Solution of rectangular bar forging with bulging of sides by strain rate vector inner-product

Abstract：ools. The effective strain rate for for determining the total pressure developed during forging of a rectangular bar forging with bulging was expressed in terms of four-dimensional strain rate vector. The inner-product of the vector was termwise integrated and summed. The integral mean value theorem was applied to determining the ratio of the strain rate components and the values of direction cosine of the vector and then an analytical solution of stress effective factor was obtained. The compression experiments of pure lead bar were performed to test the accuracy of the solution. The optimized results of total pressure by golden section search were compared with those of the indicator readings of the testing machine. It indicates that the optimized total pressures are 2.60%-10.14% higher than those measured. The solution is available and still an upper-bound solution.

Cross-sectional distortion behaviors of thin-walled rectangular tube in rotary-draw bending process

The cross-sectional distortion usually appears during rotary-draw bending process of thin-walled rectangular tube with small bending radius.To study the cross-sectional distortion of the tube,a three-dimensional finite-element model of the process was developed based on ABAQUS/Explicit code and its reliability was validated by experiment.Then,the cross-sectional distortion behaviors of the tube were investigated.The results show that a zone of larger circumferential stress appears on the tube when bending angle reaches 30°.And in the larger circumferential stress zone,the sagging phenomenon is produced obviously.The maximum cross-sectional distortion is located in the larger circumferential stress zone and the angle between the plane of maximum cross-sectional distortion and the bending reference plane is about 50°.The position of the maximum cross-sectional distortion keeps almost unchanged with the variation of the clearances between dies and tube.

Saint-Venant torsion analysis of bars with rectangular cross-section and effective coating layers

This paper investigates the torsion analysis of coated bars with a rectangular cross-section. Two opposite faces of a bar are coated by two isotropie layers with different materials of the original substrate that are perfectly bonded to the bar. With the Saint- Venant torsion theory, the governing equation of the problem in terms of the warping function is established and solved using the finite Fourier cosine transform. The state of stress on the cross-section, warping of the cross-section, and torsional rigidity of the bar are evaluated. Effects of thickness of the coating layers and material properties on these quantities are investigated. A set of graphs are provided that can be used to determine the coating thicknesses and material properties so as to keep the maximum von Mises stress on the cross-section below an allowable value for effective use of the coating layer.

New type of groove used to improve friction in roll forging

A FEM model for a failed industrial example of roll forging was established to analyze the generation mechanisms of the mismatch of size and shape of two spring board.To demonstrate the formulation of these defects,the bites condition and contact status between rectangular groove and workpiece during rolling the first and second spring boards were analyzed.Then,a new oval-diamond groove combining oval groove and diamond groove was presented to eliminate these defects.By analyzing field variables under the same deformation degree,the larger friction can be obtained on the contact surface of workpiece and the oval-diamond groove.The physical experiment validates that the oval-diamond groove can eliminate these defects effectively,and the size of part is in good agreement with design requirement.

Measurement and Correlation of Pressure Drop for Gas-Liquid Two-phase Flow in Rectangular Microchannels

The pressure drop of gas-liquid two-phase flow in microchannel is of fundamental importance in heat and mass transfer processes. In this work,the pressure drop of gas-liquid two-phase flow in horizontal rectangular cross-section microchannels was measured by a pressure differential transducer system. Water,ethanol and n-propanol were used as liquid phase to study the effects of capillary number on pressure drop;air was used as the gas phase. Four microchannels with various dimensions of 100 μm× 200 μm,100 μm× 400 μm,100 μm× 800 μm and 100 μm× 2000 μm(depth × width) were used for determining the influence of configuration on the pressure drop. Experimental results showed that in micro-scale,the capillary number also affected the pressure drop remarkably,and in spite of only one-fold difference in aspect ratio,the variation of pressure drop reached up to near three times under the same experimental conditions. Taking the effects of aspect ratio and surface tension into account,a modi-fied correlation for Chisholm parameter C in the Chisholm model was proposed for predicting the frictional multi-plier,and the predicted values by the proposed correlation showed a satisfactory agreement with experimental data.

PLASTIC POST－BUCKLING OF A SIMPLY SUPPORTED COLUMN WITH A SOLID RECTANGULAR CROSS－SECTION

The plastic post-buckling of a simply supported column with a solid rectangularcross-section is analysed by a new approach. High order terms in the asymptotic post-buckling expansions are carried out. In some aspects, the method proposed in thispaper is similar io Hutchinson's. However, the computation is simple since theintroduction is avoided of stretched coordinates. The method can be used to analyseinitial post-bifurcation of plates and shells in the plastic range.

Cross-sectional deformation behavior of double-ridged rectangular tube with fillers in different stages of H-typed bending

The bent double-ridged rectangular tube(DRRT)with high forming quality is helpful to improve the microwave transmission accuracy.For reducing the cross-sectional deformation in the H-typed bending process,in addition to using rigid mandrel to support the inside of tube,ridge groove fillers are also added to restrict the deformation of ridge grooves.Because of the change of stress and strain state of bent tube in bending,rigid mandrel retracting and specially twicespringback stages,and the springback of fillers,the cross-sectional deformation of tube in each stage may be different.Therefore,based on the ABAQUS platform,the finite element models(FEM)for H-typed bending,mandrel retracting and twice-springback stages of H96 DRRT with fillers were established and validated.It is found that,for the height and width deformation of tube and spacing deformation of ridge grooves,retraction of mandrel can make the distribution of these deformations more uniform along the bending direction.The first springback can reduce these deformations significantly,which should be emphasized.But the second springback only increases them by less amount,which can be ignored.The smaller height deformation of ridge groove and filler can be neglected.

Cross-sectional deformation of H96 brass double-ridged rectangular tube in rotary draw bending process with different yield criteria

Different yield criterion has great difference in predicting the deformation of tube with different material.In order to improve the prediction accuracy of the cross-sectional deformation of the double-ridged rectangular tube(DRRT)during rotary draw bending(RDB)process,Mises isotropic yield criterion,Hill’48 and Barlat/Lian anisotropic yield criteria commonly used in practical engineering are introduced to simulate RDB of DRRT.The inverse method combining uniaxial tensile test of whole tube and response surface methodology was proposed to identify the parameters of Hill’48 and Barlat/Lian yield criteria of small-sized H96 brass extrusion DRRT as well.Then based on ABAQUS/Explicit platform,the FE models of RDB process of DRRT considering Mises,Hill’48 and Barlat/Lian yield criteria were built.The results show that:The variation trend of cross-sectional deformation ratio is same when using different yield criteria.The cross-sectional deformation ratio by using Mises yield criterion is close to that by using Hill’48 yield criterion.However,there is a quite difference between by using Barlat/Lian yield criterion and by using Mises or Hill’48 yield criteria.The prediction values of cross-sectional height deformation by using three yield criteria all underestimate the experiment ones,and the prediction values of cross-sectional width deformation overestimate the experiment ones.By comparing the simulation results of cross-sectional deformation of the DRRT with different yield criteria and experiment ones,Barlat/Lian yield criterion is found to be suitable for describing the RDB process of DRRT.

辗环机芯辊的强度校核及其热处理

奥氏体不锈钢环形件外径5 100 mm、内径4 420 mm、高680 mm。计算了将矩形奥氏体不锈钢锻件轧制成环形所需的轧制力。结果表明:采用较细的芯辊轧制所需的轧制力较小。采用经正火、回火及调质处理的5CrNiMo钢芯辊,能满足轧制奥氏体不锈钢环形件的需要。

An exact analytical solution for convective heat transfer in rectangular ducts

An exact analytical solution is obtained for convective heat transfer in straight ducts with rectangular cross-sections for the first time.This solution is valid for both H1 and H2 boundary conditions,which are related to fully developed convective heat transfer under constant heat flux at the duct walls.The separation of variables method and various other mathematical techniques are used to find the closed form of the temperature distribution.The local and mean Nusselt numbers are also obtained as functions of the aspect ratio.A new physical constraint is presented to solve the Neumann problem in non-dimensional analysis for the H2 boundary conditions.This is one of the major innovations of the current study.The analytical results indicate a singularity occurs at a critical aspect ratio of 2.4912 when calculating the local and mean Nusselt numbers.

矩形直齿轮热锻工艺有限元模拟

针对大尺寸矩形直齿轮,提出了镦粗预锻终锻3工序"一火"连续锻造的工艺方案。利用有限元软件Deform-3D建立矩形直齿轮热锻有限元模型,并模拟其成形过程。根据模拟结果探讨成形过程中的温度场、等效应变场、材料流动情况及成形载荷的变化规律。在6.3MN高能螺旋压力机上成功试制出矩形直齿轮锻件,工艺试验与模拟结果具有较好的一致性,锻件形状满足设计要求、无折叠缺陷,证明该工艺方案切实可行。

矩形截面锻件的径向锻造力与展宽

首先针对矩形截面锻件径向锻造工艺进行了试验研究,并采用有限元法进行了三维数值模拟,不同压下率条件下模拟与试验所得的锻造力误差不超过5%,表明有限元模型是合理的。采用有限元模拟方法,分析了压下率和送进率等参数对径向锻造力与坯料展宽的影响规律。采用回归正交试验方法,将无量纲化的工艺参数对径向锻造力与坯料展宽的影响规律拟合为二次多项式,拟合结果与有限元模拟结果的误差不超过6%,表明拟合公式是合理的。这些拟合公式可用于矩形截面锻件径向锻造工艺的设计和优化。

矩形截面件径向锻造工艺优化

对于矩形截面件径向锻造问题,目前尚没有相应的锻造载荷、锻造功率和锻件质量相关的计算模型,以及工艺规划的标准。根据径向锻造变形特点,将平面变形条件下锻造载荷公式推广到矩形截面件锻造载荷计算,将预测圆截面件径向锻造锻透率的三角形法则推广到矩形截面件并进行了修正,提出一种锻造功率计算模型,计算误差都在10%左右。然后采用多目标加权的方法,将锻造效率、锻件质量和锻造载荷模型转化成单一的优化目标函数,对道次、压下率和送进率等工艺参数进行优化;同时,采用4个工艺实例验证了工艺优化算法的优化和评估能力,并最终将工艺优化算法写入软件,应用到径向锻造自动化生产过程。