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.

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.

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.

Design and Simulation of New Tooth Profile of Flexspline for Harmonic Gear Drive

2015 ◽  
Vol 741 ◽  
pp. 99-107
Author(s):  
Li Zu ◽  
Lan Lan Feng ◽  
Yan Yang Sun
Keyword(s):  
Theoretical Calculation ◽  
Process Simulation ◽  
Cutting Tool ◽  
Parametric Design ◽  
Tooth Profile ◽  
Structure Parameters ◽  
Circular Arc ◽  
Gear Drive ◽  
Calculation Results ◽  
Normal Method

We focused on the parametric design and simulation of new tooth profile “circular arc-involute-circular arc” for flexspline in this paper. Based on the MATLAB software, the basic tooth profile of hob was designed. According to gear generating cutting principle, the simulation of processing for flexspline tooth profile has been realized. By tooth profile normal method, we calculated flexspline tooth profile which is conjugated with the basic tooth profile of the cutting tool, and gave the contrastive studies on process simulation and theoretical calculation. Results show that they are feasible in solving the new tooth profile of flexspline. When changing the key structure parameters, the different changing regulations of flexspline tooth profile can be gained. The research results are meaningful to improve the capacity of harmonic gear drive.

Geometric design and analysis of gear transmission with double circular arc-involute tooth profile

2015 ◽  
Vol 231 (11) ◽  
pp. 2100-2109 ◽  
Author(s):  
Dong Liang ◽  
Bingkui Chen ◽  
Rulong Tan ◽  
Ruijin Liao
Keyword(s):  
Transmission Efficiency ◽  
Tooth Profile ◽  
Gear Transmission ◽  
Motion Simulation ◽  
Circular Arc ◽  
Gear Drive ◽  
Tooth Surfaces ◽  
New Type ◽  
Gear Geometry ◽  
Meshing Characteristics

A novel gear transmission with double circular arc-involute tooth profile is studied in this paper. The generation principle and mathematical models of this proposed gear drive are provided based on gear geometry. The meshing characteristics of tooth surfaces are evaluated according to the analyses of motion simulation, mechanics property and sliding coefficient. The transmission efficiency experiment is based on the developed gear prototype, and a comparison with an involute gear drive is presented. The further study on dynamics analysis and key manufacturing technology will be conducted, and this new type of gear drive is expected to have excellent transmission performance.

Improving the Characteristics of Gear Pumps: Part A — Discharge

2003 ◽  
Author(s):  
Ahmed M. M. El-Bahloul ◽  
Yasser Z. R. Ali
Keyword(s):  
Correction Factor ◽  
Helix Angle ◽  
Tooth Profile ◽  
Radius Of Curvature ◽  
Circular Arc ◽  
Pressure Angle ◽  
Face Width ◽  
Angle Change ◽  
Number Of Teeth ◽  
Gear Pumps

The main objective of this paper is to study the effect of gear geometry on the discharge of gear pumps. We have used gears of circular-arc tooth profile as gear pumps and have compared between these types of gearing and spur, helical gear pumps according to discharge. The chosen module change from 2 to 16 mm, number of teeth change from 8 to 20 teeth, pressure angle change from 10 to 30 deg, face width change from 20 to 120 mm, correction factor change from −1 to 1, helix angle change from 5 to 30 deg, and radii of curvature equal 1.4, 1.5, 2, 2.5, 2.75, and 3m are considered. The authors deduced that the tooth rack profile with radius of curvature equal 2.5, 2.75, 3m for all addendum circular arc tooth and convex-concave tooth profile, and derived equations representing the tooth profile, and calculated the points of intersections between curves of tooth profile. We drive the formulas for the volume of oil between adjacent teeth. Computer program has been prepared to calculate the discharge from the derived formulae with all variables for different types of gear pumps. Curves showing the change of discharge with module, number of teeth, pressure angle, face width, correction factor, helix angle, and radius of curvature are presented. The results show that: 1) The discharge increases with increasing module, number of teeth, positive correction factor, face width and radius of curvature of the tooth. 2) The discharge increases with increasing pressure angle to a certain value and then decreases with increasing pressure angle. 3) The discharge decreases with increasing helix angle. 4) The convex-concave circular-arc gears gives discharge higher than that of alla ddendum circular arc, spur, and helical gear pumps respectively. 5) A curve fitting of the results are done and the following formulae derived for the discharge of involute and circular arc gear pumps respectively: Q=A1bm2z0.895e0.065xe0.0033αe−0.0079βQ=A2bm2z0.91ρ10.669e−0.0047β

Design of backlash-free straight-curved guide devices

2014 ◽  
Vol 228 (15) ◽  
pp. 2833-2843
Author(s):  
Long-Iong Wu ◽  
Kuan-Lwun Shu
Keyword(s):  
Common Point ◽  
Transition Curve ◽  
Circular Arc ◽  
Contact Points ◽  
Straight Line ◽  
Pitch Curve ◽  
Slider Motion ◽  
Guide Device

This article presents a method for designing a planar guide device that can guide sliders to move along a straight-curved rail and can eliminate the backlash between the slider and the rail throughout the whole range of the slider travel. The guide device has many sliders and each slider has three rollers that can separately roll on both sides of the rail. The straight-curved rail is composed of straight sections, connection sections, and circular-arc sections. For each slider, the three normal lines through the contact points between the rollers and the rail must always intersect at a common point, which is an instant center. Using this as a basis, the side profiles of the straight-curved rail can be determined. To avoid infinite jerk of the slider motion, the pitch curve of the connection section should consist of a transition curve, which is interposed between the straight line and the circular arc.

Research on Mathematical Modeling and Kinematic Simulation of Elliptic Family Gears

2013 ◽  
Vol 579-580 ◽  
pp. 300-304 ◽  
Author(s):  
Lian Xia ◽  
Da Zhu Li ◽  
Jiang Han
Keyword(s):  
Performance Analysis ◽  
Tooth Profile ◽  
High Order ◽  
Numerical Control ◽  
Gear Pair ◽  
Cylindrical Gear ◽  
Kinematic Simulation ◽  
Cad Modeling ◽  
Pure Rolling ◽  
Pitch Curve

Elliptic family gears are commonly used in non-circular gears, which include elliptic gear, high-order gear, elliptic deformed gear and high-order deformed gear, thereinto high-order deformed gear can include the elliptic family gears through adjust its order and deformed coefficient. Because non-circular gear has different tooth profile in different position of pitch curve and there is difference in the left and right tooth profile of the same gear tooth, thus the CAD modeling of non-circular gear is difficult for these characteristics; but the precise model of non-circular gear has important significance to the realization of numerical control machining, kinematic simulation and relevant mechanical analysis. This paper deduce the corresponding pure rolling mathematical model based on the pure rolling contact theory that cylindrical gear and non-circular gear mesh in the end face, and realize the CAD modeling of non-circular straight and helical gears by letting the cylindrical gear and non-circular gear make solid geometry operation, which is suitable for pitch curve with convex and concave. The non-circular gear shaping methods with equal polar and equal arc length are simulated by setting different discrete polar angles, and the transmission ratio curve and the angular acceleration curve of driven gear are get through the kinematic simulation of gear pair, which realize the transmission performance analysis of elliptic family gear pair. The above research results can be applied to the modeling and kinematic performance analysis of other non-circular gears.

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