A recursive coupling-decoupling approach to improve experimental frequency based substructuring results

Substructure decoupling techniques allow identifying the dynamic behavior of a substructure starting from the dynamic behavior or the assembled system and a residual subsystem. Standard approaches rely on the knowledge of all FRFs at the interface DOFs between the two substructures. However, as these typically include also rotational DOFs which are extremely difficult and most of the time impossible to measure, several techniques have been investigated to overcome these limitations. A very attractive solution consists in defining mixed or pseudo interfaces, that allow to substitute unmeasurable coupling DOFs with internal DOFs on the residual substructure. Additionally, smoothing/denoising techniques have been proposed to reduce the detrimental effect of FRF noise and inconsistencies on the decoupling results. Starting from these results, some recent analysis on the possibility of combining coupling and decoupling FBS to validate the results and compensate for inconsistencies will be presented in this paper. The proposed method relies on errors introduced in the substructuring process when assuming that the interface behaves rigidly, while it is generally known that this assumption is seldom verified. Consequently, a recursive coupling-decoupling approach will be used to improve the estimation of the dynamic response of either the residual structure (for decoupling) or the assembly (for coupling). The method, validated on analytical data, will be here analyzed on a numerical example inspired by an experimental campaign used to validate the finite element models and on which standard substructuring techniques showed some limitations. The results discussed in this paper will be then used as guidelines to apply the proposed methodologies on experimental data in the future

Recent Advances to Estimation of Fixed-Interface Modal Models Using Dynamic Substructuring

In 2010, Allen & Mayes proposed to estimate the fixed-interface modes of a structure by measuring the modes of the structure bolted to a fixture and then applying constraints to the fixture using the transmission simulator method. While the method proved useful, and has indeed been used in studies since that point, a few peculiarities were noted. First, in some cases the estimated fixed-base natural frequencies were observed to converge very slowly to the true values (in simulated experiments) as the number of constraints was increased. To formulate these constraints, prior studies used only the free-interface modes of the fixture or the measured modes of the assembly. This work extends that to consider other sets of constraints, showing improved results. Furthermore, in some prior studies it has been observed that there were errors of more than 10% in the natural frequencies even when the fixture motion was hundreds of times smaller than the motion of the structure of interest (and so it had presumably been removed). This work explores this phenomenon, seeking to use the strain energy in the fixture, to the extent that it can be estimated using a test-analysis model for the fixture, as a metric to predict frequency error. The proposed methods are explored by applying them to simulated measurements from a beam and from the NASA Space Launch System coupled to the Mobile Launcher

Dynamic Substructuring for Evaluating Vibro-acoustic Performance

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 기계항공공학부, 2020. 8. 강연준.Generally, a mechanical system consists of various substructures that cause noise and vibration problems. This thesis proposes a dynamic substructuring method for the estimation of the dynamic characteristics of a coupled mechanical system based on substructure characteristics. The first phase of this thesis presents a method for the estimation of rotational stiffness at the coupled points of an assembled system based on a dynamic substructuring method. Conventional test-based rotational stiffness evaluation methods are sensitive to measurement errors and require a specialized jig for testing. In contrast, given that the proposed method uses the natural frequency shift phenomenon that results from the addition of mass, the measurement error is relatively small, and the accuracy is improved by excluding the interference of other modes. In addition, the proposed method solves the problem due to the complexity of the conventional method by changing the fixed condition of the system using frequency response function (FRF)-based substructuring (FBS) modeling; thus, it does not require a specialized jig for fixing parts. In this manuscript, the concepts of trial mass, virtual mass, and virtual spring are introduced to systematically explain the proposed method and its application based on frequency shifts. The results of the experiments conducted on a vehicle shock absorber verify the utility of the proposed method. In the second phase, a novel transfer path analysis (TPA) method based on a dynamic substructuring model is proposed. With the dynamic substructuring model, the FRF information of a base system can be used to evaluate the stiffness addition effect at the measurement points instead of adding the actual stiffness. In the proposed method, a spring with an infinite stiffness is virtually added to a specific transfer path among various possible paths, such that the specific path is removed. Hence, the virtual spring significantly reduces the contribution of the specific path. This method is more implementable and applicable than existing TPA methods (i.e., conventional TPA and operational TPA), as it does require part removal or the correlation information between the signals. To verify the feasibility of the FBS-based TPA method, it was applied to a significant road noise phenomenon. The test results confirm that the proposed method can be applied to the TPA of suspension linkages and vehicle bodies. In the final phase of this thesis, an improved dynamic substructuring model is presented based on the estimated FRF information at a coupling point between substructures. An assembled system generally consists of two or more such substructures, which are typically connected by a bolt. To ensure an accurate estimation of the dynamic characteristics of the assembled system, an accurate measurement of the joint properties is required. However, in most practical cases, physical constraints prevent such measurements at actual coupling points. Accordingly, this study proposes a method that uses generalized coupling properties to estimate the dynamic characteristics of a new coupling system based on the characteristics of the original substructure. In this process, the concept of virtual point transformation was used to estimate accurate FRFs at the coupling points of the assembled system based on convenient measurements. Thereafter, the proposed method was validated using a hard-mount vehicle suspension in a test jig and on an actual vehicle body for estimating the vibration characteristics of the assembled system. This research contributes towards the accurate estimation of the dynamic properties of bolt-assembled systems in several practical applications.일반적으로 기계시스템은 다양한 하위 부분구조물로 구성되며, 이들은 많은 소음 및 진동 문제를 야기한다. 본 논문은 이러한 하위 부분구조물의 동특성 정보만을 사용하여 전체 대상 시스템의 동적 특성을 추정하기 위한 동특성 합성기법을 다루고 있다. 먼저, 본 논문의 첫 장에서는, 동특성 합성기법을 활용한 결합 시스템의 회전 강성 추정 기법을 제시하였다. 기존 시험기반의 회전 강성 평가법들은 측정 오류에 민감 할 뿐 아니라, 측정을 위한 별도의 고정용 지그가 필요하다. 그러나, 본 연구에서 제시된 방법은 시스템에 부가되는 질량에 의한 고유 주파수 편이 현상을 사용하기 때문에 기존 방법에 비해 측정오차가 상대적으로 작고, 다른 모드의 간섭을 배제함으로써 추정 정확도의 향상을 기대할 수 있다. 또한, 본 기법은 주파수 응답함수 기반 합성 모델을 사용하여 실제 고정 지그를 사용하는 대신, 고정 경계조건을 수식적으로 대체함으로써 기존 방법의 복잡성을 해결하였다. 이 과정에서 시험 질량, 가상 질량 및 가상 스프링의 개념이 도입되었으며, 실제 차량의 충격 흡수장치를 이용하여 모델의 검증을 수행하였다. 다음으로, 본 논문의 두 번째 장에서는, 동특성 합성 모델을 이용한 새로운 전달 경로 분석 기법을 제시하였다. 본 연구에서는 대상 시스템의 실제 전달경로를 제거하는 대신, 무한대의 강성을 갖는 가상의 스프링을 주파수 응답 함수의 형태로 반영함으로써, 특정 전달경로의 제거 효과를 구현하였다. 본 기법은 기존의 전달경로 분석법에 비하여 실험적으로 구현이 쉬우며, 측정에 소요되는 작업량과 계산량 또한 획기적으로 줄일 수 있다. 해당 기법은 차량 현가계의 특정 진동 전달 현상을 이용하여 실험적으로 유효성이 검증되었다. 본 논문의 마지막 장에서는, 동특성 합성 모델의 정확도 개선을 위한 연구가 수행되었다. 일반적으로 결합시스템은 두 개 이상의 결합물이 볼트를 이용하여 결합되며, 결합 시스템의 동특성 예측을 위해서는 결합부의 정확한 동특성이 요구된다. 하지만 대부분의 경우, 물리적 공간의 제약으로 인하여 실제 결합 지점에서의 측정이 불가능하기 때문에, 가상 지점의 개념을 도입하여 결합지점에서의 주파수 응답함수를 추정하였다. 해당 방법 역시, 실제 차량과 서스펜션 시험 지그를 이용하여 검증되었다. 본 연구는 많은 실제 응용 분야에서 정확한 시스템의 동특성 추정에 기여하고 있다.CHAPTER 1. GENERAL INTRODUCTION 1 1.1 Research background and motivation of the work 1 1.2 Literature reviews 8 1.3 Overview of the present work 15 1.4 Contributions 17 CHAPTER 2. INTRODUCTION TO DYNAMIC SUBSTRUCTURING 21 2.1 Introduction 21 2.2 Summary 25 CHAPTER 3. VIRTUAL PARAMETERS FOR ESTIMATING ROTATIONAL STIFFNESS 27 3.1 Introduction 27 3.2 Theoretical concepts 34 3.2.1 Concept of trial masses 34 3.2.2 Concept of virtual masses 40 3.2.3 Concept of virtual springs 44 3.3 Experimental validation 47 3.3.1 Validation of trial masses 47 3.3.2 Validation of virtual masses 55 3.3.3 Validation of virtual springs 59 3.4 Summary 64 CHAPTER 4. TRANSFER PATH ANALYSIS USING A VIRTUAL SPRING 69 4.1 Introduction 69 4.2 Conventional TPA 76 4.3 FBS-based TPA 79 4.4 Experimental validation 83 4.4.1 Specific road noise phenomenon 83 4.4.2 Suspension link TPA 89 4.4.3 Body TPA 99 4.5 Summary 104 CHAPTER 5. EXPERIMENTAL METHOD FOR IMPROVED ACCURACY OF DYNAMIC SUBSTRUCTURING MODEL 109 5.1 Introduction 109 5.2 Theoretical concepts 111 5.2.1 Dynamic substructuring model considering generalized coupling properties 111 5.2.2 Virtual point transformation method to improve experimental data 117 5.2.2.1 Virtual point displacement 117 5.2.2.2 Virtual point FRF 125 5.3 Validation of virtual point transformation 128 5.3.1 Target system and system description 128 5.3.2 Validation of virtual point transformation 133 5.3.2.1 Validation of virtual point displacement 133 5.3.2.2 Validation of virtual point FRF 139 5.3.3 Dynamic substructuring with virtual point transformation 143 5.4 Summary 152 CHAPTER 6. CONCLUSIONS AND RECOMMENDATIONS 155 6.1 Conclusions 155 6.2 Recommendations 159 APPENDIX 163 REFERENCES 167 국 문 초 록 177Docto

Identification of bolted joint properties through substructure decoupling

Substructure decoupling techniques, defined in the frame of Frequency Based Substructuring, allow to identify the dynamic behaviour of a structural subsystem starting from the known dynamics of the coupled system and from information about the remaining components. The problem of joint identification can be approached in the substructuring framework by decoupling jointed substructures from the assembled system. In this case, information about the coupling DoFs of the assembled structure is necessary and this could be a problem if the interface is inaccessible for measurements. Expansion techniques can be used to obtain the dynamics on inaccessible (interface) DoFs starting from accessible (internal) DoFs. A promising technique is the System Equivalent Model Mixing (SEMM) that combines numerical and experimental models of the same component to obtain a hybrid model. This technique has been already used in an iterative coupling–decoupling procedure to identify the linear dynamic behaviour of a joint, with a Virtual Point description of the interface. In this work, a similar identification procedure is applied to the Brake Reus Beam benchmark to identify the linear dynamic behaviour of a three bolted connection at low levels of excitation. The joint is considered as a third independent substructure that accounts for the mass and stiffness properties of the three bolts, thus avoiding singularity in the decoupling process. Instead of using the Virtual Point Transformation, the interface is modelled by performing a modal condensation on remote points allowing deformation of the connecting surfaces between subcomponents. The purpose of the study is to highlight numerical and ill-conditioning problems that may arise in this kind of identification

Identification of Blade-root Joint Dynamics in Turbine Disks

L'abstract è presente nell'allegato / the abstract is in the attachmen

FRF based substructuring and decoupling of substructures

This study considers FRF (frequency response function) based substructuring and decoupling of substructures for the dynamic analysis of complicated huge structures utilizing compatibility conditions between adjacent substructures. This work includes: 1) the derivation of updated FRF matrix for dynamic system subjected to frequency or time dependent constraints in the frequency-domain, 2) the synthesis and decoupling of subsystems based on the dual domain approach using compatibility conditions between adjacent subsystems, 3) the evaluation of the validity of the proposed methods through numerical applications. It is expected that the proposed methods will be utilized as the basic formulation in investigating the dynamic characteristics of partitioned or synthesized system

On the use of Lagrange Multiplier State-Space Substructuring in dynamic substructuring analysis

In this article, the formulation of Lagrange Multiplier State-Space Substructuring (LM-SSS) is presented and extended to directly compute coupled displacement and velocity state-space models. The LM-SSS method is applied to couple and decouple state-space models established in the modal domain. Moreover, it is used together with tailored postprocessing procedures to eliminate the redundant states originated from the coupling and decoupling operations. This specific formulation of the LM-SSS approach made it possible to develop a tailored coupling form, named Unconstrained Coupling Form (UCF). UCF just requires the computation of a nullspace and does not rely on the selection of a subspace from a nullspace. By exploiting a numerical example, LM-SSS was compared with the Lagrange Multiplier Frequency Based Substructuring (LMFBS) approach, which is currently widely recognized as a reference approach. This was done both in terms of: a)coupled FRFs derived by coupling the state-space models of two substructures and b) decoupled FRFs derived by decoupling the state-space model of a component from the coupled model. LM-SSS showed to be suitable to compute minimal order coupled models and UCF turned out to have similar performance as other coupling forms already presented to the scientific community. As for the decoupling task, the FRFs derived from the LM-SSS approach perfectly matched those obtained by LM-FBS. Moreover, it was also demonstrated that the elimination of the redundant states originated from the decoupling operation was correctly performed. The approaches discussed were exploited on an experimental substructuring application. LM-SSS resulted to be a reliable SSS technique to perform coupling and decoupling operations with state-space models estimated from measured FRFs as well as to provide accurate minimal-order models

하이브리드 모델링과 베이지안 최적화를 이용한 엔진 마운트 응답개선

학위논문 (석사) -- 서울대학교 대학원 : 공과대학 기계항공공학부, 2020. 8. 강연준.This paper presents the results of a study conducted to predict and improve the response of an engine mount using a hybrid model that combines both experimental data and finite element (FE) analysis. The engine mount is the main point of transmission of engine vibration forces to the vehicle body. Therefore, improving the dynamic response of the engine mount improves the overall NVH performance of the vehicle. The hybrid modeling method adopts the substructure synthesis method based on the frequency response function based substructuring (FBS) theory, in this method, a complex dynamic structure is divided into multiple substructures, and the frequency response function (FRF) of the entire system is predicted using the FRFs of individual substructures. This method allows engineers to predict the changes in the experimental FRF of an existing physical system by applying FE analysis only to the substructures that have undergone a design modification. The change in the overall dynamic performance of the system can be predicted by modifying the CAD model of the substructure without preparing a physical model. Furthermore, the optimal design is proposed by applying the Bayesian optimization technique in this paper.본 논문에서는 차량 엔진 구조물에 대해 실험 데이터와 유한요소 해석 데이터를 모두 이용하는 Hybrid 모델의 부분구조합성법을 통해 엔진 마운트에서의 응답을 예측하는 연구를 수행하였다. Hybrid 모델 부분구조 합성법은 복잡한 전체 시스템을 여러 개의 부분구조로 나누어 각각의 Frequency Response Function(FRF)만으로 전체 시스템의 FRF를 예측하는 FRF Based Sub-structuring(FBS)이론을 기반으로 하며, 특정 부분 구조물은 실험 데이터를 다른 부분 구조물은 유한요소해석 데이터를 사용한다. 이러한 방법은 시스템 일부분의 변화가 시스템 전체에 미치는 영향을 빠르게 파악 할 수 있기 때문에 여러 분야에서 활발하게 연구하고 적용되고 있다. 특히, 제품이 개발된 후 성능개선을 위한 부분 구조물의 설계변경에 따른 전체 시스템의 FRF를 예측하는 데 유용하게 사용된다. 일반적으로 설계변경이 이뤄지는 부분 구조물의 경우 유한요소해석 데이터를 사용하는데 이는 실험 데이터와 달리 실제 물리적 모델 제작 없이 컴퓨터를 이용한 간단한 모델링 변경만으로도 전체 시스템의 성능을 예측할 수 있기 때문이다. 본 연구에서는 엔진 마운트의 응답을 예측하고 감소시키기 위해 Hybrid 모델의 부분구조합성법이 적용되었다. 엔진 마운트의 경우 그 응답이 차체로 유입되는 가진력이 되므로 차량 전체의 NVH성능 개선을 위해선 엔진 마운트의 응답 레벨을 줄이는 것이 필요하다. 유한요소해석이 적용되는 알터네이터 브라켓의 구조변경에 따라 엔진 마운트 응답이 어떻게 달라지는지 예측하고 이러한 경향성을 통해 엔진 마운트 응답을 줄이는 방안을 제시한다. 더 나아가 Hybrid 모델링 기법을 통해 많은 데이터를 빠르게 얻을 수 있다는 장점을 활용하여, Bayesian optimization 기법을 적용 하였고 이를 통해 알터네이터 브라켓의 최적화된 구조강성을 도출하였다.CHAPTER 1 INTRODUCTION 1 CHAPTER 2 LITERATURE REVIEW 4 2.1 Introduction 4 2.2 Frequency Response Function (FBS) Theory 5 CHAPTER 3 OPERATIONAL DEFLECTION SHAPE ANALYSIS 12 3.1 Introduction 12 3.2 ODS and waterfall analysis 12 CHAPTER 4 HYBRID MODELING 15 4.1 Introduction 15 4.2 Hybrid modeling formulation 15 4.3 Reliability verification of hybrid modeling method 16 4.4 Alternator bracket design modification 18 CHAPTER 5 BAYESIAN OPTIMIZATION 30 5.1 Bayesian optimization 30 5.2 Optimization of structural stiffness of alternator bracket using Bayesian optimization 31 CHAPTER 6 CONCLUSION 34 6.1 Contribution 34 6.2 Future work 35 REFERENCES 37 국문 초록 39Maste