The Mathematical Model and Tooth Surface Deviations of Internal Conical Gears

2005 ◽  
Author(s):  
Chia-Chang Liu
Keyword(s):  
Mathematical Model ◽  
Tooth Surface ◽  
Surface Deviations ◽  
Conical Gears ◽  
The Mathematical Model

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.

Effects of Powders on the Precision of a Powder Metallurgy Helical Gear

2007 ◽  
Author(s):  
Ming-Ta Yu ◽  
Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Powder Metallurgy ◽  
Helical Gear ◽  
Precision Measurements ◽  
Manufacture Process ◽  
Measurement Results ◽  
Surface Deviations ◽  
Two Parameters ◽  
The Mathematical Model ◽  
The Relationship

This study refers to the conditions of practical powder metallurgy manufacture process, and proceeds to experiments and gear precision measurements as well as investigation on the effects of two parameters, powders and pitch circle radius, on gear precision. The relationship between gear parameters and gear surface deviations was derived from the mathematical model of the involute helical gear and the analysis of gear surface deviations. In accordance with the measurement results of experiments, an ideal correction on the parameters of a forming die is obtained from the computer simulations of gear surface deviations.

scholarly journals Meshing principle analysis of 3-DOF involute spherical gear

2020 ◽  
Vol 213 ◽  
pp. 02029
Author(s):  
Baichao Wang ◽  
Xue Zhang ◽  
Litong Zhang ◽  
Xianting Lu
Keyword(s):  
Mathematical Model ◽  
Tooth Profile ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Gear Pair ◽  
Tooth Surfaces ◽  
Three Degree Of Freedom ◽  
Relationship Of ◽  
The Mathematical Model ◽  
Spherical Gear

In this paper, a mathematical model of meshing motion of three degree of freedom involute spherical gear pair is constructed. The mathematical model can realize continuous meshing transmission between gear pairs without transmission principle error. Based on the meshing principle and motion analysis of the gear, the tooth profile of the spherical gear is designed by combining the two tooth surfaces of the involute ring gear and the hemispherical bevel gear. According to the conjugate motion relationship of spherical gear pair, a mathematical model of arc tooth surface of hemispherical bevel gear is established, and the mathematical description of the tooth profile of spherical gear is completed by combining the equation of ring tooth surface. It provides the basis and Reference for the meshing design of ball gear.

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 3D Modeling of Involute Spiral Bevel Gears for Nutation Drive

2013 ◽  
Vol 694-697 ◽  
pp. 503-506 ◽  
Author(s):  
Zheng Lin ◽  
Li Gang Yao
Keyword(s):  
Mathematical Model ◽  
3D Modeling ◽  
Bevel Gear ◽  
Transition Curve ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Spiral Bevel ◽  
The Mathematical Model

The mathematical model and 3D modeling of involute spiral bevel gears for nutation drive are considered. The basic tooth profile of involute is composed of involute curve and dedendum transition curve, and the equations have been established. The mathematical model of crown gear with involute profile is obtained, and then the mathematical models of the involute spiral bevel gears are developed. The tooth surface modeling of involute spiral bevel gear is proposed, and the 3D modeling of the involute spiral bevel gear for nutation drive is illustrated.

Study of the Dynamic Behavior of Face Gear Transmission System

2012 ◽  
Vol 268-270 ◽  
pp. 1063-1066 ◽  
Author(s):  
Zhi Wang ◽  
Qing Chen ◽  
Jia Chun Lin ◽  
Li Li Yang
Keyword(s):  
Mathematical Model ◽  
Static Load ◽  
Transmission System ◽  
Gear Transmission ◽  
Tooth Surface ◽  
Cyclic Loads ◽  
Face Gear ◽  
Static Loads ◽  
Gear Transmission System ◽  
The Mathematical Model

According to the gear meshing theory, the tooth surface equation of orthogonal face gear is derived and the mathematical model is established. Also the model was provided for simulating the bevel gear transmission system concerning the time variant stiffness and face gears errors under static load and cyclic loads. Through the model the computerized analysis of speed, angle and acceleration of gear real tooth surface could be accomplished. Rattle as discussed under condition of different static loads and the constant cyclic loads.

Mathematical Model of Spherical Gears with Helix Traces

2012 ◽  
Vol 462 ◽  
pp. 398-401
Author(s):  
Jin Zhan Su ◽  
Zong De Fang
Keyword(s):  
Mathematical Model ◽  
Tooth Surface ◽  
Surface Mode ◽  
Numerical Example ◽  
The Mathematical Model

Spherical gears with helix tooth traces are proposed to enhance loaded capacity and improve the sensitivity to assembly errors. The hobbing process for spherical gears is illustrated, and then developed the mathematical model of imaginary rack cutter. The tooth surface mode of spherical gears was developed by coordinate translation and gearing theory. Finally, the paper presents a numerical example to validate the proposed new spherical gears drive

The geometric principles of general spiral bevel gears of local bearing contact from spatial conjugate curves

2015 ◽  
Vol 231 (9) ◽  
pp. 1651-1663 ◽  
Author(s):  
Rulong Tan ◽  
Bingkui Chen ◽  
Changyan Peng ◽  
Dong Liang ◽  
Dongyun Xiang
Keyword(s):  
Mathematical Model ◽  
Tooth Surface ◽  
Element Analysis ◽  
Theoretical Derivation ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Contact Points ◽  
Bearing Contact ◽  
Spiral Bevel ◽  
The Mathematical Model

This paper aims at obtaining the mathematical model of the general spiral bevel gears of local bearing contact from spatial conjugate curve theory. Differential geometry and gearing kinematics are introduced to derive this model. Meshing-correctly conditions are set in the theoretical derivation process. The final model is represented in the form of equations and inequalities. According to the arguments in this paper, a process of designing the tooth surface of spiral bevel gears of local bearing is proposed. Based on this process, the numerical example of a pair of these gears with specific profiles is represented by applying the finite element analysis. Results show that the magnitudes of the deviations between theoretical contact points and real contact points are small. Therefore, the results agree with the mathematical model of the spiral bevel gears of local bearing contact in this paper.

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.

scholarly journals Methodology of Designing the Geometry of the Bevel Gear Using Numerical Simulation to Generate the Teeth Flank Surfaces

2014 ◽  
Vol 8 (1) ◽  
pp. 5-8
Author(s):  
Jadwiga Pisula ◽  
Mieczysław Płocica
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Theoretical Basis ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Surface Geometry ◽  
Gear Design ◽  
Grid Points ◽  
The Mathematical Model

Abstract The present paper describes modern methodology of the bevel gear design with a particular focus on issues concerning the theoretical basis and the preparation of the numerical simulation of the machining. The assumptions used in developing the mathematical model of cutting teeth are given and an example of the teeth flank surfaces of a gear and a pinion resulting from the virtual processing is shown. The correctness of the mathematical model of cutting teeth was verified by comparing the resulting based on the model grid points, the side of the tooth surface, resulting from the simulation cutting teeth in CAD. A high convergence of the two surface geometry was demonstrated, which allows for the use of the analysis for each of the models independently.

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