机械长玻纤增强反应注射成型生产线带CAD图纸
收藏
资源目录
压缩包内文档预览：(预览前20页/共40页)
编号：22081987
类型：共享资源
大小：1.96MB
格式：ZIP
上传时间：2019-09-18
上传人：QQ24****1780
认证信息
个人认证
王**（实名认证）
浙江
IP属地：浙江
50
积分
- 关 键 词：
-
机械
长玻纤
增强
反应
反映
注射
成型
生产线
cad
图纸
- 资源描述：
-
机械长玻纤增强反应注射成型生产线带CAD图纸,机械,长玻纤,增强,反应,反映,注射,成型,生产线,cad,图纸
- 内容简介：
-
PLC 设计输入输出接口及通道分配输入1，小车各个工位的选择按钮SB1,SB2,SB3,SB4,SB5,SB6,SB7,SB8,SB9,SB102，启动、停止、两点输入3，为防止小车在运行过程中碰到物或者人设一红外感应器，1输入4，为使小车准确停靠，在每个工位设传感器，小车前进和后退进入工位的顺序不一样，每个工位设前进后退两个传感器，为了保证停靠准确，在小车上设前进传感器，后退传感器，和位置传感器，这样可以感知停靠偏左还是偏右，停靠准确时三个感应器均接通，共10*2+3=23输入5，每个工位设呼叫按钮（即接收模架单元的浇注申请）SA1,SA2,SA3,SA4,SA5,SA6,SA7,SA8,SA9,SA106，自动运行选择和手动选择按钮SC1,SC2,7，浇注服务的状态信息一输入共50个输入输出1，小车的前进和后退两点输出，表现为电机的正反转2，输出到位状态信息、浇注信息 给机械手3，输出浇注结束信号给模架4，小车手动，自动运行指示灯两点输出3，小车的加速、减速、匀速三点输出4，各个工位的指示灯十点输出5，小车前进，后退指示灯两点6，非正常状态报警输出共20个输出PLC选型根据输入输出点数选择西门子S7-200系列，CMP1A系列30点输入输出型，加两个扩展模块，最大I/O点数为90PLC编程分几大块1，小车自动与手动选择控制2，小车到达工位指示灯控制3，每个工位呼叫指示控制4，小车启动和运行方向选择控制5，小车的速度变换控制南 京 理 工 大 学毕业设计(论文)前期工作材料学生姓名:王万花学 号：03304980学院(系):机械工程学院专 业:机械工程及自动化设计(论文)题目:长玻纤增强反应注射成型生产线控制系统设计指导教师:孙宇教授 (姓 名) (专业技术职务)材 料 目 录序号名 称数量备 注1毕业设计(论文)选题、审题表1教师完成2毕业设计(论文)任务书1教师完成3毕业设计(论文)开题报告含文献综述1学生完成4毕业设计(论文)外文资料翻译含原文1学生完成5毕业设计（论文）中期检查表1教师完成年 月注：毕业设计（论文）中期检查工作结束后，请将该封面与目录中各材料合订成册，并统一存放在学生“毕业设计（论文）资料袋”中（打印件一律用A4纸型）。Pergamon Computers & Fluids Vol. 24, No. 1, pp. 55-62, 1995 Copyright 0 1995 Elsevier Science Ltd 0045-7930(94)00020-4 Printed in Great Britain. All rights reserved 0045-7930/95 $9.50 + 0.00 PETROV-GALERKIN FINITE ELEMENT ANALYSIS FOR ADVANCING FLOW FRONT IN REACTION INJECTION MOLDING NITIN R. ANTURKAR Ford Research Laboratory, Ford Motor Company, P.O. Box 2053, MD 3198, Dearborn, MI 48121-2053, U.S.A. (Received 4 August 1993; in revised form 4 May 1994) Abstract-A numerical scheme for computing the advancement of a flow front and related velocity, pressure, confersion and temperature distributions during mold filling in reaction injection molding (RIM) is described in this work. In the RIM process, the convective term in the energy equation is dominant. Therefore, the numerical scheme has incorporated a Petrov-Galerkin finite element method to suppress spurious oscillations and to improve accuracy of the calculations. The other feature of the numerical scheme is that the flow front locations are computed simultaneously with primary variables by using a surface parameterization technique. The numerical results compare well with the reported experimental data. Improved accuracy obtained by this numerical scheme in the flow front region is expected to assist in the predictions of the fiber orientations and the bubble growth in RIM, which are determined primarily by the flow front region. I. INTRODUCTION Reaction injection molding (RIM) is a widely used process to manufacture exterior fascias in the automobile industry. In this process, a prepolymerized isocyanate and a polyol/amine mixture are mixed together, and injected into a mold, where polymerization occurs. A fountain flow effect in the advancing flow front region during the mold-filling stage plays an important role in determining the residence time of the fluid elements and in controlling the fiber orientations in the final product 11. An accurate s:imulation of this flow front, however, poses a challenging problem. Evolving flow domain with advancing flow front requires updating of the numerical grids and prediction of the moving boundary at every time step. Low thermal conductivity of the material, high flow rates in the RIM process, and highly exothermic rapid reactions result in convection-dominated energy transport equation, which needs a special numerical treatment. Besides, moving contact lines near the walls need suitable boundary conditions that do not introduce numerical instability. A numerical scheme that incorporates all these complex features of the RIM process is required for accurate predictions near the flow front region. Previous studies either have made simplifying assumptions regarding the flow front region 2&l, or have not compared their results with the experiments 5,6. In this paper, we describe a numerical scheme in detail, which will address the above-mentioned complexities, and. present the relevent results that highlight the numerical scheme (refer to our earlier work 7 for the detailed discussion of the governing equations and additional results). No a priori assumptions are made in the numerical scheme regarding the shape of the new front or the velocity distribution in the flow domain. A free-surface parameterization technique is used, in which the shape of the flow front is calculated simultaneously with other field variables, such as pressure, velocities and conversion, by incorporating kinematic boundary condition at the surface of the flow front as one of the governing equations. A conventional Galerkin finite-element technique is notorious for its numerical instability in convection-dominated transport problems 8. The resulting spurious oscillations can be usually eliminated by mesh refinement. However, for transient problem described here, mesh refinement is an impractical and expensive alternative. The other alternatives include various upwinding schemes 9-121, a method of characteristics 6, 13, 141, and a Galerkin/least-squares technique 151. Although the “conservative” methods, such as methods of characteristics and Galerkin/least- squares techniques are more accurate, a simple Petrov-Galerkin upwinding method is easier to 55 56 NITIN R. ANTURKAR implement and cost effective, particularly for a transient problem investigated in this work. Therefore, such a scheme is implemented here following Adornato and Brown 9 to suppress numerical instability without resolving to extremely refined meshes. The governing equations are presented briefly in Section 2, and the numerical method is described in detail in Section 3. The typical results of the mold filling stage of the RIM process in a two-dimensional rectangular plaque are presented in Section 4. The results are also compared with the reported experimental data 2, and with the numerical results obtained by using conventional Galerkin finite element method. 2. GOVERNING EQUATIONS The lumped kinetic rate expression for polymerization reactions in RIM is 16, 171: ri = -A, exp( - E,/RT)Cr, (1) where, Ci is the isocyanate concentration, T the temperature, R the gas-law constant, m the order of the reaction, E, the activation energy of the reaction, and A, the rate constant. The viscosity depends on the conversion and temperature, and is expressed in the form of CastroMacosko viscosity function 2, (X,T)=rl(X)-II(T)=A,exp()(iBXi, (2) where X is the isocyanate conversion, X, the gel conversion, and A, , E, A and B are the constants. For constant thermal properties and density of the reactive mixture, and for negligible molecular diffusion, the dimensionless governing equations are, continuity equation : v.v=o; (3) conservation of momentum equation : Re$+v.Vv= -pV.I+v:(rcj); Gz7,$+v-VX=Dak.(l -X)“; mole balance equation : (4) (5) conservation of energy equation : Gz g+v VT =V*T+Brrc(j:Vv)+Darc,(l -X)m; L . 1 (6) where, v is the velocity vector, q the rate-of-strain tensor, t the time, p the pressure, and k, is the dimensionless rate constant, defined as exp( - E,/R)(l/T - l/T,). The equations are made dimensionless using the average velocity V, half of the thickness of the mold H, and the temperature T, and the viscosity qO( = r (X = 0, T = T,) at the inlet of the mold. All the dimensionless groups and their definitions are listed in Table 1. The boundary conditions in terms of dimensionless variables are 1. at the walls: v, = 0 (no-slip), T = T,; 2. at the mid-plane: aTjay = 0, &Jay = 0, V, = 0; 3. at the inlet: v = fully developed flow, T = 1, X = X,; 4. at the contact line: n * (-PI + 2) = 0 (full-slip): 5. at the flow front: n . (-PI + 2) = 0 (force balance), n . (v - ah/at) = 0 (kinematic condition); Table 1. Dimensionless groups in governing equations, where AH, is the heat of reaction, AT, the adiabatic temperature rise, and C, the initial concentration of isocyanate GZ Graetz number VHpC,lk Re Reynolds number HVlrlo K viscosity ratio 41% Br Brinkmann number to V=lkT, Da Damkohler number (AH,H*C$/kT,)A,exp(-E,/RT) T adb adiabatic temperature rise AT,IT, Flow front advancement in reaction injection molding 57 where a., and vY are the components of the velocity vector v, II the unit normal vector, r the extra stress tensor, h the location vector of the flow front and Twal, the dimensionless temperature at the mold wall. The details of incorporating the boundary conditions in the numerical analysis are explained in the next section. 3. NUMERICAL ANALYSIS In the finite element formulation the unknown velocities, temperature and conversion are expanded in terms of the biquadratic basis functions 4, the pressure in terms of the bilinear basis functions ll/i and the flow front shape h in terms of the quadratic basis functions: (7) where l and q are the coordinates in isoparametric transformation, defined as i= 1 i=l in the isoparametric domain (- 1 4 + 1, - 1 q L(5), where, Pe is the local element Peclet number (= VA/D), A the element size and c,(s) is the cubic polynomial (=(5/8)5( - l)(t + 1). The index i = 1 corresponds to the vertex nodes, and i = 2 58 NITIN R. ANTIJRKAR corresponds to the centroid nodes in the element. The standard one-dimensional convec- tiondiffusion problem has exact solution at the nodes if 25,9 c (Pe) = 2 tanh(Pe/2) l + (3/Pe)coth(Pe/4) - (X/Pe) - coth(Pe/4), (1 la) c2 = (16/Pe) - 4 coth(Pe/4). (1 lb) In a two-dimensional problem, the tensorial product of equations (10) and (11) provides the function c in the weighting functions described in equation (9). The local Peclet number is computed for each three-node group based on the average velocities at the relevant boundaries in the two-dimensional element 9. There are six such groups (three in the x-direction, and three in the y-direction) and thus, there are 12 upwinding parameters E. The calculations of the Peclet number involve linear distances, which essentially neglect the curvilinear sides of the elements. However, it is a good approximation since flow front is not severely deformed in our problem. The diffusivities are l/Gz for the energy equation and is K/R for the momentum equation. The Petrov-Galerkin weighted residual equations are, -R:= (V.v)$dl=O, s - RL=IvReg +v.VvWfdV (12) + y-PI+(K+)VWidV- s s n.-pI+(lcf)WdS=O, (13) s -Brrc(j:Vv)-Dak,(l-X)” WdV 1 + s VT.VWdV- s (n.VT)WdS=O, (15) V S - RI = s n . (v - ah/&)4(+ = 1) dS = 0. (16) s where, V is the flow domain and S the flow boundary. The boundary terms appear in the energy and momentum equations because divergence theorem is applied to the higher-order terms. The residuals R, R, R, R, and R, correspond to the variables p, v, X, T and h, respectively. The Petrov-Galerkin weighting functions are used only for momentum and energy equations due to the presence of convection terms in these equations. Before integrating the above equations using a nine-point Gaussian quadrature, the equations are mapped in the isoparametric domain (refer to 26 for details) and the boundary conditions are applied. The essential boundary conditions for v and T at the walls; for v, T and X at the inlet of the mold; and for vY at the mid-plane (axis of symmetry) are applied by substituting the boundary conditions for the equations. The natural boundary conditions, namely the symmetry conditions at the mid-plane, the full-slip (zero friction) condition at the contact point, and the zero force at the free surface are implemented by substituting the boundary terms in the residual equations. The kinematic boundary condition at the flow front is incorporated as the governing equation for predicting the flow front locations. The weak form of energy equation is extended to the flow front boundary by evaluating the boundary terms, instead of by imposing any unknown essential or natural boundary conditions 27. Such “free boundary condition”, as denoted by Papanastasiou et al. 27, minimizes the energy functional among all possible choices, at least for various types of creeping flows, and has been successfully used in several applications, including those with high Reynolds numbers. The spatial discretization reduces the time-dependent equations (12)16) to a system of ordinary differential equations, M 2 + R(q) = 0, (17) Flow front advancement in reaction injection molding 59 where, q is the vector of all nodal unknowns, such as pressure, velocities along x- and y-directions, temperature, conversion and locations of the flow front. The matrix M is the mass matrix and R the residual vector. The time-derivatives are discretized by a standard, first-order implicit scheme, Note that the temporal derivatives need to be adjusted for moving tessellation according to aq dq aq dx -=-3 at dt 8X dt (18) (19) where, left-hand side represents the local change of variable with time, the first term on tilt right-hand side rlepresents the total change of variable with time, while the second term on the right-hand side represents convective changes due to moving finite element grids. When equation (19) is substituted in equation (18), a nonlinear algebraic system of equations is obtained. These equations are solved by the Newton iteration scheme. Since the flow front locations themselves are unknowns in these equations, one must be careful in obtaining the derivatives of the residual equations with respect to the flow front locations, as the Jacobian of the isoparametric mapping also depends on these locations 28. The linearized equations are solved using the frontal numerical technique 29. The tessellation is updated at each iteration by the newly found flow front location values, which are determined simultaneously with other variables. The solution at previous time-step is used as initial guess in the Newton iteration for the next time-step. The computations were carried out on an IBM RISC/6000 machine. In all the calculations, a dimensionless time-step of 0.05 and seven elements along the transverse direction (with finer tessellation near the wall) were sufficient to give solutions that are independent of mesh refinement and time step size. Initial length of an element along x-direction was 0.1. The mesh was regenerated when the length of the element exceeded 0.2. 4. RESULTS The axial velocity at the tip of the flow front is expected to be equal to the average velocity of the flow front. In all our calculations, the dimensionless axial velocity u, was equal to 1.000 with a tolerance of 0.1%. In the numerical computations, the reaction rate can be forced to be zero. If the mold temperature is the same as the material temperature, then the results are expected to simulate isothermal injection molding process. The shape of the flow front in this simulation was identical to that reported in the earlier study on injection molding of Newtonian liquids l. Numerical results were further validated by comparing them with the experimental pressure rise data 2 at the inlet of the rectangular mold. Castro and Macosko characterized rheokinetic and thermal properties of two polyurethane RIM systems in their paper. We performed three numerical runs corresponding to three of their experiments involving these RIM systems at various filling times (refer to Table 2 for details). Although the filling times in the numerical runs were identical to those in the experiments, the aspect ratio 6 (= L/2H) of the rectangular mold was kept at 25 to save computational time. When the aspect ratio was increased in proportion to the average velocity while keeping the filling time constant, the differences in the numerical results of velocities, temperatures and conversions were less than 5%. The predicted pressure rise data was scaled by Table 2. Summary of numerical experiments, where X, is the maximum conversion, r, the maximum temperature, and r, the minimum temperature in the mold at the end of filling Experiment # 1 (9/4/l) 2 (912913) 3 (6,738) Material exp. exp. 2200 2H (cm) 0.32 0.32 0.64 t 25.0 25.0 25.0 Filling time (set) I.11 2.65 2.46 T, (“C) 74. I 21.3 65.0 To 49.3 50.8 60.0 X, 0.85 0.85 0.65 X mtix 0.05 0.14 0.60 T, I .08 I .03 I.18 T nil” 1.00 0.93 1.00 60 50 r Run NITIN R. ANTURKAR P / Time (s) Fig. 1. Comparison of the experimental data represented by symbols with the numerical predictions represented by lines. the appropriate aspect ratio of the experimental investigation. The comparisons of the measured and predicted pressure rise at the inlet of the rectangular mold are shown in Fig. 1. Note that the increase in viscosity is marginal for first two experiments because the filling times are much smaller than the gelling times. Therefore, the pressure rise at the entrance of the mold is linear and represents the length of the mold filled. However, the injection rate is much slower in the third experiment. Therefore, viscosity increases substantially during mold filling, and the pressure rise curve is not linear. In all these cases, the predictions compared well with the experimental data. In fact, the predictions were better using our model than those in 2 for experiment #3, in which substantial extent of reaction occurs during filling. These better agreements are probably due to the accurate simulation of the flow front, and that of the heat transfer in thicker mold without any simplifying assumptions. The accuracy of the Petrov-Galerkin method is compared with conventional Galerkin method in Fig. 2. In this figure, temperature profiles along the flow direction at various transverse locations are plotted for the two formulations when the flow front reaches at the end of the mold. Severe artificial oscillations are observed near the flow front at all transverse locations when the temperature profiles are obtained by conventional Galerkin formulation. These oscillations disappear when the Petrov-Galerkin formulation is used with identical mesh refinement. Thus, the Petrov-Galerkin formulation is clearly superior for accurate calculations in the advancing flow front in RIM. h 1.16 I .08 Num. Method - Petrov-Galerkin I .oo I I I I I I I I 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1 .oo x/e, flow direction Fig. 2. Comparison of temperature profiles along the flow directon at various transverse locations, obtained by the Galerkin and Petrov-Galerkin formulations for experiment #3. Flow front advancement in reaction injection molding 61 0.8 0.6 I I I I I 0 0.77 0.78 0.79 0.80 0.81 0.82 0.83 X/E, flow direction Fig. 3. Prediction of the shape of the flow fronts just before the end of mold filling for experiments # 1 and #3. Finally, representative results of the front profiles corresponding to experiments # 1 and 3 at the end of mold filling are illustrated in Fig. 3. As material advances in the mold, the maximum temperature moves from the wall to the center due to the heat evolution from the reaction, which can not be removed by conduction. The conversion follows the temperature profile. However, the viscosity is strongly dependent on the conversion, and the rise in temperature near the wall is not large enough to offset the viscosity rise due to higher conversion. Therefore, there is more resistance to the flow near the wall. This surging effect is evident in the front profile of experiment #3. In contrast to the previous assumptions 2,4, those flow fronts are not flat, which is expected from the experimental observations 11. 5. CONCLUSIONS Accurate predictions near the flow front region play a major role in predicting fiber orientations and bubble growth in reaction injection molding (RIM). The accuracy is improved in this model by incorporating three important features. 1. No assumptions were made regarding the shape of the flow front or the distribution of primary variables in the flow front region. 2. The Petrov-Galerkin formulation was incorporated instead of conventional Galerkin formu- lation to avoid spurious oscillations due to dominant convection terms in the energy equation. 3. The kinematic boundary conditions on the free surface is incorporated as a governing equation, and thereby, the shape of the flow front is calculated simultaneously along with other variables using the free-surface parameterization technique. The numerical results are validated by comparing them with the experimental pressure rise data. The results are in excellent agreement with the experiments, even close to the gel point. The spurious oscillations observed near the flow front region in the Galerkin method are suppressed by using the Petrov-Galerkin method, which is superior for accurate predictions of the advancing flow front in RIM. 1. 2. 3. 4. 5. 6. 1. REFERENCES D. J. Coyle, J. W. Blake and C. W. Macosko, The kinematics of fountain flow in mold filling. AZChE J. 33, 1168 (1987). J. M. Castro and C. W. Macosko, Studies of mold filling and curing in the reaction injection molding. AIChE J. 28, 250 (1982). N. P. Vespoli and C. C. Marken, Heat transfer and reaction effects during mold filling of fast reacting polyurea RIM systems. Presented at the Annual AIChE Meefing, New York (1987). M. A. Garcia, C. W. Macosko, S. Subbiah and S. 1. Guceri, Modeling of reactive filling in complex cavities. Int. Polym. Processing 6, 73 (1991). C. D. Lack and C. A. Silebi, Numerical simulation of reactive injection molding in a radial flow geometry. Polym. Eng. Sci. 28, 434 (1988). R. E. Hayes, H. IH. Dannelongue and P. A. Tanguy, Numerical simulation of mold filling in reaction injection molding. Polym. Eng. Sci. 31, 842 (1991). N. R. Anturkar, An advancing flow front in RIM. Polym. Eng. Sci., in press (1995). 62 NITIN R. ANTURKAR 8. P. M. Gresho and R. L. Lee, Dont suppress wiggles-theyre telling you something. In Finite Element Methods for Convection-Dominated Flows (Edited by T. J. R. Hughes), AMD Vol. 34. ASME, New York (1979). 9. P. M. Adornato and R. A. Brown, Petrov-Galerkin methods for natural convection in directional solidification of binary alloys. Int. J. Numer. Meth. Fluids 7, 761 (1987). 10. A. N. Brooks and T. J. R. Hughes, Streamline upwind/PetrovGalerkin formulation for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Meth. Appl. Mech. Eng. 32, 199 (1982). 11. T. J. R. Hughes, M. Mallet and A. Mizukami, A new finite element formulation for computational fluid dynamics: II. Beyond SUPG. Comput. Meth. Appl. Mech. Eng. 54, 341 (1986). 12. A. C. Galeao and E. G. Dutra do Carmo, A consistent approximate upwind PetrovGalerkin method for convection-dominated problems. Comput. Meth. Appl. Mech. Eng. 68, 83 (1988). 13. P. A. Tanguy and J. M. Grygiel, A slightly compressible transient finite element model of the packing phase in injection molding. Polym. Eng. Sci. 33, 1229 (1993). 14. J. M. Grygiel and P. A. Tanguy, Finite element solution for advection-dominated thermal flows. Comput. Meth. Appl. Mech. Eng. 93, 277 (1991). 15. T. J. R. Hughes, L. P. Franca and G. M. Hulbert, A new finite element formu
- 温馨提示:
1: 本站所有资源如无特殊说明，都需要本地电脑安装OFFICE2007和PDF阅读器。图纸软件为CAD,CAXA,PROE,UG,SolidWorks等.压缩文件请下载最新的WinRAR软件解压。
2: 本站的文档不包含任何第三方提供的附件图纸等，如果需要附件，请联系上传者。文件的所有权益归上传用户所有。
3.本站RAR压缩包中若带图纸，网页内容里面会有图纸预览，若没有图纸预览就没有图纸。
4. 未经权益所有人同意不得将文件中的内容挪作商业或盈利用途。
5. 人人文库网仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对用户上传分享的文档内容本身不做任何修改或编辑，并不能对任何下载内容负责。
6. 下载文件中如有侵权或不适当内容，请与我们联系，我们立即纠正。
7. 本站不保证下载资源的准确性、安全性和完整性, 同时也不承担用户因使用这些下载资源对自己和他人造成任何形式的伤害或损失。
人人文库网所有资源均是用户自行上传分享，仅供网友学习交流，未经上传用户书面授权，请勿作他用。
川公网安备: 51019002004831号