ANALYSIS OF CONTACT LOADS CONCENTRATION IN PRESSURE COUPLINGS OF THIN-WALL COMPONENTS

A number of aviation assemblies are made as pressure couplings of thin-wall components, e.g., shafts and hubs, durability of which is related to fitting contact load concentrations under cyclic and dynamic loadings. This article discusses a numeric solution to the contact problem. The solution is introducing into the calculations a conventional boundary layer, any shift of which is equivalent to a roughness deformation of fitting surfaces. The mathematical model of a pressure coupling is founded on a division of deformations into general (axisymmetric bending of components) and local deformations (microroughness compression) that are determined independently. To simplify the solution, the dependence of the contact convergence of the surfaces on the pressure is subjected to linearization in the form of a model of a rigid plastic body with linear strengthening. Convergence values in section are only determined by the pressure and do not depend on the stress-and-strain behaviors of areas adjacent to the rough interfacial space. The Green’s functions method is used to find radial shifts of components, while the solution is expressed by the Fredholm integral equation. That is reduced to a finite system of linear algebraic equations when the contact is made discrete. This approach provides solution stability through strengthening of the main diagonal of the resolving system, while the evaluation accuracy of the concentration coefficient depends on the subinterval value. It has been found that any disclosure of a coupling beneath the faces of an enveloping body is practically impossible for that model. The comprehensive approach provides a generalized solution for orthotropic and stepwise shells, as well as for components with specific design features and various strengths of areas adjacent to fitting sites. Deviations of the shape of the contact surfaces from the straightness are taken into account by its respective pressure coupling function. The analysis of the findings suggests that the concentration coefficient value slumps as the contact compliance coefficient of the borderline layer increases. Any shape deviations of the fitting surfaces, including their coning and concavity, increase the contact load concentration, while their convexity causes a reverse effect. We recommend using strengthening treatment methods, e.g., application of regular micropattern in the shape of helical flute at a certain pitch while applying a constant or a variable force on the diamond indenter, or vibration smoothing in order to control the shaft surface finishing to improve the stressand-strain behavior of the seam and to impart an artificial barrel shape of a preset value to the shaft. These technologies compensate contact load concentrations, and, together with the strengthening factor, enhance the fatigue limit of such assemblies.

shell, axisymmetric bend, contact compliance, pressure coupling roughness, concentration of stresses, surface, pressure

1. Skubachevsky, G.S. (1974). Aviatsionnyye gazoturbinnyye dvigateli. Konstruktsiya i raschet detaley [Aviation Gas Turbine Engines: Design and Analysis of Components]. Uchebnik [Textbook]. 4th ed. Moscow: Mashinostroyeniye, 520 p. (in Russian)

2. Birger, I.A., Shorr, B.F. and Ioselevich, G.B. (1979). Raschet na prochnost detaley mashin [Machine Components: Analysis of Strength]. Spravochnik [Referencebook]. 3rd ed. Moscow: Mashinostroyeniye, 702 p. (in Russian)

3. Shishkin, S.V. and Makhutov, N.A. (2007). Raschet i proektirovaniye silovykh konstruktsiy na splavakh s effektom pamyati formy [Analysis and Design of Load-Carrying Structures Based on Shape-Memory Alloys]. Uchebnoye posobiye [Training manual]. Moscow: NIC «Regulyarnaya i khaoticheskaya dinamika», 412 p. (in Russian)

4. Abramyan, B.L. and Aleksandrov, A.Y. (1966). Osesimmetrichnyye zadachi teorii uprugosti [Axisymmetric Problems of the Elasticity Theory]. Mekhanika tvyordogo tela [Mechanics of Rigid Bodies]. Trudy II Vsesoyuznogo sezda po teoreticheskoy i prikladnoy mekhanike [Proceedings of the II All-Soviet Union Congress on Theoretical and Applied Mechanics], iss. 3, pp. 7–37. (in Russian)

5. Blokh, M.V. and Tsukrov, S.Y. (1973). Ob osesimmmetrichnom kontakte tonkikh tsilindricheskikh obolochek [Axisymmetric Contact between Thin Cylindrical Shells]. International Applied Mechanics, vol. IX, no. 11, pp. 23–28. (in Russian)

6. Blokh, M.V. and Tsukrov, S.Y. (1974). O vliyanii izmeneniya tolshchiny stenki na osesimmmetrichnyy kontakt tonkikh tsilindricheskikh obolochek [The Influence of Changes in Wall Thicknesses on Axisymmetric Contact between Thin Cylindrical Shells]. International Applied Mechanics, vol. X, no. 4, pp. 31–33. (in Russian)

7. Detinko, F.M. and Fastovsky, V.M. (1967). Posadka korotkoy vtulki na tsilindricheskuyu obolochku [Fitting of a Collar around a Cylindrical Shell]. Vestnik mashinostroeniya [Russian engineering research], no. 7, pp. 42–45. (in Russian)

8. Detinko, F.M. and Fastovsky, V.M. (1974). Kontaktnaya zadacha o posadke s natyagom dvukh tsilindricheskih obolochek razlichnoy dliny [A Contact Problem of Pressure Fitting of Two Cylindrical Shells of Dissimilar Lengths]. Izv. AN SSSR. Mekhanika tverdogo tela [Mechanics of Rigid Bodies], no. 3, pp. 118–121. (in Russian)

9. Detinko, F.M. and Fastovsky, V.M. (1975). O posadke bandazha na tsilindricheskuyu obolochku [Fitting of a Bandage around a Cylindrical Shell]. International Applied Mechanics, vol. XI, no. 2, pp. 124–126. (in Russian)

10. Abramyan, B.L. (1969). Kontaktnye (smeshannye) zadachi teorii uprugosti [Contact (Mixed) Problems of the Elasticity Theory]. Izv. AN SSSR. Mekhanika tverdogo tela [Mechanics of Rigid Bodies], no. 4, pp. 181–197. (in Russian)

11. Ioselevich, G.B. (1981). Kontsentratsiya napryazheniy i deformatsiy v detalyakh mashin [Stresses and Deformations Concentration in Machine Components]. Moscow: Mashinostroyeniye, 224 p. (in Russian)

12. Treniye, iznashivaniye i smazka [Friction, Wear, and Lubrication] (1978). Spravochnik [A Handbook]. V 2-hk kn. Kn. 1 [Book 1]. Ed. I.V. Kragelsky and V.V. Alisin. Moscow: Mashinostroyeniye, 400 p. (in Russian)

13. Dyomkin, N.B. (1970). Kontaktirovaniye sherokhovatykh poverkhnostey [Contacting of Rough Surfaces]. Moscow: Nauka, 226 p. (in Russian)

14. Mikhlin, S.G. (1947). Prilozheniya integralnykh uravneniy k nekotorym problemam mekhaniki, matematicheckoy fiziki i tekhniki [Applications of integral equations to some problems of mechanics, mathematical physics and engineering]. Moscow; Leningrad: Gos. izd-vo tekhniko-teoreticheskoy lit. [State Publishing House of Technical-Academic literature], 302 p. (in Russian)

15. Tikhonov, A.N. and Arsenin, V.Y. (1974). Metody resheniya nekorrektnykh zadach [Methods for the Solution of Ill-Posed Problems]. Moscow: Nauka, 239 p. (in Russian)

16. Birger, I.A. (1956). Nekotorye matematicheskiye metody resheniya inzhenernykh zadach [Some of the Mathematical Methods of Solving Engineering Problems]. Moscow: Oborongiz, 150 p. (in Russian)

17. Birger, I.A. (1961). Kruglye plastinki i obolochki vrashcheniya [Round Plates and Rotational Shells]. Moscow: Oborongiz, 368 p. (in Russian)

18. Khvorostukhin, L.A., Shishkin, S.V., Kovalyov, A.P. and Ishmakov, R.A. (1988). Povysheniye nesushchey sposobnosti detaley mashin poverkhnostnym uprochneniyem [The Enhancement of the Load Bearing Capacity of Machine Components by Surface Strengthening]. Moscow: Mashinostroyeniye, 144 p. (in Russian)