Mathematical Model and Surface Deviation of Helipoid Gears Cut by Shaper Cutters

2003 ◽  
Vol 125 (2) ◽  
pp. 351-355 ◽  
Author(s):  
Jun-Long Wu ◽  
Chia-Chang Liu ◽  
Chung-Biau Tsay ◽  
Shigeyoshi Nagata
Keyword(s):  
Mathematical Model ◽  
Power Transmission ◽  
Tooth Surface ◽  
Cutting Mechanism ◽  
Hypoid Gears ◽  
Helical Gears ◽  
Number Of Teeth ◽  
Surface Deviations ◽  
Surface Deviation

Crossed-axis helical gears and hypoid gears are two conventional crossed-axis power transmission devices. Helipoid gears, a novel gear proposed herein, possess the merits of the crossed-axis helical and hypoid gears. A mathematical model of the proposed helipoid gear cut by shapers is also derived according to the cutting mechanism and the theory of gearing. The investigation shows that the tooth surface varies with the number of teeth of the shaper. Computer graphs of the helipoid gear are presented according to the developed gear mathematical model, and the tooth surface deviations due to the number of teeth of the shaper are also investigated.

Mathematical Model and Surface Deviation of Cylindrical Gears With Curvilinear Shaped Teeth Cut by a Hob Cutter

Volume 3 ◽  
2004 ◽  
Author(s):  
Jui-Tang Tseng ◽  
Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Tooth Surface ◽  
Design Parameters ◽  
Cutting Mechanism ◽  
Cylindrical Gear ◽  
Tooth Gear ◽  
Surface Deviations ◽  
Tool Setting ◽  
Surface Deviation ◽  
Cutter Design

The generating motion of a cylindrical gear with curvilinear shaped teeth cut by a CNC hobbing machine is proposed. Based on the cutting mechanism and the gear theory, the surface equation of this kind of gear is developed as a function of hob cutter design parameters. Computer graphs of the curvilinear-tooth gear are presented based on the developed gear mathematical model, and the tooth surface deviations due to machine-tool setting with nominal radius of circular tooth trace are also investigated.

Mathematical Model and Surface Deviation of Cylindrical Gears With Curvilinear Shaped Teeth Cut by a Hob Cutter

2004 ◽  
Vol 127 (5) ◽  
pp. 982-987 ◽  
Author(s):  
Jui-Tang Tseng ◽  
Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Tooth Surface ◽  
Design Parameters ◽  
Cutting Mechanism ◽  
Cylindrical Gear ◽  
Cylindrical Gears ◽  
Tooth Gear ◽  
Surface Deviations ◽  
Surface Deviation ◽  
Cutter Design

The generating motion of a cylindrical gear with curvilinear shaped teeth cut by a CNC hobbing machine is proposed. On the basis of the cutting mechanism and the gear theory, the surface equation of this type of gear is developed as a function of hob cutter design parameters. Computer graphs of the curvilinear-tooth gear are presented based on the developed gear’s mathematical model, and the tooth surface deviations due to machine-tool settings with nominal radius of circular tooth traces are also investigated.

Investigation of Tool Errors and Their Influences on Tooth Surface Topography for Face-Hobbed Hypoid Gears

2019 ◽  
Vol 142 (4) ◽  
Author(s):  
Chengcheng Liang ◽  
Chaosheng Song ◽  
Caichao Zhu ◽  
Yawen Wang ◽  
Siyuan Liu ◽  
...  
Keyword(s):  
Surface Topography ◽  
Rake Angle ◽  
Tooth Surface ◽  
Maximum Deviation ◽  
Angle Error ◽  
Hypoid Gears ◽  
Pressure Angle ◽  
Deviation Analysis ◽  
Surface Deviation ◽  
The Impact

Abstract Tool errors are inevitable in an actual gear-manufacturing environment and may directly affect the accuracy of machined tooth surfaces. In this paper, tool errors including spheric radius, pressure angle, rake angle, regrind angle, and cutting side relief angle errors for three-face blade are defined and considered to establish the accurate tooth surface mathematical model for face-hobbed hypoid gears based on the manufacturing process and the meshing theory. The simulation flowchart for tooth surface modeling and tooth surface topography deviation analysis are proposed and performed. Results show that the tooth surface deviation is positive with positive spheric radius and rake angle errors and contrary results can be found for other three tool errors. In addition, the impact of the pressure angle error is the strongest. In addition, the rake angle error has the weakest effect and the influence of spheric radius error on the tooth surface deviation is unsubstantial. For location of tooth surface deviation, the maximum deviation is at the top on the heel and the minimum deviation is at the middle on the toe for spheric radius error. The maximum and minimum deviations are at the top and the middle tooth on the heel for other factors, respectively.

Sensitivity Analysis and Surface-Deviation Minimization of ZK-Type Dual-Lead Worm Gear Drives

1999 ◽  
Vol 121 (3) ◽  
pp. 409-415 ◽  
Author(s):  
Biing-Wen Bair ◽  
Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Machine Tool ◽  
Gear Tooth ◽  
Data File ◽  
Worm Gear ◽  
Tooth Surface ◽  
Tool Profile ◽  
Surface Deviation ◽  
Dual Lead

This work uses the mathematical model of ZK-type dual-lead worm gear drive proposed in our recent work (1998). Based on the proposed mathematical model, coordinates and unit normals of the worm gear surface grid points can be determined and a data file subsequently formed. The data file is considered as the theoretical tooth surface data and then input into the computer of a three-dimensional coordinate measurement machine (3-D CMM) to numerically calculate the surface deviations of a real-cut worm gear. In addition, a computerized tooth surface measurement model compatible with the 3-D CMM is developed. Sensitivity analysis is also performed on machine-tool settings and tool-profile errors to the generated gear tooth surface variations. Minimization on gear tooth surface variations can be determined by applying the proposed measurement and calculation methods. In addition, optimum machine tool settings and tool-profile modifications are obtained by applying the developed computer simulation softwares. Moreover, the singular value decomposition (SVD) and sequential quadratic programming (SQP) methods are compared to establish the optimum machine-tool settings and resolve the minimum surface deviation problems.

Mathematical Model of Klingelnberg Cyclo-Palloid Hypoid Gear

2013 ◽  
Vol 341-342 ◽  
pp. 572-576 ◽  
Author(s):  
Jin Fu Du ◽  
Zong De Fang ◽  
Min Xu ◽  
Xing Long Zhao ◽  
Yu Min Feng
Keyword(s):  
Mathematical Model ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Tooth Surfaces ◽  
Normal Vectors

The geometry of the tooth surface is important for tooth contact analysis, load tooth contact analysis and the ease-off of gear pairs. This paper presents a mathematical model for the determination of the tooth geometry of Klingelnberg face-hobbed hypoid gears. The formulation for the generation of gear and pinion tooth surfaces and the equations for the tooth surface coordinates are provided in the paper. The surface coordinates and normal vectors are calculated and tooth surfaces and 3D tooth geometries of gear and pinion are obtained. This method may also applied to other face-hobbing gears.

System of Automatic Correction and Measurement for Hypoid Gears

2011 ◽  
Vol 464 ◽  
pp. 155-158 ◽  
Author(s):  
Tian Xing Li ◽  
Xiao Zhong Deng ◽  
Zhen Shan Gao ◽  
Ju Bo Li
Keyword(s):  
Closed Loop ◽  
Tooth Surface ◽  
Milling Machine ◽  
Automatic Correction ◽  
Hypoid Gears ◽  
Surface Deviation ◽  
Deviation Measurement ◽  
The Stability ◽  
Surface Precision ◽  
Correction System

The system of automatic correction and deviation measurement of hypoid gears is the basic platform for the digital closed-loop manufacturing technology. Based on the gear measuring center and the numerical controlled gear milling machine, a measurement and correction system is developed by the application of Visual C++ and Fortran. The architecture and the implement of the main modules are elaborated. Experiments and applications indicate that the tooth surface deviation can be effectively reduced by the system of automatic correction and measurement, and the stability of tooth surface precision and manufacturing quality is improved. It would provide the foundation for the digitalization of manufacture and quality control of hypoid gears.

An Ease-Off Based Method for Loaded Tooth Contact Analysis of Hypoid Gears Having Local and Global Surface Deviations

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
M. Kolivand ◽  
A. Kahraman
Keyword(s):  
Gear Tooth ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Surface Deviations ◽  
Tooth Surfaces ◽  
Loaded Tooth Contact Analysis

Actual hypoid gear tooth surfaces do deviate from the theoretical ones either globally due to manufacturing errors or locally due to reasons such as tooth surface wear. A practical methodology based on ease-off topography is proposed here for loaded tooth contact analysis of hypoid gears having both local and global deviations. This methodology defines the theoretical pinion and gear tooth surfaces from the machine settings and cutter parameters, and constructs the surfaces of the theoretical ease-off and roll angle to compute for the unloaded contact analysis. This theoretical ease-off topography is modified based on tooth surface deviations and is used to perform a loaded tooth contact analysis according to a semi-analytical method proposed earlier. At the end, two examples, a face-milled hypoid gear set having local deviations and a face-hobbed one having global deviations, are analyzed to demonstrate the effectiveness of the proposed methodology in quantifying the effect of such deviations on the load distribution and the loaded motion transmission error.

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