A new approach in producing metal bellows by local arc heating: a parametric study

Recently, dieless forming processes have been introduced to prevent the high costs of dies and tools. Local heating and axial compression process is an innovative method for producing metal bellows. In this research, producing metal bellows using simultaneous local electric arc heating and axial compression has been explained and investigated. SUS304 tubes with an outer diameter of 19 mm and a thickness of 1 mm have been employed to implement the tests. Various parameters could affect the process. Among these parameters, effects of applied displacement and device current, influencing convolution shape, thickness, and required forming force, are studied experimentally. It is found that the height, radius, and angle of the convolution and also the forming force could be controlled by alteration of these parameters. Furthermore, the result of buckling test showed that energy absorption capacity of the manufactured metal bellow has been increased in comparison to a typical tube. This method could be a suitable alternative for induction local heating and can reduce the high equipment costs.     

多层波纹管柱屈曲稳定性非线性有限元分析

多层多波波纹管柱屈曲性有限元分析模型规模大、非线性问题突出，不易于收敛。为此，文中给出了一种等效厚度模拟方法，建立了等效单层波纹管有限元模型，并在此基础上进行了波纹管的柱屈曲分析，得到了波纹管的屈曲载荷和屈曲模态。文中的工作为这类多层多波大型波纹管的柱屈曲稳定性分析提供了一种有效方法，分析结果也对该类波纹管的设计有较重要的参考价值。     

Buckling of poroelastic columns with axial diffusion

The buckling problem is investigated in this paper for fluid-saturated poroelastic beams consisting of materials for which the pore fluid flow is possible in the axial direction only. The beam material is assumed to be transversely isotropic with respect to the beam axis. The time dependent behaviours of the critical loads and deflections are considered for various diffusion and geometric boundaries.     

Exact static analysis of partially composite beams and beam-columns

The ordinary differential equations and general solutions for the deflection and internal actions and, especially, the pertaining consistent boundary conditions for partially composite Euler–Bernoulli beams and beam-columns are presented. Static loading conditions, including transverse and axial loading and first- and second-order analyses are considered. The theoretical procedure is applicable to general loading and boundary conditions for uniform composite beams and beam-columns with interlayer slip. Further, the exact closed form characteristic equations and their associated exact buckling length coefficients for composite columns with interlayer slip are derived for the four Euler boundary conditions. It is shown that these coefficients are the same as those for ordinary fully composite (solid) columns, except for the Euler clamped-pinned case. For the clamped-pinned case, the difference between the exact buckling length coefficient and the corresponding value for solid columns is less than 1.8% depending on the so-called composite action parameter and relative bending stiffness parameter. Correspondingly, the maximum deviation between the exact and approximate buckling load is at most 2.5%. These small differences can in most practical cases be neglected. Also, the maximum theoretical range for the relative bending stiffness for partially composite beams and beam-columns is derived. An effective bending stiffness, valuable in the determination of the critical buckling load for partially composite members, is derived. This effective bending stiffness is also suitable for analysing approximate deflections and internal actions or stresses in composite beams with flexible shear connection. The beam-column analysis is applied to a specific case. The difference in the approaches to the first- and second-order analysis is illustrated and the results clearly show the magnification in the actions and displacements due to the second-order effect. The magnification of the internal axial forces is different from magnifications obtained for the other internal actions, since only that portion of an internal axial force that is induced by bending is magnified by the second-order effect.     

Mechanical behavior of U-shaped bellows and shape optimal design using multiple objective optimization method

A bellows is frequently applied in piping systems for absorbing mechanical movement. Its geometry is an axial symmetric shell, which is composed of two toroidal shells and one annular plate. The mechanical behavior of U-shaped bellows under axial force and internal pressure is estimated by changing the dimensions of the geometric parameters. The changing ranges of the geometric dimensions is so selected as to invest the results with practical environments in many fields. The minimization of strength and spring rate is considered simultaneously as a multiple objective function. The weighting objective method is implemented, in which a vector function is transformed to a scalar function. The structure is analyzed by the energy method for toroidal sections. Optimization is carried out by the Recursive Quadratic Programming algorithm.     

Nonconservative dynamic axial–torsional buckling of structural frames using power series

Axial deformation is not involved in the formulation of linear buckling caused by axial force. Likewise, twisting is not present in linear buckling caused by axial torque. The dynamic axial–torsional buckling of structural frames in the presence of follower axial force will be solved by means of dynamic stiffness using power series. Variationally consistent natural boundary conditions are given so that the resulting dynamic stiffness is symmetrical for conservative loading. Some parts of the boundary forces disappeared for follower axial forces due to consistent tangency to the neutral axis. The deficiency of the power series method to deal with non-uniform sections is highlighted. New instability phenomena for a simple column are studied in detail. It is shown that columns can buckle under direct follower tension. Follower tension decreases the natural frequency initially and then increases it rapidly after a turning point. The first pair of modes about the major axis and that about the minor axis of a rectangular section column meet at one crossing point. A very small axial torque will change the crossing into flutter-like tongues. These tongues are common in compressive follower force. These tongues caused by axial torque are reported here for the first time.     

Bending of axially constrained beams on elastic foundation

Approximate analysis of bending of a pin-pointed beam under distributed load resting on elastic foundation is considered. The supports are assumed to be immovable, thereby giving rise to the axial stretching of the neutral surface under lateral loads. The resulting problem is nonlinear since the axial force of constraint is dependent on the lateral displacements. Quantitative results of axial force, benidng moment and deflections are given in terms of two dimensionless parameters which depend on the load intensity, foundation modulus and properties of the beam.     

考虑层间摩擦的多层波纹管轴向刚度非线性有限元分析

利用ANSYS程序接触有限元方法对4层U型波纹管轴向刚度的线性和非线性特性进行了研究。首先建立了轴对称弹性单元（solid element）与接触单元组合的有限元模型，然后计算得到了该多层波纹管的刚度特性，尤其是在压缩时的非线性刚度，并且讨论了不同层间接触摩擦状态的影响，分析说明了多层间接触摩擦使波纹管轴向刚度具有非线性特征的机理。     

纤维增强FGM梁的自由振动和临界屈曲载荷分析

基于经典梁理论（CBT）研究轴向力作用下纤维增强功能梯度材料（FGM）梁的横向自由振动和临界屈曲载荷问题。首先考虑由混合律模型来表征纤维增强FGM梁的材料属性,其次利用Hamilton原理推导轴向力作用下纤维增强FGM梁横向自由振动和临界屈曲载荷的控制微分方程,并应用微分变换法（DTM）对控制微分方程及边界条件进行变换,计算了纤维增强FGM梁在固定-固定（C-C）、固定-简支（C-S）和简支-简支（S-S）3种边界条件下横向自由振动的无量纲固有频率和无量纲临界屈曲载荷。退化为各向同性梁和FGM梁,并与已有文献结果进行对比,验证了本文方法的有效性。最后讨论在不同边界条件下纤维增强FGM梁的刚度比、纤维体积分数和无量纲压载荷对无量纲固有频率的影响以及各参数对无量纲临界屈曲载荷的影响。     

Real-Time Prediction of Workpiece Errors for a CNC Turning Centre, Part 4. Cutting-Force-Induced Errors

A neural network method is presented for predicting cutting-force-induced errors in real-time during turning operations based on the estimated cutting forces. Workpiece errors can be considerably affected by the deflections of the machine–workpiece–tool system. A model of the elastic deflections of the machine–workpiece–tool system due to the cutting force in turning developed. A novel radial basis function (RBF) neural network is used to map the relationship between the cutting-force components (radial, axial and tangential) and the consequent dimensional deviation of the finished parts caused by the combined deflections of the machine–workpiece–tool system. Cutting tests were performed on a two-axis CNC turning centre and the experimental results showed that the prediction accuracy of the maximum diameter error of the workpiece was within 15%. The trained RBF neural network was able to predict the cutting force induced error in real-time during turning.     

变曲率井中有重钻柱屈曲的非线性有限元分析

基于等曲率井中有重钻柱屈曲的平衡方程及对应的泛函表达式,建立了采用有限元法对变曲率井中有重钻柱屈曲过程进行分析的方法,给出了求解变曲率井中钻柱屈曲非线性方程的算法。力学模型中考虑了钻柱重力、井眼轨迹曲率半径变化率对屈曲的影响。分析结果表明:钻柱上端轴向载荷增大时,钻柱的下端先出现局部屈曲,随后屈曲向钻柱上部扩展,导致钻柱发生整体屈曲;屈曲位移、井壁约束力线密度和钻柱弯矩都呈周期性变化;井眼的弯曲对钻柱屈曲具有抑制作用,井眼轨迹曲率半径变化率越大,钻柱的屈曲也越严重。     

无油螺杆空气压缩机转子变形分析

利用ANSYS对一对中空的铝转子,在两种不同工况下进行热、力变形分析的研究。发现转子的力变形比热变形要小得多;虽然整个转子的温差不大,但是转子径向变形沿长度方向依然存在差别;对阴、阳转子沿接触线径向变形的分析发现,总变形量和温度基本呈线性变化趋势。     

Detection and localisation of multiple cracks in a shaft system: An experimental investigation

Experimental verification of an algorithm for detection and localisation of multiple cracks in a simple shaft system is presented. Cracks in a shaft cause the slope discontinuity in the shaft elastic line. The algorithm is based upon detecting the slope discontinuity due to cracks. Two simply supported non-rotating shafts are used for the experimentation. Both the shafts are tested with single as well as double artificially introduced open cracks. Transverse deflections of the shaft due to sine-sweep excitation force through an exciter are measured at regular axial locations of the shaft. The slope discontinuity is obtained by fitting shaft deflections at regular axial locations in a quadratic polynomial. The algorithm uses shaft deflections at several excitation frequencies to incorporate adequate modal information in the response to improve the crack identification. A scheme is proposed to improve the working of the algorithm in low signal to noise ratio conditions. The algorithm identifies the presence of crack and successfully locates the crack along the shaft length.     

超塑成形的钛合金波纹管壁厚分布规律研究

以DN250双波Ti-6A l-4V钛合金波纹管为例研究了采用超塑胀形/轴向加载复合超塑成形工艺成形的钛合金波纹管的壁厚分布规律。用ARVIP3D刚粘塑性壳单元有限元软件模拟了波纹管在胀形、合模和充满3个阶段的壁厚减薄情况,分析了筒坯长度和胀形阶段的变形量对超塑成形后波纹管厚度分布情况影响。通过实验研究了波纹管的实际壁厚分布曲线。结果表明,与其它成形方法相比,超塑成形的波纹管波峰壁厚减薄率较大,壁厚分布可用JIS公式粗略估算。     

机械密封焊接金属波纹管随机振动响应及优化分析*

针对焊接式金属波纹管在工作中出现的随机振动问题,运用虚拟激励法理论,采用MATLAB编程得到波纹管在随机激励下轴向和径向时域下的信号;将时域信号利用快速傅里叶变换得到频域信号,并导入Workbench软件中进行随机振动分析;同时对波纹管的危险结构尺寸(波片厚度、焊箍半径和最小弯曲半径)进行响应面优化分析。结果表明:波纹管在受外界随机激励下的频率介于固有频率一阶和三阶之间;波纹管轴向最大响应变形发生在镶嵌静环的一端即自由端,径向最大响应变形发生在靠近波纹管的固定端的波片弧度较大处,随机激励时等效应力集中在靠近焊箍侧,这些位置在工作过程中最容易损坏,与实际工作中的破坏位置相吻合。通过响应面优化分析和自适应多目标优化,得到一组优化关键材料参数,使得波纹管的振动性能得到较大改善,降低了波纹管的损坏率,为焊接金属波纹管的结构参数设计提供理论参考。     

Deformation and stability of an elastica under a point force and constrained by a flat surface

This paper studies the deformation and stability of a pinned elastica under a point force moving quasi-statically from one end to the other. The elastica is constrained by a rigid plane wall containing the two ends. Three types of equilibrium configurations can be found; they are non-contact, one-point contact, and one-line contact on the side. A vibration method is adopted to determine the stability of the calculated deformations. In order to take into account the variation of the contact region between the elastica and the plane wall during vibration, an Eulerian version of the governing equations is adopted. It is found that all the point-contact deformations are unstable. On the other hand, there are two different mechanisms a line-contact deformation becomes unstable; one through a secondary buckling and the other through a limit-point bifurcation. In the secondary buckling, the length of the line-contact segment and the axial force satisfy the Euler buckling criteria for a pinned-clamped column. On the other hand, when a line-contact deformation becomes unstable via a limit-point bifurcation, the axial force does not exceed the Euler buckling load. The theoretical predictions are confirmed by experimental observations.     

碟形金属波纹管的轴向刚度研究

采用有限元软件ANSYS对碟形金属波纹管的轴向刚度进行了非线性分析，并进行了轴向刚度试验，将试验结果、有限元分析结果与曲梁简化模型推导出的刚度计算公式，以及原有焊接波纹管的刚度计算公式进行了对比，结合U形波纹管轴向刚度的计算结果，验证了有限元和曲梁简化公式的正确性，具有一定的工程应用价值。     

On localized thermal track buckling

The thermal buckling of a railroad track in the lateral plane is analyzed with the track modelled as an elastic beam resting on an elastic-plastic foundation representing the ballast. The nonlinearity of the resistance forces exerted by the ballast on the track is accounted for, both in the lateral and axial directions. For a perfectly straight track the critical bifurcation mode is a periodic one and the effect of periodic imperfections on the instability temperature is analyzed numerically. The transition to the localized buckling pattern observed in practice takes place by a bifurcation from the periodic deflection pattern. The transition to this localized mode can occur with only little growth of the periodic deflections. The instability temperatures for some tracks with various nonperiodic initial imperfections are also determined. It is shown that the instability temperature depends on both the magnitude and the form of the initial imperfections.     

Misalignment effects on the load capacity of a hydraulic cylinder

Analytical and experimental investigations of typical hydraulic cylinders have indicated that their load capacities are significantly different from those obtained from simple buckling analysis of idealized systems. In any case, an increase in the friction coefficient at the restrained ends changes the actuator's limit load, while an increase in the initial maximum deflection (initial misalignment) decreases the limit load. A common practice of most cylinder manufacturers is to use a safety factor (between 2.5 and 4) to determine the service load after the critical load (buckling) is obtained by simple analytical procedures treating the cylinder as a perfect stepped column. The intricate aspects of friction effects have been deliberately left aside in this present work. Nevertheless, friction and interaction between mechanism and actuator in the buckling characteristics will be presented in the ongoing paper, which will follow this work. Authors know that, in a real system, the cylinder tube-rod interface is not rigid. Due to the flexibility of guide rings and clearances between components, misalignment (an angular deflection which increases with increasing axial load) exits at the interface. When initial imperfection angle exists, there is no sudden buckling. Then, stresses and deflections increase with increasing load. After repetitive use, the tolerance between the parts will become larger, consequently increasing the initial deflection, which has been proved to considerably decrease the load capacities of the power cylinders. From this analysis, a theoretical and experimental work has been carried out in order to show the advantages and disadvantages of the current design methods, characterizing the critical factors that cause the collapse and proposing useful design criterions. The present work aims to describe the behaviour of actuators under load capacity with experimental validation.     

高阻尼多层U形波纹管轴向等效刚度的有限元分析

运用ADINA有限元软件对高阻尼多层u形波纹管的轴向等效刚度进行了分析。考虑几何非线性、材料非线性、层间接触非线性以及夹层阻尼材料特性对波纹管轴向等效刚度的影响,其分析结果对含夹层阻尼波纹管的设计与研究有一定的参考意义。