Design and Modeling on Stranded Wires Helical Springs

A stranded wires helical spring is formed of a multilayer and coaxial strand of several wires twisted together with the same direction of spiral. Compared with the conventional single wire spring, the stranded wires helical spring has the notable predominance in strength, damping and vibration reduction, which is usually used in aircraft engines, automatic weapons, etc. However, due to its complicated structure, the precise computation of its strength and rigidity need be a correct mathematical model, which then will be imported to finite element analysis software for solutions. Equations on solving geometric parameters, such as external diameters of strands and screw pitches of wires, are put forward in the paper. It also proposes a novel methodology on solving geometric parameters and establishing entity models of the stranded wires helical spring, which provides foundation of computing mechanical parameters by FEA. Then mathematical models on the centre line of the strand and the surface curve of each wire, after closing two ends in a spring, are proposed. Finally, geometric parameters are solved in a case study, and a 3D entity model of a spring with 3 layers and 16 wires is established, which has validated the accuracy of the proposed methodology and the 3D entity mathematical model. The method provides a new way to design stranded wire helical spring.

Three-stage Method for Identifying the Dynamic Model Parameters of Stranded Wire Helical Springs

The dynamic behavior of the stranded wire helical spring is described by a modified Bouc-Wen model while the model parameters must be identified using an identification method and experimental data. Existing identification methods usually relies either solely nonlinear iterative algorithms or manually trial and error. Therefore, the identification process can be rather time consuming and effort taking. As a result, these methods are not ideal for engineering applications. To come up with a more practical method, a three-stage identification method is proposed. Periodic loading and identification simulations are carried out to verify the effectiveness of the proposed method. Noises are added to the simulated data to test the performance of the proposed method when dealing with noise contaminated data. The simulation results indicate that the proposed method is able to give satisfying results when the noise levels are set to be 0.01, 0.03, 0.05 and 0.07. In addition, the proposed method is also applied to experimental data and compared with an existing method. The experimental data is acquired through a periodic loading test. The experiment results suggest that the proposed method features better accuracy compared with the existing method. An effective approach is proposed for identifying the model parameters of the stranded wire helical spring.

FORMULATION AND EVALUATION OF AN ANALYTICAL STUDY FOR CYLINDRICAL HELICAL SPRINGS

The free vibration analysis of cylindrical helical springs is carried out by means of an analytical study. In the governing equations of the motion of the springs, all displacement functions are defined at the centroid axis and also the effects of the rotational inertia, axial and shear deformations are included in the proposed model. Explicit analytical expressions which give the vibrating mode shapes are derived by rigorous application of the symbolic computing package MATHEMATICA and a process of searching is used to determine the exact natural frequencies. Numerical examples are provided for fixed-fixed boundary conditions. The free vibrational pa- rameters are chosen as the number of coils （n = 4- 14）, the helix pitch angle （a = 5 - 30°） and as the ratio of the diameters of the cylinder and the wire （D/d = 4 - 18） in a wide range. Validation of the proposed model has been achieved through comparison with a finite element model using two-node standard beam elements and the results available in published literature, which in these cases indicates a very good correlation.

Equilibrium equations for 3D critical buckling of helical springs

In most cases, the research on the buckling of a helical spring is based on the column, the spring is equivalent to the column, and the torsion around the axial line is ignored. A three-dimensional （3D） helical spring model is considered in this paper. The equilibrium equations are established by introducing two coordinate systems, the Frenet and the principal axis coordinate systems, to describe the spatial deformation of the center line and the torsion of the cross section of the spring, respectively. By using a small deformation assumption, the variables of the deflection can be expanded into Taylor＇s series, and the terms of high orders are ignored. Hence, the equations can be simplified to the functions of the twist angle and the arc length, which can be solved by a numerical method. The reaction loads of the spring caused by the axial load subjected to the center point are also discussed, giving the boundary conditions for the＇solution to the equilibrium equations. The present work is useful to the research on the behavior of the post-buckling of the compressed helical spring.

STEADY STATE RESPONSE ANALYSIS ON HELICAL SPRING IMPACTED BY SHORT WAVE

The wave transmission character of helical spring is applied to establish 2-DOF model of impacted vehicle on the wave impact theory. Considering the concrete structure of helical spring, corresponding responses under different impact frequency of the vehicle are imitated. The reason why the vehicle floor overresponds in some special frequency fields is explored based on analyzing the responses. When the impactions are in low frequency, the change of the spring has not been considered, but this does not affect the results. Because the transmission characters of velocity and acceleration are unanimous in helical spring, the responses characters of velocity and acceleration arc also unanimous, the only difference is the magnitude, which can make use of acceleration responses to analyse velocity responses.

Experimental and numerical study on hysteretic performance of SMA spring-friction bearings

This paper presents an experimental and numerical study to investigate the hysteretic performance of a new type of isolator consisting of shape memory alloy springs and friction bearing called an SMA spring-friction bearing （SFB）. The SFB is a sliding-type isolator with SMA devices used for the seismic protection of engineering structures. The principle of operation of the isolation bearing is introduced. In order to explore the possibility of applying SMA elements in passive seismic control devices, large diameter superelastic tension/compression NiTi SMA helical springs used in the SFB isolator were developed. Mechanical experiments of the SMA helical spring were carried out to understand its superelastic characteristics. After that, a series of quasi-static tests on a single SFB isolator prototype were conducted to measure its force-displacement relationships for different loading conditions and study the corresponding variation law of its mechanical performance. The experimental results demonstrate that the SFB exhibits full hysteretic curves, excellent energy dissipation capacity, and moderate recentering ability. Finally, a theoretical model capable of emulating the hysteretic behavior of the SMA-based isolator was then established and implemented in MATLAB software. The comparison of the numerical results with the experimental results shows the efficacy of the proposed model for simulating the response of the SFB.