Phase Response Error Analysis in Dynamic Testing of Electric Drivetrains: Effects of Measurement Parameters

This article evaluates the use of experimental frequency response functions for damage detection and quantification of a concrete beam with the help of model updating theory. The approach is formulated as an optimization problem that intends to adjust the analytical frequency response functions from a benchmark finite element model to match with the experimental frequency response functions from the damaged structure. Neither model expansion nor reduction is needed because the individual analytical frequency response function formulation is derived. Unlike the commonly used approaches that assume zero damping or viscous damping for simplicity, a more realistic hysteretic damping model is considered in the analytical frequency response function formulation. The accuracy and anti-noise ability of the proposed approach are first verified by the numerical simulations. Next, a laboratory reinforced concrete beam with different levels of damage is utilized to investigate the applicability in an actual test. The results show successful damage quantification and damping updating of the beam by matching the analytical frequency response functions with the experimental frequency response functions in each damage scenario.

An expansion technique for the estimation of unmeasured rotational frequency response functions

Frequency response function-based model updating using Kriging model

This paper presents preliminary experimental results from a novel shaking table testing campaign investigating the dynamic response of a two-degree-of-freedom (2DOF) physical specimen with a grounded inerter under harmonic base excitation and contributes a nonlinear dynamic model capturing the behavior of the test specimen. The latter consists of a primary mass connected to the ground through a high damping rubber isolator (HDRI) and a secondary mass connected to the primary mass through a second HDRI. Further, a flywheel-based rack-and-pinion inerter prototype device is used to connect the secondary mass to the ground. The resulting specimen resembles the tuned mass damper inerter (TMDI) configuration with grounded inerter analytically defined and numerically assessed by the authors in a number of previous publications. Physical specimens with three different inerter coefficients are tested on the shake table under sine-sweep excitation with three different amplitudes. Experimental frequency response functions (FRFs) are derived manifesting a softening nonlinear behavior of the specimens and enhanced vibration suppression with increased inerter coefficient. Further, a 2DOF parametric nonlinear model of the specimen is established accounting for non-ideal inerter device behavior and its potential to characterize experimental response time-histories, FRFs, and force-displacement relationships of the HDRIs and of the inerter is verified.

In order to obtain a more accurate finite element model of a constructed structure, a new frequency response function–based model-updating approach is proposed. A general viscous damping model is assumed in this approach for better simulating the actual structure. The approach is formulated as an optimization problem which intends to minimize the difference between analytical and experimental frequency response functions. Neither dynamic expansion nor model reduction is needed when not all degrees of freedom are measured. State-of-the-art optimization algorithms are utilized for solving the non-convex optimization problem. The effectiveness of the presented frequency response function model-updating approach is validated through a laboratory experiment on a four-story shear-frame structure. To obtain the experimental frequency response functions, a shake table test was conducted. The proposed frequency response function model-updating approach is shown to successfully update the stiffness, mass, and damping parameters in matching the analytical frequency response functions with the experimental frequency response functions. In addition, the updating results are also verified by comparing time-domain experimental responses with the simulated responses from the updated model.

Frequency Response Function (FRF) residues have been widely used to update Finite Element models. They are a kind of original measurement information and have the advantages of rich data and no extraction errors, etc. However, like other sensitivity-based methods, an FRF-based identification method also needs to face the ill-conditioning problem which is even more serious since the sensitivity of the FRF in the vicinity of a resonance is much greater than elsewhere. Furthermore, for a given frequency measurement, directly using a theoretical FRF at a frequency may lead to a huge difference between the theoretical FRF and the corresponding experimental FRF which finally results in larger effects of measurement errors and damping. Hence in the solution process, correct selection of the appropriate frequency to get the theoretical FRF in every iteration in the sensitivity-based approach is an effective way to improve the robustness of an FRF-based algorithm. A primary tool for right frequency selection based on the correlation of FRFs is the Frequency Domain Assurance Criterion. This paper presents a new frequency selection method which directly finds the frequency that minimizes the difference of the order of magnitude between the theoretical and experimental FRFs. A simulated truss structure is used to compare the performance of different frequency selection methods. For the sake of reality, it is assumed that not all the degrees of freedom (DoFs) are available for measurement. The minimum number of DoFs required in each approach to correctly update the analytical model is regarded as the right identification standard.

In order to obtain a finite element (FE) model that can more accurately describe structural behaviors, experimental data measured from the actual structure can be used to update the FE model. The process is known as FE model updating. In this paper, a frequency response function (FRF)-based model updating approach is presented. The approach attempts to minimize the difference between analytical and experimental FRFs, while the experimental FRFs are calculated using simultaneously measured dynamic excitation and corresponding structural responses. In this study, the FRF-based model updating method is validated through laboratory experiments on a four-story shear-frame structure. To obtain the experimental FRFs, shake table tests and impact hammer tests are performed. The FRF-based model updating method is shown to successfully update the stiffness, mass and damping parameters of the four-story structure, so that the analytical and experimental FRFs match well with each other.

Accurate analytical models of engineering structures are of paramount importance for dynamicists to be used in predicting the dynamic behaviour (frequency response function) of the structures. The finite element method (FEM) and the experimental modal analysis (EMA) have been known as powerful and useful methods that can be used to determine the frequency response function (FRF) of the structures. However, the finite element FRF are often not in good agreement with experimental FRF due to assumption properties in finite element (FE) model. Therefore, in order to have a reliable FE model of a structure, measured FRF obtained from the experimental modal analysis can be integrated with finite element FRF to reconcile the FE model and the procedures involved in the reconciliation is a model updating process. Prior performing the updating process, the experimental FRF must be in good quality to obtain accurate FE model results. One way to reduce noise data and eliminate suspicious modes in FRF data is to use the FRF synthesised method. The main goal of this study is to use frequency response function based updating to minimise the error of a laser spot welded structure by using FRF synthesised data. In this work, MSC Software and LMS Test Lab were used to predict and measured the FRF of laser spot welded structure. The results revealed that FRF based updating method is successfully reduced the correlation gap between synthesised FRF and predicted FRF.

THE USE OF ANTIRESONANCES FOR ROBUST MODEL UPDATING

The frequency based substructuring (FBS) method allows the combination between the experimental and analytical frequency response function (FRF). The combined FRF is then used for calculation of the dynamic behaviour of an assembled structure which usually consists of a large number structural components or substructures. However, the accuracy of the dynamic behaviour calculated using the FBS method relies heavily on the quality of experimental FRF data of the interfaces on which, in practice, it is very problematic to be attained. Furthermore, in most cases, some parts of rotational FRF data are not included in the FBS method due to the complex measurement process. The exclusion of the rotational FRF data will usually lead to numerous errors in the combined FRF data. Therefore, this paper proposes a new frequency response function (FRF) coupling of the FBS method that may uniquely address the difficulties and improve the quality of predicted results of the FBS method. The proposed coupling was formulated based on the finite element method, model updating method and FRF synthesize method. The finite element model of the physical test substructure was developed and reconciled based on the mode shapes obtained from experimental modal analysis. The FRF synthesize method was performed on the updated finite element model to obtain a complete matrix with a full degree of freedom FRF data containing all the translational and rotational FRF data required. It was found that the proposed coupling has allowed generating full translational and rotational FRF data. The generation has improved significantly the FRF coupling process and the quality of the predicted dynamic behaviour of the FBS method.

The objective of this paper is to present frequency response function (FRF) based updating as a method for matching the finite element (FE) model of a laser spot welded structure with a physical test structure. The FE model of the welded structure was developed using CQUAD4 and CWELD element connectors, and NASTRAN was used to calculate the natural frequencies, mode shapes and FRF. Minimization of the discrepancies between the finite element and experimental FRFs was carried out using the exceptional numerical capability of NASTRAN Sol 200. The experimental work was performed under free-free boundary conditions using LMS SCADAS. Avast improvement in the finite element FRF was achieved using the frequency response function (FRF) based updating with two different objective functions proposed.

Due to the important contribution of flexible modal in rigid-flexible coupled multiple body system (MBS) dynamics, model updating of flex-body generation became a significant and necessary procedure. In this paper, a model updating method based on the measured frequency response function (FRF) is proposed to modify the flexible body in finite element analysis (FEA). To overcome the complexity of multiple measured responses and the huge cost of computation, the Kriging surrogate model with multi-objective function which considers the FRF’s magnitude and shape of curves is proposed. Moreover, the FRF measurement of a high-speed railway carbody is conducted and the measured FRF is transferred into proposed model updating procedure. The results show that the proposed method is performed successfully on a high-speed railway vehicle after model updating and the simulated FRFs tend to coincide with the experimental FRFs. Finally, the updated model is transferred to the rigid-flexible MBS model to validate the influence of the model updating with a comparison of the vibration spectrum and ride comfort index. The results show that the updating procedure will make the prediction of vibration and ride comfort index closer to experimental results.KeywordsModel updatingMultibody system dynamicsKriging modelHigh-speed railway

High-speed micromilling (spindle speeds 100 000 r/min) can create complex three-dimensional microfeatures in difficult-to-machine materials. The micromachined surface must be of high quality, to meet functional requirements. However, chatter-induced dynamic instability deteriorates the surface quality and can be detrimental to tool life. Chatter-free machining can be accomplished by identifying stable process parameters via stability lobe diagram. To generate accurate stability lobe diagram, it is essential to determine the microend mill dynamics. Frequency response function is required to determine the tool-tip dynamics obtained by experimental impact analysis. Note that application of impact load at the microend mill tip (typically 100 – 500 μm) is not feasible as it would invariably end with tool failure. Consequently, alternative methods need to be developed to identify the microend mill dynamics. In the present work, the frequency response function for the microend mill is obtained by finite element method modal analysis. The frequency response function obtained from modal analysis has been verified from the experimentally obtained frequency response function. The experimental frequency response function was obtained by impacting the microend mill near the taper portion with an impact hammer and measuring the vibration of the tool-tip with a laser displacement sensor. The fundamental frequency obtained from finite element method modal analysis shows a difference of 6.6% from the experimental fundamental frequency. Microend mill dynamics obtained from the finite element method is used for chatter prediction in high-speed micromilling operations. The stability lobe diagram predicts the stability boundary accurately at 60 000 r · min–1 and 80 000 r/min; however, a slight deviation is observed at 100 000 r/min.

Most of the finite element model updating method uses resonance frequencies and mode shapes. The mode shapes are not very accurate as suggested by many researchers. Whereas, antiresonance frequencies can be identified accurately from measured frequency response functions (FRFs). In this paper, a new model updating method is proposed, which uses resonance and antiresonance frequencies for better FRF matching of updated FRF and experimental FRF. The effectiveness of the proposed finite element updating method is demonstrated by measured data of fixed-fixed beam structure. The updated results have shown that the use of resonance along with antiresonance frequencies for finite element model updating can be used to derive accurate model of the system. This is illustrated by matching of the FRFs obtained from the updated model with that of experimental data.

Acording to the fact that the finite element model of electromagnetic vibration shaker for virtual experiment is not accurate enough to complete accurately spacecraft test, made a correlation analysis of the finite element output frequency response function and the measured frequency response function by their correlation coefficients. Analyzed the sensitivity of the materials for FRF and screened the parameters to update, made the correlation coefficient error of electromagnetic vibration shaker finite element model frequency response function and the measured as the optimization objective, the optimization and modification of shaker finite element model parameters were completed by iteration method. The frequency response function of the modified finite element model approximately agreed with the experimental frequency response function. It met the virtual experiments of electromagnetic vibration shaker.