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.     

In situ synthesis of TiC-Al (Ti) nanocomposite powders by thermal plasma technology

A novel processing technology was developed to investigate in situ synthesis of TiC-Al (Ti) nanocomposite powders by thermal plasma technology. Thermodynamic analysis was performed to predict possible starting materials and synthesizing conditions of TiC-Al (Ti) nanocomposite powders. A mathematical model was developed to describe temperature profile and velocity distribution in the reactor. The model is applied to optimize feeding rate, input power, and other processing parameters of TiC-Al (Ti) nanocomposite powders by thermal plasma technology, and to predict which materials can be used as starting materials. This paper emphasizes the investigation of the effect of feeding rate, input power, mole ratio, and other process parameters on synthesis of TiC-Al (Ti) nanocomposite powders by thermal plasma technology. The experimental results showed that TiC-Al (Ti) nanocomposite powders can be synthesized in situ by thermal plasma technology, and the average size of TiC-Al (Ti) nanocomposite powders was less than 100 nm.     

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.     

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.     

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.     

Forging preform design with shape complexity control in simulating backward deformation

This paper presents a preform design method which employs an alternative boundary node release criterion in the finite element simulation of backward deformation of forging processes. The method makes use of the shape complexity factor which provides an effective measure of forging difficulty. The objective is to release die contacting nodes in a sequence which will minimize the geometric complexity throughout the backward deformation simulation. This is done by calculating the effect of releasing each of a select group of boundary element nodes at each finite element solution step. The particular detached node which results in the minimum shape complexity factor will be released for the current step. This process continues for each backward step until the last few nodes remain in contact. This design method is demonstrated through the simulated forging of an integrated blade and rotor turbine disk blank. A preform shape developed by this method is compared with an empirically designed preform. Performance parameters for comparison include die fill, flash volume, effective strain variance, frictional power and die load. Comparing the results of the forward simulations indicates improved performance of the preform design using FEM based backward deformation method over that of the empirical design.