Retainer Optimization

TEKREVOLUTION is a high-tech service and consulting company from Italy with huge experience in R&D activities. One of their main activities is to explore intelligent additive manufacturing to provide higher stress-to-weight ratio solutions for the market.

Challenge

For the space sector, it is important to reduce the weight to the minimum possible, while maintaining excellent performance. That is why it is very important to choose the right selection of materials for each component of the structure, depending on the stress supported and its density.

In this case, we are analyzing the selection of the optimum material for a retainer belonging to the Spring Separation System of Interstage 2/3 of the Vega C launcher (Fig. 1). The actual design of the retainer is made of Aluminium AL7050 and the component is manufactured by machining it from an Aluminium billet. Nevertheless, due that the load supported by the retainer is not very big (around 600 N), it is possible to use polymeric materials such as PPS CF, PEEK or Carbon PEEK using Additive Manufacturing techniques making the component lighter.

For this study, two main properties of the material are considered. The density, and the Young Modulus. The objective is to see in which ranges those variables can be while matching the structural behavior in terms of maximum displacement, stress supported and natural modes to understand which kind of polymeric material is more efficient for this task. It is important to remark that some constraints on the inputs and outputs were set during the optimization process to avoid unrealistic materials, and that a Safety Factor = 2 was requested in terms of allowable Von Misses stress.

Fig 1. Retainer geometry

Tools

For this problem, we used two Uptimai new optimization features. The first one is the Direct Optimizer which aims at minimizing (or maximizing) a function of interest with one single output with so-called Evolutionary Algorithms which mimic the behavior of a population of living beings in an environment subject to natural selection. Inside the Direct Optimizer we are proposing two different algorithms, depending on the problem: Differential Evolution (DE). This algorithm creates a population of potential samples and makes it evolve at each generation. The evolution process involves independent and random mutation of each coordinate of each member of the population. This evolution process is repeated multiple times in a looping fashion and at each iteration, the population members are replaced by the new members (children) only if they provide a better result (lower function value).

The algorithm stops when the population has converged closely enough to a minimum point or the maximum allowed number of function evaluations is attained. Because each coordinate is mutated independently this algorithm is subject to the curse of dimensionality. This is why the decoupling option is recommended for high dimensional problems (dimension >= 10). Hybrid method of DE and Covariance Matrix Adaptation. The Covariance Matrix Adaptation (CMA) is an algorithm that evolves the population by generating children according to a multivariate Gaussian distribution. The best child elements are selected for the next population and the parameters of the Gaussian distribution are adjusted in a heuristic manner. Again the algorithm stops in case of convergence of the population or if the maximum number of function evaluations has been reached. The Hybrid Method performs a decoupling process to separate 1D-subproblems and ND-subproblems. Then, the DE algorithm is applied to 1D-subproblems and the CMA algorithm is applied to ND-subproblems.

To tackle the curse of dimensionality, for both algorithms, the UptimAI software use a decoupling process (also known as variable separation in the literature) that transforms the main domain into smaller subdomains. Then the optimization process is separated into lower-dimensional subproblems, providing better performance and converging faster.

On the other hand, the Multi-Objective Optimizer is designed to minimize multiple concurrent outputs. It works in a similar way that the Direct Optimizer does. However, it is not usable with decoupling and uses an evolutionary algorithm called NSGA-II. Unlike the Direct Optimizer, the Multi-Objective Optimizer provides multiple solutions approximating a Pareto Front of the problem.

Solution

We coupled the UptimAI tool with the simulation software MSC Nastran, without the need of interfering with its code or interface. Then the MSC Nastran started running simulations for the sample points (different material properties) indicated by the UptimAI algorithm for converging into the optimum solution.

Fig 2. Results obtained from Nastran MSC for a specific sample

For this case, approximately 500 simulations were performed to get a converged solution. Uptimai Multidisciplinary Optimization software gave as result the Pareto front of the duo density - young modulus that was improving both displacement, Natural mode and stress (the last one isn’t represented in Fig. 3). From the results obtained, we could extract the properties of the wanted material and by consequence the type of polymeric material that should be used to reduce the weight of the retainer while maintaining an excellent performance.

Fig 3. Pareto Front showing zone of optimum properties, and the outputs achieved

Benefits

• Interpretation of variables effect. Understanding the effect of each variable on the output
• Optimization of the results. Obtention of the Pareto Front that is improving all the outputs at the same time
• Reduction of computational cost. Our increased convergence rate makes that fewer samples are needed to achieve the solution.