Comparison of nongradient methods with hybrid Taguchi-based epsilon constraint method for multiobjective optimization of cylindrical fin heat sink

The primary aim of the paper is to compare the different nongradient methods of multiobjective optimization for optimizing the geometry parameters of a cylindrical fin heat sink. The methods studied for comparison are Taguchi-based grey relational analysis, ε (epsilon) constraint method and genetic algorithm. The various responses that have been studied are electromagnetic emitted radiations, thermal resistance and mass of the heat sink. Since the responses are obtained using complex simulation softwares (HFSS—Ansoft for emitted radiations and CFD—Flotherm for thermal resistance), there is no way of calculating the derivates of the objective functions. Hence, the Taguchi design of experiments design is used to derive the linear regression equations for the responses studied, which are then taken as the objective functions to be optimized. A new hybrid method known as Taguchi-based epsilon constraint method has been proposed in this paper for obtaining nondominated Pareto solution set. The results obtained using the proposed method show that the Pareto optimal set is competitive in terms of diversity of the solutions obtained. It is not likely that there exists a solution, which simultaneously minimizes all the objectives using any of the multiobjective techniques implemented. The value path analysis has been done to compare the trade-off among the design alternatives for the chosen multiple objective parameter optimization problem.     

Modeling and simulation of a parallel plate heat sink using computational fluid dynamics

Desktop computers have changed to accommodate increasing power, approaching 100 W. Heat dissipation becomes a significant issue in efficiency promotion and stable operation of air-cooled microelectronics and power electronics components and assemblies. Finned heat sinks are commonly used devices for enhancing heat transfer from air-cooled microelectronics and power electronics components and assemblies. The use of finned heat sinks increases the effective surface area for convective heat transfer, reducing the thermal resistance and operating temperatures in air-cooled electronics. The task of selecting the best heat sink for a particular application from the hundreds of configurations available from the various manufacturers can be a formidable task for an engineer. In a typical heat sink design, the objective is to achieve target heat dissipation, while restricting the consumption of valuable resources such as mass, fan power, pressure drop, and space claim. In this research work, preliminary studies have been carried out for the performance improvement of a parallel-plate heat sink considering the various geometric parameters, such as number of fins, fin length, fin height, and base height. The modeling and simulation of the heat sink is carried out with the computational fluid dynamics package. The results are analyzed using analysis of variance and response graphs.     

Geometry optimization of a cylindrical fin heat sink using mine blast algorithm

The heat sinks are utilized in electronic devices to eliminate heat from the chip and efficiently transmit it to the environment. Therefore, the optimal geometry sizes of fin heat sinks are the point of concern for manufacturers and designers. For this reason, the importance of optimization techniques particularly metaheuristics is understood. The design variables are width of heat sink, number of fins, fin height, and fin diameter. The various responses that have been considered are electromagnetic emitted radiations, thermal resistance, and mass of the heat sink investigated separately and simultaneously (multi-objective). Mine blast algorithm (MBA), as a recently developed optimizer, is inspired from explosion of mines. The optimum dimensions and values for each response have been obtained by the MBA and have been compared with other optimization methods in the literature. In terms of thermal resistance and mass responses, the MBA has offered better values, while for the emitted radiations, the obtained results obtained by Taguchi-based gray relational analysis (TGRA) was preferred. For manufacturing point of view, the MBA and TGRA both suggested better and efficient design. In addition, the value path analysis has been carried out to compare the trade-off among the considered responses. Finally, parametric sensitivity analyses have been implemented for design parameters, and discussions and comparisons have been carried out for the effects of each decision variable. By considering all responses, width of heat sink and fin height are considered as the most important and effective design parameters, respectively.     

Multi-objective optimization using Taguchi based grey relational analysis for micro-milling of Al 7075 material with ball nose end mill

This study was carried out to understand micro-milling of aluminum material with ball nose end mill and consisted of four stages: experimental work, modelling, mono and multi objective optimization. In the first stage (experimental work), micro-milling experiments were carried out using Taguchi method. The effects of spindle speed, feed per tooth and depth of cut on tool wear, force and surface roughness were investigated. Cutting tools and workpiece surfaces were also inspected via scanning electron microscope. Adhesion and abrasion wear mechanisms during micro-milling of aluminum were observed. Workpiece surfaces had the accumulations of plastically deformed workpiece material due to the high ductility of aluminum. In the second stage (modelling), all data gathered in the experimental works were utilized to formulate first-order models with interaction. These first-order models with interaction could be used to predict responses in micro-milling of aluminum with a minor error. In the third stage (mono-objective optimization), responses were used alone in optimization study as an objective function. To minimize all responses, Taguchi’s signal to noise ratio was used. The effect of control factors on responses was determined by analysis of variance. In the fourth stage (multi objective optimization), responses were optimized simultaneously using grey relational analysis.     

Multi-objective optimization of cutting parameters in high-speed milling based on grey relational analysis coupled with principal component analysis

This paper investigates optimization problem of the cutting parameters in high-speed milling on NAK80 mold steel. An experiment based on the technology of Taguchi is performed. The objective is to establish a correlation among spindle speed, feed per tooth and depth of cut to the three directions of cutting force in the milling process. In this study, the optimum cutting parameters are obtained by the grey relational analysis. Moreover, the principal component analysis is applied to evaluate the weights so that their relative significance can be described properly and objectively. The results of experiments show that grey relational analysis coupled with principal component analysis can effectively acquire the optimal combination of cutting parameters and the proposed approach can be a useful tool to reduce the cutting force.     

基于灰色关联分析的电火花加工不锈钢小孔工艺参数优化

采用DS307A高速穿孔机,开展在6mm厚不锈钢板上加工直径为1.2 mm小孔的试验研究。运用正交试验法,研究电火花加工电参数对加工时间、电极损耗和加工间隙的影响,并对试验结果进行灰色关联分析,得出最优加工参数。结果表明,经参数优化后,减少了加工时间、降低了电极损耗,以及表面粗糙度得以明显改善,满足快速精加工的技术要求。     

整体翅片叉排热管散热器的传热特性研究

针对三维坐标系下,整体翅片叉排热管散热器的流动和传热特性进行数值模拟研究.分析了四个主要影响因素:翅片间距、翅片厚度、排间距和管排布对努塞尔数、流动摩擦因数和热阻的影响.管排布分别为4-3叉排和3-2叉排,翅片间距分别为6mm、7mm和8mm,翅片厚度分别为0.8mm、1mm和1.2mm,排间距分别为20mm、24mm和28mm.计算结果表明:随着翅片厚度的增加,摩擦因数减小,换热能力增强,热阻有所上升;随着翅片间距的增大,摩擦因数增大,换热能力提高,而热阻基本为增加趋势;当热管排列方式从4-3叉排变为3-2叉排后,摩擦因数增加,但Re较大时,摩擦因数趋于相同,换热能力明显下降,但热阻呈下降趋势.     

Multi-objective optimization of surface roughness and cutting forces in high-speed turning of Inconel 718 using Taguchi grey relational analysis (TGRA)

In this paper, a new effective approach, Taguchi grey relational analysis has been applied to experimental results in order to optimize the high-speed turning of Inconel 718 with consideration to multiple performance measures. The approach combines the orthogonal array design of experiments with grey relational analysis. Grey relational theory is adopted to determine the best process parameters that give lower magnitude of cutting forces as well as surface roughness. The response table and the grey relational grade graph for each level of the machining parameters have been established. The parameters: cutting speed, 475?m/min; feed rate, 0.10?mm/rev; depth of cut, 0.50?mm; and CW2 edge geometry have highest grey relational grade and therefore are the optimum parameter values producing better turning performance in terms of cutting forces and surface roughness. Depth of cut shows statistical significance on overall turning performance at 95% confidence interval.     

Multi-response optimization using the Taguchi-based grey relational analysis: a case study for dissimilar friction stir butt welding of AA6082-T6/AA5754-H111

This paper presents a multi-response optimization process for dissimilar friction stir welding of AA6082/AA5754 aluminum alloys. An L₉ orthogonal array was constituted for the experiments. Three welding parameters—tool shoulder diameter-to-pin diameter (D/d) ratio, tool rotational speed (TRS), and welding speed (WS)—were associated with tensile strength and elongation. An optimization process was started to determine the signal-to-noise (S/N) ratio. Grey relational analyses were performed utilizing the S/N ratio. According to the results of a series of analyses, the optimal welding condition was determined as 4 for D/d, 1,000 rpm for TRS, and 100 mm/min for WS. The analysis of variance results showed that all the welding parameters are statistically significant at 95 % confidence level. Additionally, the joint efficiency of welding fabricated at the optimal condition was compared for both AA6082 and AA5754. This revealed that the joint efficiency is 66 % for AA6082 and 92 % for AA5754.     

翅片热板散热器的传热数值模拟研究

采用有限元法,应用ANSYS软件的热分析功能对翅片热板散热器的传热性能进行了数值模拟,并计算出该散热器表面的瞬态温度变化曲线,与实验测试结果吻合得较好.最后的研究结果表明:所研制的新型功率电子元器件翅片热板散热器散热性能良好,具有良好的启动性能和等温性能.     

翅片热板散热器的传热研究

在已设计的翅片热板散热器基础上进行了传热性能实验,对于充装不同工质、工质充装量、翅片热板散热器的工作方式等因素都进行了较深入的传热测试,分析这些因素对翅片热板散热器传热性能的影响.同时对翅片热板散热器的瞬态和稳态传热性能也进行了实验测试,分析了瞬态、稳态表面温度变化曲线,并进行了传热性能比较分析,讨论了工质充装量、倾斜角度等对翅片热板散热器传热性能的影响.     

Taguchi-based grey relational analysis for modeling and optimizing machining parameters through dry turning of Incoloy 800H

The present research focused on the optimization of machining parameters and their effects by dry-turning an incoloy 800H on the basis of Taguchi-based grey relational analysis. Surface roughness (Ra, Rq and Rz), cutting force (Fz), and cutting power (P) were minimized, whereas Material removal rate (MRR) was maximized. An L ₂₇ orthogonal array was used in the experiments, which were conducted in a computerized and numerical-controlled turning machine. Cutting speed, feed rate, and cut depth were set as controllable machining variables, and analysis of variance was performed to determine the contribution of each variable. We then developed regression models, which ultimately conformed to investigational and predicted values. The combinational parameters for the multiperformance optimization were V = 35 m/min, f = 0.06 mm/rev and a = 1 mm, which altogether correspond to approximately 48.98 % of the improvement. The chip morphology of the incoloy 800H was also studied and reported.     

Optimization of EDM process for multiple performance characteristics using Taguchi method and Grey relational analysis

Electrical discharge machining (EDM) is one of the most extensively used non-conventional material removal processes. The Taguchi method has been utilized to determine the optimal EDM conditions in several industrial fields. The method, however, was designed to optimize only a single performance characteristic. To remove that limitation, the Grey relational analysis theory has been used to resolve the complicated interrelationships among the multiple performance characteristics. In the present study, we attempted to find the optimal machining conditions under which the micro-hole can be formed to a minimum diameter and a maximum aspect ratio. The Taguchi method was used to determine the relations between machining parameters and process characteristics. It was found that electrode wear and the entrance and exit clearances had a significant effect on the diameter of the micro-hole when the diameter of the electrode was identical. Grey relational analysis was used to determine the optimal machining parameters, among which the input voltage and the capacitance were found to be the most significant. The obtained optimal machining conditions were an input voltage of 60V, a capacitance of 680pF, a resistance of 500Ω, the feed rate of 1.5μm/s and a spindle speed of 1500rpm. Under these conditions, a micro-hole of 40μm average diameter and 10 aspect ratio could be machined.     

Application of Taguchi-based gray relational analysis for evaluating the optimal laser cladding parameters for AISI1040 steel plane surface

The effect of various laser cladding process parameters like laser power, scan speed, and powder feed rate on clad bead quality characteristics (or clad bead geometry) for AISI 1040 steel substrate have been studied by performing a number of experiments with L ₉ orthogonal array. In order to find the process parametric setting for best quality clad bead based on experimental results, a multiresponse optimization technique using gray relational analysis (GRA) is presented in this paper. The GRA is applied on laser cladding process to find out the gray relational grade for each experiment. On optimization, power of 1.25 kW, scan speed of 0.8 m/min, and a powder feed rate of 11 gm/min have been found to be the best parametric setting for laser cladding operation of AISI 1040 steel substrate. Moreover, the analysis of variance is also performed to determine the contribution of each control factor on the clad quality characteristics. Finally, to ensure the robustness of GRA, a confirmatory test is performed at selected optimal parametric setting.     

平板多孔零件公差标注分析

分析尺寸差与形位公差对平板多孔零件质量的影响，结论是采用位置度标注公差方法将给该类零的设计和加工带来许多方便。     

Multi-objective optimization of air bearings using hypercube-dividing method

The commonly used genetic algorithm (GA) in solving a multi-objective optimization problem (MOOP) is replaced by the hypercube-dividing method (HDM) in this air bearing optimization study. In the new method the dividing of hypercubes in the design space is conducted based on the size and Pareto rank of hypercube. A comparison of the HDM- and GA-based method for the MOOP is performed. The results show that the solution obtained by the HDM is improved with more selections and less computing load. The search in the HDM can also be confined to some useful resolution to improve its global search capability.     

Multi-objective optimization and sensitivity analysis of tube hydroforming

Tube hydroforming is a manufacturing process used to produce structural components in cars and trucks, and the success of this process largely depends on the careful control of parameters such as internal pressure and end-feed force. The objective of this work was to establish a methodology, and demonstrate its effectiveness, to determine the optimal process parameters for a tube hydroformed in a die with a square cross section. The Taguchi method was used to establish a design of virtual hydroforming experiments, and numerical simulations were carried out with the finite element code LS-DYNA®. A sensitivity analysis was also carried out with analysis of variance. Multi-objective functions that consider necking/fracture, wrinkling, and thinning were formulated, and the response surface methodology was used with the most sensitive factors to obtain a defect-free part. An objective function, based on the final corner radius in the part, was also included in the optimization model. The forming severity of virtual hydroformed parts was evaluated using the forming limit stress diagram and the forming limit (strain) diagram. Finally, the normal-boundary intersection method and the L ₂ norm were used to obtain the Pareto-optimal solution set and the optimal solution within this set, respectively. The hydroforming process for this part was also optimized using the commercial optimization software LS-OPT®, with two different single-objective algorithms. However, the optimum load path predicted with the proposed methodology was shown to achieve a smaller corner radius. The proposed optimization technique helped to define a process window that leads to a robust manufacturing process and improved part quality.     

60MN力标准机承压板结构多目标拓扑优化研究

针对60 MN力标准机承压板结构轻量化拓扑优化时,既要求结构的刚度最大化又要求结构的低阶固有频率最大化的多目标拓扑优化问题,提出了针对多个目标采用加权平均的方法把多目标优化问题转化为单目标优化问题。通过对选定的多个低阶固有频率目标函数采用加权求平均频率的方法实现了承压板结构的动态特性优化;采用加权平均的方法确定了刚度和频率的综合目标函数,实现了承压板结构的多目标拓扑优化,最终设计出了一种新的承压板结构。研究结果表明,优化后的承压板结构的最大变形量减少了25.5%,最大应力减少了14.1%,前五阶固有频率增加了5.7%~13.2%;可以看出新的承压板结构的前五阶固有频率和静态刚度均得到显著提高,从而验证了该优化方法的可行性。     

Multi-objective optimization of green sand mould system using evolutionary algorithms

The quality of cast products in green sand moulds is largely influenced by the mould properties, such as green compression strength, permeability, hardness and others, which depend on the input (process) parameters (that is, grain fineness number, percentage of clay, percentage of water and number of strokes). This paper presents multi-objective optimization of green sand mould system using evolutionary algorithms, such as genetic algorithm (GA) and particle swarm optimization (PSO). In this study, non-linear regression equations developed between the control factors (process parameters) and responses like green compression strength, permeability, hardness and bulk density have been considered for optimization utilizing GA and PSO. As the green sand mould system contains four objectives, an attempt is being made to form a single objective, after considering all the four individual objectives, to obtain a compromise solution, which satisfies all the four objectives. The results of this study show a good agreement with the experimental results.