Computer Aided Design of Internal Involute Spur Gears

1988 ◽  
Author(s):  
Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Computer Aided Design ◽  
Gear Tooth ◽  
Gear Train ◽  
Modern Theory ◽  
Spur Gears ◽  
Tooth Contact Analysis ◽  
Computer Aided ◽  
Tooth Surfaces ◽  
Aided Design

Abstract The modern theory of gearing provides principles of generation for conjugate gear tooth surfaces while computer aided design is a very powerful tool in designing a gear train with conjugate shaped tooth surfaces. It is possible to set up a mathematical model for internal involute spur gears if the theory of gearing and the concept of differential geometry together with computer aided design technique have been applied. The derived mathematical model of internal involute spur gears can be used for computer simulation of conditions of meshing, tooth contact analysis, stress analysis, dynamic analysis, lubricating analysis, and wearing analysis of the gear train. This paper covered the solutions to the following problems : (a) method of generation for internal spur gears with conjugate tooth surfaces; (b) derivation of equations for gear tooth surfaces and their surface unit normals; and (c) computer graphics of generated internal involute spur gears.

scholarly journals Solving the problem of optimizing the cutting of wood whips with curvature

2021 ◽  
Vol 875 (1) ◽  
pp. 012009
Author(s):  
A Gudkov
Keyword(s):  
Computer Aided Design ◽  
Modern Theory ◽  
High Quality ◽  
Stem Wood ◽  
Computer Aided ◽  
Aided Design ◽  
Theory Of Graphs ◽  
Round Timber ◽  
Production Conditions ◽  
Theoretical Developments

Abstract Stem wood, obtained from the cuttings of care in low-forest areas is of low quality. Such wood has a number of vices, one of which is simple curvature, which has impact on the voluminous and commercial output of round timber. Reducing this influence can be achieved through high-quality bucking. Therefore, the purpose of the work presented is to increase the volume and commercial output of round timber harvested in low-forest areas. The developed technique using computers allows to solve the tasks of modeling the shape of wood whips and logs using multi-critical optimization and bucking whips having curvature. The use of the proposed technique allows for results adequate to the real production conditions, as evidenced by the methods of decision-making used. Scientific research and theoretical developments, taking into account the formed database, allowed to search for the optimal scheme of cutting when bucking round timber, performed according to the algorithm based on the busting of acceptable variants using modern theory of graphs and matrixes. As a result, the developed program will reduce the time for data formation, guarantee the accuracy of the results, the program easily adapts to natural and production conditions and will expand the possibilities for Computer-aided design.

scholarly journals Mathematical Modeling of a Bioluminescent E. Coli Based Biosensor

2009 ◽  
Vol 14 (4) ◽  
pp. 505-529 ◽  
Author(s):  
A. Rabner ◽  
E. Martinez ◽  
R. Pedhazur ◽  
T. Elad ◽  
S. Belkin ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Dna Repair ◽  
Computer Aided Design ◽  
Sos Response ◽  
Chromosomal Dna ◽  
Whole Cell ◽  
E Coli ◽  
Computer Aided ◽  
Lux Genes ◽  
Aided Design

In this work we present a mathematical model for the bioreporter activity of an E. coli based bioluminescent bioreporter. This bioreporter is based on a genetically modified E. coli which harbors the recA promoter, a member of the bacterial SOS response, fused to the bacterial luminescence (lux) genes. This bioreporter responds to the presence of DNA damaging agents such as heavy metals, H2O2 and Nalidixic Acid (NA) that activate the SOS response. In our mathematical model we implemented basic physiological mechanisms such as: the penetration of the NA into the biosensor; gyrase enzyme inhibition by the NA; gyrase level regulation; creation of chromosomal DNA damage; DNA repair and release of ssDNA into the cytoplasm; SOS induction and chromosomal DNA repair; activation of lux genes by the fused recA promoter carried on a plasmidal DNA; transcription and translation of the luminescence responsible enzymes; luminescence cycle; energy molecules level regulation and the regulation of the O2 consumption. The mathematical model was defined using a set of ordinary differential equations (ODE) and solved numerically. We simulated the system for different concentrations of NA in water for specific biosensors concentration, and under limited O2 conditions. The simulated results were compared to experimental data and satisfactory matching was obtained. This manuscript presents a proof of concept showing that real biosensors can be modeled and simulated. This sets the ground to the next stage of implementing a comprehensive physiological model using experimentally extracted parameters. Following the completion of the next stage, it will be possible to construct a “Computer Aided Design” tool for the simulation of the genetically engineered biosensors. We define a term “bioCAD” for a Biological System Computer Aided Design. The specific bioCAD that is described here is aimed towards whole cell biosensors which are under investigation today for functional sensing. Usage of the bioCAD will improve the biosensors design process and boost their performance. It will also reduce Non Recurring Engineering (NRE) cost and time. Finally, using a parameterized solution will allow fair and quick evaluation of whole cell biosensors for various applications.

scholarly journals Determination of contact pattern for double enveloping worm gear

2020 ◽  
Vol 44 (4) ◽  
pp. 145-154
Author(s):  
Piotr Polowniak ◽  
Mariusz Sobolak ◽  
Adam Marciniec
Keyword(s):  
Contact Area ◽  
Computer Aided Design ◽  
Worm Gear ◽  
Complete Analysis ◽  
Contact Pattern ◽  
Tooth Contact Analysis ◽  
Computer Aided ◽  
Cad Models ◽  
Aided Design

AbstractThe paper presents the method of determining geometric contact pattern by using the direct computer-aided design (CAD) method for ideal globoid worm gear in which mounting deviations are considered. The tooth contact analysis was performed for all cycle of worm rotation. Based on the results of temporary contact pattern, graphical characteristics of the contact area size depending on worm position were made. A complete analysis of the correctness of gear meshing can be obtained based on presented method. If the worm or worm wheel is incorrectly designed in terms of the geometry, the meshing simulation of CAD models can indicate the collision. Geometric contact pattern analyses were made at two pressure angles of ideal gear. The analysis of the influence of mounting deviations was done against one selected pressure angle and one gear position.

The Studying of Logix Gear Construction Principle and Parameter Simulation Using Matlab

2011 ◽  
Vol 80-81 ◽  
pp. 1118-1122
Author(s):  
Ai Qin An ◽  
Ming Hua Pang ◽  
Lian Feng Zhang ◽  
Yong Fang Nie
Keyword(s):  
Mathematical Models ◽  
Computer Aided Design ◽  
Gear Tooth ◽  
Tooth Profile ◽  
Profile Curve ◽  
Computer Aided ◽  
Base Circle ◽  
Manufacturing Methods ◽  
Aided Design ◽  
Logix Gear

Logix gear is a new gear based on new tooth profile theory. On the primary, the forming principle of the logix gear tooth profile is analysed. Then the tooth profile curve equations of logix gear are derived, and their center coordinate equations of base circle are given. According these equations, their curves are simulated using Matlab, which are corresponded to practical tests. The study lays a foundation of computer aided design of the logix gears. And the study can be used to perfect mathematical models and to optimize manufacturing methods.

A Study on the Technology of Helical Groove Formation

2010 ◽  
Vol 139-141 ◽  
pp. 1264-1267 ◽  
Author(s):  
Ru Sheng Lu ◽  
Bin Yao ◽  
Bo Shi Yao ◽  
Ming Hui Chen
Keyword(s):  
Mathematical Model ◽  
Differential Geometry ◽  
Computer Aided Design ◽  
Rake Angle ◽  
Production Costs ◽  
Element Analysis ◽  
Computer Aided ◽  
Helical Groove ◽  
Aided Design ◽  
The Impact

On the basis of analyzing the geometric characteristics of the helical groove, the interfer -ometry method for its processing is discussed. This paper establishes a mathematical model of the helical groove, using differential geometry theory and numerical analysis. This research analyzes the impact of machine adjustment parameters (i.e. setting angle) on the geometry specification (i.e. Rake angle) of the helical groove. The simulation examples are done by CAD (Computer Aided Design), and the reasonable adjustment of machine parameters will be obtained by computer simulation and statistical analysis. This will reduce the time for design, the number of trial samples, and production costs. This study provides a precise 3D helical cutter model which can be used in areas such as finite element analysis (FEA) and virtual cutting tests.

Kinematic Optimization of a Modified Helical Gear Train

1997 ◽  
Vol 119 (2) ◽  
pp. 307-314 ◽  
Author(s):  
Shinn-Liang Chang ◽  
Chung-Biau Tsay ◽  
Ching-Huan Tseng
Keyword(s):  
Mathematical Model ◽  
Gear Tooth ◽  
Optimization Method ◽  
Helical Gear ◽  
Gear Train ◽  
Tooth Contact Analysis ◽  
Numerical Examples ◽  
Kinematic Optimization ◽  
Kinematic Errors ◽  
Center Distance

A mathematical model of a modified helical gear train (MHGT), manufactured with a practical hobbing machine using a curved-template guide, and which takes considerations of center-distance variation and axial misalignment into account, is developed. Tooth contact analysis (TCA) and kinematic errors of a MHGT due to mis-assembly are investigated. A multiple optimization method is applied to reduce the level of MHGT kinematic errors, and to investigate optimal gear tooth modifications. Computer simulation programs for TCA and optimization are also developed. Two numerical examples are presented to illustrate the kinematic optimization of the proposed helical gear train. The results of this study are most helpful in designing and analyzing a MHGT.

scholarly journals Developing a Mathematical Model of a Part Based on Graphics System Models

2019 ◽  
pp. 67-76
Author(s):  
Sergey Yu. Kalyakulin ◽  
Vladimir V. Kuzmin ◽  
Eduard V. Mitin ◽  
Sergey P. Suldin ◽  
Tatiana B. Tyurbeeva
Keyword(s):  
Mathematical Model ◽  
Computer Aided Design ◽  
Geometric Shape ◽  
Design Parameters ◽  
Technological Processes ◽  
Calculation Of Parameters ◽  
Level Of Automation ◽  
Computer Aided ◽  
Design Systems ◽  
Aided Design

Introduction. The aim of the work is to develop a mathematical model of a part based on a parametric model of graphic systems. Material and Methods.The review of the status of the question of developing a mathematical model of a part based on graphic systems showed the possibility of controlling the geometric shape of a part through the variables of a parameterized drawing. A proposal was made to use design parameterization in the calculation of the parameters of technological processes in computer-aided design systems. Results. The article establishes links between the design parameters of the part drawing and tabular values of the variables. The revealed relationships between the parameters in the drawing and the variables in the table make it possible to change the geometric shape of the part by changing the values in the variable table, i.e. the drawing is managed through the table. It is proposed to use this system of work with the parametric drawing in computer-aided design systems for calculating the parameters of technological processes. Discussion and Conclusion. The tasks solved in this article allow making a step in increasing the level of automation of parameter calculations in computer-aided design systems. The implementation of the developed methodology for constructing mathematical models of parts based on graphic systems will increase the overall level of automation of developing geometric drawings of parts. The implementation of this technique in computer-aided design systems allows automating the calculation of parameters (cutting modes, time norms, technological dimensions on transitions, etc.).

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