A topology optimization approach considering the static and dynamic behaviors of rubber is proposed for the shape design of rubber in the vibration isolators. Many vibration isolators are made of rubber and they are operating under small oscillatory load due to structural vibration superimposed on the large static deformation caused by the self-weight of target structure. For the efficient design of vibration isolators, the precise analysis of the static and dynamic behaviors of isolation rubber is essentially necessary. Firstly the large static deformations of rubber with the incompressibility under very slow loads can be generally treated with the well-known hyperelastic constitutive equations and the mixed finite element methods with Lagrangian formulations for nonlinear analysis. The dynamic behaviors of the rubber in the vibration isolators under very fast and small oscillatory loads can be analyzed by the steady state viscoelastic constitutive model that is suggested by Kim and Youn and can precisely describe the influence of the large static deformations on the time effects of viscoelastic relaxation function.
The topology optimization approach is selected as the design optimization technique in order to obtain the adequate shapes of isolation rubber. The main object of the vibration isolators is the reduction of the vibrations and forces transmitted from target structures. Also the vibration isolators must have large enough static stiffness in order to stably support the target structure. The topology optimization approach considering both the high structural stability and low vibration transmissibility of the isolators is proposed. The objective functions and design constraints are formulated with the performance measures of both the static and dynamic mean compliance to represent the performance of the structures. The continuum-based design sensitivity analysis methods are formulated and actually applied to determine the effective directions of design changes to improve the system performance. The proposed sensitivity analysis methods are verified by the comparison with the sensitivity analysis results of example problem using the finite difference method. The sequentially linear programming widely used in the structural design is selected as an optimization algorithm. The penalty functions are added to the objective functions in order to remove the intermediate densities and the continuations of design constraints are applied in order to avoid the local optimal solutions.
The proposed topology optimization approach is applied to the design of the rubber shape in the example vibration isolators. Two kinds of design optimizations are performed to maximize the static stiffness and also minimize the transmissibility with a static compliance constraint. The material boundary extraction from the density distributions is carried out and then the analysis results of the extracted models are compared with the results in the topology optimization process. Since the results of both analysis models are very similar, the modeling techniques and the analysis methods in the topology optimization can be verified. In the simultaneous design optimization for the transmissibility and structural stability, the density distribution results with the various static constraints are obtained. The optimizations for the various vibrating frequencies and the multiple frequencies are carried out. Both the three-dimensional and transversely uniform distributions of the design density are considered. From the comparison of results, three-dimensional distribution has more complex shape, however, the both designs have the very similar performance. We can conclude that the transversely uniform design is the effective method for the sake of the manufacturability of isolation rubber.
Rubber shows the large variance in the material properties compared with other kinds of materials although the rubber products are made with same recipe and have the same shape. Considering such variances, the statistical treatment of design requirements of isolation rubber is essentially necessary. The reliability-based design optimization (RBDO) methods are applied to the shape design of isolation rubber in addition to the traditional deterministic optimization. In RBDO approach, the probabilistic constraint for the static mean compliance is formulated with performance measurement approach (PMA) considering the variances of the mechanical properties of rubber. The corresponding probability and design sensitivity analyses of the probabilistic constraint are performed using the advanced first-order second moment (AFOSM) method. The proposed reliability-based topology optimization method is applied for the isolation rubber design. The design result shows the larger reliability against the variance compared with the deterministic design results.
가솔린엔진의 새로운 공연비 예측기를 개발하였다. 내연기관에서 배출되는 미연탄화수소의 상당량은 시동초기에 발생된다. 상용 산소센서는 냉시동 조건에서 배출가스의 공연비를 측정하지 못한다. 본 논문에서 기술한 공연비 예측기는 배출가스온도, 공기량, 냉각수 온도 등의 측정에 기초한다. 공연비는 간접적으로 평가하는데 이는 배출가스 온도가 배출가스 중의 공연비에 의존하는 값이기 때문이다. 냉시동 시의 미연탄화수소 발생량을 급속 화염이온화 검사 장비(Fast Flame Ionization Detector)로 측정하였다. GRNN 알고리즘을 이용하여 배출가스 중의 공연비를 예상하였다. 가솔린 엔진의 미연탄화수소의 발생량을 저감하기 위해서는 배출가스 중의 연료 및 연료생성물의 양을 평가하여야 한다. 또한 흡입공기량도 측정되어야 한다. 본 연구결과 점화착화기관에서의 공연비를 평가하는 전략을 제안하였다. 실린더 내로 유입되는 공기량은 Filling-emptying 방법을 통하여 결정하였으며 흡입매니폴드와 실린더의 연료량은 액막 효과를 고려하여 평가하였다. Matlab, Simulink, Real Time workshop, xPC Target과 Watcom C++ 등을 사용하여 초기엔진 제어기를 개발하였다. 엔진으로부터의 센서 데이터는 노트북 컴퓨터로 입력되고 연료분사량을 계산할 수 있다. 컴퓨터내의 엔진 제어기에 의해 연료분사량이 계산된다. 냉시동시의 연료제어 로직은 액막 효과의 계산에 기초한다. 상기에 기술한 기술들을 접목하여 냉시동시의 미연탄화수소를 저감하기 위한 제어기의 개발이 본 연구의 목표이다. 액막모델의 파라메터들은 시간에 따라 변화하는 값으로서 액막모델 시스템의 식별이 본 연구의 중요사항이다. 프로그램 도구로서 Matlab 소프트웨어의 System Identification Toolbox가 사용되었으며 실험데이터가 같이 사용되었다. 마지막으로 엔진을 제어하기 위한 실험적 도구들을 소개하였으며 연료 분사량을 제어하기 위한 소프트웨어를 기술하였다.
