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.

New developments in the design and generation of gear drives

2001 ◽  
Vol 215 (7) ◽  
pp. 747-757 ◽  
Author(s):  
F. L. Litvin ◽  
A Fuentes ◽  
A Demenego ◽  
D Vecchiato ◽  
Q Fan
Keyword(s):  
Point Contact ◽  
Tooth Surface ◽  
Helical Gears ◽  
Transmission Errors ◽  
Bevel Gears ◽  
Bearing Contact ◽  
Analysis And Synthesis ◽  
Tooth Surfaces ◽  
Design Generation ◽  
Gear Drives

Design, generation and simulation of the meshing and contact of gear drives with favourable bearing contact and reduced noise are considered. The proposed approach is based on replacement of the instantaneous line of contact of tooth surfaces by point contact and on application of a predesigned parabolic function of transmission errors that is able to absorb linear discontinuous functions of transmission errors caused by misalignment. Basic algorithms for analysis and synthesis of gear drives are presented. The developed theory is applied for design and generation of the following gear drives with modified geometry: (a) spur and helical gears, (b) a new version of Novikov-Wildhaber (N-W) helical gears, (c) asymmetric face gear drives with a spur pinion, (d) formate-cut spiral bevel gears. Generation of the tooth surface of a worm gear is presented as the formation of a two-branch envelope. The discussed topics are illustrated with examples.

Application and Investigation of Modified Helical Gears With Several Types of Geometry

2007 ◽  
Author(s):  
Ignacio Gonzalez-Perez ◽  
Alfonso Fuentes ◽  
Faydor L. Litvin ◽  
Kenichi Hayasaka ◽  
Kenji Yukishima
Keyword(s):  
Gear Tooth ◽  
Tooth Surface ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Helical Gears ◽  
Transmission Errors ◽  
Advantages And Disadvantages ◽  
Bearing Contact ◽  
Tooth Surfaces ◽  
Gear Drives

Involute helical gears with modified geometry for transformation of rotation between parallel axes are considered. Three types of topology of geometry are considered: (1) crowning of pinion tooth surface is provided only partially by application of a grinding disk; (2) double crowning of pinion tooth surface is obtained applying a grinding disk; (3) concave-convex pinion and gear tooth surfaces are provided (similar to Novikov-Wildhaber gears). Localization of bearing contact is provided for all three types of topology. Computerized TCA (Tooth Contact Analysis) is performed for all three types of topology to obtain: (i) path of contact on pinion and gear tooth surfaces; (ii) negative function of transmission errors for misaligned gear drives (that allows the contact ratio to be increased). Stress analysis is performed for the whole cycle of meshing. Finite element models of pinion and gear with several pairs of teeth are applied. A relative motion is imposed to the pinion model that allows friction between contact surfaces to be considered. Numerical examples have confirmed the advantages and disadvantages of the applied approaches for generation and design.

The Undercutting of Circular-Cut Spiral Bevel Gears

1992 ◽  
Vol 114 (2) ◽  
pp. 317-325 ◽  
Author(s):  
Zhang-Hua Fong ◽  
Chung-Biau Tsay
Keyword(s):  
Gear Tooth ◽  
Sufficient Conditions ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Sufficient And Necessary Conditions ◽  
Spiral Bevel

Undercutting is a serious problem in designing spiral bevel gears with small numbers of teeth. Conditions of undercutting for spiral bevel gears vary with the manufacturing methods. Based on the theory of gearing [1], the tooth geometry of the Gleason type circular-cut spiral bevel gear is mathematically modeled. The sufficient and necessary conditions for the existence and regularity of the generated gear tooth surfaces are investigated. The conditions of undercutting for a circular-cut spiral bevel gear are defined by the sufficient conditions of the regular gear tooth surface. The derived undercutting equations can be applicable for checking the undercutting conditions of spiral bevel gears manufactured by the Gleason Duplex Method, Helical Duplex Method, Fixed Setting Method, and Modified Roll Method. An example is included to illustrate the application of the proposed undercut checking equations.

A Study on Forging of Spiral Bevel Gear

2007 ◽  
Author(s):  
Masaki Watanabe ◽  
Minoru Maki ◽  
Sumio Hirokawa ◽  
Yasuhiro Kishimoto
Keyword(s):  
Gear Tooth ◽  
Conjugate Point ◽  
Point Contact ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Tooth Contact ◽  
Contact Points ◽  
Tooth Surfaces ◽  
Spiral Bevel

This study reports the method of forging of spiral bevel gear. Two ideas for crowning of tooth surface to obtain point contact for forging gears are proposed. By one idea, tooth surface of pinion meshes with the gear tooth surface by conjugate point contact. And the trace of contact points on the gear tooth surface is perpendicular to the lengthwise direction of gear tooth, namely becomes the “square contact” so called in gear technology. The trace can be set arbitrarily on the gear tooth, by setting the pitch point arbitrarily. By another idea, the trace of contact points lies along the tooth trace of the gear tooth. Both ideas proposed in this report, the numerical dataset of teeth surface of pinion and gear are given by the contact lines with the cutter cone. The dataset of teeth surface of pinion and gear are calculated to cut a pair of electrodes of spiral bevel gear. Tooth contacts of proposed gearing are confirmed by the 3D drawing of tooth surfaces. The tooth contact of the master pinion and gear were made and tested by tooth contact testing apparatus. The contact marks coincide well with the theoretical contact pattern estimated by 3D/CAD expression. The good results of running test of the performance of the master gear has been given. The authors completed the forging of spiral bevel gear pairs by two methods proposed in this report.

Computerized Design of Worm Gear Drives With Improved Conditions of Meshing and Bearing Contact

2006 ◽  
Author(s):  
Ignacio Gonzalez-Perez ◽  
Alfonso Fuentes ◽  
Faydor L. Litvin ◽  
Kenichi Hayasaka ◽  
Kenji Yukishima
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Worm Gear ◽  
Tooth Surface ◽  
Tooth Contact Analysis ◽  
Parabolic Profile ◽  
Gear Drive ◽  
Bearing Contact ◽  
Basic Ideas ◽  
Gear Drives

A new geometry of a cylindrical worm gear drive is proposed for: (i) reduction of sensitivity of the drive to errors of alignment, and (ii) observation of a favorable bearing contact. The basic ideas of new geometry are as follows: (i) the worm-gear is generated by a hob that is oversized in comparison with the worm of the drive and has a parabolic profile in normal section; (ii) the tooth surface of the worm of the drive is a conventional one. Due to deviation of the hob thread surface, the bearing contact of the worm and the worm-gear is localized. Reduction of sensitivity to misalignment and improved conditions of meshing are confirmed by application of TCA (Tooth Contact Analysis). Formation of bearing contact has been investigated by finite element method applied in 3D for more than one pair of contacting teeth. Developed ideas may be applied for various types of cylindrical worm gear drives.

Fourth-Order Kinematic Synthesis for Face-Milling Spiral Bevel Gears With Modified Radial Motion (MRM) Correction

2005 ◽  
Vol 128 (2) ◽  
pp. 457-467 ◽  
Author(s):  
Pei-Yu Wang ◽  
Zhang-Hua Fong
Keyword(s):  
Fourth Order ◽  
Face Milling ◽  
Bevel Gear ◽  
Radial Motion ◽  
Numerical Control ◽  
Tooth Surface ◽  
Kinematic Synthesis ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Spiral Bevel

The use of a fourth-order motion curve is proposed by Stadtfeld and Gaiser to reduce the running noise of a bevel gear set recently. However, the methodology of synthesizing the tooth surfaces was not clearly shown in the literature. In this work, we proposed a methodology to synthesize the mating tooth surfaces of a face-milling spiral bevel gear set transmitting rotations with a predetermined fourth-order motion curve and contact path. A modified radial motion (MRM) correction in the machine plane of a computer numerical control (CNC) hypoid generator is introduced to modify the pinion tooth surface. With MRM correction, an arbitrary predetermined contact path on the pinion tooth surface with predetermined fourth-order motion curve can be achieved. Parameters of MRM correction are calculated according to the predetermined contact path and motion curve. As shown by the numerical examples, the contact path and the motion curve were obtained as expected by applying the MRM correction. The results of this work can be applied to the pinion, which is generated side-by-side (for example, fixed setting method, formate method, and Helixform method) and can be used as a basis for further study on the motion curve optimizations.

scholarly journals Computerized Design and Analysis of Face-Milled, Uniform Tooth Height Spiral Bevel Gear Drives

1996 ◽  
Vol 118 (4) ◽  
pp. 573-579 ◽  
Author(s):  
F. L. Litvin ◽  
A. G. Wang ◽  
R. F. Handschuh
Keyword(s):  
Low Noise ◽  
Contact Analysis ◽  
Spiral Bevel Gear ◽  
Tooth Contact Analysis ◽  
Spiral Bevel Gears ◽  
Numerical Example ◽  
Bevel Gears ◽  
Bearing Contact ◽  
Spiral Bevel ◽  
Gear Drives

Face-milled spiral bevel gears with uniform tooth height are considered. An approach is proposed for the design of low-noise and localized bearing contact of such gears. The approach is based on the mismatch of contacting surfaces and permits two types of bearing contact either directed longitudinally or across the surface to be obtained. Conditions to avoid undercutting were determined. A Tooth Contact Analysis (TCA) was developed. This analysis was used to determine the influence of misalignment on meshing and contact of the spiral bevel gears. A numerical example that illustrates the developed theory is provided.

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.

Surface design and tooth contact analysis of an innovative modified spur gear with crowned teeth

2005 ◽  
Vol 219 (2) ◽  
pp. 193-207 ◽  
Author(s):  
J-L Li ◽  
S-T Chiou
Keyword(s):  
Gear Tooth ◽  
Point Contact ◽  
Spur Gear ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Surface Design ◽  
Tooth Surfaces ◽  
Meshing Characteristics

An innovative modified spur gear with crowned teeth and its generating mechanism are proposed in this study. The main purpose of tooth surface modification is to change line contact to point contact at the middle of gear tooth surfaces in order to avoid edge contact resulting from possible unavoidable axial misalignment. Moreover, the surface of one gear tooth can be generated with just one cutting process, thereby facilitating easy manufacturing. Based on gearing theory, the model for surface design is developed. A tooth contact analysis (TCA) model for the modified gear pair is also built to investigate meshing characteristics, so that transmission errors (TEs) under assembly errors can also be studied. Examples are included to verify the correctness of the models developed and to demonstrate gear characteristics.

Influence of Tooth Modifications on Load Distribution in Face-Hobbed Spiral Bevel Gears

2011 ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Load Distribution ◽  
Point Contact ◽  
Surface Generation ◽  
Tooth Surface ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Distribution Calculation ◽  
Potential Contact ◽  
Tooth Surfaces ◽  
Spiral Bevel

In this study a novel method for load distribution calculation is applied to investigate the influence of tooth modifications on loaded tooth contact in face-hobbed spiral bevel gears. As a result of these modifications introduced to the teeth of the pinion, the gear pair becomes mismatched, and a point contact replaces the theoretical line contact. In the applied load distribution calculation it is assumed that the point contact under load is spreading over a surface along the whole or part of the “potential” contact line, which line is made up of the points of the mating tooth surfaces in which the separations of these surfaces are minimal. The separations of contacting tooth surfaces are calculated by applying the full theory of tooth surface generation in face-hobbed spiral bevel gears. A computer program was developed to implement the formulation provided above. By using this program the influence of tooth modifications introduced by the variation in machine tool settings and in head cutter profile on load and pressure distributions, transmission errors, and fillet stresses is investigated and discussed.

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