Vibration analysis of HDD actuator with equivalent finite element model of VCM coil

As the rate of increase in areal density of the HDD has accelerated, dynamic characteristics of the HDD actuator need to be improved with respect to the performance of the tracking servo and shock transmission. Therefore, it is important to analyze the vibration characteristic of the HDD actuator that consists of the VCM part, E-block and pivot bearing. In this paper, vibration modes of the HDD actuator are investigated the using finite element and experimental modal analyses methods. To develop a detailed finite element model, finite element models of each components of the actuator assembly are constructed and tuned to the results of the EMA. The VCM coil is modeled as an equivalent finite element model that has an orthotropic material property using auto-model updating program. Auto-model updating program with improved sensitivity based iterative method is applied to build a detailed finite element model using the result of the EMA. A detailed finite element model of the HDD actuator is then constructed and analyzed.     

有限元模型BERMAN修正算法的改进

BERMAN修正方法基于无阻尼系统的模态正交条件 ,利用实验模态矩阵和特征值对有限元理论模型进行修正。指出该方法存在的 2个缺陷 ,给出一种改进后的BERMAN修正方法 ,并编写了相应的迭代程序。通过修正一个实际例子表明 ,改进后的BERMAN修正方法有可取之处。     

Proximal-point method for finite element model updating problem

The problem of finding the optimal approximation to analytical stiffness matrix modeled by the finite element method is considered in this paper. Desired matrix properties, including satisfaction of the dynamic equation, symmetry, positive semidefiniteness and physical connectivity, are imposed as side constraints of the minimization problem. To the best of the author's knowledge, the finite element model updating problem containing all these constraints simultaneously has not been proposed in the literature earlier. By partial Lagrangian multipliers technique, the optimization problem is transformed into a matrix linear variational inequality and the proximal-point method is first used to solve the equivalent problem. The results of numerical examples show that the proposed method works well even for incomplete measured data.     

A new method for finite element model updating in structural dynamics

A method is propounded in this paper to update finite element models in the field of structural dynamics. It is especially intended to solve cases for which other methods either cannot be applied or are inefficient. It is posed as the minimization of an error function defined in the time domain. The minimization is carried out by a novel adaptive sampling algorithm, which constitutes the main contribution in this work. In this algorithm, the solution is searched by sampling the parameters to be updated within a bounded space in an iterative form. The Beta distribution, which is consistent with the bounded character of the search space, is chosen for the sampling. The characteristics of the distributions are changed in each step of the process depending on the results of the previous ones. The method has been tested through a simulated dynamic model and an experimental case. In these particular cases, the performance of the proposed adaptive algorithm was better than those of other related stochastic algorithms it was compared with.     

Model selection in finite element model updating using the Bayesian evidence statistic

This paper considers the problem of finite element model (FEM) updating in the context of model selection. The FEM updating problem arises from the need to update the initial FE model that does not match the measured real system outputs. This inverse system identification-problem is made even more complex by the uncertainties in modeling some of the structural parameters. Such uncertainty often results in a number of competing forms of FE models being proposed which leads to lack of consensus in the field. A model can be formulated in a number of ways; by the number, the location and the form of the updating parameters. We propose the use of a Bayesian evidence statistic to help decide on the best model from any given set of models. This statistic uses the recently developed stochastic nested sampling algorithm whose by-product is the posterior samples of the updated model parameters. Two examples of real structures are each modeled by a number of competing finite element models. The individual model evidences are compared using the Bayes factor, which is the ratio of evidences. Jeffrey's scale is then used to determine the significance of the model differences obtained through the Bayes factor.     

基于有限元模型修正的损伤识别方法研究

通过实验方法测得结构的模态参数,建立结构系统的有限元基准(未损)模型,同时为了避免将初始的有限元模型误差误判为损伤,需对原始的基准模型进行有限元修正,建立基准解析模型.由于系统质量参数可以准确获得且在模型修正过程中保持质量不变,因此可将刚度参数作为修正对象,通过改变弹簧刚度,使其有限元动力分析的结果与实测结果尽量吻合.随后定义损伤变量(损伤引起刚度的变化率即灵敏度),借助刚性灵敏度实现对结构损伤位置与损伤程度的识别.     

A method in model updating using Miscorrelation Index sensitivity

This paper presents a new model updating method based on minimization of an index called Miscorrelation Index (MCI), which is introduced to localize the coordinates carrying error in a finite element (FE) model. MCI can be calculated from measured frequency response functions (FRFs) and dynamic stiffness matrix of the FE model for each coordinate as a function of frequency. Nonzero numerical values for MCI of a coordinate indicate errors in one or more elements of the system matrices corresponding to this coordinate. The sensitivity-driven model updating method presented in this study (MCI Sensitivity Method) is based on minimization of MCI. The application of the method is illustrated with four case studies. In the first and second examples a discrete system is considered, and computationally generated and polluted FRFs are used as pseudo-test data. In the third and fourth case studies, real test data is used and the performance of the method in practical applications is demonstrated on the benchmark structure built to simulate the dynamic behavior of an airplane, namely, GARTEUR SM-AG19 test bed. It is concluded that MCI Sensitivity Method yields successful results even when the measured responses of only a few coordinates are used, especially when miscorrelation is due to local errors.     

C型弹簧管固有频率灵敏度的有限元分析

以C型弹簧管为研究对象,建立有限元分析模型,并利用ANSYS灵敏度分析技术对影响弹簧管固有频率的主要结构参数进行研究。得出弹簧管固有频率和其主要结构参数之间的关系,为弹簧管的减振设计和进一步的动力学分析提供了理论依据。     

Iterative finite element model updating in the time domain

An iterative time domain formulation for finite element model updating in structural dynamics is presented. The approach is supported on a derivation showing that the discrepancy between observations and model predictions can be expressed as a convolution between the state of the system and a sequence of pseudo-Markov parameters which are linear in the change of the free parameters. The approach is illustrated by updating all the stiffness and damping parameters of a twenty degree of freedom shear beam using four noise contaminated measurements.     

Statistical updating of finite element model with Lamb wave sensing data for damage detection problems

Health monitoring of large structures with embedded, distributed sensor systems is gaining importance. This study proposes a new probabilistic model updating method in order to improve the damage prediction capability of a finite element analysis (FEA) model with experimental observations from a Lamb-wave sensing system. The approach statistically calibrates unknown parameters of the FEA model and estimates a bias-correcting function to achieve a good match between the model predictions and sensor observations. An experimental validation study is presented in which a set of controlled damages are generated on a composite panel. Time-series signals are collected with the damage condition using a Lamb-wave sensing system and a one dimensional FEA model of the panel is constructed to quantify the damages. The damage indices from both the experiments and the computational model are used to calibrate assumed parameters of the FEA model and to estimate a bias-correction function. The updated model is used to predict the size (extent) and location of damage. It is shown that the proposed model updating approach achieves a prediction accuracy that is superior to a purely statistical approach or a deterministic model calibration approach.     

Adaptive regularization parameter optimization in output-error-based finite element model updating

In finite element (FE) model updating, regularization methods are required to alter the ill-conditioned system of equations towards a well-conditioned one. The present study addresses the regularization parameter determination when implementing the Tikhonov regularization technique in output-error-based FE model updating. As the output-error-based FE model updating results in a nonlinear least-squares problem which requires iteration for solution, an adaptive strategy that allows varying value of the regularization parameter at different iteration steps is formulated, where the optimal regularization parameter at each iteration step is determined based on the computationally efficient minimum product criterion (MPC). The performance of MPC in output-error-based FE model updating is examined and compared with the commonly used L-curve method (LCM) and the generalized cross validation (GCV) through numerical studies of a truss bridge using noise-free and noise-corrupted modal data. It is shown that MPC is effective and robust in determining the regularization parameter compared with the other two methods, especially when noise-corrupted data are used. The adaptive strategy is more efficient than the fixed strategy that uses a constant value of the regularization parameter throughout the iteration process.     

New iterative method for model updating based on model reduction

Model reduction technique is usually employed in model updating process. Here, a new iterative method associating the model updating method with the model reduction technique is investigated. Using the traditional iterative method, the errors resulted from replacing the reduction matrix of the experimental model with that of the finite element (FE) model are not fully considered, which needs more iterations and computing time. In order to reduce the errors produced in the replacement, a new iterative method is proposed based on the traditional method, in which the correction term related to the errors is added. The comparisons between the traditional iterative method and the proposed iterative method are shown by model updating examples of solar panels and both of these two iterative methods combine the cross-model cross-mode (CMCM) method and the succession-level approximate reduction (SAR) technique. The results indicate that the convergence rate and the computing time of the new method are significantly superior to those of the traditional iterative method with or without noise.     

The role of anti-resonance frequencies from operational modal analysis in finite element model updating

Finite element model updating traditionally makes use of both resonance and modeshape information. The mode shape information can also be obtained from anti-resonance frequencies, as has been suggested by a number of researchers in recent years. Anti-resonance frequencies have the advantage over mode shapes that they can be much more accurately identified from measured frequency response functions. Moreover, anti-resonance frequencies can, in principle, be estimated from output-only measurements on operating machinery. The motivation behind this paper is to explore whether the availability of anti-resonances from such output-only techniques would add genuinely new information to the model updating process, which is not already available from using only resonance frequencies.This investigation employs two-degree-of-freedom models of a rigid beam supported on two springs. It includes an assessment of the contribution made to the overall anti-resonance sensitivity by the mode shape components, and also considers model updating through Monte Carlo simulations, experimental verification of the simulation results, and application to a practical mechanical system, in this case a petrol generator set.Analytical expressions are derived for the sensitivity of anti-resonance frequencies to updating parameters such as the ratio of spring stiffnesses, the position of the centre of gravity, and the beam's radius of gyration. These anti-resonance sensitivities are written in terms of natural frequency and mode shape sensitivities so their relative contributions can be assessed. It is found that the contribution made by the mode shape sensitivity varies considerably depending on the value of the parameters, contributing no new information for significant combinations of parameter values.The Monte Carlo simulations compare the performance of the update achieved when using information from: the resonances only; the resonances and either anti-resonance; and the resonances and both anti-resonances. It is found that the addition of anti-resonance information improves the updating performance for some combinations of parameter values, but does not improve the update in significant other regions.The simulated results are verified using resonance and anti-resonance frequencies measured on a steel beam test rig. The investigation is extended to include the updating of parameters of a petrol generator set. It is found that the contribution of the anti-resonances to the model update is heavily dependent on the geometry of the model and the choice of variables to be updated, suggesting that, for some models, the pursuit of anti-resonance information through expensive operational modal analysis may be inappropriate.     

An improved updating parameter selection method and finite element model update using multiobjective optimisation technique

Finite element model updating is a procedure to minimise the differences between analytical and experimental results and is usually posed as an optimisation problem. In model updating process, one requires not only satisfactory correlations between analytical and experimental results, but also maintaining physical significance of updated parameters. For this purpose, setting up of an objective function and selecting updating parameters are crucial steps in model updating. These require considerable physical insight and usually trial-and-error approaches are common to use. In conventional model updating procedures, an objective function is set as the weighted sum of the differences between analytical and experimental results. But the selection of the weighting factors is not clear since the relative importance among them is not obvious but specific for each problem. In this work, multiobjective optimisation technique is introduced to extremise several objective terms simultaneously. Also the success of finite element model updating depends heavily on the selection of updating parameters. In order to avoid an ill-conditioned numerical problem, the number of updating parameters should be kept as small as possible. Such parameters should be selected with the aim of correcting modelling errors and modal properties of interest should be sensitive to them. When the selected parameters are inadequate, then the updated model becomes unsatisfactory or unrealistic. An improved method to guide the parameter selection is suggested.     

有限元建模中的几何清理问题

在有限元建模中，直接将较复杂的实体模型进行有限元造型将会遇到很多困难，必须先对模型进行几何清理，对实体进行系统、有效的几何清理，可以快速、高质地实现有限元网格的划分。文章基于HyperMesh的有限元造型，进行了几何清理问题的分析，得到了几何清理的原则、应注意的事项和几何清理过程中亟待解决的问题。     

一种夹层板结构车厢的有限元简化模型及模态分析

以某型车的车厢夹层复合板结构为例,研究了夹层板结构的有限元建模方法,建立了车厢的有限元简化模型并进行了模态分析。与传统上使用的板梁单元相比,单元自由度数减少了66.7%,大大缩短了分析时间,提高了计算效率。     

Reduced order finite element model for elastohydrodynamic lubrication: Circular contacts

This paper presents an extension of the reduced order finite element model to the case of circular elastohydrodynamic lubricated (EHL) contacts under isothermal Newtonian considerations. The line contact model was developed and validated in a previous work (Advances in Engineering Software, 2013; 56:51−62). The model is based on a finite element discretization of the EHL equations: Reynolds, linear elasticity and load balance with a reduced order model for the linear elasticity part. All equations are solved simultaneously in a fully-coupled framework using a damped-Newton procedure allowing fast convergence rates for the global solution. This model combines fast convergence rates, reduced memory requirements and negligible model reduction errors compared to the full model which makes it an attractive tool for EHL contact performance prediction.     

有限元的因次分析法

利用因次分析法对用有限元法所分析的结构进行分析,求得了模型和原型之间相似准则,对于同种材料的结构,当结构几何比为λl,外加动载荷之比为λl^2,振动频率之比为时1／λl,结构满足相似准则,则结构的振动加速度之比为1／λl,辐射声功率之比为λl^2。     

A coupled finite element analysis of independently modeled substructures by penalty frame method

A penalty frame method is proposed for the coupled analysis of finite elements with independently modeled substructures. Although previously reported hybrid interface method by Aminpour et al (IJNME, Vol 38, 1995) is accurate and reliable, it requires non-conventional special solution algorithm such as multifrontal solver. In present study, an alternative method has been developed using penalty frame constraints, which results in positive symmetric global stiffness matrices. Thus the conventional skyline solver or band solver can be utilized in the solution routine, which makes the present method applicable in the environment of conventional finite element commercial software. Numerical examples show applicability of the present method.