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.

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.

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.

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.

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.

Designing and Manufacturing Spiral Bevel Gears Using 5-Axis CNC Milling Machines

2011 ◽  
Author(s):  
Joe¨l Teixeira Alves ◽  
Miche`le Guingand ◽  
Jean-Pierre de Vaujany
Keyword(s):  
Manufacturing Process ◽  
Gear Tooth ◽  
Bevel Gear ◽  
Spiral Bevel Gear ◽  
Milling Machine ◽  
Cnc Milling ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Spiral Bevel

The design of spiral bevel gears still remains complex since tooth geometry and the resulting kinematics performance stem directly from the manufacturing process. Spiral bevel gear manufacture owes most to the works of Gleason and Klingelnberg. However, recent advances in milling machine technology and CAM (Computer Aided Manufacturing) make it possible to manufacture good quality spiral bevel gears on a standard 5-axis milling machine. This paper describes the CAD definition and manufacturing of spiral bevel gear tooth surfaces. Process performance is assessed by comparing the resulting surfaces after machining with the pre-defined CAD surfaces. Using this manufacturing process allows to propose new type of geometry. This one is more theoretical and, in some respects, easier to design than the standard spiral bevel gear as it enables simpler mesh optimization. The latter can be achieved by using the model of meshing under load recalled in this paper.

Research on Spiral Bevel Gear NC Machining Control Method

2014 ◽  
Vol 621 ◽  
pp. 549-557
Author(s):  
Kai Liu ◽  
Bo Liang Xu ◽  
Fang Li ◽  
Yang Wei Wang
Keyword(s):  
Control Method ◽  
Gear Tooth ◽  
Nc Machining ◽  
Bevel Gear ◽  
Spiral Bevel Gear ◽  
Tooth Contact Analysis ◽  
Parametric Curve ◽  
Gear Cutting ◽  
Tooth Surfaces ◽  
Spiral Bevel

Based on spiral bevel gear NC manufacture principle and generating motion of the generating gear and the work gear, the NC generation of spiral bevel gear cutting is realized by means of the vector transformation. As sophisticated calculation of the transformation is hard to implement in each interpolation cycle of NC machining, the coordinated motion of NC coordinate axes is expressed as quintic parametric spline functions, which use the rotation angle of the work gear as the parameter. The constrained optimization method of three design variables is established to obtain contacting points of gear tooth surfaces, which are acquired by solving nonlinear equations sets traditionally. The condition of normal coincidence is simplified and the object function of the equal position vectors of mating gears is established. The contacting points of gear tooth surfaces can be used for tooth contact analysis. The parametric curve interpolator is combined with spiral bevel gear NC machining, and is applied to the self-developed spiral bevel gear NC milling machine to control the gear cutting. Experimental results show that the proposed method is feasible and effective in the control of NC machining for the spiral bevel gear.

scholarly journals Application of the Bilateral Filter for the Reconstruction of Spiral Bevel Gear Tooth Surfaces From Point Clouds

2020 ◽  
Vol 143 (5) ◽  
Author(s):  
Ignacio Gonzalez-Perez ◽  
Pedro L. Guirao-Saura ◽  
Alfonso Fuentes-Aznar
Keyword(s):  
Gear Tooth ◽  
Maximum Level ◽  
Bilateral Filter ◽  
Point Clouds ◽  
Bevel Gear ◽  
Spiral Bevel Gear ◽  
Tooth Contact Analysis ◽  
Contact Patterns ◽  
Tooth Surfaces ◽  
Spiral Bevel

Abstract Reconstruction of gear tooth surfaces from point clouds obtained by noncontact metrology machines constitutes a promising step forward not only for a fast gear inspection but also for reverse engineering and virtual testing and analysis of gear drives. In this article, a new methodology to reconstruct spiral bevel gear tooth surfaces from point clouds obtained by noncontact metrology machines is proposed. The need of application of a filtering process to the point clouds before the process of reconstruction of the gear tooth surfaces has been revealed. Hence, the bilateral filter commonly used for 3D object recognition has been applied and integrated in the proposed methodology. The shape of the contact patterns and the level of the unloaded functions of transmission errors are considered as the criteria to select the appropriate settings of the bilateral filter. The results of the tooth contact analysis of the reconstructed gear tooth surfaces show a good agreement with the design ones. However, stress analyses performed with reconstructed gear tooth surfaces reveal that the maximum level of contact pressures is overestimated. A numerical example based on a spiral bevel gear drive is presented.

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.

The Measurement and Evaluation Method of Global Error of Spiral Bevel Gear

2011 ◽  
Vol 204-210 ◽  
pp. 1299-1304 ◽  
Author(s):  
Hua Zhao ◽  
Piao Sheng
Keyword(s):  
Evaluation Method ◽  
Gear Tooth ◽  
Bevel Gear ◽  
Global Error ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Spiral Bevel ◽  
The Difference ◽  
Measurement And Evaluation ◽  
3D Solid

This paper offers a method of spiral bevel gear’s global error measurement and evaluation based on three-coordinate measurement according to the characteristics of spiral bevel gear. The 3d solid modeling built in UG was regarded as the gear’s ideal factor of measure and error evaluation; the values of the measured points in the real gear tooth surface by CMM were regarded as the gear’s real factor. The global error of spiral bevel gear was reflected by the difference surface which was fitted by the deviation between real tooth surface and theoretical tooth surface. This method is very effective and feasible by measuring and evaluating the automobile rear axle’s driven gear.

scholarly journals Compensation Method for Inclination Errors in Measurement Results of Tooth Surface of Spiral Bevel Gear

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Yongsheng Liu ◽  
Suping Fang ◽  
Yixin Chen ◽  
Jianye Zhang
Keyword(s):  
Machine Tool ◽  
Gear Tooth ◽  
Great Influence ◽  
Bevel Gear ◽  
Surface Measurement ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Measurement Results ◽  
Measuring Machine ◽  
Spiral Bevel

The manufacturing error of spiral bevel gear tooth surface has a great influence on transmission efficiency and gear life. The error of the gear tooth surface needs to be measured accurately and fed back to the machine tool to adjust the parameters. When measuring the spiral bevel gear using a gear measuring machine, combined with the measurement theory of the tooth flank of spiral bevel gear, this paper proposed a method to compensate the inclination error in the measurement result precisely. Based on the iterative search method, a precision matching method for the theoretical and the measured tooth surface of the spiral bevel gear was designed to calculate the compensation results. The experimental results show that the inclination errors included in tooth surface measurement results reduced from more than 3 μm to less than 0.5 μm, and more than 70% of the errors are compensated by the proposed method. The accuracy of the measurement results improved significantly after compensation, and furthermore, it can provide a more accurate basis for the adjustment of machine tool parameters in the manufacturing process.

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