Tool Condition Monitoring Based on Nonlinear Output Frequency Response Functions and Multivariate Control Chart

Tool condition monitoring(TCM)is a key technology for intelligent manufacturing.The objective is to monitor the tool operation status and detect tool breakage so that the tool can be changed in time to avoid significant damage to workpieces and reduce manufacturing costs.Recently,an innovative TCM approach based on sensor data modelling and model frequency analysis has been proposed.Different from traditional signal feature-based monitoring,the data from sensors are utilized to build a dynamic process model.Then,the nonlinear output frequency response functions,a concept which extends the linear system frequency response function to the nonlinear case,over the frequency range of the tooth passing frequency of the machining process are extracted to reveal tool health conditions.In order to extend the novel sensor data modelling and model frequency analysis to unsupervised condition monitoring of cutting tools,in the present study,a multivariate control chart is proposed for TCM based on the frequency domain properties of machining processes derived from the innovative sensor data modelling and model frequency analysis.The feature dimension is reduced by principal component analysis first.Then the moving average strategy is exploited to generate monitoring variables and overcome the effects of noises.The milling experiments of titanium alloys are conducted to verify the effectiveness of the proposed approach in detecting excessive flank wear of solid carbide end mills.The results demonstrate the advantages of the new approach over conventional TCM techniques and its potential in industrial applications.

Dynamic design of a nonlinear energy sink with NiTiNOL-steel wire ropes based on nonlinear output frequency response functions

A novel vibration isolation device called the nonlinear energy sink(NES)with NiTiNOL-steel wire ropes(NiTi-ST)is applied to a whole-spacecraft system.The NiTi-ST is used to describe the damping of the NES,which is coupled with the modified Bouc-Wen model of hysteresis.The NES with NiTi-ST vibration reduction principle uses the irreversibility of targeted energy transfer(TET)to concentrate the energy locally on the nonlinear oscillator,and then dissipates it through damping in the NES with NiTi-ST.The generalized vibration transmissibility,obtained by the root mean square treatment of the harmonic response of the nonlinear output frequency response functions(NOFRFs),is first used as the evaluation index to analyze the whole-spacecraft system in the future.An optimization analysis of the impact of system responses is performed using different parameters of NES with NiTi-ST based on the transmissibility of NOFRFs.Finally,the effects of vibration suppression by varying the parameters of NiTi-ST are analyzed from the perspective of energy absorption.The results indicate that NES with NiTi-ST can reduce excessive vibration of the whole-spacecraft system,without changing its natural frequency.Moreover,the NES with NiTi-ST can be directly used in practical engineering applications.

Research on the iterative method for model updating based on the frequency response function

Model reduction technique is usually employed in model updating process. In this paper, a new model updat- ing method named as cross-model cross-frequency response function （CMCF） method is proposed and a new iterative method associating the model updating method with the mo- del reduction technique is investigated. The new model up- dating method utilizes the frequency response function to avoid the modal analysis process and it does not need to pair or scale the measured and the analytical frequency re- sponse function, which could greatly increase the number of the equations and the updating parameters. Based on the traditional iterative method, a correction term related to the errors resulting from the replacement of the reduction ma- trix of the experimental model with that of the finite element model is added in the new iterative method. Comparisons be- tween the traditional iterative method and the proposed itera- tive method are shown by model updating examples of solar panels, and both of these two iterative methods combine the CMCF method and the succession-level approximate reduc- tion technique. Results show the effectiveness of the CMCF method and the proposed iterative method .

Uncertainty analysis of strain modal parameters by Bayesian method using frequency response function

Structural strain modes are able to detect changes in local structural performance, but errors are inevitably intermixed in the measured data. In this paper, strain modal parameters are considered as random variables, and their uncertainty is analyzed by a Bayesian method based on the structural frequency response function （FRF）. The estimates of strain modal parameters with maximal posterior probability are determined. Several independent measurements of the FRF of a four-story reinforced concrete flame structural model were performed in the laboratory. The ability to identify the stiffness change in a concrete column using the strain mode was verified. It is shown that the uncertainty of the natural frequency is very small. Compared with the displacement mode shape, the variations of strain mode shapes at each point are quite different. The damping ratios are more affected by the types of test systems. Except for the case where a high order strain mode does not identify local damage, the first order strain mode can provide an exact indication of the damage location.

Crack detection using a frequency response function in offshore platforms

Structural cracks can change the frequency response function (FRF) of an offshore platform. Thus, FRF shifts can be used to detect cracks. When a crack at a specific location and magnitude occurs in an offshore structure, changes in the FRF can be measured. In this way, shifts in FRF can be used to detect cracks. An experimental model was constructed to verify the FRF method. The relationship between FRF and cracks was found to be non-linear. The effect of multiple cracks on FRF was analyzed, and the shift due to multiple cracks was found to be much more than the summation of FRF shifts due to each of the cracks. Then the effects of noise and changes in the mass of the jacket on FRF were evaluated. The results show that significant damage to a beam can be detected by dramatic changes in the FRF, even when 10% random noise exists. FRF can also be used to approximately locate the breakage, but it can neither be efficiently used to predict the location of breakage nor the existence of small hairline cracks. The FRF shift caused by a 7% mass change is much less than the FRF shift caused by the breakage of any beam, but is larger than that caused by any early cracks.

Pilot study on the Non-Invasive Detectability of Femoral Neck Fractures with Frequency Response Functions

A suspicion of a femoral neck fracture is a frequently recurring situation, especially in nursing homes. For the clarification of such a suspicion normally imaging techniques are used. Such equipment is expensive and therefore is located in hospitals. In addition to the costs, a transport causes stress for the patient. This pilot study is devoted to the question whether the detection of a femoral neck fracture with vibration measurements is possible in principal. In such a case, the clarification could be done on-site by an ordinary person using much cheaper equipment. This would reduce the stress for the patient and save money. For this purpose vibration measurements on a dead body with intact, with partially fractured and with complete cut femoral neck have been performed. Two different methods for the vibration initiation have been investigated, the so called impact testing and the shaker testing. The frequency response function has been determined for all combinations on both sides of the body. It turned out that there is a clear difference in the frequency response functions of the fractured bone with respect to the intact bone when shaker testing is used. This indicates that the method could have the potential to be a cost-saving alternative to imaging techniques. However, in a next step a statistically reliable clinical survey on living persons needs to be done.

Regularized automatic frequency response function acquisition of a milling robot operating in a high-dimensional workspace

Because robotic milling has become an important means for machining significant large parts,obtaining the structural frequency response function(FRF)of a milling robot is an important basis for machining process optimization.However,because of its articulated serial structure,a milling robot has an enormous number of operating postures,and its dynamics are affected by the motion state.To accurately obtain the FRF in the operating state of a milling robot,this paper proposes a method based on the structural modification concept.Unlike the traditional excitation method,the proposed method uses robot joint motion excitation instead of hammering excitation to realize automation.To address the problem of the lack of information brought by motion excitation,which leads to inaccurate FRF amplitudes,this paper derives the milling robot regularization theory based on the sensitivity of structural modification,establishes the modal regularization factor,and calibrates the FRF amplitude.Compared to the commonly used manual hammering experiments,the proposed method has high accuracy and reliability when the milling robot is in different postures.Because the measurement can be performed directly and automatically in the operation state,and the problem of inaccurate amplitudes is solved,the proposed method provides a basis for optimizing the machining posture of a milling robot and improving machining efficiency.

Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates

This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate.A nonlinear finite element(FE)formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory(FSDT)in conjunction with von Karman’s nonlinear strain displacement relations.The governing equations of the PFGS plate are derived using the principle of virtual work.The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations.The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters.The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.

基于GFRFs的非线性系统结构故障检测方法

为了能够更加准确高效地检测非线性系统的结构是否发生故障,提出了基于系统带外部输入的非线性自回归(NARX)模型的广义频率响应函数(GFRFs)故障检测方法。根据受检系统的NARX模型参数和一阶GFRF估算出系统的高阶GFRFs,通过比较受检系统与无故障系统结构的广义频率响应函数值,实现系统结构的故障检测。根据受检系统和无故障系统的GFRFs确定系统故障损害程度指数,进一步对故障程度进行评估。通过实验与其他检测方法进行对比,验证了所提检测方法的优越性。

A Contribution to the Analysis of Frequency Response and Impedance Measurements to Evaluation and Diagnosis of Power Transformers

This paper has an objective to show a developed quantitative criterion,based in two mathematical variables that explicit the deviation degree of a normal situation,applying simultaneously data from terminal impedances and frequency response.Based in more than 100-measured equipment,of different applications(step-up transformer,transmission transformer,etc.,),for a period of 10 years,the work presents some examples of practical application of this methodology in Brazilian Electrical System.

Analysis of Dynamic Cross Response between Spindles in a Dual Spindle Type Multi-Functional Turning Machine

In order to meet increasing demand for higher productivity and flexibility, recently many kinds of multi-functional machine tools, which are capable of multiple machining functions or different kinds of machining processes on one machine, have been developed and widely used in manufacturing industries. In this study, a multi-functional turning lathe, which has two spindles and two turrets so that multiple turning operations and various machining processes could be performed simultaneously, has been developed. Furthermore, the equations of correlation between whole responses and cross responses of the two spindles have been derived to examine to what extent the two spindles affect each other’s vibrations.

基于NOFRFs的非等温CSTR同步周期操作的评估优化

化学反应周期操作是利用反应非线性来提高系统性能指标的技术,对其评估与优化仍是现阶段工业应用亟待解决的关键问题.利用非线性输出频率响应函数对具有显著非线性的连续搅拌反应釜的入口浓度和入口温度同步周期操作进行评估.首先分析单个周期操作的输入对系统性能指标的单独贡献,然后确定使转化率最大化而应使用的最优相位差,最后分析入口浓度和入口温度同步周期操作的各阶交叉项的贡献.仿真结果表明:提出的方法优于传统的NFR方法和单变量NOFRFs方法,提高了周期操作评估的准确性;同时,在允许的工艺过程约束条件下进行了最优化设计,明显提高了反应物的转化率,为其他类型的化学反应过程周期操作评估和优化提供参考.

一类非线性系统的广义伴随线性方程分析研究

非线性输出频率响应函数是线性系统理论中频率响应函数在非线性系统中的一种推广,越来越多的学者已将其应用在结构损伤检测及故障诊断中.基于Volterra级数理论与由非线性微分方程描述的单输入单输出非线性系统的广义频率响应函数递归计算公式,利用多重积分性质和多维傅里叶变换,将广义频率响应函数映射到了一维频域中,推导出了一类非线性系统的广义伴随线性方程计算公式.研究表明,这类系统的第n阶非线性输出响应是以系统输入激励和前n-1阶非线性输出响应的组合函数作为广义激励作用到系统各阶广义伴随线性方程中的输出响应,最后通过求解一系列线性微分方程可得到这类非线性系统的任意阶非线性输出响应,其结果弥补了伴随线性方程无法求解这类非线性系统的不足.同时,针对广义伴随线性方程的数值计算问题,论文提出了一种耦合计算法,提高了计算非线性输出响应的精度,为非线性输出频率响应函数的计算提供了一种新思路.最后利用广义伴随线性方程与线性算子理论研究了两种典型非线性系统中非线性现象产生的原因,研究结果为非线性系统的分析与设计提供了一种有效途径.

测压管长度对单测点信号的影响及修正效果验证

测压试验中,测压管的存在会导致风压信号产生畸变,影响后续数据分析的精度。通过实际测定测压管路频响函数,获得测压管对信号的影响规律,并揭示了“B-T理论”的不足。在实际紊流作用下研究测压管长度对单测点压力数据和模型整体力的影响,并验证“B-T理论”的修正效果。结果表明:对于单测点压力数据,测压管将不会影响数据均值和变异系数,标准差随管长增加先增后减,信号时域随管长增加而整体向均值靠近,相位则不断滞后,信号频域值随管长和频率的增加逐渐偏离真实值;对于整体力,整体阻力、各力的相关性、相干性均可认为不受测压管影响,力谱的变化规律与单测点频域值相同;“B-T理论”在信号时域上修正效果较差,在频域修正方面表现良好。

基于FPGA的射频腔体系统数学模型在线辨识算法

射频系统的数学模型包含了射频腔体的关键特征参数(如腔体半带宽、谐振频率和洛伦兹力失谐系数等),数学模型对腔体性能检测、控制系统仿真及低电平控制算法优化具有重要意义。网络分析仪通常用于测量射频系统的散射参数,进而构建射频系统的数学模型,但其测量步骤繁琐且无法实现系统模型的在线自动辨识。本文通过模拟网络分析仪的工作原理,在数字低电平系统内部构建了基于数控振荡器的扫频算法,实现了射频腔体系统的在线辨识。该算法的有效性已在加速器驱动嬗变研究装置前端示范样机的超导腔上验证,其测量结果与网络分析仪测量结果吻合。此外,本文利用该辨识算法还成功测得了由洛伦兹力失谐引起的超导腔频率响应畸变曲线,并讨论了洛伦兹力失谐量的大小对腔体关键特征参数测量的影响。

一类非线性动态系统的非参数GFRF 模型辨识(英文)

本文对一类用多项式描述的非线性动态系统提出使用ＧＦＲＦ模型类的非参数辨识算法．这种算法的显著特点是需要很小的计算量和存储空间，而且辨识精度较高．仿真结果表明这种非参数模型辨识算法是有效的，而且由辨识方法获得的模型一般具有很好的泛化能力，因而是一种具有重要应用前景的实用方法．

考虑频响函数混叠误差的阻尼比识别效果研究

通过实测频响函数识别阻尼比时,识别准确性受到频谱混叠现象的影响,因此建立了考虑频响函数混叠误差的阻尼比识别有效性判断方法.首先,根据傅里叶变换原理进行理论推导,证明了采样频率不足时频响函数会发生混叠现象;然后,根据频响函数混叠原理和模态叠加原理,建立了多自由度结构的基准频响混叠误差拟合公式,进而给出考虑频响函数混叠误差的阻尼比识别结果有效性判断的步骤.通过对两自由度理论频响函数模型设置不同的等效柔度比和固有频率比,表明其对两阶模态计算频响混叠误差有显著影响;通过对比四层框架结构基准模型的响应在设置不同采样频率时对阻尼比的识别结果,验证了所提方法的可行性.

大型汽轮发电机定子端部绕组物理参数识别及数学模型建立方法研究

从结构的数字化模型频响函数出发,利用最小二乘复频域法识别模态参数,进一步用获取的模态参数修正集中质量法推导出的物理参数,从而建立符合结构动力特性的数学模型。首先通过固支梁模型算例验证该方法的可行性;然后对600 MW大型汽轮发电机端部绕组的精细化有限元模型进行模态分析,并与实测结果进行对比,验证了该模型的合理性;此后,基于该有限元模型获取的频响函数和模态参数,识别出端部绕组的物理参数并建立其数学模型。结果表明:在75~115 Hz频率段中,最小二乘复频域法识别出的端部绕组模态与有限元结果对比表明,固有频率和阻尼比的最大误差出现在第一阶模态中,分别为0.27%和0.50%,模态振型接近;通过数学模型和有限元模型计算的端部绕组固有频率最大误差为0.27%,模态振型一致;数学模型计算的频响函数与有限元结果对比表明,测点的频响函数最高匹配度可达95%,多数测点的频响函数匹配度超过85%。该方法可为大型汽轮发电机定子端部绕组动力学的准确建模提供依据。

基于NOFRF裂纹转子非线性频谱分析

建立了裂纹转子非线性逼近模型,论述了非线性输出频域响应函数(NOFRF)及其非线性频谱分析理论,基于该理论对裂纹转子系统的各阶NOFRF进行了仿真分析,该分析结果说明了裂纹转子系统新频域成份是如何产生的,对裂纹转子的超谐波成份和亚共振现象进行了解释,并进行了试验分析,结果表明了高阶NOFRF比一阶对转子裂纹深度更敏感,为裂纹转子的精确故障诊断提供了理论基础。

基于振动测量的热防护结构脱粘损伤检测方法

针对典型飞行器热防护结构脱粘损伤现场快速无损检测的需求,提出了一种基于敲击测量频响函数的脱粘损伤识别方法。首先,利用有限元方法建立了含脱粘损伤的热防护结构有限元模型并进行了振动特性分析,分析了脱粘损伤引起的结构局部刚度下降规律以及频响函数对脱粘损伤的敏感性;其次,确定了脱粘损伤识别的特征频率范围,给出了一个脱粘损伤指标;最后,采用力锤与激光多普勒测振仪对含脱粘的热防护结构进行了测量。实验结果表明,当脱粘面积达到60%时,脱粘损伤指标比健康件增加了1倍以上,当脱粘面积达到80%时,脱粘损伤指标为健康件的5倍以上,验证了所提出的方法能够有效识别出热防护结构的脱粘损伤。