Finite strain numerical analysis of elastomeric bushings under multi-axial loadings: a compressible visco-hyperelastic approach

Elastomers have wide and ever increasing applications in several industries. In this work a compressible visco-hyperelastic approach is employed to investigate the behavior of elastomeric materials. The time-discrete form of the material model is developed to be used in numerical simulations. This formulation provides a recursive relation to update the stress in any time step regarding the deformation history. By means of analytical solutions derived for pure torsion of a solid circular cylinder, the numerical implementation is validated and then, the response of an elastomeric bushing is investigated in torsional, axial and combined deformations. These bushings are used in suspension systems to reduce amplitude of vibrations as well as shocks. It is shown that, the numerical model well simulates the non-linear time dependent response of the bushing in different deformation rates. Also, a multi-step relaxation test is simulated to identify the hysteretic behavior. Finally, fully relaxed response of the bushing for torsional and combined torsional–axial deformations is predicted and compared with those of experiment as well as three other constitutive models. The comparisons reveal that, the proposed approach well predicts the coupling effect of axial displacement on torsional moment where it is not the case for other compared models.     

Elastomer bushing response: experiments and finite element modeling

Summary.  Elastomer bushings are essential components in tuning suspension systems since they isolate vibration, reduce noise transmission, accommodate oscillatory motions and accept misalignment of axes. This work presents an experimental study in which bushings are subjected to radial, torsional and coupled radial-torsional modes of deformation. The experimental results show that the relationship between the forces and moments and their corresponding displacements and rotations is nonlinear and viscoelastic due to the nature of the elastomeric material. An interesting feature of the coupling response is that radial force decreases and then increases with torsion. The experimental results were used to assess bushing behavior and to determine the strength of radial-torsional coupling. The experimental results were also compared to finite element simulations of a model bushing. While finite element analysis predicted small displacements at the relaxed state reasonably well, the response to larger radial deformations and coupled deformations was not well captured. Received January 13, 2003 Published online: May 20, 2003 The authors would like to thank Tenneco Automotive and the Great Lakes Truck and Transit Research Center for support of this project.     

双发动机工作时倾转旋翼机传动系统扭转振动的计算

为了获得双发动机工作时倾转旋翼机传动系统扭转振动的特性,进行了倾转旋翼机传动系统扭转振动的计算和分析。在简化传动系统结构的基础上,将倾转旋翼机传动系统划分为若干个轴段和圆盘的子系统,根据动量矩定理和振型叠加原理,分别列出扭转运动方程,再利用边界关系,合成子系统的扭转运动方程,得到传动系统的扭转运动方程,通过求解传动系统的扭转运动方程,并根据振型叠加原理,得到双发动机工作时倾转旋翼机传动系统扭转振动的角位移,在此基础上,给出算例,分析了传动系统的扭转频响函数。     

A nonlinear viscoelastic bushing element in multibody dynamics

This paper presents a formulation for incorporating nonlinear viscoelastic bushing elements into multibody systems. The formulation is based on the assumption that the relaxation function can be expressed as a sum of functions which are nonlinear in deformation and exponentially decreasing in time. These forces can represent elastomeric mounts or bushings in automotive suspension systems. The numerical implementation of the nonlinear viscoelastic bushing model into a general purpose rigid multibody dynamics code is described, and an extension of the formulation is also presented wherein component flexibility is included. Model validation was performed by comparing experimental data to simulation results obtained using the nonlinear viscoelastic model and a nonlinear elastic model. The experimental data were obtained at the Center's facilities by testing an automotive lower control arm/bushing system, subjected to a simulated road load event. The comparison demonstrates the better load prediction capability of the viscoelastic bushing model compared to the conventional model.     

Size factor in the fatigue of steel shafts with press-fitted parts

This article describes the results of an investigation of the effect of size factor on the fatigue (in air) of steel shafts 5, 12, 27, and 50 mm in diameter with press-fitted bushings. It was established that increasing the shaft diameter produces a reduction in the fatigue strength regardless of the composition of the steel and the bushing material. Mechanisms for fatigue fracture of shafts with press-fitted bushings and of the influence of the size factor on this process were postulated.     

Dynamic stiffness analysis for axial-lateral-torsional vibration

The dynamic stiffness method enables one to model an infinite number of natural modes by means of a finite number of degrees of freedom. The method is extended to analyse the lateral-torsional vibrations of thin-wall columns under the influence of the constant axial force. The constant in-plane moment weakens the flexural mode so that at certain critical applied moments, the flexural mode buckles as the fundamental flexural frequency reaches zero. However, the constant in-plane moment hardens the torsional mode so that the torsional mode never buckles. When both torsion and flexure are considered, the interaction of the convexity of flexural characteristic curves and the concavity torsional characteristic curves becomes very complex. Since the dynamic stiffness is exact in the classical sense, the interaction can be studied easily. Numerical examples are given to show the complexity of the characteristic diagrams.     

膨胀土地基中单桩受扭非线性分析

膨胀土地基中桩-土相互作用较为复杂,膨胀土浸水对单桩扭矩承载特性的影响机理尚未明确。该文基于荷载传递法建立桩身位移控制方程,考虑膨胀土浸水隆起对桩侧摩阻力及桩端边界条件的影响,利用有限差分法求解出桩侧竖向摩阻力的分布。在此基础上,结合边界元法提出膨胀土地基浸水后单桩受扭的非线性分析方法,揭示了桩侧环向摩阻力的分布规律,并通过模型试验验证了该文方法的正确性。研究表明:膨胀土地基浸水膨胀引起的地表隆起会使单桩的扭矩承载力大幅度降低,常规的计算方法高估了基桩的极限扭矩和桩-土体系加载刚度,偏于不安全;浸水前单桩的桩身扭矩沿桩身近似线性减小,浸水后桩-土界面"滑移段"的扭矩接近于桩顶扭矩,"未滑移段"桩身扭矩近似线性减小;随着膨胀土膨胀率的增加,单桩的抗扭能力降低,且桩-土界面"滑移段"的长度也在增加。     

Generalized wave equation in nonlocal elasticity

The refined theory of torsional deformation of a circular shaft is proposed on the basis of the classical elasticity theory. The refined theory provides the solutions of torsional deformation of a circular shaft without ad hoc assumptions. Exact solutions, including a Saint-Venant’s solution part and a transcendental part, are obtained for a circular shaft with homogeneous boundary conditions, and the decomposed theorem is given and proved. The approximate solutions are derived for a circular shaft under reverse direction surface loading by dropping terms of high order. To illustrate the application of the theory developed, two examples are examined.     

基于组件法的超大承载力端板连接节点弯矩-转角曲线计算方法

超大承载力端板连接节点是一种可以应用于大跨或重载钢结构中的新型梁柱节点形式。为了在结构分析中准确考虑该节点的抗弯承载力和转动刚度,需要确定其弯矩-转角曲线。在已有试验和有限元分析结果的基础上提出了超大承载力端板连接节点的组件模型,引入一种新组件形式并提出了其承载力和刚度的分析方法,基于组件法提出了超大承载力端板连接节点的抗弯承载力和转动刚度的计算方法。综合现有典型的节点弯矩-转角曲线模型的优点,以节点抗弯承载力和转动刚度为基本参数提出了适用于超大承载力端板连接节点的弯矩-转角曲线模型。通过与已开展的试验研究和有限元分析结果进行比较,所提方法得到的节点抗弯承载力和转动刚度较为准确,所提弯矩-转角曲线模型与试验曲线吻合良好,可以应用于采用该节点形式结构的分析和设计中。     

副车架计算模态分析中衬套动刚度的当量方法

针对副车架计算模态分析中橡胶衬套的处理问题,在有限元分析软件中以CBUSH单元模拟橡胶衬套,并以橡胶衬套动刚度的当量值作为CBUSH单元的刚度赋值。从动刚度与静刚度之比的角度出发,提出一种基于橡胶衬套静刚度的动刚度当量方法,称之为"橡胶衬套动刚度的修正系数当量方法"。运用正交试验设计,通过试验模态与计算模态的对比验证所提橡胶衬套动刚度当量方法的有效性,同时,明确不同位置的橡胶衬套对模型精度的影响规律,可应用于相关建模分析中。     

H型钢梁与矩形钢管混凝土柱平齐式端板单边螺栓连接节点弯矩-转角分析模型

为预测通过平齐端板和单边螺栓连接的钢管混凝土节点的弯矩-转角关系,该文提出基于极限弯矩、初始转动刚度和形状参数的三参数指数模型.考虑节点的可能破坏模式,提出节点极限弯矩的计算方法,基于组件法建立节点初始转动刚度分析模型,仅需节点构造尺寸和材料特性便可得到节点的极限弯矩和初始转动刚度预测值.弯矩-转角关系模型、极限弯矩计...     

Analysis of fatigue failure on the keyway of the reduction gear input shaft connecting a diesel engine caused by torsional vibration

The vibratory torque of a diesel engine caused by the reciprocating motion of the mass and gas pressure force of a cylinder is one of the main causes of the failure of the driving shaft of the diesel engine and the connecting shaft to the reduction gear. Because high cycle torsional fatigue can occur in the reduction gear shaft connecting the engine under vibratory torsional stress, the US Navy restricts it under the MIL G 17859D(SH) standard and suggests a procedure for evaluating the safety of the shaft for the reduction gear. In this study, the structural safety of the reduction gear input shaft in which fatigue failure occurs in typical naval vessels is investigated in accordance with the VDI 3822 RCA (root cause analysis) procedure based on the MIL G 17859D(SH) standard. When evaluating the safety factor in accordance with the MIL G 17859D(SH) standard, the alternating bending moment from the lateral vibration and the stress concentration factor under static load are considered. In addition, an improved design is suggested by CAE to satisfy the safety factor suggested by the MIL G 17859D(SH) standard.     

Saint-Venant’s torsion of composite shafts reinforced with arbitrarily or periodically dispersed coated fibers

It is known that a circular shaft containing a number of composite cylinders, upon suitably designed material parameters, is an exactly solvable configuration under Saint-Venant’s torsion [Chen, T., Benveniste, Y., & Chuang, P. C. (2002). Exact solutions in torsion of composite bars: Thickly coated neutral inhomogeneities and composite cylinder assemblages. Proceedings of the Royal Society A, 458, 1719–1759]. Here we consider the boundary value problem of a circular shaft containing coated fibers under torsion without any restrictions on the material parameters. The formulation is based on a complex variable method together with simple mapping techniques, representing the warping fields in Laurent or Taylor series based on different origin points. Particularly when the coated fibers are periodically dispersed inside the host shaft, we show that the unknown coefficients for each coated fiber are correlated in specific manners, and thus rendering the governing framework much simplified. We verify analytically that our results conform with the exact results of partly neutrality and complete neutrality of the exact solvable configuration of a circular shaft containing neutral coated fibers. This work presents a feasible solution procedure that complements the exact configurations in which the material parameters must follow restrictive constraint, and also provides an estimate for the torsional rigidity in which the bounds are not sufficiently close.     

古建筑木结构燕尾榫节点弯矩-转角关系理论分析

基于燕尾榫节点受力机理的分析,对燕尾榫节点的转动弯矩进行了理论分析,推导了燕尾榫节点弯矩-转角理论计算公式,并与试验结果进行了对比分析,理论分析结果与试验结果吻合较好;在计算公式的基础上,对燕尾榫节点转动弯矩的影响参数进行了分析,结果表明：在一定范围内,随着摩擦系数的增大,燕尾榫节点的转动弯矩和初始转动刚度也逐渐增大;当摩擦系数超过0.5时,节点的初始转动刚度增加幅度逐渐减小;榫头长度和榫头的“收乍”角度的增大均能够提高燕尾榫节点的转动弯矩以及初始转动刚度;榫头高度的增大能够一定程度地提高燕尾榫节点的转动弯矩,但对节点的初始转动刚度影响不大。所得结果可为古建筑木结构的受力分析提供依据。     

联轴器扭转刚度对潜油电泵细长串联轴系扭振特性的影响研究

为解决在满负荷、长周期运行工况下潜油电泵下保护器轴易断裂的问题,以潜油电泵细长串联轴系为研究对象,分析联轴器扭转刚度对细长串联轴系扭振特性的影响.采用DyRoBeS软件构建细长串联轴系扭振模型,分析轴系扭振特性,结合扭转振型与模态扭应力分布,确定轴系下保护器轴退刀槽为危险截面,研究联轴器扭转刚度与该危险截面扭应力的关系...     

带有黏弹性阻尼器穿斗木结构振动台试验研究

按照云南"一颗印"构造要求制作了一个两层传统穿斗式木结构房屋模型进行模拟振动台试验。对结构模型的破坏模式、动力响应、应变响应,扭转效应、剪力分布、弯矩变化及耗能能力进行了分析研究。结果表明:结构模型满足中国建筑抗震设计规范"小震不坏、中震可修、大震不倒"的要求;结构模型具有明显扭转效应;层间剪力分布取决于质量分布;弯矩随地震激励增大不断增大,结构模型未发生塑形破坏;层间累积耗能能力一层耗能能力最大,二层次之,屋脊最小。     

受横向约束的细长无重管柱在压扭组合作用下的后屈曲分析

井眼中管往的屈曲，将会使钻井、采油生产等作业难以顺利进行，弄清管柱屈曲后的特性对石油工程有重要的实际意义。本文首先建立了受横向约束的管往在轴向载荷和扭矩的作用下的屈曲平衡方程；并对所得四阶非线性常微分方程进行了分析、求解。结果表明，在特定边界条件下，受压扭组合作用的管柱屈曲构形为精确的圆柱螺旋线；并进而得到了管柱屈曲变形与载荷之间的解析关系；本文结果退化后与文献所得结果一致；最后讨论了管柱所受扭矩对螺旋屈曲行为的影响和扭矩对螺旋旋向的影响。     

包装动力学响应中避免缓冲材料厚度无极限的方法

在求解包装动力学响应时,缓冲材料的本构关系常简化为立方非线性、双曲正切非线性等理想的情况。由于未考虑缓冲材料厚度的有限性,不能保证所得结果可靠性。基于缓冲材料在压缩到极限位置时,缓冲材料应力接近无限大,运用正切函数表达了缓冲材料这一限制性特性。数值计算结果表明,若未考虑限制时,动力学响应会超出缓冲材料的极限位置,甚至超过厚度,且得不到优化的包装结构;考虑限制条件,就不会出现上述错误,避免了缓冲材料厚度无极限。     

Failure Investigation of a Locomotive Turbocharger Main Shaft and Bearing Sleeve

A failure investigation was conducted on a locomotive turbocharger main shaft and a bearing sleeve which had been assembled with the main shaft. The fracture of the main shaft took place at a sharp edged groove between two journals with different cross-sectional areas. The dominant failure mechanism of the main shaft was low-cycle and rotation-bending fatigue. Wear failure occurred on the bearing sleeve through a mixed mode of abrasive and adhesive wear. Detailed metallurgical analysis indicated that the bearing sleeve and the journal surface assembled with the sleeve had been subjected to abnormally high temperatures which led to increased friction between the bearing sleeve and the bearing bush, the sleeve, and the journal surface. In addition, the abnormally high temperature softened the induction-hardening case on the journal surface and decreased the fatigue strength. Fatigue crack initiation occurred at the root fillet of the groove because of the stress concentration in that area.     

Tribaloy alloy reinforced tin-bronze composite coating for journal bearing applications

This article presents an experimental study of the tribological behavior of a tin/bronze-based composite coating. The improved-ductility Tribaloy alloy (T-401) particles are selected as the reinforcement. This coating is made on the bushing of planet journals used in aerospace engines, deposited with the high velocity oxygen fuel (HVOF) thermal spray technique. The tribological properties such as friction and wear resistance of the coated bushing are investigated under the WAMsc3 Sliding Contact Test, along with the leaded tin/bronze bushing tested for comparison. The testing results show that the bushing coated with the composite exhibits superior tribological properties to the leaded tin/bronze bushing in that the former runs longer before the friction coefficient reaches 0.5 and also leads a to lower wear rate than the latter. The experimental results and wear mechanisms of these two bushings are discussed with the assistance of worn surface analyses using scanning electron microscopy (SEM).