机械系统动力学特性的综合分析及其工程应用
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摘要
随着计算机技术、网络技术、通信技术等为代表的信息技术广泛应用于机械工程的各个领域,使得机电产品发生了重大变化。当然,这些变化也包括为产品的设计提供支撑的机械学科理论与应用技术的发展。近年来,上述研究取得了一系列重要成果,这些成果在机电产品的创新开发与设计中发挥重要作用。根据系统辨识与结构动力学的基本原理以及相应的试验技术发展起来的实验模态分析(EMA)与工作模态分析(OMA)技术取得长足的发展,从而帮助设计人员根据辨识模型更好地领悟对象机理,并将这些机理应用于产品设计,有力地促进产品的原创性开发与设计,并不断地扩大它的应用领域。
近年来工作模态分析在机械系统与结构的动态分析与设计以及运行监测与故障诊断等方面获得广泛应用,在应用中也暴露出这些方法存在的问题与缺点,必须解决这些问题才能使这种方法得到有效的工业应用。本文研究适用于大型机械装备与结构的工作模态分析以及消除现有工作模态分析某些缺点的方法。研究的目的是：减少模态试验时间；允许最大限度地利用试验数据；减少分析的复杂性,可以较容易地处理数据；适用于大型机械结构模态试验存在的大量的传感器、大阻尼、带噪声数据、短的数据记录等情况；提高模态参数估计精度。为了达到上述目的,作者从模态试验与模态参数估计方法两方面入手解决工作模态分析的有关问题,取得了重要成果,并成功应用于大型工业装备。
本文回顾了模态分析的基本理论与方法,包括实验模态分析(EMA)、工作模态分析(OMA)以及有外加输入的模态分析方法(OMAX)。在OMAX架构中讨论了确定性贡献的频响函数估计和随机贡献的正功率谱估计。在此基础上指出这些方法的局限与缺点,作为展开本文研究的背景。
提出了一种基于循环倒谱的工作模态分析方法。该方法解除了输入信号为白噪声的假设,提高了模态参数的辨识精度。使用循环平稳信号的处理技术来分离响应中由于循环平稳输入信号引起的成分,非常有效地将多输入多输出(MIMO)系统降低为单输入多输出(SIMO)系统,在倒谱域进行曲线拟合,将输入和传递函数分离开,识别出系统的谐振和反谐振,进而得到系统的传递函数。通过钢梁试验对该方法进行验证,并与EMA分析结果进行比较。在这个试验中,精确估计了谐振频率和振型,并且通过增加平均次数来降低估计的不精确性。
为了解决当输入激励不是白噪声时OMA过程中尺度丢失的问题,本文提出一种恢复模态振型之间的相对比例(尺度)和所有模态振型的全局比例(尺度)的简单方法,该方法建立在循环倒谱的基础之上。这种方法包括通过响应谱识别谐振与反谐振,并用以有限元模型。然后,通过有限元模型得到等效曲线,从而恢复频率响应函数的尺度。
针对大型机械结构常常出现的由于工作或环境激励的频带较窄,致使工作模态过程中丢失模态以及计算速度慢等问题,提出准工作模态分析方法,即在大结构的部分区域结合使用可测量激励力(类似于实验模态分析)的外加局部辅助激励输入的工作模态分析方法,并提出了适合于准工作模态的基于参考的确定性随机子空间混合辨识算法,提高了模态辨识的精度和速度。
为验证基于参考的确定性随机的准工作模态分析方法,将其应用于工业振动筛工作模态的综合分析,精确地辨识了振动筛的模态参数,得到很好的效果,证明了该方法的鲁棒性与可靠性。
Significant changes have been taken place in mechanical and electrical products as the information technology, which is represented by computer technology, network technology and communication technology, is widely used in various fields of mechanical engineering. Of course, these changes also include the development of the theory of mechanical disciplines which provide support for the product design and application of technology. In recent years, the above studies have made a series of important achievements. These achievements play an important role in innovation and design of the mechanical and electrical products. Based on the academic principles of the system identification, structural dynamics and the corresponding test techniques, the Experimental Modal Analysis (EMA) and Operational Modal Analysis (OMA) technology have made considerable development, which helps the designers to get more insight of object mechanisms from the identified models and apply the mechanisms to the design of products, to promote originality exploitation and design of the products effectively and to expand its application areas continuously.
In recent years, the Operational Modal Analysis is widely used in the dynamic analysis and the design of mechanical system and structure, as well as in monitoring and fault diagnosis. The existing problems and disadvantages of these methods are also exposed in applications. In order to make these methods be effective in industrial applications, these problems must be resolved. The research in this paper is suitable for the Operational Modal Analysis of large-scale machinery equipments and structures, as well as suitable for eliminating some shortcomings of modal analysis. The purpose of this study is to reduce the test time, to allow to exploit maximal test data, to decrease the complexity of the analysis, to allow to process the data easily, to apply in modal test of large mechanical structure which existing the problems of a large number of sensors, high damping, noise data, short data records etc, to increase the accuracy of the estimate of mode. In order to achieve the above purpose, starting from modal testing and modal parameter estimation, some problems of operational modal analysis have been solved, some important achievements have been made and applied to large industrial equipments successfully.
In this paper the basic theories and methods of modal analysis are reviewed, which includes Experimental Modal Analysis (EMA), Operational Modal Analysis (OMA) and an Operational Modal Analysis with eXogenous inputs (OMAX). The frequency response function estimation of deterministic contribution and the positive power spectrum estimation of random contribution are discussed in the frame of OMAX. On this basis, the limitations and shortcomings of these methods are pointed, which is used as the background of this paper.
Operation modal analysis based on cyclic cepstrum is proposed. This method relieves the assumption that the input signal of OMA is white noise and improves the accuracy of the identification of modal parameters. The portion of the responses caused by the cyclostationary input is separated by the technique of cyclostationary signal processing. The MIMO system is effectively reduced to an SIMO system. In the cepstrum domain the SIMO responses are curve-fitted, the input and transfer function then can be separated, and the system resonances and anti-resonances are identified. The transfer functions of system can be regenerated. Through the steel beam test the method is verified and is compared with the EMA analysis results. In this trial, the resonance frequencies and mode shapes are estimated accurately and the estimated imprecision is reduced by increasing the average number of times.
In order to solve the problems of scale lost when the input stimulus is not white noise, a simple method is proposed to recover the relative proportion (scale) between mode shapes and global proportions (scale) of all mode shapes. This method is based on cyclic cepstrum. The method includes the recognition of resonance and anti-resonance by response spectrum and using them to correct the finite element model. Then, the equivalent curve is acquired by the finite element model, and then the scale of.the frequency response function is recovered.
Qusical OMA is put forward against the problem of modals lost and problem of low speed of Calculation in the process of OMA of large mechanical structures because of narrow band of the operation or ambient excitation. In part of the area of the large structure is combined with measured excitation force (similar to the experimental modal analysis), and part auxiliary excitation input is used in Operational Modal Analysis method. Suitable modal identification algorithm for Quasi OMA based on the mixed reference deterministic stochastic subspace is also proposed, the accuracy and speed of the modal identification is improved.
In order to verify Quasi OMA, it is applied to modal analysis of industrial screen; the modal parameters of the screen are accurately identified and achieved very good results. This method is proved be robust and reliable.
近年来工作模态分析在机械系统与结构的动态分析与设计以及运行监测与故障诊断等方面获得广泛应用,在应用中也暴露出这些方法存在的问题与缺点,必须解决这些问题才能使这种方法得到有效的工业应用。本文研究适用于大型机械装备与结构的工作模态分析以及消除现有工作模态分析某些缺点的方法。研究的目的是：减少模态试验时间；允许最大限度地利用试验数据；减少分析的复杂性,可以较容易地处理数据；适用于大型机械结构模态试验存在的大量的传感器、大阻尼、带噪声数据、短的数据记录等情况；提高模态参数估计精度。为了达到上述目的,作者从模态试验与模态参数估计方法两方面入手解决工作模态分析的有关问题,取得了重要成果,并成功应用于大型工业装备。
本文回顾了模态分析的基本理论与方法,包括实验模态分析(EMA)、工作模态分析(OMA)以及有外加输入的模态分析方法(OMAX)。在OMAX架构中讨论了确定性贡献的频响函数估计和随机贡献的正功率谱估计。在此基础上指出这些方法的局限与缺点,作为展开本文研究的背景。
提出了一种基于循环倒谱的工作模态分析方法。该方法解除了输入信号为白噪声的假设,提高了模态参数的辨识精度。使用循环平稳信号的处理技术来分离响应中由于循环平稳输入信号引起的成分,非常有效地将多输入多输出(MIMO)系统降低为单输入多输出(SIMO)系统,在倒谱域进行曲线拟合,将输入和传递函数分离开,识别出系统的谐振和反谐振,进而得到系统的传递函数。通过钢梁试验对该方法进行验证,并与EMA分析结果进行比较。在这个试验中,精确估计了谐振频率和振型,并且通过增加平均次数来降低估计的不精确性。
为了解决当输入激励不是白噪声时OMA过程中尺度丢失的问题,本文提出一种恢复模态振型之间的相对比例(尺度)和所有模态振型的全局比例(尺度)的简单方法,该方法建立在循环倒谱的基础之上。这种方法包括通过响应谱识别谐振与反谐振,并用以有限元模型。然后,通过有限元模型得到等效曲线,从而恢复频率响应函数的尺度。
针对大型机械结构常常出现的由于工作或环境激励的频带较窄,致使工作模态过程中丢失模态以及计算速度慢等问题,提出准工作模态分析方法,即在大结构的部分区域结合使用可测量激励力(类似于实验模态分析)的外加局部辅助激励输入的工作模态分析方法,并提出了适合于准工作模态的基于参考的确定性随机子空间混合辨识算法,提高了模态辨识的精度和速度。
为验证基于参考的确定性随机的准工作模态分析方法,将其应用于工业振动筛工作模态的综合分析,精确地辨识了振动筛的模态参数,得到很好的效果,证明了该方法的鲁棒性与可靠性。
Significant changes have been taken place in mechanical and electrical products as the information technology, which is represented by computer technology, network technology and communication technology, is widely used in various fields of mechanical engineering. Of course, these changes also include the development of the theory of mechanical disciplines which provide support for the product design and application of technology. In recent years, the above studies have made a series of important achievements. These achievements play an important role in innovation and design of the mechanical and electrical products. Based on the academic principles of the system identification, structural dynamics and the corresponding test techniques, the Experimental Modal Analysis (EMA) and Operational Modal Analysis (OMA) technology have made considerable development, which helps the designers to get more insight of object mechanisms from the identified models and apply the mechanisms to the design of products, to promote originality exploitation and design of the products effectively and to expand its application areas continuously.
In recent years, the Operational Modal Analysis is widely used in the dynamic analysis and the design of mechanical system and structure, as well as in monitoring and fault diagnosis. The existing problems and disadvantages of these methods are also exposed in applications. In order to make these methods be effective in industrial applications, these problems must be resolved. The research in this paper is suitable for the Operational Modal Analysis of large-scale machinery equipments and structures, as well as suitable for eliminating some shortcomings of modal analysis. The purpose of this study is to reduce the test time, to allow to exploit maximal test data, to decrease the complexity of the analysis, to allow to process the data easily, to apply in modal test of large mechanical structure which existing the problems of a large number of sensors, high damping, noise data, short data records etc, to increase the accuracy of the estimate of mode. In order to achieve the above purpose, starting from modal testing and modal parameter estimation, some problems of operational modal analysis have been solved, some important achievements have been made and applied to large industrial equipments successfully.
In this paper the basic theories and methods of modal analysis are reviewed, which includes Experimental Modal Analysis (EMA), Operational Modal Analysis (OMA) and an Operational Modal Analysis with eXogenous inputs (OMAX). The frequency response function estimation of deterministic contribution and the positive power spectrum estimation of random contribution are discussed in the frame of OMAX. On this basis, the limitations and shortcomings of these methods are pointed, which is used as the background of this paper.
Operation modal analysis based on cyclic cepstrum is proposed. This method relieves the assumption that the input signal of OMA is white noise and improves the accuracy of the identification of modal parameters. The portion of the responses caused by the cyclostationary input is separated by the technique of cyclostationary signal processing. The MIMO system is effectively reduced to an SIMO system. In the cepstrum domain the SIMO responses are curve-fitted, the input and transfer function then can be separated, and the system resonances and anti-resonances are identified. The transfer functions of system can be regenerated. Through the steel beam test the method is verified and is compared with the EMA analysis results. In this trial, the resonance frequencies and mode shapes are estimated accurately and the estimated imprecision is reduced by increasing the average number of times.
In order to solve the problems of scale lost when the input stimulus is not white noise, a simple method is proposed to recover the relative proportion (scale) between mode shapes and global proportions (scale) of all mode shapes. This method is based on cyclic cepstrum. The method includes the recognition of resonance and anti-resonance by response spectrum and using them to correct the finite element model. Then, the equivalent curve is acquired by the finite element model, and then the scale of.the frequency response function is recovered.
Qusical OMA is put forward against the problem of modals lost and problem of low speed of Calculation in the process of OMA of large mechanical structures because of narrow band of the operation or ambient excitation. In part of the area of the large structure is combined with measured excitation force (similar to the experimental modal analysis), and part auxiliary excitation input is used in Operational Modal Analysis method. Suitable modal identification algorithm for Quasi OMA based on the mixed reference deterministic stochastic subspace is also proposed, the accuracy and speed of the modal identification is improved.
In order to verify Quasi OMA, it is applied to modal analysis of industrial screen; the modal parameters of the screen are accurately identified and achieved very good results. This method is proved be robust and reliable.
引文
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