A Lengthwise Modification for Face-Hobbed Straight Bevel Gears

2013 ◽  
Author(s):  
Yi-Pei Shih
Keyword(s):  
Tool Path ◽  
Point Contact ◽  
Contact Condition ◽  
Tooth Contact Analysis ◽  
High Productivity ◽  
Accuracy Requirement ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Gear Contact ◽  
Straight Line Mechanism

Face hobbing has been successfully applying in manufacturing straight bevel gears using a virtual hypocycloidal straight-line mechanism. This method is a continuous indexing and double-flank cutting process, and is recognized its high productivity and precision. In order to improve gear contact condition, three types of flank modifications are frequently used in gear industry: profile crowning, lengthwise crowning, and longitudinal twist. In the design of the spiral bevel and hypoid gear, under satisfying a specified accuracy requirement, three types of modifications are blended properly during gear design to absorb assembly and manufacture errors. Circular cutter blades are normally adopted to accomplish the first type modification. The second can be achieved by a cutter radius change or a cutter tilt with adjusted pressure angles. The last can be achieved by a cutter tilt or modified tool path (for example, helical motion and modified roll). This paper proposes a lengthwise crowning method for face-hobbed straight bevel gear (SBG) using a hypocycloidal mechanism. This modification is applied to the pinion only. A numerical example drive with point-contact tooth surfaces is adopted to validate the proposed mathematical model. Finally, two evaluations, ease-off topography and tooth contact analysis (TCA), are made to investigate the contact condition of this numerical case.

Mathematical Model for Face-Hobbed Straight Bevel Gears

2012 ◽  
Vol 134 (9) ◽  
Author(s):  
Yi-Pei Shih
Keyword(s):  
Mathematical Model ◽  
Bevel Gear ◽  
Tooth Contact Analysis ◽  
Rolling Circle ◽  
High Productivity ◽  
Bevel Gears ◽  
Straight Line ◽  
Base Circle ◽  
Straight Line Mechanism ◽  
Straight Lines

Face hobbing, a continuous indexing and double-flank cutting process, has become the leading method for manufacturing spiral bevel gears and hypoid gears because of its ability to support high productivity and precision. The method is unsuitable for cutting straight bevel gears, however, because it generates extended epicycloidal flanks. Instead, this paper proposes a method for fabricating straight bevel gears using a virtual hypocycloidal straight-line mechanism in which setting the radius of the rolling circle to equal half the radius of the base circle yields straight lines. This property can then be exploited to cut straight flanks on bevel gears. The mathematical model of a straight bevel gear is developed based on a universal face-hobbing bevel gear generator comprising three parts: a cutter head, an imaginary generating gear, and the motion of the imaginary generating gear relative to the work gear. The proposed model is validated numerically using the generation of face-hobbed straight bevel gears without cutter tilt. The contact conditions of the designed gear pairs are confirmed using the ease-off topographic method and tooth contact analysis (TCA), whose results can then be used as a foundation for further flank modification.

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.

Assembly interference and its avoidance of spiral bevel gears in cyclo-palloid system

2019 ◽  
Vol 234 (2) ◽  
pp. 704-717
Author(s):  
Isamu Tsuji ◽  
Kazumasa Kawasaki
Keyword(s):  
Contact Analysis ◽  
Experimental Results ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Spiral Bevel ◽  
Good Agreement

In this article, the assembly interference of spiral bevel gears in a Klingelnberg cyclo-palloid system is analyzed based upon tooth contact analysis and is investigated experimentally. Each backlash in increasing mounting distance of the pinion is calculated step by step, using developed tooth contact analysis. When the backlash increases, the assembly interference does not occur based upon the calculated results. When the backlash decreases and is less than zero, the assembly interference occurs. When the assembly interference occurs, the tooth surfaces should be modified in order to prevent the assembly interference. In this case, a method of the modification is proposed. The experimental results showed a good agreement with the analyzed ones. As a result, the validity of the analysis and avoidance of the assembly interference in this method was confirmed.

Load Distribution in Spiral Bevel Gears

2006 ◽  
Vol 129 (2) ◽  
pp. 201-209 ◽  
Author(s):  
Vilmos Simon
Keyword(s):  
Load Distribution ◽  
Point Contact ◽  
Design Data ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Gear Teeth ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Machine Theory ◽  
Spiral Bevel

A new approach for the computerized simulation of load distribution in mismatched spiral bevel gears with point contact is presented. The loaded tooth contact is treated in a special way: it is assumed that the point contact under load spreads over a surface along the “potential” contact line (Simon, 2006, Mech. and Machine Theory, in press), which line is made up of the points of the mating tooth surfaces in which the separations of these surfaces are minimal, instead of assuming the usually applied elliptical contact area. The bending and shearing deflections of gear teeth, the local contact deformations of mating surfaces, gear body bending and torsion, the deflections of supporting shafts, and the manufacturing and alignment errors of mating members are included. The tooth deflections of the pinion and gear teeth are calculated by the finite element method. As the equations governing the load sharing among the engaged tooth pairs and load distribution along the tooth face are nonlinear, an approximate and iterative technique is used to solve this system of equations. The method is implemented by a computer program. By using this program the load and tooth contact pressure distributions, the angular displacements of the driven gear and the stresses in the pinion and gear teeth are calculated. The influence of design data and transmitted torque on load distribution parameters and fillet stresses is investigated and discussed.

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.

Analysis of Transmission Errors Under Load of Helical Gears With Modified Tooth Surfaces

1997 ◽  
Vol 119 (1) ◽  
pp. 120-126 ◽  
Author(s):  
Y. Zhang ◽  
Z. Fang
Keyword(s):  
Rigid Bodies ◽  
Contact Load ◽  
Tooth Contact Analysis ◽  
Helical Gears ◽  
Transmission Errors ◽  
Proposed Model ◽  
Tooth Surfaces ◽  
Simulation Results ◽  
Meshing Characteristics ◽  
Gear Contact

This paper presents a model for the analysis of transmission errors of helical gears under load. The model accommodates the modification of tooth surfaces, gear misalignments and the deformation of tooth surfaces caused by contact load. In this model, the gear contact load is assumed to be nonlinearly distributed along the direction of the relative principal curvature between the two contacting tooth surfaces. As compared with conventional tooth contact analysis (TCA) that assumes gear surfaces as rigid bodies, the model presented in this paper provides more realistic simulation results on the gear transmission errors and other gear meshing characteristics when the tooth surfaces are deformed under load. The proposed model is applied to a pair of helical gears in the numerical example included in the paper.

A Novel Lengthwise Crowning Method for Face-Hobbed Straight Bevel Gears

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Yi-Pei Shih
Keyword(s):  
Mathematical Model ◽  
Numerical Control ◽  
High Productivity ◽  
Bevel Gears ◽  
Cutting Machine ◽  
Performance Indexes ◽  
Tooth Surfaces ◽  
Recent Addition ◽  
Machine Setting ◽  
The Many

A recent addition to the many milling processes used in manufacturing to cut straight bevel gears (SBGs) is a new face-hobbing (FH) method that uses a virtual hypocycloid straight-lined mechanism to produce straight-lined teeth. Despite earning much attention because of its high productivity, however, this method is unable to handle lengthwise crowning on tooth surfaces, which results in poor contact performance. This paper therefore proposes a novel lengthwise crowning method, applicable on a modern six-axis computer numerical control (CNC) bevel gear cutting machine, in which the gear blank performs a swinging motion during machining. This swinging motion is enabled by machine setting modifications, which here are derived from a mathematical model of a double (profile and lengthwise) crowned gear. After the model's correctness is confirmed using ease-off and tooth contact analyses, a final investigation examines the effect of two key parameters related to contact performance indexes whose interrelations are graphed to provide a designer reference.

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.

Research on Simulating and Modeling Method for Spiral Bevel Gears with Actively Controllable Contact Patterns

2010 ◽  
Vol 431-432 ◽  
pp. 146-149
Author(s):  
Bin Yao ◽  
De Yun Zhang ◽  
Shi Min Mao
Keyword(s):  
Modeling Method ◽  
Work Condition ◽  
Modified Model ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Modeling Process ◽  
Contact Patterns ◽  
Tooth Surfaces ◽  
Spiral Bevel ◽  
Gear Contact

An innovative modeling method of spiral bevel gear is presented in detail for actively controllable contact patterns. Firstly the 3D model gear of is given, and then creates its modified model by analyzing the contact patterns of work condition. Lastly, being based upon meshing theory, the modified gear moves relatively to the pinion blank, and simultaneously carries out Boolean Subtracting on the pinion blank, which is the modeling process of a pinion’s tooth surfaces. With this method, modeling of spiral bevel gears is more convenient to get, and gear contact patterns is easier to control actively.

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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