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2. Material properties of components.Name of components Elasticitymodulus (GPa)Poisson’sratioDensity(kg/m3)ColumnBedSliding carriageSpindle box173 0.3 7300Sliding tableWork tableScrew 219 0.3 7850Nut 213 0.28 7850Guide and slider 219 0.3 7850Table 3. Stiffness values of interfaces.Name of interfaces Stiffness (X-direction) (N/mm) Stiffness (Y -direction) (N/mm) Stiffness (Z-direction) (N/mm)Guide–slider (X-direction) 0 1.3131061.623106Guide–slider (Y -direction) 1.7231060 2.413106Guide–slider (Z-direction) 1.3131063.4231060Screw–nut (X-direction) 1.263106––Screw–nut (Y -direction) – 1.263106–Screw–nut (Z-direction) – – 1.263106 Box–Behnken model; the central points of space andedges are the experimental design points. Table 5 is theorthogonal test table of three levels and three factorsbased on Box–Behnken method.X, which is the design variables’ matrix composed bydesign samples, and F, which is the matrix of the mini-mum critical values of the axial cutting depth, can beexpressed asX=0:50:50:50:25 0:25 0:25 0:25 0:250:50:50:50:25 0:25 0:25 0:25 0:2510:50 0 0 1 0:25 00:50:50:50:25 0:25 0:25 0:25 0:2500:51 0 0:500:25 1010:50 0:50 10:250:50:50:50:25 0:25 0:25 0:25 0:2500:50 0 0 0 0:25 0110:50:50:51 10:250:51 0 0 0 0:25 1 0100:50:50 1 00:250:50 0 0 0 0:25 0 00:50:50:50:25 0:25 0:25 0:25 0:250:50 1 0:500:25 0 10:51 1 0:510:25 1 1000:50 0 0 00:2510:51 1 0:510:25 126 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 437 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5, F=5:085:085:125:085:15:285:085:15:34:664:544:545:084:555:284:535:1226 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 437 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5According to equation (13), the weight coefficientmatrix K can be obtained as follows:K=½ 2:36 0:32 1:10:01 4:61 2:37 3:04 2:25 ;the constant term is 5.12.Therefore, writing to the form of equation (8), thefunctional expression of response surface model with therelationship between the position and the value of mini-mum critical axial cutting depth can be expressed asap lim(min )(x, y, z)=f (x, y, z)=5:12 2:36x+0:32y+1:1z+0:01xz+4:61yz+2:37x2 3:04y2 2:25z2ð14ÞThe quality verification equation is expressed asR2=1 P mi=1(fi f0i)2P mi=1(fi f00i)2ð15Þwhere m is the number of the samples, f0iis the value ofresponse surface calculation, fi is the value of finite ele-ment calculation, and f00iis the average value of finiteelement calculation. R2!1 indicates high fitting accu-racy. The values calculated on six non-specific positionsare used to verify the fitting precision of the establishedresponse surface model. In this model, R2=0.7405.The accuracy of established response surface model ishigh enough for application (see Table 6).Evaluation of machine tool with position-dependentmilling stabilityFigure 9 shows the minimum critical values of the axialcutting depth in right half workspace. It is a four-dimensional chart. The color indicates the differentminimum critical values of the axial cutting depth. Forthe machine tool with box-in-box structure, the varia-tion in the minimum critical values of the axial cuttingdepth is obvious; the variation range is from 1.8 to6mm. The obvious variation in the milling stability isnot the satisfied design for machine tools. The optimaldesign is that the milling stability is conformed at anyposition; certainly, it is hardly to be realized. Therefore,the designer had better make the variation of themilling stability stable as much as possible to reach theproductivity goals for machine tools. In other words,the structural stiffness of machine tools should be rein-forced at the position where the milling stability isweak.
基于响应面模型快速评估机床相关位置的铣削稳定性
1.1摘要
铣削稳定性是机床动态特性的重要评估标准之一,而且对于机床的设计和制造也至关重要。机床的铣削稳定性一般随移动部件的位置组合的变化而变化。传统的机床铣削稳定性分析是基于在机床整个工作空间里的一些具体位置而进行研究的,所得结果并不具有普遍性。此外，对于在多个不同位置进行全面的研究所要施行的操作和计算也是非常耗时的。本文中，应用了一个可以快速评估机床稳定性本新方法。在这种方法中,关键移动部件的组合位置设置为样本用SAMCEF有限元仿真分析软件来计算机床的动态特性。之后，便得到了每个样本中关键轴的最小切削深度。这些关键移动部件的位置和关键轴的最小切削深度在整个工作空间任何位置的关系可以通过建立响应面模型来获得。响应面模型的精度可以被计算出来，响应面模型也可以用来快速评估机床中独立位置处的铣削稳定性。以box-in-box结构的精密卧式加工中心为例,在任何位置的关键轴的最小向切削深度的数值都可以被得到。这种用一些独立位置来快速评估机床稳定性的方法避免了复杂的理论计算，所以在机床的设计过程的阶段，它很容易被工程师和技术人员采用。论文网