Research On The Response Characteristics Of Stranded Wire Helical Springs And Practice

A stranded wire helical spring is a spring wound by a multi-layered steel wire strand. Compared with a conventional single wire helical spring, the spring features longer fatigue life and higher reliability. Hence, they are key repositioning components of automatic weapons, heavy machinery, etc.The spring was difficult to manufacture; therefore, it was only used in certain military equipment. Nowadays, precision manufacturing of the spring is achieved. The advantages of the spring are known by the general engineers gradually. Many engineers start trying to use the springs to replace the conventional springs in their products so that the performance of their products can be improved. However, theoretical studies regarding the spring is currently mainly focused on the manufacturing and geometrical modelling of the spring whereas the response of the spring is not well studied. As a result, the engineers cannot apply the spring in their design with sufficient theoretical support and therefore cannot exploit the advantages of the spring.Aiming on solving the key problems to the application of the spring, the present work is focused on the manufacturing, static and dynamic response modelling of the spring and dynamic response analysis of systems with the spring. The following achievements will be introduced in detail:① Focusing on the absence of theoretical support for choosing the strand pitch when manufacturing the spring, a criterion of the optimal strand pitch is established. A method for deriving the optimal strand pitch is proposed. The method is useful for the rapidly development of new springs.② A two-state static response model of the spring is proposed considering the fact that existing static response model cannot describe the nonlinear stiffness of the spring properly and the problem that there is currently not sufficient theoretical support for the design of repositioning mechanisms with the spring. The model takes the change of contact state of the wires into consideration thus improving the accuracy of the analysis. The model can be applied to the design of repositioning devices with the spring.③ A dynamic response model of the spring is proposed for there is no existing model suitable for describing the dynamic behaviors of the spring. The model is a phenomenological model based on experimental data and it is a modified Bouc-Wen model in essence. The model is capable of describing the nonlinear stiffness and hysteretic damping of the spring. The model features high precision and its model parameters can be identified easily. Following studies on the response of systems with the spring can be carried based on the model.④ To identify the parameters of the proposed dynamic response model, two parameter identification methods are proposed. The first one is called a two-stage method. Compared with most existing methods, the two-stage method does not rely on iterative algorithms and therefore is free from convergence problems. The method is a practical approach. Combining the two-stage method and iterative algorithms, a three-stage method which does not require any initial guesses for the identification process is then proposed. The three-stage method features better accuracy. The proposed methods are also foundations for the application of the spring and following studies.⑤ The harmonic response of systems with the springs is a highly concerned subject in the engineering perspective. Based on the harmonic balance method for nonlinear systems, the single harmonic solution of the system is firstly derived. The solution is only suitable for systems with weak nonlinearity. An iterative multi-harmonic balance method is also proposed. The method makes use of iterative algorithms along with the harmonic balance method and turns the problem of solving nonlinear differential equations into a nonlinear optimization problem. The method is capable of analyzing system with strong nonlinearity. Experiments show that the method is an effective approach to study the harmonic response of systems with the springs.⑥ Equivalent linearization and statistical linearization methods for the dynamic response of systems with the springs is proposed considering that the spring is often used along with other linear components and the response of the systems are often found to be similar to that of linear systems. The equivalent linearization method is based on the proposed energy dissipation analysis method for the normalized Bouc-Wen model. The statistical linearization method is used to analyze the stochastic response of the system. The method can deal with systems where the power spectrum density function of the stationary excitation is given in the form of rational fractions. The linearization methods features high computation efficiency and is suitable for a rough evaluation of the response of a system when in the early stages of the designing process of a system.