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This factor affects particularly the result of theapproximation for part 3, as the original mesh has regions ofgreater detail that are not present in the reduced mesh. Finally,regions that are further away from the minimum box containingall the dots show deviations greater than those found within thementioned box. Again, parts 3 and 4 are the ones that present themost points outside the box (such box is defined from the fixationpoints), whereas in parts 1 and 2 most of the points in the modelare within the mentioned box.Table 3 summarizes the results of the tests. For the syntheticmodel the comparison is made against the model deformedapplying the FEM, and for real parts the comparison is madeagainst the data model reconstructed from the real deformedpart’s 3D data. The number of nodes for the initial CAD modeland the number of points for the reduced mesh on which thespring system is applied are indicated. The fixation points are thenodes of the reduced mesh on which forces are applied in orderto deform the part. The maximum comparison distance is a limitestablishedmanually. For parts 2 and 3, such limit is themaximumvalue of the absolute standard deviation. The positive and negativedeviations are the deviation values above and below the referencevalue, respectively. The Root Mean Square (RMS) deviation offersa global evaluation of the absolute deviation, which is, in allcases, lower than the average thickness. Since CAD mesh can bereduced beforehand, the time to calculate deformations, during theinspection of the parts, mainly depends of the time required bytheminimization process. Computation time to find theminimumvalue in the iterative optimization is also presented. The last lineis the RMS deviation obtained by applying the FEM on the fulloriginal mesh. The approximation obtained with the FEM is moreaccurate, except for the part 3. This is because the real part hasgreat variation in its thickness in some regions, but this was notconsidered to build the model to calculate the deformation. Fig. 13. Results for part 1.Table 4 shows a comparison of timing and accuracy betweenthe deformation obtained by applying the proposed spring–massmodel and the deformation obtained with the FEM. Unlike theprevious tests, instead of applying the minimization process, inthese tests, an explicit inversion of the stiffness matrix is carriedout to find the solution. The deformation obtained with the FEMis taken as the deformed reference model. In the case of reducedmesh, there is a reduction in calculation time of around 50%over the time required for the FEM solution for the same mesh.As proposed, the deformation of the full mesh is obtained byperforming a RBF interpolation on the deformed reduced meshobtained with the spring–mass model. In this case, the timereduction is about 80% with regard to the computation timeobtained with the FEM.It is appreciated that by using the matrix inversion of stiffnesslower accuracy occurs in the result, regarding the accuracyobtained by applying the minimization solution (Table 3), whichcan be explained due to the numerical approximation errors [34].
重点：1.弹性质量系统是为了壳形元件的变形建模而提出。2.计算弯曲弹簧的刚度的表达式。3.径向基函数是用来设置用于优化的初始值。4.径向基函数被施加到加速变形的计算。
文章信息：关键词：弹簧质量模型 物理变形 变形的零件检测摘要：为了检测零件变形，最近的作品是利用将虚拟的变形加载真实零件的数字化的版本上，使零件模型回到其标称的形状。这种虚拟模仿实际的过程，称为夹具，通常是制造商在一开始安装为了使零件回到标称形状的时候使用。使用这样的虚拟变形有限元方法（FEM）是为了满足该检查过程的精度要求，本文提出了一种基于弹簧质量系统的方法，它比有限元法更加简单，但是计算壳类零件的变形精度的计算却能与之媲美。此外，由于计算的简单化，使得该方法比有限元法（FEM）更容易实现。该系统由两种弹簧构成，一种是对零件的网格膜行为进行模型，第二种是对网格单元之间零件的屈曲行为进行建模，我们相信，通过对所提出的弹性质量模型系统的应用， 论文网对标准有限元方法计算开口门的实时检查可以减少80%的时间是完全有可能的。