반응표면모델과 공정능력지수를 적용한 로워암의 공차최적화

이광기(Kwang Ki Lee),노윤철(Yun Chul Noh),한승호(Seung Ho Han) (사)한국CDE학회 2013 한국 CAD/CAM 학회 학술발표회 논문집 Vol.2013 No.1

In the lower arm design process, a tolerance optimization of the variance of design variables should be preceded before manufacturing process, since it is very cost-effective rather than a strict management of tolerance of products. In this study, a design of experiments based response surface model was carried out to find optimized design variables which can meet a given requirement of probability constraint for the process capability index of the weight and maximum stress for the lower arm. The design space was explored by using the central composite design method and the 2nd order Taylor expansion to predict a standard deviation of the design variables. The optimal solutions satisfying the probability constraint of the process capability index were founded by considering both of mean value and standard deviation of the design variables.

반응표면모델과 공정능력지수를 적용한 로워암 설계변수의 공차최적화

이광기(Kwang Ki Lee),노윤철(Yun Cheol Ro),한승호(Seung Ho Han) (사)한국CDE학회 2013 한국CDE학회 논문집 Vol.18 No.5

In the lower arm design process, a tolerance optimization of the variance of design variables should be preceded before manufacturing process, since it is very cost-effective compared to a strict management of tolerance of products. In this study, a design of experiment (DOE) based on response surface model (RSM) was carried out to find optimized design variables of the lower arm, which can meet a given requirement of probability constraint for the process capability index (Cpk) of the weight and maximum stress. Then, the design space was explored by using the central composite design method, in which the 2nd order Taylor expansion was applied to predict a standard deviation of the responses. The optimal solutions satisfying the probability constraint of the Cpk were found by considering both of the mean value and the standard deviation of the design variables.

철도차량 현수장치의 식스시그마 강건 설계

이광기(Kwang Ki Lee),박찬경(Chan Kyoung Park),한승호(Seung Ho Han) 대한기계학회 2009 大韓機械學會論文集A Vol.33 No.10

The spring constants of primary suspensions for a railway vehicle are optimized by a robust design process, in which the response surface models(RSMs) of their dynamic responses are constructed via the design of experiment(DOE). The robust design process requires an intensive computation to evaluate exactly a probabilistic feasibility for the robustness of dynamic responses with their probabilistic variances for the railway vehicle. In order to overcome the computational process, the process capability index Cpk is introduced which enables not only to show the mean value and the scattering of the product quality to a certain extent, but also to normalize the objective functions irrespective of various different dimensions. This robust design, consequently, becomes to optimize the Cpk subjected to constraints, i.e. 2, satisfying six sigma. The proposed method shows not only an improvement of some Cpk violating the constraints obtained by the conventional optimization, but also a significant decrease of the variance of the Cpk.

식스시그마 제약조건을 고려한 로워암의 공차 최적설계

이광기(Kwang Ki Lee),한승호(Seung Ho Han) 대한기계학회 2011 大韓機械學會論文集A Vol.35 No.10

자동차 로워암과 같이 다양한 형상설계변수를 갖는 부품모듈의 최근 설계경향은 설계자가 관심을 갖는 설계영역을 선형 및 2 차 다항식으로 근사화시키는 반응표면모델로 탐색하고, 다음 단계로서 최적 설계를 수행하는 것이다. 본 연구에서는 로워암의 설계변수 변화에 따른 작용응력과 중량의 비선형적 변화뿐만 아니라 이의 예측에 적합한 신경망모델로 직교성과 균형성을 모두 만족시키는 다수준 전산실험계획법으로 설계영역을 탐색하였다. 구축된 신경망모델에 형상 설계변수의 공차도 같이 고려할 수 있는 식스시그마 제약조건을 적용하여 로워암의 공차 최적설계를 수행하고, 최적해의 공차 강건성을 확보하였다. In the current design process for the lower arm used in automobile parts, an optimal solution of its various design variables should be found through exploration of the design space approximated using the response surface model formulated with a first- or second-order polynomial equation. In this study, a multi-level computational DOE (design of experiment) was carried out to explore the design space showing nonlinear behavior, in terms of factors such as the total weight and applied stress of the lower arm, where a fractional-factorial orthogonal array based on the artificial neural network model was introduced. In addition, the tolerance robustness of the optimal solution was estimated using a tolerance optimization with six sigma constraints, taking into account the tolerances occurring in the design variables.

[진동·소음부문] 다구찌 직교배열의 반응표면모델에 의한 철도차량 현수장치 최적설계

이광기(Kwang Ki Lee),박찬경(Chan Kyoung Park),이태희(Tae Hee Lee) 한국자동차공학회 1999 한국자동차공학회 춘 추계 학술대회 논문집 Vol.- No.-

Optimal design of the suspension of train is performed according to the minimization of the response surface models for 34 responses that are predicted by a dynamic analysis code, VAMPIRE, where the each response surface model is made from Taguchi orthogonal away. After the whole 34 response surface models are constructed, the main effects and global sensitivities are performed by using 1?? order response surface model. Then the optimal solution is obtained by distance method and simplex nonlinear programming one after eliminating insignificant design variables by using stepwise regression. The design of experiments, especially orthogonal array, and the optimization algorithm are successfully used together to obtain the optimal design of the suspension of train. The 1" order response surface models of the 27 design variables are constructed by using Taguchi's L??2?? orthogonal array and least square estimation.

표준정규분포를 고려한 반응표면모델 기반 디스크 브레이크의 강건최적설계

이광기(Kwang Ki Lee),이용범(Yong Bum Lee),한승호(Seung Ho Han) 대한기계학회 2010 대한기계학회 춘추학술대회 Vol.2010 No.5

복잡한 시스템 계의 설계정보를 효과적으로 추출하기 위해서 형상최적설계가 수행되는 경우, 일반적으로 유한요소해석 기법과 D-최적배열을 이용한 실험계획법이 연동된 반응표면모델을 구성하고 여기에 최적설계기법이 적용된다. 그러나, 설계변수에 형상공차와 같은 변동성이 존재하면 최적해의 강건성 확보를 위하여 설계변수의 형상공차를 확률론적인 변동성으로 고려한 추가적인 강건설계가 필요하다. 본 연구에서는 계산시간이 많이 소요되는 유한요소해석에 의한 강건설계문제에 설계변수의 표준정규분포를 고려한 반응표면모델을 구축하여 최적설계를 수행하므로서 손쉽게 강건최적값을 구하는 방법을 제안하였다. 승용차용 브레이크 디스크에 제안된 방법을 적용하여 열변형과 중량을 최소화하는 설계변수의 강건최적해를 구하고, 몬테카를로 시뮬레이션 추정결과와 비교하여 이의 적합성을 검증하였다. In the practical design process, it is very important how to extract the design space information of the complex system for verifying, improving and optimizing the design process to take into account of design variables with their shape tolerance. The finite element analysis has been successfully implemented and integrated with a design of experiment such as D-Optimal array providing a response surface model and optimization tools, so that optimized design variables can be found. Then, to ensure robustness of the design variables the robust design should be performed additionally, in which the statistical variation from shape tolerance of the design variables optimized is taken into account. In this study a new approach via the response surface model considering standard normal distribution of the shape tolerance is proposed that enables to perform both of the optimization and robust design. This approach can be utilized as an efficient means to rapidly model the trade-off among many conflicting goals existed in the finite element analysis applications. For the case study the robust optimal design of disc brake under thermal loadings was carried out to apply solving multiple objective functions and constraints of the design variables such as a thermal deformation and weight.

표준정규분포를 고려한 반응표면모델 기반 디스크 브레이크의 강건최적설계

이광기(Kwang Ki Lee),이용범(Yong Bum Lee),한승호(Seung Ho Han) 대한기계학회 2010 大韓機械學會論文集A Vol.34 No.9

복잡한 시스템 계의 설계정보를 효과적으로 추출하기 위해서 형상최적설계가 수행되는 경우, 일반적으로 유한요소해석 기법과 D-최적배열을 이용한 실험계획법이 연동된 반응표면모델을 구성하고 여기에 최적설계기법이 적용된다. 그러나, 설계변수에 형상공차와 같은 변동성이 존재하면 최적해의 강건성 확보를 위하여 설계변수의 형상공차를 확률론적인 변동성으로 고려한 추가적인 강건설계가 필요하다. 본 연구에서는 계산시간이 많이 소요되는 유한요소해석에 의한 강건설계문제에 설계변수의 표준정규분포를 고려한 반응표면모델을 구축하여 최적설계를 수행하므로서 손쉽게 강건최적값을 구하는 방법을 제안하였다. 승용차용 브레이크 디스크에 제안된 방법을 적용하여 열변형과 중량을 최소화하는 설계변수의 강건최적해를 구하고, 몬테카를로 시뮬레이션 추정결과와 비교하여 이의 적합성을 검증하였다. In a practical design process, the method of extracting the design space information of the complex system for verifying, improving, and optimizing the design process by taking into account the design variables and their shape tolerance is very important. Finite element analysis has been successfully implemented and integrated with design of experiment such as D-Optimal array; thus, a response surface model and optimization tools have been obtained, and design variables can be optimized by using the model and these tools. Then, to guarantee the robustness of the design variables, a robust design should be additionally performed by taking into account the statistical variation of the shape tolerance of the optimized design variables. In this study, a new approach based on the use of the response surface model is proposed; in this approach, the standard normal distribution of the shape tolerance is considered. By adopting this approach, it is possible to simultaneously optimize variables and perform a robust design. This approach can serve as a means of efficiently modeling the trade-off among many conflicting goals in the applications of finite element analysis. A case study on the robust optimal design of disc brakes under thermal loadings was carried out to solve multiple objective functions and determine the constraints of the design variables, such as a thermal deformation and weight.

TOPSIS 를 적용한 CRT 후면유리의 다중목적 형상최적설계

이광기(Kwang Ki Lee),한정우(Jeong Woo Han),한승호(Seung Ho Han) 대한기계학회 2010 대한기계학회 춘추학술대회 Vol.2010 No.11

Technique for order preference by similarity to ideal solution (TOPSIS) has known as a classical method of multiple attribute decision making (MADM) which is often used to solve various decision making or selection problems. It is based on the concept that the chosen alternative should have the shortest distance from the positive ideal solution and, the other side, the farthest distance from the negative ideal solution. The TOPSIS can be applied to a design process carrying out the multi-objective shape optimization in which the best and worst alternatives should be decided. In this paper the shape optimization using the TOPSIS was applied to a funnel of cathode ray tube (CRT). As a performance index, relative-closeness coefficients introduced from the alternatives via the TOPSIS and design of experiment was able to explore the design space of the objective functions for the CRT funnel. It enabled the designer to decide for themselves in order to select the best and worst alternatives of weight and 1<SUP>st</SUP> principal stress influenced by control points on Rational Bezier curve for the arch-like shape of CRT funnel.

TOPSIS 를 적용한 CRT 후면유리의 다중목적 형상최적설계

이광기(Kwang Ki Lee),한정우(Jeong Woo Han),한승호(Seung Ho Han) 대한기계학회 2011 大韓機械學會論文集A Vol.35 No.7

TOPSIS(Technique for Order Preference by Similarity to Ideal Solution)는 상충되는 다수의 속성이 존재하는 상황에서 의사결정이 요구되는 다속성 의사결정법(Multi Attribute Decision Making) 중 하나이다. 이는 선택된 대체안이 최선의 이상적 대체안으로부터 가장 가까운 거리에 위치해야 하고, 동시에 부정적으로 이상적인 대체안으로부터는 가장 멀리 위치해야 한다는 논리에 입각한 의사결정 기법이다. TOPSIS 는 최소화와 최대화가 공존하는 다목적함수 형상 최적설계에 적용이 가능하다. 본 연구에서는 TOPSIS 와 베지어 곡선(Rational Bezier Curve)을 적용하여 CRT(Cathode Ray Tubes) 후면유리의 다중목적 형상최적설계를 수행하였다. 무게와 1 차 주응력의 두 가지 다중목적 함수를 최적화하기 위하여, 다중목적 함수의 성능지표를 TOPSIS 의 상대적 근접도로 정의하고 이를 반응표면모델로 구성하여 다중목적 형상최적설계가 가능한 방법론을 제안하였다. 이를 통해 하나의 최적해가 아닌 최적해의 군이 선정되어, 무게와 주응력 최적해의 모순관계를 확인하면서 다양한 설계요구 스펙을 만족시켜줄 수 있는 방안을 설계자가 스스로 선택하도록 하였다. The technique for order preference by similarity to ideal solution (TOPSIS) is regarded as a classical method of multiple attribute decision making (MADM), often used to solve various decision-making or selection problems. It is based on the concept that the chosen alternative should have the shortest distance from the positive ideal solution and the farthest distance from the negative ideal solution. The TOPSIS can be applied to a design process for carrying out multi-objective shape optimization wherein the best and worst alternatives are to be decided. In this paper, multi-objective shape optimization using the TOPSIS and Rational Bezier curve was applied to the funnel of a cathode-ray tube (CRT). In order to minimize the weight and first principal stress, a new multi-objective shape optimization methodology is proposed, wherein the relative-closeness coefficients of the TOPSIS are defined as the performance indices of a multi-objective function and evaluated by response surface models. This methodology enables the designer to decide on the best solution from a number of design specification groups by examining the various conflicts between the weight and the first principal stress.

불량률 최소화를 통한 강건 최적화의 확률제한조건 처리

이광기(Kwang Ki Lee),박찬경(Chan Kyoung Park),김근연(Geun Yeon Kim),이권희(Kwon Hee Lee),한상욱(Sang Wook Han),한승호(Seung Ho Han) 대한기계학회 2013 大韓機械學會論文集A Vol.37 No.8

강건 최적화 기법은 설계 초기 단계부터 설계변수의 변동이 목적함수에 미치는 효과를 최소화할 수 있는 유일한 방법이다. 강건 최적화의 정식화를 위해서는 분산을 정확히 예측하고 확률제한조건을 정식화하는 것이 가장 중요한 과정이 된다. 분산 및 확률제한조건을 예측하고 정식화하기 위한 방법으로 공정능력지수 및 식스시그마 기법과 같은 여러 가지 방법이 적용되고 있으나, 실제 공정에서 널리 적용되는 불량률을 이용한 확률제한조건 처리 기법에 대한 연구는 아직까지 전무한 상태이다. 본 연구에서는 자동차 로워암의 무게와 최대응력의 평균과 표준편차에 대한 설계영역을 탐색하고, 이후 로워암의 강건 최적화를 수행하였다. 변동을 예측하기 위한 표준편차의 계산은 2 차 테일러 전개를 통해 수치적인 정확도를 기하였다. 강건 최적화는 설계변수의 불연속성을 고려하기 위하여 최적화 과정에서 미분 정보를 적용하지 않은 심플렉스 알고리즘을 적용하였다. A robust optimization is only one of the ways to minimize the effects of variances in design variables on the objective functions at the preliminary design stage. To predict the variances and to formulate the probabilistic constraints are the most important procedures for the robust optimization formulation. Though several methods such as the process capability index and the six sigma technique were proposed for the prediction and formulation of the variances and probabilistic constraints, respectively, there are few attempts using a percent defective which has been widely applied in the quality control of the manufacturing process for probabilistic constraints. In this study, the robust optimization for a lower control arm of automobile vehicle was carried out, in which the design space showing the mean and variance sensitivity of weight and stress was explored before robust optimization for a lower control arm. The 2nd order Taylor expansion for calculating the standard deviation was used to improve the numerical accuracy for predicting the variances. Simplex algorithm which does not use the gradient information in optimization was used to convert constrained optimization into unconstrained one in robust optimization.