위상최적화와 적층제조의 결합을 통한 항공부품 개발

김태욱(Tae-Uk Kim) 대한기계학회 2021 대한기계학회 춘추학술대회 Vol.2021 No.4

적층 제조(Additive Manufacturing)는 기존 기계가공으로 제작이 힘든 형상을 구현할 수 있어, 경량 구조 개발 및 맞춤형 제작이 필요한 항공분야에서 활용도가 점점 높아지고 있다^(1~4). 적층 제조를 적용할 경우, 형상이 복잡하여 개념설계 단계에서 주로 활용하던 위상최적화(Topology Optimization) 결과를 최종 형상에 가깝게 제작할 수 있고, 중량 대비 하중지지 효율과 열전달 및 충격흡수 성능이 우수한 격자(Lattice) 구조의 활용도 가능해진다. 이 논문에서는 위상최적화를 통한 항공기 부품 경량 설계 및 적층 제조까지의 과정을 제시한다. 먼저 부품 제작 전에 해석 및 설계에 적용할 물성치를 확인하는 것이 필요한데, 적층 제조의 경우 기계적 성질이 적층 방향, 열처리와 HIP(Hot Isostatic Pressing) 등의 후처리 공정에 따라 달라지기 때문이다. 티타늄 합금 계열인 Ti6Al4V를 사용하여, 수직과 수평 방향, 열처리 및 HIP 공정 적용 여부에 따라 5 개씩의 시편을 제작하고, 인장시험을 수행하여 기본 물성 데이터를 확보하였다. 최적화를 적용한 대상은 착륙장치 구성품 중 토크링크(Torque Link)이며, 기존에는 단조로 제작하는 부품이다. 토크링크는 피스톤과 실린더를 연결하는 두 개의 링크가 핀으로 체결되는 구조인데, 응력해석 결과 추가적인 중량절감 가능성이 높은 것으로 판단되었다. 위상최적화는 SIMP(Solid Isotropic Material with Penalization) 기반의 Solver를 사용하는 상용 코드인 Altair OptiStruct를 이용하였다. 한편 Lattice optimization 은 2 단계로 이루어진다. 1 차 위상 최적화의 결과로 0(Void)과 1(Solid)사이의 Element density를 얻게 되는데 적절한 Threshold를 설정하여 중간 밀도 요소를 Beam으로 대체하고, 다시 Beam 요소의 두께 최적화 과정을 거쳐 최종 결과를 얻게 된다. Lattice optimization 결과는 기존 위상 최적화와 비교하여 뛰어난 중량절감 효과를 보이며, 이는 적층 제조와의 결합으로 얻는 장점으로 생각할 수 있다. 위상 최적화 결과를 적층 제조에 적용하기 위해 통상 STL(Stereolithography) 파일을 만들게 되는데, 이 과정에서 미세한 형상 수정 과정이 요구될 수 있다. 불규칙한 표면과 뾰족한 모서리를 수정하고, 최적화 과정에서 생성된 불필요한 미세 Hole 등을 제거하여 구조 성능에 영향을 주지 않는 범위에서 제작성을 향상시킨다. 특히 격자 구조 제작의 경우, Build simulation 단계에서 Support structure 가 필요한 영역이 확인된다면 이의 지지를 위한 보강 스킨을 추가로 생성해야 할 필요가 있다. 시제품은 DMLS(Direct Metal Laser Sintering) 방식의 EOS M290 장비를 사용하여, 일반 위상최적화 및 격자구조 최적화 모델을 각각 제작하였다. 시제품에 대해서는 구조시험을 수행하고 기존 제품과의 성능 비교를 통해 실제 적용 가능성을 확인하는 일이 추가로 필요하다. 또한, 적층 제조 방식의 항공부품 적용을 위해서는 공정 표준화를 통한 반복성 확인과 시험 및 인증 절차에 대한 연구가 병행되어, 제품 신뢰성을 확보할 수 있어야 한다. The topology optimization (TO) has been usually applied in the conceptual design stage, because the configurations from optimization results are too complex to produce by conventional machining process. The emergence of additive manufacturing (AM) makes it possible to realize TO results as near net shape, hence a combination of TO and AM is attracting increasing research interests. Aerospace field is also applying the AM technology to more parts development to achieve lightweight and customized designs. This paper presents a case study of the lightweight design of a landing gear part using TO and implementation via AM process.

위상 최적화 기법을 이용한 충격하중에 대한 차량 탑재형 전력변환장치의 마운트 경량화 설계

고동신,이현경,허덕재 한국전산구조공학회 2018 한국전산구조공학회논문집 Vol.31 No.6

In this study, it is describe to an optimization analysis process for the weight reduction of the voltage converter in the electric vehicle charging systems. The optimization design is a technique that finds the optimal material distribution under a given material quantity constraint by combining the design sensitivity with the material properties and the mathematical optimization. Among the topology optimization, a lightweight design is performed by a solid isotropic material with penalization with simple formula and well-convergence. The lightweight design consists of three steps. As a first step, a finite element model for the basic design of the on-board voltage converter was constructed and static analysis was performed on the load. In the second step, the optimum shape is obtained for the lightweight by performing the topology optimization using the solid isotropic material with penalization applying the stiffness coefficient of the isotropic material to the static analysis result. As a final step, impact analysis was performed by applying a half-sinusoidal pulse shape impact load which satisfies the impact test standard of the vehicle-mounted part with respect to the optimum shape. In the topology optimization, the design domain was defined as the mounting bracket area, and the design technology was finally achieved by optimizing the mounting bracket to achieve a weight reduction of 20% over the basic design. 본 연구는 전기자동차 충전시스템에서 전력변환장치의 경량화를 위한 최적화 분석프로세스에 대한 내용을 서술하였다. 최적화 설계는 재료 물성치에 대한 설계민감도와 수학적 최적화를 결합하여 주어진 재료량 제한조건 하에 최적의 재료분포를 찾는 설계기법으로 위상의 고정화, 자유도가 묶이는 문제 등을 해결할 수 있는 위상 최적화방법을 사용하였으며, 위상 최적화방법 중 비교적 수식화가 간단하고 수렴성이 좋은 SIMP법(solid isotropic material with penalization)에 의해 경량화 설계를 수행하였다. 경량화 설계는 3단계의 절차로 구성하였으며, 첫 번째 단계로 전력변환장치의 기본 설계에 대한 유한요소모델을 구성하고, 하중에 대한 정적해석을 수행하였다. 두 번째 단계로 정적해석 결과에 대해 등방성 재료의 강성계수를 적용한 밀도법을 이용하여 위상 최적화를 수행하여 경량화를 위한 최적 형상을 도출하였다. 세 번째 단계로 최적 형상에 대해 차량 탑재 부품의 충격시험기준에 만족하는 반정현파 펄스형태 충격하중을 인가하여 충격해석을 수행하였다. 위상 최적화단계에서 사용 환경조건으로 설계영역 정의는 마운팅 브래킷 영역으로 제한하였으며, 마운팅 브래킷의 설계 최적화를 통해 최종적으로 기본설계대비 20%이상의 경량화가 가능한 설계기술을 확보하였다.

신뢰성 해석을 이용한 차량 후드 보강재의 위상최적화

박재용(Jae-Yong Park),임민규(Min-Kyu Im),오영규(Young-Kyu Oh),박재용(Jae-Yong Park),한석영(Seog-Young Han) 한국생산제조학회 2010 한국생산제조학회지 Vol.19 No.5

Reliability-based topology optimization (RBTO) is to get an optimal topology satisfying uncertainties of design variables. In this study, reliability-based topology optimization method is applied to the inner reinforcement of vehicle's hood based on BESO. A multi-objective topology optimization technique was implemented to obtain optimal topology of the inner reinforcement of the hood. considering the static stiffness of bending and torsion as well as natural frequency. Performance measure approach (PMA), which has probabilistic constraints that are formulated in terms of the reliability index, is adopted to evaluate the probabilistic constraints. To evaluate the obtained optimal topology by RBTO, it is compared with that of DTO of the inner reinforcement of the hood. It is found that the more suitable topology is obtained through RBTO than DTO even though the final volume of RBTO is a little bit larger than that of DTO. From the result, multiobjective optimization technique based on the BESO can be applied very effectively in topology optimization for vehicle's hood reinforcement considering the static stiffness of bending and torsion as well as natural frequency.

유한요소 극한해석을 이용한 소성변형에서의 구조물의 위상최적화

이종섭(Jongsup Lee),허훈(Hoon Huh) 대한기계학회 2008 대한기계학회 춘추학술대회 Vol.2008 No.11

It is well known that the topology optimization for plastic problem is not easy since the iterative analyses to evaluate the objective and cost function with respect to the design variation are very time-consuming. The finite element limit analysis is an efficient tool which is possible to predict collapse modes and sequential collapse loads of a structure considering not only large deformation but also plastic material behavior with moderate computing cost. In this paper, the optimum topology of a structure considering large and plastic deformation is obtained using the finite element limit analysis. To verify the constructed optimization code, topology optimizations of some typical problems are performed and the optimal topologies by elastic design and plastic design are compared.

3-D Topology Optimization by a Nodal Density Method Based on a SIMP Algorithm

김철(Cheol Kim),팡난(Nan Fang) 대한기계학회 2008 대한기계학회 춘추학술대회 Vol.2008 No.11

In a traditional topology optimization method, material properties are usually distributed by finite element density and visualized by a gray level image. The distribution method based on element density is adequate for a great mass of 2-D topology optimization problems. However, when it is used for 3-D topology optimization, it is always difficult to obtain a smooth model representation, and easily appears a virtualconnect phenomenon especially in a low-density domain. The 3-D structural topology optimization method has been developed using the node density instead of the element density that is based on SIMP (solid isotropic microstructure with penalization) algorithm. A computer code based on Matlab was written to validate the proposed method. When it was compared to the element density as design variable, this method could get a more uniform density distribution. To show the usefulness of this method, several typical examples of structure topology optimization are presented.

위상최적설계와 형상최적설계를 이용한 크레인의 경량설계

김영철(Young Chul Kim),홍정기(Jung Kie Hong),장강원(Gang-Won Jang) 대한기계학회 2011 大韓機械學會論文集A Vol.35 No.7

CAE 기반 구조최적설계법인 위상최적설계와 형상최적설계를 크레인의 경량화에 적용하였다. 붐은 단면 형상을 설계 변수로 변화시키면서 질량의 최소화를 최적설계의 목적함수로 하고 붐의 정적강도와 동적강성이 초기 모델의 성능에 비해서 저하되지 않아야 한다는 제한조건을 설정하였다. 구조해석 및 최적설계는 상용소프트웨어인 Hyperworks를 이용하여 수행하였으며 붐의 단면 형상의 변형에 따르는 요소망의 변동은 모핑기능을 사용하여 수치 안정성을 확보하였다. 붐의 지지부는 초기 모델을 단순화시킨 설계 영역을 설정하고 이를 삼차원 솔리드 요소로 이산화한 후 위상최적설계를 수행하였다. 최적설계 결과 시스템의 전체 동적, 정적 강성을 저하시키지 않은 채로 붐은 19%, 지지부는 17% 경량화시킬 수 있었다. CAE-based structural optimization techniques are applied for the design of a lightweight crane. The boom of the crane is designed by shape optimization with the shape of the cross section of the boom as the design variable. The design objective is mass minimization, and the static strength and dynamic stiffness of the system are set as the design constraints. Hyperworks, a commercial analysis and optimization software, is used for shape and topology optimization. In order to consistently change the shape of the elements of the boom with respect to the change in the shape of its cross section, the morphing function in Hyperworks is used. The support of the boom of the original model is simplified to model the design domain for topology optimization, which is discretized by using three-dimensional solid elements. The final result after shape and topology optimization is 19% and 17% reduction in the masses of the boom and support, respectively, without a deterioration in the system stiffness.

임의의 적층미세구조를 가지는 판 구조물의 고유진동수 위상최적화에 관한 연구

한경민(Han Kyung-Min),강호근(Kang Hoo-Gun),박성수(Park Sung-Soo) 대한건축학회 2008 大韓建築學會論文集 : 構造系 Vol.24 No.2

The aim of this research is to construct eigenfrequency optimization codes for plates with Arbitrary Rank Microstructures. From among noise factors, resonance sound is main reason for floor's solid noise. But, Resonance-elusion design codes are not fixed so far. Besides, The prediction of composite material's capability and an resonance elusion by controlling natural frequency of plate depend on designer's experiences. In this paper, First, using computer program with arbitrary rank microstructure, variation on composite material properties is studied, and then natural frequency control is performed by plate topology optimization method. The results of this study are as followed. 1) Programs that calculate material properties along it's microstructure composition and control natural frequency on composite material plate are coded by Homogenization and Topology Optimization method. and it is examined by example problem. 2) Equivalent material properties, calculated by program, are examined for natural frequency. In this paper, Suggested programs are coded using MatlabTM, Feapmax and Feap Library with Homogenization and Topology Optimization method. and Adequacy of them is reviewed by performing the maximization or minimization of natural frequency for plates with isotropic or anisotropic materials. Since the programs has been designed for widely use. If the mechanism between composite material and other structural member is identified, extension application may be possible in field of structure maintenance, reinforcement etc. through application of composite material.

Design of Gas Flow Channel Routes in a PEM Fuel Cell System Using Topology Optimization

Hong Lie Sun(손홍렬),Cheol Kim(김철),Jae Uk Shin(신재욱) 대한기계학회 2011 대한기계학회 춘추학술대회 Vol.2011 No.4

연료 전지의 유동채널에 관한 효과적인 위상최적화 방법은 이미 기체유동 채널의 위상최적화 분포를 찾는 분야까지 재발되고 적용되었다. 이 논문은 주로 기본적인 밀도 계산, 기체에 관한 확산방정식 및 incompressible한 Navier-Stakes Equation들로 결합시킨 위상최적화의 수치적 공식을 파생시키고 해결하는 방법을 기술한다. FEM을 이용하여 유체의 공간적 디자인 도메인을 정의하였다. 이 과정에서 도메인과 mesh는 최적화 과정에서 변하지 않았고, 최적화 변수 0은 Stake flow, 1은 Porous flow를 표현한다. 유한요소해석법으로 Navier-Stokes Equation를 이용하여 PDE form의 유체 유동 속도와 압력을 계산하였고 차후 해석하게 될 민감도를 찾기 위해 요소 행렬을 계산하였다. Motivation of this study is to apply the topology optimization technique and to find the route of gas flow channels in the bipolar plate of a fuel cell. The goal of optimization is to maximize the mean reaction rate of gases by finding the optimal porosity distribution. In an example analysis, a solution is pumped through a catalytic bed, where a solute species reacts as it gets in contact with the catalyst. Proton exchange membrane fuel cell (PEMFC) has a lot of virtues such as high-power density, high-energy efficiency, low-temperature operation, fast start-up and zero-emission, so it can be used for a car, an electrical equipment, portable power, and stationary products. The performance degradation of PEMFC is mainly induced by the unreasonable design route of bipolar plates. The optimum shape and route of gas flow channels in bipolar plates can make the reaction rate more uniform.

위상 최적화 및 두께 최적화를 적용한 차체 동강성 개선에 관한 연구

김지언(Jieon Kim),김정호(Jungho Kim),이창건(Changkun Lee),김용석(Yongsuk Kim) 한국자동차공학회 2014 한국자동차공학회 부문종합 학술대회 Vol.2014 No.5

In all vehicle driving situations, some vibration level that is perceived by passengers is a criteria for determining the vehicle’s quality and ride comfort. The main excitations are from road, engine and wind. They can be classified as ‘Structural born vibration’ or ‘Air born vibration’ according to the load path. Among them, the most sensitive vibration paths from road and engine excitation that interface to body directly. Their performance level of vibration is dependent on a interface part’s stiffness, so generally we can improve it by increasing dynamic stiffness on this part at each frequency range. For this reason, in this study, we calculated dynamic stiffness at each frequency on interface parts with FRF(Frequency Response Function) based on CAE. Also we considered Topology optimization and size optimization process for an improved design in terms of vibration performance. The process is as follows; First of all, we identified the weak points as factors in the need to develop with FRF analysis on important interface parts. Secondly, we did topology optimization on areas that have weak dynamic stiffness which were identified in the first step. This result tells us that the load path is critical factor to improve stiffness. Thirdly, we re-organized some structure shapes based on the load path identified in the second step. In this step, we used ‘Morphing’ technology method for changing shape. Finally, we conducted size optimization for getting a final design that is optimized for dynamic stiffness improvement and mass reduction. In this study, we propose a useful method that can draw efficient solution of vehicle body’s dynamic stiffness improvement using an optimization process that sequentially covers shape change and thickness change.

무요소법을 이용한 평면구조물의 위상최적화에 대한 연구

이상진(Lee Sang-Jin),이창계(Lee Chang-Kye) 대한건축학회 2009 大韓建築學會論文集 : 構造系 Vol.25 No.7

This study proposes a topology optimization technique using meshless method for planer structures. The meshless method is developed to complement the weak point of finite element (FE) method in case of crack propagation problems which generally need the regeneration of FE mesh when cracks occur. It has been considered as a very attractive computational method since it does not need mesh generation during the analysis. We adopt the radial point interpolation method (RPIM) which uses the radial basis function (RBF). It has great advantages since it is stable and robust for arbitrary nodal distributions. So far, there is a few application of new meshless method into the structural design optimization. Therefore, we here apply the meshless method into structural topology optimization problem. The hard kill method based on fully stressed design technique is consistently combined with RPIM meshless method. In order to demonstrate the accuracy of the proposed topology optimization technique, several benchmark tests are tackled not only to investigate the accuracy of the adopted meshless method but also the performance of new topology optimization process. From numerical results, it is found to be that the proposed topology optimization technique very simple and effective to produce the optimum topologies of plane structures.