A note on large deflection of elastic composite circular springs under tension and in push-pull configuration

Large deflection analysis on specially orthotropic midplane symmetric laminated circular springs under uniaxial tension and push-pull loadings is presented. Experimental verifications for the initial stage of load application are performed using E-glass woven roving/epoxy circular rings. It is demonstrated that by mounting two springs with similar mechanical and physical properties in a push-pull configuration, it is possible to obtain a symmetrical and nonlinear load-stiffness system with adjustable spring rate characteristic.     

Light composite elliptic springs for vehicle suspension

For composites to compete in vehicle suspension applications, it is essential to control their failure by utilising their strength in principal direction instead of shear. This can be achieved efficiently by employing a new configuration instead of existing one. This study marries between an elliptical configuration and the woven roving composites.

In this paper, the influence of ellipticity ratio on performance of woven roving wrapped composite elliptical springs has been investigated both experimentally and numerically. A series of experiments was conducted for composite elliptical springs with ellipticity ratios (a/b) ranging from one to two. Typical failure histories of their failure mechanism are presented and discussed. In general, this study demonstrated that composites elliptical spring can be used for light and heavy trucks and meet the requirements, together with substantial weight saving. The results showed that the ellipticity ratio significantly influenced the spring rate and failure loads. Composite elliptic spring with ellipticity ratios of a/b 2.0 displayed the highest spring rate.     

Developing a composite based elliptic spring for automotive applications

An automotive suspension system is designed to provide both safety and comfort for the vehicle occupants. In this study, finite element models were developed to optimize the material and geometry of the composite elliptical spring based on the spring rate, log life and shear stress parameters. The influence of the ellipticity ratio on the performance of woven roving–wrapped composite elliptical springs was investigated both experimentally and numerically. The study demonstrated that composite elliptical springs can be used for light and heavy trucks with substantial weight reduction. The results showed that the ellipticity ratio significantly influenced the design parameters. Composite elliptic springs with ellipticity ratios of a/b = 2 had the optimum spring parameters.     

空气弹簧特性研究

本文介绍了空气弹簧的基本特性、结构型式和基本原理。以单曲囊式空气弹簧为例讨论了空气弹簧动、静态风度的求解方法。     

平纹机织叠层复合材料飞轮弹性参数预测及测量

针对纤维缠绕复合材料高速飞轮径向分层问题,提出环向和径向同时强化的圆环平纹织物结构,环向纱束为单一纤维束连续织造。建立了“平头梭形”截面的单胞模型,兼顾双向纱束轮廓差异。基于扇形单胞和矩形单胞结构相似性,定义了“等参数”织造约束条件。采用体积平均法预测圆环织物扇形单胞等效弹性参数,并采用轮缘径向多层分割模型,分析了机织飞轮旋转载荷下的应力和变形特征及其影响参数,轮缘理论计算位移与圆标记法径向变形测量结果一致。机织复合材料飞轮测试极限圆周速度为889 m/s,储能密度为63.7 Wh/kg。理论分析和实验表明,环形织构的双强化理论可行,能够获得比缠绕飞轮更高的旋转速度。      

Elastostatic analysis of infinite solids using finite elements

A novel technique is developed to simulate the effects of an infinite elastic solid by using multiple springs having spatially varying stiffnesses. The spring constants are computed by numerical integration of classical solutions for point or line loads in an infinite or semi-infinite elastic mass. Under certain conditions, even the 'exact' values of spring constants may become negative at some nodes. A simple and highly effective algorithm is proposed to remove this computational difficulty. The technique is applied to the computation of displacements and stresses around underground openings. For a circular opening subjected to different stress conditions, spring constants computed by the proposed numerical integration technique are found to be 'identical' to their 'exact' values. Results obtained by the proposed technique for displacements and stresses around circular and non-circular openings are found to be in an excellent agreement with classical and boundary element solutions. The principal advantages of the proposed technique are that an unbounded solid may be simulated by a relatively very small finite model and a standard finite element code requires no modification for its implementation.     

Impact Damage of 3D Orthogonal Woven Composite Circular Plates

The damages of 3D orthogonal woven composite circular plate under quasi-static indentation and transverse impact were tested with Materials Test System (MTS) and modified split Hopkinson bar (SHPB) apparatus. The load vs. displacement curves during quasi-static penetration and impact were obtained to study the energy absorption of the composite plate. The fluctuation of the impact stress waves has been unveiled. Differences of the load-displacement curves between the quasi-static and impact loading are discussed. This work also aims at establishing a unit-cell model to analyze the damage of composites. A user material subroutine which named VUMAT for characterizing the constitutive relationship of the 3-D orthogonal woven composite and the damage evolution is incorporated with a finite element code ABAQUS/Explicit to simulate the impact damage process of the composite plates. From the comparison of the load-displacement curves and energy absorption curves of the composite plate between experimental and FEM simulation, it is shown that the unit-cell model of the 3D woven composite and the VUMAT combined with the ABAQUS/Explicit can calculate the impact responses of the circular plate precisely. Furthermore, the model can also be extended to simulate the impact behavior of the 3D woven composite structures.     

Investigating the benefits of using circular die springs instead of rectangular die springs

Die springs with rectangular cross section (rectangular die springs) are common in the industry. However, the production of rectangular die springs is difficult, and the cost of production is high. In this study, we examined the use of die springs with circular cross section (circular die springs), which are both easier to produce and less costly, in place of rectangular ones. To this aim, the fatigue life values of both die spring with equivalent specifications were compared experimentally. The results obtained were transferred to the finite element methods software to run the simulation of the fatigue test. From the experimental results obtained, it has been observed that using circular die springs in place of rectangular die springs is always possible, provided that the springs are guided with cast polyamide guides.     

Modeling of textile composites with warp/weft frictional contact

A 2D modeling of textile composites is studied. The modeling is applicable to woven textile composites with flat fibers, used as reinforcing fibers of composite materials. Two 2D displacement fields are introduced, one for each layer of the fabric. The warp/weft interaction is taken into account by a nonlinear functional which characterizes the frictional contact. An explicit form of the warp/weft contact pressure is proposed. A numerical approximation of a solution of the variational problem is presented.     

Composite disc springs

The feasibility of replacing steel with composite materials in disc springs (or Belleville washers) is investigated. The objective was to reproduce the identical load/deflection characteristics and the maximum load capacity of the steel disc spring while achieving significant mass savings. Design equations for steel disc springs were modified for a quasi-isotropic composite lay-up. Several prototype disc springs were manufactured and tested, and compared with the performance of equivalent steel springs. The results show that accurate reproducibility of the steel spring’s load–deflection characteristics can be achieved by using composites, with a corresponding mass savings of almost 80%. Other composite disc springs of different geometries were tested so that preliminary observations of the effects of geometric features on load–deflection responses could be made. The failure mode (on overloading the composite spring) consisted of radial fracture arising from the hoop stress as predicted by theory. The results of this study indicate that composites can satisfactorily replace steel in disc springs with significant mass savings.     

Cracking orientation and induced anisotropy of a ceramic matrix composite under off-axis loading

The effect of matrix microcracking on the stiffnesses of a carbon-fibre/SiC-matrix woven composite is studied by means of an ultrasonic method. It provides the whole set of the stiffness tensor coefficients which are inaccessible by classical strain measurements and which are required to identify anisotropic damage. The induced anisotropy depends on the loading direction. If a tensile solicitation in a fibre direction leads to stiffnesses decreases without any rotation of principal axes, a tensile solicitation of 45° from a fibre direction creates microcracks with a predominant orientation that does not coincide with the elastic symmetry axes, and induce a fully anisotropic elastic degradation.     

燃气轮机拉杆转子考虑接触效应的扭转振动模态分析

燃气轮机转子一般是由多个层叠的轮盘通过拉杆组合而成,各轮盘接触面由磨削加工形成。粗糙度测试结果表明磨削加工的实验拉杆转子轮盘面具有两个不同分形结构的区域。利用结构函数法计算了这种双重分形面的轮廓曲线的分形维数D1、D2和分形粗糙度参数G1、G2 。采用双重分形几何描述接触表面的拓扑结构,并根据赫兹接触理论导出接触微凸体的切向接触刚度。弹塑性双重分形面的切向接触刚度等于所有微观弹性接触点的切向接触刚度的总和。粗糙层是由相接触的微凸体所构成的,其抗扭刚度模化为接触转子轮盘间的一个抗扭弹簧。通过三维有限元模态分析和实验模态分析得到了拉杆转子在不同预紧力下的扭振模态频率。通过上述计算和实验结果识别了粗糙层的抗扭刚度,实验测试结果和理论计算结果相一致,这表明上述接触层抗扭刚度的双重分形模型实合理的,可以有效地考虑接触效应对拉杆转子扭转振动模态频率的影响。     

复合材料圆柱螺旋弹簧的制造与实验研究

对玻璃纤维复合材料圆柱螺旋弹簧的加工和弯曲力学性能进行了研究。通过大量探索性试验确定了复合材料弹簧的成型工艺流程,讨论了弹簧的加工工艺及结构参数对其弯曲回弹力、回复率及拉伸性能等的影响规律。研究结果表明,复合材料弹簧的弯曲力学性能与弹簧内径、纤维束的捻度、股数及直径等有直接关系,并受弯曲、回复时间的影响,可以根据需要设计弹簧的工艺和结构参数。      

应用传递矩阵法分析电磁继电器变截面直簧片固有频率

电磁继电器中触簧系统固有频率的分析是研究其振动特性的基础。变截面直簧片结构具有更好的反力性能与抗振性能等特点,因此广泛应用于各类电磁继电器中。应用传递矩阵法建立了变截面直簧片的统一数学模型,并对包括带圆孔型、分岔型、梯形等变截面直簧片结构的固有频率进行分析求解,计算结果表明本方法准确性高,适用性广。通过改变变截面直簧片形状参数,表明在一定范围内变截面直簧片的抗振性优于等截面直簧片。     

The effect of temperature on mechanical properties and failure behaviour of hybrid yarn textile-reinforced thermoplastics

Multi-axially reinforced textile composites with thermoplastic matrix are investigated under thermomechanical loading conditions. Two groups of composites made of glass fibre/polypropylene hybrid yarn are chosen as examples: a novel 3-D textile-reinforced composite with multi-layered flat bed weft-knitted reinforcement and a composite with woven reinforcement. The presented study concentrates on determining the mechanical properties depending on temperature and investigating the complex failure behaviour and its provoking phenomenological damage processes like void growth and inter fibre damage at different temperatures by the use of optical microscopy and visual observations of specimens. With the focus on automotive applications, the elasticity constants and strength values have been determined in the range from ?40 °C up to 80 °C using uniaxial tensile and compressive tests. As a result, the basic properties like stiffnesses and strengths are mathematically described depending on the temperature. Additionally, dynamic-mechanical analysis have been used to identify the glass transition range of the thermoplastic matrix system and to find correlation to the temperature-dependent mechanical properties.     

二维机织复合材料弹性常数的有限元法预测

为了预测二维机织复合材料的弹性性能,建立了有限元力学分析模型。基于二维机织复合材料的几何特征,建立了参数化的单胞模型;考虑了织物纤维束呈现出的各向异性材料特征,将有限元中材料主方向转化到纤维屈曲方向,建立其力学分析有限元模型;分析了单胞边界面保持平面假设的不足,提出了对于二维机织复合材料通用的周期边界条件,获得了更为准确的二维机织复合材料的工程弹性常数。结果表明:织物衬垫单胞边界面,在单向拉伸载荷和纯剪切载荷下,呈凹凸翘曲变形,即为周期边界;应用给出的织物参数化几何建模方法与有限元求解方法,可以精确地获得工程弹性常数,数值计算结果与实验值吻合较好。      

A unit cell approach of finite element calculation of ballistic impact damage of 3-D orthogonal woven composite

This paper presents ballistic impact damages of 3-D orthogonal woven composite in finite element analysis (FEA) and experimental. A unit-cell model of the 3-D woven composite was developed to define the material behavior and failure evolution. A user-defined subroutine VUAMT was compiled and connected with commercial available FEA code ABAQUS/Explicit to calculate the ballistic penetration. Ballistic impact tests were conducted to investigate impact damage of 3-D kevlar/glass hybrid woven composite. Residual velocities of conically-cylindrical steel projectiles (Type 56 in China Military Standard) and impact damage of the composite targets after ballistic perforation were compared both in theoretical and experimental. The reasonable agreements between FEA results and experimental results prove the validity of the unit-cell model in ballistic limit prediction of the 3-D woven composite. We believe such an effort could be extended to bulletproof armor design with the 3-D woven composite.     

考虑接触刚度的燃气轮机拉杆转子动力特性研究

基于弹塑性理论对具有粗糙表面的长方微元体进行有限元接触分析,根据受力和变形关系得到了不同载荷作用下的法向和切向界面接触刚度。将微元体界面接触刚度与宏观结构应力分析结果相结合,给出了考虑接触刚度的组合结构动力特性研究方法,分析了压气段轮盘接触刚度对某重型燃气轮机拉杆转子固有振动频率的影响。结果表明,界面接触刚度导致转子固有频率降低,随着接触刚度的增加,其对固有频率的影响逐渐减小。接触刚度对转子各阶固有频率的影响不同,法向刚度对第一阶弯曲频率影响较大,切向刚度对第二阶弯曲频率影响较大。     

电磁继电器触簧系统振动加速度的分析方法

电磁继电器触簧系统固有振动频率和极限加速度是衡量其力学环境防护性能的两个重要指标。综合分析了静触簧为刚性结构和柔性结构的触簧系统，建立其抗振性分析数学模型，给出了簧片振动加速度的解析表达式及检验电磁继电器触簧系统抗振性的合理判据。通过分析影响电磁继电器触簧系统振动加速度的相关因素(主要包括材料特性参数、尺寸参数、触点初压力、触点质量)，得出了若干有关提高电磁继电器触簧系统抗振性能的重要结论。这些结论可为电磁继电器机械反力系统参数优化设计提供理论基础。     

囊式空气弹簧刚度特性的非线性有限元法研究

利用非线性有限元方法，研究由多层复合材料组成的空气弹簧的垂向和横向刚度特性，分析大变形的几何非线性、空腔内空气的状态非线性和胶囊与金属裙板形成的接触非线性，得到了空气弹簧刚度非线性特性的精确描述，并讨论了橡胶囊各参数对空气弹簧垂向和横向特性的影响。通过与试验结果比较，证明了该方法确实可行。