures In Casementioning

confidence: 99%

“…Then, from the no-meshing interference condition of gear meshing, the relative normal curvatures must remain non-negative, which means the minimum of k (12) ≥ 0. Therefore, from Eq., (57) the constraint condition is obtained as follows If equation ( 62) is investigated further, it can be found that only N (12) is unknown after the contact path, and the corresponding contact directions and relative motions are determined. There are two equations and one unknown, so the maximum and minimum of the relative normal curvatures are not independent of each other in case 1.…”

Section: Relative Normal Curvatures In Casementioning

confidence: 99%

“…Dooner 10 proposed methods for establishing limiting values for the extreme relative curvatures of conjugate gear tooth flanks in direct contact and amending the transverse profiles by applying first-and second-order reciprocity. Wang and Zhang 11 introduced a tensor analysis method to study the second-order geometry characteristics of gear tooth surfaces, and Wang et al 12 studied the third-order geometry characteristics analysis method of gear tooth surfaces based on tensor theory. Park 13 proposed the tooth surface of hypoid gears generated by a common crown rack and studied the corresponding geometric design characteristics.…”

Section: Introductionmentioning

confidence: 99%

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An analytical framework of the kinematic geometry for general point-contact gears from contact path

Tan

Zhang

Guo

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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Based on the idea that the relative curvature relationships along total contact path will better reflect the contact characteristics of gears, this study attempts to develop an analytical framework for the kinematic geometry of point-contact gears from the contact paths. First, a general method for obtaining the contact path of a gear from a pinion is proposed. Second, a normal curvature and geodesic torsion calculation method in the contact path direction is developed. Then, based on the linearly dependent condition of the tangent vectors of the two contact paths, two relative normal curvature analysis methods are proposed by applying the fundamental form theory. Finally, a sample case is presented to show the application and complete the verification of the kinematic geometry methods. The sample case agrees with the analytical model.

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“…Based on the extremum condition of a continuous function, taking the first-order derivation of k (12) with respect to C (qp) , we obtain…”

Section: Relative Normal Curvatures In Casementioning

confidence: 99%

Section: Relative Normal Curvatures In Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An analytical framework of the kinematic geometry for general point-contact gears from contact path

Tan

Zhang

Guo

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

show abstract

“…Based on the discussions above, the tooth profile of the noncircular gear can be presented as the envelope curves of the tooth profile of the shaper cutter, that is 28,42 …”

Section: Mathematical Model For Variable Speed Pinion–rack Drivementioning

confidence: 99%

“…Based on the discussions above, the tooth profile of the noncircular gear can be presented as the envelope curves of the tooth profile of the shaper cutter, that is 28,42 It needs to be pointed out that, while equation ( 13) signifies the tooth profile envelope curve, the real tooth profile comprised only the boundary of the envelope curve. In order to obtain the tooth profile, the meshing equation should be used 35 f m ð', u, vÞ…”

Section: Generated Tooth Profilementioning

confidence: 99%

Geometric characteristics and tooth modification for variable speed pinion–rack drive

Zheng

Han

Min

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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Variable speed steering system has been used by cars of various brands, including BMW and Toyota, with the purpose of improving the stationarity and controllability of the vehicle. Until now, relevant investigations are focused on the theory and traditional application, while the geometric characteristics and tooth modification for the rack are left untouched upon, hindering the prospect of a wider application. Focusing on this, the paper synthesizes the mathematical model, geometry characteristics, and tooth modification method for the variable pinion–rack drive. The major contributions lie in the contact analysis and the modification methodology for the pinion–rack drive, which combined forms a solid foundation for the application that has never been discussed.

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Fundamental equation of mechanism kinematic geometry: Mapping curve in se(3) to counterpart in SE(3)

Zhang

Zhao

2020

Mechanism and Machine Theory

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Third order curvature analysis of conjugate surfaces

Cited by 3 publications

References 31 publications

An analytical framework of the kinematic geometry for general point-contact gears from contact path

An analytical framework of the kinematic geometry for general point-contact gears from contact path

Geometric characteristics and tooth modification for variable speed pinion–rack drive

Fundamental equation of mechanism kinematic geometry: Mapping curve in se(3) to counterpart in SE(3)

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