Multi-Stage Multidisciplinary Design Optimization Method for Enhancing Complete Artillery Internal Ballistic Firing Performance

To enhance the comprehensive performance of artillery internal ballistics—encompassing power,accuracy,and service life—this study proposed a multi-stage multidisciplinary design optimization(MS-MDO)method.First,the comprehensive artillery internal ballistic dynamics(AIBD)model,based on propellant combustion,rotation band engraving,projectile axial motion,and rifling wear models,was established and validated.This model was systematically decomposed into subsystems from a system engineering perspective.The study then detailed the MS-MDO methodology,which included Stage I(MDO stage)employing an improved collaborative optimization method for consistent design variables,and Stage II(Performance Optimization)focusing on the independent optimization of local design variables and performance metrics.The methodology was applied to the AIBD problem.Results demonstrated that the MS-MDO method in Stage I effectively reduced iteration and evaluation counts,thereby accelerating system-level convergence.Meanwhile,Stage II optimization markedly enhanced overall performance.These comprehensive evaluation results affirmed the effectiveness of the MS-MDO method.

Experiment and Simulation of Metal Flow in Multi-stage Forming Process of Railway Wheel

To investigate the metal flow during the railway wheel forming process, experiments and finite element method （FEM） simulation were carried out. An axisymmetric modeling for the wheel rolling process was proposed to predict the metal flow in radial direction, by which the whole multi-stage forming process could be simulated in axisymmetric and integral way. The result shows that the axisymmetric simulation method was an effective method to explore the metal flow in radial direction and to analyze the relationships of tools motion during the wheel rolling. The detail information about metal flow in railway wheel forming process was obtained. The metal in the wheel web was from the area near the half radius of the original billet; the chill zone of the billet became an envelope of the rim and part of the web with a maximum thickness of about 6 mm below the tread. At the wheel rolling stage, the metal in the rim flowed towards the web; the metal near the surfaces of the conjunction region between the web and rim suffered severe shear deformation.

Design of an innovative multi-stage forming process for a complex aeronautical thin-walled part with very small radii

In this paper, an aeronautical thin-walled part with a complex geometry which has several sharp bends and curvatures in different directions was investigated. This kind of part is difficult to be manufactured only in one stage. Therefore, an innovative multi-stage active hydroforming process assisted by the rigid forming method was designed. In addition, an optimized blank geometry is obtained. In fact, the main focused point of this paper is to propose a new small radius rounded corner forming technique and analyze the mechanism. Two kinds of forming modes of changing a big rounded corner into a small one, which are related to different tangential positions of the die in the process of calibration, are analyzed theoretically. Meanwhile, the stress and strain states of the deformation region are compared. The relationships between the minimum relative radii of rounded corners I and II in the first stage and the hydraulic pressure are calculated by the bending theory. Finally, the influences of the tensile-bulging effect and the interface condition of the double-layer sheet on the forming quality of the specimen are investigated. The achieved results can make a foundation for utilizing the proposed method in forming of thin-walled parts with very small radii.

Microstructure and forming mechanism of metals subjected to ultrasonic vibration plastic forming: A mini review

Compared with traditional plastic forming,ultrasonic vibration plastic forming has the advantages of reducing the forming force and improving the surface quality of the workpiece.This technology has a very broad application prospect in industrial manufactur-ing.Researchers have conducted extensive research on the ultrasonic vibration plastic forming of metals and laid a deep foundation for the development of this field.In this review,metals were classified according to their crystal structures.The effects of ultrasonic vibration on the microstructure of face-centered cubic,body-centered cubic,and hexagonal close-packed metals during plastic forming and the mech-anism underlying ultrasonic vibration forming were reviewed.The main challenges and future research direction of the ultrasonic vibra-tion plastic forming of metals were also discussed.

Research on Regulation Method of Energy Storage System Based on Multi-Stage Robust Optimization

To address the scheduling problem involving energy storage systems and uncertain energy,we propose a method based on multi-stage robust optimization.This approach aims to regulate the energy storage system by using a multi-stage robust optimal control method,which helps overcome the limitations of traditional methods in terms of time scale.The goal is to effectively utilize the energy storage power station system to address issues caused by unpredictable variations in environmental energy and fluctuating load throughout the day.To achieve this,a mathematical model is constructed to represent uncertain energy sources such as photovoltaic and wind power.The generalized Benders Decomposition method is then employed to solve the multi-stage objective optimization problem.By decomposing the problem into a series of sub-objectives,the system scale is effectively reduced,and the algorithm’s convergence ability is improved.Compared with other algorithms,the multi-stage robust optimization model has better economy and convergence ability and can be used to guide the power dispatching of uncertain energy and energy storage systems.

MPI/OpenMP-Based Parallel Solver for Imprint Forming Simulation

In this research,we present the pure open multi-processing(OpenMP),pure message passing interface(MPI),and hybrid MPI/OpenMP parallel solvers within the dynamic explicit central difference algorithm for the coining process to address the challenge of capturing fine relief features of approximately 50 microns.Achieving such precision demands the utilization of at least 7 million tetrahedron elements,surpassing the capabilities of traditional serial programs previously developed.To mitigate data races when calculating internal forces,intermediate arrays are introduced within the OpenMP directive.This helps ensure proper synchronization and avoid conflicts during parallel execution.Additionally,in the MPI implementation,the coins are partitioned into the desired number of regions.This division allows for efficient distribution of computational tasks across multiple processes.Numerical simulation examples are conducted to compare the three solvers with serial programs,evaluating correctness,acceleration ratio,and parallel efficiency.The results reveal a relative error of approximately 0.3%in forming force among the parallel and serial solvers,while the predicted insufficient material zones align with experimental observations.Additionally,speedup ratio and parallel efficiency are assessed for the coining process simulation.The pureMPI parallel solver achieves a maximum acceleration of 9.5 on a single computer(utilizing 12 cores)and the hybrid solver exhibits a speedup ratio of 136 in a cluster(using 6 compute nodes and 12 cores per compute node),showing the strong scalability of the hybrid MPI/OpenMP programming model.This approach effectively meets the simulation requirements for commemorative coins with intricate relief patterns.

Analysis and Optimization of the Electrohydraulic Forming Process of Sinusoidal Corrugation Tubes

Aluminum alloy thin-walled structures are widely used in the automotive industry due to their advantages related to light weight and crashworthiness.They can be produced at room temperature by the electrohydraulic forming process.In the present study,the influence of the related parameters on the forming quality of a 6063 aluminum alloy sinusoidal corrugation tube has been assessed.In particular,the orthogonal experimental design(OED)and central composite design(CCD)methods have been used.Through the range analysis and variance analysis of the experimental data,the influence degree of wire diameter(WD)and discharge energy(DE)on the forming quality was determined.Multiple regression analysis was performed using the response surface methodology.A prediction model for the attaching-die state coefficient was established accordingly.The following optimal arrangement of parameters was obtained(WD=0.759 mm,DE=2.926 kJ).The attaching-die state coefficient reached the peak value of 0.001.Better optimized wire diameter and discharge energy for a better attaching-die state could be screened by CCD compared with OED.The response surface method in CCD was more suitable for the design and optimization of the considered process parameters.

Method of fabricating artificial rock specimens based on extrusion free forming(EFF)3D printing

Three-dimensional(3D)printing technology has been widely used to create artificial rock samples in rock mechanics.While 3D printing can create complex fractures,the material still lacks sufficient similarity to natural rock.Extrusion free forming(EFF)is a 3D printing technique that uses clay as the printing material and cures the specimens through high-temperature sintering.In this study,we attempted to use the EFF technology to fabricate artificial rock specimens.The results show the physico-mechanical properties of the specimens are significantly affected by the sintering temperature,while the nozzle diameter and layer thickness also have a certain impact.The specimens are primarily composed of SiO_(2),with mineral compositions similar to that of natural rocks.The density,uniaxial compressive strength(UCS),elastic modulus,and tensile strength of the printed specimens fall in the range of 1.65–2.54 g/cm3,16.46–50.49 MPa,2.17–13.35 GPa,and 0.82–17.18 MPa,respectively.It is capable of simulating different types of rocks,especially mudstone,sandstone,limestone,and gneiss.However,the simulation of hard rocks with UCS exceeding 50 MPa still requires validation.

A Hybrid Optimization Approach of Single Point Incremental Sheet Forming of AISI 316L Stainless Steel Using Grey Relation Analysis Coupled with Principal Component Analysiss

We investigated the parametric optimization on incremental sheet forming of stainless steel using Grey Relational Analysis(GRA) coupled with Principal Component Analysis(PCA). AISI 316L stainless steel sheets were used to develop double wall angle pyramid with aid of tungsten carbide tool. GRA coupled with PCA was used to plan the experiment conditions. Control factors such as Tool Diameter(TD), Step Depth(SD), Bottom Wall Angle(BWA), Feed Rate(FR) and Spindle Speed(SS) on Top Wall Angle(TWA) and Top Wall Angle Surface Roughness(TWASR) have been studied. Wall angle increases with increasing tool diameter due to large contact area between tool and workpiece. As the step depth, feed rate and spindle speed increase,TWASR decreases with increasing tool diameter. As the step depth increasing, the hydrostatic stress is raised causing severe cracks in the deformed surface. Hence it was concluded that the proposed hybrid method was suitable for optimizing the factors and response.

Thickness distribution of multi-stage incremental forming with different forming stages and angle intervals

Although multi-stage incremental sheet forming has always been adopted instead of single-stage forming to form parts with a steep wall angle or to achieve a high forming performance, it is largely dependent on empirical designs. In order to research multi-stage forming further, the effect of forming stages(n) and angle interval between the two adjacent stages(Δα) on thickness distribution was investigated. Firstly, a finite element method(FEM) model of multi-stage incremental forming was established and experimentally verified. Then, based on the proposed simulation model, different strategies were adopted to form a frustum of cone with wall angle of 30° to research the thickness distribution of multi-pass forming. It is proved that the minimum thickness increases largely and the variance of sheet thickness decreases significantly as the value of n grows. Further, with the increase of Δα, the minimum thickness increases initially and then decreases, and the optimal thickness distribution is achieved with Δα of 10°.Additionally, a formula is deduced to estimate the sheet thickness after multi-stage forming and proved to be effective. And the simulation results fit well with the experimental results.

Process design for multi-stage stretch forming of aluminium alloy aircraft skin

A process design approach for multi-stage stretch forming was proposed by combining the strain distribution method and finite element method(FEM)to determine the minimum stage number and deformation amount of each stage.The strain distribution method was used to calculate the deformation amount of each stage and evaluate the formability through a safety criterion.FE simulation was taken as an analysis tool to reveal the deformation behaviour,to predict the strain contour and to determine the process parameters at each stage.To evaluate the effect of heat treatment after pre-strain on occurrence of deformation defects during the subsequent deformation,a multi-stage uniaxial tension test for 2B06 aluminium alloy sheet was carried out.A case study demonstrates that the approach has high reliability and good practicability.

Trace Elements of Multi-stage Minerals and Titanite U-Pb Dating for the Gneisses from Liansan Island,Sulu UHPM Belt

Gneisses with anatectic characteristics from the Liansan island in the Sulu UHPM(ultra-high pressure metamorphic)belt were studied for petrography,titanite U-Pb dating and mineral geochemistry.Three origins of garnets are distinguished:metamorphic garnet,peritectic garnet and anatectic garnet,which are formed in the stages of peak metamorphism,retrograde anatexis and melt crystallization,respectively.The euhedral titanite has a high content of REE and high Th/U ratios,which is interpreted as indicating that it was newly-formed from an anatectic melt.The LA-ICP-MS titanite U-Pb dating yields 214-217 Ma ages for the titanite(melt)crystallization.The distribution of trace elements varies in response to the different host minerals at different stages.At the peak metamorphic stage,Y and HREE are mainly hosted by garnet,Ba and Rb by phengite,Sr,Nb,Ta,Pb,Th,U and LREE by allanite and Y,U and HREE by zircon.During partial melting,Y,Pb,Th,U and REE are released into the melt,which causes a dramatic decline of these element contents in the retrograde minerals.Finally,titanite absorbs most of the Nb,U,LREE and HREE from the melt.Therefore,the different stages of metamorphism have different mineral assemblages,which host different trace elements.

Overview of multi-stage charging strategies for Li-ion batteries

To reduce the carbon footprint in the transportation sector and improve overall vehicle efficiency,a large number of electric vehicles are being manufactured.This is due to the fact that environmental concerns and the depletion of fossil fuels have become significant global problems.Lithium-ion batteries(LIBs)have been distinguished themselves from alternative energy storage technologies for electric vehicles(EVs) due to superior qualities like high energy and power density,extended cycle life,and low maintenance cost to a competitive price.However,there are still certain challenges to be solved,like EV fast charging,longer lifetime,and reduced weight.For fast charging,the multi-stage constant current(MSCC) charging technique is an emerging solution to improve charging efficiency,reduce temperature rise during charging,increase charging/discharging capacities,shorten charging time,and extend the cycle life.However,there are large variations in the implementation of the number of stages,stage transition criterion,and C-rate selection for each stage.This paper provides a review of these problems by compiling information from the literature.An overview of the impact of different design parameters(number of stages,stage transition,and C-rate) that the MSCC charging techniques have had on the LIB performance and cycle life is described in detail and analyzed.The impact of design parameters on lifetime,charging efficiency,charging and discharging capacity,charging speed,and rising temperature during charging is presented,and this review provides guidelines for designing advanced fast charging strategies and determining future research gaps.

Study on the hot deformation behavior of Al-Zn-Mg-Cu-Cr aluminum alloy during multi-stage hot compression

The mechanical behavior and microstructures of an Al-Zn-Mg-Cu-Cr aluminum alloy during multi-stage hot deformation were investigated by thermal stimulation test, optical microscopy, and transmission electron microscopy. The true stress vs true strain curves and the microstructure evolution of two hot deformation procedures were gained. The flow stress of the alloy studied decreases with increasing the deforming passes and declining the temperature, and the larger the temperature decline between adjacent stages, the larger the peak stress fall is. The stress-strain behavior mainly result from the dynamic recovery during deformation, the static recovery and recrystallization in the delay time, and the second phases precipitated from the matrix at high temperature.

Dynamic performance of cable-stayed bridge tower with multi-stage pendulum mass damper under wind excitations——I:Theory

In this paper, wind-induced vibration control of a single column tower of a cable-stayed bridge with a multi- stage pendulum mass damper （MSPMD） is investigated. Special attention is given to overcoming space limitations for installing the control device in the tower and the effect of varying natural frequency of the towers during construction. First, the finite element model of the bridge during its construction and the basic equation of motion of the MSPMD are introduced. The equation of motion of the bridge with the MSPMD under along-wind excitation is then established. Finally, a numerical simulation and parametric study are conducted to assess the effectiveness of the control system for reducing the wind-induced vibration of the bridge towers during construction. The numerical simulation results show that the MSPMD is practical and effective for reducing the along-wind response of the single column tower, can be installed in a small area of the tower, and complies with the time-variant characteristics of the bridge during its entire construction stage.

Prediction and Verifcation of Forming Limit Diagrams Based on a Modifed Shear Failure Criterion

The forming limit diagram plays an important role in predicting the forming limit of sheet metals.Previous studies have shown that,the method to construct the forming limit diagram based on instability theory of the original shear failure criterion is efective and simple.The original shear instability criterion can accurately predict the left area of the forming limit diagram but not the right area.In this study,in order to improve the accuracy of the original shear failure criterion,a modifed shear failure criterion was proposed based on in-depth analysis of the original shear failure criterion.The detailed improvement strategies of the shear failure criterion and the complete calculation process are given.Based on the modifed shear failure criterion and diferent constitutive equations,the theoretical forming limit of TRIP780 steel and 5754O aluminum alloy sheet metals are calculated.By comparing the theoretical and experimental results,it is shown that proposed modifed shear failure criterion can predict the right area of forming limit more reasonably than the original shear failure criterion.The efect of the pre-strain and constitutive equation on the forming limits are also analyzed in depth.The modifed shear failure criterion proposed in this study provides an alternative and reliable method to predict forming limit of sheet metals.

Multi-Stage Improvement of Marine Predators Algorithm and Its Application

The metaheuristic algorithms are widely used in solving the parameters of the optimization problem.The marine predators algorithm(MPA)is a novel population-based intelligent algorithm.Although MPA has shown a talented foraging strategy,it still needs a balance of exploration and exploitation.Therefore,a multi-stage improvement of marine predators algorithm(MSMPA)is proposed in this paper.The algorithm retains the advantage of multistage search and introduces a linear flight strategy in the middle stage to enhance the interaction between predators.Predators further away from the historical optimum are required to move,increasing the exploration capability of the algorithm.In the middle and late stages,the searchmechanism of particle swarmoptimization(PSO)is inserted,which enhances the exploitation capability of the algorithm.This means that the stochasticity is decreased,that is the optimal region where predators jumping out is effectively stifled.At the same time,self-adjusting weight is used to regulate the convergence speed of the algorithm,which can balance the exploration and exploitation capability of the algorithm.The algorithm is applied to different types of CEC2017 benchmark test functions and threemultidimensional nonlinear structure design optimization problems,compared with other recent algorithms.The results show that the convergence speed and accuracy of MSMPA are significantly better than that of the comparison algorithms.

Local Buckling-Induced Forming Method to Produce Metal Bellows

A novel buckling-induced forming method is proposed to produce metal bellows.The tube billet is firstly treated by local heating and cooling,and the axial loading is applied on both ends of the tube,then the buckling occurs at the designated position and forms a convolution.In this paper,a forming apparatus is designed and developed to produce both discontinuous and continuous bellows of 304 stainless steel,and their characteristics are discussed respectively.Furthermore,the influences of process parameters and geometric parameters on the final convolution profile are deeply studied based on FEM analysis.The results suggest that the steel bellows fabricated by the presented buckling-induced forming method have a uniform shape and no obvious reduction of wall thickness.Meanwhile,the forming force required in the process is quite small.

Dynamic performance of cable-stayed bridge tower with multi-stage pendulum mass damper under wind excitations—Ⅱ: Experiment

The possibility of using a multi-stage pendulum mass damper （MSPMD） to control wind-induced vibration of a single column tower of a cable-stayed bridge during construction was studied theoretically in part I of this work. In this paper, the performance of the MSPMD for reducing bridge tower vibration is studied experimentally. A MSPMD model and a tower model of the bridge with geometry scaling of 1：100 were designed and manufactured. Calibration of the MSPMD model with different wire lengths is conducted to verify the analytical model of the damper. A series of tests for the uncontrolled freestanding tower, tower with cables, and tower with MSPMD model are then performed under harmonic and white noise excitations. The experimental results show that the responses of the tower model significantly decrease with the installation of the MSPMD model, which demonstrates the effectiveness of the M SPMD to mitigate the vibration of the bridge tower.

Design and analysis of longitudinal–flexural hybrid transducer for ultrasonic peen forming

Ultrasonic peen forming(UPF)is an emerging technology that exhibits great superiority in both its flexible operating modes and the deep residual stress that it produces compared with conventional plastic forming methods.Although ultrasonic transducers with longitudinal vibration have been widely studied,they have seldom been incorporated into UPF devices for machining in confined spaces.To meet the requirements of this type of machining,a sandwich-type piezoelectric transducer with coupled longitudinal-flexural vibrational modes is proposed.The basic structure of the transducer is designed to obtain large vibrational amplitudes in both modes.Experimental results obtained with a prototype device demonstrate the feasibility of the proposed transducer.The measured vibrational amplitude for the working face in the longitudinal vibrational mode is 1.0μm,and electrical matching increases this amplitude by 40%.The flexural vibration characteristics of the same prototype transducer are also tested and are found to be slightly smaller than those of longitudinal mode.The resultant working strokes of the UPF impact pins reach 1.7 mm and 1.2 mm in the longitudinal and flexural modes,respectively.The forming capability of the prototype has been evaluated via 15-min machining on standard 2024-T351 aluminum plates.After UPF,an improved surface morphology with lower surface roughness is obtained.The aluminum plate test piece has an apparent upper deformation with an arc height of 0.64 mm.The measured peak value of the compressive residual stress is around 250 MPa,appearing at a depth of 100μm.The proposed longitudinal-flexural hybrid transducer thus provides a high-performance tool for plate peen forming in confined spaces.