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1、山東建筑大學畢業(yè)設計外文文獻及譯文 FEM Optimization for Robot Structure Wang Shijun, Zhao Jinjuan* Department of Mechanical Engineering, Xian University of Technology Shaanxi Province, Peoples Republic of China Institute of Printing and Packing Engineering, Xian University of Technology Abstract In optimal

2、design for robot structures, design models need to he modified and computed repeatedly. Because modifying usually can not automatically be run, it consumes a lot of time. This paper gives a method that uses APDL language of ANSYS 5.5 software to generate an optimal control program, which mike optima

3、l procedure run automatically and optimal efficiency be improved. 1） Introduction Industrial robot is a kind of machine, which is controlled by computers. Because efficiency and maneuverability are higher than traditional machines, industrial robot is used extensively in industry. For the sake of

4、 efficiency and maneuverability, reducing mass and increasing stiffness is more important than traditional machines, in structure design of industrial robot. A lot of methods are used in optimization design of structure. Finite element method is a much effective method. In general, modeling and mod

5、ifying are manual, which is feasible when model is simple. When model is complicated, optimization time is longer. In the longer optimization time, calculation time is usually very little, a majority of time is used for modeling and modifying. It is key of improving efficiency of structure optimizat

6、ion how to reduce modeling and modifying time. APDL language is an interactive development tool, which is based on ANSYS and is offered to program users. APDL language has typical function of some large computer languages. For example, parameter definition similar to constant and variable definitio

7、n, branch and loop control, and macro call similar to function and subroutine call, etc. Besides these, it possesses powerful capability of mathematical calculation. The capability of mathematical calculation includes arithmetic calculation, comparison, rounding, and trigonometric function, exponent

8、ial function and hyperbola function of standard FORTRAN language, etc. By means of APDL language, the data can be read and then calculated, which is in database of ANSYS program, and running process of ANSYS program can be controlled. Fig. 1 shows the main framework of a parallel robot with three

9、bars. When the length of three bars are changed, conjunct end of three bars can follow a given track, where robot hand is installed. Core of top beam is triangle, owing to three bars used in the design, which is showed in Fig.2. Use of three bars makes top beam nonsymmetrical along the plane that is

10、 defined by two columns. According to a qualitative analysis from Fig.1, Stiffness values along z-axis are different at three joint locations on the top beam and stiffness at the location between bar 1 and top beam is lowest, which is confirmed by computing results of finite element, too. According

11、to design goal, stiffness difference at three joint locations must he within a given tolerance. In consistent of stiffness will have influence on the motion accuracy of the manipulator under high load, so it is necessary to find the accurate location of top beam along x-axis. To the questions prese

12、nted above, the general solution is to change the location of the top beam many times, compare the results and eventually find a proper position, The model will be modified according to the last calculating result each time. It is difficult to avoid mistakes if the iterative process is controlled ma

13、nually and the iterative time is too long. The outer wall and inner rib shapes of the top beam will be changed after the model is modified. To find the appropriate location of top beam, the model needs to be modified repetitiously. Fig. 1 Solution of Original Design This paper gives an optimi

14、zation solution to the position optimization question of the top beam by APDL language of ANSYS program. After the analysis model first founded, the optimization control program can be formed by means of modeling instruction in the log file. The later iterative optimization process can be finished b

15、y the optimization control program and do not need manual control. The time spent in modifying the model can be decreased to the ignorable extent. The efficiency of the optimization process is greatly improved. 2）Construction of model for analysis The structure shown in Fig. 1 consists of three p

16、arts: two columns, one beam and three driving bars. The columns and beam are joined by the bolts on the first horizontal rib located on top of the columns as shown in Fig.1. Because the driving bars are substituted by equivalent forces on the joint positions, their structure is ignored in the model.

17、 The core of the top beam is three joints and a hole with special purpose, which can not be changed. The other parts of the beam may be changed if needed. For the convenience of modeling, the core of the beam is formed into one component. In the process of optimization, only the core position of b

18、eam along x axis is changed, that is to say, shape of beam core is not changed. It should be noticed that, in the rest of beam, only shape is changed but the topology is not changed and which can automatically be performed by the control program. Fig.1, six bolts join the beam and two columns.

19、 The joint surface can not bear the pull stress in the non-bolt joint positions, in which it is better to set contact elements. When the model includes contact elements, nonlinear iterative calculation will be needed in the process of solution and the computing time will quickly increase. The trial

20、computing result not including contact element shows that the outside of beam bears pulling stress and the inner of beam bears the press stress. Considering the primary analysis object is the joint position stiffness between the top beam and the three driving bars, contact elements may not used, hut

21、 constructs the geometry model of joint surface as Fig.2 showing. The upper surface and the undersurface share one key point in bolt-joint positions and the upper surface and the under surface separately possess own key points in no bolt positions. When meshed, one node will be created at shared key

22、 point, where columns and beam are joined, and two nodes will be created at non shared key point, where column and beam are separated. On right surface of left column and left surface of right column, according to trial computing result, the structure bears press stress. Therefore, the columns and b

23、eam will share all key points, not but at bolts. This can not only omit contact element but also show the characteristic of bolt joining. The joining between the bottoms of the columns and the base are treated as full constraint. Because the main aim of analysis is the stiffness of the top beam, it

24、can be assumed that the joint positions hear the same as load between beam and the three driving bars. The structure is the thin wall cast and simulated by shell element . The thickness of the outside wall of the structure and the rib are not equal, so two groups of real constant should he set. For

25、the convenience of modeling, the two columns are also set into another component. The components can create an assembly. In this way, the joint positions between the beam core and columns could he easily selected, in the modifying the model and modifying process can automatically be performed. Analy

26、sis model is showed Fig.1. Because model and load are symmetric, computing model is only half. So the total of elements is decreased to 8927 and the total of nodes is decreased to 4341. All elements are triangle. 3.）Optimization solution The optimization process is essentially a computing and modi

27、fying process. The original design is used as initial condition of the iterative process. The ending condition of the process is that stiffness differences of the joint locations between three driving bars and top beam are less than given tolerance or iterative times exceed expected value. Consideri

28、ng the speciality of the question, it is foreseen that the location is existent where stiffness values are equal. If iterative is not convergent, the cause cannot be otherwise than inappropriate displacement increment or deficient iterative times. In order to make the iterative process convergent qu

29、ickly and efficiently, this paper uses the bisection searching method changing step length to modify the top beam displacement. This method is a little complex but the requirement on the initial condition is relatively mild. The flow chart of optimization as follows: 1. Read the beam model data in

30、 initial position from backup file; 2. Modify the position of beam; 3. Solve; 4. Read the deform of nodes where beam and three bars are joined; 5. Check whether the convergent conditions are satisfied, if not, then continue to modify the beam displacement and return to 3, otherwise, exit the ite

31、ration procedure. 6. Save the results and then exit. The programs primary control codes and their function commentaries are given in it, of which the detailed modeling instructions are omitted. For the convenience of comparing with the control flow, the necessary notes are added. the flag of the

32、batch file in ANSYS BATCH RESUME, robbak.db, 0 read original data from the backup file robbak,.db /PREP7 enter preprocessor delete the joint part between beam core and columns move the core of the beam by one :step length apply load and constraint on the geo

33、metry meshing the joint position between beam core and columns FINISH exit the preprocessor ISOLU enter solver SOLVE solve FINISH exit the solver POST1 enter the postproces

34、sor *GET ,front,NODE,2013,U,Z read the deformation of first joint node on beam *GET,back,NODE, 1441 ,U,Z read the deformation of second joint node on beam into parameter hack lastdif-1 the absolute of initial difference between front and hack last time flag=

35、- 1 the feasibility flag of the optimization step=0.05 the initial displacement from initial position to the current position *D0,1,1,10,1 the iteration procedure begin, the cycle variable is I and its value range is 1-10 and step

36、length is 1 dif=abs(front-back) the absolute of the difference between front and hack in the current result *IF,dif,LE,l .OE-6,THEN check whether the absolute difference dif satisfies the request or no flag=l yes, set flag equal to 1 *EXIT

37、 exit the iterative calculation *ELSEIF,dif,GE,lastdif,THEN check whether the dif value becomes great or not flag=2 yes, set flag 2 modify step length by bisection method perform the next iterative calculation, use the last position as the current position and modifi

38、ed last step length as the current step length ELSE if the absolute of difference value is not less than expected value and become small gradually, continue to move top beam read the initial condition from back up file enter the preprocessor MEN, ,P51X, , , step,, , ,1

39、 move the core of the beam by one step length modify the joint positions between beam core and column apply load and constraint meshing FINISH exit preprocessor ISOLU enter solver SOLVE solve FINISH

40、 exit the solver /POST1 exit the postprocessor *GET,front,NODE,201 3,U,Z read the deformation of first joint node to parameter front *GET,back,NODE, 144 1 ,U,Z read the deformation of second joint node to parameter back lastdif-dif update the

41、value of last dif *ENDIF the end of the if-else *ENDDO the end of the DO cycle Most of the control program above is copied from log file, which is long. The total of lines is up to about 1000 lines. Many codes such as modeling and post-process codes are used

42、repeatedly. To make the program construct clear, these instructions can he made into macros, which are called by main program. This can efficiently reduce the length of the main program. In addition, modeling instructions from log file includes lots of special instructions that are only used under g

43、raphic mode but useless under hatch mode. Deleting and modifying these instructions when under batch mode in ANSYS can reduce the length of the file, too. In the program above, the deformation at given position is read from node deformation. In meshing, in order to avoid generating had elements, tr

44、iangle mesh is used. In optimization, the shape of joint position between columns and beam continually is changed. This makes total of elements different after meshing each time and then element numbering different, too. Data read from database according to node numbering might not he data to want.

45、Therefore, beam core first needs to he meshed, then saved. When read next time, its numbering is the same as last time. Evaluating whether the final result is a feasible result or not needs to check the flag value. If only the flag value is I, the result is feasible, otherwise the most proper posi

46、tion is not found. The total displacement of top beam is saved in parameter step. If the result is feasible, the step value is the distance from initial position to the most proper position. The sum of iterative is saved in parameter 1. According to the final value of I, feasibility of analysis resu

47、lt and correctness of initial condition can he evaluated. 4） Optimization results The sum of iterative in optimization is seven, and it takes about 2 hour and 37 minutes to find optimal position. Fig.3 shows the deformation contour of the half-construct. In Fig.3, the deformations in three joints

48、between beam and the three driving bars is the same as level, and the corresponding deformation range is between -0.133E-04 and -0.1 15E-O4m, the requirement of the same stiffness is reached. At this time, the position of beam core along x-axis as shown in Fig. 1 has moved -0.71E-01m compared with t

49、he original designed position Because the speed of computer reading instruction is much faster than modifying model manually, the time modifying model can be ignored. The time necessary for optimization mostly depends on the time of solution. Compared with the optimization procedure manually mod

50、ifying model, the efficiency is improved and mistake operating in modeling is avoided. 5） Conclusion The analyzing result reveals that the optimization method given in this paper is effective and reaches the expected goal. The first advantage of this method is that manual mistakes do not easily oc

51、cur in optimization procedure. Secondly, it is pretty universal and the control codes given in this paper may he transplanted to use in similar structure optimization design without large modification. The disadvantage is that the topology structure of the optimization object can not be changed. The

52、 more the workload of modifying the model, the more the advantages of this method are shown. In addition, the topology optimization function provided in ANSYS is used to solve the optimization problem that needs to change the topology structure. The better optimization results can he achieved if th

53、e method in this paper combined with it. 中文譯文： 機器人機構優(yōu)化設計有限元分析 王世軍 趙金娟 西安大學機電工程系 中國 陜西 西安大學出版社 摘要 機器人結構最優(yōu)化設計，設計模型需要反復的修正和計算。應為修改后的模型通常不能自動運行，需要大量的時間進行調試。本論文給出一種采用有限元分析軟件ANSYS 5.5參數化設計語言生成一種最優(yōu)化控制的方法，這種方法能給出最優(yōu)自動運行過程和提高效率。 1）簡介 工業(yè)機器人是一種用電腦控制的機

54、械機構。因為效率和可操作性比傳統(tǒng)機械要高，因此工業(yè)機器人廣泛的用于工業(yè)生產中。相對傳統(tǒng)機械來說，在工業(yè)機器人的結構設計中，為了達到高效率和可操作性的目的，減少重量和增加剛度顯得更加重要。 在結構設計中有很多的方法，一般而言，有限元法是最有效的方法之一。當所需模型比較簡單時，建模和修改采用手工操作是可行的。當模型復雜時，優(yōu)化時間是比較長的。在相當長的優(yōu)化時間內，計算時間是非常少的，大多數時間是用來建模和修改模型的。如何減少結構優(yōu)化過程中的建模和修改模型所用時間是提高效率的關鍵所在。 ANSYS參數化設計語言是一種基于有限元分析的交互式開發(fā)工具，通常被程序設計人員使用。ANSYS參數化設計語言

55、具有一個典型功能及它包含多數大型計算機語言，例如，定義參數像定義常量和變量，條件轉移和循環(huán)控制，以及宏調用像調用函數和子程序等。除此之外，它具有強大的數學計算控制能力。這種數學計算能力包括算法，計算，對比，湊整和三角函數功能，指數函數功能和標準福傳語言的雙曲線功能等。依靠ANSYS參數化設計語言，數據能夠在ANSYS數據庫中被閱讀和計算，并且在ANSYS程序運行過程中受到控制。 圖1表示三連桿平行機器人的主要框架。 沿Z軸的剛性值在頂部梁的三個連接處是不一樣的。在連桿1和頂部梁連接處得剛性是最小的，這也是通過有限元分析計算結果來確定的。根據設計目的，在三個連接點的不同的剛性必須要有給定的公

56、差。當機械手在進行高強度工作時，一致的剛性會對它的運行精度產生影響，因此在沿X軸設置一個精確的位置是非常有必要的。 根據上面提出的問題，一般的解決方法經常是改變頂部梁連接點的位置，對比結果，然后找到一個合適的位置，模型每次都要根據最后的計算結果進行修改。如果采用人工的控制這個重復的過程且重復時間過長，這樣就難免出現錯誤。當模型被修改時，頂部梁外壁和內部肋板的形狀也隨之發(fā)生改變。模型需要重復的去修改才能找出恰當的位置。 圖1 初始設計方案 本論文通過ANSYS程序的參數化設計語言給出一個尋找最優(yōu)位置問題的最佳解決方法。經過對

57、事先建立的模型進行分析，通過建模系統(tǒng)指令在新的文件里形成一個最佳的控制程序，通過這個最佳的控制程序可以完成以后的重復最優(yōu)化過程，而且不需要手工控制。在修改模型上消耗的時間可以減少到被忽略的程度。最優(yōu)化步驟的效率得到很大提高。 2）建筑模型分析 圖1所示結構包括了三個部分：兩個支柱，一個頂部梁和三個操作連桿。支柱和橫梁通過位于支柱上面的水平肋板連接在一起，如圖1所示。因為操作連桿被連接位置的等效構件代替，所以在模型中它們的結構被忽略了。 頂部橫梁的核心是三個連接處和一個特殊作用的孔，這些都是固定不變的。其他部件可以根據需求進行修改。 為了建模的方便，橫梁的核心被制成一個零件。在進行最

58、優(yōu)化的過程中，只有沿著X軸的橫梁中心位置是變化的，也就是說，橫梁核心的形狀是不變的.應該注意的是，橫梁的其余部分只有形狀變化而拓撲是固定的，可以通過控制程序自動執(zhí)行. 圖2 頂部橫梁核心 圖1.六個螺栓連接橫梁和支柱。在沒有螺栓連接的位置，其結合面不能承受拉應力，最好在該位置設置接觸件。當模型中包括接觸件，非線性元件時，在解決方案過程中重復計算是必要的，并且計算時間會快速增加。不包括接觸件的實驗計算結果顯示橫梁外部承受拉伸應力，橫梁內部承受壓應力。考慮到主要的分析對象是頂部橫梁和三個連桿連接位置的剛性，接觸件可能不使用，房屋建設的幾何模型的結合面如圖2所示。在螺栓連接中，上表面和下

59、表面共享一個關鍵位置；在沒有螺栓連接時，上表面和下表面各自分別擁有一個關鍵位置。配合的時候，在共享的關鍵點會產生一個節(jié)點，當支柱和橫梁連接，在支柱和橫梁分開處，沒有共享的關鍵點會產生兩個節(jié)點。在左側支柱的右表面和右側支柱的左表面，根據實驗計算結果，結構承受壓應力。因此支柱和橫梁將分享所有的節(jié)點不僅是螺栓。這不僅是忽略連接件而且展示了螺栓連接的特征。在支柱底部和底架之間連接是完整約束。因為主要的分析目的是頂部橫梁的剛性,可以假設頂部橫梁和三個連桿的連接位置承受同樣的載荷。結構是薄壁件和殼件模型。機構外壁厚度和肋板厚度是不相同的。因此兩組實常數是要設定的。為了建模的方便，兩個支柱可是設置成其它組件

60、。這個組件可以設成一個集合。這樣橫梁核心和支柱連接位置可以很容易的分辨出來。在修改過程中，建模和修改可以自動執(zhí)行。分析模型如圖1所示。因為模型和負載是對稱的，模型計算可以節(jié)省一半時間。因此基礎組件可以減少到8927，而且總的節(jié)點可以減少到4341.所有的組件都是三角形的。 3）最優(yōu)化解決方案 最優(yōu)化過程是計算和修改過程的本質。初始設計被用來做重復計算過程的初始條件。計算過程的結束條件是三個連桿和頂部橫梁連接位置的剛性偏差小于給定公差或者重復計算時間超出期望值?？紤]到問題的特性，可以猜想，剛性值相同的位置是存在的。如果迭代不是收斂的，原因不可能是不相稱偏轉增大或者是計算時間不足。為了使迭

61、代過程快速高效收斂，本論文采用等分搜索的方法改變步長去修改頂梁束位移。這種方法有點復雜但是在初始條件上的要求不苛刻。 以下是最優(yōu)化生產的流程圖： 1 在備份文件中確定橫梁初始位置的模型基準 2 修改橫梁位置 3解決 4 確定橫梁和三個連桿連接處的節(jié)點變形 5 檢查收斂條件是否合適，如果不合適，那么繼續(xù)去修改束位移并且返回到步驟3，否則退出迭代程序。 6 保存數據然后退出 程序的主要控制代碼和功能評注要保存一起，詳細的建模指令被忽略。為了比較的方便，要添加必要的注釋。 BATCH RESUME, robbak.db, 0 從備份文件中讀取原始資料 /PREP7

62、 預處理程序 刪除橫梁核心和支柱連接部分 以一個步長移動橫梁核心 應用載荷和約束 橫梁核心和支柱嚙合 FINISH 退出預處理程序 ISOLU 進入計算器 SOLVE

63、 解答 FINISH 退出解答 POST1 進入后處理程序 *GET ,front,NODE,2013,U,Z 讀取橫梁第一個節(jié)點的變形 *GET,back,NODE, 1441 ,U,Z 讀取橫梁第二個節(jié)點的變形 lastdif-1 前后時間差計算 flag=- 1 最優(yōu)化可行性標志 step=0.05

64、 計算 從初始位置到當前位置的位移 *D0,1,1,10,1 迭代過程開始，循環(huán)變量I，變化范圍從1到10，步長為1 dif=abs(front-back) 前后結果的絕對值 *IF,dif,LE,l .OE-6,THEN 檢查絕對值是否滿足要求 flag=l 如果滿足要求，設置標志位1 *EXIT 退出迭代過程 *ELSEIF,dif,

65、GE,lastdif,THEN 檢查離差值是否變大或者flag=2 如果是，設置標志位2，用差分法修改步長，執(zhí)行下一個迭代計算，用最后位置作為當前位置，修改步長為當前步長 ELSE 如果絕對值離差值不少于期望值，逐步的變小，繼續(xù)移動橫梁核心去確定初始位置從備份文件中進入預處理程序 MEN, ,P51X, , , step,, , ,1 以一個步長來移動橫梁核心，修改支柱和橫梁連接位置提供載荷和約束 FINISH

66、 退出預處理程序 ISOLU 進入計算器 SOLVE 解答 FINISH 退出求解器 /POST1 退出后處理程序 *GET,front,NODE,201 3,U,Z 確定前后節(jié)點的變形 *GET,back,NODE, 144 1 ,U,Z 確定第二個節(jié)點的變形 lastdif-dif 校正最終離差值 *ENDIF 結束if else *ENDDO 結束Do循環(huán) 上面的較長控制程序大多數的是從記錄文件中復制下來的，總的程序指令能達到1000多條，許多代碼像建模和處理代碼都是重復使用，為了使程序結構清晰，這些指令通常被制成稱作主程序宏指令，這樣可以有