The non-linear coupling dynamic behaviour of a hydrodynamic bearing-flexible rotor system is analysed. A local iteration method consisting of the improved Wilson-θ method, the predictor-corrector mechanism, and the Newton-Raphson method is proposed to calculate the non-linear dynamic response. Using the proposed method, the iterations are executed only on non-linear degrees of freedom. The iteration process shows improved convergence by taking the prediction value as the initial value. The stability and bifurcation type of periodic responses are determined by the Floquet theory. According to the physical characteristics of the oil film, a variational constraint approach is proposed to revise continuously the variational form of the Reynolds equation at each step of the iterative process. Non-linear oil film forces and their Jacobians are calculated simultaneously without an increase in computational costs, and compatible accuracy is obtained. Numerical results reveal periodic, quasi-periodic, coexisting, and jump solutions of rich and complex non-linear behaviours of the system and show that the proposed methods not only save computational costs but also have high precision. simulation for the symmetrical single-disc flexible rotor-bearing system [4]. Based on the symmetrical flexible rotor model with a single disc, the journal orbit of the rotor and the stability of the system are determined using the shooting method and the generalized shooting method [5,6]. Non-linear dynamic behaviours of a large flexible rotor system are obtained by the Newmark method and the predictor-corrector mechanisms [7,8]. From references [3] and [9], it is seen that the predictor-corrector mechanism and the Newton shooting method are used to calculate the unbalance periodic responses and bifurcation point of the system. In this article, an improved Wilson-θ method is developed to obtain a local iteration method for calculating non-linear responses. The iteration for non-linear responses needs to be performed only on non-linear degrees of freedom by the proposed method. According to the physical characteristics of the oil film, a variational constraint approach is proposed to revise continuously the variational form of the Reynolds equation at each step of the iterative process. Non-linear oil film forces and their Jacobians JMES1190

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A profilometer used for 3 dimension measurement of micro-surface topography is presented. The instrument is based on the vertical scanning microscopic interferometry (VSMI). A Linnik type interference microscope is used and the interferograms which present changes of surface profile are recorded with a CCD camera. A developed nano-positioning work stage with an integrated optical grating displacement measuring system realizes the precise vertical scanning motion during profile measurement. By a white-light phase shifting algorithm of arbitrary step, frames of interferograms are processed by a computer to rebuild and evaluate the measured profile. Because of the specialty of VSMI, the profilometer is suitable for both smooth and rough surface measurement. It can also be used to measure curved surfaces, dimension of micro electro mechanical systems (MEMS), etc. The vertical resolution of the profilometer is 0.5 nm, and lateral resolution 0.5 μm.