Tooth flank reconstruction and optimizations after simulation process modeling for the spiral bevel gear

2015 ◽  
Vol 230 (13) ◽  
pp. 2260-2272 ◽  
Author(s):  
Ding Han ◽  
Tang Jin-yuan ◽  
Zhou Zhen-yu ◽  
Cui Wei
Keyword(s):  
Process Modeling ◽  
Bevel Gear ◽  
Least Square ◽  
Spiral Bevel Gear ◽  
Simulation Process ◽  
Spline Fitting ◽  
Fitting Method ◽  
Spiral Bevel ◽  
Tooth Flank ◽  
Design And Manufacture

Tooth flank reconstruction and optimization methodologies after simulation process modeling are presented, in order to provide accurate model and tooth data for digitized design and manufacture of the spiral bevel gear. Firstly, a simulation process modeling utilizing universal machine settings is developed for an initial solid model. Then, due to its poor accuracy, tooth flank reconstruction exploiting the Non-Uniform B-Spline fitting method is carried out. Finally, some tooth flank optimizations are introduced for higher tooth flank precision and accurate tooth data: (1) Overall tooth flank interpolations based on the Energy method; (2) Tooth flank approximation based on the least square (LSQ); (3) Tooth flank parameterization based on the Newton Iteration method. Results obtained from some numerical examples indicate that validation of the proposed approaches and tooth flank form error is significantly reduced.

scholarly journals Angular velocity and contact force simulation of the spiral bevel gear meshing based on the hertz contact theory

2019 ◽  
Vol 39 (2) ◽  
pp. 148-156
Author(s):  
Lizhi Gu ◽  
Tieming Xiang ◽  
Can Zhao ◽  
Shuailiang Guo
Keyword(s):  
Angular Velocity ◽  
Contact Force ◽  
Tangential Component ◽  
Bevel Gear ◽  
Contact Theory ◽  
Spiral Bevel Gear ◽  
Hertz Contact ◽  
Bevel Gears ◽  
Spiral Bevel ◽  
Tooth Flank

To obtain the change tendency of the wheel’s angular velocity and tangential component of contact force with time of the pinion under the step input during spiral bevel gear meshing, the tooth flank equation of spiral bevel gear was constructed based on the Non-Uniform Rational B-splines curve. The three-dimensional model of the pinion and the wheel were built based on the tooth flank equation. The calculation equation and relative parameters set for the contact force of spiral bevel gear meshing were done based on the Hertz contact theory. A mating of spiral bevel gears was taken as an example for dynamics simulation and the simulation results show that the relative error rate of the angular velocity between simulation and theoretical calculation is 0.054%, and that the relative error rate of tangential component of the contact force between simulation and theoretical calculation is 4.82%. These findings provide the theoretical basis for dynamic characteristics optimization of the spiral bevel gears.

scholarly journals Cutter Head Approximation Machining Method of Line Contact Spiral Bevel Gear Pairs Based On Controlling Topological Deviations

2021 ◽  
Author(s):  
Mingyang Wang ◽  
Yuehai Sun
Keyword(s):  
Simulation Analysis ◽  
Gear Tooth ◽  
Bevel Gear ◽  
Spiral Bevel Gear ◽  
Line Contact ◽  
Bevel Gears ◽  
Spiral Bevel ◽  
Tooth Flank ◽  
Cutter Head ◽  
The Mathematical Model

Abstract To improve the meshing performance and increase the bearing capacity and service life of spiral gear pairs, the cutter head approximation machining method based on controlling topological deviations was proposed to solve the problem where line contact spiral bevel gears with tapered teeth depth cannot be directly machined by cutter heads. First, the mathematical model of line contact conjugate flanks was established, and meshing equations and conjugate flank equations of bevel gear pairs were derived. Second, the gear tooth flank was set as the datum tooth flank for priority machining, and the pinion theoretical tooth flank which is fully conjugate with the gear tooth flank and the pinion machining tooth flank matching with the gear were solved. Then, the geometric topological deviations model of the comparison between the pinion machining tooth flank and its theoretical tooth flank can be established. Finally, with the pinion machining tooth flank approaching its theoretical tooth flank as the modification, the additional cutting motions and machining compensation parameters of cutter heads were obtained to control the pinion machining tooth flank deviations and reduce them to the allowable deviations of its theoretical tooth flank. The contact simulation analysis and rolling test verified the correctness of the line contact conjugate flank model and feasibility of the cutter head approximation machining method.

Characterization of Global Form Deviations for Spiral Bevel Gear and Correction of Machine-Setting Parameters

2011 ◽  
Vol 130-134 ◽  
pp. 616-620
Author(s):  
Zhong Si Xu ◽  
Lei Jin ◽  
Jin Tai Tian
Keyword(s):  
Least Square Method ◽  
Bevel Gear ◽  
Least Square ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Machining Accuracy ◽  
Global Form ◽  
Machine Setting ◽  
Spiral Bevel ◽  
Setting Parameters

In order to improve the machining accuracy of spiral bevel gear, difference surface was adopted to characterize its global form deviations quantifiably and correct its deviations. The quantitative mathematical relationship between the actual tooth surface deviations of spiral bevel gear and the corrected values of the machine-setting parameters had been referred, and the theoretical correction formula of the global form deviations had been gotten by the least square method. Finally, the pinion of spiral bevel gear in the automobile rear axle has been set for an example to account for the effectiveness of the deviation correction by use of the difference surface method.

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.

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