机械基于CADCAE的桶形件变压边力冲压成形工艺研究带CAD图纸
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南京理工大学泰州科技学院毕业设计(论文)前期工作材料学生姓名:王敏佳学 号：0501510140系部:机械工程系专 业:机械工程及自动化设计(论文)题目:基于CAD/CAE桶形件的变压边力冲压成形工艺设计指导教师:张卫高级工程师 材 料 目 录序号名 称数量备 注1毕业设计(论文)选题、审题表12毕业设计(论文)任务书13毕业设计(论文)开题报告含文献综述14毕业设计(论文)外文资料翻译含原文15毕业设计（论文）中期检查表1 2009年5月南京理工大学泰州科技学院学生毕业设计（论文）中期检查表学生姓名王敏佳学 号0501510140指导教师张卫选题情况课题名称基于CAD/CAE的桶形件变压边力冲压成形工艺设计难易程度偏难适中偏易工作量较大合理较小符合规范化的要求任务书有无开题报告有无外文翻译质量优良中差学习态度、出勤情况好一般差工作进度快按计划进行慢中期工作汇报及解答问题情况优良中差中期成绩评定： 良所在专业意见： 负责人： 2009 年 4 月 3 日 南京理工大学泰州科技学院毕业设计（论文）任务书系部：机械工程系专 业：机械工程及自动化学 生 姓 名：王敏佳学 号：0501510140设计(论文)题目：基于CAD/CAE的桶形件变压边力冲压成形工艺设计起 迄 日 期:2009年3 月 9 日 6 月 14日设计(论文)地点:南京理工大学泰州科技学院指 导 教 师:张 卫 专业负责人:龚光容发任务书日期: 2009 年 2 月 26 日任务书填写要求1毕业设计（论文）任务书由指导教师根据各课题的具体情况填写，经学生所在专业的负责人审查、系部领导签字后生效。此任务书应在第七学期结束前填好并发给学生；2任务书内容必须用黑墨水笔工整书写或按教务处统一设计的电子文档标准格式（可从教务处网页上下载）打印，不得随便涂改或潦草书写，禁止打印在其它纸上后剪贴；3任务书内填写的内容，必须和学生毕业设计（论文）完成的情况相一致，若有变更，应当经过所在专业及系部主管领导审批后方可重新填写；4任务书内有关“系部”、“专业”等名称的填写，应写中文全称，不能写数字代码。学生的“学号”要写全号；5任务书内“主要参考文献”的填写，应按照国标GB 77142005文后参考文献著录规则的要求书写，不能有随意性；6有关年月日等日期的填写，应当按照国标GB/T 74082005数据元和交换格式、信息交换、日期和时间表示法规定的要求，一律用阿拉伯数字书写。如“2009年3月15日”或“2009-03-15”。毕 业 设 计（论 文）任 务 书1本毕业设计（论文）课题应达到的目的：桶形件由于属于轴对称件，是研究复杂几何形状件的冲压成形工艺的基础。通过本课题旨在让学生了解并熟练运用有限元分析，通过对桶形件冲压成形工艺的研究，探讨不同变压边力曲线下桶形件冲压成形性能，了解有限元分析在冲压工艺中的实际运用。通过本课题可以培养学生解决实际问题的能力，提高学生的综合应用能力和独立工作能力，为学生最终走向工作岗位打下基础。2本毕业设计（论文）课题任务的内容和要求（包括原始数据、技术要求、工作要求等）：本课题首先选取了简单的轴对称件桶形件作为研究起点，针对智能数控冲压机床对压边力控制的要求，借助CAE手段通过改变压边力方式，进行桶形件的成形性能的有限元分析仿真，探讨桶形件冲压成形工艺。原始数据：所选的原材料为低碳钢，其它尺寸如下（mm）：毛坯凸模凹模直径d直径dp圆角半径rp直径Dd圆角半径rd10056.87.060.08.0技术要求: 取凸模的模拟运动速度为2000mm/s。行程为20mm，凹模、凸模和板料间及压边圈和板料间的摩擦系数都为0.125，通过实验对不同变压边力曲线下FLD图进行观察，最终确定并选择较优的变压边力曲线。工作要求：（1）文献查阅有关板材冲压和有限元方面的资料（2）建立桶形件凸凹模CAD模型；（3）对桶形件冲压成形过程借助DYNAFORM软件进行CAE有限元仿真分析；（4）选取不同变压边力曲线对桶形件冲压成形性能进行分析；（5）按要求提供各种设计文档，并完成毕业论文。毕 业 设 计（论 文）任 务 书3对本毕业设计（论文）课题成果的要求包括毕业设计论文、图表、实物样品等：（1）不同变压边力下桶形件的有限元分析数据 （2）毕业设计论文4主要参考文献：1 姜奎华. 冲压工艺与模具设计M.北京:机械工业出版社,2002.2 胡世光. 板料冷压成形原理M.北京:国防工业出版社,1979.3 王骥. 筒形件液压拉深过程的计算机控制C.西安交通大学.2002.4 李硕本. 冲压工艺理论与新技术M. 北京：机械工业出版社.2002.11.5 吴诗惇. 冲压工艺及模具设计M. 北京：西北工业大学出版社.2002.11. 6 姜雷,陈君若,沈选举,孙东明. 圆筒形零件拉深压边力的数值模拟J.机械.2004,(5).7 S.Thiruvarudchelvan, F.W.Travis et al. On the deep drawing of cups with punch and blank-holder forces proportional to a hydraulic pressureJ. Materials Processing Technology, 2000(88):92-93. 8 谢晖,杨旭静,成艾国,李光耀,钟志华. 计算机仿真中板料冲压成形压边力的优化J.中国机械工程,2002,(11):1910-1914.9 王新云，夏巨諶等.多点压边圈压力分布的理论模型与数值分析J.机械工程学报，2005(16):843-845.10 Leonid BShulkin, Ronald et al. Blank holder force(BHF) control in Viscous pressure forming (VOF) of sheet MetalJ. Materials Processing Technology, 2000:97-99.毕 业 设 计（论 文）任 务 书5本毕业设计（论文）课题工作进度计划：起 迄 日 期工 作 内 容2009年3月9 日 3 月29日3月30日4 月12 日4月13日 4 月 27日4月28日 5 月 16日5月17日 5 月 31日6月 1 日 6 月 5 日完成外文资料翻译、文献综述和开题报告完成基于有限元分析的桶形件冲压成形工艺研究总体方案设计。使用Pro/E软件完成对桶形件的凸模、凹模及板料模型进行CAD建模选取不同变压边力曲线使用DYNAFORM软件对桶形件冲压成形性能进行分析讨论。完成毕业论文并准备毕业答辩论文答辩所在专业审查意见：负责人： 年 月 日系部意见：系部主任： 年 月 日南京理工大学泰州科技学院本科生毕业设计（论文）选题、审题表系部机械工程系指导教师姓 名张卫专业技术职 务高级工程师课题名称基于CAD/CAE的桶形件变压边力冲压成形工艺研究适用专业机械工程及自动化课题性质ABCDE课题来源ABCD课题预计工作量大小大适中小课题预计难易程度难适中易课题简介冲压成形工艺被广泛应用于汽车航天等领域，桶形件由于属于轴对称件，是研究复杂几何形状件的冲压成形工艺的基础。本课题首先选取了桶形件作为研究起点，针对智能数控冲压机床对压边力控制的要求，借助CAD/CAE手段通过改变法兰分区和压边力方式进行板料的成形性能的有限元分析仿真，探讨桶形件冲压成形工艺。课题应完成的任务和对学生的要求1 论文要求：（1）文献查阅有关板材冲压和有限元方面的资料（2）桶形件CAD模型建立；（3）桶形件冲压成形CAE有限元分析；（3）仿真调试； （4）按要求提供各种设计文档2要求学生具备机械设计、CAD等方面的基础知识。所在专业审定意见： 专业负责人(签名)： 年 月 日本课题由 王敏佳 同学选定，学号： 0501510140 注：1该表由指导教师填写，经所在专业负责人签名后生效，作为该专业学生毕业设计（论文）选题使用；2有关内容的填写见背面的填表说明，并在表中相应栏内打“”； 3课题一旦被学生选定，此表须放在学生“毕业设计（论文）资料袋”中存档。填 表 说 明1该表的填写只针对1名学生做毕业设计（论文）时选择使用，如同一课题由2名及2名以上同学选择，应在申报课题的名称上加以区别（加副标题），并且在“设计（论文）要求”一栏中说明。2“课题性质”一栏：A产品设计；B工程技术研究；C软件开发；D研究论文或调研报告；E其它。3“课题来源”一栏：A自然（社会）科学基金与省（部）、市级以上科研课题；B企、事业单位委托课题；C校、院（系）级基金课题；D自拟课题。4“课题简介”一栏：主要指该课题的背景介绍、理论意义或实用价值。Proceedings of the American Control Conference San Diego, Cahfornla June 1999 Process Controller Design for Sheet Metal Forming Cheng-Wei Hsu and A. Galip Ulsoy Mechanical Engineering and Applied Mechanics University of Michigan Ann Arbor, MI 48109-2125, USA Mahmoud Y. Demeri Ford Research Laboratories Ford Motor Company Dearbom, MI 48121, USA Abstract In-process adjustment of the blank holder force can lead to higher formability and accuracy, and better part consistency. There are many studies on the application of process con- trol to sheet metal forming. However, process controller de- sign has not been thoroughly addressed, and is studied in this paper. A constant gain proportional plus integral (PI) con- troller with approximate inverse dynamics will be presented to achieve small tracking error regardless of model uncer- tainty and disturbances. 1 Introduction Sheet metal stamping is an important manufacturing process because of its high speed and low cost for mass production. Figure 1 shows a schematic of a simplified stamping process. Holder Figure 1 : Schematic of a stamping process The basic components are a punch, and a set of blank holders which may include drawbeads. The punch draws the blank to form the shape while the blank holder holds the blank to control the flow of metal into the die cavity. Some process variables are also shown: Fp is the punch force, Fb is the blank holder force, and F, is the restraining force within the blank. The good quality (i.e., no tearing, no wrinkling, and high di- mensional accuracy) of stamped parts is critical in avoiding problems in assembly and in the final product performance. Consistency (i.e., dimensional variations between parts) in the stamping process also significantly affects subsequent assem- bly in mass production. New challenges emerge from the use of new materials. For example, lightweight materials (e.g., aluminum) are essential for reduction of car weight to achieve high fuel economy. However, aluminum has reduced forma- bility and produces more springback l, 21. The control of flow of material into the die cavity is crucial to good part quality and consistency. Previous research showed that variable blank holder force during forming improves ma- terial formability 3, 41, reduces springback l, 2, 51, and achieves part consistency 1,2. One strategy (i.e. process control) for the application of variable blank holder force is shown in Fig. 2 l, 21. Figure 2 : Process control of sheet metal forming In this strategy, a measurable process variable (e.g., punch force) is controlled by following a predetermined (e.g., punch force-displacement) trajectory through manipulating the blank holder force. A similar approach has also been re- ported 5,6,7. Recent work on process control in sheet metal forming led to the following conclusions 8: 1. Consistency of part quality can be improved through 2. Better part quality can be achieved through selection of It is important to realize that a badly designed process con- troller cannot ensure good tracking performance, and, in turn, cannot guarantee good part quality and consistency. Clearly, the process controller plays an important role in the feedback control system and needs further investigation. Issues of process controller design for sheet metal forming have not been properly addressed, especially, from a control point of view. Modeling sheet metal forming for process con- troller design has been investigated 9. Hsu et al. lo re- cently proposed a first-order non-linear dynamic model for u- channel forming which can capture the main characteristics of the process dynamics observed during experiments. Propor- tional plus integral (PI) control has been used for sheet metal forming and controller parameters were typically determined by trial and error ll. The disadvantage of PI control is that high controller gains can achieve good tracking performance but cannot maintain good stability robustness while low controller gains can main- tain good stability robustness but cannot achieve good track- ing performance. Since sheet metal forming is a highly non- linear process, it is difficult to tune a PI controller to stabilize the closed-loop system with good tracking performance. Hsu the tracking property of feedback control. the reference punch force trajectory. 0-7803-4990-6/99 $10.00 0 1999 AACC 192 et al. 8 investigated constant gain PI control with feedfor- ward action (PIF). Although PIF control worked well under dry condition, it generated a huge peak in the blank holder force under lubricated condition. The purpose of this investigation is to systematically develop a process controller for sheet metal forming to stabilize the closed-loop system with good tracking performance. A con- stant gain PI process controller with approximate inverse dy- namics for sheet metal forming will be proposed. The first- order non-linear dynamic model for u-channel forming lo will be explored to obtain the approximate inverse dynamics, which is related to tracking performance. The constant gain PI control will be designed to ensure the tracking performance regardless of disturbance and model uncertainty. Numerical simulation results will demonstrate the capabilities of the pro- posed controller. 2 Systematic Process Controller Design A schematic of the constant gain PI controller with inverse dynamics is shown in Fig. 3. The block “Plant” refers Plant Figure 3: Schematic of the constant gain PI controller with inverse to the real stamping process or its process model. Fpd is the reference punch force trajectory, Fb is the blank holder force applied to the plant, and Fp is the punch force generated by the plant. A systematic development of the proposed controller requires the following steps: 1. Model sheet metal forming (i.e., “Plant”) for process controller design. 2. Design the process controller (i.e., “Inverse Dynamics” and “PI”). 3. Adjust and test the performance of the process con- troller through simulation. 4. Adjust and verify the performance of the process con- troller through experiment. Adjustment and verification of the performance of the process controller will not be presented in this paper. 2.1 Modeling of Sheet Metal Forming The process model for u-channel forming can be represented by the following first-order non-linear dynamic model 8, 101: dynamics. where F P C oI(Fb) = 1.3537- 1.8511 X 10-2*Fb (3) Z ( f i ) = 1.5689+5.6906 X lo-*-& (4) +1.2340 x Fz - 1.2669 x F Z + 1.0279 x lod5. F: oI(Fb) and Z(Fb) are the DC gain and the time constant, de- rived from constant blank holder force experiments. 2.2 Design of the Constant Gain PI Controller with Ap- proximate Inverse Dynamics For a given reference punch force trajectory, a controller is designed to generate the blank holder force to achieve: 1. Stabilization of the closed-loop system. 2. Asymptotic convergence of the punch force and the ref- The proposed controller consists of two parts: approximate inverse dynamics and PI control. The approximate inverse dynamics tracks the reference trajectory while the PI control ensures good tracking performance regardless of disturbance and model uncertainty. A schematic of the inverse dynamics is shown in Fig. 4. Fm is the out- erence punch force trajectory. 2.2.1 Approximate Inverse Dynamics: Model F P Figure 4: Schematic of the inverse dynamics. put of the inverse dynamics and also part of the calculated blank holder force through the proposed controller, and e is the tracking error due to using the inverse dynamics alone. In fact, the inverse dynamics is feedforward control. The tracking error is defined by e(t) = Fp(Fb,t) -Fpd(t) (5) The tracking error dynamics, obtained from the derivative of e(t) with respect to time, t, and the substitution of Eq. 1, becomes Lyapunov theorem is applied to prove the asymptotic stability of the tracking error dynamics, which means asymptotic con- vergence of e to zero. Choose a candidate Lyapunov function as Its derivative with respect to t is If 193 then Eq. 8 becomes approximated by Equation 10 is negative definite because r(Fb) 0 lo. Ac- cording to Lyapunov theorem, the tracking error dynamics is asymptotically stable if Eq. 9 is satisfied. Therefore, Eq. 9 is the inverse dynamics since F b can be solved for a given Fpd. Solving F b from Eq. 9 depends on because W. could be zero. Figure 5 shows contours of w. The BhkbolderhlC%Fb (kN) Figure 5: Contours of a - . figure shows that ? * could be zero. This will cause nu- merical problems about solving Fb, because F b could be very large or become indeterminable, which implies that F b will change abruptly or cannot be found. To reconcile this prob- lem, that F b = 0 when I I lo-* will be assumed in simulation. The inverse dynamics (i.e., Eq. 9) with this as- sumption will be called the approximate inverse dynamics. Later, Fm will denote the solution of Eq. 9. Generally, the in- verse dynamics or the feedforward control cannot sustain any disturbance or model uncertainty. A feedback control us- ing a constant gain PI controller is built to reject disturbance and improve robustness to model uncertainty. The constant gain PI controller is designed based on the perturbed process model. The perturbed process model is derived as follows. Assuming that the disturbance, Fd, comes at the input of the process model in Fig. 4, then 2.2.2 Constant Gain PI Control: The tracking error, E, becomes E consists of e and the error due to Fd. Assuming that F d is much smaller than Fm. then Fp(Fb,t) in Eq. 12 can be where 3 E $ is applied lo. Substituting Eq. 13 into Eq. 12 leads to Although e decays asymptotically, E is still influenced by Fd. The perturbed process model is To maintain tracking performance (i.e., E approaches e), a feedback loop is designed to force to converge to zero. A constant gain PI controller is investigated here. Figure 6 shows the block diagram. Kp is the proportional gain and Perturbed Process Model I I I I Figure 6 Block diagram for feedback loop design. Ki is the integral gain. dFb is the output of the PI controller and also part of the calculated blank holder force through the proposed controller. Assuming that the perturbed process model is a constant gain, Go, then for the constant gain PI controller, the dynamic equa- tion of the closed-loop system becomes Its solution is where TO is the time constant and z is the dummy variable. For a given GO, choose Ki and Kp such that zo is as small as possible and TO K i as large as possible. Hence, Ed will decrease as quickly as possible. However, generally depends on Fd. 194 2.3 Constant Gain PI Controller with Approximate In- verse Dynamics The block diagram for the constant gain PI controller with approximate inverse dynamics is shown in Fig. 7. Figure 7: Block diagram for the constant gain PI controller with approximate inverse dynamics. 3 Simulations and Results The simulation is used to show the performance of the pro- posed controller on disturbance rejection and robustness to model uncertainty. In the following simulations, the refer- ence punch force trajectory, Fpd, is generated by Eq. 1 using the constant blank holder force, 60 kN. 3.1 No Disturbance and No Model Uncertainty Fd in Fig. 7 is 0 kN. The mathematical relations for the blocks of “Plant” and “Process Model” in Fig. 7 are identical. Fig- ure 8 shows the simulation results. Figure (a) shows that h 18) h 640 iJ0 2 lo Y P f ” 0 Figure 8: Performance of approximate inverse dynamics: (a) mea- sured Fb (i.e., Fb), ) reference Fp (i.e., Fpd) and mea- sured Fp (i.e., Fp), (c) tracking error, I&l= IFp -Fpdl, and (d) relative tracking error, y= l&l/Fpd. Fb is very close to 60 kN. The maximum overshoot is less than 0.03 kN. The reasons for Fb # 60 kN are the previously mentioned numerical problem (i.e., when 0.01 allows fib not to be zero while the area where 5 0.01 assumes Fb to be zero. This assumption in fact limits the upper bound of IFbl. According to this assumption, the approximate inverse I Fb I 195 Model uncrrlainty: 6 (= 0.1 0 5 10 Figure 10: Performance of robustness to model uncertainty ( 6 , = 0.1 and S, = 0.1): (a) measured Fb, (b) reference Fp (i.e., Fd) and measured Fp (i.e., Fp), (c) tracking er- ror, I E = IFp - Fdl, and (d) relative tracking error, Y= kl/Fpd* dynamics can successfully generate a blank holder force tra- jectory (i.e., Fm) corresponding to a given reference punch force trajectory. The tracking error, E, can be divided into two parts: e due to the inverse dynamics and &d due to the disturbance. (See Eqs. 14 and 15.) When there is no disturbance and no model uncertainty, E is in fact the same as e. When there is distur- bance or model uncertainty, E will be larger than e. For ex- ample, Figs. 9(c) and 1O(c) show larger tracking errors than Fig. 8(c). Therefore, the inverse dynamics will determine the tracking performance. As shown in Fig. 4, the inverse dynamics is actually feed- forward control; therefore, it cannot maintain its performance when disturbance or model uncertainty appears. The feed- back control (i.e., the constant P I controller) is designed to maintain the tracking performance regardless of disturbance or model uncertainty. Although the tracking errors in Figs. 9(c) and 1O(c) are larger than the tracking error in Fig. 8(c), they decay asymptotically. Therefore, the tracking perfor- mance can be maintained through the constant P I controller regardless of disturbance or model uncertainty. 5 Summary and Conclusions A constant gain P I controller with approximate inverse dy- namics is systematically designed based on the first-order non-linear dynamics. The proposed controller has a feedfor- ward loop (i.e., the approximate inverse dynamics) and a feed- back loop (i.e., the constant gain P I control). The feedforward loop determines the tracking performance while the feedback loop relates to disturbance rejection and robustness to model uncertainty. Simulation shows that the proposed controller can track the reference regardless of disturbance and model uncertainty. Future work will include experimental imple- mentation and validation of the proposed controller. Acknowledgements The authors gratefully acknowledge the technical and finan- cial support provided by the Ford Motor Company. References 1 3 Adamson, A. M., 1995, “Closed-Loop Dimensional Control in Sheet Metal Forming via the Blank Restraining Force”, M.S. thesis, University of Michigan, Ann Arbor
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