A Novel Method for Linear Systems of Fractional Ordinary Differential Equations with Applications to Time-Fractional PDEs

This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering and science.An approximate solution of the system is sought in the formof the finite series over the Müntz polynomials.By using the collocation procedure in the time interval,one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure.This technique also serves as the basis for solving the time-fractional partial differential equations(PDEs).The modified radial basis functions are used for spatial approximation of the solution.The collocation in the solution domain transforms the equation into a system of fractional ordinary differential equations similar to the one mentioned above.Several examples have verified the performance of the proposed novel technique with high accuracy and efficiency.

Characteristic of Torsional Vibration of Mill Main Drive Excited by Electromechanical Coupling

In the study of electromechanical coupling vibration of mill main drive system, the influence of electrical system on the mechanical transmission is considered generally, however the research for the mechanism of electromechanical interaction is lacked. In order to research the electromechanical coupling resonance of main drive system on the F3 mill in a plant, the cycloconverter and synchronous motor are modeled and simulated by the MTLAB/SIMULINK firstly, simulation result show that the current harmonic of the cycloconverter can lead to the pulsating torque of motor output. Then the natural characteristics of the mechanical drive system are calculated by ANSYS, the result show that the modal frequency contains the component which is close to the coupling vibration frequency of 42 Hz. According to the simulation result of the mechanical and electrical system, the closed loop feedback model including the two systems are built, and the mechanism analysis of electromechanical coupling presents that there is the interaction between the current harmonic of electrical system and the speed of the mechanical drive system. At last, by building and computing the equivalent nonlinear dynamics model of the mechanical drive system, the dynamic characteristics of system changing with the stiffness, damping coefficient and the electromagnetic torque are obtained. Such electromechanical interaction process is suggested to consider in research of mill vibration, which can induce strong coupling vibration behavior in the rolling mill drive system.

Dynamic and Static Characteristics of Double Push Rods Electromechanical Converter

Due to the influence of material characteristics and winding power, single output electromagnet has limited ability to improve the dynamic characteristic of electro-hydraulic valve. Therefore, an electromechanical converter with double push rods is proposed in this paper, which can simultaneously output two electromagnetic forces, can push or pull the valve core and sleeve according to the current direction and realize rapid operation of load. According to the electromagnetic principle and the magnetic circuit analysis method, the mathematical model and equivalent circuit of the electromechanical converter with double push rods are established. Through the finite element simulation model of the electromechanical converter with double push rods with the same magnetization directions, the changing rules of its magnetic field distribution and force–displacement behaviors are studied and analyzed. According to the analysis results, the electromagnetic mechanical parameters and mechanical structure of the electromechanical converter with double push rods are determined, and the prototype is made. The test platform for the push-pull characteristics of the electromechanical converter with double push rods is built, and its static and dynamic characteristics are tested and analyzed. The results show that the thrust and pull output characteristics of the internal and external push rods are basically consistent with the simulation output, and proportional to the current density of the coil;the push-pull hysteresis of internal and external push rods output force is less than 5%;and the dynamic time response characteristics of the displacement and force are obtained. The hysteresis e ect of output force is improved e ectively through the H bridge drive control circuit modulated by PWM. Compared with the displacement response of a singlewinding electromagnet with a similar volume, it can e ectively improve the dynamic displacement response. Followup work will further optimize the structure of the electromechanical converter and test the corresponding pilot valve. The research results provide a new theory for improving the output characteristics of electro-hydraulic pilot valve and have an extremely high engineering application value and broad application prospect.

A Smooth Bidirectional Evolutionary Structural Optimization of Vibrational Structures for Natural Frequency and Dynamic Compliance

A smooth bidirectional evolutionary structural optimization(SBESO),as a bidirectional version of SESO is proposed to solve the topological optimization of vibrating continuum structures for natural frequencies and dynamic compliance under the transient load.A weighted function is introduced to regulate the mass and stiffness matrix of an element,which has the inefficient element gradually removed from the design domain as if it were undergoing damage.Aiming at maximizing the natural frequency of a structure,the frequency optimization formulation is proposed using the SBESO technique.The effects of various weight functions including constant,linear and sine functions on structural optimization are compared.With the equivalent static load(ESL)method,the dynamic stiffness optimization of a structure is formulated by the SBESO technique.Numerical examples show that compared with the classic BESO method,the SBESO method can efficiently suppress the excessive element deletion by adjusting the element deletion rate and weight function.It is also found that the proposed SBESO technique can obtain an efficient configuration and smooth boundary and demonstrate the advantages over the classic BESO technique.

Numerical Investigation of the Multiphase Flow Originating from the Muzzle of Submerged Parallel Guns

A two-dimensional model,employing a dynamic mesh technology,is used to simulate numerically the transient multiphaseflowfield produced by two submerged parallel guns.After a grid refinement study ensuring grid inde-pendence,five different conditions are considered to assess the evolution of cavitation occurring in proximity to the gun muzzle.The simulation results show thatflow interference is enabled when the distance between the par-allel barrels is relatively small;accordingly,the generation and evolution of the vapor cavity becomes more com-plex.By means of the Q criterion for vorticity detection,it is shown that cavitation causes the generation of vorticity and the evolution of the vapor cavity can result in an asymmetric distribution of vorticity for a certain distance of the barrels.In particular,the evolution of the vapor cavity can hinder the expansion of the gas and force it toflow outward,while an asymmetric distribution of vorticity can lead to a gas jetflowing outward and rotating simultaneously.

Phase field simulation of grain refinement in silver-based filler metal

Numerical simulation is one of the important auxiliary methods for studying materials-related problems. In this study, phase field simulation was employed to investigate the refinement behavior of BAg55CuZn-x B brazing alloys. Simulation and experimental studies were conducted for B contents ranging from 0 wt.% to 0.2 wt.%. The results demonstrated that the addition of 0.05 wt.% B in the brazing alloy leads to a significant refinement effect. As the B content increases, the grain size further reduces, and a refinement stagnation phenomenon occurs after exceeding 0.15 wt.%. The solidification process of brazing alloys with different B content was predicted by simulation, and the simulation results showed that with the increase of B content, the initial number of nucleation increased, and the radius of the dendrite tip decreased. The simulation results are in good agreement with the experimental findings, providing further evidence of the refining effect of the B element and the reliable predictive capability of the phase field model.

Research on the heat conduction mechanism of induction brazecoating

Induction brazecoating technology is an important means to improve the surface properties of materials.In this paper,copper plate and corundum are selected as substrates for induction brazecoating respectively.The temperature variation of powder and paste coating is systematically studied,and the heat conduction mode and path in the brazecoating process are analyzed.The results show that rise of the coating temperature mainly depends on the heat absorption from the substrate.The liquid-solid interface conducts heat violently and advances step by step,which promotes the melting spread of metal filler metal.The powdery brazecoating material is in a free state,and there is a gas insulation film between the powder particles and the diamond,making it difficult for substrate to conduct heat to the coating.The binder not only assists forming,shell making and oxygen isolation,but also plays an important role during melting.

Influence of Process Factors on Electrode Wear Rate when EDM 90CrSi Steel using Graphite Electrodes

The findings of a study on the optimization of Electric Discharge Machining(EDM)procedure for processing cylindrically shaped components with graphite electrodes are presented in this paper.Tool steel 90CrSi was the material of choice for the study’s workpiece.Additionally,the Electrode Wear Rate(EWR)was chosen as the optimization problem’s objective function.An experiment using the Taguchi design was conducted to address this issue.Additionally,experiments were created and their outcomes were analyzed using the Minitab R19 program.The impact of the input process factors on EWR was investigated,including the powder concentration,the pulse on and off times,the servo current,and the servo voltage.Additionally,the best process variables for a minimal EWR were provided.

A Novel Accurate Method forMulti-Term Time-Fractional Nonlinear Diffusion Equations in Arbitrary Domains

Anovel accuratemethod is proposed to solve a broad variety of linear and nonlinear(1+1)-dimensional and(2+1)-dimensional multi-term time-fractional partial differential equations with spatial operators of anisotropic diffusivity.For(1+1)-dimensional problems,analytical solutions that satisfy the boundary requirements are derived.Such solutions are numerically calculated using the trigonometric basis approximation for(2+1)-dimensional problems.With the aid of these analytical or numerical approximations,the original problems can be converted into the fractional ordinary differential equations,and solutions to the fractional ordinary differential equations are approximated by modified radial basis functions with time-dependent coefficients.An efficient backward substitution strategy that was previously provided for a single fractional ordinary differential equation is then used to solve the corresponding systems.The straightforward quasilinearization technique is applied to handle nonlinear issues.Numerical experiments demonstrate the suggested algorithm’s superior accuracy and efficiency.

A review of rare earth minerals flotation: Monazite and xenotime

This paper reviews rare earth minerals(monazite and xenotime) separation by flotation. A wide range of monazite and xenotime flotation test results are summarized including: reasons of variation in the point of zero charges on these minerals, the effects of various flotation conditions on zeta potential of monazite and xenotime, interactions of collectors and depressants on the surface of these minerals during flotation separation, relationship between surface chemistry of the minerals and different types of collector adsorptions and effects of the conditioning temperature on flotation of rare earth minerals. This review collects various approaches for the selective separation of monazite and xenotime by flotation and gives perspectives for further research in the future.

Die design for cold precision forging of bevel gear based on finite element method

The finite element analysis (FEA) software Ansys was employed to study the stress state of the dies of both plane and non-plane parting face structures with uniform interference and the die of plane parting face structure with non-uniform interference. Considering the symmetry of the die, a half gear tooth model of the two-ring assembled die with 2.5 GPa inner pressure was constructed. Four paths were defined to investigate the stress state at the bottom corner of the die where stress concentration was serious. FEA results show that the change of parting face from non-plane to plane can greatly reduce the stress at the teeth tips of the die so that the tip fracture is avoided. The interference structure of the die is the most important influencing factor for the stress concentration at the bottom corner. When non-uniform interference is adopted the first principal stress at the corner on the defined paths of the die is much lower than that with uniform interference. The bottom hole radius is another important influencing factor for the corner stress concentration. The first principal stress at the corner of the plane parting face die with non-uniform interference is reduced from 2.3 to 1.9 GPa when the hole radius increases from 12.5 to 16.0 mm. The optimization of the die structure increases the life of the die from 100 to 6 000 hits.

Parameter identification and pressure control of dynamic system in shield tunneling using least squares method

An estimation approach using least squares method was presented for identificationof model parameters of pressure control in shield tunneling.The state equation ofthe pressure control system for shield tunneling was analytically derived based on themass equilibrium principle that the entry mass of the pressure chamber from cutting headwas equal to excluding mass from the screw conveyor.The randomly observed noise wasnumerically simulated and mixed to simulated observation values of system responses.The numerical simulation shows that the state equation of the pressure control system forshield tunneling is reasonable and the proposed estimation approach is effective even ifthe random observation noise exists.The robustness of the controlling procedure is validatedby numerical simulation results.

Wear resistance of Zr/WC composite coatings on Cr12MoV steel surface by electric spark deposition

Zr/WC composite coating was prepared on the surface of Cr12MoV steel by electric spark deposition technology to change its surface properties. The surface and worn surface morphology of the coating were observed using scanning electron microscope. Dry friction and wear tests of the coatings were carried out at room temperature. The results show that the coating is continuous and uniform, and the thickness was about 50-60 μm. The microhardness of the coating surface was highest at 1140 HV_(200g), which was significantly higher than that of the substrate. The ear tests results show that the wear weight loss, wear volume and wear rate follow the following rules: Cr12MoV>WC coating> Zr/WC composite coating.

Parametric optimization and performance comparison of organic Rankine cycle with simulated annealing algorithm

Taking the ratio of heat transfer area to net power and heat recovery efficiency into account,a multi-objective mathematical model was developed for organic Rankine cycle(ORC).Working fluids considered were R123,R134a,R141b,R227ea and R245fa.Under the given conditions,the parameters including evaporating and condensing pressures,working fluid and cooling water velocities were optimized by simulated annealing algorithm.The results show that the optimal evaporating pressure increases with the heat source temperature increasing.Compared with other working fluids,R123 is the best choice for the temperature range of 100-180 °C and R141b shows better performance when the temperature is higher than 180 °C.Economic characteristic of system decreases rapidly with the decrease of heat source temperature.ORC system is uneconomical for the heat source temperature lower than 100 °C.

Variational analysis of mid-span deflection of gantry cranes

In practical application, it is very important to master the influence of structure parameters on the mid-span deflection quantificationally. For large-span and heavy-duty gantry cranes, the influence of the rigid leg and the soft leg on mid-span deflection has not been considered in the past. In the paper, the mathematical model is established for universal large-span and heavy-duty gantry cranes. The analytical solution for the mid-span deflection of gantry-frame structure girder is derived and obtained based on the variation principle by considering the coupling effect of the bending moments of girder and legs, the axial force and the secondary bending moments. The relation between the load and the deflection on the mid-span of the gantry-frame structure girder is known. Then, the experimental model is designed according to dimensional analysis method. And experiments were performed on the WEW-600 B type testing machine. Hackling experimental data, the regular of the load and deflection on the girder mid-span is obtained, namely, the deformation of the gantry-frame structure resists the external load to do work. The validity of the nonlinear analytical solution of the girder deflection is verified. Experimental results show that the analytical solution of the gantry-frame structure deflection has much higher calculation accuracy than previous calculation method. This work provides a theoretical basis for the design and inspection of gantry-frame structures.

Thermal fatigue behavior of copper/stainless steel explosive welding joint

Thermal fatigue performance of copper/stainless steel explosive welding joint was investigated by using a highly effective thermal fatigue test device. The testing device adopted induction coil to heat and carry out two groups of thermal fatigue test at the same time. Metallurgical microscope and scanning electron microscope were used to respectively measure the surface crack and cross-section crack propagation morphology of the explosive welding joint specimen that were conducted thermal cycling for different upper limit temperatures and different cycle time.Experimental results indicated that the cyclic thermal stress and oxidation corrosion was the major factors for fatigue damage behavior of explosive welding joints, where the oxidation corrosion of the interface has become more serious with the increasing the upper limit temperature or the number of cycles rising. Thermal fatigue cracks initiation was mainly beginning from the wavy interface between copper and stainless steel, the vortex-like cast microstructure formed by explosive welding can prevent the crack from propagating along the interface edge and change the direction of crack propagation.The initiation and expansionof thermal fatigue cracks were observed in the copper matrix.

A 2-D FINITE ELEMENT MODEL SIMULATION OF THE MELTING PROCESS OF Al-Ti ALLOY IN VACUUM INDUCTION FURNACE WITH COLD CRUCIBLE(VIFCC)

The development of a numerical model for the melting process of AI-Ti alloy target material in vacuum induction furnace with cold crucible (VIFCC) was described. It is a two-dimensional computational methodology to calculate electromagnetic field, heat transfer field and fluid flow field . Based on the aid of the finite element method with the commercial software--ANSYS, a superimposition method of a layer of copper and a slit to simulate the VIFCC melting process was used. The method was effective to save large quantity of memory and computing time. Meanwhile, a temperature distribution profile during the melting process was obtained. Validity of the model was confirmed by comparison between the result from calculation and those from direct measurement by optical pyrometer and indirect investigation by ingot macrostructure. A relatively good agreement was found. Further, a nearly directional solidification structure was obtained under properly controlling the cooling rate and heating power. Therefore. such model developed in this article is feasible.

Comparative Study on Constitutive Modeling of Tantalum and Tantalum Tungsten Alloy

As a model bcc metal, tantalum and its alloys have wide applications in defense-related fields. The KHL (Khan, Huang, Liang, 1999) model and the constitutive model proposed by Nemat-Nasser et al (Nemat-Nasser and Kapoor, 2001) for tantalum and its alloys were analyzed and compared with each other. A set of published data recorded during elastic-plastic deformations of tantalum, tantalum alloy containing tungsten of 2.5% (Ta-2.5W), over a wide range of strains, strain rates, and temperatures were used to correlate the two models. Overall, it can be concluded that KHL model correlates much better with the data than the model used by Nemat-Nasser et al.

Impact and Friction Sensitivity of Energetic Materials：Methodical Evaluation of Technological Safety Features

Key methods developed and used in the USSR and in the Russian Federation to determine the impact and friction sensitivity of energetic materials and explosives have been discussed.Experimental methodologies and instruments that underlie the assessment of their production and handling safety have been described.Studies of a large number of compounds have revealed relationships between their sensitivity parameters and structure of individual compounds and compositions.The range of change of physical and chemical characteristics for the compounds we examined covers the entire region of their existence.Theoretical methodology and equations have been formulated to estimate the impact and friction sensitivity parameters of energetic materials and to evaluate the technological safety in use.The developed methodology is characterized by high-accuracy calculations and prediction of sensitivity parameters.