Open Access Open Access  Restricted Access Subscription Access

Main Tasks of Classical Theory of Gearing and Problems of Optimization Synthesis of Tooth Surface

Babichev D.T.

Abstract


The classical theory of gearing (by Faydor Litvin) includes two main tasks: 1) Task of Synthesis: the tooth surface of one gearwheel is known, the tooth surface of the second gearwheel is to be determined. 2) Task of Analysis (reverse task): the tooth surfaces of two moving members are known, the law of motion is to be determined. It is proposed to add the third task to two main tasks of the theory of gearing: tooth surface synthesis according to the assigned surface of meshing. From mathematical point of view, this task is different significantly as compared to two common ones. It is not reduced to the Task of Synthesis by Litvin. It is solved by integrating the differential equation of meshing by numerical methods. One of the reasons of innovation is the perspective of optimization synthesis of the tooth surface based on analysis of quality indicators in all possible contact points (by Sergey Lagutin - in all space of meshing). Within such a synthesis, the line or surface of meshing is firstly synthesized: they are drawn in areas with the most favorable or assigned values of the chosen criterion of the load capacity. Surfaces of contacting teeth are determined after synthesis of the line (surface) of meshing. Certain problems are considered, that appear at optimization synthesis based on analysis of features of the space of meshing: the dualism of the task of gear synthesis when using the reduced radius of curvature in the target function, the problem of the target function degeneration and oth. For eliminating some of these problems, the local quality criteria is required that estimates the local positive effect and simultaneously influences the global indicator (first of all, the contact ratio). It is proposed and substantiated to apply the specific work of surfaces AF as such a criterion.

Keywords


theory of gearing; quality parameters of higher pairs; optimization synthesis of tooth flanks

Full Text

Galleys

PDF (Русский)
References References

Литвин Ф. Л. Теория зубчатых зацеплений. - М. : Наука. - 1968. - 584 с.

Там же.

Там же.

Там же.

Там же.

Там же.

Там же.

Шишов В. П., Носко П. Л., Филь П. В. Теоретические основы синтеза передач зацеплением. - Луганск : СНУ им. Даля, 2006. - 408 с.

Babichev D., Storchak M. Synthesis of cylindrical gears with optimum rolling fatigue strength // Production Engineering. Research and Development. - 2015. - Vol. 9, no. 1. - P. 87-97. - ISSN 0944-6524.

Лагутин С. А. Пространство зацепления и его элементы // Машиноведение. - 1987. - № 4. - С. 69-73.

Там же.

Справочник по геометрическому расчету эвольвентных зубчатых и червячных передач / И. А. Болотовский, В. И. Безруков, О. Ф. Васильев [и др.]. - М. : Машиностроение,1986. - 448 с.

Гольдфарб В. И., Tкачёв А. А. Проектирование эвольвентных цилиндрических передач. Новый подход. - Ижевск : Изд-во ИжГТУ, 2004. - 94 с.

Babichev D., Storchak M. Указ. соч.

Лагутин С. А. Указ. соч.

Шишов В. П., Носко П. Л., Филь П. В. Указ. соч.

Babichev D., Storchak M. Указ. соч.

Лагутин С. А. Указ. соч.

Гольдфарб В. И., Tкачёв А. А. Указ. соч.

Lebeck Alan O., Radzimovsky E. J. The Synthesis of profile shapes and spur gears of high to-ad Capacity // Trans. ASME, 1970, B92, no. 3, p. 543-553.

Goldfarb V., Malina O., Trubachev E. New Concept of the Process of Designing Gearboxes and Gear Systems // Mechanisms and Machine Science. - 2016. - No. 4. Theory and Practice of Gearing and Transmissions. - Pp. 405-423.

Бабичев Д. Т. Развитие теории зацеплений и формообразования поверхностей на основе новых геометро-кинематических представлений : дис. … д-ра техн. наук. - Тюмень, 2005. - 421 с.

Бабичев Д. Т., Сторчак М. Г., Бабичев Д. А. Основы концепции синтеза рабочих поверхностей зубьев цилиндрических передач, обладающих заданной контактной прочностью // Современное машиностроение. Наука и образование. - 2012. - С. 150-160. - SSN 2223-0807.

Lebeck Alan O., Radzimovsky E. J. Указ. соч.

Babichev D., Storchak M. Указ. соч.

Бабичев Д. Т. Указ. соч.

Бабичев Д. Т., Сторчак М. Г., Бабичев Д. А. Указ. соч.

Бабичев Д. Т. Указ. соч.

Babichev D., Storchak M. Указ. соч.

Шишов В. П., Носко П. Л., Филь П. В. Указ. соч.




DOI: http://dx.doi.org/10.22213/2413-1172-2017-2-71-74

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM


Copyright (c) 2017 Bulletin of Kalashnikov ISTU

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.


ISSN 1813-7903 (Print)
ISSN 2413-1172 (Online)