Curvature Analysis and Hertzian Contact Stress of a Modified Curvilinear Gear Set With Localized Bearing Contact

2013 ◽  
Author(s):  
Yi-Cheng Chen ◽  
Chien-Cheng Lo ◽  
Wei-Cheng Chen
Keyword(s):  
Contact Stress ◽  
Point Contact ◽  
Transmission Error ◽  
Hertzian Contact ◽  
Tooth Contact Analysis ◽  
Curvature Analysis ◽  
Bearing Contact ◽  
Tooth Surfaces ◽  
Hertzian Contact Stress ◽  
Principal Directions

This paper investigates the contact ellipse and contact stress of a modified curvilinear gear set with localized bearing contact. The proposed modified curvilinear gear set with profile modifications was generated by male fly cutters with a circular-arc normal section. This gear drive exhibits point contact and parabolic transmission error under an ideal meshing condition according to the results of tooth contact analysis. The principal directions and curvatures of the mating pinion and gear surfaces were derived from those of the generating surfaces on the basis of differential geometry and theory of gearing. The Hertzian contact stress and contact ellipses of the mating tooth surfaces were determined with our developed computer program based on formulae of curvature analysis and Hertzian contact theory. Numerical examples were also provided to demonstrate the computational results.

Bearing contact of a helical gear pair with involute teeth pinion and modified circular-arc teeth gear

2001 ◽  
Vol 215 (10) ◽  
pp. 1175-1187 ◽  
Author(s):  
Y-C Chen ◽  
C-B Tsay
Keyword(s):  
Point Contact ◽  
Transmission Error ◽  
Helical Gear ◽  
Circular Arc ◽  
Curvature Analysis ◽  
Bearing Contact ◽  
Tooth Surfaces ◽  
Principal Directions ◽  
Helical Gear Pair

This paper investigates the contact ellipse of a helical gear set, composed of an involute pinion and a modified circular-arc gear based on curvature analysis. This gear drive exhibits point contact and parabolic transmission error due to the double crowning effect of the gear, i.e. crowning in both profile and longitudinal directions. The principal directions and curvatures of the generating tool surfaces were derived by means of differential geometry and Rodrigues’ equation. The principal directions and curvatures of the pinion and gear surfaces were obtained directly from the generating surfaces. Finally, the determination of the contact ellipses of the mating tooth surfaces was achieved. Numerical examples are also provided to demonstrate the computational results.

Crowned Spur Gears: Methods for Generation and Tooth Contact Analysis—Part 2: Generation of the Pinion Tooth Surface by a Surface of Revolution

1988 ◽  
Vol 110 (3) ◽  
pp. 343-347 ◽  
Author(s):  
F. L. Litvin ◽  
J. Zhang ◽  
R. F. Handschuh
Keyword(s):  
Parabolic Type ◽  
Maximum Level ◽  
Transmission Error ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Surface Of Revolution ◽  
Bearing Contact ◽  
Tooth Surfaces

A method for generation of crowned pinion tooth surfaces using a surface of revolution is developed. The crowned pinion meshes with a regular involute gear and has a prescribed parabolic type of transmission errors when the gears operate in the aligned mode. When the gears are misaligned the transmission error remains parabolic with the maximum level still remaining very small (less than 0.34 arc second for the numerical examples). Tooth Contact Analysis (TCA) is used to simulate the conditions of meshing, determine the transmission error, and the bearing contact.

Generation and TCA of Straight Bevel Gear Drive with Modified Geometry

2011 ◽  
Vol 86 ◽  
pp. 403-406 ◽  
Author(s):  
Ji Song Jiao ◽  
Xue Mei Cao
Keyword(s):  
Point Contact ◽  
Longitudinal Direction ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Tooth Contact Analysis ◽  
Bevel Gears ◽  
Straight Bevel Gear ◽  
Bearing Contact ◽  
Tooth Surfaces ◽  
Gear Drives

In order to reduce the sensitivity of straight bevel gear drives to misalignment, a new geometry of such gear drives is proposed in longitudinal direction. Point contact instead of line contact of tooth surfaces is achieved by longitudinal crowning of pinion tooth surface. The tooth surface modeling and tooth contact analysis (TCA) of straight bevel gear drives have been established. TCA program of a pair of straight bevel gears was performed in MATLAB and tooth bearing contact and transmission errors were obtained.

Manufacturing Process for a Face Gear Drive With Local Bearing Contact and Controllable Unloaded Meshing Performance Based on Ease-Off Surface Modification

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Xian-long Peng ◽  
Le Zhang ◽  
Zong-de Fang
Keyword(s):  
Surface Modification ◽  
Manufacturing Process ◽  
Point Contact ◽  
Transmission Error ◽  
Contact Analysis ◽  
Face Gear ◽  
Tooth Contact Analysis ◽  
Numerical Examples ◽  
Gear Drive ◽  
Bearing Contact

A manufacturing process for fabricating ease-off surfaces of a face gear drive that is provided with controllable unloaded meshing performance and local bearing contact is proposed. In order to control the unloaded meshing performance, a predesigned transmission error, a predesigned contact path, and the length of contact ellipse are applied in the redesign of the ease-off surfaces of the pinion and face gear. A method of point contact between the grinding disk and the manufactured pinion is proposed to generate the pinion's ease-off surface, the grinding disk is driven by a series of parabolic motions. Numerical examples are used to illustrate the application of the proposed method, the proposed method is proven to be feasible, and the redesigned face gear is proven to be able reproduce the predesigned unloaded meshing performance simulated by tooth contact analysis (TCA). The influence of misalignment on unloaded meshing performance is also analyzed.

Simulation of Plunge Shaving Operation for Spur and Helical Gear, and Tooth Contact Analysis of Finished Gear Drive

2003 ◽  
Author(s):  
David H. Kim
Keyword(s):  
Gear Tooth ◽  
Point Contact ◽  
Transmission Function ◽  
Disk Surface ◽  
Parametric Representation ◽  
Tooth Contact Analysis ◽  
Gear Drive ◽  
Bearing Contact ◽  
Tooth Surfaces ◽  
Motion Parameters

A math model of the re-sharpening operation of shaving cutter by grinding disk, and the plunge shaving process for spur and helical gears has been developed. It has been achieved by three steps: a parametric representation of grinding disk surface, the derivation of shaving cutter surface as a function of grinding disk surface and re-sharpening motion parameters, and the derivation of the finished gear surface as a function of cutter surface and synchronized plunge shaving motion parameters. The study is complemented with a methodology of determining the bearing contact as a set of instantaneous contact ellipses and the transmission function for the finished gear drive by plunge shaving. It simulates meshing and contact of two mating gear tooth surfaces in point contact. The described methods will give manufacturers better insight on the interrelationship between the shaving cutter and the plunge-shaved gear tooth topologies, and a tool to enhance existing design and manufacturing practices.

scholarly journals Computerized Design and Generation of Low-Noise Helical Gears with Modified Surface Topology

1995 ◽  
Vol 117 (2A) ◽  
pp. 254-261 ◽  
Author(s):  
F. L. Litvin ◽  
N. X. Chen ◽  
J. Lu ◽  
R. F. Handschuh
Keyword(s):  
Gear Tooth ◽  
Error Function ◽  
Transmission Error ◽  
Low Noise ◽  
Surface Topology ◽  
Helical Gears ◽  
Transmission Errors ◽  
Bearing Contact ◽  
Pinion Gear ◽  
Tooth Surfaces

An approach for the design and generation of low-noise helical gears with localized bearing contact is proposed. The approach is applied to double circular arc helical gears and modified involute helical gears. The reduction of noise and vibration is achieved by application of a predesigned parabolic function of transmission errors that is able to absorb a discontinuous linear function of transmission errors caused by misalignment. The localization of the bearing contact is achieved by the mismatch of pinion-gear tooth surfaces. Computerized simulation of meshing and contact of the designed gears demonstrated that the proposed approach will produce a pair of gears that has a parabolic transmission error function even when misalignment is present. Numerical examples for illustration of the developed approach are given.

Simulation Analysis of Contact Pattern and Strength of WN Gears Having Tooth Surface Deviations

2012 ◽  
Vol 479-481 ◽  
pp. 944-948 ◽  
Author(s):  
Dian Hua Chen ◽  
Zhong Wei Zhang
Keyword(s):  
Simulation Analysis ◽  
Practical Method ◽  
Transmission Error ◽  
Tooth Surface ◽  
Contact Pattern ◽  
The Finite Element Method ◽  
Tooth Contact Analysis ◽  
Surface Deviations ◽  
Tooth Surfaces ◽  
Loaded Tooth Contact Analysis

A practical method based on normal gaps topography is proposed here for loaded tooth contact analysis of WN gear having tooth surface deviations. The simulation of meshing state and tooth strength of WN gear are provided with real tooth surfaces. In the study normal gaps distribution is adopted to calculate tooth surface contact elastic deformation and local deviations due to manufacturing errors and tooth surface wear. For WN gear, the loaded distribution on the contact zone in meshing tooth surface has not been investigated because of their complexity in the contact state. The finite element method is adopted to analyze the contact pattern and tooth strength. The study has concretely calculated the contact pressure and zone of meshing in different loaded and transmission error. At the end examples are analyzed to demonstrate the effectiveness of the proposed method in quantifying effect of such deviations on the loaded distribution and tooth stress distribution.

Planar Tooth Profile Synthesis for Relative Curvature

2017 ◽  
Author(s):  
Zhiyuan Yu ◽  
Kwun-Lon Ting
Keyword(s):  
Contact Stress ◽  
Tooth Profile ◽  
Hertzian Contact ◽  
Rolling Motion ◽  
Special Cases ◽  
Systematic Methodology ◽  
Hertzian Contact Stress ◽  
Curvature Theory ◽  
The Given ◽  
Tooth Pair

This paper is the first that uses the new conjugation curvature theory [1] to directly synthesize conjugate tooth profiles with the given relative curvature that determines the Hertzian contact stress. Conjugation curvature theory offers a systematic methodology to synthesize the relative curvature for a tooth pair. For any given relative curvature between the contact tooth profiles, a generating point can be located on an auxiliary body. Under the rolling motion among the pinion pitch, the gear pitch and the pitch on the auxiliary body, the generating point will trace fully conjugate profiles on the pinion and gear bodies with the given relative curvature at the instant of the contact. Full conjugation throughout the contact of the profiles is guaranteed with the three instant centers remaining coincident [1]. The methodology is demonstrated with a planar tooth profile synthesis with given relative curvature. One may find that the Wildhaber-Novikov tooth profile, which is known to have low relative curvature and Hertzian contact stress, and its variations become special cases under such methodology.

Tooth contact analysis of a curvilinear gear set with modified pinion tooth geometry

2011 ◽  
Vol 225 (4) ◽  
pp. 975-986 ◽  
Author(s):  
Y-C Chen ◽  
M-L Gu
Keyword(s):  
Finite Element ◽  
Transmission Error ◽  
Contact Analysis ◽  
Design Parameters ◽  
Stress Distributions ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Numerical Examples ◽  
Bearing Contact ◽  
Parallel Axis

This article investigated the contact behaviours of a modified curvilinear gear set for parallel-axis transmission, which exhibits a pre-designed parabolic transmission error (TE) and localized bearing contact. The proposed gear set is composed of a modified pinion with curvilinear teeth and an involute gear with curvilinear teeth. Tooth contact analysis enabled the authors to explore the influences of assembly errors and design parameters on TEs and contact ellipses of this gear set. It is observed that TEs were continuous and the contact ellipses were localized in the middle of the tooth flanks, even under assembly errors. Finite-element contact analysis was performed to study stress distributions under different design parameters. In addition, numerical examples are presented to demonstrate the contact characteristics of the modified curvilinear gear set.

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