ANALYSIS ON NONLINEAR BEHAVIOR OF MULTI-DEGREE-OF-FREEDOM SYSTEM RELATED WITH DYNAMIC STIFFNESS OF MACHINE TOOL

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Machine tool structure consists of combining elementary ones. Stiffness at the joints where the element structures are joined is made weaker than structure without them, whose property indicate nonlinearity. Bearing and slide still have stiffness which allows relative motion in terms of slight clearance. The stiffness characteristic at the joints obviously shows nonlinearity. These have been analyzed by linearized approach was not demonstrated definite basis, in spite that existence of the nonlinearity has been pointed out. This leads to serious errors in evaluating system parameters. Head investigator and others have proposed approximate modal approach by introducing describing function to the nonlinear characteristic, which express the nonlinearity by a transfer function for the amplitude of sinusoidal input to nonlinear element to that of output for the fundamental harmonic, and this was combined with the nonlinear stiffness in the equation of motion. The method was extended to mult … More i-degree-of-freedom system in terms of nonlinear building block approach utilizing the function at the joints. It has been shown that the characteristics of nonlinear system can be successfully characterized by the approach.Nonlinear property at the bearing and the slide often appears as that with hysteresis which traces different path in applying and removing force. The describing function for this property is defined by several different descriptions. To obtain the solution for the equation of motion for the multi-degree-of-freedom system is attempted in the investigation. However, expression with respect to phase characteristic could not have been completely accomplished. This leaves that comparison of the analytical results with the characteristics in practical system difficult in detail, in spite that the general characteristics of the system with hysteresis property can be proved. As an example in machine tool structure, nonlinearity in bearing is analyzed and the tendency of region for stable cutting is discussed. It is indicated that the approach can be applied not only to the machine tool structure, but to general machine structure. Less