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Loss of circularity when creating metal ring-shaped products by ring rolling is a significant industrial issue. This paper explores the previously tacit knowledge that plastic changes in curvature - required to maintain circularity - principally occur as material passes through the roll gap. Through a series of experiments and numerical simulations on half-ring workpieces, the ‘free curvature change’ is explored for the first time, finding that the ring can ‘curl up’ - the radius reducing by as much as -39% in a single pass - unless the inner roll is much smaller than the outer roll. An analytical model of free curvature change is proposed based on force equilibrium and compatibility. Under a range of ‘normal’ operating conditions this predicted free curvature change to within 7%. In (full) ring rolling the radius of curvature must continually increase. This paper proposes that regulation of curvature is achieved through bending moments at the roll entry and exit; largest when the tool size ratio is furthest from the optimum. This hypothesis is supported by Finite Element simulations of full ring rolling, finding entry and exit moments up to a quarter of the moment for a fully plastic hinge. This work could be of direct use to process designers in choosing tool sizes and guide roll force limits and suggests new ways to use guide rolls to better maintain circularity in challenging situations.

A new ductile fracture criterion for skew rolling has been proposed in this paper. The prediction of internal fractures is crucial given that internal fractures cause loss of product strength and are difficult to detect. The proposed criterion considers the effect of cyclic shear stress on void evolution in a cylindrical coordinate system. This paper covers the following four points: (1) evaluation of the predictability of the conventional ductile fracture criteria for the internal fracture in three-roll skew rolling, (2) clarification of the internal fracture mechanism and proposal of a new criterion, (3) application of the criterion to predict internal fractures in two-roll skew rolling, and (4) relationship between hot workability and damage value determined using the proposed criterion. Given that the hot rolling experimental results did not agree with the prediction provided by the conventional ductile fracture criteria, composed of stress invariants, we evaluated the stress and strain state of the rolled material through elasto-plastic finite element analysis. The results of the numerical analysis led to the hypothesis that the cyclic shear stress is effective in determining the internal fractures caused by skew rolling. The proposed criterion, based on the above hypothesis, accurately predicted the internal fracture initiation, which is specific to skew rolling, regardless of the number of rolls.

Optical measuring systems provide much more detail on the deformation of the blank in the bulge test than classical mechanical measuring systems. Within the practical limitations of mechanical measuring systems the shape of the bulged surface has been approximated by a sphere. The additional information that is available from optical measuring systems allows a more accurate description of the bulged surface and in general a more accurate determination of the stress and strain state at the pole. A detailed analysis is presented of all assumptions and simplifications in the evaluation of the test and their contribution to the accuracy of the result. It is shown that higher accuracy can be achieved by fitting the surface coordinates to an ellipsoid shape function. With this fit and by considering the local strain data to approximate the curvature for the midplane, the flow curve is retrieved with very high accuracy. The accuracy of the evaluation procedure is assessed by numerical experiments, using surface coordinates that were obtained from finite element calculations. The new accurate evaluation method has been tried for a variety of yield loci and hardening curves. A realistic level of measurement noise has been applied on the nodal coordinates of the finite element results per time step to demonstrate the robustness of the fitting procedure. Numerical experiments with strong planar anisotropic properties show a deviation from the assumed balanced biaxial stress state. Despite the fact that the stresses in different directions are not equal, it is proven that the obtained flow curve is an accurate representation of the work hardening behaviour in this non-balanced biaxial stress state. A final draft of an international standard on the determination of biaxial stress–strain curves by means of the hydraulic bulge test with optical measuring systems (ISO 16808) has been published. This paper will discuss the recommendations of that standard and compare the results for a steel (DC06) and aluminium (AA5182) example with the proposed procedure in this paper.

In previous paper [Fourier series based finite element analysis of tube hydroforming—An axisymmetric model, Eng. Comput. 23 (7) (2006) 697–728], an axisymmetric analysis of tube hydroforming process was discussed. In the present paper, a generalized plane strain implicit formulation of the cross-sectional expansion of an extruded aluminum tube with pressurized fluid to fill a hydroforming die is presented. The cross-section of the tube is modeled with thin straight and circular segments with constant thickness, and Fourier series are used to approximate nodal displacements. The material of the tube is assumed to obey a rate-independent, elastoplastic model that takes into account work hardening and normal anisotropy. At the tube-die interface, frictional stress is assumed, based on Coulomb friction, to be proportional to the contact pressure whenever relative sliding occurs. The kinematics relationships are derived based on thin shell theory, and the equilibrium equation is derived based on virtual work principle. The axial feed is implemented by imposing either a compressive force or strain in the tube length direction. Frictional boundary condition is introduced into the formulation in the form of a penalty function, which imposes the constraints directly into the tangent stiffness matrix. The Newton-Raphson iterative method is used to incrementally solve the resulting nonlinear equations. Two examples of tube hydroforming problems are solved and numerical predictions of the deformed shape, hydroforming pressure, and deformation strains are compared with experimental and ABAQUS results.

The prime objective of the paper is the application of the fully automatic hp adaptive Finite Element Method (FEM) code to solve heat transfer problems over the domain with various materials. Large changes in material data generate singularities: non-continuities or large gradients of the solution to the heat equation. To minimize the error of FEM solution the mesh should be refined close to the singularities by sub-dividing elements and increasing the polynomial order of approximation. It is very difficult to design an optimal hp mesh by hand. This paper presents a typical application of the fully automatic 3D hp adaptive FE code to the problem of modelling of the resistance heating of an Al–Si billet in a steel die for thixoforming process. The code automatically produces an FE mesh with minimal number of degrees of freedom, resolving all singularities within a prescribed error tolerance.

The key to realizing fast and accurate flatness control is to establish a mathematical model between the flatness error character parameters and the flatness adjustment parameters. In this paper, the concepts and the mathematical models of transfer function and transfer matrix are proposed for the flatness control of strip mills. For a 900 mm HC 6-high mill, the transfer matrix is set up by GA-BP network model, and successfully applied into the flatness setting control. This paper provides a theoretical framework for flatness control.

The main purpose of this paper is to establish an inverse method, where by using this inverse method the history of the change in thermal conductivities of the workpiece material and the change in average temperatures of workpiece during upsetting process can be obtained. The inverse method is based on the measurement temperatures of an upsetting experiment and combines the matrix-presentation linear least-squares error method of an inverse heat-transfer finite element model proposed in this paper with the regularization of the Tikhonov method. Since the change of the thermal conductivities between the successive finite element analysis stages is very slight and continuous, the square of the difference of the thermal conductivities between successive finite element analysis stages is adopted as the stabilizing function of the regularization of the Tikhonov method in this paper. From the results, it can be shown and demonstrated that the inverse method proposed in this paper can make the history of the change in thermal conductivities during upsetting process has a better stability.

This paper proposes a method for the rapid prototyping (RP) of self-similar objects. RP technology makes available the physical generation of a solid object. However, the contemporary design capability of a computer-aided design (CAD) system can atmost use the non-uniform rational B-spline (NURBS) modelling method. When the design has a very complicated shape with self-similarity, contemporary CAD systems can no longer handle the object. In fact, most objects in nature are self-similar. It is valuable to develop a method that can fabricate self-similar objects. Natural objects, such as mountains, clouds, and trees have irregular or fragmented features with self-similarity. These natural objects can be realistically described the by fractal geometry method, while Euclidean geometry is mainly used to represent simple man-made objects such as polyhedra. A typical self-similar fractal solid, the Menger sponge, will be used to illustrate the method. In order to represent a self-similar fractal object for RP, the first task is to develop a method to model the object in a computable form. In this paper, a new data structure, called the radial-blossoming tree (RBT) structure, is proposed and implemented in order to bridge the gaps among CAD, RP and fractal geometry. Based on the RBT representation, an RP toolpath can be traced out more efficiently. The Menger sponge will then be produced layer by layer from the RP machine.

This paper puts forward a new integrated design method based on fuzzy matter-element optimization. On the based of analyzing the model of multi-objective fuzzy matter-element R , the paper defines the matter-element weighting and changes solving a multi-objective fuzzy optimization into solving a dependent function K ( x ) of the single-objective optimization according to the optimization criterion. The paper particularly describes the realization approach of the GA process of multi-objective fuzzy matter-element optimization: encode, produce initial population, confirm fitness function, select operator, etc. In the process, the adaptive macro genetic algorithms (AMGA) are applied to enhance the evolution speed. The paper improves the two genetic operators: cross-over and mutation operator. The modified adaptive macro genetic algorithms (MAMGA) are put forward simultaneously, and adopted to solve the optimization problem. Three optimization methods, namely the fuzzy matter-element optimization method, the linearity weighted method and the fuzzy optimization method, are compared using tables and figures, showing that not only is MAMGA a little better than AMGA, but also it reaches the extent to which the effective iteration generation is 62.2% of simple genetic algorithms (SGA). By the calculation of an optimum example, the improved genetics method of reported in the paper is much better than the methods in the references of the paper.

The problem of contact in forging simulation is overviewed and revised in this paper. The integral form of equilibrium equations must be solved subject to the incompressibility and impenetrability or contact conditions. Minimization techniques such as the Lagrange multipliers method, the penalty function method or the augmented Lagrangian method have been used to convert the problem to the unconstrained form. These approaches are based on solving the equilibrium equations while preventing any constraints to be violated. An alternative is to solve the equilibrium equations regardless of the constraints. Then, if any of the constraints is found to be violated, a simple projection is used to force the node back to the contact zone. The major drawback of this simpler approach is the loss of volume/mass in the time steps. A quick remedy is to choose very small loading steps. In this paper, a simple velocity-based projection technique will be proposed to overcome the above mentioned deficiency. In this method the projection procedure is performed iteratively using a modified velocity field in such a way that the final position of the node will be exactly on the contact surface. This is very similar to the so-called “Return Mapping” algorithm in computational plasticity.

Ring rolling finite element simulation for profiled rings is currently not practicable with existing Lagrangian codes and on any realistic computational platform. The main reason for this is that a large number of incremental stages are typically required for completion of a full simulation and the computational cost per increment is high. The nature of ring rolling means that the amount of deformation that takes place in a given increment is relatively small when compared with typical metal forming processes. Small errors generated over each increment can grow to give highly inaccurate predictions after not so many ring revolutions. Inaccuracies manifest themselves in volume growth, incomplete profile filling, overall dimensional inaccuracy and inaccurate force and stress level predictions. This paper describes measures that make the analysis of profiled ring rolling a more practicable proposition. A model has been developed comprising the finite element flow formulation, an arbitrary Lagrangian–Eulerian update strategy, and a novel iterative solution scheme called the successive preconditioned conjugate gradient method. The focus of the paper is on methods developed to produce accurate predictions and that ensure numerical stability for an arbitrary high number of ring revolutions. The approach adopted includes methods for volume control, circular movement stability, circular interpolation techniques for accurate transfer of state variables, contact evolution, etc. The methods are validated by comparison with earlier experimental work and previously developed models for both pure radial, and radial–axial ring rolling. In addition, some results are presented for the analysis of commercially produced railway wheels and rings.

This paper presents applications of the single parameter accelerated modified Newton–Raphson (mN–R) methods (often referred to as the acceleration techniques in this paper) to the solution of nonlinear rigid–plastic finite element equations. A new formulation procedure used to derive acceleration techniques for the mN–R method is first described. Two new single parameter acceleration techniques of secant properties are obtained by using the modified BFGS and DFP quasi-Newton updates. Evaluation of the accelerators does not involve additional residual force calculation and requires little extra computational effort as compared to the standard mN–R method. The single parameter acceleration techniques are used to solve rigid–plastic finite element equations. Numerical performance of the techniques is compared with those of the standard N–R method (sN–R), standard mN–R method and other existing single parameter acceleration techniques. It is shown that the newly proposed techniques are more robust and efficient than the existing techniques.

This paper discusses the problems associated with detecting displacement phenomena during a NC-controlled heat-bending process. To ensure accurate heat-bending results, it is necessary to control the displacement of a point located at the edge of the plate undergoing heat bending. This is achieved by varying the operating parameters of the numerical control heat-bending (NCHB) machine, e.g. the ratio of Q / V where Q represents the heat input intensity and V the speed of the servomotor driving the heat source (an oxy-acetylene torch in this particular study). It is not easy to accurately predict the plate shape after heating along multiple heating lines. Furthermore, it is difficult to describe the state equation for the dynamic behavior of the displacement since the heat-bending phenomena are described by partial differential equations representing elasto-plastic behavior. In order to predict and control the plate shape after heat bending, this paper proposes a method which combines the inverse method and fuzzy control. Using this method, it is possible to estimate the displacement and, therefore, the plate shape, based upon the values of Q and V , and the position of the heating lines. The quality of the fuzzy inference process depends upon the fuzzy variables chosen. In this paper, a fuzzy rule table is used to control the speed of the NCHB servomotor. The table is based upon fuzzy logic and is used to fine-tune the value of Q / V . The effectiveness of the fuzzy controller is verified by carrying out heat-bending experiments.

This paper mainly defines and solves minimum circumscribed and maximum inscribed cones which are used to evaluate the contact surface of conically tapered parts. The optimal model of the minimum circumscribed cone employs the concept of the minimum volume cone, and the maximum inscribed cone uses the maximum volume cone. Examples are given to verify that the model is admissible and reliable. The results show that the optimization procedures presented in this paper provide exact values of minimum circumscribed and maximum inscribed cones. The mathematical model is superior to the existing method in terms of computation time in material processing and mechanical assembly.

The rigid–plastic finite-boundary element method (FBEM) is formulated with mixed-type. Therefore, this method can meet the need for compatibility of not only the nodal velocity but also the deritives of the nodal velocity. Then nodal velocities and derivatives of the nodal velocity can be calculated with the same precision for the rigid–plastic FBEM. Whilst the penalty rigid–plastic finite element method (FEM) is formulated with single-type like the other conventional rigid–plastic FEMs, the penalty rigid–plastic FEM cannot meet the need for compatibility of the derivitive of nodal velocity. On the other hand, the rigid–plastic FBEM is a kind of solution in open form, so that this method possesses another merit in that it does not need repetitive calculations, and there is not any possibility of divergence with the repetitive calculations. However, the penalty rigid–plastic FEM is a kind of solution in closed form like the other conventional rigid–plastic FEMs, so that there are some divergence possibilities with the repetitive calculations for the penalty rigid–plastic FEM. This paper makes analyses of an axisymmetric forging process by the two methods. It is found that the outline of the workpiece calculated by the rigid–plastic FBEM is smoother than that calculated by the penalty rigid–plastic FEM from the calculated results of this paper.

An upper bound analysis for an axisymmetric forging with a double ram action has been developed. The results of the analysis provide the geometric and processing conditions that can be used to avoid the development of unacceptable side-surface cracks. Kinematically admissible velocity fields that satisfy the incompressibility condition and the velocity boundary conditions have been determined and the corresponding upper bound solution for the flow pattern has been developed. To determine the conditions under which the process-induced surface cracks would occur, a kinematically admissible velocity field for defective flow was developed and analyzed by the upper bound approach. An extra power term that accounts for the power dissipated during crack formation has been added to the upper bound power for defective flow. This first paper in a two-part series presents the velocity fields and the individual power terms that were derived based upon these flow patterns, whilst the second paper shows the characteristics of the upper bound solution for this forging process. The second paper also presents the criteria for the prevention of the side-surface defects that were determined based upon the upper bound solution.

The fluid leakage across the contact line between two conjugate helical surfaces applied to fluid compression or pumping is the major concern in terms of the machine efficiency. A new quality index, the average comprehensive radius of curvature (ACRC), is proposed in this paper to characterize the geometrical shape of the leak-age path. A numerical approach is accordingly developed for the comprehensive curvature analysis along the contact line. Numerical examples are provided at the end of the paper.

Tandem cold rolling mills are comprehensive dynamic systems coupling with structure and rolling technology. A frequent problem is mill chatter, often occurring when rolling hard, thin materials at high speed and affecting the quality of the strip. In this paper, a dynamic increment model for chatter in a Universal Crown Control mill (UCM mill) is proposed with the considering of strip hardening, elastic deformation of the work roll, non-linear friction, transfer delay of the strip, and dynamic coupling effect of tension between adjacent stands. Mathematically, this model is based on the Taylor series expansion of the Bland-Ford-Hill rolling force equation. The comparative results of both simulation and experimental data show that this chatter model has a high accuracy. A novel, time-varying stability criterion is proposed to evaluate mill stability. Further study is provided on the optimal friction coefficient and reduction ratio required to increase the critical rolling speed and vibration stability in a tandem cold rolling mill. This mathematical criterion is validated by comparing the actual rolling speed with the calculated critical rolling speed. The present work provides a more accurate prediction of mill chatter and a basis for optimal design of rolling conditions.

The effect of stress release on the shape and deformation of strip between stands are rarely considered or quantified in the traditional strip shape model. In order to make up this deficiency, a high precision shape model is established by the mechanism of the strip shape forming and the deformation of roll system in this paper. Special concentration is placed on the effect of roll wear, roll thermal expansion, metal transverse flow and stress release on the shape. In addition, a tolerance factor which is used to describe the attenuation and tolerance abilities of each stand for longitudinal strain difference is proposed as a foundation for a presetting strategy. Compared to the traditional presetting strategies using the empirical coefficient or Shohet theory, the presetting strategy on the basis of the tolerance factor can better play the control ability of each stand. A systematical description of the presetting strategy and the modeling process of the high precision shape model is given in the present study. The calculated results agree well with experiments, and the actual production data show that the shape model has satisfactory accuracy.

To obtain a better strip shape, this paper proposes a new micro-scale roll profile control technology. According to the principle of the technology, it can be called roll profile electromagnetic control technology (RPECT). To achieve multi-point and real-time measurement the profile of electromagnetic control roll, the new roll profile test technology is proposed. Relying on the RPECT and new roll profile test technology, a φ270 mm×300 mm roll profile electromagnetic control experimental platform (RPECEP) is designed and built. An electromagnetic-thermal- mechanical coupled axisymmetric simulation model with the same size is established. Through experiments and simulations, RPECT is confirmed to achieve micro-scale flexible roll profile adjustment. An all-around comparison of experimental results and calculated results confirms that the new roll profile test technology is feasible and the calculatde results agree well with the experimental results. Based on the model, the variation of the roll profile is analysed for different electromagnetic parameters; the structures and positions of the electromagnetic stick, reasonable electromagnetic parameters and optimal time period for the roll profile control are determined, and methods for changing the number of roll profile curves are given.

Aiming at the low efficiency of three-point mold bending straightening, a new method of three-roll continuous straightening is proposed in this paper, which is full in consideration of the geometric features and bending characteristics of LSAW pipes. Using the characteristics of the roll straightening device, a straightness detection method for large pipes is proposed just by adding a laser displacement sensor, and the calculation model for overall deflection based on local deflection is established. Based on the detected deflection data, a piecewise fitting algorithm with constraints by introducing the Kuhn-Tucker condition is proposed for straightness calculation, and a simple polynomial fitting method with fourth order is determined for the calculation of curvature and straightening moment. Further, using the semi-automatic experimental prototype for small pipes, the deflection detection experiments show that the overall deflection error is less than 3.5% compared with that of CMM, the piecewise fitting results show that the ideal order of the mid-segment is 10-th, and the three-roll continuous straightening experiments show that the novel method can correct the straightness to less than 0.2%, meeting the standard requirements.

Residual stress in metal cutting is critical due to its direct influence on the performance of components. An analytical model of residual stress in orthogonal cutting is established in this paper. A constitutive stress updating algorithm based on the radial return (R-R) method is firstly employed in the plastic stress calculation of the residual stress analytical model. A thermal-mechanical model for the elastic stress in orthogonal cutting is established. Subsequently, the plastic stress is calculated based on the R-R method. The R-R method and corresponding stress release method are employed to model the residual stress on the machined surface. Orthogonal cutting experiments and residual stress measurements are conducted to verify the theoretical model proposed in this work. The consistency between the prediction values and the experiment results demonstrates the accuracy of the prediction model developed in this work. According to the theoretical model, the variations in the stress components, equivalent stress and yield stress during the stress updating process are analyzed. Comparisons for the discrepancy of the accuracy between the R-R method and the present plastic stress updating methods are carried out. The characteristics and advantages of the R-R method are discussed in detail to explain the reasons for the discrepancy in the accuracy compared with current methods. The results show that the analytical model proposed in this work can achieve a better prediction accuracy than the existing models, since the R-R method can avoid the problems of stress mutation and yield drift, and exhibits excellent flexibility and extensibility by reasonable assumptions and implicit calculation method.

A new theoretical model to analyze arbitrary profiles of extrusion dies is proposed in this paper. In this model, generalized rigid-plastic boundaries with optional variables are used to minimize the power by the upper-bound method. To satisfy the velocity boundary conditions at the entrance and exit, the streamline function is designed in the normal form of r(η, z), which satisfies the flow conditions and the rigid-plastic boundaries. Four sets of profile dies (cosine, elliptic, hyperbolic, and conic) are represented with different slopes at the entrance and exit in order to illustrate this method. Experiments were conducted in order to compare the results with those of the theoretical model. It was found that the predicted load and flow patterns were in agreement with the experimental observation and the results from the literature.

Injection molded parts with three-dimensional complex geometry, like thick or nonuniform thickness configurations, are widely used today, which boosts the need for 3D simulation replacing the 2.5D model. However, finite element methods of 3D simulation present numerical spurious oscillations, which give an unsatisfactory result associated with the classical Galerkin formulations of Navier–Stokes equations. The Streamline-Upwind/Petrov-Galerkin (SUPG) and Pressure-Stabilizing/Petrov-Galerkin (PSPG) methods were employed in this paper to prevent the potential numerical instabilities, by adding the weighting functions with their derivatives. Stabilized finite element formulations using equal-order interpolation functions for velocity and pressure were thus obtained. Numerical examples show that the developed numerical algorithms perform stable and give accurate results by comparing with the well-known commercial software Moldflow.

This paper proposes an advanced optimal unfolding algorithm of curved shell plates with unstructured meshes. An unfolding algorithm was developed in authors’ previous study. The unfolding process is formulated into a constrained nonlinear programming problem on a basis of nonlinear deformation theory of plates and shells and finite element. In order to make progresses on this unfolding and to fully automate it, unstructured meshing is combined. By applying the unstructured meshing to curved shell plates, their local curvature property can be taken into account. It takes advantages in implementing computational codes for unfolding curved shell plates defined by multiple and trimmed geometrical surfaces. Consequently, such considerations enable the unfolding results to be closer to what are expected mechanically and geometrically. And finally there are samples and discussions of this advanced unfolding algorithm.

This paper deals with scheduling jobs in an m-machine no-wait with the objective of minimising the maximum completion time of the jobs. The problem is known to be NP-hard for more than two machines, so we focus on obtaining good (although not necessarily optimal) solutions in a short time interval. To do so, we propose a new heuristic based on an analogy between the problem under consideration and the well-known travelling salesman problem (TSP). The proposal is compared with other improvement strategies reported in the literature. Results from computational experience show that, for problems up to five machines and 80 jobs, the new heuristic outperforms, on average, existing methods. Regarding the computational effort, there are no significant differences between the suggested heuristic and the other heuristics under comparison.

In this paper, the incomplete triangular mesh including reversed faces and gaps between boundary edges is directly offset for NC machining. For three-axis machining, vertical faces are deleted and the face normal vectors directing the lower part of model are changed to upward. The complete mesh is offset by the multiple normal vectors of a vertex, and boundary edges and boundary vertices are offset by the virtual multiple normal vectors of a boundary vertex. For five-axis machining, mesh is offset to both directions by the reversed multiple normal vectors. Using this method, the CL surface is directly obtained from an incomplete triangular mesh. To show that the proposed offset method is effective for NC machining, the tool path generated from the CL surface is verified by simulation and real NC machining.

In this paper, a new computational technique is presented based on the extended arbitrary Lagrangian–Eulerian finite element model (X-ALE–FEM) in plasticity forming of powder compaction. An arbitrary Lagrangian–Eulerian (ALE) technique is employed to capture the advantages of both Lagrangian and Eulerian methods and alleviate the drawbacks of the mesh distortion in Lagrangian formulation. In order to remove the limitation of the mesh conforming to the boundary conditions in this process, the extended finite element method (X-FEM) is implemented by incorporating discontinuous fields through a partition of unity method. The implementation of X-FEM technique in the framework of ALE model is finally presented in modeling of a shaped tablet component.

In this paper, an uncertain optimization method is suggested to obtain the optimal variable binder force in U-shaped forming. The friction coefficient is regarded as the uncertain coefficient, and the stepped variable binder force model is used. The finite element method is employed to simulate the forming process, and an uncertain objective function which represents the springback magnitude is created. The uncertain friction coefficient is treated as an interval, no need to know its probabilistic distribution. Through a nonlinear interval number programming method, the uncertain optimization problem is converted into a deterministic two-objective optimization problem. A hybrid optimization algorithm based on the intergeneration projection genetic algorithm and neural network is used to obtain the optimum. The presented method is applied to optimize the variable binder force parameters of the model from NUMISHEET’93. The forming quality based on the optimal variable binder force from the presented method is compared with constant binder force. The results indicate that the presented method can find the fair variable binder force to obtain both of the small springback and strain under the uncertain friction coefficient.

In this paper, we study a method to analyze eddy current testing (ECT) by using surface integral equations. When the skin depth is small, the surface integral equations with surface electric and magnetic currents, J s and K s , as unknowns give accurate solutions. However, the equations are singular at the sharp edge and so, we can’t expect accurate solutions. In ECT, the skin depth is thick, and so the electromagnetic fields are affected strongly by those around the edge. Some edges and corners of the crack are so close that it is difficult to get accurate solutions, moreover, as the width of the crack becomes narrower compared with its depth, the surface integral equations become ill conditioned and so it is more difficult to get accurate results. In order to overcome these problems and get accurate solutions for studying how to get better ECT system, we utilize electromagnetic fields produced by eddy currents at 90° edge in formulating the eddy current. It is assured that the magnetic field is formulated by the surface integral equation for J s even at the edge and corner. To meet boundary condition for K s at the edge, a semi-linear edge element and a loop magnetic current are introduced in discretization of the surface integral equation. So as to check adequacy of the proposed method, we have solved a typical eddy current problem and confirmed that eddy current problems with a narrow crack can be solved accurately.

Due to non-linearity of the cutting parameters, tool–work combination and rigidity of machine tool, it has been proved that a fuzzy logic concept gives a better way to model a complex manufacturing process, such as grinding, ultraprecision turning, etc. In this paper, an Takagi–Sugeno–Kang (TSK)-type fuzzy logic controller (FLC) is designed to model the input–output relationship of ultraprecision turning. The performance of an FLC primarily depends on its knowledge base, which consists of rule base and the membership function distributions (fuzzy subsets) considered for the variables. In TSK-type fuzzy system, the output of a fuzzy rule is a linear combination of the input variables, which is characterized by function coefficients and the variable's exponential parameters. In the present work, two approaches are considered to design the TSK-type FLC: one is based on linear regression (LR) method with constant and same exponential parameters for all the rule, and the other is based on LR with simultaneous optimization of exponential parameter using genetic algorithm (GA). The results of the proposed approaches are compared with the empirical expression, which is not accurate, as well as real experimental data to predict surface roughness in ultraprecision turning.

In this paper, the extended finite element method (X-FEM) is developed for modeling of frictional contact problems. In order to model the frictional contact behavior within the standard finite element framework, the special functions are included in standard FE method to simulate discontinuity without considering the boundary conditions in meshing the domain. The classical finite element approximation is therefore enriched by applying additional terms to simulate the frictional behavior of contact between two bodies. These terms, which are included for enrichment of nodal displacements, depend on the contact condition between two surfaces. The partition of unity method is applied to discretize the contact area with triangular sub-elements whose Gauss points are used for integration of the domain of elements. Finally, the numerical example of sliding of two bodies is presented to demonstrate the applicability of the X-FEM in modeling of frictional contact behavior.

Results of numerical simulation of the SICO test, including the resistance heating of samples and metal flow during the test, are described in this paper. The main goal of the work is the determination of the sensitivity of fracture criteria with respect to the test parameters: temperature, die velocity and material parameters—strain rate sensitivity, hardening coefficient, hardening exponent and temperature sensitivity coefficient. It was shown in earlier research that sensitivity analysis allowed the determination of the extent that the value of the fracture criterion changes with change of the SICO test parameters. Beyond this, the sensitivity analysis reveals which parameters interact with each other. This information is crucial for the inverse analysis if larger numbers of parameters are optimized. The present work is an extension of the authors’ earlier research and the variance-based method with correlation ratios is used in the analysis. The results of this analysis contribute to development of more efficient optimization algorithms in the inverse method.

Multi-attribute equipment selection is a very important activity for an effective manufacturing system. The information axiom proposes the selection of the proper alternative that has minimum information. Selection of the convenient equipment under determined criteria (such as costs and technical characteristics) using the information axiom will be realized in this study. The unweighted and weighted multi-attribute axiomatic design (AD) approaches developed in this paper include both crisp and fuzzy criteria. The fuzzy set theory has the capability of capturing the uncertainty under the conditions of incomplete, non-obtainable and unquantifiable information. These approaches were applied to the selection among punching machines while investing in a manufacturing system. The selection process has been accomplished by aiding a software program called MAXD.

The scope of the paper is a method of modelling vibrating mechanical systems with discrete–continuous distribution of parameters and couplings by means of hybrid graphs. The method is focused on broadening hybrid graphs formalism by mechanical systems and improving their description and design methods so that the mathematical formalism can reflect the essence of the problem involved in the designation of dynamic characteristics of such systems.

An enhanced higher order finite-difference time-domain (FDTD) algorithm for the precise analysis of complex 3-D electromagnetic compatibility (EMC) structures and arbitrary interface material distributions in general curvilinear, skewed and stretching lattices is presented in this paper. Introducing a systematic topological tessellation, the novel methodology develops a family of robust higher order non-standard forms, which exactly represent the material properties and significantly suppress the artificial dispersion errors. To handle inherent mesh deficiencies an enhanced low-pass filtering procedure is implemented, while a consistent class of self-adaptive compact operators ensures the correct evaluation of electromagnetic components near boundary walls. Moreover, for more involved media interfaces that do not follow the lines of the grid, a convergent transformation around these discontinuities leads to precise simulations. Therefore, this optimal field-preserving technique along with suitably tuned perfectly matched layers (PMLs), achieve high levels of accuracy, decrease the required number of points per wavelength and provide considerable computational savings, as indicated by extensive numerical results addressing 3-D EMC and hard-to-model material applications.

The paper presents a methodology of computer modelling of continual surface induction hardening of axi-symmetric bodies. The body is heated by a cylindrical inductor moving at a given velocity along it and the heated part is then cooled by spraying water. While the mathematical model of induction heating is given by two partial differential equations describing the harmonic electromagnetic and non-stationary temperature fields with one moving subregion, the process of cooling is modelled by a theoretically empirical algorithm based on experimental data and providing the value of the convective heat transfer coefficient. Theoretical analysis of the task is supplemented with an illustrative example and discussion of the results. Computations are performed by combination of professional codes and single-purpose user programs developed and written by the authors.

This paper presents a method for analog and topological measurement error identification in generalized state estimation. Errors of analog measurements depend on measurement equipment accuracy. Errors of topological measurements (switching device statuses) result in erroneous network models. In generalized state estimation, analog and topological data are processed as a single interacting information set. The conventional measurement model is extended by incorporating the breaker statuses (open or closed) and the active and reactive power flows as continuous state variables. Depending on breaker statuses, additional pseudomeasurements are introduced. The method treats the analog and status measurements as regular measurements. Hypothesis testing for detection and identification of bad analog and topological measurements is used ( J ( x ˆ ) and r ˆ N , test respectively). Test results for the RTS substation system are reported.

In this paper, a fast algorithm of wavelet transform was applied to recognize the tool wear states in automatic machining processing. The fast algorithm is based on a quadrature mirror filter (QMF) pair designed by Daubechies and can be implemented by a Mallat's tree algorithm. The expansion coefficients d ( j , k ), the output of the j times resolution, with time-frequency feature of the cutting force signals obtained by the fast algorithm of wavelet transform were used as recognizing parameters of tool wear states. The large number of experimental and analytical results have shown that the wavelet analysis based on the fast algorithm is more sensitive, more reliable and faster than the Fourier analysis for recognizing the tool wear states for the different cutting conditions in automatic turning.

In this paper, an attempt at designing discrete vibrating systems as machine subsystems of the required dynamical properties and at assessing the sensitivity of the obtained system in view of the values of the derived synthesised parameters has been made. A fundamental advantage of the graph and structural numbers method is a possibility of a topological isolation of the sensitivity edges in the polar graph and their algebraic representation by the structural numbers. The isolation of the sensitivity edge makes it possible to trace the impact of the changes in a given parameter on the behaviour of the system. The parametric sensitivity does not change the graph structure, these are only the edge weigh values that are subjected to the change. Thus, it is possible to generate a sequence of the system models with diverse nominal values of the parameters, while preserving the graph structure. Also, it is possible to test the structural sensitivity by a modification of the prime graph structure

In this paper we analyse the applications of MaxInf principle in a real problem of optimisation of a typical industrial manufacturing. After we reminded the theory of information we examine an example where is possible to determine a polynomial equation that approximates a set of value with a constant deviation that represents the same error for every point or the same information.

The idea of information, in the classic theories of Fisher and Wiener–Shannon, is a measure only of probabilistic and repetitiveness events. The idea of information is broader than the probability. The Wiener–Shannon's axioms are extended to the non-probabilistic and repetitiveness events. It is possible the introduction of a Theory of Information for events not connected to the probability therefore for non-repetitive events. On the basis of so called Laplace's principle of insufficient knowledge, the MaxInf principle is defined for choose solutions in absence of knowledge. In this paper the value of information, as a measure of equality of data among a set of values, is applied in numeric analysis as method for approximation of data, as an example of application.

The dynamical flexibility of continuous free systems with definite frequency spectrum and with cascade structure has the alternating: pole, zero, pole, zero, etc. The frequency with the zero value is always a pole. On the other hand, in the case of systems with cascade structure but fixed at one side, the dynamical flexibility has the alternating: zero, pole, zero, pole, etc. respectively. The frequency with the zero value is always a zero. In this paper the method distribution of characteristics into partial fraction and recurrent cascade method represented by graphs were applied in order to structural modification of the vibrating mechanical system with cascade structure.

According to a basic definition, complexity index for a given die profile is the ratio of the pressure required to extrude the profile relative to the extrusion pressure for a round cross-section of the same area. However, both intuitively and by definition, complexity index is a function of geometry only. Various researchers and experimenters have coined different definitions for shape complexity of extrusion dies, based solely on geometrical parameters. The simplest definition depicts complexity index as the ratio of profile perimeter to profile cross-sectional area. Other definitions are in terms of ratios of perimeter to weight, circumscribing circle diameter to minimum wall thickness, profile perimeter and equivalent circular perimeter, etc. Unfortunately, these definitions do not yield a consistent ranking of die profiles in terms of shape complexity. Moreover, the extrusion pressure predicted by these definitions often gives widely fluctuating values. The current paper aims at a new and more consistent definition of complexity for extrusion profiles. All extrusion runs for the study have been carried out in collaboration with a local commercial extrusion facility (hot extrusion of structural aluminum). A total of 27 different dies are used, profile complexity ranging from simple solids and hollows to quite complex ones. Die material (heat treated and surface hardened H-13 steel) and billet material (Al-6063) is the same for all experiments. Various runs at a ram speed of 3.8±0.1 mm/s have been carried out for 15 different die profiles, while another set of 12 profiles are extruded at 3.2±0.1 mm/s speed. After running a variety of regression runs, using various exponential, logarithmic and power law formats, the best-suited model for die complexity has been determined to be of the form C=α+β P s P 0 γ , where Ps and P0 are the perimeters of the actual profile section and an equivalent circular section of equal area, respectively. The constants α, β and γ are determined statistically by regression of experimental hot extrusion data obtained for a variety of die complexities and somewhat different operating conditions. In comparison with the existing definitions, the curve that follows the reference complexity curve (ratio of actual to circular-area pressure) most closely is that for the new definition.