The Nonlinear Vibration Analysis Of The Overhanging Structure With Elastic Supports In Consideration Of The Bearing Clearance

It is a widespread phenomenon for an overhanging structure with support clearance. The effect of the support clearance on structure vibration not only embodies the stability in some precision equipment such as the spindle of a machine tool, but also reflects in the accuracy of the measurement of a structure performance as a result of the bearing clearance. The performance parameters mainly contain natural frequencies and mode shapes, etc. Usually, the parameters of the vibration performance are difficult to be accurately determined, especially when the structure support with clearance is mounted on an elastic base. In fact, the measured natural frequencies are usually lower than that of theoretical analysis because of the existence of support clearance. However, it is not clear of what degree the clearance influences on structure vibration as well as the effect mechanism, which needs further research. It is studied through a simplified overhanging structure with support clearance of an actual model, which is mounted on an elastic base in this paper.Firstly, the system is simplified as an overhanging structure with support clearance according to the modal test structure of an actual model. Then an effective method is adopted to obtain accurate analytical modal solutions of the overhanging structure with several boundary conditions, such as elastic supports and additional mass.Secondly, the mode shapes of the same order are compared for the overhanging structure out of touch or touch to the support with clearance. Then, the identical mode method and mode transfer method are adopted to establish the model of the overhanging structure vibration, respectively. For the 2nd or 3rd order vibration, the system is equivalent to a single-degree-of-freedom system with piecewise-linear stiffness in the identical mode method and single mode approximation method. For the 1st or 2nd order vibration, the system is equivalent to a single-degree-of-freedom system with multiple piecewise-linear parameters in the mode transfer method and single mode approximation method.Thirdly, the incremental harmonic balance method and improved arc-length increment method are adopted to solve the system with piecewise-linear stiffness. Then the continuous amplitude-frequency response curves are obtained. The effect of the elastic support clearance on the vibration of the overhanging structure is analyzed in frequency domain according to different clearance magnitudes. The central difference method is adopted to solve the system with multiple piecewise-linear parameters. The effect of the elastic support clearance on the vibration of the overhanging structure is analyzed in time and frequency domain with combination of the phase portrait and Poincare map according to different clearance magnitudes.Lastly, the nonlinear vibration phenomena of the overhanging structure are summarized for the 1 st,2nd and 3rd order. The variation rule is also illustrated for the natural frequency. It provides a significant reference value for analyzing the vibration of an overhanging structure with elastic support companied by small clearance.