Showing papers on "Modal testing published in 2015"

Prediction of frequency response function (FRF) of asymmetric tools from the analytical coupling of spindle and beam models of holder and tool

Abstract: The prediction of chatter stability diagrams in milling requires accurate frequency response functions (FRF) at the tool – workpiece contact zone. Traditionally, the most accurate FRFs are best obtained through the experimental modal testing of each tool, which is costly. This paper presents analytical modeling and coupling procedures for spindle–holder–tool assemblies with asymmetric tools. Tools and holders are analytically modeled with continuous Timoshenko beams, while considering variation of the cross section geometry of the fluted sections and helix angle. While each solid part segments with varying geometry are assembled with rigid receptance coupling, the holder–spindle and tool–holder are coupled using contact stiffness and damping. The asymmetric cross sections of the helical end mills cause the variation of FRF as a function of the spindle's angular position. It is experimentally proven that the proposed method can predict the FRFs as the asymmetric tools rotate.

Modal testing for model validation of structures with discrete nonlinearities.

Abstract: Model validation using data from modal tests is now widely practiced in many industries for advanced structural dynamic design analysis, especially where structural integrity is a primary requirement. These industries tend to demand highly efficient designs for their critical structures which, as a result, are increasingly operating in regimes where traditional linearity assumptions are no longer adequate. In particular, many modern structures are found to contain localized areas, often around joints or boundaries, where the actual mechanical behaviour is far from linear. Such structures need to have appropriate representation of these nonlinear features incorporated into the otherwise largely linear models that are used for design and operation. This paper proposes an approach to this task which is an extension of existing linear techniques, especially in the testing phase, involving only just as much nonlinear analysis as is necessary to construct a model which is good enough, or ‘valid’: i.e. capable of predicting the nonlinear response behaviour of the structure under all in-service operating and test conditions with a prescribed accuracy. A short-list of methods described in the recent literature categorized using our framework is given, which identifies those areas in which further development is most urgently required.

Interactive Acoustic Transfer Approximation for Modal Sound

Abstract: Current linear modal sound models are tightly coupled with their frequency content. Both the modal vibration of object surfaces and the resulting sound radiation depend on the vibration frequency. Whenever the user tweaks modal parameters to adjust frequencies the modal sound model changes completely, necessitating expensive recomputation of modal vibration and sound radiation.We propose a new method for interactive and continuous editing as well as exploration of modal sound parameters. We start by sampling a number of key points around a vibrating object, and then devise a compact, low-memory representation of frequency-varying acoustic transfer values at each key point using Prony series. We efficiently precompute these series using an adaptive frequency sweeping algorithm and volume-velocity-preserving mesh simplification. At runtime, we approximate acoustic transfer values using standard multipole expansions. Given user-specified modal frequencies, we solve a small least-squares system to estimate the expansion coefficients, and thereby quickly compute the resulting sound pressure value at arbitrary listening locations. We demonstrate the numerical accuracy, the runtime performance of our method on a set of comparisons and examples, and evaluate sound quality with user perception studies.

Modal Analysis of Woven Fiber Composite Plates with Different Boundary Conditions

Abstract: Most of the work done for the vibration of composite plates published in the literature is either analytical or numerical studies with few experimental results available on composites with unidirectional fibers. The present study involves extensive experimental works to investigate the free vibration of industry driven woven fiber glass/epoxy composite plates with different boundary conditions including free–free cases. The modern modal testing and subsequent analysis with powerful computer and digital analysis system is an important tool for prediction of behavior of structures. The specimens of woven glass fiber and epoxy matrix composite plates are manufactured by the hand-layup technique. Elastic parameters of the plate are also determined experimentally by tensile testing of specimens using INSTRON 1195. An experimental investigation is carried out using modal analysis technique with Fast Fourier Transform Analyzer, PULSE lab shop, impact hammer and contact accelerometer to obtain the frequency response functions. The computational results are compared with results of previous studies in literature wherever available. The experimental results are also compared with the FEM numerical analysis based on first-order shear deformation theory. The effects of different geometrical parameters including number of layers, aspect ratio, fiber orientation and different boundary conditions of woven fiber composite plates are studied in detail. It is observed that comparisons performed between numerical predictions and experimental tests have a good correlation. The natural frequency is very less for cantilever than simply supported and fully clamped boundary conditions. The prediction of dynamic behavior of laminated composite plates plays a significant role in the future applications of structural composites.

On the bistable zone of milling processes

Abstract: A modal-based model of milling machine tools subjected to time-periodic nonlinear cutting forces is introduced. The model describes the phenomenon of bistability for certain cutting parameters. In engineering, these parameter domains are referred to as unsafe zones, where steady-state milling may switch to chatter for certain perturbations. In mathematical terms, these are the parameter domains where the periodic solution of the corresponding nonlinear, time-periodic delay differential equation is linearly stable, but its domain of attraction is limited due to the existence of an unstable quasi-periodic solution emerging from a secondary Hopf bifurcation. A semi-numerical method is presented to identify the borders of these bistable zones by tracking the motion of the milling tool edges as they might leave the surface of the workpiece during the cutting operation. This requires the tracking of unstable quasi-periodic solutions and the checking of their grazing to a time-periodic switching surface in the infinite-dimensional phase space. As the parameters of the linear structural behaviour of the tool/machine tool system can be obtained by means of standard modal testing, the developed numerical algorithm provides efficient support for the design of milling processes with quick estimates of those parameter domains where chatter can still appear in spite of setting the parameters into linearly stable domains.

Investigation of mode identifiability of a cable-stayed bridge : comparison from ambient vibration responses and from typhoon-induced dynamic responses

Abstract: Modal identification of civil engineering structures based on ambient vibration measurement has been widely investigated in the past decades, and a variety of output-only operational modal identification methods have been proposed. However, vibration modes, even fundamental low-order modes, are not always identifiable for large-scale structures under ambient vibration excitation. The identifiability of vibration modes, deficiency in modal identification, and criteria to evaluate robustness of the identified modes when applying output-only modal identification techniques to ambient vibration responses were scarcely studied. In this study, the mode identifiability of the cable-stayed Ting Kau Bridge using ambient vibration measurements and the influence of the excitation intensity on the deficiency and robustness in modal identification are investigated with long-term monitoring data of acceleration responses acquired from the bridge under different excitation conditions. It is observed that a few low-order modes, including the second global mode, are not identifiable by common output-only modal identification algorithms under normal ambient excitations due to traffic and monsoon. The deficient modes can be activated and identified only when the excitation intensity attains a certain level (e.g., during strong typhoons). The reason why a few low-order modes fail to be reliably identified under weak ambient vibration excitations and the relation between the mode identifiability and the excitation intensity are addressed through comparing the frequency-domain responses under normal ambient vibration excitations and under typhoon excitations and analyzing the wind speeds corresponding to different response data samples used in modal identification. The threshold value of wind speed (generalized excitation intensity) that makes the deficient modes identifiable is determined.

Structural identification with incomplete instrumentation and global identifiability requirements under base excitation

Abstract: Summary Estimating the mass and stiffness parameters of a structural system via its vibration response measurements is the primary objective in the field of modal testing and structural health monitoring. The attainment of this objective, however, is hindered by various practical and theoretical issues. One such issue is incomplete instrumentation, leading to spatially incomplete mode shapes and often nonunique identification results. When the excitation is induced by ground motion, the problem is further complicated because of arbitrary normalization of mode shapes. This study attempts to address these issues for shear-building type structures. Mode shape normalization and expansion approaches are developed that utilize the topology of the structural matrices. Theoretical constraints regarding minimal instrumentation and the necessity for any a priori information are addressed vis-a-vis the requirements for global identifiability. Some practical implementation issues are discussed. The performance of the method is evaluated using numerical simulations and shake table experiments. Copyright © 2015 John Wiley & Sons, Ltd.

Stability analysis in milling of flexible parts based on operational modal analysis

Abstract: The classic approach to stability analysis in milling is based on the frequency response function (FRF) of the system obtained by the impact test. Application of this technique for a flexible workpiece with variable dynamics such as thin-walled structures may be difficult or impossible because the modal parameters of a part change due to material removal or tool position. Besides the workpiece vibration are significant compared to that of the tool. Therefore precise determination of the varying FRF is vital. It can be achieved by application of operational modal analysis based on workpiece acceleration measured during machining. The novelty of the proposed procedure lies in using the cutting force model for scaling modal residues that enables constructing stability lobes diagram from output-only data.

Modal analysis of back-to-back planetary gear: experiments and correlation against lumped-parameter model

Abstract: In order to characterize the dynamic behaviour of a back-to-back planetary gear, experimental and numerical modal analysis techniques are achieved. Rotational and translational modal deflections are highlighted. Natural frequencies are compared to the results from the lumped-parameter model. The modes are presented in the numerical studies in low-frequency and high-frequency bands. Distributions of modal kinetic and strain energies are studied.

Estimation of elastic and modal parameters in composites using vibration analysis

Abstract: This study presents the application of vibration analysis in the determination of elastic constants (i.e. Young’s modulus in fiber direction, transverse Young’s modulus, and shear modulus) and moda...

Design Criteria Based on Modal Analysis for Vibration Sensing of Thin-Wall Plate Machining

Abstract: Machining complex thin-wall components, such as casings and compressor disks in aircraft engines, is a challenging task because continuous deformation and vibration renders poor precision and quality in final products. However, monitoring workpiece vibration is hindered by harsh working conditions like cutting fluids, not to mention investigation into the vibration principle during cutting. In order to establish criteria for designing noncontact sensors to monitor workpiece vibration, this study presents a plate dynamic model along with experimentally identified damping ratios for an annular workpiece under constraints emulating those of a duplex turning machine. Formulated as a dimensionless boundary value problem, the solutions that have been numerically verified with finite element analysis provide a rational basis for identifying key cutting process parameters and quantifying their effects on thin-wall component vibration sensing. With a detailed modal analysis, the dynamic model provides a simple yet practical method for vibration measurements using an eddy-current sensing approach. Experiments were carried out to justify the proposed method, validate the stability of eddy-current sensing under the harsh cutting condition, and investigate the effect of sensor placement on sensing configuration design.

Effective approach for calculating critical speeds of high-speed permanent magnet motor rotor-shaft assemblies

Abstract: An effective approach is presented for large errors in calculating critical speed of rotor-shaft assembly with the commercial finite element software, is intended to develop the discrete model of the rotor-shaft assembly by using lumped mass method, which is supported by active magnetic bearings. The first two bending critical speeds are analysed by optimising the flexural rigidity coefficient based on transfer matrix method. Compared with experimental modal testing and finite element analysis, the results of the transfer matrix method are in good agreement with modal measurement, the percentage errors of the first two bending natural frequencies are 0.21 and 2.1%, respectively. Owing to the higher accuracy and numerical stability, the method used in this study is an effective way to calculate the critical speed of the rotor-shaft assembly.

Seismic Modal Contribution Factors

Abstract: Over the years, the belief that the first mode of vibration governs the seismic response of shear-type frame structures has been widely accepted and proved to be effective for preliminary structural design. Indeed, most of the actual seismic design procedures are based on drift profiles which are typically an approximation of the shape of the fundamental mode of vibration. In this paper, an analytical study on the dynamic properties of multi-storey shear-type frames is carried out with the purpose of precisely identifying the contribution of the modes of vibration to the seismic response of such structures, both in terms of maximum inter-storey displacement profiles (which govern the beams and columns maximum actions) and maximum inter-storey velocity profiles (which govern the viscous dampers maximum forces, of fundamental importance for building structures equipped with additional viscous dampers). A new parameter, referred to as Seismic Modal Contribution Factor, which represents the contribution of the generic mode to the seismic response of the structure, is introduced. With respect to the well-known Modal Contribution Factor, grounded on the concept of modal static response, the Seismic Modal Contribution Factor explicitly takes into account also the dynamic nature of the response due to earthquake excitation. The Seismic Modal Contribution Factor could be a meaningful parameter to be implemented in a professional structural design software and used in conjunction with the common modal participating mass ratios to identify the number of modes to be included in the analyses.

Parametric Instability of Beams with Transverse Cracks Subjected to Harmonic In-Plane Loading

Abstract: Cracks in structural members lead to local changes in their stiffness and consequently their static, dynamic and stability behavior is altered. The influence of cracks on dynamic characteristics like free vibration, buckling and parametric resonance characteristics of a cracked beam with a transverse crack using finite element method (FEM) is investigated in the present work. Modal testing of beams with transverse open crack is conducted using FFT analyzer to verify the frequencies of vibration of beams. The crack is assumed to be open type and the analysis is linear based on small deformation theory neglecting damping. The loading on the beam is considered as axial with a simple harmonic fluctuation with respect to time. A two-noded Timoshenko beam element with provision of crack is used in this study. The equation of motion represents a system of second-order differential equations with periodic coefficients of the Mathieu–Hill type. The development of the regions of instability arises from Floquet's theory and the periodic solution is obtained by Bolotin's approach using FEM. It is observed that the frequencies of vibration and buckling load of the beam are influenced significantly by location and depth of cracks. It is observed that, for a given location of crack, the onset of instability occurs earlier with increase in depth of crack. As the location of crack moves from the fixed end to the free end the excitation frequency increases. The instability occurs later and the width of the instability regions reduces. When the damage is near to the free end, the instability region almost coincides with the instability region for the undamaged beam. This means that the damage near the fixed end is more severe on the dynamic instability behavior than that of the crack located at other positions. The vibration and instability results can be used as a technique for structural health monitoring or testing of structural integrity, performance and safety.

A Fast Maximum Likelihood-Based Estimation of a Modal Model

Abstract: In this paper, the ML-MM estimator, a multivariable frequency-domain maximum likelihood estimator based on a modal model formulation, will be represented and improved in terms of the computational speed and the memory requirements. Basically, the design requirements to be met in the ML-MM estimator were to have accurate estimate for both of the modal parameters and their confidence limits and, meanwhile, having a clear stabilization chart which enables the user to easily select the physical modes within the selected frequency band. The ML-MM method estimates the modal parameters by directly identifying the modal model instead of identifying a rational fraction polynomial model. In the ML-MM estimator, the confidence bounds on the estimated modal parameters (i.e., frequency, damping ratios, mode shapes, etc.) are derived directly by inverting the so-called Fisher information matrix and without using many linearization formulas that are normally used when identifying rational fraction polynomial-based models. Another advantage of the ML-MM estimator lies in its potential to overcome the difficulties that the classical modal parameter estimation methods face when fitting an FRF matrix that consists of many (i.e., 4 or more) columns, i.e., in cases where many input excitation locations have to be used in the modal testing. For instance, the high damping level in acoustic modal analysis requires many excitation locations to get sufficient excitation of the modes. In this contribution, the improved ML-MM estimator will be validated and compared with some other classical modal parameter estimation methods using simulated datasets and real industrial applications.