0412 Multi-Objective Optimal Design of Spur Gear Train Mechanisms using the Satisficing Trade-off Method

2013 ◽  
Vol 2013.50 (0) ◽  
pp. 041201-041202
Author(s):  
Ken IIJIMA ◽  
Takashi GOTO ◽  
Masayuki NAKAMURA
Author(s):  
Leonard P. Pomrehn ◽  
Panos Y. Papalambros

Abstract The use of discrete variables in optimal design models offers the opportunity to deal rigorously with an expanded variety of design situations, as opposed to using only continuous variables. However, complexity and solution difficulty increase dramatically and model formulation becomes very important. A particular problem arising from the design of a gear train employing four spur gear pairs is introduced and formulated in several different ways. An interesting aspect of the problem is its exhibition of three different types of discreteness. The problem could serve as a test for a variety of optimization or artificial intellegence techniques. The best known solution is included in this article, while its derivation is given in a sequel article.


2021 ◽  
Vol 11 (9) ◽  
pp. 3958
Author(s):  
Adrian Bekasiewicz ◽  
Slawomir Koziel ◽  
Piotr Plotka ◽  
Krzysztof Zwolski

Antenna structures for modern applications are characterized by complex and unintuitive topologies that are difficult to develop when conventional, experience-driven techniques are of use. In this work, a method for the automatic generation of antenna geometries in a multi-objective setup has been proposed. The approach involves optimization of a generic spline-based radiator with an adjustable number of parameters using a nested, trust region-based algorithm. The latter iteratively increases the dimensionality of the radiator in order to gradually improve its performance. The method has been used to generate a set of nine antenna designs, representing a trade-off between minimization of reflection within 3.1 GHz to 10.6 GHz and a reduction of size. The properties of the optimized designs vary along the Pareto set from −10 dB to −20 dB and from 230 mm2 to 757 mm2 for the first and second objectives, respectively. The presented design approach has been validated against a genuine, population-based optimization routine. Furthermore, the smallest Pareto-optimal design has been compared to the antennas from the literature.


Author(s):  
Jakob Weström ◽  
Xiaolong Feng ◽  
Hans Andersson ◽  
Stefan Lunderius

This article presents an automated approach in optimal design of the spring balancing cylinder of an industrial robot using multi-disciplinary and multi-objective design optimization. Spring balancing cylinder is a mechanical device typically used in industrial robots of high load handling capacity. The objective of use of such device is to effectively balance one of main axes (typically axis-2) subject to the most severe gravitational torque. The spring balancing cylinder consists typically of multiple springs (two or three) co-axially installed inside the cylinder. Design of such balancing device involves about 16 design parameters, including both geometric parameters (free length, wire diameter, spring outer diameter, and number of turns) and parameters defining mounting positions of the device on a robot. Optimal design of such device is to achieve desired balancing, measured by maximum unbalanced static torque of the balanced axis, with minimum weight and volume of the cylinder. More desirably, the trade-off relationship between the maximum static torque measured by a balancing degree index and weight of the balancing cylinder is explored. Design of such balancing device is subject to a number of hard constraints defining fatigue lifetime of the springs and geometric interference between adjacent springs both in radial and axial directions. Solving of this design problem requires use of two different design tools. The first design tool is a robot static design tool. The entire robot statics is modeled. The maximum static torque of the balanced axis is calculated by finding the maximum value of static torques of the axis as function rotational angles of the axis within its limits. The maximum static torque is used as one of the design objectives. The second design tool is a detailed spring dimensioning tool. The overall spring constant and pre-loading force are determined subject to constraints of geometric and fatigue lifetime. The integration of the design tools is accomplished using a commercial software tool modeFrontier. This challenging design problem is formulated into an optimization problem of mixed design variables, multi-objective and multi-constraint nature and solved fully automatically using Multi-Objective Genetic Algorithm (MOGA) implemented in the modeFrontier modeling and optimization environment. The trade-off relationship between the balancing degree and the weight of the springs have been quantitatively explored. Even though some limitations of the developed methodology do exist and need further improvement, it is convinced that the developed approach is ready to be applied in industrial design practice.


2012 ◽  
Vol 2012.22 (0) ◽  
pp. _2207-1_-_2207-7_
Author(s):  
Ken IIJIMA ◽  
Takashi GOTO ◽  
Kazuma FUJITA ◽  
Masayuki NAKAMURA
Keyword(s):  

1995 ◽  
Vol 117 (3) ◽  
pp. 419-424 ◽  
Author(s):  
L. P. Pomrehn ◽  
P. Y. Papalambros

The use of discrete variables in optimal design models offers the opportunity to deal rigorously with an expanded variety of design situations, as opposed to using only continuous variables. However, complexity and solution difficulty increase dramatically and model formulation becomes very important. A particular problem arising from the design of a gear train employing four spur gear pairs is introduced and formulated in several different ways. An interesting aspect of the problem is its exhibition of three different types of discreteness. The problem could serve as a test for a variety of optimization or artificial intelligence techniques. The best known solution is included in this article, while its derivation is given in a sequel article.


Author(s):  
Praveen Kumar Dwivedi ◽  
Surya Prakash Tripathi

Background: Fuzzy systems are employed in several fields like data processing, regression, pattern recognition, classification and management as a result of their characteristic of handling uncertainty and explaining the feature of the advanced system while not involving a particular mathematical model. Fuzzy rule-based systems (FRBS) or fuzzy rule-based classifiers (mainly designed for classification purpose) are primarily the fuzzy systems that consist of a group of fuzzy logical rules and these FRBS are unit annexes of ancient rule-based systems, containing the "If-then" rules. During the design of any fuzzy systems, there are two main objectives, interpretability and accuracy, which are conflicting with each another, i.e., improvement in any of those two options causes the decrement in another. This condition is termed as Interpretability –Accuracy Trade-off. To handle this condition, Multi-Objective Evolutionary Algorithms (MOEA) are often applied within the design of fuzzy systems. This paper reviews the approaches to the problem of developing fuzzy systems victimization evolutionary process Multi-Objective Optimization (EMO) algorithms considering ‘Interpretability-Accuracy Trade-off, current research trends and improvement in the design of fuzzy classifier using MOEA in the future scope of authors. Methods: The state-of-the-art review has been conducted for various fuzzy classifier designs, and their optimization is reviewed in terms of multi-objective. Results: This article reviews the different Multi-Objective Optimization (EMO) algorithms in the context of Interpretability -Accuracy tradeoff during fuzzy classification. Conclusion: The evolutionary multi-objective algorithms are being deployed in the development of fuzzy systems. Improvement in the design using these algorithms include issues like higher spatiality, exponentially inhabited solution, I-A tradeoff, interpretability quantification, and describing the ability of the system of the fuzzy domain, etc. The focus of the authors in future is to find out the best evolutionary algorithm of multi-objective nature with efficiency and robustness, which will be applicable for developing the optimized fuzzy system with more accuracy and higher interpretability. More concentration will be on the creation of new metrics or parameters for the measurement of interpretability of fuzzy systems and new processes or methods of EMO for handling I-A tradeoff.


Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2261
Author(s):  
Evgeniy Ganev ◽  
Boyan Ivanov ◽  
Natasha Vaklieva-Bancheva ◽  
Elisaveta Kirilova ◽  
Yunzile Dzhelil

This study proposes a multi-objective approach for the optimal design of a sustainable Integrated Biodiesel/Diesel Supply Chain (IBDSC) based on first- (sunflower and rapeseed) and second-generation (waste cooking oil and animal fat) feedstocks with solid waste use. It includes mixed-integer linear programming (MILP) models of the economic, environmental and social impact of IBDSC, and respective criteria defined in terms of costs. The purpose is to obtain the optimal number, sizes and locations of bio-refineries and solid waste plants; the areas and amounts of feedstocks needed for biodiesel production; and the transportation mode. The approach is applied on a real case study in which the territory of Bulgaria with its 27 districts is considered. Optimization problems are formulated for a 5-year period using either environmental or economic criteria and the remainder are defined as constraints. The obtained results show that in the case of the economic criterion, 14% of the agricultural land should be used for sunflower and 2% for rapeseed cultivation, while for the environmental case, 12% should be used for rapeseed and 3% for sunflower. In this case, the price of biodiesel is 14% higher, and the generated pollutants are 6.6% lower. The optimal transport for both cases is rail.


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