This article is concerned with finite element implementations of the three- dimensional geometrically exact rod. The special attention is paid to identifying the con- dition that ensures the frame invariance of the re...This article is concerned with finite element implementations of the three- dimensional geometrically exact rod. The special attention is paid to identifying the con- dition that ensures the frame invariance of the resulting discrete approximations. From the perspective of symmetry, this requirement is equivalent to the commutativity of the employed interpolation operator I with the action of the special Euclidean group SE（3）, or I is SE（3）-equivariant. This geometric criterion helps to clarify several subtle issues about the interpolation of finite rotation. It leads us to reexamine the finite element for- mulation first proposed by Simo in his work on energy-momentum conserving algorithms. That formulation is often mistakenly regarded as non-objective. However, we show that the obtained approximation is invariant under the superposed rigid body motions, and as a corollary, the objectivity of the continuum model is preserved. The key of this proof comes from the observation that since the numerical quadrature is used to compute the integrals, by storing the rotation field and its derivative at the Gauss points, the equiv- ariant conditions can be relaxed only at these points. Several numerical examples are presented to confirm the theoretical results and demonstrate the performance of this al- gorithm.展开更多
This paper discusses the application of several techniques involved in the development of the 3D finite element (FE) models of rod and wire continuous rolling process.The FE models are implemented into the FE-program ...This paper discusses the application of several techniques involved in the development of the 3D finite element (FE) models of rod and wire continuous rolling process.The FE models are implemented into the FE-program MSC.Marc and used to investigate the thermal and mechanical behavior of billet during the rolling process.All nonlinear equations included in the models are solved by the static and dynamic procedures,respectively.Data transfer technique is proposed to keep the continuity of simulation results.And the computational time of static procedure is significantly reduced by using a rigid pushing body.In all models,the constant time step method and the auto time step method are respectively used to define time step for the solution of equations.Simulation results of the models with different time step methods are compared.And comparison between calculated values and measured ones of the temperature at the surface of billet shows the validity of the FE models.展开更多
Microfiltration is widely used in fine filtration operations, with dead-end filtration and cross-flow filtration. The microfiltration filter element or the microfiltration membrane is easy to be polluted by impurities...Microfiltration is widely used in fine filtration operations, with dead-end filtration and cross-flow filtration. The microfiltration filter element or the microfiltration membrane is easy to be polluted by impurities in the water and causes fouling, resulting in flux attenuation. The flux can be expressed by Darcy’s law and attenuation model. In this paper, two industrial titanium rod sintered filter elements (<span style="white-space:nowrap;"><span style="white-space:nowrap;">?</span></span>60 × 960 mm and <span style="white-space:nowrap;"><span style="white-space:nowrap;">?</span></span>60 × 960 mm) of different specifications are selected, and tap water (1.0 NTU) is used for constant pressure dead-end filtration. The amount tends to be the same, about 0.435 m<sup>3</sup><span style="white-space:nowrap;">·</span>m<sup><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">?</span></span></span>2</sup><span style="white-space:nowrap;">·</span>h<sup><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">?</span></span></span>1</sup>, which has nothing to do with the filtration accuracy of the filter element but only depends on the characteristics of the filter cake and the filter membrane. Through the analysis of the two models, it is found that the two filtration flux models are not universal and difficult to be applied in engineering.展开更多
The effect of rare earth element Ce on mechanical performance and electrical conductivity of aluminum rod for electrical purpose were studied under industrial production condition. Using optical microscope, SEM, TEM, ...The effect of rare earth element Ce on mechanical performance and electrical conductivity of aluminum rod for electrical purpose were studied under industrial production condition. Using optical microscope, SEM, TEM, EDS and X-ray diffractometer, the microstructure and phase composition of aluminum rod were measured and analyzed. The results indicate that the content of rare earth element Ce is between 0.05% -0.16% in the aluminum rod for electrical purpose. Its tensile strength is enhanced to some extent. The research also discovers that the tensile strength is enhanced remarkably with impurity element Si content increases. Because influence of Si is big to the conductivity, the Si content should be controlled continuously strictly in the aluminum for electrical purpose. Adding rare earth element Ce reduces the solid solubility of Si in the aluminum matrix, and the negative effect of Si on the aluminum conductor reduces effectively. So the limit of in Si content in aluminum rod for electrical purpose can be relaxed moderately.展开更多
The microhardness of piston rods treated with different induction hardening processes was tested. The experimental results reveal that the depth of the hardened zone is proportional to the ratio of the moving speed of...The microhardness of piston rods treated with different induction hardening processes was tested. The experimental results reveal that the depth of the hardened zone is proportional to the ratio of the moving speed of the piston rod to the output power of the induction generator. This result is proved correct through the Finite Element Method (FEM) simulation of the thermal field of induction heating. From tensile and impact tests, an optimized high frequency induction hardening process for piston rods has been obtained, where the output power was 82%×80 kW and the moving speed of workpiece was 5364 mm/min. The piston rods, treated by the optimized high frequency induction hardening process, show the best comprehensive mechanical performance.展开更多
【目的】棒销式砂磨机的工作过程存在复杂的气体、液体和固体的三相耦合现象,为了使仿真工况更接近实际工况,构建气-液-固三相耦合仿真模型,提高棒销式砂磨机仿真设计的准确性。【方法】采用离散单元法(discrete element method,DEM)和...【目的】棒销式砂磨机的工作过程存在复杂的气体、液体和固体的三相耦合现象,为了使仿真工况更接近实际工况,构建气-液-固三相耦合仿真模型,提高棒销式砂磨机仿真设计的准确性。【方法】采用离散单元法(discrete element method,DEM)和计算流体动力学(computational fluid dynamics,CFD)分别研究固体相和流体相,并引入流体体积模型(volume of fluid model,VOF)区分流体相所包含的液体相和气体相,分析固体相运动方程、流体相控制方程,确定气-液界面的识别方法和耦合计算方法,制定仿真流程;通过单球落水仿真、颗粒群落水仿真试验分析CFD-DEM-VOF三相耦合模型仿真计算的精度,并进行准确性验证;在设置仿真参数、进行网格划分及其无关性分析基础上,针对棒销式砂磨机的CFD-DEM-VOF三相耦合模型进行仿真试验;对流体速度、颗粒总能量和颗粒的速度的仿真结果进行分析,并通过实验验证仿真结果。【结果】在单球落水仿真试验中,根据CFD-DEM-VOF三相耦合模型的仿真结果与根据Stokes定律的理论计算结果基本吻合;在颗粒群落水仿真过程中,液面上升高度的仿真值与理论值之间的相对误差为1.37%,VOF模型的体积守恒性较好;棒销四面体网格边长小于2 mm、研磨桶四面体网格边长小于2.5 mm时,满足网格独立性的精度要求,同时计算量也较少;随着棒销转速的增大,流体速度、颗粒总能量、颗粒平均速度也逐渐增大;当棒销转速为1400~2000 r/min时,CFD-DEM-VOF三相耦合模型流体速度的仿真与实验结果最为接近;当棒销转速为1400~2200 r/min时,CFD-DEM-VOF三相耦合模型的颗粒总能量仿真值与实验值的最大相对误差为1%。【结论】与仅仅采用流体相、固体相单相模型或固-液两相模型相比,采用CFD-DEM-VOF三相耦合模型设计棒销式砂磨机的计算精度和准确性较高,仿真性能好。展开更多
文摘This article is concerned with finite element implementations of the three- dimensional geometrically exact rod. The special attention is paid to identifying the con- dition that ensures the frame invariance of the resulting discrete approximations. From the perspective of symmetry, this requirement is equivalent to the commutativity of the employed interpolation operator I with the action of the special Euclidean group SE（3）, or I is SE（3）-equivariant. This geometric criterion helps to clarify several subtle issues about the interpolation of finite rotation. It leads us to reexamine the finite element for- mulation first proposed by Simo in his work on energy-momentum conserving algorithms. That formulation is often mistakenly regarded as non-objective. However, we show that the obtained approximation is invariant under the superposed rigid body motions, and as a corollary, the objectivity of the continuum model is preserved. The key of this proof comes from the observation that since the numerical quadrature is used to compute the integrals, by storing the rotation field and its derivative at the Gauss points, the equiv- ariant conditions can be relaxed only at these points. Several numerical examples are presented to confirm the theoretical results and demonstrate the performance of this al- gorithm.
基金the financial support received from the Dalian City Government and the Dongbei Special Steel Group Corpo-ration
文摘This paper discusses the application of several techniques involved in the development of the 3D finite element (FE) models of rod and wire continuous rolling process.The FE models are implemented into the FE-program MSC.Marc and used to investigate the thermal and mechanical behavior of billet during the rolling process.All nonlinear equations included in the models are solved by the static and dynamic procedures,respectively.Data transfer technique is proposed to keep the continuity of simulation results.And the computational time of static procedure is significantly reduced by using a rigid pushing body.In all models,the constant time step method and the auto time step method are respectively used to define time step for the solution of equations.Simulation results of the models with different time step methods are compared.And comparison between calculated values and measured ones of the temperature at the surface of billet shows the validity of the FE models.
文摘Microfiltration is widely used in fine filtration operations, with dead-end filtration and cross-flow filtration. The microfiltration filter element or the microfiltration membrane is easy to be polluted by impurities in the water and causes fouling, resulting in flux attenuation. The flux can be expressed by Darcy’s law and attenuation model. In this paper, two industrial titanium rod sintered filter elements (<span style="white-space:nowrap;"><span style="white-space:nowrap;">?</span></span>60 × 960 mm and <span style="white-space:nowrap;"><span style="white-space:nowrap;">?</span></span>60 × 960 mm) of different specifications are selected, and tap water (1.0 NTU) is used for constant pressure dead-end filtration. The amount tends to be the same, about 0.435 m<sup>3</sup><span style="white-space:nowrap;">·</span>m<sup><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">?</span></span></span>2</sup><span style="white-space:nowrap;">·</span>h<sup><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">?</span></span></span>1</sup>, which has nothing to do with the filtration accuracy of the filter element but only depends on the characteristics of the filter cake and the filter membrane. Through the analysis of the two models, it is found that the two filtration flux models are not universal and difficult to be applied in engineering.
基金Project supported by the Baotou Aluminum Co. Ltd.
文摘The effect of rare earth element Ce on mechanical performance and electrical conductivity of aluminum rod for electrical purpose were studied under industrial production condition. Using optical microscope, SEM, TEM, EDS and X-ray diffractometer, the microstructure and phase composition of aluminum rod were measured and analyzed. The results indicate that the content of rare earth element Ce is between 0.05% -0.16% in the aluminum rod for electrical purpose. Its tensile strength is enhanced to some extent. The research also discovers that the tensile strength is enhanced remarkably with impurity element Si content increases. Because influence of Si is big to the conductivity, the Si content should be controlled continuously strictly in the aluminum for electrical purpose. Adding rare earth element Ce reduces the solid solubility of Si in the aluminum matrix, and the negative effect of Si on the aluminum conductor reduces effectively. So the limit of in Si content in aluminum rod for electrical purpose can be relaxed moderately.
文摘The microhardness of piston rods treated with different induction hardening processes was tested. The experimental results reveal that the depth of the hardened zone is proportional to the ratio of the moving speed of the piston rod to the output power of the induction generator. This result is proved correct through the Finite Element Method (FEM) simulation of the thermal field of induction heating. From tensile and impact tests, an optimized high frequency induction hardening process for piston rods has been obtained, where the output power was 82%×80 kW and the moving speed of workpiece was 5364 mm/min. The piston rods, treated by the optimized high frequency induction hardening process, show the best comprehensive mechanical performance.
