Theory of Gearing

Litvin, F. L.; Seireg, A.

doi:10.1115/1.2916919

Cited by 43 publications

(66 citation statements)

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“…The technology for the generation of the active tooth surfaces of these mechanisms is based on the second Olivier's principle (Abadjiev, 2007;Litvin, 1968 . 0…”

Section: Methodology Of the Synthesis Of The Conjugate Tooth Surfacesmentioning

confidence: 99%

“…n is a normal vector at arbitrary point from 1  , which is written in the coordinate system, p S is of the form (Abadjiev, 2007;Litvin, 1968Litvin, , 1989Litvin, , 1994: …”

Section: Methodology Of the Synthesis Of The Conjugate Tooth Surfacesmentioning

confidence: 99%

“…In accordance with the kinematic approach to synthesis, the contact lines on the tooth surface 1  can be defined by direct application of the basic theorem of meshing (Abadjiev, 2007;Litvin, 1968Litvin, , 1989Litvin, , 1994 ( , , , , , , T , , , T , , , T T , , , Generally, the defined geometry, dimensions and location of the mesh region in the fixed space, as part of the action surface are optimal ones, if:…”

Section: Methodology Of the Synthesis Of The Conjugate Tooth Surfacesmentioning

confidence: 99%

“…Mechanisms, in which the rotations transformation between non-coplanar axes is realized by set of high kinematic joints, which elements comes in and goes out of tangential contact, by following a certain logical sequence, are known in the literature (Abadjiev, 2007;Abadjiev and Abadjieva, 2016 a, b;Litvin, 1968Litvin, , 1989Litvin, , 1994 as hyperboloid gear drives (spatial gear mechanisms with crossed axes of rotations). The rotations transformation is realized as a result of the normal forces, which acts in the places of tangential contact of the elements of high kinematic joints.…”

Section: Introductionmentioning

confidence: 99%

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Synthesis of hyperboloid gear drives: Controlling of the singularity on the active tooth surfaces

Abadjieva¹,

Abadjiev²

2017

J. Mech. Eng. Res.

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The study illustrates the mathematical model, applied to the synthesis of hyperboloid gear drives with taking into account the singularity appearance on the contacting active tooth surfaces. A kinematic approach for registration of the singularity on the tooth surfaces of the synthesized spatial transmissions is shown. The analytical dependencies applicable for defining and controlling of the singularities on the conjugates active surfaces are illustrated.

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“…The technology for the generation of the active tooth surfaces of these mechanisms is based on the second Olivier's principle (Abadjiev, 2007;Litvin, 1968 . 0…”

Section: Methodology Of the Synthesis Of The Conjugate Tooth Surfacesmentioning

confidence: 99%

“…n is a normal vector at arbitrary point from 1  , which is written in the coordinate system, p S is of the form (Abadjiev, 2007;Litvin, 1968Litvin, , 1989Litvin, , 1994: …”

Section: Methodology Of the Synthesis Of The Conjugate Tooth Surfacesmentioning

confidence: 99%

Section: Methodology Of the Synthesis Of The Conjugate Tooth Surfacesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Synthesis of hyperboloid gear drives: Controlling of the singularity on the active tooth surfaces

Abadjieva¹,

Abadjiev²

2017

J. Mech. Eng. Res.

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“…One possible extension of this work is to improve the kinematic interference model and make the addendum and dedendum ratios independent parameters in the design problem. For this work, these ratios are held to the standard values of equations (3) to (6).…”

Section: (6) Pdmentioning

confidence: 99%

Maximum life spiral bevel reduction design

Savage

Prasanna

Coe

1992

28th Joint Propulsion Conference and Exhibit

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SUMMARYOptimization is applied to the design of a spiral bevel gear reduction for maximum life at a given size. A modified feasible directions search algorithm permits a wide variety of inequality constraints and exact design requirements to be met with low sensitivity to initial values. Gear tooth bending strength and minimum contact ratio under load are included in the active constraints. The optimal design of the spiral bevel gear reduction includes the selection of bearing and shaft proportions in addition to gear mesh parameters. System life is maximized subject to a fixed back-cone distance of the spiral bevel gear set for a specified speed ratio, shaft angle, input torque and power. Significant parameters in the design are: the spiral angle, the pressure angle, the numbers of teeth on the pinion and gear and the location and size of the four support bearings. Interpolated polynomials expand the discrete bearing properties and proportions into continuous variables for gradient optimization. After finding the continuous optimum, a designer can analyze near optimal designs for comparison and selection. Design examples show the influence of the bearing lives on the gear parameters in the optimal configurations. For a fixed back-cone distance, optimal designs with larger shaft angles have larger service lives.

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On the generation of conjugate flanks for arbitrary gear geometries

Johann

Scheurle

2009

GAMM-Mitteilungen

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In this paper, we present a novel approach to three-dimensional mathematical gearing theory. We start from a general formulation of the so called basic law of gear kinematics. Based on that we derive an analytic closed form solution for the generation of conjugate tooth flanks, given a (local) parametric representation for any prescribed flank profile. Also, we study the problem of constructing pairs of tooth flanks that give rise to a prescribed surface of action. Surfaces of action will be represented in an implicit global rather than in a parametric way. To illustrate the general theory, we consider a number of specific examples including the standard involute profile for spur gears as well as a more sophisticated three-dimensional generalization of that.

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Theory of Gearing

Cited by 43 publications

References 0 publications

Synthesis of hyperboloid gear drives: Controlling of the singularity on the active tooth surfaces

Synthesis of hyperboloid gear drives: Controlling of the singularity on the active tooth surfaces

Maximum life spiral bevel reduction design

On the generation of conjugate flanks for arbitrary gear geometries

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