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利用有限元模型对钻机进行动态分析的研究,有限元模型进行,有限元分析模型,进行有限元分析
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【中文5220字】 利用有限元模型对钻机进行动态分析的研究摘要现在的工作的目的是使用分析和实验的结果发展和改进钻机的有限元分析模型，这种有限元分析已经用在监测将钻机的工作特性修改后对钻机动态的结构的影响；对钻机将有两个研究就进行。第一个研究是：使用工具对钻机进行冲击来观察这种冲击对钻机的影响的实验已经在进行，通过人们公认对模型的证明我门已经知道这种方法的可行性；为了这一个有限元模型分析的机器，一个计算机程序已经被设计出来。有限元分析获得的结果是将通过实验得到模型的比较与测量和控制的价值联系起来。有限元分析模型已经被改进，是由于一个已经使用的有限元分析模型程序的改进。第二个研究是：模式上的测试已经完成，这种测试包括运用各种任意的声音和模式的刺激。公认的模式的测试方法被用来作为这种有限元分析模型的证据。利用I-DEAS软件已经对有限元分析模型的作了分析。利用FEMtools软件已经对有限元分析模型和实验得到的结果的联系进行了分析，利用以上两种软件已经对有限元分析模型进行了间接的改进。灵敏度基于对参数估量的技术。通过以上两种研究，对这种分析模型进行结构和动态的修改。我们对动态设计的结果和结构和动态的修改相当的满意。目录1. 绪论；2. 模型的测试和结论；3. 钻机的有限元分析元素的表达；4. 有限元分析的结果和实验结果的比较；5. 有限元分析的发展；6. 利用有限元分析对动态设计的动态和结构的修正；7. 结论。参考文献1 绪论动态设计的目的在于获得想要的机器和构件的动态参数，这些动态参数包括震荡频率，想要得到的结构尺寸和震荡响应，而根本的目的是有一个安静和舒适的环境，高的可靠性和更好的产品质量。常规的动态设计是通过很多的原形的分析和实验来获得自己想要的参数。这个设计的缺点是：要进行这个实验和分析需要很多的时间和精力，所以根本就没有效率所言。然而，新型的有限元分析节省了时间节省了有关的花费。动态设计所用的各种方法是：实验的模型分析（形态测试和实验确认），模型改进和结构上的，形态上的修改。EWINS，MAIN和SILVA对模型测试进行了基本概念的解释。模型测试是通过实验的方法获得机构的数学模型。在这个实验中，构件用一个锤子进行打击或用刺激物进行刺激，是它发生变形，在这个过程中，构件的变形已经被仪器所记录。然后，用一个接口将这种变形的信号传递的分析器里面，以构件的响应函数的形式进行分析。这种实验模型提给给我们一个正常的频率相应的外形和模型的制动因数是非常有用的对模型的改进来说。改进后的有限元分析技术帮助我们使得分析有限元要素模型接近于真实的系统。在模型更新起初，有限元模型分析因为结构的动力学，模型构造是精确或者最新的。用标准的，最新的测试数据的使用，以至于对机构模型的描述是非常准确的。当将有限元分析应用于不准确的边界条件和结构减震时，将会出现错误。Friswen 和Mottershead 在结构动力学中讨论有限元模型分析的发展；在Baruch和Bar-Itzhach中考虑分析的大众点阵式是精确的而且在后来通过最新的实验数据对发展为一种直接的数学方法；Berman和Nijy发明了一种改进模型的方法。这种方法使用标准的dos命令和正常的频率来提高对大多数和坚硬金属分析的精确。结构的动态休整技术是一种方法，通过增加改进参数（刚性连接，节气阀等）。因而，利用最新的模型来准确的和快速的预测动态设计是非常有用的，在动态设计时，计算机利用自身程序对模型进行结构动态特性的有可能修正，这样即节省时间又节省花费，Sestieri讨论将结构动态修正运用到工作母机和发动机上Kundra提供了一种结构动态的修正方法。Modak讨论通过最新的有限元模型分析对构件动态修正的预测，在边界条件，利用硬度参数时对最新的机床，它常常不是非线性最优化的方法。这篇论文要处理最新的有限元模型分析通过使用指导方法和间接方法来解决动态设计构件动态参数的修正与预测。一个钻机，两重不同的设计方法被报道使用不同的技术方法来分析和解决最新的动态分析设计。现在多种研究工作被实施的目的是：（1） 来发现一种最新的有限元分析系统来解决象钻机一样复杂结构的设计和使用这种有限元分析模型来预测各种参数在机器模具上的响应。（2） 让这种变形的模型和正常的模型相比较来看象钻机一样复杂结构对其进行冲击时产生变形是否有好的方面出现。（3） 利用这种最新研究的模型分析方法来分析获得机构动态修正参数的测试结果。2. 模型的测试和结论；在二项研究被提及更加早期， 对模型的测试和结论，人们引用了不同的技术。在第一个实验中，用冲击的方法使钻机的构件发生变形，其数值的变化如图1和图2：(12K)图1实验进行前(4K) 图2实验后变形是在过载器件的帮助下对一个固定点的取样；在现在的研究中，使用仪器使得在钻机的30个部位进行刺激使之发生变形，则这样就能获得30个响应函数。这些响应函数在变化以前就已经被记录下来。同时就这些获得响应函数输送到计算机里面，将获得的数据以曲线的形式表达出来，再将其进行分析就能获得标准的，最新的钻机的参数数据。第二个实验是：使机械机构地部的28个点发生变形并用压电式加速仪进行测量，通过ICATS软件对频率响应函数的正确性进行了证明，结果显示这种方法得到的数据是准确的。表1是通过两种不同的方法得到的频率的数据，从数据来看，它们是完全不一样的：表1 方式110.29 Hz8.67 HZ0.95311.20 Hz8.79 Hz0.946方式265.14 Hz47.34 HZ0.90163.37 Hz44.40 Hz0.9063.钻机的有限元分析元素的表达；像Zienkiewicz 和 Bathe一样，人们对有限元分析的一些概念进行了定义。与其他的机器和构件相比，钻机的构件是非常复杂的；因此，对实际的构件分析是很难的，而且会花费大量的时间和精力。然而，对有限元模型分析来说，钻机的简单化的模型被使用。在实验1中，有限元分析模型被MATLAB作成一个计算机程序；光线元素已经被应用到分析当中，刚性连接和边界条件被认为对结构减震是有影响的在模型参量上，但是，人们往往将其忽略。钻机的相关使用数据如下：25毫米的柱子模型；高度= 1.655 m； 质量密度= 7800 kg/m3；杨氏系数= 200 Gpa； 连节点的个数= 30； 设计元素的个数= 29； 每个元素的节点个书= 2； 每个节点的自由度= 3。图3表示了实验1中钻机结构的节点数：(7K)图3钻机结构的有限元分析现在，钻机的特征值和特征向量已经被计算出来。结构的有限元分析的数据包括9090-的外行参数和材料硬度（303,30个节点，每个节点的自由度= 3）。但是，实验只有30个坐标可以测量，有限元模型分析在MATLAB设计的一个程序下得到了简化。在实验2中，通过使用I-DEAS软件将有限元分析模型制作出来，模型是用射线滤网制作的。虽然有限元分析模型是单一化的但是射线元素有旋转的自由度，使得无法实验性地被测量。因此，有限元分析模型需要进一步的简化。在以后的发展过程中，通过使用FEM软件有限元分析模型得到进一步简化。图4和图5显示了在使用I-DEAS软件以后实验1和实验2的结构形式：(31K)图4.实验1的结构形式(23K) 图5.实验二的结构形式4. 有限元分析的结果和实验结果的比较；第一阶段的调试的准确程度将直接影响有限元分析模型与实验的模型的接近程度，如果，我们不能使实验得到的数据和有限元分析得到的模型相吻合，那么，这种取得成功的方法是不可靠的；因此，得到的数据和有限元分析得到的模型相吻合是至关重要的。表1提供给我们：实验的频率和分析得到的频率的区别，这儿存在很大的不同对于有限元分析得到的结果和实验得到的结果。因而，有限元模型分析需要进行改进。除了与正常的频率做比较的到结论之外，还有一种方法是：将要分析的模型与其相近的模型作比较从而得到想要的结果。具体的方法是：做模型的外型比较；我们将不规整的模型分割成一些特殊的模型，以便与实验和分析得到的结果做比较。将模型分割成一块一块的相同摸小模型，这样就可以做快速对比。通过使用ICATS这种软件，是模型之间可以相似到图6所示的情形；图6显示给我们清晰的，准确的实验分析与有限元分析之间的联系。(87K)图6一些科学家发明了一种定量的进行标准的和预测的模型的比较方法。作为一种图形示的方法，它将成为保证模型质量依据。测试与控制是评估两种方法模型相近程度的广泛使用的方法，它给我们提供了模型的尺寸上下直线的偏差。关于标准模型和分析的模型之间有如下的公式：式中 m 和 a 是标准的或实验分析模型各自的外型尺寸。测试与控制的价值可以用0和1来表示：1就表示实验和分析模型的尺寸接近与标准模型的尺寸；则0就有相反的结果。从表1中我们可以发现经有限元分析得到的尺寸虽然与模型2比较数值有一点小但还是接近与数字1的；从表中还可以发现两个实验的数据是很接近的。5. 有限元分析的发展趋势在有限元分析中使用从相关实验模型中得到的数据改正个别参数的含义的程序描述了服从结构的动态变化。各种改进的模型分析的方法可以被分为两类： 直接点阵法； 间接或反复法。直接的方法可以精确的计算出标准的数据，但是，对使用者来说没有机会来改进所涉及到的参数。在这儿参数就以为着像杨氏模数，泊松比，质量密度等这样的物理量，当使用直接方法的时候，所有的硬度参数和部分的点阵被更新在一个专门的参数设计阶段。因此，一些物理方法只注重于更新过程，而往往忽略结果使得这种最后被否定。科学的技术（间接的方法）容许选择性的使用标准的参数。如果模型要被改进的话，那么敏锐的观察力是必须的。通过它不但可以获得结果，而且还能解释一些参数的含义。另外，我们还要在计算机上花费大多数的时间反复的进行计算与演算。两种科学方法通过改进的模型已经被使用，同时，计算机程序通过MATLAB也别应用到设计当中。在第一个实验中，两种直接方法被应用于改进钻机机构有限元分析模型。Baruch ，Bar-ltzhack和Baruch认为模型点阵分析法是准确的，而且，通过下面的公式修正了标准的参数； 有限元分析模型的力矩系数通过下式也被更新； Ku=Ka-KaTMa+MaTKa+MaTKaTMa+MaTMaBerman和 Nagy使用的方法和Baruch的相似；他们在保证有限元分析的正交性的同时改进了力矩的系数，随之力矩也就发生改变； 力矩系数通过下式改变； 改进后的力矩则被分散，这样使得构件受力平衡；同时，劲度矩阵也接近了真实的。Berman和 Nagy所得的实验数据如表2所示；从表中可以看出实验数据非常的接近于标准数值，因此，测试与控制的一些数据被给出。与以前的数据相比这些数据有了很大的改变。表2实验得到的，有限元分析模型得到的和测试与控制得到的数据的比较：模型 方法1方法2标准频率Baruch 方法Berman 方法标准频率间接方法改正后的频率MAC改正后的频率MAC改正后的频率MAC模型18.67 Hz8.67 Hz0.9258.67 Hz0.9348.79 Hz8.79 Hz0.947模型247.34 Hz47.34 Hz0.96647.34 Hz0.94744.40 Hz44.43 Hz0.913改进后的数据被制成表格，从表格中的数据来看，改进后的有限元分析模型非常的接近于真实的结构，同时我们也看到测试与控制的数据也被改进。6. 元分析对动态设计的动态和结构的修正结构的动态特性被提高通过动态修正的方法，所使用大方法如：集中力偶，加弹簧，加阻尼等。其中，集中力偶是在垂直方向的柱子的顶端形成13.4Kg的集中质量，就像图3中设有20个节点一样。Modak使用冲击模型来对改良后的钻机进行测试，同时，将得到的数据在ICATS中进行分析，从而获得改良后钻机结构的动态特性。如表3所示：模型 标准频率使用有限元分析进行预测Baruch的方法Berman and Nagy的方法间接法18.37 Hz8.34 Hz8.17 Hz8.40 Hz246.05 Hz47.15 Hz46.96 Hz43.20 Hz表3 力偶集中后，标准频率和预测频率的比较力偶集中对钻机动态特性的影响与有限元分析模型所得的结果几乎一样。表3对比了Baruch，Berman and Nagy通过直接方法获得的数值和间接方法获得的数值与标准值进行比较。从比较的结果看，有限元分析得到的频率非常接近于标准频率。从而说明有限元分析模型对钻机力偶集中后钻机的动态特性的预测是正确的。因此，这种改良后的有限元分析模型的方法被大量的使用，通过对修正结构动态特性的预测就能设计出更为完善的产品。力偶集中对改变机构的频率是十分有意义的，通过预测，就可以在钻机上加20和25个节点。图8和图9分别显示了FRFS对机构的影响。表4和表5表示了通过有限元分析模型和ICATS软件修改后的模型对机构频率的预测。(33K) 图8加20节点对机构的影响(29K) 图9加25个节点对机构的影响表4在20个节点加20Kg的质量集中后对频率的预测（A面）；在20个节点加40Kg的质量集中后对频率的预测（B面）；有限元分析对频率预测的比较Baruch 法Berman 法间接法ICATS修改标准频率A面 20Kg的质量集中8.22 Hz7.99 Hz8.3 Hz8.2 Hz8.3 Hz47.08 Hz46.83 Hz42.87 Hz47.1 Hz42.8 HzB面40Kg的质量集中7.83 Hz7.45 Hz7.76 Hz7.75 Hz7.8 Hz46.86 Hz46.44 Hz41.27 Hz46.6 Hz41.3 Hz表5在25个节点加20Kg的质量集中后对频率的影响；在25个节点加40Kg的质量集中后对频率的影响；有限元分析对频率预测的比较Baruch 法Berman 法间接法ICATS修改标准频率A面Mass modification of 20kg8.34 Hz8.44 Hz8.41 Hz8.35 Hz8.4 Hz42.24 Hz43.74 Hz41.67 Hz42.2 Hz41.6 HzB面Mass modification of 40kg8.03 Hz8.21 Hz8.04 Hz8.1 Hz8.1 Hz38.89 Hz41.02 Hz39.67 Hz39.15 Hz39.5 Hz7. 结论通过对实验模型和有限元分析模型的比较，可以看出有限元分析模型需要改进。为了能够得到合理的，精确的复杂机构，这种改进是必须的。利用外界加压的方法使钻机变形来观察钻机的动态特性的实验在进行中，必须有好的结果出现以后，这种有限元分析的方法才能运用到别的机构。利用直接或间接的方法得到的数据来改进有限元分析模型，通过在机构的不同部位填加质量来使两种预测结果很相似，这种预测结果是有效的，而且是真确的尤其是利用灵敏度分析的间接方法得到的结果。Studies in dynamic design of drilling machine using updated finite element models AbstractThe aim of the present work is to develop updated FE models of a drilling machine using analytical and experimental results. These updated FE models have been used to predict the effect of structural dynamic modifications on vibration characteristics of the drilling machine. Two studies have been carried out on the machine. In the first study, modal tests have been carried out on a drilling machine using instrumented impact hammer. Modal identification has been done using global method of modal identification. For analytical FE modeling of the machine, a computer program has been developed. The results obtained using FEM, have been correlated with the experimental ones using mode shape comparison and MAC values. Analytical FE model has been updated, with the help of a program, which has been developed using direct methods of model updating. In the second study, modal testing has been carried out using random noise generator and modal exciter. Global method has been used for modal identification. Analytical FE modeling has been done using I-DEAS software. Correlation of FE results with the experimental ones has been carried out using FEMtools software. Updating of the analytical FE model has also been done using the above software, based on an indirect technique viz. sensitivity based parameter estimation technique. The updated FE models, obtained from both the studies have been used for structural dynamic modifications (SDM), for the purpose of dynamic design and the results of SDM predictions are seen to be reasonably satisfactory. Article Outline1. Introduction 2. Modal testing and identification 3. Finite element formulation of drilling machine 4. Comparison of analytical FE and experimental results (model correlation) 5. Finite element model updating 6. SDM studies using updated models for dynamic design 7. Conclusions References1. IntroductionDynamic design aims at obtaining desired dynamic characteristics in machines and structures, which may include shifting of natural frequencies, desired mode shapes and vibratory response. The ultimate objectives are to have a quieter and more comfortable environment, higher reliability and better quality of product. The conventional dynamic design is basically hit and trial method in which we try to achieve desired dynamic characteristics by making several prototypes. The disadvantage of this technique is that actual design cycle takes a lot of time and therefore it is not cost effective. However, model updating based dynamic design saves design cycle time as well as reduces the cost involved. Various tools used for updating based dynamic design are: experimental modal analysis (EMA) including modal testing and modal identification, model updating and structural dynamic modification. Ewins 1 and Maia and Silva 2 have explained the basic concepts of modal testing, which is an experimental approach to obtain mathematical model of a structure. In a modal test, the structure under test is excited either by an impact hammer or by a modal exciter, and the response of the structure is recorded at several experimental points, in the form of frequency response functions (FRFs), using a dual channel FFT analyzer. The experimental modal model gives information about the natural frequencies, corresponding mode shapes and modal damping factor and is useful for model updating. The model updating techniques helps us to bring analytical finite element models closer to real systems. In model updating an initial analytical FE model constructed for analyzing the dynamics of a structure is refined or updated using test data measured on actual structure such that the updated model describes the dynamic properties of the structure more correctly. The inaccuracies in FEM, when applied to dynamic problems are due to uncertainties in boundary conditions and structural damping etc. Friswell and Mottershead 3 have discussed the finite element model updating in structural dynamics. Baruch and Bar-Itzhack and Baruch 4 and 5 considered analytical mass matrix to be exact and developed a direct method for updating using test data. Berman and Nagy 6 developed a method of model updating, which uses measured modes and natural frequencies to improve analytical mass and stiffness matrices. Structural dynamic modification (SDM) techniques 7 and 8 are the methods by which dynamic behaviour of the structure is improved by predicting the modified behaviour brought about by adding modifications like those of lumped masses, rigid links, dampers etc. Thus the dynamic design using updated model is expected to be helpful in order to predict accurately and quickly, the effect of possible modifications on the dynamic characteristics of the structure at computer level itself, thus saving time and cost. Sestieri 7 has discussed SDM application to machine tools and engines. Kundra 8 gave the method of structural dynamic modification via models. Modak 9 has discussed SDM predictions using updated FE model for an F-structure. He used constrained nonlinear optimization method for updating of a machine tool using stiffness parameters at the boundary 10. The present paper deals with the FE model updating using direct as well as indirect method, and to use this updated FE model for dynamic design based on SDM predictions of a machine tool viz. a drilling machine. Two different studies are reported using different techniques for analytical and experimental analysis and for updating. Various objectives with which the present research work has been carried out are To develop updated FE models of a complex structure like that of a drilling machine and to use these updated models to predict the effect of various modifications on modal properties of the machine. To see whether hammer excitation yields good results for fairly complex structures like drilling machine or not, and to compare these results with those obtained from modal exciter. To analyze the results of SDM predictions obtained using the updated models derived in the studies.2. Modal testing and identificationIn the two studies mentioned earlier, different techniques have been used, for modal testing and identification. In the first study, impact hammer is used to excite the drilling machine structure, at various points as shown in Fig. 1 and Fig. 2. Response is taken at a fixed point with the help of an accelerometer. (12K) Fig. 1.Experimental setup (Study 1). (4K) Fig. 2.Hammer excitation locations. In the present study, the drilling machine is excited at 30 locations and therefore, 30 FRFs are obtained. These FRFs are recorded in the form of inertance. The experimental FRFs, thus obtained are transferred to computer. Modal identification or modal parameter extraction consists of curve fitting a theoretical expression for an individual FRF to the actual measured data obtained. The experimental FRFs are analyzed by GRF-M method using modal analysis software ICATS 11 to obtain modal parameters of the drilling machine. In the second study, the machine tool structure has been excited at the base at point 28, referring to Fig. 2, using modal exciter and response has been measured at various points using piezoelectric accelerometers. The modal identification of the FRFs, thus measured has been carried out using global method GRF-M method in ICATS software. Table 1 compares the experimental natural frequencies obtained from both the methods, which shows minor differences in the two modal frequencies Table 1. Mode110.29 Hz8.67 HZ0.95311.20 Hz8.79 Hz0.946Mode 265.14 Hz47.34 HZ0.90163.37 Hz44.40 Hz0.9063. Finite element formulation of drilling machineSeveral books have given the basic concepts of finite element analysis, some of them are: Zienkiewicz 12 and Bathe 13. The drilling machine structure is very complicated with different mountings and accessories. Therefore exact modeling and analysis of the actual structure is difficult and it takes more computational effort. However for analytical FE analysis, simplified model of drilling machines has been considered. In study 1, the finite element modelling has been done using a program developed in MATLAB. Beam elements have been used for the analysis. The joints and boundary conditions are considered to be rigid and influence of structural damping on modal model parameters, is ignored. The relevant data used for the drilling machine is given below: 25 mm pillar type, height=1.655m, mass density=7800kg/m3, Youngs modulus=200Gpa, number of nodes=30, number of elements=29, number of nodes per element=2, degrees of freedom per node=3. Fig. 3 shows the structure of the drilling machine with the node numbers given for study 1. (7K) Fig. 3.Drilling machine structure for FE analysis. The eigenvalues and eigenvectors have been calculated. The analytical FE model of the structure consists of 9090-size mass and stiffness matrices (303, 30 nodes and 3 d.o.f. per node). But by experiment only 30 coordinates can be measured. Therefore FE model has been reduced using Guyan 14 reduction method with the help of a program developed in MATLAB. In study 2, the finite element modelling has been done using I-DEAS software. The model has been made using beam mesh. Although the FE model has been simplified but the beam elements has rotational degree of freedom, which cannot be measured experimentally. Therefore the FE model needs to be reduced. The FE model has been reduced using model reduction utility in FEMtools software. Fig. 4 and Fig. 5 shows the mode shape animation for the first and second mode respectively, using I-DEAS software. (31K) Fig. 4.Mode shape animation (first mode). (23K) Fig. 5.Mode shape animation (second mode). 4. Comparison of analytical FE and experimental results (model correlation)The first stage of any reconciliation exercise is to determine how closely the experimental and analytical models correspond. If we are unable to obtain a satisfactory degree of correlation between the initial analytical FE model and the test data, then it is extremely unlikely that any form of model updating will succeed. Thus, a successful correlation is crucial for the success of model updating. Table 1 gives the comparison between experimental and analytical natural frequencies. There are differences between analytical FE model predictions and experimental results. Thus the FE models need to be updated. However, the differences between the corresponding results of both studies are minor. Apart from natural frequency comparison (as given in Table 1), another method of model correlation is mode shape comparison. To compare the mode shapes, we plot the deformed shapes of the structure for a particular mode, using experimental as well as analytical model. These mode shapes are plotted side-by-side for quick comparison. Mode shape corresponding to second mode is shown in Fig. 6, using ICATS software. It shows a fairly good level of correlation between the experimental and analytical FE model. (87K) Fig. 6.Mode shape comparison. Several researchers have developed techniques for quantifying the comparison between measured and predicted mode shapes. As an alternative to the graphical approach, Model Assurance Criterion i.e. MAC, 15) is a widely used technique to estimate the degree of correlation between mode shape vectors. This provides a measure of the least squares deviation or scatter of the points from the straight-line correlation. The MAC between a measured and analytical mode is:(1)where m and a represents measured or experimental and analytical mode shapes respectively. MAC is a scalar quantity whose value is between 0 and 1. A value of MAC close to 1 shows a good degree of correlation between experimental and analytical FE model. We can see in Table 1 that the MAC numbers are close to 1, though somewhat lower for the second mode. Table 1 also shows that the results obtained from both the studies are quite close to each other. 5. Finite element model updatingModel updating can be defined as “the process of correcting the numerical values of individual parameters in a analytical FE model using data obtained from an associated experimental model such that the updated model correctly describes the dynamic properties of the subject structure”. Various model updating methods can be classified into two major groups: Direct matrix methods Indirect or iterative methodsDirect methods are capable of reproducing measured data exactly, but they provide no opportunity for the user to select parameters for updating. Here parameter means any physically realizable quantity like Youngs modulus, Poissons ratio, mass density etc. When using the direct methods, the entire stiffness and mass matrices are updated in a single (non-iterative) solution step. Consequently any physical meaning, which the initial finite element model might have possessed, is lost in the updating process. Techniques like the indirect methods, allow the updating parameters to be selected. So, considerable physical insight is required if the model is to be improved, not only in its ability to reproduce test results, but also in interpreting the parameters physically. Methods in this second group are iterative and, as such, considerably more expensive of computer effort. Two studies have been carried out for model updating and computer programs for the same were developed in the present work using MATLAB. In the first study, two direct methods are applied to update the analytical FE model of the drilling machine structure. Baruch and Bar-ltzhack 4 and Baruch 5 considered the mass matrix of the analytical model to be exact. The measured eigenvectors are corrected by using the relation:(2)The stiffness matrices of the analytical FE model after updating is given as:Ku=Ka-KaTMa+MaTKa+MaTKaTMa+MaTMa(3)Berman and Nagy 6 used a method similar to that of Baruch. They update mass and stiffness matrices while the mass matrix is updated to ensure the orthogonality of the exact FE model modes. The mass matrix is updated as:(4)(5)The stiffness matrix is updated using following equation:(6)The updated mass matrix obtained will be symmetric and stiffness matrix will be close to that of exact stiffness matrix. Results obtained from Baruch and BermanNagy model updating methods are tabulated in Table 2. It is clear from Table 2, that the updated model reproduces the measured frequencies. After updating, MAC values have been calculated again using Eq. It can be observed that updated MAC values show some improvement over the initial MAC values. Table 2. Comparison of experimental and updated FE frequencies and MAC values Mode number Study 1 Study 2 Measured frequency Baruch method Berman method Measured frequencySensitivity method Updated frequencyMACUpdated frequencyMACUpdated frequencyMACMode 18.67 Hz8.67 Hz0.9258.67 Hz0.9348.79 Hz8.79 Hz0.947Mode 247.34 Hz47.34 Hz0.96647.34 Hz0.94744.40 Hz44.43 Hz0.913The results after updating have been tabulated in Table 2. It clearly shows that after updating, the updated FE model closely represents the actual machine tool structure. It also shows that MAC values have also been improved after updating. 6. SDM studies using updated models for dynamic designStructural dynamic modification (SDM) techniques are methods by which dynamic characteristics of the structure can be improved by adding the modifications like changing mass, spring, damping etc. The mass modification has been considered here for predicting dynamic characteristics using updated FE model. A mass modification on drilling machine is introduced in the form of a lumped mass of 14.3kg at the top of the vertical pillar, i.e. node 20 as in Fig. 3. The modal test for the mass modified machine is carried out by Modak 10, using impact hammer for excitation. The FRFs are analyzed in ICATS in order to obtain an experimental estimate of the altered dynamic characteristics of the drilling machine, as given in Table 3. Table 3. Comparison of measured and predicted frequencies, after mass modification, using updated FE model Mode no. Measured frequencies SDM prediction using updated FE model Baruchs methodBerman and Nagys methodSensitivity method18.37 Hz8.34 Hz8.17 Hz8.40 Hz246.05 Hz47.15 Hz46.96 Hz43.20 HzThe effect of the same mass modification on the dynamic characteristics of the drilling machine has also been predicted by updated FE model. Table 3 gives a comparison of the predictions based on the updated FE models obtained by direct methods of Baruch, Berman and Nagy and by indirect method based on sensitivity analysis, with that of the measured modified characteristics. It is seen from the Table 3 that the updated FE model predictions of the natural frequencies are quite close to the measured value of natural frequencies. This shows the capability of the updated FE model to accurately predict the effect of structural modifications on the dynamic properties of the structure. Now, this updated FE model has been further used to predict, at computer level, the effect of various mass modifications on the structural dynamics of the drilling machine, for the purpose of dynamic design. The mass modification can bring about significant changes in the natural frequencies of a structure. For predicting the effect of modifications using updated FE model, modification at node 20 and node 25, on the drilling machine has been considered. The effects on FRFs due to these modifications have been shown in Fig. 8 and Fig. 9 respectively. The values of the first two natural frequencies have been predicted using updated FE models and MODIFY module of ICATS software and are shown in Table 4 and Table 5. (33K) Fig. 8.Regenerated FRF due to mass modification at node 20. (29K) Fig. 9.Regenerated FRF due to mass modification at node 25. Table 4. Predicted natural frequencies after mass modification using 20kg at node 20 (Panel A), predicted natural frequencies after mass modification using 40kg at node 20 (Panel B) Comparisons of SDM predictions using updated FE modelBaruch methodBerman methodSensitivity methodICATS MODIFYMeasured FrequenciesPanel AMass modification of 20 kg8.22 Hz7.99 Hz8.3 Hz8.2 Hz8.3 Hz47.08 Hz46.83 Hz42.87 Hz47.1 Hz42.8 HzPanel BMass modification of 40 kg7.83 Hz7.45 Hz7.76 Hz7.75 Hz7.8 Hz46.86 Hz46.44 Hz41.27 Hz46.6 Hz41.3 HzTable 5. Predicted natural frequencies after mass modification using 20kg at node 25 (Panel A), predicted natural frequencies after mass modification using 40kg at node 25 (Panel B) Comparisons of SDM predictions using updated FE modelBaruch methodBerman methodSensitivity methodICATS MODIFYMeasured frequenciesPanel AMass modification of 20kg8.34 Hz8.44 Hz8.41 Hz8.35 Hz8.4 Hz42.24 Hz43.74 Hz41.67 Hz42.2 Hz41.6 HzPanel BMass modification of 40kg8.03 Hz8.21 Hz8.04 Hz8.1 Hz8.1 Hz38.89 Hz41.02 Hz39.67 Hz39.15 Hz39.5 Hz7. ConclusionsComparison of results obtained from experimental modal analysis and FE models of a drilling machine, indicate that its finite element models need to be updated. This is necessary in order to predict dynamic behavior of the complex structure with an acceptable accuracy. An experimentation involving modal testing has been carried out on the drilling machine using impact hammer as well as modal exciter. It has been observed that both impact hammer and modal exciter yield good results for fairly complex structures like drilling machine. Analytical FE model has been updated in the light of experimental data using direct as well as indirect methods. Both the methods give results, which are fairly close when used for predicting results of SDM attaching additional mass on the machine at different locations. The predicted results have been validated by comparison with measured results and are seen to be fairly accurate in particular for the indirect method using sensitivity analysis. References1 D.J. Ewins, Modal Testing: Theory and Practice, John Willey and Sons, New York (2000). 2 N.M.M. Maia and J.M.M. Silva, Theoretical and Experimental Modal Analysis, John Willey and Sons, New York (1997). 3 M.I. Friswell and J.E. Mottershead, Finite Element Model Updating in Structural Dynamics, Kluwer Academic Publishers, Dordrecht (1995). 4 M. Baruch and I.Y. Bar-ltzhack, Optimal weighted orthogonalization of measured modes, AIAA Journal 16 (1978), pp. 346351. 5 M. Baruch, Optimisation procedure to correct stiffness and flexibility matrices using vibration test data, AIAA Journal 16 (1978), pp. 12081210. 6 A. Berman and E.J. Nagy, Improvement of a large analytical model using test data, AIAA Journal 21 (1983), pp. 11681173. 7 A. Sestieri, SDM application to machine tools and engines, Sadhana 25 (2000), pp. 305317. 8 T.K. Kundra, Structural dynamic modification via model, Sadhana 25 (2000), pp. 261276. 9 S.V. Modak, Studies in Finite Element Model Updating and Application to Dynamic Design, Ph.D. Thesis, Department of Mechanical Engineering, IIT Delhi, 2001. 10 S.V. Modak, T.K. Kundra, B.C. Nakra, Dynamic design of machine tool structures using an updated model Pro. IMAC- XX, 2002, pp. 14891494. 11 ICATS Reference Manual, Imperial College, London, 1996. 12 O.C. Zienkiewicz, The Finite Element Method in Engineering Science, McGraw-Hill Publishing Company, London (1977). 13 K.J. Bathe and E.J. Wilson, Numerical Methods in Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ (1982). 14 R.J. Guyan, Reduction of stiffness and mass matrices, AIAA Journal 3 (1965), p. 380. 15 R.L. Allemang, BD.L. Rown. A correlation coefficient for modal vector analysis, Proc. 1st IMAC, 1982, pp. 110116. 16 FEMtools Manual Version 2.0, Dynamic design solutions, 2000. Corresponding author. Steam Turbine Engineering, TCGT Division, Bharat Heavy Electricals Limited, Hyderabad-502032, India 利用有限元模型对钻机进行动态分析的研究摘要现在的工作的目的是使用分析和实验的结果发展和改进钻机的有限元分析模型，这种有限元分析已经用在监测将钻机的工作特性修改后对钻机动态的结构的影响；对钻机将有两个研究就进行。第一个研究是：使用工具对钻机进行冲击来观察这种冲击对钻机的影响的实验已经在进行，通过人们公认对模型的证明我门已经知道这种方法的可行性；为了这一个有限元模型分析的机器，一个计算机程序已经被设计出来。有限元分析获得的结果是将通过实验得到模型的比较与测量和控制的价值联系起来。有限元分析模型已经被改进，是由于一个已经使用的有限元分析模型程序的改进。第二个研究是：模式上的测试已经完成，这种测试包括运用各种任意的声音和模式的刺激。公认的模式的测试方法被用来作为这种有限元分析模型的证据。利用I-DEAS软件已经对有限元分析模型的作了分析。利用FEMtools软件已经对有限元分析模型和实验得到的结果的联系进行了分析，利用以上两种软件已经对有限元分析模型进行了间接的改进。灵敏度基于对参数估量的技术。通过以上两种研究，对这种分析模型进行结构和动态的修改。我们对动态设计的结果和结构和动态的修改相当的满意。目录1. 绪论；2. 模型的测试和结论；3. 钻机的有限元分析元素的表达；4. 有限元分析的结果和实验结果的比较；5. 有限元分析的发展；6. 利用有限元分析对动态设计的动态和结构的修正；7. 结论。参考文献1 绪论动态设计的目的在于获得想要的机器和构件的动态参数，这些动态参数包括震荡频率，想要得到的结构尺寸和震荡响应，而根本的目的是有一个安静和舒适的环境，高的可靠性和更好的产品质量。常规的动态设计是通过很多的原形的分析和实验来获得自己想要的参数。这个设计的缺点是：要进行这个实验和分析需要很多的时间和精力，所以根本就没有效率所言。然而，新型的有限元分析节省了时间节省了有关的花费。动态设计所用的各种方法是：实验的模型分析（形态测试和实验确认），模型改进和结构上的，形态上的修改。EWINS，MAIN和SILVA对模型测试进行了基本概念的解释。模型测试是通过实验的方法获得机构的数学模型。在这个实验中，构件用一个锤子进行打击或用刺激物进行刺激，是它发生变形，在这个过程中，构件的变形已经被仪器所记录。然后，用一个接口将这种变形的信号传递的分析器里面，以构件的响应函数的形式进行分析。这种实验模型提给给我们一个正常的频率相应的外形和模型的制动因数是非常有用的对模型的改进来说。改进后的有限元分析技术帮助我们使得分析有限元要素模型接近于真实的系统。在模型更新起初，有限元模型分析因为结构的动力学，模型构造是精确或者最新的。用标准的，最新的测试数据的使用，以至于对机构模型的描述是非常准确的。当将有限元分析应用于不准确的边界条件和结构减震时，将会出现错误。Friswen 和Mottershead 在结构动力学中讨论有限元模型分析的发展；在Baruch和Bar-Itzhach中考虑分析的大众点阵式是精确的而且在后来通过最新的实验数据对发展为一种直接的数学方法；Berman和Nijy发明了一种改进模型的方法。这种方法使用标准的dos命令和正常的频率来提高对大多数和坚硬金属分析的精确。结构的动态休整技术是一种方法，通过增加改进参数（刚性连接，节气阀等）。因而，利用最新的模型来准确的和快速的预测动态设计是非常有用的，在动态设计时，计算机利用自身程序对模型进行结构动态特性的有可能修正，这样即节省时间又节省花费，Sestieri讨论将结构动态修正运用到工作母机和发动机上Kundra提供了一种结构动态的修正方法。Modak讨论通过最新的有限元模型分析对构件动态修正的预测，在边界条件，利用硬度参数时对最新的机床，它常常不是非线性最优化的方法。这篇论文要处理最新的有限元模型分析通过使用指导方法和间接方法来解决动态设计构件动态参数的修正与预测。一个钻机，两重不同的设计方法被报道使用不同的技术方法来分析和解决最新的动态分析设计。现在多种研究工作被实施的目的是：（1） 来发现一种最新的有限元分析系统来解决象钻机一样复杂结构的设计和使用这种有限元分析模型来预测各种参数在机器模具上的响应。（2） 让这种变形的模型和正常的模型相比较来看象钻机一样复杂结构对其进行冲击时产生变形是否有好的方面出现。（3） 利用这种最新研究的模型分析方法来分析获得机构动态修正参数的测试结果。2. 模型的测试和结论；在二项研究被提及更加早期， 对模型的测试和结论，人们引用了不同的技术。在第一个实验中，用冲击的方法使钻机的构件发生变形，其数值的变化如图1和图2：(12K)图1实验进行前(4K) 图2实验后变形是在过载器件的帮助下对一个固定点的取样；在现在的研究中，使用仪器使得在钻机的30个部位进行刺激使之发生变形，则这样就能获得30个响应函数。这些响应函数在变化以前就已经被记录下来。同时就这些获得响应函数输送到计算机里面，将获得的数据以曲线的形式表达出来，再将其进行分析就能获得标准的，最新的钻机的参数数据。第二个实验是：使机械机构地部的28个点发生变形并用压电式加速仪进行测量，通过ICATS软件对频率响应函数的正确性进行了证明，结果显示这种方法得到的数据是准确的。表1是通过两种不同的方法得到的频率的数据，从数据来看，它们是完全不一样的：表1 方式110.29 Hz8.67 HZ0.95311.20 Hz8.79 Hz0.946方式265.14 Hz47.34 HZ0.90163.37 Hz44.40 Hz0.9063.钻机的有限元分析元素的表达；像Zienkiewicz 和 Bathe一样，人们对有限元分析的一些概念进行了定义。与其他的机器和构件相比，钻机的构件是非常复杂的；因此，对实际的构件分析是很难的，而且会花费大量的时间和精力。然而，对有限元模型分析来说，钻机的简单化的模型被使用。在实验1中，有限元分析模型被MATLAB作成一个计算机程序；光线元素已经被应用到分析当中，刚性连接和边界条件被认为对结构减震是有影响的在模型参量上，但是，人们往往将其忽略。钻机的相关使用数据如下：25毫米的柱子模型；高度= 1.655 m； 质量密度= 7800 kg/m3；杨氏系数= 200 Gpa； 连节点的个数= 30； 设计元素的个数= 29； 每个元素的节点个书= 2； 每个节点的自由度= 3。图3表示了实验1中钻机结构的节点数：(7K)图3钻机结构的有限元分析现在，钻机的特征值和特征向量已经被计算出来。结构的有限元分析的数据包括9090-的外行
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