Mathematical design and meshing analysis of a new internal gear transmission based on spatial involute-helix curve

Liang, Dong; Zhao, Weicheng; Meng, Sheng; Peng, Shuai

doi:10.1177/09544062221119079

Cited by 5 publications

(3 citation statements)

References 37 publications

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“…Based on the transformation theory between coordinate systems, 2 the transformation matrix can be expressed as:…”

Section: Design Principle Of the Gear Tooth Profilementioning

confidence: 99%

“…In order to ensure higher precision and transmission efficiency of internal gear pairs in practical applications, form grinding is usually an integral part of gear machining. 1,2 A number of scholars have conducted studies on form grinding. Simon 3 presented a new method for grinding hypoid gears by applying generating and Waguri motions and also researched on the influence of the grain size and the relation of motions in the grinding process on the obtained roughness of the ground tooth surface.…”

Section: Introductionmentioning

confidence: 99%

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Grinding wheel profile design and temperature field analysis of the pinion for internal meshing gear with curve configuration

Liang,

Hao,

Zhao

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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To further develop the performance testing and practical application of internal meshing gear with curve configuration, the grinding manufacturing method is proposed in this paper. Based on basic principle of internal meshing gear with curve configuration, Newton’s iterative method is used to derive the contact line condition equation during the process of form grinding. Then, the spatial coordinate transformation relationship of the pinion is established, and normal profile of the grinding wheel is derived. An improved transversal algorithm is proposed to analyze the tooth profile error after form grinding simulation, and the results verify the correctness of the designed grinding wheel. A meshing model with single tooth is established. The effects of different parameters on the grinding temperature field under dry and wet grinding conditions are simulated respectively, which will be helpful to the optimization and control of temperature in grinding process. The research results lay the essential theoretical foundation and engineering analysis for practical form grinding applications of the new internal gears. Further study on experimental analysis of grinding manufacturing process of the new tooth surfaces will be carried out.

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“…Based on the transformation theory between coordinate systems, 2 the transformation matrix can be expressed as:…”

Section: Design Principle Of the Gear Tooth Profilementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Grinding wheel profile design and temperature field analysis of the pinion for internal meshing gear with curve configuration

Liang,

Hao,

Zhao

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part C:

Self Cite

View full text Add to dashboard Cite

show abstract

“…Mathematical design and meshing analysis of tooth surfaces were studied. 8 Song et al 9 studied the design of the conjugated straight-line internal gear pairs for fluid power gear machines. Mathematical models of the rack-cutter and the conjugated internal gear were derived.…”

Section: Introductionmentioning

confidence: 99%

Optimization design and analysis of internal gear transmission with double contact points

Liang

Jiang

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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Internal gear transmission with double contact points is consist of the pinion having circular-arc tooth profile and the internal gear having parabola tooth profile. To further improve load capacity and reduce total volume of internal gear drive with double contact points, a multi-objective and multi-parameter optimization mathematical model is established based on genetic algorithm. Through the comparison analysis, contact stress of tooth surfaces after optimization design is reduced by 21.9% and the volume of gear after optimization design is reduced by 3.93%. Furthermore, contact characteristics of tooth surfaces are discussed considering the parameters optimization of contact angles and pressure angles. Based on Hertz contact theory, theoretical calculations of contact stresses under different contact angles and pressure angles are provided. And finite element method is used to analyze the contact conditions of tooth surfaces to verify theoretical calculation results. Research results show that contact angle of the internal gear pair with double contact points should less than 12.5° and pressure angle of the internal gear pair with double contact points should be 20°–30°.

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Involutes of null Cartan curves and their representations in Minkowski 3-space

2023

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Mathematical design and meshing analysis of a new internal gear transmission based on spatial involute-helix curve

Cited by 5 publications

References 37 publications

Grinding wheel profile design and temperature field analysis of the pinion for internal meshing gear with curve configuration

Grinding wheel profile design and temperature field analysis of the pinion for internal meshing gear with curve configuration

Optimization design and analysis of internal gear transmission with double contact points

Involutes of null Cartan curves and their representations in Minkowski 3-space

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