scholarly journals Computerized Design of Low-Noise Face-Milled Spiral Bevel Gears

1994 ◽  
Author(s):  
F. L. Litvin ◽  
Yi Zhang ◽  
R. F. Handschuh
Keyword(s):  
Low Noise ◽  
Tooth Surface ◽  
Principal Curvatures ◽  
Surface Geometry ◽  
Local Synthesis ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Gear Drive ◽  
Geometry Design ◽  
Spiral Bevel

Abstract An advanced design methodology is proposed for the face-milled spiral bevel gears with modified tooth surface geometry that provides a reduced level of noise and has a stabilized bearing contact. The approach is based on the local synthesis of the gear drive that provides the “best” machine-tool settings. The theoretical aspects of the local synthesis approach are based on the application of a predesigned parabolic function for absorption of undesirable transmission errors caused by misalignment and the direct relations between principal curvatures and directions for mating surfaces. The meshing and contact of the gear drive is synthesized and analyzed by a computer program. The generation of gears with the proposed geometry design can be accomplished by application of existing equipment. A numerical example that illustrates the proposed theory is presented.

scholarly journals Surface Geometry of Circular Cut Spiral Bevel Gears

1982 ◽  
Vol 104 (4) ◽  
pp. 743-748 ◽  
Author(s):  
R. L. Huston ◽  
J. J. Coy
Keyword(s):  
Logarithmic Spiral ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Surface Geometry ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Spiral Bevel

An analysis of the surface geometry of spiral bevel gears formed by a circular cutter is presented. The emphasis is upon determining the tooth surface principal radii of curvature of crown (flat) gears. Specific results are presented for involute, straight, and hyperbolic cutter profiles. It is shown that the geometry of circular cut spiral bevel gears is somewhat simpler than a theoretical logarithmic spiral bevel gear.

Surface Geometry of Straight and Spiral Bevel Gears

1987 ◽  
Vol 109 (4) ◽  
pp. 443-449 ◽  
Author(s):  
Y. C. Tsai ◽  
P. C. Chin
Keyword(s):  
Mathematical Modeling ◽  
Tooth Surface ◽  
Surface Geometry ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Geometrical Characteristics ◽  
Spiral Bevel

The fundamental geometrical characteristics of bevel gears have been discussed in this study. The mathematical modeling of the tooth surface geometry of bevel gears can be developed based on the basic gearing kinematics and involute geometry along with the tangent planes geometry. The parametric representations of the spherical involute and the involute spiraloid, which are the tooth surface geometry of straight bevels and spiral bevels, respectively, have been derived in this paper. This study may provide some fundamentals for computer numerical controlled manufacturing of bevel gears.

Manufacture of Optimized Face-Hobbed Spiral Bevel Gears on Computer Numerical Control Hypoid Generator

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Machine Tool ◽  
Angular Displacement ◽  
Transmission Error ◽  
Numerical Control ◽  
Tooth Surface ◽  
Surface Geometry ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Spiral Bevel

In this study, a method is proposed for the advanced manufacture of face-hobbed spiral bevel gears on CNC hypoid generators with optimized tooth surface geometry. An optimization methodology is applied to systematically define optimal head-cutter geometry and machine tool settings to introduce optimal tooth modifications. The goal of the optimization is to simultaneously minimize tooth contact pressures and angular displacement error of the driven gear (the transmission error). The optimization is based on machine tool setting variation on the cradle-type generator conducted by optimal polynomial functions. An algorithm is developed for the execution of motions on the CNC hypoid generator using the relations on the cradle-type machine. Effectiveness of the method was demonstrated by using a face-hobbed spiral bevel gear example. Significant reductions in the maximum tooth contact pressure and in the transmission errors were obtained.

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.

scholarly journals Precision of Spiral-Bevel Gears

1983 ◽  
Vol 105 (3) ◽  
pp. 310-316 ◽  
Author(s):  
F. L. Litvin ◽  
R. N. Goldrich ◽  
J. J. Coy ◽  
E. V. Zaretsky
Keyword(s):  
Tooth Surface ◽  
Surface Geometry ◽  
Spiral Bevel Gears ◽  
Gear Teeth ◽  
Bevel Gears ◽  
Bearing Contact ◽  
Order Of Magnitude ◽  
Gear Trains ◽  
Spiral Bevel ◽  
Kinematic Errors

An analytical method was derived for determining the kinematic errors in spiral-bevel gear trains caused by the generation of nonconjugate surfaces, by axial displacements of the gear assembly, and by eccentricity of the assembled gears. Such errors are induced during manufacturing and assembly. Two mathematical models of spiral-bevel gears were included in the investigation. One model corresponded to the motion of the contact ellipse across the tooth surface (geometry I) and the other along the tooth surface (geometry II). The following results were obtained: 1) Kinematic errors induced by errors of manufacture may be minimized by applying special machine settings. The original error may be reduced by an order of magnitude. The procedure is most effective for geometry II gears. 2) When trying to adjust the bearing contact pattern between the gear teeth for geometry I gears, it is more desirable to shim the gear axially; for geometry II gears, shim the pinion axially. 3) The kinematic accuracy of spiral-bevel drives is most sensitive to eccentricities of the gear and less sensitive to eccentricities of the pinion. The pecision of mounting accuracy and manufacture is most crucial for the gear, and less so for the pinion.

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.

scholarly journals Parametric surface and properties defined on parallelogrammic domain

2014 ◽  
Vol 1 (1) ◽  
pp. 27-36 ◽  
Author(s):  
Shuqian Fan ◽  
Jinsong Zou ◽  
Mingquan Shi
Keyword(s):  
Mathematical Model ◽  
Logarithmic Spiral ◽  
Tooth Surface ◽  
Parametric Surface ◽  
Surface Geometry ◽  
Spiral Bevel Gears ◽  
Geometrical Properties ◽  
Bevel Gears ◽  
Geometrical Characteristics ◽  
Spiral Bevel

Abstract Similar to the essential components of many mechanical systems, the geometrical properties of the teeth of spiral bevel gears greatly influence the kinematic and dynamic behaviors of mechanical systems. Logarithmic spiral bevel gears show a unique advantage in transmission due to their constant spiral angle property. However, a mathematical model suitable for accurate digital modeling, differential geometrical characteristics, and related contact analysis methods for tooth surfaces have not been deeply investigated, since such gears are not convenient in traditional cutting manufacturing in the gear industry. Accurate mathematical modeling of the tooth surface geometry for logarithmic spiral bevel gears is developed in this study, based on the basic gearing kinematics and spherical involute geometry along with the tangent planes geometry; actually, the tooth surface is a parametric surface defined on a parallelogrammic domain. Equivalence proof of the tooth surface geometry is then given in order to greatly simplify the mathematical model. As major factors affecting the lubrication, surface fatigue, contact stress, wear, and manufacturability of gear teeth, the differential geometrical characteristics of the tooth surface are summarized using classical fundamental forms. By using the geometrical properties mentioned, manufactura-bility (and its limitation in logarithmic spiral bevel gears) is analyzed using precision forging and multi-axis freeform milling, rather than classical cradle-type machine tool based milling or hobbing. Geometry and manufacturability analysis results show that logarithmic spiral gears have many application advantages, but many urgent issues such as contact tooth analysis for precision plastic forming and multi-axis freeform milling also need to be solved in a further study.

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.

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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