title: ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð½ÐµÑÐ°Ð²Ð½Ð¾Ð¼ÐµÑÐ½Ð¾ÑÑÐ¸ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ ÑÐ´ÐµÐ»ÑÐ½Ð¾Ð¹ ÑÐ¸Ð»Ñ Ð² Ð·ÑÐ±ÑÐ°ÑÐ¾Ð¼ Ð·Ð°ÑÐµÐ¿Ð»ÐµÐ½Ð¸Ð¸
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Study of the uneven distribution of specific force in gearing
Creators: name: ÐÐ²Ð°Ð½Ð¾Ð², ÐÐµÐ¾ÑÐ³Ð¸Ð¹
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·ÑÐ±ÑÐ°ÑÐ¾Ðµ Ð·Ð°ÑÐµÐ¿Ð»ÐµÐ½Ð¸Ðµ
ÐºÐ¾Ð½ÑÐ°ÐºÑÐ½Ð¾Ðµ Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð¸Ðµ
ÐÐ­ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð¾Ð±Ð»Ð°ÑÑÑ ÐºÐ¾Ð½ÑÐ°ÐºÑÐ°
ÐºÐ¾ÑÑÑÐ¸ÑÐ¸ÐµÐ½Ñ Ð½ÐµÑÐ°Ð²Ð½Ð¾Ð¼ÐµÑÐ½Ð¾ÑÑÐ¸ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ ÑÐ´ÐµÐ»ÑÐ½Ð¾Ð¹ Ð½Ð°Ð³ÑÑÐ·ÐºÐ¸ Ð¿Ð¾ Ð´Ð»Ð¸Ð½Ðµ Ð·ÑÐ±Ð°
Ð·ÑÐ±ÑÐ°ÑÐ°Ñ Ð¿ÐµÑÐµÐ´Ð°ÑÐ°
Ð¿ÐµÑÐµÐºÐ¾Ñ Ð¾ÑÐµÐ¹
Ð¾ÑÐºÐ»Ð¾Ð½ÐµÐ½Ð¸Ðµ Ð¾Ñ Ð¿Ð°ÑÐ°Ð»Ð»ÐµÐ»ÑÐ½Ð¾ÑÑÐ¸ Ð¾ÑÐµÐ¹
Ð½Ð°ÑÐ°Ð»ÑÐ½ÑÐ¹ Ð´Ð¸Ð°Ð¼ÐµÑÑ Ð·ÑÐ±ÑÐ°ÑÐ¾Ð³Ð¾ ÐºÐ¾Ð»ÐµÑÐ°
Ð´Ð»Ð¸Ð½Ð° Ð·ÑÐ±Ð°
gearing
contact stress
FE modeling
contact area
coefficient of uneven distribution of specific load along the tooth length
gear transmission
axis misparallelity
axis parallelity deviation
pitch diameter
tooth length

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ Ð½ÐµÑÐ°Ð²Ð½Ð¾Ð¼ÐµÑÐ½Ð¾ÑÑÐ¸ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ ÑÐ´ÐµÐ»ÑÐ½Ð¾Ð¹ ÑÐ¸Ð»Ñ Ð² Ð·ÑÐ±ÑÐ°ÑÐ¾Ð¼ Ð·Ð°ÑÐµÐ¿Ð»ÐµÐ½Ð¸Ð¸ Ð¾Ñ Ð½Ð°Ð³ÑÑÐ·ÐºÐ¸, ÑÑÐ»Ð¾Ð²Ð¸Ð¹ ÑÐ°Ð±Ð¾ÑÑ Ð¸Ð»Ð¸ Ð¿Ð¾Ð³ÑÐµÑÐ½Ð¾ÑÑÐµÐ¹ Ð¸Ð·Ð³Ð¾ÑÐ¾Ð²Ð»ÐµÐ½Ð¸Ñ Ð·ÑÐ±ÑÐ°ÑÐ¾Ð¹ Ð¿ÐµÑÐµÐ´Ð°ÑÐ¸. Ð ÐºÐ°ÑÐµÑÑÐ²Ðµ Ð±Ð°Ð·Ð¸ÑÐ° ÑÐµÑÐµÐ½Ð° Ð·Ð°Ð´Ð°ÑÐ° Ð¾ ÐºÐ¾Ð½ÑÐ°ÐºÑÐµ ÑÐµÐ» Ð¿ÑÐ¾ÑÑÐ¾Ð¹ ÑÐ¾ÑÐ¼Ñ. Ð ÐµÑÐµÐ½Ð¸Ðµ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¾ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸, Ð° ÑÐ°ÐºÐ¶Ðµ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÐ¼ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ Ñ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸ÐµÐ¼ ÑÐ¾Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÐµÑÐ¿ÐµÑÐµÐ½Ð¸Ñ (CAE) ÑÐ¸Ð¿Ð° ANSYS. ÐÐ° Ð±Ð°Ð·Ðµ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾ ÐºÐ¾Ð½ÑÐ°ÐºÑÐµ ÑÐµÐ» Ð¿ÑÐ¾ÑÑÐ¾Ð¹ ÑÐ¾ÑÐ¼Ñ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð° Ð½Ð°Ð¸Ð±Ð¾Ð»ÐµÐµ Ð¿Ð¾Ð´ÑÐ¾Ð´ÑÑÐ°Ñ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ ÐºÐ¾Ð½ÑÐ°ÐºÑÐ° Ð´Ð»Ñ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÐºÐ¾Ð½ÑÐ°ÐºÑÐ° Ð² Ð·ÑÐ±ÑÐ°ÑÐ¾Ð¹ Ð¿ÐµÑÐµÐ´Ð°ÑÐµ, Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð° Ð¾ÑÐµÐ½ÐºÐ° Ð²Ð»Ð¸ÑÐ½Ð¸Ñ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ ÑÐ¾ÑÐ¼ÑÐ»Ð¸ÑÐ¾Ð²Ð¾Ðº Ð¸ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÐºÐ¾Ð½ÑÐ°ÐºÑÐ° Ð½Ð° Ð¸ÑÐºÐ¾Ð¼ÑÐ¹ ÑÐµÐ·ÑÐ»ÑÑÐ°Ñ. ÐÐ¾ÑÑÑÐ¾ÐµÐ½Ð° ÐºÐ¾Ð¼Ð¿Ð°ÐºÑÐ½Ð°Ñ (ÑÐµÐ´ÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½Ð°Ñ) ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð·ÑÐ±ÑÐ°ÑÐ¾Ð¹ Ð¿ÐµÑÐµÐ´Ð°ÑÐ¸, Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÑÑÐ°Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°ÑÑ ÑÐ°ÐºÑÐ¾ÑÑ, Ð²Ð»Ð¸ÑÑÑÐ¸Ðµ Ð½Ð° ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ ÑÐ´ÐµÐ»ÑÐ½Ð¾Ð¹ ÑÐ¸Ð»Ñ Ð² Ð¾Ð±Ð»Ð°ÑÑÐ¸ ÐºÐ¾Ð½ÑÐ°ÐºÑÐ°, Ð² ÑÐ¸ÑÐ¾ÐºÐ¾Ð¼ Ð´Ð¸Ð°Ð¿Ð°Ð·Ð¾Ð½Ðµ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ð¹. ÐÑÐ¾Ð´ÐµÐ¼Ð¾Ð½ÑÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾, ÑÑÐ¾ Ð½Ð° ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ ÑÐ´ÐµÐ»ÑÐ½Ð¾Ð¹ Ð½Ð°Ð³ÑÑÐ·ÐºÐ¸ Ð¿Ð¾ Ð´Ð»Ð¸Ð½Ðµ Ð·ÑÐ±Ð° ÑÑÑÐµÑÑÐ²ÐµÐ½Ð½Ð¾ ÑÐºÐ°Ð·ÑÐ²Ð°ÑÑÑÑ Ð½ÐµÑÐ¾Ð²ÐµÑÑÐµÐ½ÑÑÐ²Ð° ÐºÐ¾Ð½ÑÑÑÑÐºÑÐ¸Ð¸ Ð·ÑÐ±ÑÐ°ÑÐ¾Ð¹ Ð¿ÐµÑÐµÐ´Ð°ÑÐ¸, Ð° ÑÐ°ÐºÐ¶Ðµ ÑÐ¿ÑÑÐ³Ð¸Ðµ ÑÐ²Ð¾Ð¹ÑÑÐ²Ð° ÐµÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð². ÐÐ¾Ð»ÑÑÐµÐ½Ð½ÑÐµ Ð² ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¼Ð¾Ð³ÑÑ Ð¿ÑÐ¸Ð¼ÐµÐ½ÑÑÑÑÑ Ð² ÑÐ°Ð¼ÑÑ ÑÐ°Ð·Ð½ÑÑ ÑÑÐµÑÐ°Ñ Ð¿ÑÐ¾Ð¼ÑÑÐ»ÐµÐ½Ð½Ð¾ÑÑÐ¸, Ð³Ð´Ðµ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÑÑÑÑ Ð·ÑÐ±ÑÐ°ÑÑÐµ Ð¿ÐµÑÐµÐ´Ð°ÑÐ¸.
description: The given work is devoted to determining the dependence of the uneven distribution of the specific force in the gearing depending on the load, operating conditions or manufacturing errors of the gear. As a basis, the contact problem was solved in a simple form. The solution was obtained analytically, as well as numerically using modern software (CAE) such as ANSYS. The contact problem is based on simple shapes determined by the most suitable mathematical contact model for incorporating a contact indicator in a gear train, and various formulas and parameters of the mathematical contact model are evaluated to obtain the desired result. A compact (reduced) numerical model of a gear transmission has been constructed, which makes it possible to take into account the factors influencing the distribution of the distributed force in the contact area in a number of cases. It has been demonstrated that with a large load along the length of the tooth, imperfections in the shape of the gear transmission, as well as in the elasticity of its elements, are observed. The results obtained during the work can be applied in a wide variety of industries where gears are used.