The generation principle and mathematical model of a new involute-helix gear drive

2013 ◽  
Vol 227 (12) ◽  
pp. 2834-2843 ◽  
Author(s):  
Dong Liang ◽  
Bingkui Chen ◽  
Yane Gao
Keyword(s):  
Mathematical Model ◽  
Basic Principle ◽  
Three Dimensional ◽  
Point Contact ◽  
Solid Model ◽  
Gear Pair ◽  
Circular Arc ◽  
Gear Drive ◽  
Center Distance

A new involute-helix gear drive, which is point contact with convex and concave circular-arc tooth profiles, is proposed in this article. The basic principle characterized by the advantages of involute and circular-arc gears is put forward. Based on the theory of conjugates curves, generation and mathematical model of this new transmission are presented. The separability of center distance on involute-helix gear is discussed and meshing characteristic of point contact is also analyzed. Finally, the three-dimensional solid model of a gear pair is developed to demonstrate the properties of this new transmission.

Geometry design and mathematical model of a new kind of gear transmission with circular arc tooth profiles based on curve contact analysis

2014 ◽  
Vol 228 (17) ◽  
pp. 3200-3208 ◽  
Author(s):  
Bingkui Chen ◽  
Dong Liang ◽  
Yane Gao
Keyword(s):  
Mathematical Model ◽  
High Performance ◽  
Plane Curve ◽  
Gear Transmission ◽  
Circular Arc ◽  
Smooth Curves ◽  
Gear Drive ◽  
Geometry Design ◽  
Meshing Equation ◽  
The Given

A new meshing relationship for gear drive to characterize the conjugation geometry is studied in this paper based on conjugate curves. Conjugate curves are described as two smooth curves always keep continuous and tangent contact with each other in given contact direction under motion law. The general principle of curve meshing is developed for the given spatial or plane curve. The meshing equation along arbitrary direction of contact angle is derived. The properties of geometric and motion of the contact of conjugate curves are discussed. According to the equidistance-enveloping method, tubular meshing surfaces are proposed to build up circular arc tooth profiles, which inherit all properties of conjugate curves. The geometry design and mathematical model of the gears are established. Three types of contact pattern of tooth profiles are generated: convex-to-convex, convex-to-plane and convex-to-concave. A calculation example for convex-to-concave tooth profiles of gears is provided. Theoretical and numerical results demonstrate the feasibility and correctness of proposed conjugate curves theory and it lays the foundation for the design of high performance gear transmission.

Study on the Meshing Feature and Contact Strength of WN Gear Driving in Load Bearing

2012 ◽  
Vol 229-231 ◽  
pp. 406-409
Author(s):  
Cheng Chao Li ◽  
Dian Hua Chen ◽  
Yu Guang Li ◽  
Xiao Kai Mu
Keyword(s):  
Simulation Analysis ◽  
Three Dimensional ◽  
Helix Angle ◽  
Contact Strength ◽  
Analysis Model ◽  
Element Analysis ◽  
Gear Drive ◽  
Gear Contact ◽  
Dynamic Meshing ◽  
Center Distance

According to characteristics of WN gear multi-point meshing and double-arc tooth contact, the finite element analysis model of the WN gear drive is established by Pro/E and ANSYS modeling techniques. The contact way and meshing feature of the WN gear under the different conditions and parameters are studied by three-dimensional dynamic meshing simulation analysis of gear drive. The analysis model of contact strength at loading driving is established by three dimensional geometric contact characteristics and elastic deform theory. Impact of helix angle and center distance error in the calculation of WN gear contact strength on maximum contact stress is analyzed. The results show that increase of the helix angle and a slight decrease of the center distance can improve the contact strength.

The Reconstruction for Han Dynasty Stone Images Based on Three-Dimensional Vision

2014 ◽  
Vol 556-562 ◽  
pp. 5009-5012
Author(s):  
Guang Dong Pan
Keyword(s):  
Mathematical Model ◽  
3D Reconstruction ◽  
Basic Principle ◽  
Projective Transformation ◽  
Three Dimensional ◽  
Reconstruction Algorithm ◽  
Han Dynasty ◽  
Dimensional Reconstruction ◽  
New Research ◽  
Three Dimensional Vision

Mainly studying the three-dimensional reconstruction for multiple Han Dynasty stone images, this paper proposes a 3D reconstruction algorithm based on two images. The author analyzes the basic principle of SIFT matching points detection according to Epipolar geometry constraints and projective transformation of images in 2D plane, and establishes mathematical model for the 3D reconstruction on foundation of sequence images. The feasibility of 3D reconstruction based on the sequence images is approved by simulation for three gray-scale Han Dynasty stone digital images which provides a new research way for identifying the feature of a target by the camera.

scholarly journals Evaluation and Optimization of the Oil Jet Lubrication Performance for Orthogonal Face Gear Drive: Modelling, Simulation and Experimental Validation

Energies ◽  
2019 ◽  
Vol 12 (10) ◽  
pp. 1935 ◽  
Author(s):  
Yu Dai ◽  
Feiyue Ma ◽  
Xiang Zhu ◽  
Qiao Su ◽  
Xiaozhou Hu
Keyword(s):  
Mathematical Model ◽  
Volume Fraction ◽  
Tooth Surface ◽  
Design Parameters ◽  
Gear Pair ◽  
Face Gear ◽  
Gear Drive ◽  
Lubrication Performance ◽  
Jet Nozzle ◽  
Oil Jet

The oil jet lubrication performance of a high-speed and heavy-load gear drive is significantly influenced and determined by the oil jet nozzle layout, as there is extremely limited meshing clearance for the impinging oil stream and an inevitable blocking effect by the rotating gears. A novel mathematical model for calculating the impingement depth of lubrication oil jetting on an orthogonal face gear surface has been developed based on meshing face gear theory and the oil jet lubrication process, and this model contains comprehensive design parameters for the jet nozzle layout and face gear pair. Computational fluid dynamic (CFD) numerical simulations for the oil jet lubrication of an orthogonal face gear pair under different nozzle layout parameters show that a greater mathematically calculated jet impingement depth results in a greater oil volume fraction and oil pressure distribution. The influences of the jet nozzle layout parameters on the lubrication performance have been analyzed and optimized. The relationship between the measured tooth surface temperature from the experiments and the corresponding calculated impingement depth shows that a lower temperature appears in a situation with a greater impingement depth. Good agreement between the mathematical model with the numerical simulation and the experiment validates the effectiveness and accuracy of the method for evaluating the face gear oil jet lubrication performance when using the impingement depth mathematical model.

Tooth Profile Generation of Point-Contact Involute Planetary Gear Drive with Small Teeth Difference

2013 ◽  
Vol 441 ◽  
pp. 561-567 ◽  
Author(s):  
Wen Cui Yi ◽  
Bao Ying Wang ◽  
Shu He
Keyword(s):  
Three Dimensional ◽  
Point Contact ◽  
Planetary Gear ◽  
Smooth Curve ◽  
Tooth Surface ◽  
Three Dimensional Model ◽  
Gear Drive ◽  
Tooth Surfaces ◽  
Meshing Characteristics ◽  
Internal Gear

A new kind of involute planetary gear drive with small teeth difference which meshes in point contact is put forward based on the kinematic method of gear geometry in this paper. The generation principle of tubular tooth surface is proposed according to a selected smooth curve attached to the planetary wheel tooth surface. The general equations of conjugate tooth surfaces are derived and its conjugated contact curve on the internal gear is also determined. Then the mathematical model is established. The parameter selection and meshing characteristics of point-contact involute planetary gear drive with small teeth difference are discussed respectively. The three dimensional model is finally established and its motion simulation is worked out. It lays the significant theoretical foundation and practical meaning for improving the gear transmission performance.

scholarly journals Mathematical model and characteristics analysis of crossed-axis helical gear drive with small angle based on curve contact element

2021 ◽  
Vol 104 (2) ◽  
pp. 003685042110162
Author(s):  
Dong Liang ◽  
Sheng Meng ◽  
Rulong Tan
Keyword(s):  
Mathematical Model ◽  
Small Angle ◽  
Performance Test ◽  
Load Capacity ◽  
Helical Gear ◽  
Contact Element ◽  
Gear Pair ◽  
Manufacturing Method ◽  
Gear Drive ◽  
Milling Method

To improve load capacity and transmission characteristics of crossed-axis helical gear drive, a generation approach of the gear pair with small-angle based on the curve contact element is proposed. Contact principle based on spatial curve meshing relationships is introduced and geometric models of tooth profiles are developed according to a pair of mated conjugate curves. Furthermore, a mathematical model of crossed-axis helical gear drive with small-angle is established. Numerical examples are illustrated for this research using the 10° shaft angle, and the computerized simulation is also developed based on the solid models. According to gear geometry and finite element method, general characteristics including undercutting conditions, sliding ratios and contact stress for tooth profiles are analyzed. Comparisons with crossed-axis involute gears are also carried out. Finally, the gear prototype is processed using the gear milling method and a basic performance test is conducted. Analysis results show that the new gear pair has well contact characteristics. Further studies on the dynamic analysis and precision manufacturing method will be carried out.

scholarly journals Time-varying dynamic analysis for a helical gear pair system with three-dimensional motion due to bearing deformation

2020 ◽  
Vol 12 (5) ◽  
pp. 168781402091812
Author(s):  
Ying-Chung Chen
Keyword(s):  
Three Dimensional ◽  
Helix Angle ◽  
Helical Gear ◽  
Dynamic Responses ◽  
Time Varying ◽  
Gear Pair ◽  
Contact Ratio ◽  
Transverse Pressure ◽  
Helical Gear Pair ◽  
Center Distance

The dynamic response of a helical gear pair system is investigated. A new dynamic model for a helical gear pair system, considering three-dimensional motion due to bearing deformation, is proposed. The proposed model considers the helix angle, gear pair center distance, transverse pressure angle, and the contact ratio as time-dependent variables, which are considered as constants in other models. In fact, three-dimensional motion due to bearing deformation will lead to the changes in a series of dynamic responses. The system equations of motion were obtained by applying Lagrange’s equation and the dynamic responses are computed by the fourth-order Runge–Kutta method. The time-varying dynamic displacements, helix angle, gear pair center distance, transverse pressure angle, and the contact ratio are investigated with bearing deformation, different radial bear stiffness, different axial bear stiffness, and gear eccentricity. The results show that, due to the time-varying effect, this new helical gear pair model provides more accurate dynamic responses than those previous models which are considered as constant. In the future, this study can provide some useful information for the time-varying dynamic design of a helical gear pair system.

USING DOUBLE ENVELOPE METHOD ON A PLANETARY GEAR MECHANISM WITH DOUBLE CIRCULAR-ARC TOOTH

2008 ◽  
Vol 32 (2) ◽  
pp. 267-282 ◽  
Author(s):  
Chun-Fang Tsai ◽  
Tsang-Lang Liang ◽  
Shyue-Cheng Yang
Keyword(s):  
Mathematical Model ◽  
Planetary Gear ◽  
Ring Gear ◽  
Circular Arc ◽  
Distance Error ◽  
Planet Gear ◽  
Gear Mechanism ◽  
Double Envelope ◽  
Center Distance ◽  
Planetary Gear Mechanism

A geometric model and mathematical model of planetary gear mechanism with double circular-arc teeth is determined using the imaginary rack cutters and double envelope concept. The mathematical model of a ring gear with double circular-arc teeth in a second envelope has been developed. In this paper, the conditions of the gear meshing and contact load of the gears are simulated by assembly errors. The goal of the stress analysis is to determine the contact stress on the planet gear and ring gear, and planet gear and sun gear. Given the assembly errors of the planetary gear mechanism including center distance error and mis-aligmment error, the maximum von-Mises stress in the planetary gear mechanism with double circular-arc teeth is analyzed using visualNastran desktop package. It is found that the center distance error is more critical to mis-alignment error.

Tooth Profile Generation and Analysis of Crowned Elliptical Gears

2009 ◽  
Vol 131 (7) ◽  
Author(s):  
Biing-Wen Bair
Keyword(s):  
Mathematical Model ◽  
Three Dimensional ◽  
Major Axis ◽  
Tooth Profile ◽  
Numerical Examples ◽  
Gear Drive ◽  
Computer Simulation Program ◽  
Geometric Relation ◽  
Contact Position ◽  
The Mathematical Model

This study develops a crowned elliptical gear drive that prevents edge contact when an elliptical gear drive has axial misalignment. According to the theory of gearing and a gear-generation mechanism with longitudinal crowing, the mathematical model of a crowned elliptical gear is derived using a rack cutter. Pointed teeth typically appear on the tips of the teeth of elliptical gears at major axis. Additionally, a three-dimensional geometric relation is applied to prevent pointed teeth from developing on elliptical gears. Moreover, a computer simulation program is employed to generate the tooth profiles of crowned elliptical gears without pointed teeth and locate the contact position for longitudinal middle tooth profiles. Two numerical examples demonstrate the design process and the tooth profile graphs.

A Real-Time Mathematical Model for Three-Dimensional Tidal Flow and Water Quality

1991 ◽  
Vol 24 (6) ◽  
pp. 171-177 ◽  
Author(s):  
Zeng Fantang ◽  
Xu Zhencheng ◽  
Chen Xiancheng
Keyword(s):  
Mathematical Model ◽  
Water Quality ◽  
Real Time ◽  
Control Volume ◽  
Tidal Flow ◽  
Three Dimensional ◽  
River Estuary ◽  
Pearl River Estuary ◽  
Practical Application ◽  
The Pearl River

A real-time mathematical model for three-dimensional tidal flow and water quality is presented in this paper. A control-volume-based difference method and a “power interpolation distribution” advocated by Patankar (1984) have been employed, and a concept of “separating the top-layer water” has been developed to solve the movable boundary problem. The model is unconditionally stable and convergent. Practical application of the model is illustrated by an example for the Pearl River Estuary.

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