Sensitivity analysis based preform die shape design using the finite element method

This paper uses a finite element-based sensitivity analysis method to design the preform die shape for metal forming processes. The sensitivity analysis was developed using the rigid visco-plastic finite element method. The preform die shapes are represented by cubic B-spline curves. The control points or coefficients of the B-spline are used as the design variables. The optimization problem is to minimize the difference between the realized and the desired final forging shapes. The sensitivity analysis includes the sensitivities of the objective function, nodal coordinates, and nodal velocities with respect to the design variables. The remeshing procedure and the interpolation/transfer of the history/dependent parameters are considered. An adjustment of the volume loss resulting from the finite element analysis is used to make the workpiece volume consistent in each optimization iteration and improve the optimization convergence. In addition, a technique for dealing with fold-over defects during the forming simulation is employed in order to continue the optimization procedures of the preform die shape design. The method developed in this paper is used to design the preform die shape for both plane strain and axisymmetric deformations with shaped cavities. The analysis shows that satisfactory final forging shapes are obtained using the optimized preform die shapes.     

Sensitivity analysis based preform die shape design for net-shape forging

A sensitivity analysis method for preform die shape design in net-shape forging processes is developed in this paper using the rigid viscoplastic finite element method. The preform die shapes are represented by cubic B-spline curves. The control points or coefficients of B-spline are used as the design variables. The optimization problem is to minimize the zone where the realized and desired final forging shapes do not coincide. The sensitivities of the objective function, nodal coordinates and nodal velocities with respect to the design variables are developed in detail. A procedure for computing the sensitivities of history-dependent functions is presented. The remeshing procedure and the interpolation/transfer of the history-dependent parameters, such as effective strain, are stated. The procedures of sensitivity analysis based preform die design are also described. In addition, a method for the adjustment of the volume loss resulting from the finite element analysis is given in order to make the workpiece volume consistent in each optimization iteration. The method developed in this paper is used to design the preform die shape of H-shaped forging processes, including plane strain and axisymmetric deformations. The results show that a flashless forging with a complete die fill is realized using the optimized preform die shape.     

Design of forging process variables under uncertainties

Forging is a complex nonlinear process that is vulnerable to various manufacturing anomalies, such as variations in billet geometry, billet/die temperatures, material properties, and workpiece and forging equipment positional errors. A combination of these uncertainties could induce heavy manufacturing losses through premature die failure, final part geometric distortion, and reduced productivity. Identifying, quantifying, and controlling the uncertainties will reduce variability risk in a manufacturing environment, which will minimize the overall production cost. In this article, various uncertainties that affect the forging process are identified, and their cumulative effect on the forging tool life is evaluated. Because the forging process simulation is time-consuming, a response surface model is used to reduce computation time by establishing a relationship between the process performance and the critical process variables. A robust design methodology is developed by incorporating reliability-based optimization techniques to obtain sound forging components. A case study of an automotive-component forging-process design is presented to demonstrate the applicability of the method.     

People-to-People-to-Geographical-Places: The P3 Framework for Location-Based Community Systems

In this paper we examine an emerging class of systems that link People-to-People-to-Geographical-Places; we call these P3-Systems. Through analyzing the literature, we have identified four major P3-System design techniques: People-Centered systems that use either absolute user location (e.g. Active Badge) or user proximity (e.g. Hocman) and Place-Centered systems based on either a representation of peoples use of physical spaces (e.g. ActiveMap) or on a matching virtual space that enables online interaction linked to physical location (e.g. Geonotes). In addition, each feature can be instantiated synchronously or asynchronously. The P3-System framework organizes existing systems into meaningful categories and structures the design space for an interesting new class of potentially context-aware systems. Our discussion of the framework suggests new ways of understanding and addressing the privacy concerns associated with location aware community system and outlines additional socio-technical challenges and opportunities.     

A global structural optimization technique using an interval method

This paper deals with a global optimization scheme for structural systems that require finite element analysis to evaluate the constraints or the objective function. The paper proposes a strategy for finding the global optimum using an interval method in conjunction with a multipoint function approximation. The highly nonlinear and nonconvex objective and constraint functions are first represented in the design space using linear and adaptive local approximations and these approximations are blended globally with the use of proper weighting functions. The interval method is then employed to trace the global optimum in the approximated function space. The procedure is tested with several examples with known global solutions and it is successfully applied to optimize the fiber-orientation angles of laminated composite plates for minimum deflections. Received December 22, 2000     

Structural reliability optimization using an efficient safety index calculation procedure

The objective of this paper is to conduct reliability-based structural optimization in a multidisciplinary environment. An efficient reliability analysis is developed by expanding the limit functions in terms of intermediate design variables. The design constraints are approximated using multivariate splines in searching for the optimum. The reduction in computational cost realized in safety index calculation and optimization are demonstrated through several structural problems. This paper presents safety index computation, analytical sensitivity analysis of reliability constraints and optimization using truss, frame and plate examples.     

Design of optimal process parameters for non-isothermal forging

This paper presents a state space model and an optimal design scheme for non-isothermal metal forming processes. By selecting nodal velocity and temperature as the state variables, a non-isothermal state equation with coupled deformation and thermal terms is established. Based on this state space model, a control design scheme is developed to obtain the optimal die velocity and initial die temperature which will ensure that the effective strain-rate and temperature satisfy the design requirements. A titanium alloy engine disk forging is used to demonstrate two design examples. The results show that the proposed model and design scheme behave well for different design requirements.     

Multidisciplinary optimization of gas-quenching process

Distortion as a result of the quenching process is predominantly due to the thermal gradient and phase transformations within the component. Compared with traditional liquid quenching, the thermal boundary conditions during gas quenching are relatively simple to control. By adjusting the gas-quenching furnace pressure, the flow speed, or the spray nozzle configuration, the heat-transfer coefficients can be designed in terms of both the component geometry and the quenching time. The purpose of this research is to apply the optimization methodology to design the gas-quenching process. The design objective is to minimize the distortion caused by quenching. Constraints on the average surface hardness, and its distribution and residual stress are imposed. The heat-transfer coefficients are used as design variables. DEFORM-HT is used to predict material response during quenching. The response surface method is used to obtain the analytical models of the objective function and constraints in terms of the design variables. Once the response surfaces of the objective and constraints are obtained, they are used to search for the optimum heat-transfer coefficients. This process is then used instead of the finite-element analysis. A one-gear blank case study is used to demonstrate the optimization scheme.     

State-space representation and optimal control of non-linear material deformation using the finite element method

A state-space model for representing the non-linear material deformation and an optimal control scheme for obtaining desired process conditions in the deforming material are presented in this paper. The formulation is general for various metal-forming processes including forging and extrusion operations. The state variables selected in the formulation are the die/billet contact nodal velocities and the nodal velocities of the critical finite elements of the billet. The control input is the ram velocity, which is determined by using the linear quadratic regulator (LQR) theory to maintain desired strain rates within the selected finite elements. The influence of an optimally designed ram velocity on the deforming material is studied using performance measures. This paper includes the development of the state-space model from non-linear finite element formulation, optimal control strategy and numerical example cases with discussions.