Comparison of Loading Functions in the Modelling of Automobile Aluminium Alloy Wheel under Static Radial Load

Formulation of exact loading function for radial loading situation has been a major challenge in wheel modeling. Hence, approximate loading functions such as Cosine, Boussinesq, Eye-bar, Polynomial, Hertzian etc., have been developed by different researchers. In this paper, analysis of different loading functions—Cosine (CLF), Boussinesq (BLF) and Eye-bar (ELF) at deferent inflation pressure of 0.3, 0.15 and 0 MPa at specified radial load of 4750N is carried out on a selected aluminium with ISO designation (6JX14H2;ET 42). The 3-D computer model of the wheel is generated and discretised into 3785 hexahedral elements and analysed with Creo Elements/Pro 5.0. Loading angle of 90 degree symmetric with the point of contact of the wheel with the ground is used for ELF, while 30 degrees contact angle is employed for both CLF and BLF. Von Mises stress is used as a basis for comparison of the different loading functions investigated with the experimental data obtained by Sherwood et al while the displacement values (as obtained from the FEM tool) are used as a basis for comparison of the different loading functions, as displacement is not covered by Sherwood et al. Results show that at 0.3MPa inflation pressure, the maximum stress value of CLF approaches the Sherwood value of about 14 MPa and that the CLF function values coincide with Sherwood values at three points along the curve, with values of about 13.8 MPa, 13 MPa and 6.4 MPa at about 0 degree, 15 degree and 20 degree respectively. The BLF value coincides with the Sherwood value at about 18 degree with a magnitude of about 10.6 MPa, while ELF equals the Sherwood value at magnitude of about 6.2 MPa at about 22 degree. At 0.15 and 0 MPa inflation pressure, values CLF, BLF and ELF deviate significantly from the Sherwood values (due to under inflation) with the maximum CLF stress value approaching a value of about 13 and 12MPa respectively. The CLF, BLF and the Sherwood values are the same at about 6 and 3 MPa at 0.15 and 0 MPa inflation pressure respectively. The displacement values for ELF are lesser than those of CLF and BLF for all range of values. The different loading functions values being equal the Sherwood values (used as refernce) at different points, with the CLF having more coincident points along the curve. Higher stress and displacement magnitudes are clustered between 0 degree and about 35 degree. Although, the CLF and BLF offer greater stress and displacement values than ELF, hence the type of loading function adapted for any analysis depends on the type of tyres to be fitted on the wheel. CLF and BLF offers greater prospect for non run flat tyres, while ELF is most suited for run flat tyres. In all cases the right inflation pressure as specified by the tyre manufacture should be employed in any analysis.

Performance Analysis of Unbalance Radial Feeder with Time Varying Composite Load

The focus of this paper is to present performance indices for unbalance radial feeder having different characteristic and composition of time varying static ZIP load models. These provide a framework for benchmarking of distribution automation projects. 15 minutes characteristics time interval for load flow and load modeling are considered to meet smart grid implementation criterion. A forward-backward sweep method is employed for load flow solution. Developed performance indices were illustrated on modified IEEE 37 node test feeder. Performance indices are useful for analysis, operational, planning and integration of stochastic renewable sources.

Fuzzy vs. Probabilistic Techniques to Address Uncertainty for Radial Distribution Load Flow Simulation

For Power distribution system the most important task for distribution engineer is to efficiently simulate the system and address the uncertainty using a suitable mathematical method. This paper presents a comparison of two methods used in analyzing uncertainties. The first method is Montecarlo simulation (MCS) that considers input parameters as random variables and second one is fuzzy alpha cut method (FAC) in which uncertain parameters are treated as fuzzy numbers with given membership functions. Both techniques are tested on a typical Load flow solution simulation, where connected loads are considered as uncertain. In order to provide a basis for comparison between above two approaches, the shapes of the membership function used in the fuzzy method is taken same as the shape of the probability density function used in the Monte Carlo simulations. For more than one uncertain input variable, simulation result indicates that MCS method provides better output results compared to FAC, however takes more time due to number of runs. FAC provides an alternate method to MCS when addressing single or limited input variables and is fast.

RADIAL VIBRATIONS OF AXISYMMETRICALLY LOADED STEPPED PRESSURE VESSELS

Differential equations of free/forced radial vibrations of axisymmetrically loaded stepped pressure vessels are established by using singular functions. Furthermore, their general solutions are solved, the expression of vibration mode function and frequency equations on usual supports are derived with W operator and the forced response of such vessels are calculated.

微涡轮角接触球轴承打滑性能分析

在赫兹接触理论的基础上,通过拟静力学方程对高速旋转,承受联合载荷和角偏斜的微涡轮角接触球轴承进行计算,得到不同轴向预紧力、径向载荷及偏转角下的轴承受力及其打滑情况,并基于Hirano打滑准则得到轴承的打滑临界曲线。结果表明:为了防止球打滑,以较高转速运转的角接触球轴承需要较大的轴向预紧力;当不承受径向载荷且轴向预紧力低于100 N时,轴承在20000~70000 r/min转速内均发生打滑,当径向载荷增至2000 N时,轴承在20000~70000 r/min转速内均不发生打滑;随着转速的增加,轴承所受离心力增加,球与外圈间的接触载荷增加,球与内圈间的接触载荷减小,导致轴承在高速下的打滑加剧;随着轴承力矩载荷或轴向预紧力的增大,偏转角增大;存在角偏斜的情况下,随着轴向预紧力的增大,球受力增大,离径向载荷作用线越近的球受力更明显,球Hirano打滑系数增大,轴承越不易打滑。

双列调心非对称球面滚子轴承接触应力计算方法

为实现双列调心非对称球面滚子轴承在径向载荷下的接触应力分析,基于该类轴承的内部几何关系及非赫兹接触理论,建立了轴承数值分析模型,采用牛顿法求解,并以某双列调心非对称球面滚子轴承为例,计算分析了径向载荷、径向游隙、内滚道半径、滚子轮廓修形半径、滚子轮廓峰值点位置对轴承接触应力的影响。结果表明:随着径向载荷、径向游隙增大,内滚道中央区域和边缘接触应力均增大;随着内滚道半径增大,内滚道中央区域接触应力增大,边缘应力减小;随着滚子轮廓修形半径增大,内滚道中央区域接触应力减小,边缘应力增大;随着滚子轮廓峰值点位置与滚子大端面距离增大,内滚道中央区域接触应力变化较小,边缘应力减小。

Forecasting of Short-term Load based on LMD and BBO-RBF Model

Short-term load forecasting is a basis of power system dispatching and operation. In order to improve the short term power load precision, a novel approach for short-term load forecasting is presented based on local mean decomposition (LMD) and the radial basis function neural network method (RBFNN). Firstly, the decomposition of LMD method based on characteristics of load data then the decomposed data are respectively predicted by using the RBF network model and predicted by using the BBO-RBF network model. The simulation results show that the RBF network model optimized by using BBO algorithm is optimized in error performance index, and the prediction accuracy is higher and more effective.

镁合金尾翼类构件径向同步加载工艺研究

目的针对常规挤压工艺成形尾翼类构件飞行时翼片径向产生挠曲变形的问题,提出了一种可调控金属流动的径向同步加载成形方法。方法结合ANSYS、Deform-3D有限元模拟和物理实验,分析径向同步加载的金属流动行为、等效应变和金属流线分布,通过拉伸实验测试成形翼片挤压方向(Extrusion Direction,ED)和横截面方向(Transverse Direction,TD)的力学性能,并通过观察显微组织揭示径向强化机理。结果径向同步加载通过对坯料施加周向压应力促进了金属径向流动,形成了沿径向分布良好的金属流线,有利于提升径向力学性能;采用该工艺试制构件表面质量良好,无宏观缺陷,且形成沿径向分布的宏观流线;翼片径向力学性能显著提升,屈服强度提升了57.8 MPa,抗拉强度提升了80.1 MPa,延伸率提升了1.4%,其强塑性的提升与纤维组织和块状LPSO相的纤维强化密切相关。结论实现了尾翼类构件的径向同步加载整体成形,通过调控金属流动形成径向分布良好的金属流线,提升了成形翼片径向强度,为高性能镁合金尾翼类构件的整体成形提供了理论基础和技术支撑。

Binary Gravitational Search based Algorithm for Optimum Siting and Sizing of DG and Shunt Capacitors in Radial Distribution Systems

This paper presents a binary gravitational search algorithm (BGSA) is applied to solve the problem of optimal allotment of DG sets and Shunt capacitors in radial distribution systems. The problem is formulated as a nonlinear constrained single-objective optimization problem where the total line loss (TLL) and the total voltage deviations (TVD) are to be minimized separately by incorporating optimal placement of DG units and shunt capacitors with constraints which include limits on voltage, sizes of installed capacitors and DG. This BGSA is applied on the balanced IEEE 10 Bus distribution network and the results are compared with conventional binary particle swarm optimization.

径向游隙对深沟球轴承疲劳寿命影响精细分析

采用Romax Designer工程分析软件,应用ISO/TS 16281寿命计算方法,根据经典的滚动轴承理论,对某风机用电机轴深沟球轴承,在不同径向游隙时的轴承内部载荷分布、接触应力、套圈滚道当量动载荷和ISO/TS 16281寿命进行了大量的计算,重点对轴承的疲劳寿命进行了精细分析,分析了径向游隙对轴承ISO/TS 16281寿命的影响。研究结果表明,径向游隙对寿命的影响不仅仅是通过对轴承内部载荷分布、接触应力和套圈滚道当量动载荷的影响而对寿命产生影响,还通过对寿命修正系数等因素的影响而对寿命产生影响;相同工况条件下,存在一个相对最优的径向游隙,由于所研究电机的两个轴承所受载荷不同,因而相对最优的径向游不同。研究结果可为深沟球轴承的优化设计提供参考。

Numerical Analysis of Stresses on Layer-by-Layer Basis in FML Composite Cylinder Subjected to External Hydrostatic Loading

The aim of the research work was to numerically investigate the residual stresses induced between the layers of fiber metal laminate (FML) cylinder (glass/epoxy reinforced aluminum laminates) under buckling hydrostatic loading. For the analysis of buckling behavior of FML cylinders, various fiber orientations such as 0/90&deg, 60/30&deg, ±45&deg and ±55&deg and different FRP thickness of 1, 2, and 3 mm were considered. The aluminum cylinder of inner diameter 80 mm, length 800 mm and wall thickness 1 mm was modeled with SHELL281 element type and a total of 1033 elements were used for computing the induced residual stresses between the layers. The results show that magnitude of residual stresses between the layers decreased along the thickness from outer layer towards the inner layer in sine wave form. The maximum residual Von-Mises stress was at inner aluminum layer while the maximum residual radial stress was at the outermost layer of FML cylinder due to the inward pressure. Among all types of FML cylinder 0/90&deg fiber oriented FML cylinder exhibited the least radial stress and a maximum Von-Mises stress along the FRP thickness.

考虑纵径向热应变的竖向受荷能量桩简化分析方法

为探究温度对能量桩荷载传递机理及相关力学响应的影响,引入平面瞬态温度场方程,将温度场与应力场解耦。基于平面应力模型,将能量桩与桩周土考虑为具有协调变形的整体,计算了径向热应力。在此基础上,将其与双曲线荷载传递模型结合,对桩土界面处的极限摩阻力进行修正。将纵向热应变考虑在竖向荷载传递方程中,得到可同时衡量纵向和径向热效应的竖向受荷能量桩承载特性分析方法。利用增量法对能量桩荷载传递控制方程进行求解,得到桩身轴力、桩侧阻力、桩身位移等相关力学响应。通过与既有文献进行对比,验证了该模型的合理性。通过参数分析,研究了温度和竖向力作用下能量桩的荷载传递特性。结果表明:温度会改变能量桩的荷载传递特性,提高能量桩的运行温度可小幅增加其承载力。该文方法的计算流程清晰,可为能量桩的设计提供参考。

外负载对径向柱塞泵滑靴副流场特征和强度的影响

针对高压大排量径向柱塞泵在重载领域出现的滑靴副失效问题,在考虑油液黏温黏压特性的基础上,对滑靴副流体域展开数值计算和流固耦合仿真分析,探讨外负载对滑靴副流体域压力、流速、泄漏以及滑靴结构强度的影响。结果表明:当外负载从1.1×10^(8)N增加到1.2×10^(8)N时,吸油区滑靴副流体域的压力分布和数值基本不变,排油区滑靴副中心油腔压力增大1.5 MPa,流体域油膜的高压区面积增大,油液压力增大了0.05 MPa,油液流速稍有增加;滑靴副油液泄漏主要位于滑靴副边界处,高、低阻尼孔泄漏较小,随着外负载的增大,3处泄漏量都增大,单个滑靴副总泄漏量增大0.05 mL/s;外负载对滑靴强度影响较小,在排油区滑靴最大应力与变形发生在中心油腔处,此处是滑靴结构强度较为薄弱的地方。

圆柱滚子轴承摩擦力矩试验机

针对现阶段圆柱滚子轴承摩擦力矩试验机测量载荷较小以及大径向载荷条件下测量精度不高的问题,基于平衡法研制了圆柱滚子轴承摩擦力矩试验机,试验机主体为卧式结构,最大载荷可施加至10 k N,可以在不同转速和润滑条件下测量圆柱滚子轴承的摩擦力矩。基于试验分析了径向载荷对圆柱滚子轴承摩擦力矩的影响规律,结果表明圆柱滚子轴承摩擦力矩随径向载荷的增加逐渐增大,摩擦力矩测量值与理论计算值相差较小,验证了圆柱滚子轴承摩擦力矩试验机的实用性。

基于Stacking融合的LSTM-SA-RBF短期负荷预测

为了解决单个神经网络预测的局限性和时间序列的波动性,提出了一种奇异谱分析(singular spectrum analysis,SSA)和Stacking框架相结合的短期负荷预测方法。利用随机森林筛选出与历史负荷相关性强烈的特征因素,采用SSA为负荷数据降噪,简化模型计算过程;基于Stacking框架,结合长短期记忆(long and short-term memory,LSTM)-自注意力机制(self-attention mechanism,SA)、径向基(radial base functions,RBF)神经网络和线性回归方法集成新的组合模型,同时利用交叉验证方法避免模型过拟合;选取PJM和澳大利亚电力负荷数据集进行验证。仿真结果表明,与其他模型比较,所提模型预测精度高。

考虑游隙变化的圆柱滚子轴承疲劳寿命分析

针对传统的轴承寿命计算方法难以探究工作径向游隙对圆柱滚子轴承寿命的影响问题,提出了一种圆柱滚子轴承工作游隙的理论计算模型和考虑工作径向游隙的轴承寿命计算模型。首先,研究了过盈配合、离心力、温度、径向载荷、动压润滑油膜对径向游隙的影响机制,建立了圆柱滚子轴承工作游隙理论计算模型;然后,根据轴承工作游隙理论计算模型,将最大滚动体载荷与轴承工作游隙联系起来,建立了考虑工作径向游隙的轴承寿命计算模型;最后,以SFW250-8/850卧式水力发电机主轴上的圆柱滚子轴承SKF N324为研究对象,针对标准中定义的五个原始径向游隙组,根据轴承工作游隙理论计算模型计算得到了五个工作径向游隙组,再根据考虑工作径向游隙的轴承寿命计算模型,分析了五个工作径向游隙组的载荷分布和寿命,以此确定最佳工作游隙组,模型结果与ISO/TS 16281:2008计算结果、RomaxDesigner仿真结果作对比,验证了计算模型的可靠性。研究结果表明:过盈配合对轻载和中载条件下轴承的径向游隙影响最大,变化量分别为-30.768μm和-16.413μm;温度对重载条件下轴承的径向游隙影响最大,变化量为-16.866μm;轻载工况下游隙值为-43μm时,承担载荷的滚子数量为9个,寿命达到最大值48187 h,径向游隙的变化会影响轴承接触应力分布和受载滚子数量,进而影响轴承的寿命,不同载荷下轴承的最佳工作游隙值不同;轴承寿命计算模型的计算结果与ISO/TS 16281:2008的计算结果误差为3.48%,与Romax仿真结果误差为4.71%。该模型更贴近实际工况,可为轴承设计提供参考,并可根据实际工况选择合适的游隙来延长轴承使用寿命。

放射状楔形槽气浮支承静态性能分析

为提升小孔节流气浮支承的静态性能,设计一种放射状楔形槽气浮支承,该楔形槽呈放射状,其周向截面、径向截面和轴向截面分别为扇形、矩形和梯形。建立放射状楔形槽气浮支承的CFD模型,分析楔形槽结构参数对气浮支承静态性能的影响规律。结果表明:采用放射状楔形槽能够改善气浮支承的气膜压力分布,并提升其承载力和刚度;气浮支承承载力随楔形槽放射角度、入口高度和楔形角的增加逐渐增大,随楔形槽半径增加先升高后降低;气浮支承刚度随楔形槽放射半径、角度、入口高度和楔形角的增加逐渐提高。实验结果与预测结果吻合较好,验证了模型的可行性和准确性。

径向游隙对圆柱滚子轴承疲劳寿命的影响

应用经典的滚动轴承理论和“切片法”的基本思想,以某大兆瓦风电机组齿轮箱输出轴轴承为例,采用Romax Designer工程分析软件,计算了圆柱滚子轴承不同径向游隙时的轴承内部载荷分布、接触应力、套圈滚道当量动载荷和寿命,分析径向游隙对轴承ISO/TS 16281寿命的影响。研究结果表明:径向游隙不仅通过对轴承内部载荷分布、接触应力和套圈滚道当量动载荷的影响而对寿命产生影响,还通过对寿命修正系数等因素的影响而对寿命产生影响。研究结果可为滚子类轴承的优化设计提供参考。

船闸反弧门设计要点

反弧门设计边界条件复杂、计算参数难以选定,目前缺乏相关设计指导文献,设计难度大。通过大藤峡船闸反弧门相关的模型试验研究,并总结葛洲坝、三峡和大藤峡船闸反弧门设计经验,得出可有效抑制空化现象的廊道体形;依据闭门速度快慢选取动水荷载系数;采用全包板门体结构和流线型底缘可减小水流扰动,改善流态,减小气蚀破坏;启闭力计算时需要考虑水柱力和水阻力等设计要点和合理化建议。

滚子偏斜工况下的圆柱滚子轴承弹流润滑分析

以存在滚子偏斜工况的圆柱滚子轴承为研究对象,基于轴承拟静力学模型与有限长线接触弹流润滑模型建立圆柱滚子轴承弹流润滑理论计算模型,并基于力学特性分析工况参数对圆柱滚子轴承滚子与滚道接触区域润滑性能的影响,结果表明:力矩载荷作用后,油膜压力与油膜厚度呈非对称分布;力矩载荷越大,油膜压力和油膜厚度的偏斜程度越明显,易导致轴承润滑性能恶化;径向载荷和内圈转速越大,油膜压力偏斜程度越小。