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.

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.

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.

scholarly journals Study and Computer-aided Design of Flux-cored Wire Rolling in Round Gauges

2021 ◽  
Author(s):  
Eduard P. Gribkov ◽  
Serhii O. Malyhin ◽  
Svetlana S. Hurkovskaya ◽  
Elena V. Berezshnaya ◽  
Dmytro V. Merezhko
Keyword(s):  
Mathematical Model ◽  
Deformation Zone ◽  
Computer Aided Design ◽  
Plasticity Condition ◽  
Cored Wire ◽  
Power Characteristics ◽  
Sintered Copper ◽  
Powder Density ◽  
Aided Design ◽  
The Mathematical Model

Abstract The mathematical model of the stress-strain state during flux-cored wire rolling in round gauges has been developed. Simulation was based on dividing the deformation zone into elementary volumes and simultaneous solution of the plasticity condition for porous materials and power static equilibrium equation inside the elementary volume. A distinctive feature of this model is taking into account the porous medium strain in the deformation zone. The experiments have confirmed the validity of the mathematical model for predicting the powder density and the energy-power characteristics of the process. Based on the developed mathematical model, the criteria and conditions for optimization were formulated, and the algorithm was developed for the automated design of technology for flux-cored wire rolling in round gauges. As an example of the obtained solutions implementation, the calculation of sintered copper flux-cored wire rolling technology was given.

scholarly journals The Influence of Exposure Energy Density on Porosity and Microhardness of the SLM Additive Manufactured Elements

Materials ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 2304 ◽  
Author(s):  
Janusz Kluczyński ◽  
Lucjan Śnieżek ◽  
Krzysztof Grzelak ◽  
Janusz Mierzyński
Keyword(s):  
Computer Aided Design ◽  
Complex Geometry ◽  
Final Analysis ◽  
Machine Building ◽  
Layer By Layer ◽  
Laser Melting ◽  
Measurement Results ◽  
Computer Aided ◽  
Exposure Energy ◽  
Aided Design

Selective laser melting (SLM) is an additive manufacturing technique. It allows elements with very complex geometry to be produced using metallic powders. A geometry of manufacturing elements is based only on 3D computer-aided design (CAD) data. The metal powder is melted selectively layer by layer using an ytterbium laser. This paper contains the results of porosity and microhardness analysis made on specimens manufactured during a specially prepared process. Final analysis helped to discover connections between changing hatching distance, exposure speed and porosity. There were no significant differences in microhardness and porosity measurement results in the planes perpendicular and parallel to the machine building platform surface.

scholarly journals An Interactive Tool for Automatic Predimensioning and Numerical Modeling of Arch Dams

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
D. J. Vicente ◽  
J. San Mauro ◽  
F. Salazar ◽  
C. M. Baena
Keyword(s):  
Computer Aided Design ◽  
Complex Geometry ◽  
Design Procedure ◽  
Software Tool ◽  
Gravity Dams ◽  
Detailed Model ◽  
Arch Dams ◽  
Double Curvature ◽  
Aided Design ◽  
Mass Volume

The construction of double-curvature arch dams is an attractive solution from an economic viewpoint due to the reduced volume of concrete necessary for their construction as compared to conventional gravity dams. Due to their complex geometry, many criteria have arisen for their design. However, the most widespread methods are based on recommendations of traditional technical documents without taking into account the possibilities of computer-aided design. In this paper, an innovative software tool to design FEM models of double-curvature arch dams is presented. Several capabilities are allowed: simplified geometry creation (interesting for academic purposes), preliminary geometrical design, high-detailed model construction, and stochastic calculation performance (introducing uncertainty associated with material properties and other parameters). This paper specially focuses on geometrical issues describing the functionalities of the tool and the fundamentals of the design procedure with regard to the following aspects: topography, reference cylinder, excavation depth, crown cantilever thickness and curvature, horizontal arch curvature, excavation and concrete mass volume, and additional elements such as joints or spillways. Examples of application on two Spanish dams are presented and the results obtained analyzed.

Mathematical Model of Cam Profile Based on Heald Frame Motion Characteristics

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Honghuan Yin ◽  
Hongbin Yu ◽  
Junqiang Peng ◽  
Hongyu Shao
Keyword(s):  
Mathematical Model ◽  
Simulation Analysis ◽  
Kinematics Simulation ◽  
Movement Characteristics ◽  
Cam Profile ◽  
Motion Characteristics ◽  
Pitch Curve ◽  
Frame Motion ◽  
The Mathematical Model ◽  
The Given

In this paper, the transmission process of the heald frame driven by the dobby is analyzed. The equivalent motion model of the dobby modulator, the eccentric mechanism, and the motion transmission unit are constructed. Then, based on the given movement characteristics of the heald frame, the mathematical model is built to achieve the cam pitch curve and the cam profile of the modulator. The numerical solution method for this is developed. The preparation of a mathematical model for the new concept of the solving cam profile based on the motion characteristics of heald frames is explained in this study. By setting a 11th polynomial motion law of the heald frame, due to the inconsistency between the outward and return motion laws of the crank-rocker mechanism, an asymmetrical cam profile is obtained under the premise of ensuring that the heald frame’s ascending and descending motions are consistent. Through the kinematics simulation analysis, the correctness of the reverse process is verified.

scholarly journals Micromechanical Characterisation of Ni/PU Hybrid Foams

Materials ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 3746
Author(s):  
Martin Reis ◽  
Kristian König ◽  
Stefan Diebels ◽  
Anne Jung
Keyword(s):  
Computer Aided Design ◽  
Complex Geometry ◽  
Tensile Tests ◽  
Experimental Investigations ◽  
Outer Diameter ◽  
Three Point Bending ◽  
Mechanical Characterisation ◽  
Energy Absorbers ◽  
Hybrid Foams ◽  
Aided Design

The computer-aided design of individual parts and the desire for weight reduction and material savings require further development of new hybrid materials. Ni/PU hybrid foams as a new hybrid material offer great potential for the production of components that are lightweight and yet can absorb large amounts of energy. The development of this structured material is at its beginning and mechanical characterisation on all scales is necessary. Experimental investigations on individual struts must be carried out on the micro scale to understand the structure-properties-relationship. Inspite of the challenges raising due to the complex geometry of the struts, tensile tests, three-point bending tests and micro sections are presented in this work. Due to the stiff Ni coating on the outer diameter of the struts, the resistance against bending is around five times as high as against tensile loading. The correlation between the behaviour of the struts and the macroscopic material behaviour validates the planned use of the foams as energy absorbers.

scholarly journals Mathematical model and geometrical design method of noncircular face gear with intersecting axes

2021 ◽  
pp. 095440622199070
Author(s):  
Dawei Liu ◽  
Zhenzhen Lv ◽  
Bingbing Li
Keyword(s):  
Mathematical Model ◽  
Fourier Series ◽  
Design Method ◽  
Experimental Results ◽  
Transmission Mechanism ◽  
Design Parameters ◽  
Cnc Milling ◽  
Face Gear ◽  
Pitch Curve ◽  
The Mathematical Model

In order to establish the design method of a noncircular face gear (NFG) with intersecting axes, the meshing theory of this gear is investigated based on the principle of space gear meshing. A generalized approach for designing closed pitch curve of the NFG with intersecting axes was proposed based on Fourier series. The mathematical model of the NFG generated by a shaper cutter was established. The fundamental design parameters of the gears were defined, with the principle for determining their values discussed. The prototype of a NFG was machined by 5-axis CNC milling and the motion rule was tested. Experimental results verify the feasibility of the innovative transmission mechanism and the correctness of the mathematical model of NFG with intersecting axes.

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