Научная электронная библиотека ULRICH'S Periodicals Directory

Сибирский государственный университет
науки и технологий имени академика М.Ф. Решетнева

Сибирский аэрокосмический журнал
ISSN 2712-8970 (Print) ISSN 2782-5760 (on-line)

Сведения об образовательной организации

UDK 628.822
NONSTEADY OSCILLATIONS OF THE ROLLER CONTACTING WITH RIGID SURFACE WITH LUBRICATION LAYER
V. A. Ivanov1, N. V. Erkaev2
1Siberian Federal University, Polytechnic Institute 26, Kirenskogo Str., Krasnoyarsk, 660074, Russian Federation 2Institute of Computational Modelling SB RAS 50/44, Akademgorodok, Krasnoyarsk, 660036, Russian Federation
Analytical solution is obtained for the problem of non-steady hydrodynamic contact between roller and solid body in a presence of liquid lubrication material. This problem is very actual one because nonsteady regime is dominating during launching of spaceсrafts. Distribution of the pressure along the lubrication layer is obtained by integration of the Reynolds equation taking into account both the tangential and normal velocities of the roller. Normal oscillations of the roller contacting with lubrication layer is described by a stiff second order ordinary differential equation. Solution of this equation is presented as an asymptotic series expansion with respect to the singular small parameter. It was found that the relaxation process is characterized by two different time scales. The first one determines a steep growth of the pressure maximum just after the loading jump. The second one is related to a relatively slow process of the pressure relaxation to its stationary state corresponding to the enhanced loading value. The obtained results indicate clearly that simulation and analysis of nonsteady relaxations processes in bearing devices of flight vehicles is of great importance. In particular, in case of slow quasi-stationary increase of loading in 2 times the pressure maximum over the lubrication layer has approximately two-fold enhancement. However, similar in amplitude, but sudden jump of loading yields much stronger enhancement (more than in 10 times) of the pressure maximum over the lubrication layer during the time-relaxation process. Such strong and fast pressure jump in the lubrication layer can make a crucial influence on the operation resources of vehicles.
Keyword: lubrication layer, hydrodynamic lubrication, roller oscillation, asymptotic series expansion.
References

1. Kodnir D. S. Kontaktnaya gidrodinamika smazki detaley mashin [Contact hydrodynamics of lubrication of machine parts]. Moscow, Mashinostroyeniye Publ., 1976, 304 p.

2. Galakhov M. A, Usov P. P. Differentsial’nye i integral’nye uravneniya matematicheskoy modeli teorii treniya [Differential and integral equations of the mathematical model of the friction theory]. Moscow, Nauka, Fiz.-mat. Lit. Publ., 1990, 280 p.

3. Terent’ev V. F., Erkaev N. V. Tribonadezhnost’ podshipnikovykh uzlov v prisutstvii modifitsirovannykh smazochnykh kompozitsiy [Tribo-durability of bearing units in a presence of modified lubricant compositions]. Novosibirsk, Nauka Publ., 2003, 142 p.

4. Kodnir D. S. Kontaktnaya gidrodinamika smazka detaley mashin [Contact hydrodynamics of lubrication of machine parts]. Moscow, Mashinostroenie Publ., 1976, 304 p.

5. Aleksandrov V. M., Romalis B. L. Kontaktnye zadachi v mashinostroenii [Contact problems in mechanical engineering]. Moscow, Mashinostroenie Publ., 1986, 176 p.

6. Aleksandrov V. M., Chebakov M. I. Analiticheskie metody v kontaktnykh zadachakh teorii uprugosti. [Analytical methods in contact problems of elasticity theory]. Moscow, Fizmatlit. Publ., 2004, 301 p.

7. Argatov I. I. Asimptoticheskie modeli uprugogo kontakta [Asymptotic models of elastic contact]. St. Petersburg, Nauka Publ., 2005, 447 p.

8. Besportochnyy A. I. [The asymptotic regimes of hydrodynamic contact of a hard cylinder covered with a thin elastic layers]. Trudy MFTI. 2011, Vol. 3, No. 1. P. 28–34 (In Russ.).

9. Besportochnyy A. I., Galakhov M. A. Matematicheskoe modelirovanie v tribotekhnike. [Mathematical modeling in tribology]. Moscow, MFTI Publ., 1991, 88 p.

10. Galin L. A. Kontaktnye zadachi teorii uprugosti i vyazkouprugosti [Contact problems of the theory of elasticity and viscoelasticity]. Moscow, Fizmatlit. Publ., 1980, 304 p.

11. Ivanov V. A., Erkaev N. V. [Simulation of nonsteady contact in rolling bearings]. Vestnik SibGAU. 2015, Vol. 16, No. 3, P. 580–586 (In Russ.).

12. Galakhov M. A., Gusyatnikov P. B., Novikov A. P. Matematicheskie modeli kontaktnoy gidrodinamiki [Mathematical models of contact hydrodynamics]. Moscow, Fizmatlit. Publ., 1985, 296 p.

13. Tikhonov A. N. Arsenin V. Ya. Metody resheniya nekorrektnykh zadach [Methods of solving ill-posed problems]. Moscow, Nauka Publ., 1979, 288 p.

14. Vasil’eva A. B., Butuzov V. F. Asimptoticheskie metody v teorii singulyarnykh vozmushcheniy [Asymptotic methods in the theory of singular perturbations]. Moscow, Vyssh. Shk., 1990, 208 p.

15. Vasil’eva A. B., Butuzov V. F. Asimptoticheskie razlozheniya resheniy singulyarno vozmushchennykh uravneniy [Asymptotic expansions of solutions of singularly perturbed equations]. Moscow, Nauka Publ., 1973, 272 p.


Ivanov Viktor Andreevich – assistant, Department of Applied Mechanics, Polytechnic Institute, Siberian Federal

University. E-mail: Vintextrim@yandex.ru.

Erkaev Nikolai Vasilevich – Dr. Sc., professor, head of department #7, Institute of Computational Modeling SB

RAS. E-mail: nerkaev@gmail.com.