| A stranded wire helical spring(SWHS)is a cylindrical coil spring made of a steel wire which twisted by a plurality of steel wires.The middle and outer layers of the cable are usually wound by 2 to 7 strands of carbon spring wires,and the diameter of wire is 0.4 mm to 3 mm.It exhibits obvious strong nonlinearity,strong damping,and hysteresis of resilience in the dynamic response,which makes it suitable for application conditions with requires high load strength,good damping effect and high reliability.SWHS can be used as a re-entry spring to undertake the function of weapon firing and energy storage,and also,it can be used as a reset spring of the equipment to ensure that the equipment is in the normal position.When used as a reset element or an energy storage element of a specific system,it is inevitably subjected to an impact load or a periodic harmonic load.In order to accelerate the engineering promotion process of the SWHS,it seems especially necessary to analyze the response characteristics under these two conditions.In addition,during the test of the dynamic characteristics of the SWHS,it was found that the work piece was extremely poor in molding quality due to the uneven tension of the machine tool,which adversely affected the dynamic characteristics test.As a result,this paper also studies the issue together.This article has carried out research on the following issues:(1)Dynamic model of steel wire tension generation mechanism and interaction between steel wires was established.And a three-wire channel tension simulation platform was built based on Matlab/Simulink.Simulation of the sudden change of the wire tension of a certain channel during the machining process is realized by applying a step signal at a specified time.Combining engineering experience to set different PID parameter combinations,found the most effective parameters.Actually,the essence of this research is the tension simulation of the machine tool processing.Through the research,the debugging efficiency of the tension control system can be greatly improved.In addition,the optimal PID parameter configuration is realized without occupying the hardware resources of machine.(2)This paper also deeply analyzes the characteristics of the normalized Bouc-Wen model describing resilience hysteresis of SWHS.Through numerical simulation analysis,it is found that the nonlinear amplification factor term described by the Bouc-Wen model has a quadratic nonlinear relationship with the free end velocity of the spring in one motion cycle.This paper proposes a method to degenerate the two-degree-of-freedom Bouc-Wen model into a single-degree-of-freedom nonlinear model.This part of the study laid the foundation for the model analysis of SWHS dynamics.(3)Differential equation of motion transient response is established by introducing the degenerate Bouc-Wen model.The performance parameters of the motorcycle damper are selected to obtain the displacement,velocity of the free-end mass,and the energy dissipation caused.Improved L-P method is used to transform the original strong nonlinear system into a weak nonlinear system,and the closed-form solution of the dynamic response of the SWHS system is obtained by multi-scale method.This part of the study fills in the model vacancy of the nonlinear response parameter identification of the black box system,and the obtained results can be used to estimate the dynamic parameters of the system.Under the premise of obtaining the transient response curve of the system,the dynamic parameters of the system can be solved inversely by the nonlinear parameter identification method.(4)Aiming at the harmonic excitation conditions widely used in engineering,the steady-state differential equation of single mass SWHS system is established by introducing the degraded Bouc-Wen model.Firstly,SHB method is used to derive the single harmonic solution of the original equation.By comparing with the fourth-order RK algorithm,it is found that SHB method can not describe the subharmonic resonance characteristics of nonlinear vibration accurately.Then,IHB method is applied to transfer the original equation into a nonlinear optimization problem.Finally,the accuracy of these two method for the amplitude-frequency response is computed by experiments result.The research shows that the SHB method is only suitable for the analysis of weak nonlinear system with small amplitude and weak harmonic component excitation,while IHB method is more suitable for steady-state harmonic response of strong nonlinear SWHS system.(5)The influence of molding quality on the dynamic response characteristics of SWHS-mass system was explored.Based on the transient response and steady-state harmonic response quantitative analysis method,the SWHS parameters of different forming qualities are selected for numerical calculation.The results show that the structural damage makes the static stiffness of the spring weakened,and the maximum load capacity and spring stability of the multi-strand spring are reduced.Simultaneously,the stiffness damage reduces the dynamic response speed of the multi-strand spring system,and the damping damage causes a greatly reduce of the vibration absorption and vibration damping capability of the SWHS.This research guides the manufacture processing of SWHS,also,it provides forward design and reverse analysis for SWHS system under impact conditions,and it provides an effective solution for response analysis of SWHS damping system.The results contribute to the application of SWHS engineering applications and has great application value. |
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