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

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

Influence of Interfacial Dynamics and Multi-Dimensional Coupling from Isolator Brackets on Exhaust Isolation System Performance

An automotive exhaust structure is a primary structure-borne noise path by which vibratory forces from the powertrain are transmitted to the vehicle body. The exhaust structure is typically connected to the vehicle body through a system of brackets containing elastomeric isolators, serving as the principal means of vibration isolation. In exhaust isolator system design, the isolator brackets are often modeled as simple springs. This approach neglects the effects of interfacial dynamics and multi-dimensional coupling, which result from distributed mass and stiffness throughout the isolator brackets. Accordingly, the objective of this research is to better understand how the interfacial dynamics and multi-dimensional coupling of the isolator brackets affect the exhaust isolation system performance in the 0-100 Hz range. Therefore, models with a proper representation of these interfacial dynamics and multi-dimensional coupling are created using finite element analysis (FEA) and then parameterized into multi-dimensional lumped parameter models through correlation of static and modal testing on the components and assembled system. The dynamic responses from the models for the exhaust structure and isolator brackets are then combined into a system-level model through a frequency-response-function-based substructuring method. A design study is conducted on the system-level model by systematically changing component parameters and evaluating the effect on the transmitted vertical body forces. The results show that the inclusion of these interfacial dynamics have nominal influence on isolation performance; however, the coupling terms show an observable influence, typically increasing the force transmitted to the vehicle body. In addition, the study identified additional design modifications that could improve isolation performance, such as an increase in isolator material loss factor and an increase in the isolator fore-aft stiffness. Although the results are specific to this isolation system design, the modeling procedure outlined has the potential to be used early in the vehicle design process to identify improvements to other baseline designs.NSF I/UCRC Smart Vehicle Concepts CenterTenneco, Inc.A three-year embargo was granted for this item.Academic Major: Mechanical Engineerin

AIRBORNE PATH FREQUENCY BASED SUBSTRUCTURING METHOD AND ITS APPLICATIONS

Frequency based substructuring (FBS) is routinely used to model structural dynamics. It provides a framework for connecting structural subsystems together, assessing path contributions, determining the effect of mount modification, and identifying inverse forces. In this work, FBS methods are extended to include acoustic subsystems and connecting pipes and ducts. Connecting pipes or ducts are modeled using the transfer matrix approach which is commonly used for modeling mufflers and silencers below the plane wave cutoff frequency. The suggested approach is validated using boundary element method (BEM) simulation. Applications of the procedure include determining airborne path contributions, the effect of treating ducts and apertures, and the effect of making lumped acoustic impedance modifications to a subsystem. The method can be simplified and used for determining the effect of design changes on the insertion loss of enclosures

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

Application of bolt joints dynamic parameters identification in machine tools based on partially measured frequency response functions

This paper presents a method to identify the bolt joints dynamic parameters based on partially measured frequency response functions (FRFs) and demonstrates its application in machine tools. Basic formulas are derived to identify the joint dynamic properties based on the substructuring method and an algorithm to estimate the unmeasured FRFs is also developed. The identification avoids direct inverse calculation to the frequency response function matrix, and its validity is demonstrated by comparing the simulated and measured FRFs of the assembled free-free steel beams with a bolt joint. An approach is put forward to apply the identification in machine tools by constructing structures assembled of substructures and joint structures to substitute the bolt joints in machine tools and assuring the contact conditions unchanged. The identification of the bed-column bolt joint in a vertical machining center is provided to describe the application procedure and show the feasibility of the proposed approach

FRF 합성법을 이용한 차량 로드노이즈 저감방안에 대한 연구

학위논문 (석사)-- 서울대학교 대학원 공과대학 기계항공공학부, 2017. 8. 강연준.본 연구에서는 서스펜션 부시와 차체로 전달되는 구조기인 로드노이즈 사이의 관계를 파악하고, 부시 동강성 변화를 통한 로드노이즈 저감 방안에 대하여 연구하였다. 구조기인 로드노이즈는 서스펜션을 통해 차체로 전달되는 가진력에 의해서 결정이 되기 때문에 부시 동강성과 차체 전달 가진력 사이의 관계를 파악하는 것이 이 연구의 목표이다. 부시와 로드노이즈 사이의 관계를 파악하기 위하여, 부시가 차체와 서스펜션 결합 사이에서 조인트 역할을 한다고 가정하고 FRF Based Substructuring 기법을 사용하였다. 검증을 위하여 현가장치 리그 테스터와 힘 변환기를 이용하여 실제 가진력을 측정, 부시의 동강성 변화에 따라서 실제로 가진력을 예측할 수 있는지 예측과 실험을 함께 수행하였다. 또한, 서스펜션에 압입되어있는 부시의 동강성을 간단하게 간접적으로 구하기 위해서 FRF 관계식을 이용하였으며, 이를 검증하기 위하여 부시를 뺄 수 있는 특별한 서스펜션을 제작하여 검증실험을 진행하였다. 본 연구를 통하여 서스펜션에 사용되는 부시의 동강성이 실제로 차량 로드노이즈에 미치는 영향을 확인할 수 있고, 정량적인 부시 동강성을 개선안을 도출해내는데 본 연구가 이용될 것이라고 생각한다.1. 서론 1 2. 기초 이론 3 2.1. 로드노이즈 특성 3 2.2. 주파수응답함수 합성기법 3 2.3 Receptance Method 5 2.4 FBS 기법을 이용한 여러 경로조건에서의 반력 추정 6 2.5 동특성 추정 방법 7 3. 실험 구성 및 측정 방법 11 3.1 구조물 FRF 측정 실험 11 3.1.1 부쉬키트 FRF 측정 11 3.1.2 서브프레임 FRF 측정 13 3.1.3 포스리그 FRF 측정 14 3.1.4 부쉬 FRF 측정 15 3.1.5 부쉬 동강성 증가 후 FRF 측정 15 3.2 구조물 결합 및 반력 측정 16 3.2.1 포스리그와 서브프레임 체결 및 전달 힘 측정 16 4. 실험결과 및 분석 26 4.1 부쉬 키트 반력 측정 및 예측 결과 비교 26 4.2 서브프레임 반력 측정 및 예측 결과 비교 27 4.3. 부쉬강성 변화에 따른 전달률 비교 28 5. 결론 37 참고문헌 39Maste

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

EFFECTS OF SUPPORT STRUCTURE DYNAMICS ON CENTRIFUGAL COMPRESSOR ROTOR RESPONSE

LectureAccurate modeling of complicated dynamic phenomena characterizing rotating machineries represents a critical aspect in the rotor dynamic field. A correct prediction of rotor behavior is fundamental to identify safe operating conditions avoiding unstable operating range that may lead to erroneous project solution or possible unwanted consequences for the plant. Considering generic rotating machineries as mainly partitioned in four components (rotors, bearings, stator and supporting structure), most research activities have been addressed so far with strong focus more on the single components rather than on the whole system assembly. The importance of a combined analysis of rotors and elastic supporting structure (Kruger 2013) arises with the continuous development of turbo machinery applications, in particular in the Oil & Gas field, where a wide variety of solutions, such as off-shore installations or modularized turbo compression and turbo generator trains, lead to the need of a more complete study not only limited to the rotor-bearing system