Multi-Goal Optimization and Robust Design of a Carry-Mould

Figure 1: The blowing machinery (left) and a particular of the carry-mould (right)

Optimization of a mechanical component is frequently a difficult task due to the fact that simultaneous optimization of more than one target function may be required. At the same time, attention must also be directed to satisfaction of predefined design constraints, thus limiting the exploitable optimization tools.
Typical engineering systems are described by a very large number of variables which even the most skilled designers are unable to take simultaneously into account without proper powerful numerical simulation tools. Moreover, engineers have often to optimize mechanical components that are part of complex assemblies. In this scenario, extrapolating and defining boundary conditions can be a lengthy process.

Application
In this work, multi-goal optimization and robust design of a carry-mould – part of a blowing machinery – were performed by means of modeFRONTIER (Figure 1).

Three initial parametric geometries of the carry-mould were generated for a computationally efficient investigation of a number of potential designs. Contact pressures and displacements imposed to the finite element (FE) model of the carry-mould (Figure 2) were computed from the 3D FE model of the multi-body assembly (Figure 3).

Figure 2: (a) Contact pressure (compressive stress) on the carry-mould as derived by the 3D FE model; (b) pressure applied to the single-body model; (c) resulting compressive stress on the equivalent single-body model.

Figure 3: (left) 3D FE model of the blowing machinery with boundary conditions, (right) Main displacement (UX)

The multi-goal optimization of the carry-mould was performed by means of modeFRONTIER MDO (Multi Design Objective) tool. Results were expressed by a set of feasible non-dominated solutions, the Pareto optimal set (the so named Pareto front). The Non-dominated Sorting Genetic (NSGA-II) algorithm was used with an initial population of 30 configurations identified by a pseudo random SOBOL DOE sequence that reduced the clustering effect in the design space uniform sampling. As a result of the optimization step, a total of 3 candidate solutions to the optimum final design of the carry-mould was found, one for each initial geometric configuration. The following entities were set to perform the optimization process:

Input variables:

• Geometric variables that are parameterized in the CAD model of the carry-mould.
  

Objective functions:

• Minimization of the global mass of the component
  
• Minimization of the moment of inertia
  

A general indication to minimize the barycentre coordinates has been also given.

Constraints:

• Maximum allowable displacement of a number of control points (purposely defined by means of a grid of areas) in the contact plate of the carry-mould with the blow-mould shell.

Successively, robustness and stability of each candidate solution were investigated in relation to uncertainties in manufacturing errors, material properties and applied loads by means of the Multi-Objective Robust

Design Optimization (MORDO) tool in modeFRONTIER. The final optimum design was the configuration characterized by the lowest standard deviation of the objective functions.

Figure 4:The modeFRONTIER workflow	Figure 5: Probability density function of normal distribution for the normalized global mass objective of the 3 final geometric configurations.

Results
The optimization procedure performed by means of modeFRONTIER gave a total of 3 solutions that were potential candidate as the final optimum design. These solutions were the “best” achieved for each original geometry, where the term “best” indicates designs that meet the highest number of constraints on displacements with the highest percentage improvement of the output objective functions. Among these solutions, the optimum design was chosen to be the more stable, in terms of objective functions, with respect to the uncertainties of the input parameters. (Figure 5).
The resulting optium design was characterized by a reduction of global mass and moment of inertia of 10% and 11% rispectively over the previously adopted configuration.

Conclusions
An application of multi-goal optimization of components integrated in complex assemblies, which successfully used modeFRONTIER in the optimization and robust design phases was presented in this work.
modeFRONTIER allowed for an easy interface with FE and CAD codes, permitting an extensive and efficient investigation of design spaces. Moreover, it assisted the user in the choice of proper analysis and simulation tools, thus resulting extremely user friendly.

Francesca Cosmi, Barbara Reggiani Università degli Studi di Trieste, Dipartimento di Ingegneria Meccanica