Consideration of contact interactions when modelling stiffness characteristics of roll bearings

Аuthors

Degtiarev S. A.^1*, Kutakov M. N.^2**, Leontiev M. K.^2***, Popov V. V.^3****, Romashin Y. S.^2*****

1. Scientific and technical centre of rotor dynamic «Alfa-Tranzit», 1, Leningradskaya str., Khimky, Moscow region, 141400, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
3. Bauman Moscow State Technical University, MSTU, 5, bldg. 1, 2-nd Baumanskaya str., Moscow, 105005, Russia

*e-mail: degs@alfatran.com
**e-mail: maxim.kutakov@alfatran.com
***e-mail: lemk@alfatran.com
****e-mail: vvpopov@bmstu.ru
*****e-mail: romashin@alfatran.com

Abstract

When solving rotor dynamic tasks of rotating machines including aviation gas turbine engines, calculation accuracy of the system elements is highly important. One of the most widespread elements are roll bearings. In the first place stiffness characteristics of roll bearings are determined by the contact phenomena appearing between rolling elements and rings. As a whole the other elements of the roll bearing (such as inner and outer rings) influence stiffness no more than 5%. Interaction between the roll and the ring may be considered as linear contact between two cylindrical solids with parallel axes. For the first time solution for this task was obtained in the Lunberg- Sjövall paper [1]. However, equation in [1] has implicit dependence of outer force on appeared displacement and so cannot be used for tasks of stiffness characteristics determination. In Harris work [2] empirical Palmgren equation [2] was used to solve this task:

,

where — contact force, — contact length, —displacement in contact line.

To verify results in paper [2], the task of contact interaction between a half cylinder and a plane was solved using FEM. It was obtained that there was significant divergence (up to 30%) between solutions obtained using Palmgen’s equation and FEM. It was found out that Palmgren’s equation was correct with error of 5% for lengths of contact lines from 10 to 20 mm. According to the results of the FEM solution, the new dependence for linear contact tasks was proposed. It gives no more than 4% results’ divergence in the contact lengths range from 0,5 to 50 mm.

.

The obtained dependence may be used to simulate stiffness characteristics of the roll bearings and to describe linear contact in tasks of contact interaction mechanics.

Keywords:

roll bearing, stiffness, contact interaction

References

1. Lundberg G., Sjovall H. Stress and deformation in elastic Contacts, Pub. 4, Division of Solid Mechanics, Chalmers University of Technology, Gothenburg, Sweden, 1958, 47p.

2. Harris T.A. Rolling bearing analysis, 5-th edition, Wiley- Interscience Publication, USA, 2006, 258 p.