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.

Mathematical Model and Characteristic Analysis of Elliptical Gears Manufactured by Circular-Arc Shaper Cutters

2006 ◽  
Vol 129 (2) ◽  
pp. 210-217 ◽  
Author(s):  
Biing-Wen Bair ◽  
Chien-Fa Chen ◽  
Shih-Fa Chen ◽  
Chung-Yi Chou
Keyword(s):  
Complex Geometry ◽  
Major Axis ◽  
Tooth Profile ◽  
Characteristic Analysis ◽  
Circular Arc ◽  
Gear Drive ◽  
Computer Simulation Program ◽  
Geometric Relation ◽  
Pitch Curve ◽  
Tool Profiles

A circular-arc elliptical gear drive with convex (or concave) tooth profiles, which is used in an oil pump with a larger pumping volume, was simulated by using circular-arc shaper cutters with concave (or convex) tool profiles. Mathematical models of circular-arc elliptical gears, based on the theory of gearing and the gear generation mechanism, were also developed. The generated elliptical gear drive has a convex–concave tooth profile contact. Because of its complex geometry, the profile of circular-arc elliptical gears may exhibit tooth undercutting, and pointed teeth. Pointed teeth usually appear on the major axis of the elliptical pitch curve. A geometric relation was developed and applied to prevent the pointed teeth on the elliptical gears. A larger pressure angle at major axis and circular-arc radius can eliminate tooth undercutting and increase its tooth thickness at the addendum circle for small teeth. Moreover, a computer simulation program was developed to generate the tooth profile of circular-arc elliptical gears without tooth undercutting and pointed teeth.

Computer Aided Design of Elliptical Gears

2002 ◽  
Vol 124 (4) ◽  
pp. 787-793 ◽  
Author(s):  
Biing-Wen Bair
Keyword(s):  
Mathematical Model ◽  
Computer Aided Design ◽  
Complex Geometry ◽  
Rotation Axis ◽  
Major Axis ◽  
Computer Simulation Program ◽  
Geometric Relation ◽  
Pitch Curve ◽  
Aided Design ◽  
The Mathematical Model

An elliptical gear drive, whose rotation axis coincides with its geometric center, is simulated using generation with a rack cutter. The mathematical model of an elliptical gear based on the theory of gearing and gear generation mechanism is also developed. Owing to its complex geometry, the profile of elliptical gears may exhibit tooth undercutting, and pointed teeth. In addition, tooth undercutting of an elliptical gear based on the developed mathematical model of the elliptical gear and the theory of gearing is also investigated. Pointed teeth usually appear on the major axis of the gear elliptical pitch curve. Moreover, a geometric relation is developed and applied to prevent the pointed teeth appearing on elliptical gears. Furthermore, a computer simulation program is developed to generate the tooth profile of elliptical gears without tooth undercutting and pointed teeth. Various numerical examples illustrate the effectiveness of the computerized design process.

Computer aided design of non-standard elliptical gear drives

2001 ◽  
Vol 216 (4) ◽  
pp. 473-482 ◽  
Author(s):  
B-W Bair
Keyword(s):  
Mathematical Model ◽  
Computer Aided Design ◽  
Major Axis ◽  
Oil Pump ◽  
Compact Size ◽  
Computer Simulation Program ◽  
Geometric Relation ◽  
Pitch Curve ◽  
Gear Drives ◽  
Aided Design

An oil pump with a larger pumping volume and more compact size than conventional pumps is designed with elliptical gear drives. In this work, an elliptical gear drive with few teeth is used in the design of pumps with a large pumping volume. Also, a mathematical model of a profile-shifted elliptical gear is developed, based on the theory of gearing and the gear generation mechanism. This study also investigates the tooth undercutting of a non-standard elliptical gear, based on the proposed mathematical model of the profile-shifted elliptical gear and the theory of gearing. Pointed teeth generally appear on the major axis of the gear elliptical pitch curve. Moreover, a geometric relation is developed and applied to prevent pointed teeth on non-standard elliptical gears. Moreover, a computer simulation program is developed to generate the tooth profiles of non-standared elliptical gears with few teeth and a compact size, without tooth undercutting and pointed teeth. Numerical examples demonstrate the effectiveness of the computerized design process.

The Research on Three-Dimensional Model of Non-Circular Gear

2012 ◽  
Vol 479-481 ◽  
pp. 953-956
Author(s):  
Guo Xing Sun ◽  
Chuan Qiong Sun ◽  
Qiang Liu
Keyword(s):  
Mathematical Model ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Gear Tooth ◽  
Three Dimensional ◽  
Tooth Profile ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Element Analysis ◽  
The Mathematical Model

According to the principles of engagement and the mathematical model of non-circular gear tooth profile, the tooth profile of non-circular gear is draw. Then the three-dimensional model of the non-circular gear is created in Pro/E three-dimensional software to provide the basis for a non-circular gear motion analysis, dynamic analysis and finite element analysis.

Research on cargo-loading optimization based on genetic and fuzzy integration

2021 ◽  
Vol 40 (4) ◽  
pp. 8493-8500
Author(s):  
Yanwei Du ◽  
Feng Chen ◽  
Xiaoyi Fan ◽  
Lei Zhang ◽  
Henggang Liang
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Three Dimensional ◽  
Distribution Center ◽  
Long Time ◽  
Low Efficiency ◽  
Decision Making Model ◽  
The Mathematical Model ◽  
Loading Scheme

With the increase of the number of loaded goods, the number of optional loading schemes will increase exponentially. It is a long time and low efficiency to determine the loading scheme with experience. Genetic algorithm is a search heuristic algorithm used to solve optimization in the field of computer science artificial intelligence. Genetic algorithm can effectively select the optimal loading scheme but unable to utilize weight and volume capacity of cargo and truck. In this paper, we propose hybrid Genetic and fuzzy logic based cargo-loading decision making model that focus on achieving maximum profit with maximum utilization of weight and volume capacity of cargo and truck. In this paper, first of all, the components of the problem of goods stowage in the distribution center are analyzed systematically, which lays the foundation for the reasonable classification of the problem of goods stowage and the establishment of the mathematical model of the problem of goods stowage. Secondly, the paper abstracts and defines the problem of goods loading in distribution center, establishes the mathematical model for the optimization of single car three-dimensional goods loading, and designs the genetic algorithm for solving the model. Finally, Matlab is used to solve the optimization model of cargo loading, and the good performance of the algorithm is verified by an example. From the performance evaluation analysis, proposed the hybrid system achieve better outcomes than the standard SA model, GA method, and TS strategy.

Simulation Investigation on Environment-Induced Pitting Corrosion on the Metal Surface

2021 ◽  
Vol 13 (5) ◽  
pp. 820-828
Author(s):  
Wei Zhang ◽  
Shengli Lv ◽  
Leijiang Yao ◽  
Xiaoyan Tong
Keyword(s):  
Mathematical Model ◽  
Pitting Corrosion ◽  
Three Dimensional ◽  
Corrosion Damage ◽  
Sudden Onset ◽  
Ion Concentration ◽  
Two Dimensional Image ◽  
Aging Aircraft ◽  
Efficient Calculation ◽  
The Mathematical Model

The prediction of corrosion damage is one of effective research methods in the safety inspection of aging aircraft structures. A mathematical model for quantifying corrosion damage is used in this paper to predict the onset of corrosion on structural surfaces exposed to aggressive environments. Based on the finite difference technique, the evolution process of local pitting corrosion on the surface of aluminum alloy in the medium is simulated, which can consider the sudden onset and the randomness of pitting corrosion. The effect of local ion concentration and oxide film damage on subsequent pitting nucleation was analyzed. Based on the efficient calculation program, the effectiveness of the mathematical model is verified by the comparison between the corrosion damage morphology and the experimental data in the literature. The results show a more widespread distribution of subsequent pits because of stronger aggressive ions are released during the life cycle of active pits and the higher diffusion coefficient of the aggressive ions. The three dimensional morphology is generated by image processing method based on the gray value of the two dimensional image of pits.

Mobile Robots Characterized by Kinematic and Dynamic Equations: Motion Planning, Trajectory Tracking, and Group Control

2008 ◽  
Author(s):  
Amit Ailon
Keyword(s):  
Mathematical Model ◽  
Motion Planning ◽  
Mobile Robots ◽  
Dynamic Equations ◽  
Kinematics And Dynamics ◽  
Control Problems ◽  
Reference Trajectory ◽  
Numerical Examples ◽  
Group Control ◽  
The Mathematical Model

The paper solves some control problems of mobile robots as both kinematics and dynamics are intertwined in the mathematical model. The problems of driving the vehicle to a desired configuration in a specified time and tracking a reference trajectory are considered. The control problems associated with motion in convoy and rigid formations of a group of vehicles are studied and some results are demonstrated by numerical examples.

Mathematical modeling of a generic multi-profile form milling cutter

2012 ◽  
Vol 227 (5) ◽  
pp. 1036-1046 ◽  
Author(s):  
Mohammed Rajik Khan ◽  
Puneet Tandon
Keyword(s):  
Mathematical Model ◽  
Three Dimensional ◽  
Sculptured Surfaces ◽  
Three Dimensional Model ◽  
Machining Time ◽  
Milling Cutter ◽  
Machined Parts ◽  
Rotary Cutting ◽  
Three Dimensional Models ◽  
The Mathematical Model

In order to machine multiple sculptured surfaces with reduced machining time and high accuracy of the machined parts, shape design of a customised multi-point rotary cutting tool needs to be evolved. In the present work, a novel design of a generic multi-profile form milling cutter is developed for machining various multiple sculptured surfaces. This article describes in detail the mathematical model to design an accurate three-dimensional geometry of a generic multi-profile form milling cutter. Use of non-uniform rational B-spline curve(s) and sweep surfaces enables to control the shape of cutting flutes of the generic multi-profile form milling cutter. The article also discusses the methodology to develop a variety of cutters lying in the same conceptual family of multi-profile form milling cutter. To physically visualise the cutter and to show one of the downstream applications once a three-dimensional model of the cutter is available, one of the multi-profile form milling cutters is fabricated. The proposed methodology offers an intuitive high-quality mathematical model for a generic family of multi-profile form milling cutters, which is different from the traditional three-dimensional models.

Computations of Three-Dimensional Gas-Turbine Combustion Chamber Flows

1979 ◽  
Vol 101 (3) ◽  
pp. 326-336 ◽  
Author(s):  
M. A. Serag-Eldin ◽  
D. B. Spalding
Keyword(s):  
Mathematical Model ◽  
Turbulent Flows ◽  
Combustion Process ◽  
Three Dimensional ◽  
Solution Algorithm ◽  
Physical Models ◽  
Turbulence Energy ◽  
Experimental Conditions ◽  
Diffusion Controlled ◽  
The Mathematical Model

The paper presents a mathematical model for three-dimensional, swirling, recirculating, turbulent flows inside can combustors. The present model is restricted to single-phase, diffusion-controlled combustion, with negligible radiation heat-transfer; however, the introduction of other available physical models can remove these restrictions. The mathematical model comprises differential equations for: continuity, momentum, stagnation enthalpy, concentration, turbulence energy, its dissipation rate, and the mean square of concentration fluctuations. The simultaneous solution of these equations by means of a finite-difference solution algorithm yields the values of the variables at all internal grid nodes. The prediction procedure, composed of the mathematical model and its solution algorithm, is applied to predict the fields of variables within a representative can combustor; the results are compared with corresponding measurements. The predicted results give the same trends as the measured ones, but the quantitative agreement is not always acceptable; this is attributed to the combustion process not being truly diffusion-controlled for the experimental conditions investigated.

Calculations of three-dimensional viscous flow in a multiblade centrifugal fan by modelling blade forces

2003 ◽  
Vol 217 (3) ◽  
pp. 287-297 ◽  
Author(s):  
S-J Seo ◽  
K-Y Kim ◽  
S-H Kang
Keyword(s):  
Mathematical Model ◽  
Turbulent Flows ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Centrifugal Fan ◽  
Complex Flows ◽  
Flow Through ◽  
Volume Method ◽  
The Mathematical Model

A numerical study is presented for Reynolds-averaged Navier-Stokes analysis of three-dimensional turbulent flows in a multiblade centrifugal fan. Present work aims at development of a relatively simple analysis method for these complex flows. A mathematical model of impeller forces is obtained from the integral analysis of the flow through the impeller. A finite volume method for discretization of governing equations and a standard k-ɛ model as turbulence closure are employed. For the validation of the mathematical model, the computational results for velocity components, static pressure, and flow angles at the exit of the impeller were compared with experimental data. The comparisons show generally good agreement, especially at higher flow coefficients.

Sign in / Sign up

Export Citation Format

Share Document