title: ÐÐ¾Ð½ÐµÑÐ½Ð¾-ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð³Ð¾ ÑÐµÐ´ÑÐºÑÐ¾ÑÐ°
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Finite element modelling of a wave gearbox
Creators: name: ÐÑÐ¾ÑÐ¾ÑÐµÐ½ÐºÐ¾Ð²Ð°, ÐÑÐ¸Ð½Ð°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2024
Subjects: Ð ÐµÐ´ÑÐºÑÐ¾ÑÑ
ÐÐ¾Ð½ÐµÑÐ½ÑÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð² Ð¼ÐµÑÐ¾Ð´

description: Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¾ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð·ÑÐ±ÑÐµÐ², Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð° Ð²Ð°Ð»Ð¸Ð´Ð°ÑÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð³Ð¸Ð±ÐºÐ¾Ð³Ð¾ ÐºÐ¾Ð»ÐµÑÐ°. Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð° Ð¼ÐµÑÐ¾Ð´Ð¸ÐºÐ° Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð³Ð¾ ÑÐµÐ´ÑÐºÑÐ¾ÑÐ°, Ð´Ð»Ñ Ð¿Ð¾Ð´ÑÐ²ÐµÑÐ¶Ð´ÐµÐ½Ð¸Ñ ÐºÐ¾ÑÐ¾ÑÐ¾Ð¹ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¾ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð³Ð¸Ð±ÐºÐ¾Ð³Ð¾ ÐºÐ¾Ð»ÐµÑÐ° Ð² ÑÐ¾ÑÑÐ°Ð²Ðµ ÑÐµÐ´ÑÐºÑÐ¾ÑÐ°. ÐÑÐ½Ð¾Ð²Ð½ÑÐ¼ Ð¿ÑÐµÐ¸Ð¼ÑÑÐµÑÑÐ²Ð¾Ð¼ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð½Ð¾Ð¹ Ð¼ÐµÑÐ¾Ð´Ð¸ÐºÐ¸ ÑÐ²Ð»ÑÐµÑÑÑ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ÑÑÑ ÑÐ¾ÐºÑÐ°ÑÐµÐ½Ð¸Ñ Ð²ÑÐµÐ¼ÐµÐ½Ð¸ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ñ Ð¿Ð¾Ð»Ð½Ð¾ÑÐ°Ð·Ð¼ÐµÑÐ½Ð¾Ð³Ð¾ ÑÐ°ÑÑÐµÑÐ° Ð¼ÐµÑÐ°Ð½Ð¸Ð·Ð¼Ð°, ÑÐ°ÑÑÑÑ ÐºÐ¾ÑÐ¾ÑÐ¾Ð³Ð¾ ÑÐ²Ð»ÑÐµÑÑÑ Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð¹ ÑÐµÐ´ÑÐºÑÐ¾Ñ. ÐÐ¾Ð²Ð°Ñ Ð¼ÐµÑÐ¾Ð´Ð¸ÐºÐ° Ð·Ð°ÐºÐ»ÑÑÐ°ÐµÑÑÑ Ð² Ð¾ÑÐºÐ°Ð·Ðµ Ð¾Ñ ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ð¸Ñ Ð³Ð¸Ð±ÐºÐ¾Ð³Ð¾ ÐºÐ¾Ð»ÐµÑÐ° ÐºÐ°Ðº ÑÐ²ÑÑÐ´Ð¾Ð³Ð¾ ÑÐµÐ»Ð° Ð¸ Ð¿ÐµÑÐµÑÐ¾Ð´ Ðº Ð¾Ð±Ð¾Ð»Ð¾ÑÐµÑÐ½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð² ÑÑÐµÑÐ¼ÐµÑÐ½Ð¾Ð¹ Ð¿Ð¾ÑÑÐ°Ð½Ð¾Ð²ÐºÐµ Ð´Ð»Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð·ÑÐ±ÑÐ°ÑÐ¾Ð³Ð¾ Ð·Ð°ÑÐµÐ¿Ð»ÐµÐ½Ð¸Ñ Ð¸ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ ÑÐ°ÑÑÐ¸ Ð³Ð¸Ð±ÐºÐ¾Ð³Ð¾ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ°. Ð¢Ð°ÐºÐ¾Ð¹ Ð¿Ð¾Ð´ÑÐ¾Ð´ Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÐµÑ Ð·Ð½Ð°ÑÐ¸ÑÐµÐ»ÑÐ½Ð¾ ÑÐ¾ÐºÑÐ°ÑÐ¸ÑÑ Ð²ÑÐµÐ¼Ñ ÑÐ°ÑÑÐµÑÐ¾Ð² Ð·Ð° ÑÑÐµÑ ÑÑÑÐµÑÑÐ²ÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐ¼ÐµÐ½ÑÑÐµÐ½Ð¸Ñ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð° ÑÑÐµÐ¿ÐµÐ½ÐµÐ¹ ÑÐ²Ð¾Ð±Ð¾Ð´Ñ Ð² Ð¼Ð¾Ð´ÐµÐ»ÑÑ Ð¿Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÑÐ²ÐµÑÐ´Ð¾ÑÐµÐ»ÑÐ½ÑÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð². ÐÑÐ¸ ÑÑÐ¾Ð¼ Ð´Ð¾ÑÑÐ¸Ð³Ð°ÐµÑÑÑ Ð°Ð½Ð°Ð»Ð¾Ð³Ð¸ÑÐ½Ð°Ñ ÑÐ¾ÑÐ½Ð¾ÑÑÑ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ð±Ð»Ð°Ð³Ð¾Ð´Ð°ÑÑ Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð° ÑÐ·Ð»Ð¾Ð² Ð¸Ð½ÑÐµÐ³ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¿Ð¾ ÑÐ¾Ð»ÑÐ¸Ð½Ðµ Ð¾Ð±Ð¾Ð»Ð¾ÑÐµÑÐ½Ð¾Ð³Ð¾ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ° Ð¸ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð² Ð²ÑÐ¾ÑÐ¾Ð³Ð¾ Ð¿Ð¾ÑÑÐ´ÐºÐ°. ÐÐ¾Ð¼Ð¸Ð¼Ð¾ ÑÐ¼ÐµÐ½ÑÑÐµÐ½Ð¸Ñ Ð²ÑÐµÐ¼ÐµÐ½Ð½ÑÑ Ð·Ð°ÑÑÐ°Ñ Ð½Ð° ÑÐ°ÑÑÐµÑÑ, Ð½Ð¾Ð²Ð°Ñ Ð¼ÐµÑÐ¾Ð´Ð¸ÐºÐ° ÑÐ°ÐºÐ¶Ðµ ÑÐ½Ð¸Ð¶Ð°ÐµÑ ÑÑÑÐ´Ð¾Ð·Ð°ÑÑÐ°ÑÑ Ð½Ð° Ð¿Ð¾Ð´Ð³Ð¾ÑÐ¾Ð²ÐºÑ Ð¼Ð¾Ð´ÐµÐ»Ð¸, Ð¿Ð¾ÑÐºÐ¾Ð»ÑÐºÑ Ð½Ðµ ÑÑÐµÐ±ÑÐµÑÑÑ ÑÐ¿ÑÐ¾ÑÐµÐ½Ð¸Ðµ ÑÐ»Ð¾Ð¶Ð½Ð¾Ð¹ Ð³ÐµÐ¾Ð¼ÐµÑÑÐ¸Ð¸ Ð·Ð°ÑÐµÐ¿Ð»ÐµÐ½Ð¸Ñ Ð´Ð»Ñ Ð¿Ð¾ÑÐ»ÐµÐ´ÑÑÑÐµÐ³Ð¾ Ð·Ð°Ð¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ñ Ð¾Ð±ÑÐµÐ¼Ð¾Ð² ÑÐ²ÐµÑÐ´Ð¾ÑÐµÐ»ÑÐ½ÑÐ¼Ð¸ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ°Ð¼Ð¸.
description: In this paper, a study of tooth modelling methods has been carried out and a flexible wheel model has been validated. The method of wave gearbox modelling has been developed, for the validation of which the flexible wheel as a part of the gearbox has been modelled. The main advantage of the developed methodology is the possibility to reduce the time of full-size calculation of the mechanism, part of which is the wave gearbox. The new technique consists in refusing to consider the flexible wheel as a solid body and switching to a shell model in a three-dimensional formulation for modelling the gear mesh and the cylindrical part of the flexible element. This approach allows to reduce considerably the calculation time due to the substantial reduction of the number of degrees of freedom in the models in comparison with the use of solid elements. At the same time, similar accuracy of results is achieved due to the change of the number of integration nodes along the thickness of the shell element and the use of second-order elements. In addition to the reduction in computational time, the new methodology also reduces the labour required for model preparation, as there is no need to simplify the complex meshing geometry to fill the volumes with solid elements.