Proposed Velocity Field Research Articles

Face stability of shield tunnels considering a kinematically admissible velocity field of soil arching

Existing mechanism of simulating soil movement at tunnel face is generally based on the translational or rotational velocity field, which is, to some extent, different from the real soil movement in the arching zone. Numerical simulations are carried out first to investigate the characteristics of the velocity distribution at tunnel face and above tunnel vault. Then a new kinematically admissible velocity field is proposed to improve the description of the soil movement according to the results of the numerical simulation. Based on the proposed velocity field, an improved failure mechanism is constructed adopting the spatial discretization technique, which takes into account soil arching effect and plastic deformation within soil mass. Finally, the critical face pressure and the proposed mechanism are compared with the results of the numerical simulation, existing analytical studies and experimental tests to verify the accuracy and improvement of the presented method. The proposed mechanism can serve as an alternative approach for the face stability analysis. • A proper velocity field is proposed to agree with soil movement in soil arch zone. • An improved failure mechanism is constructed based on spatial discretization. • Proposed mechanism provides a better upper bound solution of critical face pressure. • Proposed mechanism corresponds well with numerical simulation and experiment test.

Deduction of a quadratic velocity field and its application to rolling force of extra-thick plate

A quadratic velocity field that meets the kinematically admissible condition is constructed. To check the reliability of the proposed velocity field, the software ANSYS/LS-DYNA is used, and the change law of metal flow in the deformation zone is analyzed. Based on this velocity field, a three-dimensional rolling force model of extra-thick plate is established. During the analysis, the problem of integral difficulty due to the nonlinear Mises yield criterion is settled, and the internal power of deformation is deduced based on the method of inner product and accumulative summation of vector component. Meanwhile, the friction power and the shear power are also calculated by the method of co-line vector inner product and the variable upper bound integration method, respectively. The rolling force is acquired by the energy method and validated with the site measured value. The calculated deviations of the rolling forces between the model and the measured data are within 5.14%. Furthermore, the influences of the temperature difference of the workpiece, relative reduction, thickness-radius ratio, and friction factor on the rolling force model are analyzed. It is showing that the change law of the metal flow by simulation is consistent with the proposed velocity field, and the rolling force model accounting for the temperature difference of the workpiece is much closer to the actual situation.

NALYSIS OF CLOSED DIE COLD FORGING FOR SPUR GEAR USING THREE DIMENSIONAL SLAB TECHNIQUE

The present study is concerned with upset forging of arbitrarily-shaped prismatic blocks which is characterized by three-dimensional deformation. From the proposed velocity field, the upper-bound load and deformed configuration are determined by minimizing the total power consumption with respect to some chosen parameters; such as the proposed method of analysis in this work can be used for prediction of forging load and deformation in upset forging of arbitrarily-shaped prismatic blocks. Closed-die forging of toothed disk is investigated using the slab method technique The tooth regions are approximated by prismatic rectangular sections. The velocity field comprising three-unit deformation regions is used. A constant frictional stress between work-piece and forging die is assumed. The average punch pressure normalized by the flow stress of the billet material is determined theoretically and compared with the present experimental results The experimental work is carried out on a commercial pure Aluminum (Al 1100) at room temperature The forging process is carried out using one die geometry without using any additional blocker dies. The theoretical predictions of forging pressures and deformation configurations are in good agreement with the experimental results. The experimental work proves that the analysis is good within approximately 36% of error according to many parameters.

Upper bound analysis of a shape-dependent criterion for closing central rectangular defects during hot rolling

• A shape-dependent closure criterion for closing central defects during hot plate rolling is proposed. • The decrease in initial plate thickness or the increases in relative reduction and in roller radius are in favor of defect closure. • A defect tends to be closed well if the actual shape factor reaches or exceeds the corresponding critical shape factor. • A flatter defect with larger value of aspect ratio can be closed much easier. A triangular velocity field for central defect closure is proposed in this paper. With the proposed velocity field, the minimum upper bound power is calculated. Then, the stress state coefficient as a function of defect thickness δ and aspect ratio η is obtained by the upper bound theorem. By applying the limit condition of the stress state coefficient with respect to defect size and letting the defect size be zero, the analytical solution of critical shape factor depending on aspect ratio solely is derived from a quadratic equation. Ultimately, a shape-dependent criterion for closing rectangular defects during hot rolling is established by relating the derived critical shape factor to the actual one. It is shown that as the aspect ratio increases, the critical defect size decreases and the applied energy required for closing central defects increases. The increases in relative reduction and roller radius or the decrease in initial plate thickness are in favor of defect closure. Validation of the present result with available simulation result and a current rolling schedule shows that the present analytical criterion matches well with the simulation result and can be used for optimizing rolling parameters to close central defects. Experimental research in laboratory shows that a defect can be closed well if the actual shape factor reaches or exceeds the corresponding critical shape factor.

A dynamic closure criterion for central defects in heavy plate during hot rolling

A new continuous velocity field used to analyze central defect closure for heavy plate rolling is proposed by modifying a two-dimensional velocity field. By using the proposed velocity field and mean yield criterion (or called MY criterion for short), the internal deformation energy rate is obtained. With co-line vector inner-product method, the frictional energy rate is then integrated. Ultimately, an analytical solution of the rolling torque and rolling force is obtained by minimizing the total energy rate with respect to neutral angle. Based on the assumption that when a central defect tends to be closed the stress state coefficient will obtain its critical value, a mathematical expression of critical shape factor together with a dynamic closure criterion for rectangular shape defects are derived. It is found that the critical shape factor is a function of initial plate thickness, relative reduction, work roll radius, and friction factor. The effects of independent rolling parameters such as plate thickness, relative reduction, work roll radius, and friction factor on the critical shape factor are discussed systematically. The results show that the increases in relative reduction, work roll radius and friction factor benefit defect closure, while a large value of initial plate thickness induces central burst formation. In addition, the proposed criterion is validated by comparison with available theoretical results and very good agreement is found.

Upper bound analysis of wire drawing through a twin parabolic die

According to the demand of stream function, a twin parabolic die as a streamline for wire drawing was designed and its kinematically admissible velocity field was then developed. Using the specific energy rate of MY (mean yield) criterion, the mathematical expression of internal deformation energy rate is obtained. Through surface integral of the proposed velocity field, the friction energy rate is also determined. Based on upper bound method, an analytical solution of drawing force is ultimately obtained. The effect of percentage reduction and die semi-angle on the drawing force are discussed. Comparison shows that the calculated drawing forces of the proposed die closely match its numerical drawing forces, and are the lowest compared with those based on conical die, hyperbolic die and elliptic die.

Analysis of broadside rolling for heavy plate by weighted velocity field and mean yield criterion

A new weighted velocity field for broadside rolling is proposed, in which the effect of double-barrel shape has been taken into account. By using the proposed velocity field and mean yield criterion (or called MY criterion for short), the internal deformation energy rate is obtained. With co-line vector inner-product method, the frictional energy rate between the roll and the work piece is integrated. Using the double integrals in polar coordinates, the shear energy rate at the entry section is also derived. Ultimately, an analytical solution of roll torque and separating force for broadside rolling is first obtained. The theoretical predictions of roll torque and separating force are compared with actual measured data. The result reveals that the proposed solution is appropriate for solving broadside rolling, and the roll torque and separating force are in good agreement with the actual measured ones since the maximum errors are <15.41 %. Moreover, the effects of various rolling conditions such as thickness reduction, friction factor and shape factor, upon separating force, location of neutral angle, and stress state coefficient are discussed systematically.

Continuous velocity fields for collapse and blowout of a pressurized tunnel face in purely cohesive soil

SUMMARYFace stability analysis of tunnels excavated under pressurized shields is a major issue in real tunnelling projects. Most of the failure mechanisms used for the stability analysis of tunnels in purely cohesive soils were derived from rigid block failure mechanisms that were developed for frictional soils, by imposing a null friction angle. For a purely cohesive soil, this kind of mechanism is quite far from the actual velocity field. This paper aims at proposing two new continuous velocity fields for both collapse and blowout of an air‐pressurized tunnel face. These velocity fields are much more consistent with the actual failures observed in undrained clays. They are based on the normality condition, which states that any plastic deformation in a purely cohesive soil develops without any volume change. The numerical results have shown that the proposed velocity fields significantly improve the best existing bounds for collapse pressures and that their results compare reasonably well with the collapse and blowout pressures provided by a commercial finite difference software, for a much smaller computational cost. A design chart is provided for practical use in geotechnical engineering. Copyright © 2012 John Wiley &amp; Sons, Ltd.

A kinematics study of variable lead axisymmetric forward spiral extrusion

Variable lead axi-symmetric forward spiral extrusion (VLAFSE) allows far more efficient strain accumulation than constant lead counterpart AFSE. It eliminates the rigid body rotation of the sample in an AFSE die which only causes frictional loss and has no contribution to the deformation. Based on a proposed velocity field, the kinematic formulation for VLAFSE is presented, utilized to predict strain components in the deformation zone and compared with experimental measurements. A simple closed form solution of the VLAFSE problem is presented which describes the flow of material inside the extrusion die. The results confirm that the effective strain of the process accumulates non-linearly in the both radial and extrusion directions.

Axi-symmetric forward spiral extrusion, a kinematic and experimental study

A modified axi-symmetric forward spiral extrusion process has been proposed here to allow for a near zero area reduction process. The axi-symmetric forward spiral extrusion, AFSE, can be carried out through a die with a number of engraved spiral grooves. This paper investigates the kinematics of the AFSE process. A velocity field is derived using principle of mass conservation along the extrusion axis. The proposed model has been developed to calculate strain components in the deformation zone during the process. An experimental method has been designed which uses composite lead samples with embedded copper wires to trace the strain path to verify the proposed velocity field. A good agreement between experimental results and the proposed analytical model was observed. The proposed velocity field, verified by experimental results, shows that the deformation develops away from the AFSE die–sample interface. A linear gradient of velocity in the radial direction was observed which is in good agreement with the proposed velocity field. Based on the estimated strains, velocity gradient, and nearly no change in sample cross section during AFSE, the process seems to have good potential for application as a new severe plastic deformation process in both continuous and batch modes.

A projection-based level-set approach to enhance conductivity anomaly reconstruction in electrical resistance tomography

In this paper we consider level-set-based methods for anomaly reconstruction for applications involving low-sensitivity data concentrating specifically on the problem of electrical resistance tomography (ERT). Typical descent-based inversion methods suffer from poor reconstruction precision in low-sensitivity regions and typically display quite slow convergence. In this paper, we develop a method for constructing the level-set speed function that is capable of overcoming these problems. In the case of the gradient-descent-based level-set evolution, the speed function is defined in terms of the dot products of residual and sensitivity functions. For Gauss–Newton-type methods, however, the speed function is the solution of the linearized inverse problem at each iteration. Here we propose a projection-based approach where the displacement of the level zero, i.e. estimated anomaly contour, at each point depends on the correlation coefficients between the sensitivity of the data to conductivity perturbations and the residual error. In other words, the proposed velocity field is invariant to the absolute amplitudes of both residual and sensitivity, but rather is a reflection of the angle between these two quantities. We demonstrate that our method is a descent-based reconstruction and we relate the mathematical formulation of the projection-based speed function to that of the gradient-descent method and the Gauss–Newton-type approach. The comparison suggests that the proposed technique can be seen as a diagonal approximation of the Gauss–Newton formulation. Using a quasi-linear source-type formulation of the forward problem, we describe an efficient implementation of the projection-based approach for finite-domain imaging problems. The proposed algorithm is simulated with numerical 2D and 3D data and its performance and efficiency are compared to those of the gradient-descent method.

Analysis of spur gear forms with tapered tooth profile

This paper presents an analysis of the lateral extrusion of spur gear forms and a comparative evaluation of the methods of lateral extrusion and closed die forging of spur gear forms in terms of mechanical properties of the product. An upper bound solution for lateral extrusion of spur gear forms with tapered tooth profile has been developed. A kinematically admissible velocity field has been proposed. From the proposed velocity field the upper bound solution on relative punch pressure and extrusion load are determined with respect to chosen process parameters. The obtained results are compared with experimental results in order to illustrate the validity of the proposed velocity fields. This indicates that the analysis presented here renders better upper bound solution before corner filling occurs. In addition, gear forms of the same dimension have been produced by both lateral extrusion and closed die forging. The fatigue and hardness tests were applied to gear teeth produced by both processes. The fatigue tests were applied in a manner of three point bending tests. The effect of forming method on the fatigue behavior at the roots of gear teeth and hardness distribution along the radial direction of the tooth are investigated.

A study of lateral extrusion of gear like elements and splines

An upper bound solution for lateral extrusion of spline and spur gear forms has been developed. A simple kinematically admissible velocity field with optimization parameter is proposed. From the proposed velocity field the upper bound solution on relative punch pressure and extrusion load are determined with respect to chosen process parameters. The results are compared with theoretical and experimental results from a reference to illustrate the validity of the proposed velocity fields. This indicates that the analysis presented here renders better upper bound solution than that given by Plancak et al. [Non-conventional cold extrusion, J. Mater. Process. Technol. 34 (1992) 465–472].

An analysis of the closed-die forging of a general non-axisymmetric shape by the upper-bound elemental technique

A kinematically admissible velocity field suitable for the closed-die forging of a general non-axisymmetric shape such as the forging of a cylindrical billet is proposed. By using the proposed velocity field, the upper-bound forging load and the velocity field for the closed-die forging of elliptic and trochoidal shapes by the forging of cylindrical billets are determined with respect to a chosen parameter. Experiments were carried out with commercially pure aluminum billets at room temperature. The forging loads between theory and experiment are shown to agree well, thus validating the proposed velocity field.

A generalized velocity field for axisymmetric tube drawing through an arbitrarily curved die with an arbitrarily curved plug

A generalized kinematically admissible velocity field suitable for axisymmetric tube drawing through arbitrarily curved die with an arbitrarily curved plug is proposed. By using the proposed velocity field, the upper-bound drawing stress and optimal die and plug profiles for the tube drawing process are determined with respect to chosen parameters related to the velocity field. The effects on the solution of various process parameters are discussed.

A UBET analysis of non-axisymmetric forward and backward extrusion

In this study, UBET is used to analyze the forward and backward extrusion of hexagonal- and trochoidal-shaped wrench bolts. For the UBET analysis, the extrusion process is assumed to have two stages. In the first stage, axisymmetric forward extrusion and non-axisymmetric backward extrusion simultaneously take place until the backward extrusion of a wrench socket is completed. In the second stage, only the cylindrical forward extrusion process takes place. New kinematically admissible velocity fields are proposed to determine the forming load, the extruded length and the deformation pattern with respect to the punch stroke. From the proposed velocity fields, the upper-bound load and the average length of the extruded billet are determined by minimizing the total energy consumption rate with respect to chosen parameters. Experiments are carried out with antimony–lead billets at room temperature using hexagonal- and trochoidal-shaped punches. The forming load and the extruded length with respect to the punch stroke are compared with the theoretical predictions, good agreement being found.

The forging of helical gears (II): comparisons of the forging processes

In this study, the forging processes of helical gears have been investigated wherein they have been classified into two types: the guiding type and the clamping types. These two types of forgings of helical gears have been analyzed by using the upper-bound method. New kinematically admissible velocity fields of the clamping-type forging of helical gears have been proposed, where an involute curve has been introduced to represent the tooth profile of the gear. The proposed velocity fields of the clamping-type forging of helical gears have been applied to the non-symmetric lateral extrusion forging and the result has been compared with the solution proposed by Plancak et al. [J. Mater. Process. Technol. 1992; 34:465–472]. Numerical calculations have been carried out to investigate the effects of various parameters, such as modules, number of teeth, helix angles and friction factors on the clamping-type forging of helical gears. For the forging of helical gears, the results of the upper-bound analysis of the clamping type have been compared with those of the guiding ones. Some experiments of the clamping-type forging were carried out with commercial aluminum alloy to show the validity of the analysis. Good agreement was found between the predicted values of the forging load and the experimental forging load.

A General Velocity Field for Shape Rolling of a V-Sectioned Sheet

A general kinematically admissible velocity field has been proposed in this work to examine the plastic deformation behavior of the sheet at the roll gap during shape rolling of a V-sectioned sheet. This velocity field is employed to examine the geometry of the rolled product, which are effected by various rolling conditions such as the sizes of the raw sheet and the vacancy, thickness reduction, etc. Furthermore, experiments on cold shape rolling of aluminum sheet have also been conducted. The rolling forces and the shape of the rolled product were measured to compare with the analytical values. Through the comparisons between them, the validity of this newly proposed velocity field was verified. [S1087-1357(00)71301-3]

A General Formulation for Hydroforming of Arbitrarily-Shaped Boxes and Its Application to Hydroforming of an Elliptic-Circular Box

A general kinematically admissible velocity field is suggested for the upper-bound solution of hydroforming of arbitrarily-shaped boxes. The suggested formulation is then applied to hydroforming of an elliptic-circular box. From the proposed velocity field, the fluid pressure vs. punch stroke relationship to render uniform thickness and the deformed configuration are determined by minimizing the total power consumption with respect to some chosen parameters. Experiments are carried out in the hydroforming press according to the computed pressure vs. punch stroke curve. The assumption of uniform wall thickness is confirmed by measuring the thickness variation. The effects of various process parameters including blank size, work-hardening exponent and frictional coefficient on the pressure curve are analyzed and discussed. It is thus shown that the proposed method of analysis in the present study can be effectively used for hydroforming of arbitrarily shaped boxes.

An upper bound analysis of the square-die extrusion of non-axisymmetric sections

A simple kinematically-admissible velocity field is proposed to determine the final-stage extrusion load and average length of the extruded products in the square die extrusion of non-axisymmetric bars from round billets. The proposed velocity field is applied to the square-die extrusion of regular polygonal-shaped bars, trochoidal gear-shaped bars and rectangular-shaped bars. The profile function of a rectangular is approximated by using a Fourier series. Experiments have been carried out with hard-solder billets at room temperature using various shaped dies. The theoretical predictions of the extrusion load are in good agreement with the experimental results and there is generally reasonable correlations of average length of the extruded products, between theory and experiment.