Applied Theory of Gearing: State of the Art

1995 ◽  
Vol 117 (B) ◽  
pp. 128-134 ◽  
Author(s):  
F. L. Litvin
Keyword(s):  
Gear Tooth ◽  
Point Contact ◽  
Applied Theory ◽  
New Developments ◽  
Transmission Errors ◽  
Paper Cover ◽  
Design And Manufacturing ◽  
Tooth Surfaces ◽  
History Of

The contents of the paper cover: a brief history of some concepts of the theory of gearing, and new developments in this area, (i) theory of enveloping curves and surfaces, (ii) simulation of meshing and contact of gear tooth surfaces, (iii) basic kinematic relations as the key to the determination of direct relations between the curvatures of contacting surfaces, and avoidance of singularities, (iv) transfer from line contact of tooth surfaces to point contact, and (v) design and manufacturing of gears with compensated transmission errors caused by misalignment.

Applied Theory of Gearing: State of the Art

1995 ◽  
Vol 117 (B) ◽  
pp. 128-134
Author(s):  
F. L. Litvin
Keyword(s):  
Gear Tooth ◽  
Point Contact ◽  
Applied Theory ◽  
New Developments ◽  
Transmission Errors ◽  
Paper Cover ◽  
Design And Manufacturing ◽  
Tooth Surfaces ◽  
History Of

The contents of the paper cover: a brief history of some concepts of the theory of gearing, and new developments in this area, (i) theory of enveloping curves and surfaces, (ii) simulation of meshing and contact of gear tooth surfaces, (iii) basic kinematic relations as the key to the determination of direct relations between the curvatures of contacting surfaces, and avoidance of singularities, (iv) transfer from line contact of tooth surfaces to point contact, and (v) design and manufacturing of gears with compensated transmission errors caused by misalignment.

Application of Finite Element Analysis for Determination of Load Share, Real Contact Ratio, Precision of Motion, and Stress Analysis

1996 ◽  
Vol 118 (4) ◽  
pp. 561-567 ◽  
Author(s):  
F. L. Litvin ◽  
J.-S. Chen ◽  
J. Lu ◽  
R. F. Handschuh
Keyword(s):  
Finite Element ◽  
Stress Analysis ◽  
Point Contact ◽  
Principal Curvatures ◽  
Contact Ratio ◽  
Element Analysis ◽  
Transmission Errors ◽  
Real Contact ◽  
Tooth Surfaces

A loaded gear drive with point contact between tooth surfaces is considered. The principal curvatures and directions at a current point of tangency, the contact paths on tooth surfaces, and the transmission errors caused by misalignment we consider as known. In this paper the following topics are covered: (1) Determination of the contact force and its distribution over the contact ellipse; (2) Determination of the tooth deflection, the load share, and the real contact ratio; and (3) Stress analysis by application of the finite element method. The discussed approach is illustrated with a numerical example.

scholarly journals Computerized Design and Generation of Low-Noise Helical Gears with Modified Surface Topology

1995 ◽  
Vol 117 (2A) ◽  
pp. 254-261 ◽  
Author(s):  
F. L. Litvin ◽  
N. X. Chen ◽  
J. Lu ◽  
R. F. Handschuh
Keyword(s):  
Gear Tooth ◽  
Error Function ◽  
Transmission Error ◽  
Low Noise ◽  
Surface Topology ◽  
Helical Gears ◽  
Transmission Errors ◽  
Bearing Contact ◽  
Pinion Gear ◽  
Tooth Surfaces

An approach for the design and generation of low-noise helical gears with localized bearing contact is proposed. The approach is applied to double circular arc helical gears and modified involute helical gears. The reduction of noise and vibration is achieved by application of a predesigned parabolic function of transmission errors that is able to absorb a discontinuous linear function of transmission errors caused by misalignment. The localization of the bearing contact is achieved by the mismatch of pinion-gear tooth surfaces. Computerized simulation of meshing and contact of the designed gears demonstrated that the proposed approach will produce a pair of gears that has a parabolic transmission error function even when misalignment is present. Numerical examples for illustration of the developed approach are given.

Computerized Simulation of Transmission Errors and Shift of Bearing Contact for Hypoid Gear Drive With Conjugate Gear Tooth Surfaces

1994 ◽  
Author(s):  
Faydor L. Litvin ◽  
Jui-Sheng Chen ◽  
Thomas M. Sep ◽  
Jyh-Chiang Wang
Keyword(s):  
Gear Tooth ◽  
Low Noise ◽  
Linear Functions ◽  
Hypoid Gear ◽  
Transmission Errors ◽  
Gear Drive ◽  
Bearing Contact ◽  
Parabolic Function ◽  
Tooth Surfaces ◽  
Computerized Simulation

Abstract Computerized investigation of the influence of alignment errors on the transmission errors and the shift of the bearing contact is proposed. The investigation is performed for an imaginary hypoid gear drive with conjugate tooth surfaces. It is proven that the transmission functions caused by misalignment are periodic discontinues almost linear functions with the frequency of cycle of meshing. The above functions can be totally absorbed by a predesigned parabolic function. The shift of the bearing contact caused by misalignment has been determined as well. The performed investigation is based on computerized simulation of meshing and contact of gear tooth surfaces. The machine-tool settings for the generation of the designed gear drive have been determined. Numerical example that illustrates the developed theory is given. The performed investigation allows to determine the influence of gear misalignment on transmission errors, and design a low-noise hypoid gear drive by a properly predesigned parabolic function of transmission errors.

Computerized Design, Generation and Simulation of Meshing and Contact of Modified Flender Worm-Gear Drives

1996 ◽  
Author(s):  
I. H. Seol ◽  
Faydor L. Litvin
Keyword(s):  
Gear Tooth ◽  
Worm Gear ◽  
Numerical Examples ◽  
Transmission Errors ◽  
Gear Drive ◽  
Bearing Contact ◽  
Tooth Surfaces ◽  
Design Generation ◽  
Computerized Simulation ◽  
Gear Drives

Abstract The worm and worm-gear tooth surfaces of existing design of Flender gear drive are in line contact at every instant and the gear drive is very sensitive to misalignment. Errors of alignment cause the shift of the bearing contact and transmission errors. The authors propose : (1) Methods for computerized simulation of meshing and contact of misaligned worm-gear drives of existing design (2) Methods of modification of geometry of worm-gear drives that enable to localize and stabilize the bearing contact and reduce the sensitivity of drives to misalignment (3) Methods for computerized simulation of meshing and contact of worm-gear drives with modified geometry The proposed approach was applied as well for the involute (David Brown) and Klingelnberg type of worm-gear drives. Numerical examples that illustrate the developed theory are provided.

Optimal Tooth Modifications in Hypoid Gears

2003 ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Angular Position ◽  
Point Contact ◽  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Transmission Errors ◽  
Tool Profile

A method for the determination of optimal tooth modifications in hypoid gears based on improved load distribution and reduced transmission errors is presented. The modifications are introduced into the pinion tooth surface by using a cutter with bicircular profile and by changing the cutter diameter. In the optimization of tool parameters the influence of shaft misalignments of the mating members is included. As the result of these modifications a point contact of the meshed teeth surfaces appears instead of line contact; the hypoid gear pair becomes mismatched. By using the method presented in [1] the influence of tooth modifications introduced on tooth contact and transmission errors is investigated. Based on the results that was obtained the radii and position of circular tool profile arcs and the cutter diameter for pinion teeth generation were optimized. By applying the optimal tool parameters, the maximum tooth contact pressure is reduced by 16.22% and the angular position error of the driven gear by 178.72%, in regard to the hypoid gear pair with a pinion manufactured by a cutter of straight-sided profile and of diameter determined by the commonly used methods.

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.

Mathematical models of hobs for conjugate-curve gears having three contact points

2014 ◽  
Vol 229 (13) ◽  
pp. 2402-2411 ◽  
Author(s):  
Yan’e Gao ◽  
Bingkui Chen ◽  
Dong Liang
Keyword(s):  
Mathematical Models ◽  
Contact Stress ◽  
Gear Tooth ◽  
Load Capacity ◽  
Point Contact ◽  
Curvature Radius ◽  
Circular Arc ◽  
Normal Section ◽  
Contact Points ◽  
Tooth Surfaces

Conjugate-curve gears are the gears which are point contact and the locus curves of the contact points are conjugate curves. The contact pattern of the conjugate-curve gear tooth surfaces are convex to concave, which reduces the contact stress of the tooth surfaces due to the small value of the relative curvature radius at the contact point. The tubular tooth surfaces of the conjugate-curve gears have one pair of conjugate curves. To decrease the running-in time and increase the load capacity, the conjugate-curve gears having three pairs of conjugate curves are designed. The contact stress of the tooth surfaces having three contact points is much smaller than that of the tubular tooth surfaces in the computer contact analysis. For the further study of the performance of the conjugate-curves gears having three contact points, hobs are considered to manufacture the gears. Two mismatched rack cutters having three contact points are applied for the design of hobs. The working edge in the normal section profile of the rack cutter for the hob generating the pinion is a circular arc and the working edges in the normal section of the rack cutter for the hob generating the gear are two parabolic curves that are tangent to the convex circular arc. By applying the designed rack cutter profiles, the principle of coordinate transformation, the differential geometry theory, and the theory of gearing, mathematical models of the hobs are established. To verify the proposed tooth profile and the hobs, the experimental cutting trials and the load capacity test are carried out. The final accuracy of the gear satisfies the design requirements. The results demonstrate the feasible of the proposed design method.

Application and Investigation of Modified Helical Gears With Several Types of Geometry

2007 ◽  
Author(s):  
Ignacio Gonzalez-Perez ◽  
Alfonso Fuentes ◽  
Faydor L. Litvin ◽  
Kenichi Hayasaka ◽  
Kenji Yukishima
Keyword(s):  
Gear Tooth ◽  
Tooth Surface ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Helical Gears ◽  
Transmission Errors ◽  
Advantages And Disadvantages ◽  
Bearing Contact ◽  
Tooth Surfaces ◽  
Gear Drives

Involute helical gears with modified geometry for transformation of rotation between parallel axes are considered. Three types of topology of geometry are considered: (1) crowning of pinion tooth surface is provided only partially by application of a grinding disk; (2) double crowning of pinion tooth surface is obtained applying a grinding disk; (3) concave-convex pinion and gear tooth surfaces are provided (similar to Novikov-Wildhaber gears). Localization of bearing contact is provided for all three types of topology. Computerized TCA (Tooth Contact Analysis) is performed for all three types of topology to obtain: (i) path of contact on pinion and gear tooth surfaces; (ii) negative function of transmission errors for misaligned gear drives (that allows the contact ratio to be increased). Stress analysis is performed for the whole cycle of meshing. Finite element models of pinion and gear with several pairs of teeth are applied. A relative motion is imposed to the pinion model that allows friction between contact surfaces to be considered. Numerical examples have confirmed the advantages and disadvantages of the applied approaches for generation and design.

New developments in the design and generation of gear drives

2001 ◽  
Vol 215 (7) ◽  
pp. 747-757 ◽  
Author(s):  
F. L. Litvin ◽  
A Fuentes ◽  
A Demenego ◽  
D Vecchiato ◽  
Q Fan
Keyword(s):  
Point Contact ◽  
Tooth Surface ◽  
Helical Gears ◽  
Transmission Errors ◽  
Bevel Gears ◽  
Bearing Contact ◽  
Analysis And Synthesis ◽  
Tooth Surfaces ◽  
Design Generation ◽  
Gear Drives

Design, generation and simulation of the meshing and contact of gear drives with favourable bearing contact and reduced noise are considered. The proposed approach is based on replacement of the instantaneous line of contact of tooth surfaces by point contact and on application of a predesigned parabolic function of transmission errors that is able to absorb linear discontinuous functions of transmission errors caused by misalignment. Basic algorithms for analysis and synthesis of gear drives are presented. The developed theory is applied for design and generation of the following gear drives with modified geometry: (a) spur and helical gears, (b) a new version of Novikov-Wildhaber (N-W) helical gears, (c) asymmetric face gear drives with a spur pinion, (d) formate-cut spiral bevel gears. Generation of the tooth surface of a worm gear is presented as the formation of a two-branch envelope. The discussed topics are illustrated with examples.

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