Optimization software drives Multi Body simulations in a Circuit Breaker design at ABB

Introduction

Figure 1: Two variable and one performance index design space: B is the Robust Optimum design

Let’s consider a generic design process, where the product performance index should be maximized (“Performance” in Figure 1). Supposing a vastly simplified case that the performance depends mainly on two design parameters (Variable 1 and 2), the physical behavior of the product can be investigated by means of several CAE simulations. Results can then be plotted as in Figure 1, where designer should pick solutions A and B as optima candidates. While A guarantees absolute peak performance, the surrounding surface area is locally very steep: hence, the solution is prone to fast decay due to small changes of Variable 1 and/or 2. This might easily happen when the variables are affected by manufacturing tolerances or operational uncertainties. B, instead, is called a “robust” optimum: it is much less sensitive to variables’ scatter, being located in a more flat (stable) zone of the Performance function. The search for such a design point B is called “robust design optimization”, and represents the solution of the design challenge previously described.
This paper presents such an innovative robust design optimization for high-voltage circuit breaker components. The available numerical model of such device includes 15 main variable parameters, while 4 performance indexes should be investigated simultaneously and several constraints respected. In this case, even finding a design that meets simultaneously all the constraints and has acceptable performance, represents a long process. In fact, numerical simulation should be repeated several times following an inefficient and arbitrary “trial-and-error” process. modeFRONTIER greatly speeds up all of these processes, and also encapsulates the search for robust designs, allowing engineers to focus on the result analysis and on the trade-off decision process.

The Challenge

Figure 2: Representations of the parameterized latch mechanism

High voltage circuit breakers have to fulfill several functions, such as conduct the nominal current when closed (in the range of several thousand amperes); withstand the maximum rated voltage when fully open (up to megavolts); open and close under short circuit conditions and, above all, interrupt the circuit with current values ranging from very low up to the maximum rated short circuit (effective value up to 80kA). To do so, CAE modeling and simulation techniques are applied starting from the early stages of the design. Still, the difficulty of simultaneously satisfying all the demands and handling many parameters represents a bottleneck in the design process. Moreover, developing a robust configuration in terms of reduced sensitivity to unmanageable external parameters and manufacturing tolerances is mandatory. The solution proposed here integrate the CAE model(s) with an optimization software such as modeFRONTIER, taking advantage of its process automation and robust design optimization capabilities. A crucial component in a circuit breaker is the drive system, that stores the energy required for the circuit breaker operation, including mechanical motion when triggered by an external control system. Essential for any circuit breaker drive unit is the ability to release the stored energy in a controlled, repeatable and robust way. This is typically done through a specialized latch mechanism (see Figure 2) which serves as an interface between a high speed electromagnetic actuator and a circuit breaker drive element.

This planar mechanism is comprised of five main bodies (plus the ground) consisting of the drive tooth, two rolling bodies that are centrally constrained to the ground (main bearing and second bearing), another rolling body (main roller), that has intermittent contact with the tooth and main bearing, and finally a body (link) which is constrained by a revolute joint to the main roller and surface contact on the second bearing. The mechanism is driven completely by the force of the drive tooth, and released through removal of the holding force. Critical performance criteria for latch mechanisms include response time, response time repeatability, force reduction ratio (driving force / holding force), maximum holding force capacity, and minimum required tripping input (force and displacement). From these, the response time and force reduction ratio are of primary importance. To minimize response time (and contact stress), a tooth with a varying instantaneous contact radius was desired: for the purposes of optimization, the profile was parameterized using an elliptical profile. A parametric Multi-Body numerical model of the latch has been created in the MD Adams simulation software to predict the mechanism performance, taking into account all the thirteen angle and length variables indicated in Figure 2, plus two parameters that describe the main roller and main bearing lengths. Such model contains also slot constraints, Herzian line contact stress, kinematic collision calculations and the extraction of the performance parameters. In order to simplify the parameterization and expedite the solution time, the interaction between bodies and slot constraints were modeled using curve-to-curve contacts. Additionally, any interaction from the drive was neglected (such as downstream transmission dynamics). Under these conditions, typical simulation time for a single case was less than 7 seconds while running on a standard workstation.

The Solution: latch robust design optimization using modeFRONTIER

Figure 3: modeFRONTIER’s workflow representing the automated design optimization process, with the latch MD Adams multi-body numerical model integrated

The developed MD Adams parametric dynamic simulation model was coupled with the modeFRONTIER software in order to automate the parametric study, and perform the holding force and latch opening time optimization and robustness analysis. The first phase of this process is the “workflow” building. The workflow (Figure 3) represents the operations that should be automated in order to evaluate a parameter combination that represents a design. The considered independent parameters (called also “input variables”) define a 15-dimensional variable space search (joint and contact friction parameters were considered initially constant). Six independent objectives, all to be minimized simultaneously, include: the latch mechanism opening time; holding force; contact stresses between the tooth and main roller; between main roller and main bearing; between second roller and second bearing. Three constraints have been set up, including an upper holding force limit, a maximum allowable response time and an upper contact pressure limits.

Due to the relatively fast simulation cycle time, and to the fact that modeFRONTIER automates completely the MD Adams’ simulations and the performance indexes extraction, a 10000-designs study was set up and completed in half a day. Initially wide parameter limits were considered, in order to explore the valid design space, as well as to obtain knowledge about the significance and influence of key input to output relationships. This sampling (referred to as “Design Of Experiments”, DOE) has been performed by modeFRONTIER following a quasi-random “Sobol” scheme. These results, collected in a simple table, were post-processed within modeFRONTIER: only 1700 out of the 10000 designs were kinematically feasible. Within this subset, only 15 are also satisfying the relatively strict opening time, holding force and three contact stress constraints. This result in itself confirmed the difficulty in obtaining good designs through simple techniques such as DOE sampling, and the complete impossibility to tackle the problem with a traditional “trial-and-error” approach. Instead, a designer should rather use more sophisticated techniques such as optimization algorithms.

Figure 4: Latch holding force with respect to opening time results from the MOGA-II optimization study. Yellow solutions are not respecting assigned constraints. Highlighted designs indicate those used in robustness analyzes.

Accordingly to these considerations, the 15 promising configurations found were then used as an initial population to start the modeFRONTIER Genetic Optimization Algorithm (MOGA-II), by simply switching an option in the Figure 3 workflow. MOGA-II mimics evolution in biological species: it is able to focus the search on the most promising species (designs) that better adapts to the environment requests (objectives and constraints). The results of such optimization campaign are represented in Figure 5, where the axis are the two main objectives to be minimized, and each point a CAE solution. The optimization succeeded in finding several promising solutions that respects the constraints (black points), and represent different trade-offs between the four objectives simultaneously. All these points are belonging to the so-called “Pareto Frontier”, which represents the set of optima in a truly multi-objective search.

At this stage, the robust design optimization concept comes in. In fact, the standard multi-objective optimization described so far found a large set of optima: that is already a very good result, given the difficulty of finding proper solutions to the challenge. Between this set of optima (trade-offs between the objectives), a designer can easily select the most diverse ones in terms of input variable values, thanks to data clustering capabilities of modeFRONTIER (see green colored designs in Figure 4): they represent the optimal solutions of the challenge, without considering the stability of their performances.
The idea is to use these ten solutions as starting points for an other MOGA-II optimization, that now should include the design stability itself as a target: a robust design optimization. In robust design optimization the deterministic values of performance criteria are replaced by their mean and standard deviation values, which can then be separately optimized. The following input parameters (see Figure 2) A1, MR_r, L_l, L_r, µ1, µ2, are considered to behave stochastically causing the performance uncertainty, and are assigned normal distributions. Moreover, the three revolute joint frictions were allowed to vary with uniform distributions. All the remaining variables are still considered as deterministic ones.

Figure 5: MOGA-II minimization results of holding force and latch response time standard deviations while subject to respective means and stress constraints

The size of the stochastic input sampling set should be big enough to guarantee the statistical validity of the conclusions, but should cope with computational time limitation. In fact, robust design optimization requires a non-trivial amount of computational time, even with a short simulation time for a single evaluation, since each individual design needs to be simulated multiple times in order to achieve statistically significant estimates for the outputs. For this reason, a relatively small 50-design sized modeFRONTIER’s “Latin Hyper-cube” sampling has been used for the stochastic inputs: it is capable to approximate accurately the prescribed multi-dimensional normal distributions also with few samples.
Conversely, a sophisticated “Polynomial Chaos” expansion scheme is available to improve the accuracy in the esteem of both the mean and the standard deviation of the output distributions (that derives from the small-sized sampling of the stochastic inputs). After 150 deterministic optimization steps, several designs with reduced latch time and holding force standard deviations were found that are still capable of satisfying all constraints: in Figure 5 bubble chart all the objective standard deviations and means are plotted together.

Designs 1 through 4 are highlighted for their respective minimums of latch time standard deviation, latch time mean, holding force standard deviation and holding force mean. Design 2 was among those selected in the initial MOGA-II population, resulting from the previous deterministic-only optimization. Such four latch designs are the four robust design solutions that have been brought to the further steps of the whole Circuit Breaker mechanism design.

Conclusions
This article demonstrates the process and benefits of adding multi-objective optimization and robustness analysis in the early stages of the product design, by linking available computational models. In this case, even finding a design that simultaneously meets all the constraints while having acceptable performance, represents a challenging process. modeFRONTIER achieved this in a more than reasonable timeframe, allowing ABB engineers to focus on the results analysis and on the trade-off decision process. Moreover, it also encapsulates the search for robust designs: this concept is especially important for the design of devices which are to be incorporated into public safety systems or critical infrastructure, such as high voltage circuit breaker drives. A final remark should be done regarding robust design optimization in all the design processes involving numerical models with longer simulation time. modeFRONTIER offers also Response Surface Models that are able to interpolate accurately available data, and hence replace long simulations with almost instantaneous design performance forecasts. This enables a robust design approach also for longer runtime simulation models.

Acknowledgments

Dr. Sami Kotilainen - ABB Switzerland
Dr. Ryan Chladny - ABB Corporate Research Germany
Dr. Luca Fuligno - EnginSoft Italy