資源目錄里展示的全都有，所見即所得。下載后全都有,請放心下載。原稿可自行編輯修改=【QQ：401339828 或11970985 有疑問可加】 目 錄 設(shè)計任務(wù)書--------------------------------------1 一.零件的分析 ---------------------------------2 二.工藝規(guī)程設(shè)計 （一）確定毛坯的制造形式---------------------- 3 （二）基面的選擇 ----------------------------- 3 （三）制訂工藝路線 --------------------------- 3 （四）機械加工余量、工序尺寸及毛坯尺寸的確定 -5 （五）確定切削用量及基本工時 -----------------6 三.夾具設(shè)計 --------------------------------11 （一）問題的提出 --------------------------11 （二）卡具設(shè)計 ------------------------------12 四.參考文獻 --------------------------------- 13 一． 零件的分析 零件的工藝分析 后鋼板彈簧吊耳共有三組加工表面，現(xiàn)分述如下： 1）以?37mm孔為中心的加工表面 這一組加工表面包括：一個?37mm的孔，尺寸為76mm的與?37mm孔相垂直的平面，其中主要加工表面為?37mm的孔； 2）以?30mm孔為中的加工表面 這一組加工表面包括：兩個?30mm的孔，以及尺寸為77與兩個?30mm 孔相垂直的內(nèi)平面，以及兩個孔的外表面； 3）以?10.5mm孔為中心的加工表面 這一組加工表面包括：兩個?10.5mm的孔 二． 工藝規(guī)程設(shè)計 （一） 確定毛坯的制造形式 零件材料為35鋼，考慮到該零件在汽車中的受力并保證零件的工作可靠性，零件為中批生產(chǎn)，因此，毛坯可采用模鍛成型 （二） 基面的選擇 基準面選擇是工藝規(guī)程設(shè)計中的重要工作之一?；孢x擇的正確與合理，可以使加工質(zhì)量得到保證，生產(chǎn)效率得以提高。否則，加工工藝過程中會問題百出，更有甚者，還會造成零件大批報廢，使生產(chǎn)無法正常進行。 （1）粗基準的選擇。以?30mm孔一側(cè)端面為粗基準，以消除，，三個自由度，然后加一個輔助支承。 （2）精基準的選擇。根據(jù)基準重合和互為基準原則，選用設(shè)計基準作為精基準,當(dāng)設(shè)計基準與工序基準不重合時，應(yīng)該進行尺寸換算。 （三）制訂工藝路線 制訂工藝路線的出發(fā)點，應(yīng)當(dāng)是使零件的幾何形狀，尺寸精度及位置精度等技術(shù)要求得到合理的保證。在生產(chǎn)綱領(lǐng)為中批生產(chǎn)的條件下，可以考慮采用萬能性機床配以專用夾具來提高生產(chǎn)效率。除此以外，還應(yīng)當(dāng)考慮經(jīng)濟效率，以便使生產(chǎn)成本盡量下降。 1.工藝路線方案一 工序Ⅰ 粗銑?37mm孔端面。 工序Ⅱ 精銑?37mm孔端面。 工序Ⅲ 擴，粗鉸，精鉸?37mm孔并加工倒角1.5×45°。 工序Ⅳ 粗銑?30mm孔端面。 工序Ⅴ 擴，粗鉸? 30mm孔并加工倒角1×45° 工序Ⅵ 粗銑尺寸為77mm的孔端面。 工序Ⅶ 精銑尺寸為77mm的孔端面。 工序Ⅷ 鉆2-? 10.5mm孔。 工序Ⅸ 銑寬為4mm的槽 工序Ⅹ 去毛刺 工序Ⅺ 檢查。 2.工藝路線方案二 工序Ⅰ 粗銑?37mm孔端面。 工序Ⅱ 粗鏜?37mm孔，倒角1.5×45°。 工序Ⅲ 粗銑?30mm孔外端面。 工序Ⅳ 粗銑?30mm孔內(nèi)端面。 工序Ⅴ 擴，粗鉸? 30mm孔并加工倒角1×45°。 工序Ⅵ 粗鏜?37mm孔。 工序Ⅶ 半精銑?37mm孔端面。 工序Ⅷ 半精銑?37mm孔端面。 工序Ⅸ 鉆2-?10.5mm孔。 工序Ⅹ 銑寬為4mm的槽 工序Ⅺ 去毛刺。 工序Ⅻ 檢查。 工藝方案的比較與分析 上述兩個工藝方案的特點在于：方案一是先加工?37mm孔端面，再以該加工平面為基準加工其余平面，最后加工各個孔；方案二是先以?30mm孔外端面為基準加工?37mm孔端面，再以?37mm孔端面為基準加工其它端面和孔。兩相比較可以看出，方案二遵循互為基準原則能夠較好的保證加工精度，對設(shè)備要求較低，而方案一工序比較集中，考慮實際設(shè)備條件，可將兩個方案進行綜合考慮。具體工藝過程如下： 工序Ⅰ 粗銑?37mm孔端面。 工序Ⅱ 粗鏜?37mm孔，倒角1.5×45°。 工序Ⅲ 粗銑?30mm孔外端面。 工序Ⅳ 粗銑?30mm孔內(nèi)端面。 工序Ⅴ 擴，粗鉸? 30mm孔并加工倒角1×45°。 工序Ⅵ 粗鏜?37mm孔。 工序Ⅶ 半精銑?37mm孔端面。 工序Ⅷ 半精銑?37mm孔端面。 工序Ⅸ 鉆2-?10.5mm孔。 工序Ⅹ 銑寬為4mm的槽 工序Ⅺ 去毛刺。 工序Ⅻ 檢查。 （四）機械加工余量、工序尺寸及毛坯尺寸的確定 “后鋼板彈簧吊耳”零件材料為35鋼，毛坯重量約為2.6Kg，生產(chǎn) 類型為中批生產(chǎn)，采用鍛造。 根據(jù)上述原始資料及加工工藝，分別確定各加工表面的餓機械加工余量 工序尺寸及毛坯尺寸如下： 1.?37mm孔 毛坯為空心，參照《機械加工工藝手冊》，確定工序尺寸為 Z=2.6mm。 由鍛件復(fù)雜系數(shù)為S1,鍛件材質(zhì)系數(shù)取M1, 毛坯尺寸為?34.4。根據(jù)《機械加工工藝手冊》加工余量分別為： 粗鏜：?36mm 2Z=1.6mm 精鏜：?36mm 2Z=1.0mm 2.?30mm孔 毛坯為空心，參照《機械加工工藝手冊》，確定工序尺寸為 Z=2.0mm。 由鍛件復(fù)雜系數(shù)為S1,鍛件材質(zhì)系數(shù)取M1, 毛坯尺寸為?26根據(jù)《機械加工工藝手冊》加工余量分別為： 擴孔：?29.8mm 2Z=1.8mm 鉸孔：?30mm 2Z=0.2mm 3. ?37mm孔、?30mm孔端面的加工余量 參照《機械加工工藝手冊》，取加工精度F2 ,由鍛件復(fù)雜系數(shù)為S3, 兩孔外側(cè)單邊加工余量為Z=2mm。鍛件材質(zhì)系數(shù)取M1, 復(fù)雜系數(shù)為S3, 確定鍛件偏差為 mm和mm。 根據(jù)《機械加工工藝手冊》加工余量分別為： ?37mm孔端面： 粗銑 2Z=3.0mm 精銑 2Z=1.0mm ?30mm孔端面： 粗銑 2Z=4.0mm 4. ?10.5mm孔 毛坯為實心，不出孔 ，為自由工差。根據(jù)《機械加工工藝手冊》加工余量分別為： 鉆孔：?10.5mm 2Z=10.5mm 由于本設(shè)計規(guī)定的零件為中批生產(chǎn)，可采用調(diào)整法加工，因此在計算最大、最小加工余量時，可按調(diào)整法加工方式予以確定。 毛坯名義尺寸：122+2×2=126mm 毛坯最大尺寸：126+2×1.3=128.6mm 毛坯最小尺寸：126-2×0.7=124.6mm 銑后最大尺寸：122+0=122mm 銑后最小尺寸：122-0.17=121.83mm 將以上計算的工序間尺寸及公差整理成下表： （mm） 工 序 工 尺 加 寸 鍛造毛坯 銑削加工 ?30mm孔處 加工前 最大 128.6 mm 最小 124.6 mm 加工后 最大 128.6 mm 112 mm 最小 124.6 mm 121.83 mm 加工余量 （單邊） 2 mm 最大 3.65 mm 最小 1.435 mm 加工公差 mm -0.17/2 mm （五） 確定切削用量及基本工時 工序Ⅰ：粗銑?37mm孔端面。本設(shè)計采用查表法確定切削用量。 1. 加工條件 工件材料：35鋼，鍛造。 加工要求：銑?37mm端面，Ra6.3μm。 機床：X51立式銑床。 刀具：YT15硬質(zhì)合金面銑刀，齒數(shù)Z=5，=100mm。 2. 計算切削用量 根據(jù)《切削手冊》 mm/z 切削速度：根據(jù)相關(guān)手冊 取 m/min （r/min） 現(xiàn)采用X51立式銑床，根據(jù)機床說明書，取n=375 r/min。 故實際切削速度 （m/min） 當(dāng)n=375 r/min時，工作臺每分鐘進給量應(yīng)為 （mm/min） 查機床說明書，取 mm/min 切削工時 （min） 為加工一側(cè)端面的時間，總工時 （min） 工序Ⅱ.粗鏜?37mm孔、倒角°。 根據(jù)《機械加工工藝手冊》查得鏜?37mm孔的進給量?=0.3——1.0mm，按機床 規(guī)格取=0.6mm，切削速度，根據(jù)相關(guān)手冊及機床說明書，取v=30mm/s，加工孔徑=?36mm。則 （r/min） 根據(jù)機床選取n=300 r/min。 實際切削速度 （m/min） 切削工時 （min） 工序Ⅲ：粗銑?30mm孔外端面。 根據(jù)《切削手冊》 mm/z 切削速度：根據(jù)相關(guān)手冊 取 m/min 刀具與工序Ⅰ所使用刀具相同 mm （r/min） 現(xiàn)采用X51立式銑床，根據(jù)機床說明書，取n=300 r/min。 故實際切削速度 （m/min） 當(dāng)n=300 r/min時，工作臺每分鐘進給量應(yīng)為 （mm/min） 查機床說明書，取 mm/min 切削工時 （min） 為加工一側(cè)端面的時間，總工時 （min） 工序Ⅳ：粗銑?30mm孔內(nèi)端面。 根據(jù)《切削手冊》 mm/z 切削速度：根據(jù)相關(guān)手冊 取 m/min 刀具與工序Ⅰ所使用刀具相同 mm （r/min） 現(xiàn)采用X51立式銑床，根據(jù)機床說明書，取n=300 r/min。 故實際切削速度 （m/min） 當(dāng)n=300 r/min時，工作臺每分鐘進給量應(yīng)為 （mm/min） 查機床說明書，取 mm/min 切削工時 （min） 為加工一側(cè)端面的時間，總工時 （min） 工序Ⅴ：1.擴?29.8mm孔。 確定進給量：根據(jù)《機械加工工藝手冊》 =0.81 mm/r。 切削速度：根據(jù)相關(guān)手冊，查得切削速度m/min ，所以 （r/min） 根據(jù)機床說明書選取n=140 r/min，故實際切削速度 （m/min） 切削工時 （min） 2.鉸?30mm孔。 確定進給量：根據(jù)《機械加工工藝手冊》 =1.17 mm/r。 切削速度：根據(jù)相關(guān)手冊，查得切削速度m/min ，所以 （r/min） 根據(jù)機床說明書選取n=63 r/min，故實際切削速度 （m/min） 切削工時 （min） 工序Ⅵ:精鏜孔至?36mm 根據(jù)《機械加工工藝手冊》查得 f=0.5mm/r n=1000r/min=16.6r/s 切削速度 v=40m/min=0.67m/s 切削工時 （min） 工序Ⅶ：半精銑?30mm孔端面 根據(jù)《切削手冊》 mm/z 切削速度：根據(jù)相關(guān)手冊 取 m/min （r/min） 現(xiàn)采用X51立式銑床，根據(jù)機床說明書，取n=375 r/min。 故實際切削速度 （m/min） 當(dāng)n=375 r/min時，工作臺每分鐘進給量應(yīng)為 （mm/min） 查機床說明書，取 mm/min 切削工時 （min） 為加工一側(cè)端面的時間，總工時 （min） 工序Ⅷ:半精銑?30mm孔端面。 根據(jù)《切削手冊》 mm/z 切削速度：根據(jù)相關(guān)手冊 取 m/min 刀具與工序Ⅰ所使用刀具相同 mm （r/min） 現(xiàn)采用X51立式銑床，根據(jù)機床說明書，取n=300 r/min。 故實際切削速度 （m/min） 當(dāng)n=300 r/min時，工作臺每分鐘進給量應(yīng)為 （mm/min） 查機床說明書，取 mm/min 切削工時 （min） 為加工一側(cè)端面的時間，總工時 （min） 工序Ⅸ：鉆2-?10.5mm孔 確定進給量：根據(jù)《機械加工工藝手冊》 鍛件硬度149-187HBS 取=0.234 mm/r。 切削速度：根據(jù)相關(guān)手冊，查得切削速度 m/min ，所以 （r/min） 根據(jù)機床說明書選取n=394 r/min，故實際切削速度 （m/min） 切削工時 （min） 工序Ⅹ：銑寬為4mm的槽 根據(jù)《切削手冊》 mm/z 切削速度：根據(jù)相關(guān)手冊 取 m/min 刀具采用YT15硬質(zhì)合金面銑刀， mm （r/min） 根據(jù)機床說明書，取n=600 r/min。故實際切削速度 （m/min） 當(dāng)n=600r/min時，工作臺每分鐘進給量應(yīng)為 （mm/min） 查機床說明書，取 mm/min 切削工時 （min） 最后，將以上各工序切削用量、工時定額的計算結(jié)果，連同其他加工數(shù)據(jù)一并填入機械加工工序過程綜合卡片。 三.夾具設(shè)計 為了提高勞動生產(chǎn)率，保證加工質(zhì)量，降低勞動強度，需要設(shè)計專用夾具。 經(jīng)過與指導(dǎo)老師協(xié)商，決定設(shè)計第Ⅳ道工序——鉆?37mm孔的鉆床夾具。本夾具將用于Z3040搖臂鉆床，刀具為高速鋼錐柄麻花鉆 （一） 提出問題 本夾具用來鉆?37mm孔加工本道工序時，該孔有過高的精度要求。因此，在本道工序加工時，主要考慮如何保證孔的定位，如何降低勞動強度、提高勞動生產(chǎn)率。 （二） 夾具設(shè)計 1. 定位基準的餓選擇 由零件圖可知，以?37mm孔和?37mm孔的一個端面為定位基準，采用支承釘為輔助支承，同時為了縮短本工序的輔助時間，應(yīng)設(shè)計一個可以快速更換工件的夾緊裝置。 2. 切削力和夾緊力的計算 刀具：高速鋼錐柄麻花鉆，?37mm 軸向力： （N） 扭距： Nm 在計算切削力時必須把安全系數(shù)考慮在內(nèi)，安全系數(shù) 為基本安全系數(shù)1.5； 為加工性質(zhì)系數(shù)1.1； 為刀具鈍化系數(shù)1.2。 所以 （N） 夾緊力：在此夾具中，只是為了防止工件在加工過程中的振動和轉(zhuǎn)動，因此 很小。 3. 定位誤差分析 定位尺寸公差的確定。夾具的主要定位元件是一根定位軸，該定位軸的尺寸與公差現(xiàn)定與本零件在工作時與其相配的軸的尺寸與公差相同,取其公差為，即?37mm。 定位軸與零件的最大間隙為 max=0.05-(-0.033)=0.083mm 而零件要求的最小偏差為 min=0-(-0.01)=0.01 因此最大間隙滿足精度要求. 4. 夾具設(shè)計及操作的簡要說明 如前所述，在設(shè)計夾具時，應(yīng)該注意提高勞動生產(chǎn)率，為此，應(yīng)首先著眼于 采用何種夾緊裝置以減少更換工件的輔助時間。本夾具設(shè)計采用開口墊圈夾緊裝置，只要松開螺母即可取下工件，可以提高勞動生產(chǎn)率，而且本夾具總體結(jié)構(gòu)設(shè)計比較簡單、緊湊。 四、參考文獻 1.《機械制造工藝學(xué)課程設(shè)計指導(dǎo)書》 機械工業(yè)出版社 趙家齊 編 2.《簡明機械加工工藝手冊》 上?？茖W(xué)技術(shù)出版社 徐圣群 主編 3. 《機床夾具設(shè)計手冊》第二版 上海科學(xué)技術(shù)出版社 4．《切削手冊》 機械工業(yè)出版社 艾興 肖詩綱 編 ORIGINAL ARTICLEDeformation control through fixture layout designand clamping force optimizationWeifang Chen&Lijun Ni&Jianbin XueReceived: 2 February 2007 /Accepted: 4 July 2007#Springer-Verlag London Limited 2007Abstract Workpiece deformation must be controlled in thenumerical control machining process. Fixture layout andclamping force are two main aspects that influence thedegree and distribution of machining deformation. In thispaper, a multi-objective model was established to reducethe degree of deformation and to increase the distributinguniformity of deformation. The finite element method wasemployed to analyze the deformation. A genetic algorithmwas developed to solve the optimization model. Finally, anexample illustrated that a satisfactory result was obtained,which is far superior to the experiential one. The multi-objective model can reduce the machining deformationeffectively and improve the distribution condition.Keywords Fixturelayout.Clampingforce.Geneticalgorithm.Finiteelementmethod1 IntroductionFixture design is an important procedure in manufacturingengineering. It is critical to machining accuracy. Aworkpiece should be constrained in a fixture duringmachining with fixture elements such as locators, clamps,and supports. The positions of locators, clamps andsupports should be strategically designed and appropriateclamping forces should be applied. The fixture elementscan be placed anywhere within the candidate regions on theworkpiece surfaces. Clamping force must be large enoughto hold the workpiece during machining. Typically, it reliesheavily on the designers experience to choose the positionsof the fixture elements and to determine the clampingforces. Thus there is no assurance that the resultant solutionis optimal or near optimal for a given workpiece.Consequently, the fixture layout and the clamping forceoptimization become two main aspects in fixture design.The positions of locators and clamps, and the values ofclamping force should be properly selected and calculatedso that the workpiece deformation due to clamping andcutting force is minimized and uniformed.The objective of fixture design is to find an optimallayout or positions of the fixture elements around theworkpiece and optimal clamping force. In this paper, amulti-objective optimization method is presented for thefixture layout design and clamping force optimization.The objective is two folded. One is to minimize themaximum elastic deformation of the machined surfaces,and another is to maximize the uniformity of deforma-tion. The ANSYS software package is used to calculatethe deformation of the workpiece under given clampingforce and cutting force. A genetic algorithm is devel-oped, and the direct search toolbox of MATLAB isemployed to solve the optimization problem. Finally, acase study is given to illustrate the application of theproposed approach.2 Literature reviewWith the wide applications of optimization methods inindustry, fixture design optimization has gained moreinterests in recent years. Fixture design optimizationincludes fixture layout optimization and clamping forceoptimization. King and Hutter presented a method forInt J Adv Manuf TechnolDOI 10.1007/s00170-007-1153-2W. Chen:L. Ni:J. Xue (*)College of Mechanical and Electronical Engineering,Nanjing University of Aeronautics and Astronautics,No. 29, Yudao Street,Nanjing 210016, Chinae-mail: optimal fixture layout design using a rigid body model of thefixture-workpiece system 1. DeMeter also used a rigidbody model for the analysis and synthesis of optimalfixture layouts and minimum clamping force 2. Hepresented a finite element method (FEM) based supportlayout optimization procedure with computationally attrac-tive qualities 3. Li and Melkote used a nonlinearprogramming method and a contact elasticity model tosolve the layout optimization problem 4. Two years later,they presented a method for determining the optimalclamping force for a multiple clamp fixture subjected toquasi-static machining force 5. They also presented anoptimal synthesis approach of fixture layout and clampingforce that considers workpiece dynamics during machining6. A combined fixture layout and clamping forceoptimization procedure was presented. Other researchers7, 8 used the FEM for fixture design and analysis. Cai etal. 9 extended the work of Menassa and DeVries 8 toinclude synthesis of fixture layout for sheet metal assembly.Qin et al. 10 established an elastic contact model betweenclamp and workpiece to optimize the clamping force withan objective to minimize the position error of theworkpiece. Deng and Melkote 11 presented a model-based framework for determining the minimum requiredclamping force, which ensures the dynamic stability of afixtured workpiece during machining.Most of the above studies used nonlinear programmingmethods, which seldom gave global or near-global opti-mum solutions. All of the fixture layout optimizationprocedures must start with an initial feasible layout. Inaddition, solutions obtained from these models are verysensitive to the initial feasible fixture layout. The problemof fixture design optimization is nonlinear because there isno direct analytical relationship between the objectivefunction and design variables, i.e. between the machinedsurface error and the fixture parameters (positions of locatorand clamp, and clamping forces).Previous researchers had shown that genetic algorithm(GA) was a useful technique in solving such optimiza-tion problems. Wu and Chan 12 used the GA todetermine the most statically stable fixture layout. Ishikawaand Aoyama 13 applied GA to determine the optimalclamping condition for an elastic workpiece. Vallapuzha etal. 14 used spatial coordinates to encode in the GA basedoptimization of fixture layout. They also presented themethodology and results of an extensive investigation intothe relative effectiveness of the main competing fixtureoptimization methods, which showed that continuous GAyielded the best quality solutions 15. Krishnakumar andMelkote 16 developed a fixture layout optimizationtechnique that used GA to find the fixture layout thatminimized the deformation of the machined surface due toclamping and cutting force over the entire tool path.Locator and clamp positions were specified with nodenumbers. Krishnakumar et al. 17 presented an iterativealgorithm that minimized the workpiece elastic deformationfor the entire cutting process by alternatively varying thefixture layout and clamping force. Lai et al. 18 set up ananalysis model that treated locator and clamps as the samefixture layout elements for the flexible part deformation.Hamedi 19 discussed a hybrid learning system that usednonlinear FEA with a supportive combination of artificialneural network (ANN) and GA. The ANN was used tocalculate workpiece maximum elastic deformation, the GAwas used to determine the optimum clamping forces.Kumar 20 proposed to combine the GA and ANN todevelop a fixture design system. Kaya 21 used the GAand FEM to find the optimal locators and clampingpositions in 2D workpiece and took chip removal effectsinto account. Zhou et al. 22 presented a GA based methodthat optimized fixture layout and clamping force simulta-neously. Some of the studies did not consider theoptimization of the layout for entire tool path. Some ofthe studies used node numbers as design parameters.Some of the studies addressed fixture layout or clampingforce optimization methods but not both simultaneously.And there were few studies taking friction and chipremoval into account. The effects of chip removal andfrictional contact cannot be neglected for achieving amore realistic and accurate workpiece-fixture layoutverification analysis 23, so it is essential to take chipremoval effects and friction effect into account to achieve abetter machining accuracy.In this paper, the friction and chip removal are takeninto account to achieve the minimum degree of themaximum deformation of the machined surfaces underclamping and cutting force and to uniform the deforma-tion. A multi-objective optimization model is established.An optimization process based on GA and FEM ispresented to find the optimal fixture layout and clampingforce. Finally, the result of the multi-objective optimiza-tion model is compared with the single objectiveoptimization method and the experience method for a lowrigidity workpiece.3 A multi-objective optimization model for fixturedesignA feasible fixture layout has to satisfy three constraints.First, the locators and clamps cannot apply tensile forces onthe workpiece. Second, the Coulomb friction constraintmust be satisfied at all fixture-workpiece contact points.The positions of fixture element-workpiece contact pointsmust be in the candidate regions. For a problem involving pfixture element-workpiece contacts and n machining loadInt J Adv Manuf Technolsteps, the optimization problem can be mathematicallymodeled as followsmin max1jj; 2jj;:; j?;:; njj? s?;j 1;2;:;n1Subject tom Fnijj ?ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiF2ti F2hiq2Fni? 03pos i 2 V i ;i 1;2;:;p4where jrefers to the maximum elastic deformation at amachining region in the j-th step of the machiningoperation,ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXnj1j ? ?2?nvuutis the average of jFniis the normal force at the i-th contact pointis the static coefficient of frictionFti;Fhiare the tangential forces at the i-th contact pointpos(i)is the i-th contact pointV(i)is the candidate region of the i-th contact point.The overall process is illustrated in Fig. 1 to design afeasible fixture layout and to optimize the clamping force.The maximal cutting force is calculated in cutting modeland the force is sent to finite element analysis (FEA) model.Optimization procedure creates some fixture layout andclamping force which are sent to the FEA model too. InFEA block, machining deformation under the cutting forceand the clamping force is calculated using finite elementmethod under a certain fixture layout, and the deformationis then sent to optimization procedure to search for anoptimal fixture scheme.4 Fixture layout design and clamping force optimization4.1 A genetic algorithmGenetic algorithms (GA) are robust, stochastic and heuristicoptimization methods based on biological reproductionprocesses. The basic idea behind GA is to simulate “survivalof the fittest” phenomena. Each individual candidate in thepopulation is assigned a fitness value through a fitnessfunction tailored to the specific problem. The GA thenconducts reproduction, crossover and mutation processesto eliminate unfit individuals and the population evolvesto the next generation. Sufficient number of evolutions ofthe population based on these operators lead to anincrease in the global fitness of the population and thefittest individual represents the best solution.The GA procedure to optimize fixture design takesfixture layout and clamping force as design variables togenerate strings which represent different layouts. Thestrings are compared to the chromosomes of naturalevolution, and the string, which GA find optimal, ismapped to the optimal fixture design scheme. In this study,the genetic algorithm and direct search toolbox of MATLABare employed.The convergence of GA is controlled by the populationsize (Ps), the probability of crossover (Pc) and theprobability of mutations (Pm). Only when no change inthe best value of fitness function in a population, Nchg,reaches a pre-defined value NCmax, or the number ofgenerations, N, reaches the specified maximum number ofevolutions, Nmax., did the GA stop.There are five main factors in GA, encoding, fitnessfunction, genetic operators, control parameters and con-straints. In this paper, these factors are selected as what islisted in Table 1.Since GA is likely to generate fixture design strings thatdo not completely restrain the fixture when subjected tomachining loads. These solutions are considered infeasibleand the penalty method is used to drive the GA to a feasiblesolution. A fixture design scheme is considered infeasible orunconstrained if the reactions at the locators are negative, inother words, it does not satisfy the constraints in equations(2) and (3). The penalty method essentially involvesMachiningProcess ModelFEAOptimizationprocedurecutting forcesfitnessOptimization resultFixture layout and clamping force Fig. 1 Fixture layout and clamp-ing force optimization processTable 1 Selection of GAs parametersFactorsDescriptionEncodingRealScalingRankSelectionRemainderCrossoverIntermediateMutationUniformControl parameterSelf-adaptingInt J Adv Manuf Technolassigning a high objective function value to the scheme thatis infeasible, thus driving it to the feasible region insuccessive iterations of GA. For constraint (4), when newindividuals are generated by genetic operators or the initialgeneration is generated, it is necessary to check up whetherthey satisfy the conditions. The genuine candidate regionsare those excluding invalid regions. In order to simplify thechecking, polygons are used to represent the candidateregions and invalid regions. The vertex of the polygons areused for the checking. The “inpolygon” function inMATLAB could be used to help the checking.4.2 Finite element analysisThe software package of ANSYS is used for FEAcalculations in this study. The finite element model is asemi-elastic contact model considering friction effect,where the materials are assumed linearly elastic. As shownin Fig. 2, each locator or support is represented by threeorthogonal springs that provide restrains in the X, Y and Zdirections and each clamp is similar to locator but clampingforce in normal direction. The spring in normal direction iscalled normal spring and the other two springs are calledtangential springs.The contact spring stiffness can be calculated accordingto the Herz contact theory 8 as followskiz16R?iE?2i9?13fiz13kiz kiy6E?i2?vfiGfi2?vwiGwi?1? kiz8:5wherekiz, kix, kiyare the tangential and normal contactstiffness,1R?i1Rwi1Rfiis the nominal contact radius,1E?i1?V2wiEwi1?V2fiEfiis the nominal contact elastic modulus,Rwi, Rfiare radius of the i-th workpiece andfixture element,Ewi, Efiare Youngs moduli for the i-thworkpiece and fixture materials,wi, fiare Poisson ratios for the i-th workpieceand fixture materials,Gwi, Gfiare shear moduli for the i-th workpieceand fixture materials and fizis thereaction force at the i-th contact point inthe Z direction.Contact stiffness varies with the change of clampingforce and fixture layout. A reasonable linear approximationof the contact stiffness can be obtained from a least-squaresfit to the above equation.The continuous interpolation, which is used to applyboundary conditions to the workpiece FEA model, isFig. 2 Semi-elastic contact model taking friction into accountSpring positionFixture element position12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849Fig. 3 Continuous interpolationFig. 4 A hollow workpieceTable 2 Machining parameters and conditionsParameterDescriptionType of operationEnd millingCutter diameter25.4 mmNumber of flutes4Cutter RPM500Feed0.1016 mm/toothRadial depth of cut2.54 mmAxial depth of cut25.4 mmRadial rake angle10Helix angle30Projection length92.07 mmInt J Adv Manuf Technolillustrated in Fig. 3. Three fixture element locations areshown as black circles. Each element location is surroundedby its four or six nearest neighboring nodes. These sets ofnodes, which are illustrated by black squares, are 37, 38,31 and 30, 9, 10, 11, 18, 17 and 16 and 26, 27, 34, 41,40 and 33. A set of spring elements are attached to each ofthese nodes. For any set of nodes, the spring constant iskijdijPk2hidikki6wherekijis the spring stiffness at the j-th node surrounding thei-th fixture element,dijis the distance between the i-th fixture element and thej-th node surrounding it,kiis the spring stiffness at the i-th fixture elementlocation.iis the number of nodes surrounding the i-th fixtureelement location.For each machining load step, appropriate boundaryconditions have to be applied to the finite element model ofthe workpiece. In this work, the normal springs areconstrained in the three directions (X, Y, Z) and thetangential springs are constrained in the tangential direc-tions (X, Y). Clamping forces are applied in the normaldirection (Z) at the clamp nodes. The entire tool path issimulated for each fixture design scheme generated by theGA by applying the peak X, Y, Z cutting forces sequentiallyto the element surfaces over which the cutter passes 23.In this work, chip removal from the tool path is takeninto account. The removal of the material during machiningalters the geometry, so does the structural stiffness of theworkpiece. Thus, it is necessary to consider chip removalaffects. The FEA model is analyzed with respect to toolmovement and chip removal using the element deathtechnique. In order to calculate the fitness value for a givenfixture design scheme, displacements are stored for eachload step. Then the maximum displacement is selected asfitness value for this fixture design scheme.The interaction between GA procedure and ANSYS isimplemented as follows. Both the positions of locators andclamps, and the clamping force are extracted from realstrings. These parameters are written to a text file. Theinput batch file of ANSYS could read these parameters andcalculate the deformation of machined surfaces. Thus thefitness values in GA procedure can also be written to a textfile for current fixture design scheme.It is costly to compute the fitness value when there are alargenumber of nodes in an FEM model.Thus itis necessaryto speed up the computation for GA procedure. As thegeneration goes by, chromosomes in the population aregetting similar. In this work, calculated fitness values arestored in a SQL Server database with the chromosomes andfitness values. GA procedure first checks if currentchromosomes fitness value has been calculated before, ifnot, fixture design scheme are sent to ANSYS, otherwisefitness values are directly taken from the database.The meshing of workpiece FEA model keeps same inevery calculating time. The difference among everycalculating model is the boundary conditions. Thus, themeshed workpiece FEA model could be used repeatedly bythe “resume” command in ANSYS.5 Case studyAn example of milling fixture design optimization problemfor a low rigidity workpiece displayed in previous researchpapers 16, 18, 22 is presented in the following sections.Fig. 5 Candidate regions for thelocators and clampsTable 3 Bound of design variablesMinimumMaximumX /mmZ /mmX /mmZ /mmL10076.238.1L276.20152.438.1L3038.176.276.2L476.238.1152.476.2C10076.276.2C276.20152.476.2F1/N06673.2F2/N06673.2Int J Adv Manuf Technol5.1 Workpiece geometry and propertiesThe geometry and features of the workpiece are shown inFig. 4. The material of the hollow workpiece is aluminum390 with a Poisson ration of 0.3 and Youngs modulus of71 Gpa. The outline dimensions are 152.4 mm127 mm76.2 mm. The one third top inner wall of the workpiece isundergoing an end-milling process and its cutter path is alsoshown in Fig. 4. The material of the employed fixtureelements is alloy steel with a Poisson ration of 0.3 andYoungs modulus of 220 Gpa.5.2 Simulating and machining operationA peripheral end milling operation is carried out on theexample workpiece. The machining parameters of theoperation are given in Table 2. Based on these parameters,the maximum values of cutting forces that are calculatedand applied as element surface loads on the inner wall ofthe workpiece at the cutter position are 330.94 N(tangential), 398.11 N (radial) and 22.84 N (axial). Theentire tool path is discretized into 26 load steps and cuttingforce directions are determined by the cutter position.5.3 Fixture design planThe fixture plan for holding the workpiece in the machiningoperation is shown in Fig. 5.