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 comer 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 comer. When non-uniform interference is adopted the first principal stress at the comer 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 comer stress concentration. The first principal stress at the comer 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.

Die structure optimization of equal channel angular extrusion for AZ31 magnesium alloy based on finite element method

Three-dimensional（3D） geometric models with different comer angles （90° and 120°） and with or without inner round fillets in the bottom die were designed. Some important process parameters were regarded as the calculation conditions used in DEFORMTM-3D software, such as stress--strain data of compression test for AZ31 magnesium, temperatures of die and billet, and friction coefficient. Influence of friction coefficient on deformation process was discussed. The results show that reasonable lubrication condition is important to plastic deformation. The change characteristics for distributions of effective stress and strain during an equal channel angular extrusion （ECAE） process with inner angle of 90° and without fillets at outer comer were described. Inhomogeneity index （C） was defined and deformation heterogeneity of ECAE was analyzed from the simulation and experiment results. The deformation homogeneity caused by fillets at outer comer increased compared with the die without fillets. The cumulated maximum strains decrease with increasing the fillets of outer comer in ECAE die and the inner comer angle. The analysis results show that better structures of ECAE die including appropriate outer comer fillet and the inner comer angle of 90° for the die can improve the strain and ensure plastic deformation homogenization to a certain extent. The required extrusion force drops with increasing the fillet made at outer comer in ECAE die. It is demonstrated that the prediction results are in good agreement with experiments and the theoretical calculation and the research conclusions in literatures.

Optimal design of butterfly-shaped linear ultrasonic motor using finite element method and response surface methodology

A new method for optimizing a butterfly-shaped linear ultrasonic motor was proposed to maximize its mechanical output. The finite element analysis technology and response surface methodology were combined together to realize the optimal design of the butterfly-shaped linear ultrasonic motor. First, the operation principle of the motor was introduced. Second, the finite element parameterized model of the stator of the motor was built using ANSYS parametric design language and some structure parameters of the stator were selected as design variables. Third, the sample points were selected in design variable space using latin hypercube Design. Through modal analysis and harmonic response analysis of the stator based on these sample points, the target responses were obtained. These sample points and response values were combined together to build a response surface model. Finally, the simplex method was used to find the optimal solution. The experimental results showed that many aspects of the design requirements of the butterfly-shaped linear ultrasonic motor have been fulfilled. The prototype motor fabricated based on the optimal design result exhibited considerably high dynamic performance, such as no-load speed of 873 ram/s, maximal thrust of 27.5 N, maximal efficiency of 43%, and thrust-weight ratio of 45.8.

STRESS FIELD ANALYSIS OF EXTRA-HEIGHT FORGING DIE USING FINITE ELEMENT METHOD

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Simulation of isothermal precision extrusion of NiTi shape memory alloy pipe coupling by combining finite element method with cellular automaton

In order to present the microstructures of dynamic recrystallization(DRX) in different deformation zones of hot extruded NiTi shape memory alloy(SMA) pipe coupling,a simulation approach combining finite element method(FEM) with cellular automaton(CA) was developed and the relationship between the macroscopic field variables and the microscopic internal variables was established.The results show that there exists a great distinction among the microstructures in different zones of pipe coupling because deformation histories of these regions are diverse.Large plastic deformation may result in fine recrystallized grains,whereas the recrystallized grains may grow very substantially if there is a rigid translation during the deformation,even if the final plastic strain is very large.As a consequence,the deformation history has a significant influence on the evolution path of the DRX as well as the final microstructures of the DRX,including the morphology,the mean grain size and the recrystallization fraction.

Influence of radial forging process on strain inhomogeneity of hollow gear shaft using finite element method and orthogonal design

Due to the current trend towards lightweight design in automotive industry,hollow stepped gear shafts for automobile and its radial forging process are widely investigated.Utilizing coupled finite element thermo-mechanical model,radial forging process of a hollow stepped gear shaft for automobile was simulated.The optimal combination of three process parameters including initial temperature,rotation rate and radial reduction was also selected using orthogonal design method.To examine the strain inhomogeneity of the forging workpiece,the strain inhomogeneity factor was introduced.The results reveal that the maximum effective strain and the minimum effective strain appeared in the outermost and innermost zones of different cross sections for the hollow stepped gear shaft,respectively.Optimal forging parameters are determined as a combination of initial temperature of 780°C,rotation rate of 21°/stroke and radial reduction of 3 mm.

Applications of the Finite Element Method to PDC Mold Design

This paper describes the structure of the molds for making polycrystalline diamond compact （PDC） drilling bits. It represents the mold shapes by using the Finite Element technique, and compares the analytical results with available experimental data. Based on the results of Finite Element analysis, some areas of stress concentrations are determined, and modifications made, to the PDC （polycrystalline diamond compact） mold. A displacement plot and several stress contour plots are presented. Techniques of the mold design are discussed.

OPTIMUMDESIGNOFSTREAMLINEDEXTRUSIONDIESBASEDONUPPERBOUNDMETHODANALYSIS

A more universal and flexible method of constructing the streamlined die surfaces is presented. The streamlined die surfaces are interpolated by the arbitrarily cross sectional shapes of the die entrance and exit. The boundaries of the die entrance and exit are represented by Ferguson curves with tension parameters. By adjusting the tension parameter, the cross sectional shapes of the die entrance and exit with line segments can be accurately constructed. The upper bound method is used to analyze the procedure of extrusion, the pseudo independent parameters in kinematically admissible velocity and die surface are computed by minimizing the extrusion load, so the optimum die surface is obtained. The effects of frictional condition, die length, area reduction and product shaped complexity are discussed in relation to the extrusion load.

Aerodynamic Design of Airfoils Based on Variable-Domain Variational Finite Element Method

Designing airfoils according to given pressure (or velocity) distribution is one kind of free boundary problems. Free boundary condition can be coupled with the flow governing equations by variable-domain variational calculus, which makes it possible to calculate simultaneously the flow field and the free boundary. An accurate deduction of the variable-domain variational principles is taken herein to design airfoils in compressible and incompressible flows. Furthermore, two grid types (H and O) are used in the calculation with better results for the O-type grid. It is shown that convergence is accelerated and good results can be obtained even if the initial guessed airfoil shape is a triangle, demonstrating the strong adaptability of this method.

Finite Element Method for Design of Reinforced Concrete Offshore Platforms

A design method of reinforced concrete (R. C.) offshore platforms with nonlinear finite element analysis is proposed. According to the method, a computer program is developed. In this program nonlinear constitutive relationships and strength criteria of concrete and steel bars are included, and the progressive cracking and crushing of the concrete are taken into account. Based on the stress distribution obtained by the nonlinear finite element analysis, the amount of reinforcement in the control sections can be computed and adjusted automatically by the program to satisfy the requirement of the design. The amount of reinforcement required in the control sections, which are obtained with the nonlinear finite element analysis, is agreeable to that obtained in the experiment. This shows that the design method of R. C. offshore platform with the nonlinear finite element method proposed by the authors is reliable for practical use.

Finite element analysis of strain distribution in ZK60 Mg alloy during cyclic extrusion and compression

Finite element method was used to study the strain distribution in ZK60 Mg alloy during multi-pass cyclic extrusion and compression （CEC）. In order to optimize the CEC processing, the effects of friction condition and die geometry on the distribution of total equivalent plastic strain were investigated. The results show that the strain distributions in the workpieces are inhomogeneous after CEC deformation. The strains of the both ends of the workpieces are lower than that of the center region. The process parameters have significant effects on the strain distribution. The friction between die and workpiece is detrimental to strain homogeneity, thus the friction should be decreased. In order to improve the strain homogeneity, a large corner radius and a low extrusion angle should be used.

SHAPE OPTIMIZATION DESIGN OF CRUSH TOOTH USING FINITE ELEMENT METHOD

The load condition of the mineral sizer is discussed. Acoording to three typical load cases presented, FEM and optimization models are established. Computed the model problems by use of ANSYS software and sequential unconstrained minimization technique, the stress distribution on c rush tooth and it's optimal shape are aquired. After analyzing the results, the relation between stress distribution and structural parameters is presented.

Damage prediction for magnesium matrix composites formed by liquid-solid extrusion process based on finite element simulation

A damage prediction method based on FE simulation was proposed to predict the occurrence of hot shortness crocks and surface cracks in liquid-solid extrusion process. This method integrated the critical temperature criterion and Cockcroft ＆ Latham ductile damage model, which were used to predict the initiation of hot shortness cracks and surface cracks of products, respectively. A coupling simulation of deformation with heat transfer as well as ductile damage was carried out to investigate the effect of extrusion temperature and extrusion speed on the damage behavior of Csf/AZ91D composites. It is concluded that the semisolid zone moves gradually toward deformation zone with the punch descending. The amplitude of the temperature rise at the exit of die from the initial billet temperature increases with the increase of extrusion speed during steady-state extrusion at a given punch displacement. In order to prevent the surface temperature of products beyond the incipient melting temperature of composites, the critical extrusion speed is decreased with the increase of extrusion temperature, otherwise the hot shortness cracks will occur. The maximum damage values increase with increasing extrusion speed or extrusion temperature. Theoretical results obtained by the Deform^TM-2D simulation agree well with the experiments.

NUMERICAL DESIGN OF DIE LAND FOR SHAPE EXTRUSION

In the extrusion of shapes with flat faced die,the proper design of die land is of critical importance in avoiding the generations of geometry defects.A methodology for the design of die land,which consists of a simulation adjustment iteration,is proposed.The metal flow in extrusion is simulated by the three dimensional finite element method and the die land is adjusted according to the simulation result.Both the formulae for adjustment of the die land and the criterion for the judgment of proper die land are suggested.The extrusion of an L section shape is chosen as the computational example and the result is compared with the industrial design.

THEORETICAL ANALYSES ON DESIGN OF SHEAR EXTRUSION DIE

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Mathematical model of determination of die bearing length in design of aluminum profile extrusion die

Based on the finite element simulation of profile extrusion process, the effect of local extrusion ratio, die bearing area and the distance between extrusion cylindrical center and local die orfice center on mental flow velocity was investigated. The laws of deformed metal flow on profile extrusion process were obtained. The smaller the local extrusion ratio, the faster the metal flow velocity; the smaller the area of die bearing, the faster the metal flow velocity; the smaller the distance of position of local die orifice(the closer the distance of position of local die orifice from extrusion cylindrical axis), the faster the metal flow velocity. The effect of main parameters of die structure on metal flow velocity was integrated and the mathematical model of determination of die bearing length in design of aluminum profile extrusion die was proposed. The calculated results with proposed model were well compared with the experimental results. The proposed model can be applied to determine die bearing length in design of aluminum profile extrusion die.

Finite Element Analysis and Optimal Design Based on ANSYS in a XH2408 Gantry Style NC Machining Center

ANSYS, the software of construction analysis, is used to analyze static and dynamic performances of a XH2408 gantry style numerical control （NC） milling machining center and optimize its construction using the finite element method. First, a finite element model is established and the static and dynamic analysis are completed as constraints and loads applied on the finite element model. It is found that both spindle box and gantry are the worst components of assembly in performance. Secondly, the spindle box and gantry are chosen as objects of optimal design separately, aiming to improve their performance. The optimal plans are accomplished on the basis of the minimum volume for the spindle box and the maximum inherent frequency for the gantry subject to the constrains. Finally, the machine tool improved is analyzed statically and dynamically based on the optimal results of the spindle box and gantry. The results show that optimal design with the finite element method increases static and dynamical performances of the XH2408 gantry style numerical control milling machining center and the technique is effective and practical in engineering applications.

FINITE ELEMENT ANALYSIS OF THE FREE EXTRUSION FLOWS OF BOGER FLUIDS

The stream-line finite element method proposed by Luo and Tanner has been improvedand used to simulate the extrudate swell of the so called Boger fluid.The element withdiscontinuous pressure proves to be a successful choice and superior to that with continuous pressureIt is revealed that the visccsity of Newtonian solvent of the Boger fluid has a great influence on thecalculated swelling.The Weissenberg number is suggested to take the place of recoverable shear strainin Tanner′s formula to estimate the swelling of the Boger or Oldroyd-B fluids.

FINITE ELEMENT ANALYSES OF THE EXTRUSION FLOWS OF BOGER FLUIDS WITH END-DRAWING AND GRAVITY-DRAWING

The spinning flow of Boger fluids and the gravity-drawing extrusion flow of a Newtonianas well as a Boger fluid have been simulated by using the stream-line finite element method and thetechnique of matching the finite element solutions with those of one-dimensional spinning equations.The recoverable shear strain is proved not to be a basic parameter in characterising thespinning flow of Boger fluids.For Newtonian fluids this technique predicts the experimental jetshape accurately.For Boger fluids,the numerical simulation agrees with the experimental data of spin-ning flow reported by Sridhar et al.,but seems to give an insufficient swelling and over contractionof the jets when drawn by its own weight,compared with the experimental results of Trang andYeow.It implies that the Oldroyd-B model fitting the viscometric-flow data fails to describeaccurately the elasticity and extensional viscosity in the extrusion flow of Boger fluids with gravi-ty-drawing.

Seismic analysis of cantilever earth retaining walls embedded in dry sand by simplified approaches and finite element method

In engineering practice simplified methods are essential to the seismic design of embedded earth retaining walls,as fullydynamic numerical analyses are costly,time-consuming and require specific expertise.Recently developed pseudostatic methods provide earth stresses and internal forces,even in those cases in which the strength of the soil surrounding the structure is not entirely mobilised.Semiempirical correlations or Newmark sliding block method provide an estimate of earthquake-induced permanent displacements.However,the use of these methods is hindered by uncertainties in the evaluation of a few input parameters,affecting the reliability of the methods.This study uses 1 D site response analyses and 2 D fully-dynamic finite element analyses to show that simplified methods can provide a reasonable estimate of the maximum bending moment and permanent displacements for stiff cantilever walls embedded in uniform sand,providing that a few input parameters are evaluated through semiempirical correlations and a simple 1 D site response analysis.