The Mathematical Model of Spiral Bevel Gears - A Review

Wang, Jixin; Kong, Long; Liu, Bangcai; Xin-peng, HU; Yu, Xiaoli; Kong, Weikang

doi:10.5545/sv-jme.2013.1357

Cited by 17 publications

(5 citation statements)

References 57 publications

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“…The mathematical modeling of the tooth surface of spiral bevel gears based on cutting machining parameters is the process of establishing the mapping relationship between cutting machining parameters and tooth surface shape. Based on the meshing principle of gear and the cutting principle of spiral bevel gear, combined with the kinematical relationship between the cutting tool, the machine tool components and the wheel blank, the equation of tooth surface can be derived from the blade equation through the coordinate transformation [27,28]. In this paper, the machining method of small spiral bevel gear is the tool inclination method, and the machining method of large spiral bevel gear is the generating method, taking the establishment of the equation of pinion gear tooth surface as an example.…”

Section: Establishment Of Theoretical Tooth Surface Equationmentioning

confidence: 99%

Control of Tooth Form Deformation in Heat Treatment of Spiral Bevel Gears Based on Reverse Adjustment of Cutting Parameters

Huo

Deng

2023

Materials

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The tooth surface structure of spiral bevel gear is complex and requires high machining accuracy. In order to reduce the tooth form deformation of heat treatment, this paper proposes a reverse adjustment correction model of tooth cutting for heat treatment tooth form deformation of spiral bevel gear. Based on the Levenberg–Marquardat method, a stable and accurate numerical solution for the reverse adjustment amount of the cutting parameters is solved. Firstly, a mathematical model of the tooth surface of spiral bevel gears was established based on the cutting parameters. Secondly, the effect law of each cutting parameter on tooth form was studied by using the method of small variable perturbation. Finally, based on the tooth form error sensitivity coefficient matrix, a reverse adjustment correction model of tooth cutting is established to compensate the heat treatment tooth form deformation by reserving the tooth cutting allowance in the tooth cutting stage. The effectiveness of the reverse adjustment correction model of tooth cutting was verified through experiments on reverse adjustment of tooth cutting processing. The experimental results show that the accumulative tooth form error of the spiral bevel gear after heat treatment is 199.8 μm, which is reduced by 67.71%, and the maximum tooth form error is 8.7 μm, which is reduced by 74.75%, after reverse adjustment of cutting parameters. This research can provide technical support and a theoretical reference for heat treatment tooth form deformation control and high-precision tooth cutting processing of spiral bevel gears.

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Section: Establishment Of Theoretical Tooth Surface Equationmentioning

confidence: 99%

Control of Tooth Form Deformation in Heat Treatment of Spiral Bevel Gears Based on Reverse Adjustment of Cutting Parameters

Huo

Deng

2023

Materials

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“…Because the tooth surface is arc-shaped, the strength and driving are smooth. Wang 3 reviewed the mathematical model of the spiral bevel gear and its manufacturing method. Fong and Tsay 4,5 used circular cutters to establish the mathematical and the geometrical models of spiral bevel gears through homogeneous coordinate transformation matrix and gearing theory.…”

Section: Introductionmentioning

confidence: 99%

Investigation on the generation of bevel gear by disk tool with curved tooth surface of trapezoidal tooth profile

Yang

2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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A bevel gear pair with curved tooth surface is widely used for power transmission of intersecting shafts. The bevel gear pair with curved tooth surface has higher load bearing capacity than straight bevel gears, longer line length, quieter, center distance assembly error, and does not change the speed ratio. This paper proposes a disk cutter with curved tooth surface of trapezoidal tooth profile to generate a bevel gear pair. One continuously distributed a trapezoidal tooth profile with curved tooth surface on a disc into an imaginary disc cutter to generate a bevel gear pair with curved tooth surface. This method has never appeared in the literature. Therefore, a mathematical model of a disc cutter with curved tooth surface of trapezoidal tooth profile was established and used to generate the mathematical model of the bevel gear pair via the theory of gearing. Through the undercutting analysis, explore the undercutting conditions of the proposed disc cutter and determine the parameter size limit. Based on tooth contact analysis (TCA), the transmission error and the contact pattern of the bevel gear pair with curvilinear teeth is calculated under the assembly error of the bevel gear. The advantage of the proposed disc cutter is that the transmission error of the parabolic type without modification of the tooth surface of the bevel gear pair can be obtained.

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“…The spiral bevel gear (SBG), with its high contact ratio, high strength and stable transmission, is widely used to transmit dynamic power in various mechanical products, including vehicles, mining machinery, aerospace engineering and helicopters [1][2][3][4]. The SBG has been a subject of research for almost a century.…”

Section: Introductionmentioning

confidence: 99%

Review on logarithmic spiral bevel gear

Jiang

Luo

Wang

et al. 2020

J Braz. Soc. Mech. Sci. Eng.

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Logarithmic spiral bevel gear (LSBG) has received increasing attention among industry and academy in the past four decades. This paper attempts to survey and summarize the recent research and development of LSBG, provides comprehensive references for researchers concerning with this topic and helps them identify further research topics. The objective of this paper is to review published papers about LSBG focused on three topics: mathematical model, simulation analysis, processing and manufacturing. More specifically, this review is composed of three related parts according to the above three topics. The first part summarizes the method of building the three-dimensional (3D) gear models of LSBG including sweeping method, cutting principle method and tooth surface equation method. The second part involves the dynamic research of LSBG based on 3D gear models, which provides a basis in the design of LSBG. The final part reviews the method of manufacturing LSBG including CNC machining centers and special machine tools. The special machine tool processing method involves local conjugate principle and generating method. The well-known open problems about LSBG are finally stated, and some new research interests are also pointed out. The review will provide valuable references for further research on LSBG and other types of spiral bevel gears.

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The Mathematical Model of Spiral Bevel Gears - A Review

Cited by 17 publications

References 57 publications

Control of Tooth Form Deformation in Heat Treatment of Spiral Bevel Gears Based on Reverse Adjustment of Cutting Parameters

Control of Tooth Form Deformation in Heat Treatment of Spiral Bevel Gears Based on Reverse Adjustment of Cutting Parameters

Investigation on the generation of bevel gear by disk tool with curved tooth surface of trapezoidal tooth profile

Review on logarithmic spiral bevel gear

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