Geometry of Tooth Profile and Fillet of Face-Hobbed Spiral Bevel Gears

2007 ◽  
Author(s):  
Yi Zhang ◽  
Zhi Wu
Keyword(s):  
Gear Tooth ◽  
Mathematical Formulation ◽  
Tooth Profile ◽  
Tooth Surface ◽  
Generation Process ◽  
Tooth Contact Analysis ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Spiral Bevel

The determination of the geometry for the whole tooth profile, including the meshing profile and the tooth fillet, is important for tooth contact analysis and the mesh generation for FEM analysis of gear pairs. This paper presents a systematic approach for the determination of the complete tooth geometry of face-hobbed hypoid and spiral bevel gears. The detailed mathematical formulation for the generation of gear tooth surface and the equations for the tooth surface coordinates are provided in the paper. The surface coordinates and normal vectors are calculated at grid points selected based on the gear blank dimension. Using the machine tool settings as input, the computer model simulating the gear generation process precisely calculates the tooth geometry parameters on the selected grid. A numerical example is included in the paper to illustrate the presented approach.

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.

scholarly journals Theoretical and Experimental Study on Contact Characteristics of Spiral Bevel Gears under Quasi-Static and Large Loading Conditions

2020 ◽  
Vol 10 (15) ◽  
pp. 5109 ◽  
Author(s):  
Yimeng Fu ◽  
Yaobing Zhuo ◽  
Xiaojun Zhou ◽  
Bowen Wan ◽  
Haoliang Lv ◽  
...  
Keyword(s):  
Finite Element ◽  
Performance Test ◽  
Element Model ◽  
Transmission Error ◽  
Tooth Surface ◽  
Tooth Contact Analysis ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Transition Surface ◽  
Spiral Bevel

The precise mathematical model for the tooth surface and transition surface of spiral bevel gears is derived. Taking a pair of spiral bevel gears of a heavy vehicle as an example of calculation and analysis, a finite element model of spiral bevel gears transmission system is established. Through the finite element tooth contact analysis under quasi-static loading and high loading condition, the influences of torque on the root stress distribution, contact stress, and transmission error are discussed, and the results are compared with the empirical formula results. Finally, a contact performance test bench of spiral bevel gear pair is developed, then the root bending stress, contact pattern, and transmission error tests are carried out. These experiment results are compared with analyzed ones, which showed a good agreement.

Design and Manufacture of Spiral Bevel Gears With Reduced Transmission Errors

2008 ◽  
Author(s):  
V. Simon
Keyword(s):  
Contact Point ◽  
Tooth Surface ◽  
Initial Contact ◽  
Generation Process ◽  
Polynomial Functions ◽  
Spiral Bevel Gears ◽  
Transmission Errors ◽  
Bevel Gears ◽  
Spiral Bevel ◽  
Two Sides

A method for the determination of the optimal polynomial functions for the conduction of machine-tool setting variations in pinion teeth finishing in order to reduce the transmission errors in spiral bevel gears is presented. Polynomial functions of order up to five are applied to conduct the variation of the cradle radial setting and of the cutting ratio in the process for pinion teeth generation. Two cases were investigated: in the first case the coefficients of the polynomial functions are constant throughout the whole generation process of one pinion tooth-surface, in the second case the coefficients are different for the generation of the pinion tooth-surface on the two sides of the initial contact point. The obtained results have shown that by the use of two different fifth-order polynomial functions for the variation of the cradle radial setting for the generation of the pinion tooth-surface on the two sides of the initial contact point, the maximum transmission error can be reduced by 81%. By the use of the optimal modified roll, this reduction is 61%. The obtained results have also shown that by the optimal variation of the cradle radial setting, the influence of misalignments inherent in the spiral bevel gear pair and of the transmitted torque on the increase of transmission errors can be considerably reduced.

Design and Manufacture of Spiral Bevel Gears With Reduced Transmission Errors

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Contact Point ◽  
Tooth Surface ◽  
Initial Contact ◽  
Generation Process ◽  
Polynomial Functions ◽  
Spiral Bevel Gears ◽  
Transmission Errors ◽  
Bevel Gears ◽  
Spiral Bevel ◽  
Two Sides

A method for the determination of the optimal polynomial functions for the conduction of machine-tool setting variations in pinion teeth finishing in order to reduce the transmission errors in spiral bevel gears is presented. Polynomial functions of order up to 5 are applied to conduct the variation in the cradle radial setting and in the cutting ratio in the process for pinion teeth generation. Two cases were investigated: In the first case, the coefficients of the polynomial functions are constant throughout the whole generation process of one pinion tooth-surface; in the second case, the coefficients are different for the generation of the pinion tooth-surface on the two sides of the initial contact point. The obtained results have shown that by the use of two different fifth-order polynomial functions for the variation in the cradle radial setting for the generation of the pinion tooth-surface on the two sides of the initial contact point, the maximum transmission error can be reduced by 81%. By the use of the optimal modified roll, this reduction is 61%. The obtained results have also shown that by the optimal variation in the cradle radial setting, the influence of misalignments inherent in the spiral bevel gear pair and of the transmitted torque on the increase in transmission errors can be considerably reduced.

Realization of Expected Direction Angle of SGM Spiral Bevel Gears Based on Local Synthesis

2010 ◽  
Vol 37-38 ◽  
pp. 927-933 ◽  
Author(s):  
Guang Lei Liu ◽  
Yue Jun Tian ◽  
Ping Jiang
Keyword(s):  
Objective Function ◽  
Contact Point ◽  
Optimization Method ◽  
Function Optimization ◽  
Tooth Surface ◽  
Tooth Contact Analysis ◽  
Local Synthesis ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Spiral Bevel

The authors propose an optimization method based on local synthesis to fulfill the expected contact path (ECP) at mean contact point (M) of spiral bevel gears. The method is a combination of local synthesis, tooth contact analysis (TCA) and application of optimization. Machine-tool settings based on local synthesis are found and contact path (CP) on tooth surface is formed. TCA extracts the information from CP and transforms it to a projected CP (PCP) by rotation in a plane across gear axis. An objective function is established by contrasting ECP to PCP. A program in Matlab language is developed for the simulation of objective function optimization. A spiral bevel gear drive in aviation accessory gear box is used to prove the feasibility of the proposed method. It shows that the method is effective and does not affect transmission errors very much for the realization of ECP.

Computerized Investigation of Real Tooth Contact Analysis of Face-milled Spiral Bevel Gears

2021 ◽  
Author(s):  
GuangLei Liu ◽  
Weidong Yan ◽  
Yao Liu
Keyword(s):  
Contact Analysis ◽  
Tooth Surface ◽  
Surface Boundary ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Gear Drive ◽  
Spiral Bevel ◽  
Manufacturing Parameters

Abstract Real tooth contact analysis of spiral bevel gears is based on the original tooth surface grids (OTSG) formed by coordinate measuring machine (CMM). Since the size of OTSG is smaller than the tooth surface, it is sometimes impossible to get full meshing information. Reverse engineering is a way to solve the problem. The basic idea is to expand OTSG to the tooth surface boundary by reversing the manufacturing parameters of the spiral bevel gear drive. Thus a generalized reversing objective is set up for both of the gear and the pinion, which is the summation of deviations of all nodes between OTSG and corresponding computational tooth surface grids (CTSG) expressed by manufacturing parameters. The gear manufacturing parameters are reversed by observing duplex method. The pinionmanufacturing parameters are reversed by attempting the meshing behavior taken as input to local synthesis with modified roll motion. The initial meshing behavior is approximately ascertained by discrete tooth contact analysis based on OTSG, and meshing behavior at the mean contact point is figured out by interpolation method for function of transmission errors and contact path. Having reversed the manufacturing parameters, OTSG is expanded to the tooth surface boundary and real tooth contact analysis is conducted. A zero bevel gear drive of an aviation engine was employed to demonstrate the validity of the proposed methodology. The proposed method makes the real tooth contact analysis practical and provides prospect to improve meshing behavior more precisely.

Quantitative Analysis of the Influence of Installation Errors on the Contact Pattern of Spiral Bevel Gears

2011 ◽  
Vol 86 ◽  
pp. 278-282
Author(s):  
Guang Lei Liu ◽  
Rui Ting Zhang ◽  
Ning Zhao
Keyword(s):  
Quantitative Analysis ◽  
Tooth Surface ◽  
Test Machine ◽  
Contact Pattern ◽  
Tooth Contact Analysis ◽  
Local Synthesis ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Contact Patterns ◽  
Spiral Bevel

A method—characteristic parameters analysis (CPA) is put forward, which is used for quantitative analysis of contact pattern of spiral bevel gears with installation errors. For forming the tooth surface of spiral bevel gears, local synthesis is used. To imitate rolling test machine, the pinion drive torque is calculated under the indentation depth 0.00635mm. Driven by this torque, the size, shape, location and variation of contact pattern are obtained by loaded tooth contact analysis (LTCA). A pair of aviation spiral bevel gears was taken to quantitatively analyze the various contact patterns under different installation errors. The results indicate that the contact pattern is more sensitive to pinion axis installation error.

Determination of Basic Machine-Tool Settings for Generation of Spiral Bevel Gears From Blank Data

2007 ◽  
Author(s):  
Alfonso Fuentes ◽  
Ignacio Gonzalez-Perez ◽  
Faydor L. Litvin ◽  
Kenichi Hayasaka ◽  
Kenji Yukishima
Keyword(s):  
Machine Tool ◽  
Analytical Determination ◽  
Generation Process ◽  
Local Synthesis ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Gear Drive ◽  
Spiral Bevel ◽  
Gear Machine

Many researchers and gear designers are applying their own methods to obtain appropriate machine-tool settings for each case of design, according to their own experience, manufacturing machines and type of generating process. In this paper, the analytical determination of basic machine-tool settings for generation of spiral bevel gears from blank data is proposed. Determination of gear machine-tool settings is carried out through an analytical procedure that will allow to obtain identities between gear machine-tool settings and blank data of the spiral bevel gear drive. In this work, the face-milling generation process has been considered. The blank data that have been considered are: number of teeth of the pinion and the gear, module, spiral and pressure angles, face width, shaft angle, depth factor, clearance factor, and mean addendum factor. These basic starting data are known or can be established following the directions of the Standard ANSI/AGMA 2005-D03. Once the basic gear machine-tool settings are determined, the existing approach of local synthesis is applied to determine the pinion machine-tool settings that provide the desired conditions of meshing and contact of the gear drive. The developed theory is illustrated with numerical examples.

Transient Thermal Analysis of Spiral Bevel Gears under Loss of Lubrication

2010 ◽  
Vol 34-35 ◽  
pp. 566-570 ◽  
Author(s):  
Yu Tao Yan ◽  
Zhi Li Sun ◽  
R.J. Guo
Keyword(s):  
Thermal Analysis ◽  
Finite Element ◽  
Normal Load ◽  
Gear Tooth ◽  
Tooth Surface ◽  
Transient Temperature ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Spiral Bevel

Based on loaded tooth contact analysis of spiral bevel gears, the thermal analysis model and finite element model of spiral bevel gears were established by making use of tribological theory and thermal transferring theory. The distribution on transient temperature field of spiral bevel gears under loss of lubrication was found via finite element methods. The results are as follows: the sliding speed and normal load had obvious influence on friction heat. Transient temperature peak value of the gear tooth was obtained in midpoint position of the tooth contact path. The temperature gradient increases with the increase of meshing times of gear tooth, the transient temperature of the gear tooth surface had increased 32°C in one minute. However, the transient temperature of the tooth surface had increased 232°C in three minutes.

scholarly journals Lubrication characteristics of gear after shot peening base on 25-pellet model

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401879065 ◽  
Author(s):  
Shuai Mo ◽  
Shengping Zhu ◽  
Guoguang Jin ◽  
Jiabei Gong ◽  
Zhanyong Feng ◽  
...  
Keyword(s):  
Shot Peening ◽  
High Speed ◽  
Target Material ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Spiral Bevel ◽  
Lubrication Characteristics

High-speed heavy-load spiral bevel gears put forward high requirement for flexural strength; shot peening is a technique that greatly improves the bending fatigue strength of gears. During shot peening, a large number of fine pellets bombard the surface of the metal target material at very high speeds and let the target material undergo plastic deformation, at the same time strengthening layer is produced. Spiral bevel gear as the object of being bombarded inevitably brought the tooth surface micro-morphology changes. In this article, we aim to reveal the effect of microtopography of tooth shot peening on gear lubrication in spiral bevel gear, try to establish a reasonable description of the microscopic morphology for tooth surface by shot peening, to reveal the lubrication characteristics of spiral bevel gears after shot peening treatment based on the lubrication theory, and do comparative research on the surface lubrication characteristics of a variety of microstructures.

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