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

机床结构由基本结构组合而成。单元结构连接节点处的刚度比不连接节点处的刚度弱，其特性表现为非线性。轴承和滑动仍然有刚度，允许在轻微间隙方面的相对运动。节点处的刚度特征表现出明显的非线性。尽管指出了非线性的存在，但用线性化的方法对其进行了分析，并没有给出明确的依据。这将导致在评估系统参数时出现严重错误。研究负责人等人提出了近似模态方法，通过对非线性特性引入描述函数，将非线性单元的正弦输入幅值与基谐波输出幅值的传递函数表示非线性，并将其与运动方程中的非线性刚度相结合。利用关节处的函数，将该方法推广到多自由度系统的非线性构造块方法中。结果表明，该方法可以很好地表征非线性系统的特性。轴承和滑动处的非线性特性往往表现为在施力和卸力时走不同路径的滞回。此属性的描述函数由几个不同的描述定义。在研究中试图得到多自由度系统的运动方程的解。但是，关于相位特性的表达式还不能完全完成。这使得分析结果很难与实际系统的特性进行详细的比较，尽管可以证明具有迟滞特性的系统的一般特性。以机床结构为例，分析了轴承的非线性，讨论了稳定切削区域的趋势。结果表明，该方法不仅适用于机床结构，而且适用于一般机床结构。少

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