Nikiforov
Vladimir O.
D.Sc., Prof.
doi: 10.17586/2226-1494-2019-19-4-756-766
RESEARCH OF FLEXURAL VIBRATIONS OF ROTATING SHAFTS WITH DISTRIBUTED INERTIAL, ELASTIC AND ECCENTRICITY PROPERTIES
Read the full article
';
For citation:
Murtazin I.R., Lukin A.V., Popov I.A. Research of flexural vibrations of rotating shafts with distributed inertial, elastic and eccentricity properties. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2019, vol. 19, no. 4, pp. 756–766 (in Russian). doi: 10.17586/2226-1494-2019-19-4-756-766
Abstract
Subject of Research. The paper presents the study of one of the main problems of elastic stabilization and long-term strength of the system under cyclically changing external impacts. Rotary systems have a wide range of applications: power, machine and aircraft-building industries; medicine cannot exist without equipment with rotational elements (turbines, engines, drills). One of the main problems is to ensure the system elastic stability and long-term strength during cyclically changing external impacts. Method. The paper presents a survey and comparative research for a number of analytical and numerical methods of calculating the flexural vibrations of rotating shafts. The direct analytical solution was received by the continuation method in MATLAB/MATCONT module. We also considered such approximate method as bvp4c-method, that is a MATLAB built-in function. The numerical problem was solved by the finite element method using ANSYS и COMSOL software. Main Results. For determination of the rotation critical speeds Campbell’s diagrams are plotted using a distributed model of deformable shaft described by partial differential equations with variable coefficients. This model takes into account the distribution of elastic, inertial and eccentricity properties of the system, and is applicable to any range of working frequencies. Free and forced vibrations caused by the eccentricity are studied. Practical Relevance. Considered general model and verified methods give the possibility to carry out numerical simulation of the experimental facility. The inverse problem of determining the facility element eccentricity was solved. The anisotropic support stiffness and damping were determined by experimental data and theoretical estimation. The facility sensitivity to an additional external force is researched. The frequency characteristics are built up and their comparison with the results of full-scale tests is given. The methods of the shaft vibration damping by means of controlled (active) magnetic bearings are proposed.
Acknowledgements. The research was supported by Siemens scholarship program
References
2. Ziegler H. Principles of Structural Stability. Blaisdell Publ., 1968.
3. Bolotin V.V. Dynamic Stability of Elastic Systems. Moscow, Tekhniko-Teoreticheskaya Literatura Publ., 1956, 600 p. (in Russian)
4. Mikhlin S.G. Variational Methods in Mathematical Physics. 2nd ed. Moscow, Nauka Publ., 1970, 512 p. (in Russian)
5. Yamamoto T., Ishida Y. Linear and Nonlinear Rotordynamics. Wiley, 2012, 474 p. doi: 10.1002/9783527651894
6. Saeed N.A., Kamel M. Active magnetic bearing-based tuned controller to suppress lateral vibrations of a nonlinear Jeffcott rotor system. Nonlinear Dynamics, 2017, vol. 90, no. 1, pp. 457– 478. doi: doi:10.1007/s11071-017-3675-y
7. Collatz L. Eigenwert auf gaben Mit Technischen Anwendungen. Leipzig, 1963.
