In Atomic force microscope (AFM) examination of a vibrating microcantilever, the nonlinear tip-sample interaction would greatly influence the dynamics of the cantilever. In this paper, the nonlinear dynamics and chaos of a tip-sample dynamic system being run in the tapping mode (TM) were investigated by considering the effects of hydrodynamic loading and squeeze film damping. The microcantilever was modeled as a spring-mass-damping system and the interaction between the tip and the sample was described by the Lennard-Jones (LJ) potential. The fundamental frequency and quality factor were calculated from the transient oscillations of the microcantilever vibrating in air. Numerical simulations were carried out to study the coupled nonlinear dynamic system using the bifurcation diagram, Poincaré maps, largest Lyapunov exponent, phase portraits and time histories. Results indicated the occurrence of periodic and chaotic motions and provided a comprehensive understanding of the hydrodynamic loading of microcantilevers. It was demonstrated that the coupled dynamic system will experience complex nonlinear oscillation as the system parameters change and the effect of squeeze film damping is not negligible on the micro-scale.

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In this paper, a new slip model based on kinetic theory of gases for gas-lubricated journal bearings in micro-electro-mechanical systems (MEMS) is applied using a physical approach. The corresponding modified governing equation and mathematic model are presented and the flow rate is plotted versus the inverse Knudsen number. Pressure distributions along the gas bearing at various Knudsen numbers and bearing numbers are plotted and the load carrying capacities are also obtained. A numerical analysis of a rigid rotor supported by gas-lubricated journal bearings is presented for dynamic behaviour. The slip flow effect on the properties, including pressure distribution, load carrying capacity and dynamic coefficients, of the micro-gas-lubricated journal bearings and dynamic responses of the micro rotor-bearing system are estimated and analysed in detail. It is shown that the dynamic coefficients increase with increasing bearing number except for two damping coefficients and the rotor-bearing system runs at a much higher rotating speed to keep stable when slip flow occurs. Moreover, the oscillation period of the rotor operating with the slip model is longer than that with the continuum flow. In addition, the whirl frequency is reduced from 0.422 to 0.079 under the slip effect. Therefore, the results of this study contribute to a further understanding of the characteristics and nonlinear dynamics of gas-film rotor-bearing systems in MEMS.