Digital Conjugate of Tooth Surface of Logarithmic Spiral Bevel Gear

2014 ◽  
Vol 556-562 ◽  
pp. 1079-1082
Author(s):  
Qiang Li ◽  
Yun Long Diao
Keyword(s):  
Gear Tooth ◽  
Logarithmic Spiral ◽  
Bevel Gear ◽  
Conjugate Points ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Surface Meshing ◽  
Spline Fitting ◽  
Spiral Bevel ◽  
Surface Precision

Based on the surface of the envelope principle and the digital conjugate surface theory, The taper logarithm helical gear meshing theory further perfect. According to the mathematical model of logarithmic spiral bevel gear tooth surface meshing, using MATLAB powerful scientific analysis and calculation visual features and functions for the conjugate tooth surface equation to get the enveloping surface discrete conjugate points and draw out the conjugate tooth surface. Again through the optimization of surface get rid of the noise, end up with conjugate tooth surface precision, and can B spline fitting. Said for further analysis of spiral bevel gear drive are very valuable.

New Geometry of Generating Spiral Bevel Gear

2007 ◽  
Author(s):  
Kaihong Zhou ◽  
Jinyuan Tang ◽  
Tao Zeng
Keyword(s):  
Gear Tooth ◽  
Previous Method ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Surface Geometry ◽  
Numerical Examples ◽  
Cone Surface ◽  
Spiral Bevel ◽  
Involute Curve

New geometry of generating spiral bevel gear is proposed. The key idea of the new proposed geometry is that the gear tooth surface geometry can be investigated in a developed curved surface based on the planar engagement principle. It is proved that the profile curve on the back of generating cone surface is a conical involute curve. The equations of generated gear tooth surface are achieved by the conical involute curve sweeping along the tooth trace of gear. The obtained equations are explicit and independent of the machine-tool settings. This differs from previous studies. The developed theory is illustrated with numerical examples to compare with the previous method, the comparison approves that the method is possible in this way. The new method indicates that there are new solutions to the design the production of spiral bevel gear.

A New Method of Constructing Tooth Surface for Logarithmic Spiral Bevel Gear

2010 ◽  
Vol 129-131 ◽  
pp. 235-240 ◽  
Author(s):  
Qiang Li ◽  
Zi Liang Wei ◽  
Hong Bo Yan ◽  
Hai Yan Hu
Keyword(s):  
Logarithmic Spiral ◽  
Strength Distribution ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Surface Equation ◽  
Complex Curves ◽  
Logarithmic Spirals ◽  
Cone Surface ◽  
Spiral Bevel

For a new type of bevel gear—logarithmic spiral bevel gear, establish its tooth direction curves and the mathematical model of tooth surface equation. With CAD software platform which can intuitive understanding of complex curves and combined with conical logarithmic spiral parameter equation build the logarithmic spiral on cone surface. Then array logarithmic spiral to make them evenly distributed in the cone surface, without any interference and to meet the strength distribution on both ends of circular truncated cone equally. Use two logarithmic spirals from different starpoint as tooth direction curves of lift and right tooth surface. Finally, use space geometric knowledge to build tooth surface equation by tooth direction curves and tooth profile curves.

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.

Digital Precision Measuring of Spiral Bevel Gear Based on CAD/CAM/CMM

2007 ◽  
Vol 339 ◽  
pp. 158-162 ◽  
Author(s):  
Wei Min Pan ◽  
Ji Shun Li ◽  
Y. Lei
Keyword(s):  
Manufacturing Industry ◽  
Gear Tooth ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Cad Model ◽  
Machining Parameters ◽  
Precision Measuring ◽  
Cad Cam ◽  
Spiral Bevel

Precision measuring techniques have been developed interdependently with the techniques of design and manufacturing in the history. Computer aided inspection plays a very important role in modern manufacturing industry. On account of the CMM (Coordinates Measurement Machine) being applied widely and the precision model inspection concept coming true, it is possible to implement the digital inspection of the spiral bevel gear on the CMM. In this paper the framework of the spiral bevel gear digital inspection based on the integration of CAD/CAM/CMM is put forward. The key techniques of the scheme are investigated, which consist of exact modeling of spiral bevel gear based on manufacturing process, datum matching of CAD model and CMM inspection, CMM Inspection path planning, reconstruction of the tooth surface based on the CMM inspection results, Analysis of the deviation between the real gear tooth and CAD model, adjusting strategy of machining parameters.

Logarithmic Spiral Bevel Gear Tooth Contact Inspection

2010 ◽  
Vol 44-47 ◽  
pp. 1345-1349
Author(s):  
Qiang Li ◽  
Wen He ◽  
Hong Bo Yan ◽  
Hong Xiang Zhang
Keyword(s):  
Contact Area ◽  
Detection Method ◽  
Gear Tooth ◽  
Logarithmic Spiral ◽  
Bevel Gear ◽  
Spiral Bevel Gear ◽  
Tooth Contact ◽  
Ideal Number ◽  
Spiral Bevel ◽  
Gear Contact

Introduction of spiral bevel gear tooth contact detection method, detection method based on the principle of EPG in the Y9550-type bevel gear roll tester on a pair of spiral bevel gear tooth contact area of sample detection experiment, obtained by experiment logarithmic spiral bevel gear contact area of the location, shape and size of the result. The experimental results with the Gleason spiral bevel gear contact area and the ideal number of spiral bevel gears on the contact area were compared, obtained on the number of spiral bevel gear tooth contact of the correlation.

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.

Error Analysis of the Tooth Surface of Logarithmic Spiral Bevel Gear

2013 ◽  
Vol 19 (7) ◽  
pp. 2003-2006
Author(s):  
Qiang Li ◽  
Wen Kong ◽  
Hongbo Yan
Keyword(s):  
Error Analysis ◽  
Logarithmic Spiral ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Spiral Bevel

Research on Curvature of Tooth Flank of Gleason Spiral Bevel Gears

2011 ◽  
Vol 189-193 ◽  
pp. 4256-4260
Author(s):  
Ai Mei Zhang ◽  
Lin Yan Li ◽  
Da Wei Li
Keyword(s):  
Mean Curvature ◽  
Gear Tooth ◽  
Three Dimensional ◽  
Processing Parameters ◽  
Bevel Gear ◽  
Machining Process ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Tooth Surfaces ◽  
Spiral Bevel

According to spiral bevel gear machining process, use the method of computer simulation to get the discrete points’ three-dimensional coordinates of Gleason spiral bevel gear tooth surface, and then solve the tooth surfaces’ NURBS surface as the unified mathematical model. On this basis, research the curvature of tooth surfaces of various types of Gleason spiral bevel gear, draw the mean curvature diagram, and study the link between the adjustment of processing parameters and the change of tooth surfaces’ mean curvature. Establish a theoretical foundation for the processing error adjustment based on tooth surface’s curvature diagram.

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.

An Improved Method of Solving Contact Trajectory Boundary for Spiral Bevel Gear

2012 ◽  
Vol 490-495 ◽  
pp. 1971-1975
Author(s):  
Wei Wei
Keyword(s):  
Gear Tooth ◽  
Contact Point ◽  
Initial Point ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Initial Value ◽  
Step Size ◽  
Vector Operation ◽  
Spiral Bevel

A method of solving contact trajectory boundary is developed for spiral bevel gear. Tooth surfaces of pinion and gear are projected to axial cross section based on rotation transformation, vector operation is used to distinguish whether contact point belongs to tooth surface or not. Distances between contact point and every boundary of tooth surface are calculated, if the minimum distance is less than preset value, this contact point is considered to be contact trajectory boundary. Starting from initial point of TCA, contact point approaches contact trajectory boundary by adaptive step size, when currently step size is greater than preset step size, the value of the last contact point is used as initial value for new contact point, otherwise initial value is calculated by particle swarm optimization with penalty function, this method can improve the solving speed greatly while keeping stable. Finally, the validity and practicability of this method are proved by a numerical example.

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