1、山东建筑大学毕业设计外文文献及译文FEM Optimization for Robot StructureDepartment of Mechanical Engineering, Xian University of TechnologyShaanxi Province, Peoples Republic of ChinaInstitute of Printing and Packing Engineering, Xian University of TechnologyAbstractIn optimal design for robot structures, design models
2、 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 optimal procedure run automatically and optimal
3、efficiency be improved. 1） IntroductionIndustrial 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 efficiency and maneuverability, reducing mass
4、 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 modifying are manual, which is feasible when model
5、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 optimization how to reduce modeling and modifying time.AP
6、DL 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 definition, branch and loop control, and macro call similar
7、 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, exponential function and hyperbola function of standard FO
8、RTRAN 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 bars. When the length of three bars are changed, con
9、junct 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 defined by two columns. According to a qualitative
10、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 to design goal, stiffness difference at three joint
11、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 presented above, the general solution is to change the loca
12、tion 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 manually and the iterative time is too long. The outer w
13、all 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 optimization solution to the position optimization question of the t
14、op 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 by the optimization control program and do not need manual cont
15、rol. 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 analysisThe structure shown in Fig. 1 consists of three parts: two columns, one beam and three driving bars. The columns an
16、d 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. The core of the top beam is three joints and a hole with special
17、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 beam along x axis is changed, that is to say, shape of beam core is n
18、ot 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. The joint surface can not bear the pull stress in the non-bolt joint posi
19、tions, 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 computing result not including contact element shows that the outside of b
20、eam 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 constructs the geometry model of joint surface as Fig.2 showing. The uppe
21、r 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 point, where columns and beam are joined, and two nodes will be created a
22、t 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 beam will share all key points, not but at bolts. This can not only omit co
23、ntact 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 can be assumed that the joint positions hear the same as load between beam
24、 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 the convenience of modeling, the two columns are also set into another com
25、ponent. 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. Analysis model is showed Fig.1. Because model and load are symmetric, computing
26、 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 solutionThe optimization process is essentially a computing and modifying process. The original design is used as initial condition of the iterati
27、ve 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. Considering the speciality of the question, it is foreseen that the location is existen
28、t 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 quickly and efficiently, this paper uses the bisection searching method changing
29、 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 initial position from backup file;2. Modify the position of beam;3. Solve;4. Read
30、 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 iteration procedure.6. Save the results and then exit.The programs primary control codes and
31、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 batch file in ANSYSBATCH RESUME, robbak.db, 0read original data from the backup file robbak,.db/
32、PREP7 enter preprocessor delete the joint part between beam core and columns move the core of the beam by one :step lengthapply load and constraint on the geometry meshing the joint position between beam core and columnsFINISH exit the preprocessorISOLU enter solverSOLVE solveFINISH exit the solverP
33、OST1 enter the postprocessor*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 hacklastdif-1 the absolute of initial difference between front and hack last timeflag=- 1 the feasibility
34、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 length is 1dif=abs(front-back) the absolute of the difference between front and hack in th
35、e current result*IF,dif,LE,l .OE-6,THEN check whether the absolute difference dif satisfies the request or noflag=l yes, set flag equal to 1*EXIT 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 bi
36、section method perform the next iterative calculation, use the last position as the current position and modified 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 initia
37、l condition from back up file enter the preprocessorMEN, ,P51X, , , step, , ,1 move the core of the beam by one step length modify the joint positions between beam core and column apply load and constraint meshingFINISH exit preprocessorISOLU enter solverSOLVE solveFINISH exit the solver/POST1 exit
38、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 value of last dif*ENDIF the end of the if-else*ENDDO the end of the DO cycleMost of the
39、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 repeatedly. To make the program construct clear, these instructions can he made into macros, which are called by main program. This
40、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 graphic mode but useless under hatch mode. Deleting and modifying these instructions when under batch mode in ANSYS can reduce the le
41、ngth 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, triangle mesh is used. In optimization, the shape of joint position between columns and beam continually is changed. This makes total of
42、 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. Therefore, beam core first needs to he meshed, then saved. When read next time, its numbering is the same as last time. Evaluating whe
43、ther 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 position is not found. The total displacement of top beam is saved in parameter step. If the result is feasible, the step value is the dista
44、nce 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 result and correctness of initial condition can he evaluated.4） Optimization resultsThe sum of iterative in optimization is seven, and it ta
45、kes 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 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
46、, 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 the original designed positionBecause the speed of computer reading instruction is much faster than modifying model manually, the time modify
47、ing model can be ignored. The time necessary foroptimization mostly depends on the time of solution. Compared with the optimization procedure manually modifying model, the efficiency is improved and mistake operating in modeling is avoided.5） ConclusionThe 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 occur in optimization proc
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