Study Of Modeling And Response Characteristics Of Stranded Wire Helical Springs Under Periodic Loading

Stranded wire helical spring, or multi-wire helical spring, is a unique cylindricalhelical spring wound from a strand, which usually consists of2-7carbon steel wires. Ithas the unique characteristic of better shock resistance and vibration reduction, greaterstiffness and nonlinear damping; therefore, the spring is widely used in militaryequipment and vibration isolator systems. However, due to the lack of the dynamiccharacteristics of the spring, only the static design could been carry out when design thevibration isolator. In order to improve the design standards, the present thesis makesefforts to detailed studies on the dynamic behavior of the spring. The model isestablished to represent the dynamical behavior of the spring, the identification methodis developed to obtain the parameters of the model, and the calculation method isproposed to analyze the dynamical characteristics of typical stranded wire helical springnonlinear system. The main research workin the dissertation are as follows:①The dynamical behavior of the spring under cycle loading is experimentallyinvestigated by executing dynamic test. Nonlinear hysteresis behavior, hardeningoverlap phenomenon and asymmetry of the loop are observed from the experiment. Thecharacteristics of the Bouc-Wen model, one of the most typical hysteretic models, isdemonstrated in the present work. The normalized Bouc-Wen model and the analyticalexpression are provided, the efficient precision calculation of the Bouc-Wen model isproposed, and the dissipated energy of the model is determined. In recognizing theincapacity of the Bouc-Wen model, a modified Bouc-Wen model, which combines anonlinear elastic component and a nonlinear amplifier, is proposed to capture thedynamic behavior of the spring.②An identification method is developed to obtain the parameters of the modelusing experimental data. First of all, a denosing method is applied to smooth themeasured data. Second, the nonlinear elastic component and the nonlinear amplifier isextracted base on the properties of the max output approaches1when the hystereticcurve enters into thesteady section, and the least square method is followed to identifythe parameters of non-hysteretic component.In the end, the Bouc-Wencomponent isextracted from the overall restoring force using the results, then the IUKF method isapplied to identify the parameter of the pure hysteretic part. Both the numericalsimulation and the experiment results verify the validity and effectiveness of the identification method, as well as the robustness of the IUKF on initial values. Theexperiment results also collaborate the validity of the proposed model.③The model of the typical nonlinear systems with stranded wire helical spring isestablished. The principal parameters of the model is obtained bynondimensionalization of the equation and the properties of the dynamical model of thespring. The equivalent linear damping ration is obtained through the combination of thedissipated energy of the Bouc-Wen model and the principle of the energyequivalent.Then the equivalent linearization equation is derived. The dynamical analysismethod is proposed using frequency scan to get the response of typical stranded wirehelical spring nonlinear system. The result indicated the convenience, validity andeffectiveness of the method by comparingwith the numerical simulationand experimentresult,and the method is feasible for engineering practice.