Envelope-approximation theory of manufacture technology for point-contact tooth surface on six-axis CNC hypoid generator

2011 ◽  
Vol 46 (6) ◽  
pp. 806-819 ◽  
Author(s):  
Zhou Kaihong ◽  
Tang Jinyuan
Keyword(s):  
Approximation Theory ◽  
Point Contact ◽  
Tooth Surface ◽  
Manufacture Technology

Optimal Tooth Modifications in Hypoid Gears

2004 ◽  
Vol 127 (4) ◽  
pp. 646-655 ◽  
Author(s):  
Vilmos Simon
Keyword(s):  
Load Distribution ◽  
Angular Position ◽  
Point Contact ◽  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Transmission Errors ◽  
Tool Profile

A method for the determination of optimal tooth modifications in hypoid gears based on improved load distribution and reduced transmission errors is presented. The modifications are introduced into the pinion tooth surface by using a cutter with bicircular profile and optimal diameter. In the optimization of tool parameters the influence of shaft misalignments of the mating members is included. As the result of these modifications a point contact of the meshed teeth surfaces appears instead of line contact; the hypoid gear pair becomes mismatched. By using the method presented in (Simon, V., 2000, “Load Distribution in Hypoid Gears,” ASME J. Mech. Des., 122, pp. 529–535) the influence of tooth modifications introduced on tooth contact and transmission errors is investigated. Based on the results that was obtained the radii and position of circular tool profile arcs and the diameter of the cutter for pinion teeth generation were optimized. By applying the optimal tool parameters, the maximum tooth contact pressure is reduced by 16.22% and the angular position error of the driven gear by 178.72%, in regard to the hypoid gear pair with a pinion manufactured by a cutter of straight-sided profile and of diameter determined by the commonly used methods.

Optimal Tooth Modifications in Hypoid Gears

2003 ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Angular Position ◽  
Point Contact ◽  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Transmission Errors ◽  
Tool Profile

A method for the determination of optimal tooth modifications in hypoid gears based on improved load distribution and reduced transmission errors is presented. The modifications are introduced into the pinion tooth surface by using a cutter with bicircular profile and by changing the cutter diameter. In the optimization of tool parameters the influence of shaft misalignments of the mating members is included. As the result of these modifications a point contact of the meshed teeth surfaces appears instead of line contact; the hypoid gear pair becomes mismatched. By using the method presented in [1] the influence of tooth modifications introduced on tooth contact and transmission errors is investigated. Based on the results that was obtained the radii and position of circular tool profile arcs and the cutter diameter for pinion teeth generation were optimized. By applying the optimal tool parameters, the maximum tooth contact pressure is reduced by 16.22% and the angular position error of the driven gear by 178.72%, in regard to the hypoid gear pair with a pinion manufactured by a cutter of straight-sided profile and of diameter determined by the commonly used methods.

New CNC Machining Method for Sculptured Surface Using Non-Ball-End Tools

2012 ◽  
Vol 628 ◽  
pp. 469-475
Author(s):  
Kai Hong Zhou ◽  
Dian Ting Liu
Keyword(s):  
Differential Geometry ◽  
Approximation Theory ◽  
Cnc Machining ◽  
Moving Frame ◽  
Sculptured Surface ◽  
Machining Efficiency ◽  
Manufacture Technology ◽  
Machining Quality ◽  
Tool Surface ◽  
Optimized Model

In current multi-axis CNC manufacture technology, the sculptured surface has to be approximated to simplify its complexity, therefore, the current machining methods can not fully exploit the flexibility of the multi-axis CNC tools and offer the prospect of higher machining efficiency and better machining quality. A new theory (Envelope-Approximation Theory) was presented to generate the sculptured surface by maximizing the machined strip width based on the moving frame. The differential geometry based on the idea of the moving frame was discussed to determine the related motion of the tool and the workpiece. The optimized model of the related motion of the tool was established to enable the envelope of the tool surface approximate to the predesigned surface aiming at the least warping. Simulated examples based on Matlab7.0 demonstrate the improved machining efficiency and precision of the Envelope-Approximation Theory over current published methods.

Gear-Cutting Method of Parallel Depth Hypoid Gears

2003 ◽  
Author(s):  
Akira Homma ◽  
Sumio Hirokawa ◽  
Akira Yamamoto
Keyword(s):  
Angular Velocity ◽  
Velocity Ratio ◽  
Point Contact ◽  
Constant Angular Velocity ◽  
Tooth Surface ◽  
Cutting Method ◽  
Hypoid Gears ◽  
The Third ◽  
Gear Cutting ◽  
Red Lead

The purpose of this study is to develop a gear-cutting method of hypoid gears to achieve a good tooth bearing and good performance for practical use. In this report, the authors propose a new cutting method of parallel depth hypoid gears, which mesh with each other at one point keeping a constant angular velocity ratio, and describe the theory for the gear-cutting method. Next, the theory of the trace of the point contact mark is shown. One of the features of this method is that the designer can control the trace of the point contact mark on the tooth surface as desired. The third, the theory of the ellipse of tooth bearing is shown minutely. In order to confirm the validity of the method, some hypoid gears were designed and manufactured, and ellipse of tooth bearing on red lead corresponded to those of the theory.

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.

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.

scholarly journals The Mathematical Model of Curve-Face Gear and Time-Varying Meshing Characteristics of Compound Transmission

2021 ◽  
Vol 11 (18) ◽  
pp. 8706
Author(s):  
Yanan Hu ◽  
Chao Lin ◽  
Shuo Li ◽  
Yongquan Yu ◽  
Chunjiang He ◽  
...  
Keyword(s):  
Screw Theory ◽  
Point Contact ◽  
Transmission Ratio ◽  
Tooth Surface ◽  
Time Varying ◽  
Gear Pair ◽  
Surface Geometry ◽  
Face Gear ◽  
Meshing Characteristics ◽  
Curve Face

The curve-face gear pair is a new type of gear pair with variable transmission ratio for spatial finite helical motion. In this paper, mathematical models of a new developed curve-face gear were simplified and obtained directly by the standard shaper. The subsequent studies on the curve-face gear compound transmission characteristics were further analyzed by the combinations of the principle of space gearing and screw theory. Firstly, the conjugate tooth surface geometry as well the point contact traces of curve-face gears were derived. Secondly, the geometric relationships between gear pair and the corresponding meshing characteristics were evaluated by several basic geometric elements, including instantaneous screw, axodes, striction curve, and conjugate pitch surface. Based on that analysis, it was found that the tooth contact normal was reciprocal to the instantaneous twist, which demonstrated that the conjugate motion with the desired transmission ratio could be realized in current curve-face gear compound transmission. Moreover, the time-varying slip characteristics of the curve-face gear pair were also revealed, that is, rolling and sliding action coexist at all contact on the tooth surfaces. In brief, this work provided the theoretical basis for following researches on machining curve-face gear with standard shaper.

Function-Oriented Designing and Generating Technology for the Point-Contact Tooth Surfaces of Spiral Bevel and Hypoid Gears

2008 ◽  
Vol 44-46 ◽  
pp. 495-502 ◽  
Author(s):  
Xun Cheng Wu ◽  
Cong Li ◽  
Ruo Ping Zhang ◽  
Hai Bo Zhang
Keyword(s):  
Point Contact ◽  
Transmission Function ◽  
Tooth Surface ◽  
Free Form ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Contact Points ◽  
Tooth Surfaces ◽  
Spiral Bevel ◽  
Basic Equations

A function-oriented designing and generating technology for the point-contact tooth surfaces of spiral bevel and hypoid gears is introduced. The tooth surface parameters are determined directly with the designing variables of the instantaneous transmission function, the locus of tooth contact points and the tooth contact ellipse dimension to design the point-contact tooth surfaces with the expected performances. The formulae for designing are provided. The designed tooth surfaces are generated with the free-form bevel gear machine, and the basic equations and formulae for the four-axis generating of the tooth surfaces are presented. The generating motions are expressed as the functions of the work gear rotary angle, which is taken as a motion parameter. The methods to determine the motion functions and the other machine setting parameters are explained through an example.

Tooth Profile Generation of Point-Contact Involute Planetary Gear Drive with Small Teeth Difference

2013 ◽  
Vol 441 ◽  
pp. 561-567 ◽  
Author(s):  
Wen Cui Yi ◽  
Bao Ying Wang ◽  
Shu He
Keyword(s):  
Three Dimensional ◽  
Point Contact ◽  
Planetary Gear ◽  
Smooth Curve ◽  
Tooth Surface ◽  
Three Dimensional Model ◽  
Gear Drive ◽  
Tooth Surfaces ◽  
Meshing Characteristics ◽  
Internal Gear

A new kind of involute planetary gear drive with small teeth difference which meshes in point contact is put forward based on the kinematic method of gear geometry in this paper. The generation principle of tubular tooth surface is proposed according to a selected smooth curve attached to the planetary wheel tooth surface. The general equations of conjugate tooth surfaces are derived and its conjugated contact curve on the internal gear is also determined. Then the mathematical model is established. The parameter selection and meshing characteristics of point-contact involute planetary gear drive with small teeth difference are discussed respectively. The three dimensional model is finally established and its motion simulation is worked out. It lays the significant theoretical foundation and practical meaning for improving the gear transmission performance.

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