Torsional Vibration of a System with a Friction Clutch Under Random Torque Excitation
The paper presents a theoretical study of torsional vibration in a two-mass model of a transmission system with a multi-disc flexible friction clutch under random excitation. Energy is dissipated through micro-slip processes between discs, characterized by a hysteresis loop. It is assumed that the nominal driving torque is disturbed by a stationary Gaussian random excitation with known moments. Spectral density as well as the mean value and standard deviation of both the relative torsional vibration and the driven part vibration are derived using a stochastic linearization technique applicable in hysteretic systems. The role of system parameters is shown by examples in which a band model of random excitation is assumed.
C.F. BEARDS, The damping of structural vibration by controlled interfacial slip in joints, J. Vibration, Acoustics, Stress and Reliability in Design, Transactions ASME, 105, 369-373, 1983.
T.K. CAUGHEY, Random excitation of a system with bilinear hysteresis, J. Applied Mech., 27, Transactions ASME, 82, Series E, 649-652, 1960.
T. FRISCHGESELL, T. SZOLC, Vibration control of beam-string structures utilizing piezoelectricity and dry friction, 3-rd Polish-German Workshop on Dynamical Problems in Mechanical Systems, 1993, [to be published in the Proceedings].
J. GIERGIEL, Problems of structural friction in machine dynamics [in Polish], Prace Naukowe Akademii Górniczo-Hutniczej, No. 44, Kraków 1970.
L.E. GOODMAN, I.H. KLAMP, Analysis of slip damping, with reference to turbine-blade vibration, J. Applied Mech., 23, Transactions ASME, 78, 421-429, 1956.
K. GRUDZIŃSKI, W. KISSING, L. ZAPŁATA, Untersuchung selbsterregter Reibungsschwingungen mit Hilfe eines numerischen Simulationsverfahrens, Technische Mechanik, 13, 7-141, 1992.
W. KURNIK, N.C. MENH, Z. OSIŃSKI, On a method of analysis of weakly nonlinear random vibrations with a hysteresis loop, Machine Dynamics Problems, No. 2, 3, 69-81, 1984.
B.R. LEVIN, Theoretircal foundations of statistical radio engineering, t. I, Sovietskoje Radio, Moscov 1969.
A.N. MALAKHOV, Cumulative analysis of random non-Gaussian processes and their transformations, Moscov 1978.
Z. OSIŃSKI, Damping of mechanical vibrations [in Polish], PWN, Warszawa 1979.
T.H.H. PIAN, Structural dumping of a simple built-up beam with riveted joints in bending, J. Applied Mech., 24, 35-38, 1957.
M. PIETRZAK0WSKI, Analysis of a simple system with structural friction by the space-time FEM, XII Symposium on Vibrations in Physical Systems, 222-223, Błażejewko 1986.
Z. SKUP, Analysis of a multi-plate clutch operated by magnetic means, structural friction being taken into consideration [in Polish], Zesz. Na.nk. Instytutu Podstaw Budowy Maszyn Polit. Warszawskiej, No 15, 86-107, 1987.
Z. SKUP, Free vibration of a system with friction clutch with consideration of structural friction [in Polish], Mining and Metallurgical Academy, Cracow, Mechanics, 2, 106-115, 1987.
Z. SKUP, Forced vibration of a nonlinear stationary system with a friction clutch, structural friction being taken into consideration, Engng. Trans., 39, 3-4, 69-87, 1991.
Z. SKUP, Vibration of a system with friction clutch with consideration of structural friction due to a random process, Nonlinear Vibrations Problems, 24, 195-209, 1991.
E. TITCHMARSH, lntroduction to the theory of Fourier integrals, Claredon Press, Oxford 1918.