组合机床的部件合成(中英)

1、Modular Synthesis of Machine ToolsM. Zatarain, E. Lejardi, F. EgatiaSubmitted by R. BuenoReceived on December 30, 1997AbstractIn the current state of the art, calculation of static and dynamic behaviour of machine tools requires themodelling of the complete structure and components by the Finite Ele

2、ment Method. If calculation at several machine positions is required, major adaptations of the FEM model are needed.The article shows a method by means of which "precalculated structures" can be used to obtain the complete model of the machine at any position of its axis in a very straight

3、foward way. Besides being ahelpful tool for the analysis of a particular machine, the method permits the organisation of a database in which general-purpose modules can be introduced for the calculation of the complete machine in a very short time.The whole method and database have been programmed,

4、and results obtained correlate very closely with the ones obtained by the classical FEM.Kevwords: Machine, Module, Dynamics.I. INTRODUCTIONCurrently, there is a tendency in the direction of the conception of modular machine tools 3. This concept would permit to produce better machines with lower cos

5、ts.Another important advantage derives from the reconfigurability of the machines produced, as the automotive industry is requiring nowadays.One of the reasons for the cost reduction of modular machines is the speed gained in the design. The designer just selects the modules out from a catalogue and

6、 fit them together. Then, he evaluates if all the design requirements are fulfilled.Amongst the requirements demanded from machine tools,we can point up that of the static and dynamic behaviour.The Finite Element Method (F.E.M.) is, nowadays, the most powerful tool for structural analysis, and is sy

7、stematically used by many machine tool manufacturers as a means to guarantee the performance of their new designs.Unfortunately, structural calculation by the Finite Element Method is very time consuming, and takes up a significant amount of the total workpower required for the design task.Ideally,

8、the module producer could prepare and give to the module user the FEM model of the module, so that the behaviour of the complete machine could be calculated.But when the FEM models are developed it is not possible to define a mesh compatible and coincident with the meshes made by different module ma

9、nufacturers.A further problem arises when calculation at several axis locations is required. In this case it would be very difficult,or even impossible, to mesh the structures in such a way that a coincident mesh is obtained at several positions of the slides.Because of these problems, several F.E.M

10、. users have estimated that the time required for the modelling of a complete machine tool could be halved if compatibility of meshing at the interfaces was not required.As mentioned before, one of the advantages of modular machine tools is the short time required for the design of a new machine. If

11、 a completely new Finite Element model was required for the estimation of its behaviour, the design speed advantage would be lost.It is due to these considerations that the necessity of a method for avoiding the compatibility requirement at the meshes on both sides of the interfaces is evident.A fur

12、ther consideration for the case of modular machines would be the possibility of reducing the amount of memory required for the storage of the stiffness and mass matrices of the modules. The memory requirements of these matrices are around several Megabytes, typically higher than 10 MB each. It would

13、 not be practical to store these matrices for many modules. If a database with information for the calculation of the behaviour of modular machines is required, the information for each module should be reduced to a minimum.A fast calculating system would offer the possibility of optimising the conf

14、iguration of the machine and correctly selecting the modules from the available ones. After this work is done, more traditional methods of optimisation could be applied l.2. STATE OF THE ART OF CALCULATION OF INDEPENDENTLY MODELLED SUBSTRUCTURESMuch effort has been paid to the problem of gluing inde

15、pendently modelled over the last few years.One of the approaches is the automatic remeshing of the elements and nodes of the interfaces. But the current tendency is towards developing methods for guaranteeing the achievement of the displacement and force compatibility at the interfaces, even if mesh

16、es are not compatible. Very important advances have been made in this methodology, but to the best of our knowledge, all the methods published use interface formulations very similar to the interpolation functions of the elements themselvesl456. That means that a new mesh at the interface is require

17、d, something which is not wanted if a very rapid calculation of the behaviour of the ensemble is needed.While the accuracy obtained by the use of the interface elements proposed in the above mentioned references is excellent, the 'democratisation' of the Finite Element Method to the calculat

18、ion of the behaviour of modular machine tools requires a much more agile solution for gluing the independently meshed modules.3. PROPOSED APPROACHIn the above-mentioned previous developments, gluing of the substructures is done by the use of an interpolation function independently defined on the int

19、erface. This function can be written asv=Tq (1) where v is the displacement of any point of the interface, T is a function of the position of the interface point, and q is a vector containing the parameters of the interpolation function. The function T is defined element by element, in a similar way

20、 to the ones used for the interpolation of displacements at any finite element.The approach that we propose for gluing substructures (modules) is the direct definition of T as a function of the point co-ordinates, that is, without using any remeshing technique. So:v = T(x, y, Z ) q (2)The T function

21、 will have different values depending on the type of joint used between the modules.In the next sections the way of joining theoretically (FEM) precalculated modules will be shown, but the method permits the utilisation of the results of Experimental Modal Analysis applied to the module in free cond

22、ition.3.1 Static jointsIt would be natural to use a polynomial function for T. The function used was the simplest possible, that is, a linear polynomial with shear blocking (rigid body displacement). With this formulation, equation (2) can be written as A first formulation can be obtained by all the

23、 points at both sides of the interface to fulfil this formulation exactly. This condition can give rise to an artificial increase of the stiffness of both modules. An alternative approach is to oblige the points of the borders at both modules to follow the formulation in a minimum square error sense

24、, that is where Ui stands for the displacement vector of point i of the border. This formulation is known in the Finite Element Method developing world as a "weak formulation" 8 7. This is equivalent to considering a force distribution at the boundary of each module with the function: If t

25、he simplest case of only two modules is considered, by using the a subindex for one of them and b for the other, and using the superscript i for the nodes at the boundaries and o for the nodes outside the boundaries, the following equations are obtained: In this equation, matrices K and M are obtain

26、ed from the Finite Element Method applied at modules a and b separately. f contains the external loads at both modules. When more modules are joined together the joint matrices are obtained in exactly the same way as the one shown for only two modules.The static problem can be solved by equating the

27、 externally applied force to the elastic force (stiffness matrix times displacement vector).The resolution of the static problem requires the inversion or triangularisation of the complete stiffness matrix. Stiffness matrices obtained by the Finite Element Method are definite positive, which means t

28、hat some straightfonrvard optimised resolution methods can be applied (Cholesky, skyline, etc.). But the stiffness matrix obtained here is not definite positive. For this reason, other methods of resolution are required. In our case, a Gauss triangularisation with pivoting was used.3.2 Movable joint

29、sNowadays, most machine tools use rolling guides. The usual solution consists of using two roller ways and four rolling pads. Each pad has a certain stiffness in the two directions perpendicular to the rollerway, and also a small amount of rotational stiffness in each of the three directions of spac

30、e. Because of the small value of these three last components, this system can be (and usually is)modelled by two linear springs, the centre point of the pad being their application point.Usually, the centre point of the pad is not a nodal point of the FEM model. because it does not belong to the str

31、ucture itself but to a component that is screwed into it. It is equally unlikely for the other substructure, since the pad can be located at any point of the rolling way.The solution used consists of using independent interface elements at both components. The interface elements are correlated with

32、the nodes of the boundaries, and the forces at the pad are calculated from the difference between displacements of its centre point when obliged to follow the movement of one and other interface elements.组合机床的部件合成M. Zatarain, E. Lejardi, F. EgatiaSubmitted by R. BuenoReceived on December 30, 1997摘要在

33、当前技术水平下，机床静态和动态性能的计算需要通过有限元法进行完整结构成分建模。如果需要对机床多个部位进行计算，那么需要对有限元模型做较多的修改。本文介绍了一种方法，该方法用“预先计算的结构”非常直接地得到机床的轴上任意位置处的完整模型。除了作为一种对特定机床分析的有用工具，该方法还可以建立一个数据库，在这个数据库里，通用部件能够在很短时间内被整个机床的计算所采用。全部方法和数据库已经编程，所得的结果与传统有限元法所得的结果非常接近。关键词：机床，部件，动态1. 引言 目前，在组合机床概念上出现了发展趋势，该概念允许以更低的成本生产出更好的机械。另一个重要优点源自所生产出的机械的可重构性，这是出

34、于当今汽车产业的需要。 组合机床能降低成本，原因之一是设计出了更高的速度。设计者只需从目录中选出部件并把它们组装在一起，然后评估是否满足了所有的设计需求。在机床所需的要求中，我们突出对机床静态和动态性能的要求。如今，有限元法成为结构分析的最得力工具，并作为机床制造商确保其新设计业绩的一种手段而被广泛地使用。然而，用有限元法进行结构计算很费时，而且占用大量的设计任务所需的工作量。理想情况下，部件生产商可以为用户准备并提供部件的有限元模型，从而使整个机床的性能够被计算出来。但是，有限元模型的开发并不能定义这样一个单元格，这个单元格要能和不同部件的生产商制造出的单元格保持兼容。在进行多个轴的位置的计

35、算时，更进一步的问题出现了。在这个情况下，以这种在多个移动位置处获得一致单元格的方式来捕捉结构，是很困难的甚至是不可能的。由于这些问题，一些有限元的用户估计，如果在边界处划分单元格无需考虑兼容性，那么，整个机床的建模时间将会减半。如前所述，组合机床的优点之一是缩短了设计新机械所需的时间。如果机床的性能评估需要一个全新的有限元模型，设计速度的优势将会失去。正是由于这些因素，一种为避免在双方边界处对单元格兼容性要求的方法显然是必要的。对于组合机床的这种情况，一个更深层的考虑将是减少部件的刚度矩阵和质量矩阵所需内存量的可能性。这些矩阵占用的内存通常在几兆左右，个别高的会超过十兆。在存储许多部件的矩阵

36、时，是不实际的。如果需要一个关于组合机床性能估算的信息数据库，每个部件的信息将减少到最低限度。一种快速计算系统将为优化机床配置和从可用的部件中选出正确的部件提供可能。这项工作完成后，更多传统的优化方法将得到运用。2. 现代独立模型结构的计算技术过去几年里，人们在独立模型的连接问题上作出了很大努力。方法之一就是边界单元节点的自动重连。但是目前的发展趋势是朝向确保实现边界节点力和节点位移的兼容性的方法，即使各个单元格之间并不兼容。这个理论已经取得重大进展，但据我们所知，所以公布出的方法中所使用的形状函数跟原插值函数（【1】【4】【5】【6】）非常逼近。这意味着需要新的边界单元格。而在需要对机床整体性能进行快速计算时，