Analysis of Nonlinear Dynamic Models, Parametric Vibrations and Resonance States of Cam Mechanisms
Abstract
This paper investigates nonlinear dynamic models of cam mechanisms used for cutting ball-rolling mill rolls, including the contact elasticity of higher kinematic pair elements, parametric vibrations, and resonance states. An elastic-dissipative model of the cam–follower system was developed, and Mathieu–Hill type differential equations were derived considering time-varying stiffness coefficients and parametric excitations. Dynamic coefficients, amplitude-frequency characteristics, resonance zones, and dynamic loads for sinusoidal, cosinusoidal, and constant-acceleration motion laws were analyzed using numerical simulation methods. Based on the obtained results, optimal operating ranges for the modernized RT117 screw-cutting lathe system were recommended.
Keywords
Downloads
References
- Vulfson I.I. Cam Mechanisms. — Leningrad: Mashinostroyeniye, 1973.
- Rothbart H.A. Cam Design Handbook. — New York: McGraw-Hill, 2004.
- Pater Z., Tomczak J. Helical Rolling of Steel Balls / Archives of Metallurgy and Materials. — 2012. — Vol. 57, No. 3. — pp. 879–885.
- Shakhоbutdinov R.E. Analysis of cam mechanisms for cutting ball-rolling rolls / TSTU Bulletin. — 2022. — No. 4. — pp. 52–61.
- Korchemnyi L.N. Dynamics of Cam Mechanisms. — Kyiv: Tekhnika, 1981.
- Savvin E.A. Contact Stresses in Higher Kinematic Pairs. — Moscow: Nauka, 1985.
- Johnson K.L. Contact Mechanics. — Cambridge University Press, 2007.
- Nayfeh A.H., Mook D.T. Nonlinear Oscillations. — New York: Wiley, 2005.
- Rubtsov V.Yu. Improvement of Ball-Rolling Roll Calibration. Doctoral dissertation. — Yekaterinburg, 2021.
- Karimov R.I., Shakhоbutdinov R.E., Khojibekov T.D. Study of factors affecting relative velocities in cam mechanisms / TSTU Bulletin. — 2018. — No. 2. — pp. 44–51.