Adaptive dynamic optimization design of machining center pillar*

Kui－zhou SUN，Jin－yu ZHOU

Jiangsu University of Technology，Changzhou 213001，China

Adaptive dynamic optimization design of machining center pillar*

Kui－zhou SUN?，Jin－yu ZHOU

Jiangsu University of Technology，Changzhou 213001，China

Analysis has been made on the adaptive dynam ic optim ization design of machining center pillar by using the quantitative analysis tools.The adaptive com prehensive evaluation index is proposed and the adaptive com prehensive eva luation m odel of p roduct is established.On the basis of primary evaluation on various indicators such as product function adaptability with methods of Multilevel Fuzzy Integrative Evaluation，the secondary com prehensive evaluation w ill be continued and com prehensive adaptability evaluation level of VMC850 machining center pillar w illbe gained，thus it could provide guides and evidence for further improvement of product design.Through p resenting adaptive m easuring values of all proposals in schematic design phase，the quantitated could be evaluated on the complexity ofmodifying the design.

Adaptive design，Dynam ic optim ization，Machining center pillar

*Project supported by National High Technology Research and Development Program of China((863 project)，No.2012AA040104)

? Kui－zhou SUN，E－mail:sunkuizhou@126.com

1.Introduction

Pillar，an important part of the machining center，bears a direct link with the working performance of the completemachine.Therefore，it is very necessary to enhance static－dynamic performance of the pillar.Empirical design has been adopted inmachine tool parts and it basically remains in static design stage［1］.In recent years，scholars have come to realize the importance of CAE analysis［2］.In particular，they proposed many methods of dynamic design to analyze the influence exerted by the dynamic behavior ofmachine tools on precision machine finish.For instance，Zhang Xueling［3］in Tianjin University adopted the principals of dynamic structure and variational analysis technology of finite elementmethod to realize the optimum structural design of lathe bed of numerically－controlledmachine tool.And also，Zhang Jianrun and Ni Xiangyang in Southeast University began to carry out the research to establish the structural dynamics modeling of gantry machining center and optimization design.They adopted the methods of sensitivity analysis and optimization design，as well as by using the tuned damper to improve dynamic property of completemachine［4］.

All of the abovework could improve the dynamic behavior ofmachine tool to some extent and also offer some reference for dynamic optimization design of machining center pillar.While all of the above are almost dynamic designs under single target，this paper is about to apply adaptive dynamic design［5］，a concept proposed by professor Gu Peihua，to utilize principals of similarity and reusability to finish the rapid modification，reusing and substitute of products ofmechanical structure and thus to explore systematic products of serialization on that base and at the same time to realize rapid modification so as to meet the rapid and personalized market demand of small amount.

Adaptive dynamic design is an integrated design under multi－target control and constraint and also a function－driven physical design，of which key is u－sing the dynamic design technique to study the product life cycle of adaptive products and the dynamic design based on CAEmechanical structure under the constraint of social economy，resources and environment.This paper is about to choose VMC850 pillar in verticalmachining center of precision as research object，to analyze adaptive dynamic design ofmachining center pillar structure，adopt CAD/CAE integrated simulation technology to conduct parametric design and finite element analysis on pillar structure，and continue to improve the structure as well as dynamic parameter optimization on that basis so as to offer fundamental basis for the design of precision verticalmachining center pillar and evidence for the optimization design.

2.Finite element analysis of the original pillar

2.1.Modeling of finite elementmodel of pillar

VMC850 precision verticalmachining center(as shown in Figure 1)is a kind of numerically－controlled machine tool with three axes association and the pillar have to be equipped with excellent static and dynamic performance because it functions as a link between spindle box and workbench.The pillar geometric model adopts parametric 3D modeling software UG to obtain themodel(as shown in Figure 2)and thematerials of the pillar is HT300.Because of the seamless connection between UG and ANSYS WOKBENCH，we can directly import the modeling based on UG into ANSYSWOKBENCH to conduct finite element analysis.Because the shape of the pillar is very complex，methods of exquisitemesh generation in ANSYSWOKBENCH are employed in this paper.Aftermesh is generated，the total number of node for this finite elementmodel is 39662 and number of element is 21528.As shown in Figure 3，7 bolts serving as a fix between themain body of pillar and the slide.After finishing all the above－mentioned steps，we can simulate the practical operating condition to carry out the finite element analysis on the pillar and draw some conclusions for further optimization design.

2.2.Statics analysis of pillar

The pillar needs to be carried out a statics analysis because it locates in a crucial part in machine tool and has to meet a high stiffness requirement.Force applied on the pillar is complex to analyze，so we just equal it to a respective 300 N concentrated load imposed in X，Y and Z direction，three parts linked with the pillar and lead screw of up－and－down motion.And at the same time，we also need to impose fixed constraint in the part of connection between the lower end face of the pillar and the slide while there is no constraint on the upper end face.

Figure 1.VMC850 machining center

Figure 2.3D model of original pillar

Figure 3.Finite elementmodel of original pillar

The result of the static finite element analysis is presented in Table 1 and Table 2.Table 1 tells that all of themaximum deflection in various directions of pillar is small，and Table 2 tells that static rigidity of pillar in X direction is the worst，and In Y direction is the second and In Z direction is the best.Stiffness in X and Y direction is a weak part in the whole process of the machine tool part，exerting a restriction on the improvement of the engine performance.From the pointof stress analysis，the stress ofmaterial is far smaller than the maximum permissible stress，so the key to enhance stiffness lies in structure optimization of the pillar with machine precision being the guarantee.

Table 1.Static mechanics of primary structure

Table 2.Static stiffness of primary pillar

2.3.Modal analysis of pillar

Due to vibration caused by alternating load when themachine tool ismachining the parts，amajor dynamic stress arises in internal structure，exerting a serious deformation and a big damage on the pillar，thus itwill affect the precision and stability ofmachining.As a result，modal analysis is essential part.In order to improve accuracy and efficiency of the result，modal analysis of finite element is needed to ascertain vibration performance of pillar structure—inherent frequency and mode of vibration.During the structural dynamic analysis，weight factor of all stages of models decreases as the modal frequency increases［6］，so the conclusion is that characteristics ofmode of lower stage basically determinates dynamic property of the pillar structure.In this paper，we only study the first 4 stages of inherent frequency and mode of vibration in pillar structure.By using subspace iterationmethod in ANSYSWORKBENCH，we try to seek for a finite element solution of inherent frequency and mode of vibration proposed there is no damping and the vibration is free.The results are listed in Table 3 and Table 4.

Table 3.The inherent frequency and mode of vibration in the 4 first orders of the primary pillar

Table 4.Three kinds of improved designs

The Table 4 tells that the 1st order twists in Z direction，3rd order protrudes and vibrates in X direction，and both the 2rd and the 4th order swing in X and Y direction.Themain reason leading to protrusion and vibration is the lack of appropriate strengthening rib plate in the inner part of the pillar and the unreasonable size of open hole in the back of the pillar，so we have to improve the design of the pillar structure.

Figure 4.Modal cloud table of pillar

3.The improved design and optimal selection of schemes of pillar structure

Based on statics and the simulation results of modal finite element，we analyze the form of removed area in the center of the back of pillar as well as influence on structural dynamic and static performances exerted by the change of arrangement form of strengthening rib plate in the inner pillar so as to improve the pointed structure and thus realizemulti－target dynamic optimization design to enhance static and dynamic performance of pillar.

3.1.The im proved design of pillar structure

The object of improving the pillar structure is to guarantee the numerical value of static rigidity and improve inherent frequency or its weak modal at the premise of controlling the pillar quality.Based on the above improvement ideas and analysis results of static and dynamic finite element，we propose 3 improvement solutions as listed in Table 4 and its three－dimensional geometricalmodeling in Figures 5～7.

Then we import the geometric model of various improved designs into ANSYS WORKBENCH to build finite element modeling，and proceed to the process of respective dynamic and static simulation solution after pretreatment，finally we get analyzed data(as listed in Table 5).We regard light weight as quality indicator，displacement of the maximum deformation and themaximum stress as indicators for static performance check;in addtion，we regard inherent frequency in the first4 orders as indicators for vibration resistance check［7］.

Figure 5.Design S1

Figure 6.Design S2

Figure 7.Design S3

Table 5.Performance data of all designs

3.2.Optimal selection method of the improved designs

According to principals of adaptive design［8］，we give a comprehensive assessment on the improved design through comprehensive evaluation method of static and dynamic performance，and pick out the best design.Ifwe assume that S={S1，S2，…，Sn}is the improved design based on primary design S0and U={U1，U2，…，Um}is a group of evaluation index.Based on principals of fuzzy conversion，evaluation model could be expressed as follows:

In this formula，W is weight vector of performance index;R is matrix of performance evaluation;Ciis evaluation of the ith designing scheme，and i=1～n.

“Sign”in this formula serves as symbol“±”，which will be“－”when the performance index is high(such as inherent frequency of pillar)，or“+”in the other way(such as quality，themaximum displacement，the maximum stress of pillar).Through finite element analysis in ANSYSWORBENCH，we gain uj0and uji，structural performance index of pillar，uj0means the jth performance index in the initial design S0and the formula to figure out the degree of performance improvement is as follows:

The various designs could be ranked according to the numerical value of Ei，and thus the best improved design will be picked out.

3.3.The finalization of the best im proved design of pillar

S={S1，S2，…，Sn}is a series of improved designs based on the initial one S0.Themain static and dynamic performance indexes to evaluate the improved designs are quality m，themaximum deformation d，themaximum stressσ，and inherent frequency f.Table 6 tells that quality m and the maximum deformation d includes 3 second－grade indexes，the maximum stress σ includes 2 second－grade indexes，inherent frequency f includes 4 second－grade indexes.For a convenient analysis of degree of performance improvement，this paper will ascertain weight coefficient of all levels of indexes in line with expert evaluation method［9 －11］，as shown in Table 6.

The weight vector of performance index is:

Table 6.Weight coe fficient of all levels of indexes

Based on the evaluation indexes in Table 5，matrix of performance evaluation could be obtained in line with formula(3):

Then，E=(1.078 0，1.080 5，1.087 4)，so a conclusion can be drawn that S3＞S2＞S1in terms of degree of performance improvement of all the 3 improved designs and the improved one S3is the best.

4.Size optim ization of structure of the best improved design

As compared the 3 kinds of improved designs with the original design，we gain the best design S3，which demonstrates that double X reinforcing rib plus two square holes will decrease the weight of pillar without weakening static and dynamic performance.Since static characteristics have alreadymet the accuracy requirement，we can conduct size optimization of the two square holes in order to enhance its utmost dynamic behavior.

Assuming that the length and width of removed rectangular region in the center of the back of pillar is the design variable t1and t2，and the weighted average of the first4 orders’modal frequency inmodal analysis is this objective function“f=0.4f1+0.3f2+0.2f3+0.1f4”.In this formula，f1is first－ordermodal frequency，f2is second－ordermodal frequency，f3is third－ordermodal frequency，and f4is fourth－order modal frequency;0.4，0.3，0.2 and 0.1 are weight coefficient，respectively according with the first4 orders’modal frequency.Then themathematicalmodel of optimization design is as follows:

The relations between the design variable t1，t2and the objective function f can be gained with the help of finite element analysis in ANSYS WORKBENCH and abovemathematicmodel，just like Table 8.We assume that t2=t1/2 according to the practical structure size of the pillar and convenience for drawing.By analyzing Table 8，a conclusion can be drawn that the first4 orders’modal frequency is the lowest onewhen t1=540，t2=270，and the first4 orders’modal frequency is the highest one when t1=0，t2=0.

Figure 8.Relations between design variable t1，t2 and the objective function

The above Table tells that the frequency is the highestwhen the center of the back is the shape of double X reinforcing rib and keeps the rectangular region，while the design of removing a piece of rectangular region is the best one if taking weight and other factors into a comprehensive consideration.Only in terms of dynamic behavior of pillar，the comparison between the first4 orders’inherent frequency of design before and after(as listed in Table 7)tells that all the first4 orders’inherent frequency is improved to a great extent against the initial design after optimization，thus it is beneficial to enhance the vibration resistance and achieves the object of optimization design.

5.Conclusion

This paper put forward the concept of adaptive dynamic design which is based on adaptive design with VMC850 pillar in vertical machining center of precision as the object of study，and established mathematicalmodel of adaptive dynamic design，conducted procedure analysis on the adaptive dynamic design of machining center pillar and established quantitative analysis tool of adaptive dynamic design，including analysis of improvement rate and adaptive measurement.Then we adopted CAD/CAE integrate emulation technique to conduct parametric design and finite elementanalysis on the pillar structure and then improve the structure and optimize the dynamic parameter on that base，thus this paper could provide theoretical basis and evidence for the improvement of the design of this pillar in verticalmachining center of precision.

Table 7.Changes of inherent frequency before optim ization and after

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加工中心立柱可適應(yīng)動(dòng)態(tài)優(yōu)化設(shè)計(jì)*

孫奎洲?，周金宇
江蘇理工學(xué)院，江蘇常州 213001

應(yīng)用定量化的分析工具，對(duì)加工中心立柱結(jié)構(gòu)進(jìn)行了可適應(yīng)動(dòng)態(tài)設(shè)計(jì)過(guò)程分析。提出產(chǎn)品可適應(yīng)性的綜合評(píng)價(jià)指標(biāo)，建立了產(chǎn)品可適應(yīng)性綜合評(píng)價(jià)模型。應(yīng)用多級(jí)模糊綜合評(píng)價(jià)方法在對(duì)產(chǎn)品功能適應(yīng)性等多種評(píng)價(jià)指標(biāo)進(jìn)行初級(jí)評(píng)價(jià)的基礎(chǔ)上，進(jìn)行了二級(jí)綜合評(píng)價(jià)，得到了VMC850加工中心立柱產(chǎn)品可適應(yīng)性綜合評(píng)價(jià)等級(jí)，從而為進(jìn)一步改進(jìn)產(chǎn)品設(shè)計(jì)提供了指導(dǎo)和修改依據(jù)。在方案設(shè)計(jì)階段，通過(guò)給出各方案的可適應(yīng)性度量數(shù)值以及對(duì)修改設(shè)計(jì)的難易程度做出定量評(píng)價(jià)，可有效地指導(dǎo)機(jī)床結(jié)構(gòu)設(shè)計(jì)過(guò)程。

可適應(yīng)性設(shè)計(jì);動(dòng)態(tài)優(yōu)化;加工中心

TG502.1

10.3969/j.issn.1001－3881.2014.12.015

2014－03－20