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.

The Axial and Radial Solid Loadings up the CFB-Riser

1 INTRODUCTIONThe determination of the solids hold-up and local solidfluxes is of paramount importance in the study ofthe hydrodynamics of a two-phase flow.Several tech-niques have been used during the past decades(Table1).These methods can be classified in two groups,depending on their possible disturbance of the two-

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.

Dynamic load sharing characteristics and sun gear radial orbits of double-row planetary gear train

A new non-linear bending-torsional coupled model for double-row planetary gear set was proposed, and planet's eccentricity error, static transmission error, and time-varying meshing stiffness were taken into consideration. The solution of differential governing equation of motion is determined by applying the Fourier series method. The behaviors of dynamic load sharing characteristics affected by the system parameters including gear eccentricities error, ring gear's supporting stiffness, planet's bearing stiffness, torsional stiffness of first stage carrier and input rotation rate were investigated qualitatively and systematically, and sun gear radial orbits at first and second stage were explored as well. Some theoretical results are summarized as guidelines for further research and design of double-row planetary gear train at last.

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。

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。

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。

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。

农田耕整载荷六维力传感器结构优化与解耦研究

针对农田耕整载荷大、测量精度低等问题,在经典十字梁结构基础上,设计了一种辐梁式六维力传感器,可同时测量力和力矩,通过仿真方法对传感器结构进行了优化,确定了应变梁长、宽、高分别为9、10、6 mm;分析了传感器结构在载荷下的应变能力,确定了应变片贴片位置。对传感器开展了静态标定试验,基于标定数据采用改进型XGBoost(Extreme gradient boosting)机器学习网络对力信号进行解耦,并与常规网络进行比对。试验结果表明,改进型XGBoost模型在X、Y、Z方向力和力矩6种加载方式的测试集决定系数R^(2)_(P)分别达到0.9804、0.9418、0.9434、0.9868、0.9969、0.9822,预测效果较好,避免了陷入局部最优解。改进型XGBoost模型在六维加载力、力矩的R^(2)_(P)、测试集平均绝对误差(MAEP)均明显优于随机森林模型、传统多元线性回归,相较于传统多元线性回归方式,六维加载力、力矩的R^(2)_(P)分别提升22.57%、20.99%、23.32%、26.27%、26.05%、18.72%。基于机器学习的解耦算法可明显减少耦合误差的影响,提高传感器的测量精度,为农机优化提供了技术支撑。

基于SOM特征聚类及RBF神经网络的电力负荷预测方法研究

为了提高电力系统负荷预测的精度,维护电力系统运行的安全稳定性,提出一种基于特征向量的自组织映射聚类和改进的径向基函数神经网络相结合的电力负荷预测模型。通过提取能够体现每日电力负荷特性的特征向量,对样本进行聚类,采用具有相似特征的数据作为神经网络的训练样本,提高了样本规律性。采用粒子群算法(particle swarm optimization,PSO)修正神经网络粒子群速度及位置,以克服梯度下降、局部最优等问题对网络预测精度的影响。基于某地配电网电力负荷数据,验证了所提模型的有效性及良好的适应性。

Radial explosion strain and its fracture effect from confined explosion with charge of cyclonite

Instrumented experiments were conducted in concrete models to study the explosion-induced radial strain and fracture effect of rock-like media under confined explosion with a charge of cyclonite. As a charge was exploded, two different radial strain waves were sequentially recorded by a strain gage at a distance of 80 mm from the center of charge. Through the attenuation formula of the maximum compressive strain(εrmax), the distribution of εrmax and its strain rate（ ） between the charge and gage were obtained. The effect of the two waves propagating outwards on the radial fracture of surrounding media was discussed. The results show that the two waves are pertinent to the loading of shock energy （Es） and bubble energy （Eb） against concrete surrounding charge, respectively. The former wave lasts for much shorter time than the latter. The peak values of εrmax and of the former are higher than those of the latter, respectively.

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.

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.

Development of a Test Rig for Axial Strains Measurement in Automobile Wheel

In automobile wheel application, a test rig is vital and used to simulate conditions of the wheel in service in order to affirm the safety and reliability of the wheel. The present work designed a test rig for measuring axial strains in automobile wheel. The wheel used was a five-arm wheel (6JX14H2;ET 42) and Tyre (175 × 65 R 14). Experimental (EXP) test was carried out, with a radial load of 4750 N and inflation pressure of 0.3 MPa, to measure the axil strains which were converted to maximum principal strain values and, compared with data from Finite Element Analysis (FEA) using Creo-Element/Pro 5.0 at wheel’s contact angles of 90 degree (FEA 90 deg), 40 degree (FEA 40 deg) and 30.25 degree (FEA 30.25 deg), respectively. Results show that at the wheel’s point of contact with the ground, maximum principal strain values were highest at the inboard bead seat with a value of about 5.69 × 10-4 mm/mm, followed by the values at the well of about 5.66 × 10-4 mm/mm. The value at the outboard bead seat was least at about 2.22 × 10-4 mm/mm, which was due to the presence of spikes at this location that tends to resist imposed radial loads. However, the highest mean maximum principal strain values at the locations of inboard, well and outboard, were about 2.11 × 10-4 mm/mm, 3.78 × 10-4 mm/mm and .99 × 10-4 mm/mm, respectively. With the highest single value of about 5.69 × 10-4 mm/mm, the inboard bead seat was the most strained location of the wheel. Overall results showed that all values of maximum principal strains were below the threshold value of about 1 × 10-2 mm/mm. The values obtained for EXP and FEA could be said to be in close agreement when compared with the threshold value. With this in mind, the rig is recommended for use in related experimental procedures.

动静荷载作用下岩石裂纹扩展应力阈值识别

压缩荷载作用下岩石裂纹扩展应力阈值的识别是理解岩石渐进破坏过程和分析岩石宏观破坏机制的重要基础。对大理岩、粗花岗岩和细花岗岩开展了单轴压缩和动态冲击试验,引入岩石裂纹轴向应变和裂纹径向面积应变两个参数,根据岩石单轴压缩破坏时裂纹径向面积应变曲线斜率的不同,把以上三种岩石分成类型Ⅰ(大理岩)和类型Ⅱ(粗花岗岩和细花岗岩)岩石。研究表明,对于类型Ⅰ和类型Ⅱ岩石,分别利用其裂纹轴向应变和裂纹轴向应变刚度曲线特征点能准确识别出岩石在静态压缩荷载下裂纹稳定扩展应力σ_(sd)、裂纹不稳定扩展应力σusd以及裂纹相互贯通应力σct,证明了仅利用轴向应变数据就可对类型Ⅰ和类型Ⅱ岩石静荷载下应力阈值进行识别。而后将裂纹轴向应变法推广至动态冲击荷载下岩石的应力阈值识别,解决了动态冲击压缩载荷作用下试样难以进行裂纹扩展应力阈值识别的问题。与静态荷载下岩石的裂纹扩展应力阈值不同,在动态冲击荷载下,岩石裂纹稳定扩展应力与峰值强度的比值有所减小,裂纹不稳定扩展应力和裂纹相互贯通应力阈值相等,且与峰值强度的比值也有所减小,岩石产生更多的贯通裂纹,试样破坏时破碎程度更高。

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.

考虑尺寸误差与径向载荷的双螺母滚珠丝杠静刚度分析

同时考虑尺寸误差和外部径向载荷,改进了一种预紧双螺母滚珠丝杠的轴向静刚度计算模型。首先,基于赫兹理论,考虑制造过程中的尺寸误差和因装配不当等因素引起的径向外部载荷,改进了滚珠载荷分布和轴向静刚度模型。其次,采用Newton-Raphson迭代法计算了双螺母滚珠丝杠的轴向静刚度,并在自行研制的加载试验台上进行了加载变形试验,验证了模型的正确性。最后,通过仿真分析,研究了外部轴向载荷、外部径向载荷和滚珠尺寸误差对双螺母滚珠丝杠轴向静刚度的影响。研究结果表明,所建立的双螺母滚珠丝杠静刚度模型对描述轴向变形位移和轴向静刚度有较好的效果,对指导预紧双螺母滚珠丝杠在静止或低速工况下的承载能力评估和精度设计有一定的参考意义。

Radially loading rotary extrusion for manufacturing large-size conical cylinders with inner transverse high ribs

The Large-size Conical Cylinders with Inner Transverse High Ribs(LCCWITHR) can reduce the weight of the parts while maintaining high rigidity and strength. Radially Loading Rotary Extrusion(RLRE) forming technology can achieve integral forming of LCCWITHR through the synergy of radial and rotary movements of dies. The flow law of the material during the forming process is the key to forming large-size inner ribs. At present, there is no unified understanding of the metal flow law of RLRE forming technology. An analytical expression was derived to predict the Radial Direction(RD) deformation loads. The FE simulation and process experiment were carried out to investigate the effects of the inclination angle, thickness factor and transition arc radius of the split top dies on the spacing of the metal diversion plane, the metal flow velocity of the rib area and the final radius of the inner rib. The influence of the split top dies loading distance and the bottom die rotation angle of each pass on the inner radius of the inner rib was verified. And the optimal combination of dies shape parameters and loading paths which can make the metal flow orderly was obtained: the inclination angle is 140°, the thickness factor is 3.64, the transition arc radius is 16 mm;the top dies loading distance is 15 mm, the bottom die rotation angle is 45°.The FE simulation results have been found to be in close agreement with physics experiment.The research results reveal the metal flow law of rib growth in the RLRE of LCCWITHR, which lays a theoretical foundation for subsequent thorough research and process optimization.