Revisiting Plane-Generated Gear Tooth Surfaces: A Novel Design Perspective

2015 ◽  
Author(s):  
Alessio Artoni ◽  
Massimo Guiggiani
Keyword(s):  
Gear Tooth ◽  
Transmission Function ◽  
Tooth Surface ◽  
Generation Process ◽  
Noise Emission ◽  
Helical Gears ◽  
Beveloid Gears ◽  
Tooth Surfaces ◽  
Involute Gears ◽  
The One

The teeth of ordinary spur and helical gears are generated by a (virtual) rack provided with planar generating surfaces. The resulting tooth surface shapes are a circle-involute cylinder in the case of spur gears, and a circle-involute helicoid for helical gears. Advantages associated with involute geometry are well known: in particular, the motion transmission function is insensitive to center distance variations, and contact lines (or points, when a corrective surface mismatch is applied) evolve along a fixed plane of action, thereby reducing vibrations and noise emission. As a result, involute gears are easier to manufacture and assemble than non-involute gears, and silent to operate. A peculiarity of their generation process is that the motion of the generating planar surface, seen from the fixed space, is a rectilinear translation (while the gear blank is rotated about a fixed axis): the component of such translation that is orthogonal to the generating plane is the one that ultimately dictates the shape of the generated, envelope surface. Starting from this basic fact, we set out to investigate this type of generation-by-envelope process and to profitably use it to explore new potential design layouts. In particular, with some similarity to the basic principles underlying conical involute (or Beveloid) gears, but within a broader scope, we propose a generalization of these concepts to the case of involute surfaces for motion transmission between skew axes (and intersecting axes as a special case). Analytical derivations demonstrate the theoretical possibility of involute profiles transmitting motion between skew axes through line contact and, perihaps more importantly, they lead to apparently novel geometric designs featuring insensitivity of transmission ratio to all misalignments within relatively large limits. The theoretical developments are confirmed by various numerical examples.

Revisiting Generation and Meshing Properties of Beveloid Gears

2017 ◽  
Vol 139 (9) ◽  
Author(s):  
Alessio Artoni ◽  
Massimo Guiggiani
Keyword(s):  
Tooth Surface ◽  
Generation Process ◽  
Spur Gears ◽  
Helical Gears ◽  
Additional Degree ◽  
Beveloid Gears ◽  
Fixed Space ◽  
Fixed Axis ◽  
The One ◽  
Special Case

The teeth of ordinary spur and helical gears are generated by a (virtual) rack provided with planar generating surfaces. The resulting tooth surface shapes are a circle-involute cylinder in the case of spur gears, and a circle-involute helicoid for helical gears. Advantages associated with involute geometry are well known. Beveloid gears are often regarded as a generalization of involute cylindrical gears involving one additional degree-of-freedom, in that the midplane of their (virtual) generating rack is inclined with respect to the axis of the gear being generated. A peculiarity of their generation process is that the motion of the generating planar surface, seen from the fixed space, is a rectilinear translation (while the gear blank is rotated about a fixed axis); the component of such translation that is orthogonal to the generating plane is the one that ultimately dictates the shape of the generated, envelope surface. Starting from this basic fact, we set out to revisit this type of generation-by-envelope process and to profitably use it to explore peculiar design layouts, in particular for the case of motion transmission between skew axes (and intersecting axes as a special case). Analytical derivations demonstrate the possibility of involute helicoid profiles (beveloids) transmitting motion between skew axes through line contact and, perhaps more importantly, they lead to the derivation of designs featuring insensitivity of the transmission ratio to all misalignments within relatively large limits. The theoretical developments are confirmed by various numerical examples.

Tooth Undercutting of Beveloid Gears

2000 ◽  
Author(s):  
Chia-Chang Liu ◽  
Chung-Biau Tsay
Keyword(s):  
Gear Tooth ◽  
Singular Points ◽  
Tooth Surface ◽  
Involute Gear ◽  
Beveloid Gears ◽  
Tooth Surfaces

Abstract A beveloid gear can be viewed as an involute gear of which the profile-shifted coefficient linearly decreases from the heel to the toe. Therefore, tooth undercutting occurs and singular points appear on the tooth surfaces near the toe. When undercutting occurs, the gear tooth is comparatively weak. In this study, the conditions of tooth undercutting of beveloid gears were derived and specific phenomena were also investigated by numerical illustrated examples. In addition, according to the characteristics of tooth undercutting on the beveloid gear tooth surface, a novel type hob cutter with varying cutting depths was designed to avoid tooth undercutting of the beveloid gear.

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.

Investigation of tooth contact deviations from the plane of action and their effects on gear transmission error

2005 ◽  
Vol 219 (5) ◽  
pp. 501-509 ◽  
Author(s):  
C H Wink ◽  
A L Serpa
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Contact Analysis ◽  
Gear Transmission ◽  
Tooth Surface ◽  
Tooth Contact ◽  
Helical Gears ◽  
Influence Coefficients ◽  
Manufacturing Errors ◽  
Tooth Surfaces

In this paper tooth contact deviations from the plane of action and their effects on gear transmission error are investigated. Tooth contact deviations come from intentional modification of involute tooth surfaces such as tip and root profile relief; manufacturing errors such as adjacent pitch error, profile errors, misalignment and lead errors; and tooth elastic deflections under load, for example, bending and local contact deflections. Those deviations are usually neglected on gear tooth contact models. A procedure to calculate the static transmission error of spur and helical gears under loading is proposed. In the proposed procedure, contact analysis is carried out on the whole tooth surface, eliminating the usual assumption that tooth contact occurs only on the plane of action. Lead and profile modifications, manufacturing errors and tooth elastic deflections are considered in the calculation procedure. The method of influence coefficients is employed to calculate the tooth elastic deflections. Load distribution on gear meshing is determined using an iterative-incremental method. Results of some numerical examples of spur and helical gears are analysed and discussed. The results indicate that the tooth contact deviations from the plane of action can lead to imprecision on the gear transmission error calculation if they are not take into account. Therefore, the proposed procedure provides a more accurate calculation methodology of gear transmission error, since a global contact analysis is done.

Tooth Undercutting of Beveloid Gears

2000 ◽  
Vol 123 (4) ◽  
pp. 569-576 ◽  
Author(s):  
Chia-Chang Liu ◽  
Chung-Biau Tsay
Keyword(s):  
Gear Tooth ◽  
Singular Points ◽  
Tooth Surface ◽  
Involute Gear ◽  
Beveloid Gears ◽  
Tooth Surfaces

A beveloid gear can be viewed as an involute gear of which the profile-shifted coefficient linearly decreases from the heel to the toe. Therefore, tooth undercutting occurs and singular points appear on the tooth surfaces near the toe. When undercutting occurs, the gear tooth is comparatively weak. In this study, the conditions of tooth undercutting of beveloid gears were derived and specific phenomena were also investigated by numerical illustrated examples. In addition, according to the characteristics of tooth undercutting on the beveloid gear tooth surface, two practicable methods were also proposed to avoid the tooth undercutting of beveloid gears.

Kinematic and Geometric Models of Gear Drives

1996 ◽  
Vol 118 (4) ◽  
pp. 544-550 ◽  
Author(s):  
F. L. Litvin ◽  
I. H. Seol ◽  
D. Kim ◽  
J. Lu ◽  
A. G. Wang ◽  
...  
Keyword(s):  
Gear Tooth ◽  
Helical Gears ◽  
Transmission Errors ◽  
Bevel Gears ◽  
Bearing Contact ◽  
Tooth Surfaces ◽  
Involute Gears ◽  
Computerized Simulation ◽  
Gear Drives ◽  
The Impact

A methodology is proposed for the modification of gear tooth surfaces that reduces the impact of gear drive misalignment, the shift of the bearing contact (accompanied in some cases with edge contact), and the occurrence of discontinuous functions of transmission errors. The proposed approach is tested by computerized simulation of meshing and contact for unloaded and loaded gear drives. Applications of geometry modifications to the design of spur and helical involute gears, double-circular helical gears, face-gear drives, face-milled spiral bevel gears with constant tooth height and worm-gear drives are represented.

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.

Shaping Principle in Hobbing and Analysis on Errors of Involute Gear Tooth Surfaces

2011 ◽  
Vol 189-193 ◽  
pp. 4173-4176 ◽  
Author(s):  
Wen Long Li ◽  
Li Wei ◽  
Shao Jun He
Keyword(s):  
Gear Tooth ◽  
Tooth Surface ◽  
Spur Gears ◽  
Helical Surface ◽  
Helical Gears ◽  
Surface Errors ◽  
Error Characteristics ◽  
Involute Gear ◽  
Characteristic Lines ◽  
Tooth Surfaces

An involute helical surface is one of the surfaces widely used in engineering. There are four characteristics lines ( involute, helix, straight generatrix, pathofcontact) on it. On the basis of characteristic lines, the shaping principle in hobbing is studied, the error characteristics and their interrelations are analyzed. The analysis formula of involute gear tooth surface errors is given for spur gears and helical gears.

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.

Estimation of Gear Friction Coefficient using Directional Parameter of Tooth Surface

2021 ◽  
pp. 1-27
Author(s):  
Junichi Hongu ◽  
Ryohei Horita ◽  
Takao Koide
Keyword(s):  
Friction Coefficient ◽  
Contact Surface ◽  
Gear Tooth ◽  
Correction Term ◽  
Tooth Surface ◽  
Oil Film ◽  
Tooth Surfaces ◽  
Frictional Coefficients ◽  
Finishing Processes ◽  
The Relationship

Abstract This study proposes a modification of the Matsumoto equation using a directional parameter of tooth surfaces to adapt various gear finishing processes. The directional parameters of a contact surface, which affect oil film formations, have been discussed in the field of tribology; but this effect has been undetermined on the meshing gear tooth surfaces having directional machining marks. Thus, this paper investigates the relationship between the gear frictional coefficients and the directional parameters (based on ISO25178) of their tooth surfaces with the various finishing processes; and modifies the Matsumoto equation by introducing a new directional parameter to augment the various gear finishing processes. Our findings indicate that through optimizing the coefficient of the correction term the include the new directional parameter, the calculated friction values using the modified Matsumoto equation correlate more highly to the experimental friction values than that using the unmodified Matsumoto equation.

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