Lightweight Frame Topology Optimization Method Based
DJournal of Materials Science and Engineering B 8 (3-4) (2018) 49-55doi: tweight Frame Topology Optimization MethodBased on Multi-objectiveRui Lyu1, Hai Liu2 and Dongying Ju11. Department of Electronic Science and Engineering, Saitama Institute of Technology University, Fukaya 369-0293, Japan2. School of Mechanical Engineering, He Bei University of Technology, TianJin 300387, ChinaAbstract: The application of new materials is an important direction for automotive lightweighting. On the basis of ensuring thecomprehensive performance of components, the optimization of new material structures through topology optimization methods canfurther improve the level of lightweight components. This paper takes the automobile frame as the research object, based on themagnesium alloy, studies the frame topology with the objective function of mass and strength under multiple working conditions, andrealizes the lightweight of the automobile frame structure through the multi-objective topology optimization method. According tothe topological optimization method of penalty function for solid isotropic materials, the objective function of the quality topologyoptimization and the objective function of intensity topology optimization under multi-operating conditions are defined by thecompromised programming approach. This method avoids the disadvantage that single-target topology optimization cannot considerother factors and is suitable for multi-objective topology optimization of continuum structures.Key words: Frame, multi-objective topology optimization, magnesium alloy, lightweight.1. Introduction In recent years, the crisis of energy and theenvironment has accelerated the strict control ofnational governments’ energy consumption andemissions from the automotive industry with thecontinuous development of modern industry. By 2020,the fuel consumption of passenger vehicles incountries and regions other than the United States willbe strictly limited to 5 L/100km and the carbonemissions will be more stringent (domestic at 2020).The use of national VI emission standards will forcethe lightweight design of automobiles to become oneof the necessary ways to improve energy consumption.The future direction of automotive lightweightingincludes the systematic design and integration ofoptimized design methods for automotive structuralparts, multi-material integration, and lightweightingtechnologies. Therefore, the use of modernoptimization methods to improve the design ofCorresponding author: Dongying Ju, professor, researchfields: material processing, mechatronics.automotive lightweight structural parts can achievemultiple goals of reducing vehicle energyconsumption, reducing emissions and improving theoverall performance of the vehicle [1-3].In the early conceptual design process ofmechanical structures, given the design goals andconstraints, finding the best and most likely producttopology or material layout is very important for thedevelopment of new products. The topologyoptimization of the continuum structure can providedesigners with a conceptual design scheme at theinitial stage of the engineering structure design, so thatthe structure can be optimized in terms of layout,thereby changing the previous design, verification,and revision of an ever-repeated development process.Compared with structural optimization and shapeoptimization, topology optimization of continuumstructures can achieve greater economic benefits. It isconsidered to be a more challenging field and hasbecome a popular topic in structural design researchtoday.This article focuses on the lightweight of the
Lightweight Frame Topology Optimization Method Based on Multi-objective50automobile frame, applies the topology optimizationtheory, and studies the lightweight structure of theautomobile. Through the rational and accurate designof the structure, the main bearing components of theautomobile frame are optimized and strengthened, andthe strength is satisfied. At the same time, the size ofthe cross-section is reduced, material thickness isimproved to achieve lightweight design.2. Multi-objective Topology OptimizationTheory SetupThe most common topology optimization is thevariable density material interpolation method, whichincludes SIMP and RAMP. The theory of variabledensity is to convert the discrete optimization probleminto a continuous optimization problem by intermediate density unit does not exist and cannot bemanufactured. Therefore, the intermediate density unitshould be reduced as much as possible, the number ofwhich needs to be penalized only for the intermediatedensity that appears in the design variables [4].The most commonly used material interpolationmodel method, SIMP formula, is expressed as:(1)where E0 is the initial elastic modulus; p is the penaltyfactor, p 1;is the density value of the materialat .2.1 Topology Optimization Function with Quality asIts l optimization model of the frame wasestablished with the strain energy as the constrainedmass as the optimization goal. At each load condition,a structural strain energy is used to replace all stressconstraints on all elements, and the method is used toobtain the strain energy required for the structure.According to the ICM optimization method proposedby YunkangYan [9], for the continuum structure, theMass is taken as the objective function, and thestructure of the individual working conditions needs tobe used as the constraint, and the structural topologyoptimization formula model is shown below:min01s. t.1, , ;(2)1,,where t is the element topology design variable vector;E is the elastic modulus; N is the number of unittopology design variables; W is the structural weight;is the strain energy of the i-th cell.In this paper, under the two working conditions ofbending and torsion, and the constraints of eachworking condition are different, different topologystructures are obtained through topology optimization.Therefore, multi-quality topology optimization is amulti-objective topology optimization problem. Thetraditional multi-objective optimization problem useslinear weighting and the multi-objective problem ofthe paradigm is transformed into a single-objectiveproblem. However, for the non-convex optimizationproblem, this method cannot ensure that all paretooptimal solutions are obtained [5]. This question usesthe compromise planning method to studymulti-objective topology optimization problems.Therefore, the objective function of mass topologyoptimization under multiple operating conditions isobtained.min(3)where m is the total load conditions; n is the totalnumber of units;is the weight of the k-th workingcondition; q is the penalty factor, q 2;is thequality objective function of the k-th workingcondition;andare the maximum andminimum values of the quality objective function ofthe k-th working condition, respectively.
Lightweight Frame Topology Optimization Method Based on Multi-objective2.2 Topology Optimization Function with Intensity asIts GoalIn isotropic materials, Von Mises stress is the mostcommonly used criterion. For planar problems, VonMises stress is defined as:VMIn the formula,andthe x and y directions, and3/51steady state is reached under the effect of the erasurerate, an evolution rate EP is introduced toincrease the original erasure rate. As shown in Eq. (6),the structure is optimized under the new erasure rate[6]. When the desired optimization goal is reached,stop iterative optimization.(4)(6)are normal stresses inis the shear stress.2.3 Multi-objective Topology Optimization Functionwith Quality and Strength IndicatorsThe stress valueof each cell will becompared with the maximum valueof all thestress, and all cells that satisfy the following formulawill be retained.(5)wherein the formula is the current deletion rate,which is a gradually changing quantity, and thestructure is optimal after multiple iterations. WhenIn the multi-objective topology optimization of thestructure, the stiffness is taken as the constraint, thetopological optimization of the quality and strengthtargets in static multi-operating conditions is alsoperformed. The objective function of multi-objectivetopology optimization is obtained by combining thethird-intensity theory with the compromise planningmethod:1(7)whereandare the maximum and minimumstress value of the frame.requirements of new energy electric vehicles. The3. Multi-objective Topological OptimizationModel of Lightweight Frame Structureis shown in Fig. 1. This model was divided into 0.53.1 The Establishment of Topology OptimizationModelon both sides of the main beam at the rear of the frame;CAE model of the new energy electric vehicle framemm-sized tetrahedral meshes using hypermesh, a totalof 32,826 units; it is loaded with 35 kg motor, actingpassengers and goods are 350 kg, on the middle of theThis research model refers to the subaru-sanbaframe; the body is 150 kg, as indicated by the greenframe model currently on the market for researcharrow in Fig. 2; the support points are the 8 hinges ofpurposes. This frame is an un-load body. In thethe triangle in Fig. 2. Detailed loading conditions areoriginal car, components such as engine, steering gearshown in Fig. 2.and transmission are mounted on this frame. All partsMagnesium alloy material was selected as theare connected to the frame through brackets, and thelightweight material of the frame, and referenced toweight of the entire body is loaded on various parts ofotherthe frame. This article is to modify the frame on themagnesium alloy frame topology optimization designbasis of the original car to meet the strengthwas carried out to achieve the goal of lightweight frame.conventionalmaterials,amulti-objective
Lightwweight Framee Topology Optimization MethodMBasedd on Multi-obbjective52to achieveathe gooal of light wweighting.3.2 Frame Topollogy Optimizaation AnalysiisFig. 1TakingTinto account the acctual operatioon of the car,,the frame operaating modes mainly incllude bendinggconnditions and twistingtmodees, showed inn Table 2, sooin thhe frame topology optimization designn process, weeshould take intto account thhe impact ofo the actuallopeerating modess.Framme finite elemennt model.4. Lightweigght Framee Design Based onnMuulti-objectivve Topologgy OptimizaationFig. 2Load and constrainnt boundary coonditions.The frame materialmis thhe three mateerials in Tablle 1.The ultimaate goal of this paper is to perfformtopological optimizatioon analysis of the frramestructure unnder the magnesium alloyy AZ91 mateerial,and the reesults obtained are commpared with thestrength ressults and quuality resultss of the currrentSPFH540 stteel and T60061 aluminumm alloy materialsTable 1Thee mechanical propertiespof AluminumA,Steeel and Magnesium.SSPFH540Density (kg/mm³)Coefficient off elasticity (GPaa)Poisson ratioYield strengthh (MPa)Tensile strenggth (MPa)Table 76310MagnesiumAZ911,830450.35160340Connstrained posittion for each workingwcondition[7].Suspension poositionLeft front susppensionRight front suuspensionLeft rear suspensionRight rear susspensionTable 3BasedBon the multi-objectiive topology optimizationntheoory and the liightweight fraame finite eleement model,,a custom functiion providedd in optistrucct is used toodefifine the comppromise plannning formula and strengthhtheoory formula in this papper. The muulti-objectiveetopoology is propposed by usinng the customm function innoptiistruct whichh is used as an objectivee function tooperfform topologgy optimizatiion. Becausee the load offun-load body mostlymacts onn the two maain beams offthe frame, this paper mainlyy analyzes annd optimizessthe section of thee main beam of the frame [8].BendingBx y, zx,x zx,y zy,zTorsionx, y, zx, zy, zThrree kinds of maaterials analyssis results.SSpfh540Mass (kg)Displacementt (mm)Stress umAZ91428.43349.5
Lightweight Frame Topology Optimization Method Based on Multi-objective53(a) Displacement and stress of steel(b) Displacement and stress of aluminum alloy(c) Displacement and stress of magnesium alloyFig. 3Three kinds of materials analysis results.The strength analysis of the above three differentmaterials was carried out and based on the calculationresults of Spfh540 steel and T6061 aluminum alloystrength, the design goals of the magnesium alloyframe were determined. Fig. 3 shows the stress anddeformation of the three materials. Beforeoptimization, according to the properties of thematerial, only the Sphf540 steel material meets therequirements in terms of displacement and stress andmeets the actual requirements.Table 3 compares the deformation and stress of thethree materials and determines the target values ofdisplacement and stress under magnesium alloymaterials.In this study, due to reference to the frame of theexisting vehicle model, the optimized optimizationfunction of the optistruct is applied under thecross-sectional conditions of the main beam, and thesection of the main frame beam is mainly optimized toachieve the best section size. In the static topologyoptimization of the frame, two kinds of workingconditions are considered, namely bending conditionsand torsional conditions. The two working conditionsare equally important, and the weights of all workingconditions are 0.5. Similarly, in the multi-objectivetopology optimization synthesis function, the weightof the intensity is 0.4 and the weight of the qualitygoal is 0.6 [9, 10].
Lightweight Frame Topology Optimization Method Based on Multi-objective54Fig. 4 shows the iterative process of ons. It is shown in the iteration processing thefigures, the section thickness of the main beamincreases or decreases in different degrees, amongwhich Fig. 4d is the optimal topology.Fig. 5 shows the iterative curve of the maximumstress value of the frame under both bending and(a) Iteration k 1torsion conditions. With the increase in the number ofiterations, the stress is always maintained below themagnesium alloy material yield strength (160 MPa),which is 33.4 MPa and 104 MPa, satisfying thestructural strength requirements.Fig. 6 shows the quality optimization curve for thebeam in the design area. With the increase in thenumber of iterations, the mass Mass decreases gently.After the 18th iteration, the mass Mass stabilizes andeventually reaches 27 kg. Since the weight of theun-designed area beam is 6 kg, the total mass of theoptimized frame is 33 kg. As shown in Table 4, beforethe optimization of the frame, the density of themagnesium alloy is the smallest, so the unoptimizedmagnesium alloy frame has a weight reduction of76.7% and 31.1%, respectively, compared with thesteel and aluminum alloy materials, initially achievedthe purpose of lightweight frame. Aftermulti-objective topology optimization in this paper,while satisfying the stress intensity, the mass ratio isreduced by 21.4% before optimization, which meansthat the goal of lightening the frame is achieved.120100Von Mises (Mpa)(b) Iteration k 580Bending60Torsion402000Fig. 41020Iteration30(c) Iteration k 15Fig. 5Multi-condition stress iteration graph.(d) Iteration k 30Car frame iteration diagram.Fig. 6Mass iterative graph.40
Lightweight Frame Topology Optimization Method Based on Multi-objectiveTable 455Quality comparison.MaterialsFrame mass(kg)Mg optimize weight loss (%)SteelAl-AlloyMg 4%4. ConclusionInstitute of Technology University.(1) A multi-objective optimization theoreticalmodel was established that satisfies the strength andlight weight of the automobile frame.(2) The optimization study of the magnesium alloyframe was carried out based on the strength targets ofdifferent materials, and the strength analysis results ofthree different materials were compared, and themultiple goals of strength and mass of the magnesiumalloy frame were determined; For the purpose ofdesigning variables, satisfying strength and lightweight, a topological optimization analysis wasperformed on the frame.(3) Taking into account the actual operatingconditions of the car, the topology optimizationanalysis of the vehicle frame takes into account thebending and torsion conditions of the vehicle andrealizes the optimization of the vehicle frameperformance with multiple operating conditions andmultiple objectives. According to the analysis results,after using the magnesium alloy material forreplacement and analyzing the topology of theautomobile frame structure, the goal of reducing theweight of the automobile frame can be achieved whilesatisfying the frame strength requirements. Theoptimized magnesium alloy frame is 81% lighter thanthe original steel frame.ReferencesAcknowledgmentsThis material is based on the work supported by theLight Weighting Electric Vehicle Project of Saitama[1]Kiani, M., and Gandikota, I. 2014. “Design ofLightweight Magnesium Car Body Structure under Crashand Vibration Constraints.” Journal of Magnesium andAlloys 2: 99-108.[2] De Gaetano, G., Mundo, D., Maletta, C., Kroiss, M., andCremers, L. 2015. “Multi-objective Optimization of aVehicle Body by Combining Gradient-Based Methodsand Vehicle Concept Modelling.” Present at Case Studiesin Mechanical Systems and Signal Processing, 1-7.[3] Porro, R. 1998. “The Innovative Use of Magnesium inCar Design and an Analysis of Cost Versus WeightSavings.” SAE Paper, 980084.[4] Fan, W. J., Fan, Z. J., and Su, R. Y. 2007. “Research onMulti-objective Topology Optimization Method on BusChassis Frame.” China Mechanical Engineering 29:1505-8.[5] Jiao, H. Y., Zhou, Q. C., Li, W. J., and Li, Y. 2013.“Periodic Topology Optimization Using Variable DensityMethod.” Journal of Mechanical Engineering 7: 132-8.[6] Yao, F., and Wang, M. Q. 2007. “Evolutionary StructuralOptimization of Contimuum Structure Based onConstraints of Stress and Stiffness.” Journal of JiangsuUniversity of Science and Technology (Natural ScienceEdition 12: 39-43.[7] Xiang, X., Zuo, K., Xiang, Y., and Zeng, Z. 2012.“Multi-objective Topology Optimization Design on SUVFrame.” Computer Aided Engineering 10: 20-4.[8] Chiandusssi, G., Gaviglio, I., and Ibba, A. 2004.“Topology Optimization of an Automotive Componentwithout Final Volume Constraint Specigication.”Advances in Engineering Software 35: 609-17.[9] Sui, Y. K., and Ye, H. L. 2013. Continuum TopologyOptimization Methods ICM. Beijing: Science Press, 77-83.[10] Yin, Y. S. 2014. “Topology Optimization Methods ofContimuum Structure Based on Variable DensityMethod.” Northeastern University 7: 45-55.
Lightweight Frame Topology Optimization Method Based on Multi-objective 50 automobile frame, applies the topology optimization theory, and studies the lightweight structure of the automobile. Through the rational and accurate design of the structure, the main bearing components of
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