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.

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.

Compensating analysis of a double circular-arc helical gear by computerized simulation of meshing

2001 ◽  
Vol 215 (7) ◽  
pp. 759-771 ◽  
Author(s):  
C-K Chen ◽  
C-Y Wang
Keyword(s):  
Mathematical Model ◽  
Helical Gear ◽  
Tooth Contact Analysis ◽  
Angular Misalignment ◽  
Circular Arc ◽  
Numerical Examples ◽  
Transmission Errors ◽  
Bearing Contact ◽  
Tooth Surfaces ◽  
Computerized Simulation

A mathematical model of a stepped double circular-arc helical tooth profile with two centre offsets is developed. The conditions of gear meshing that reflect manufacturing and assembly errors are simulated. The locations of bearing contact and the contact path pattern of mating tooth surfaces are determined by tooth contact analysis (TCA). By applying the proposed mathematical model and TCA, single error impact can be determined. To compensate for offset and angular misalignment, the authors propose an adjustable bearing whereby transmission errors can be minimized. The investigation is illustrated with several numerical examples.

Tooth Contact Analysis for Helical Gears with Pinion Circular Arc Teeth and Gear Involute Shaped Teeth

1989 ◽  
Vol 111 (2) ◽  
pp. 278-284 ◽  
Author(s):  
C.-B. Tsay ◽  
Z. H. Fong
Keyword(s):  
Gear Tooth ◽  
Tooth Surface ◽  
Tooth Contact Analysis ◽  
Circular Arc ◽  
Helical Gears ◽  
Numerical Examples ◽  
Bearing Contact ◽  
Tooth Surfaces ◽  
Helical Gearing ◽  
Center Distance

In this paper, the theory of gearing and the concept of differential geometry have been applied to deal with the relations of two mating gears and of their bearing contact. The gear tooth surfaces of this type of gearing contact with each other at every instant at one point instead of one line. The bearing contact of the gear tooth surface is localized and the center of the bearing contact moves along the tooth surface. Thus, this type of helical gearing is not as sensitive to center distance variation and gear axes misalignment. This paper covered the solutions to the following problems: (1) Computer simulation of the conditions of meshing and bearing contact and (2) Investigation of the sensitivity of gears to the errors of manufacturing and assembly. A method of compensation for the dislocation of the bearing contact induced by errors of manufacturing and assembly has been proposed. Five numerical examples have also been presented to illustrate the influence of the above mentioned errors and the method of compensation for the dislocation of bearing contact.

Generation of the Anti-Twist Crowned Helical Gear by Modifying the Gear Rotation Angle in the Hobbing Process

2017 ◽  
Vol 749 ◽  
pp. 161-170
Author(s):  
Ruei Hung Hsu ◽  
Yu Ren Wu ◽  
Shih Sheng Chen
Keyword(s):  
Rotation Angle ◽  
Gear Tooth ◽  
Helical Gear ◽  
Gear Hobbing ◽  
Tooth Flank ◽  
Center Distance

In the gear-hobbing process, the work gear tooth flank is usually longitudinally crowned by varying the center distance between the hob and the work gear. Without crossed angle compensation, however, this center distance variation produces a twisted tooth flank on the work gear. This paper therefore proposes a methodology to reduce this tooth flank twist and achieve anti-twist in longitudinal crowning by modifying the gear rotation angle in the hobbing process which is practiced using a CNC hobbing machine with three synchronous axes.

The Biot Model and Its Application in Viscoelastic Composite Structures

2007 ◽  
Vol 129 (5) ◽  
pp. 533-540 ◽  
Author(s):  
J. Zhang ◽  
G. T. Zheng
Keyword(s):  
Mathematical Model ◽  
Dynamic Behavior ◽  
Composite Structures ◽  
Optimization Method ◽  
Noise Attenuation ◽  
Viscoelastic Materials ◽  
Numerical Techniques ◽  
Viscoelastic Composite ◽  
Biot Model ◽  
Numerical Examples

Application of viscoelastic materials in vibration and noise attenuation of complicated machines and structures is becoming more and more popular. As a result, analytical and numerical techniques for viscoelastic composite structures have received a great deal of attention among researchers in recent years. Development of a mathematical model that can accurately describe the dynamic behavior of viscoelastic materials is an important topic of the research. This paper investigates the procedure of applying the Biot model to describe the dynamic behavior of viscoelastic materials. As a minioscillator model, the Biot model not only possesses the capability of its counterpart, the GHM (Golla-Hughes-McTavish) model, but also has a simpler form. Furthermore, by removing zero eigenvalues, the Biot model can provide a smaller-scale mathematical model than the GHM model. This procedure of dimension reduction is studied in detail here. An optimization method for determining the parameters of the Biot model is also investigated. With numerical examples, these merits, the computational efficiency, and the accuracy of the Biot model are illustrated and proved.

A study of an elbow mechanism generated by a conical cutter

2007 ◽  
Vol 221 (6) ◽  
pp. 727-738 ◽  
Author(s):  
S-C Yang
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Von Mises Stress ◽  
Tooth Contact Analysis ◽  
Rapid Prototyping And Manufacturing ◽  
Von Mises ◽  
Design And Manufacture ◽  
The Mathematical Model ◽  
Further Development ◽  
Kinematic Errors

This paper presents a method for determining the mathematical model of an elbow mechanism with a convex tooth and a concave tooth. Based on this method, the mathematical model presents the meshing principles of a conical cutter meshed with a tooth that is either convex or concave. Using the developed mathematical models and the tooth contact analysis, kinematic errors are investigated according to the obtained geometric modelling of the designed gear meshing when assembly errors are present. The influence of misalignment on kinematic errors has been investigated. The goal of the current study is to investigate von-Mises stress for three teeth contact pairs. A structural load is assumed to act on a gear of the proposed mechanism. The von-Mises of the proposed gear is determined. The conical cutter used in the design and manufacture of the convex and concave gear is shown. For example, the proposed mechanism with a transmission ratio of 3:2 was determined with the aid of the proposed mathematical model. Using rapid prototyping and manufacturing technology, an elbow mechanism with a convex gear, a concave gear and a frame was designed. The RP primitives provide an actual full-size physical model that can be analysed and used for further development. Results from these mathematical models are applicable to the design of an elbow mechanism.

Tooth Contact Analysis of Longitudinal Cycloidal-Crowned Helical Gears With Circular Arc Teeth

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Wei-Shiang Wang ◽  
Zhang-Hua Fong
Keyword(s):  
Gear Tooth ◽  
Longitudinal Direction ◽  
Transmission Error ◽  
Helical Gear ◽  
Contact Analysis ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Circular Arc ◽  
Tooth Flank ◽  
Assembly Error

This paper proposes a new type of double-crowned helical gear that can be continuously cut on a modern Cartesian-type hypoid generator with two face-hobbing head cutters and circular-arc cutter blades. The gear tooth flank is double crowned with a cycloidal curve in the longitudinal direction and a circular arc in the profile direction. To gauge the sensitivity of the transmission errors and contact patterns resulting from various assembly errors, this paper applies a tooth contact analysis technique and presents several numerical examples that show the benefit of the proposed double-crowned helical gear set. In contrast to a conventional helical involute gear, the tooth bearing and transmission error of the proposed gear set are both controllable and insensitive to gear-set assembly error.

Helical Gears With Circular Arc Teeth: Simulation of Conditions of Meshing and Bearing Contact

1985 ◽  
Vol 107 (4) ◽  
pp. 556-564 ◽  
Author(s):  
F. L. Litvin ◽  
Chung-Biau Tsay
Keyword(s):  
Gear Tooth ◽  
Circular Arc ◽  
Helical Gears ◽  
Numerical Examples ◽  
Technological Method ◽  
Bearing Contact ◽  
Paper Cover ◽  
Tooth Surfaces ◽  
Center Distance

Methods proposed in this paper cover: (a) generation of conjugate gear tooth surfaces with localized bearing contact; (b) derivation of equations of gear tooth surfaces; (c) simulation of conditions of meshing and bearing contact; (d) investigation of the sensitivity of gears to the errors of manufacturing and assembly (to the change of center distance and misalignment); and (e) improvement of bearing contact with the corrections of tool settings. Using this technological method we may compensate for the dislocation of the bearing contact induced by errors of manufacturing and assembly. The application of the proposed methods is illustrated by numerical examples. The derivation of the equations is given in the Appendix.

A Novel Loaded Tooth Contact Analysis Procedure with Application to Internal-External Straight Bevel Gear Mesh in Pericyclic Drive

2020 ◽  
pp. 1-22
Author(s):  
Tanmay D. Mathur ◽  
Edward C. Smith ◽  
Robert C. Bill
Keyword(s):  
Gear Tooth ◽  
Contact Analysis ◽  
Bevel Gear ◽  
Gear Train ◽  
Initial Surface ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Gear Mesh ◽  
Number Of Teeth ◽  
Loaded Tooth Contact Analysis

Abstract A comprehensive numerical loaded tooth contact analysis (LTCA) model is proposed for straight bevel gears that exhibit large number of teeth in contact, well beyond involute line of action limits. This kind of contact is observed when the meshing gears have conformal surfaces, as in a Pericyclic mechanical transmission, and is traditionally analysed using finite element simulations. The Pericyclic drive is kinematically similar to an epicyclic bevel gear train, and is characterized by load sharing over large number of teeth in an internal-external bevel gear mesh, large shaft angles (175° - 178°), nutational gear motion, and high reduction ratio. The contact region spreads over a large area on the gear tooth flank due to high contacting surface conformity. Thus, a thick plate Finite Strip method (FSM) was utilized to accurately calculate the gear tooth bending deflection. Based on tooth deformation calculation model, and accounting for initial surface separation, a variational framework is developed to simultaneously solve for load distribution and gear tooth deformation. This is followed by calculation of contact stress, bending stress, mesh stiffness, and transmission error. The results demonstrate the high power density capabilities of the Pericyclic drive and potential for gear noise reduction. The model developed herein is applied with real gear tooth surfaces, as well.

Gear-tolerance optimization based on a response surface method

2018 ◽  
Vol 42 (3) ◽  
pp. 309-322
Author(s):  
Rui Xu ◽  
Kang Huang ◽  
Jun Guo ◽  
Lei Yang ◽  
Mingming Qiu ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Response Surface ◽  
Response Surface Method ◽  
Tolerance Analysis ◽  
Optimization Method ◽  
Small Displacement ◽  
Tooth Contact Analysis ◽  
Tolerance Optimization ◽  
Surface Method ◽  
Low Efficiency

To address the low efficiency of gear-tolerance analysis and optimization, a gear-tolerance optimization method based on a response surface method (RSM) and optimization algorithm is presented. A gear-tolerance mathematical model, including profile deviation, pitch deviation, and geometric deviation, was developed by combining traditional profile modeling with a small displacement torsor (SDT) method. Based on this mathematical model, a tooth-contact analysis method, which takes a variety of deviations into account, and a program to compute transmission error were developed. Using the RSM and a genetic algorithm, a gear-tolerance optimization model was created to consider a variety of gear tolerances as design variables and process cost as an optimization objective. An example of gear-tolerance optimization was analyzed, and the result indicates that the method presented in this paper may help improve the efficiency of gear-tolerance optimization and is practicable for precision gear design.

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