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附錄A
Dynamic Simulation of an Injection Molding
Author1, Author2, Author3.
Applied Thermal Engineering, 2016, 8(6):556-568.
Abstract: An integrated design method is discussed which thoroughly considers related parameters of the various subsystems in order to optimize the overall system that mainly consists of opto--mechanical structure CAD, CAE and the integrated information platform PDM. Based on the parameter drive of the virtual main model, the method focuses on the model transformation and data share among different design and analysis steps, and so the concurrent simulation and design optimization are carried out. As an example of application, the integrated design for a large-scale opto-mechanical structure is introduced, including optical design, structure design and analysis, which further validates the advantages of the method. Due to comprehensive consideration of the design and analysis process by CAD and CAE based on PDM, the integrated design well attains the structure optimization with high efficiency.
Keywords: integrated design; CAD/CAE; large-scale structure; optical instrument.
1. Introduction
The analysis of products integrating different technologies, e.g. mechanical, hydraulic and controls systems, becomes more and more feasible with the constant development of simulation software and more performing computer hardware. The combination of specialized software packages is possible and allows the simulation of so-called mechatronic systems. If in the past such tools were mainly used in the aeronautic and automobile industries, they now find their way into more common engineering applications. In this case,the dynamic characteristics of the clamp unit of an injection molding machine from HUSKY is investigated. For this purpose, the finite-element (FE) program ANSYS, the multi-body simulation (MBS) software ADAMS, the fluid power simulation software DSHplus and the controls design tool MATLAB/Simulink are used. Combining these different simulation tools and applying them to the damp unit, we can analyze and understand the dynamic behavior of the machine and the interaction between the different sub-systems. This is necessary to improve the performances, like reducing wear, cycle time or noise, or avoiding premature failure of parts.
The damp unit Is the mechanism that doses and opens the mold and keeps it effectively closed during the injection and the holding-pressure stages. The HUSKY OUADLOC' damp is a two-platen hydraulic damping system. The main components are the moving platen, the clamp base and the stationary platen with the four tie bars. The platen locking and the damping force are realized with the damp pistons, which are integrated in the moving platen. The damp pistons can be rotated by 45' to engage the tie bar teeth in order to lock the moving platen in its position. The main functions of the damp unit are actuated hydraulically;hydraulic pressure is applied to the damp pistons to generate the necessary damping force and two hydraulic cylinders are used for the displacement of the moving platen. [1]
Figure1: HUSKY QUADLOC clamp unit
The analysis focuses on two aspects: first, the quantification of the forces acting on the pads between the damp base and the foundation in order to foresee and prevent any creep of the machine during operation, and second, the optimization of the stroke command signal in order to reduce the overall cycle time. Therefore the simulation model Is limited to the moving platen stroke.
2． Simulation Models
The mechanical, hydraulic and controls systems are modeled in ADAMS, DSHplus and MATLAB/Simulink, respectively. ADAMS gives the possibility to Include non-standard phenomena by linking user-written FORTRAN or C subroutines In the model. DSHplus uses this feature to make a co-simulation between both programs possible. Besides, ADAMS disposes of a plug-In that allows the user to conned the MBS model with Simulink. Thus it is possible to link the three simulation tools and simulate the complete machine. There are two
possibilities for the computation: first, each program Integrates its own set of differential equations and exchanges the necessary parameters with the other ones, second, the three models are completely integrated and only the Slmulink solver Integrates the differential equations set.
Figure2:co-simulation of moving platen stroke
Additionally, the flexibility of mechanical parts can be included in ADAMS. We use ANSYS to generate the necessary FE models and to reduce these large models to a few degrees of freedom before being integrated Into ADAMS. The reduction method Is based on the component mode synthesis technique Introduced by Craig and Bampton.
Mechanical Model
The rgid-body model of the damp unit Is very simple and consists only of two parts: the moving platen and the stationary platen with damp base and tie bars (refer to figure 4). The damp base is fixed with linear spring-damper elements to the ground and the sliding of the moving platen is modeled with contact statements. Basically, the contact statement is a nonlinear spring-damper element where the force is proportional to the penetration depth x and the penetration velocity it :x
k and d are the contact stiffness and damping coefficients, respectively and a is an exponent that for numerical reasons should be chosen greater then 1. If there is no penetration, then no force is applied, otherwise the location of contact, the normals at the points of contact and the force acting between both parts are computed. The statement also includes a Coulomb friction model. The transition from the static to the dynamic friction coefficient Is based on the relative velocity of the two colliding geometries. Finally, the two stroke cylinder forces and a contact statement are defined between both platens. In order to have a more accurate mechanical model, also In view of a more realistic distribution of the forces on the damp-base pads, the different parts are included as flexible bodies. These flexible bodies are derived from FE models that are reduced before being imported. The reduction method Implemented In ADAMS is based on the component mode synthesis (CMS) technique, i.e. the deformation is written as a linear combination of mode shapes. In ADAMS, constraint modes and fixed-boundary normal modes are used to generate the component-made matrix 0. This approach is known as the Craig-Bampton method. In the following, the basic principles and steps of Integrating flexible bodies In ADAMS are shown; a more detailed theoretical presentation can be found in
First of all, a FE model Is created that is detailed enough to comedy represent the mode shapes of interest. The user has then to choose the nodes that serve as interface to the MBS model. The kinematic constraints or forces are applied to these boundary nodes; the remaining nodes are referred to as interior nodes.
By fixing the degrees of freedom (DOF) u, of the boundary nodes and solving an elgenproblem, we get the fixed-bounder, normal modes d>r. This normal mode set is usually truncated. The constraint modes dc are defined as the static deformation of the structure when a unit displacement Is applied to one DOF of a boundary node while the remaining DOF of the boundary nodes are restrained (Guyan reduction). Finally the component mode reduction matrix m Is defined by the normal modes set φand the constraint modes set d>r.
The relationship between the physical displacement coordinates u and the component generalized coordinates q is
With equation (2) the generally large number of physical DOF u is drastically reduced to few mixed physical and modal DOF q.
However, the Craig-Bampton modal basis q has certain disadvantages that make it sometimes difficult to directly use it in a multi-body simulation. The set of constraint modes contains the 6 rigid-body DOF that must be replaced by the large displacement DOF of the local body reference frame in ADAMS. They have to be removed and therefore the component-mode matrix Is transformed by solving the eigenproblem
where K and M are the reduced stiffness and mass matrix, respectively. The manipulation results In a modal basis where q - N4; N containing the elgenvectors from equation (3).
The last step Is a purely mathematical approach and does not further reduce the number of DOF. The new modal basis q has no direct physical meaning anymore but addresses the problems mentioned above
Table 1: First 13 eigenfequencies of the moving platen
The motion of a flexible body is derived from the same equation as for a rigid-body, I.e. Lagrange's equations. In order to calculate the kinetic and potential energy, the position and velocity of an arbitrary point on the flexible body Is expressed with the generalized coordinates.
M the generalized mass matrix depending on,
K the generalized stiffness matrix only depending on q
V the gravitational energy,
D the damping matrix defined using modal damping ratios Is
Q the kinematic constraint equations applied to the flexible body.
Adding flexible bodies to an ADAMS model is quite straightforward. Nevertheless, there are some limitations regarding forces and joints that can be defined to them. Especially the problem of a moving force on a flexible body.
I.e. moving platen sliding on clamp base, is an open Issue in multi-body dynamics. However, there are "standard" workarounds which work well and which have proven their usefulness.
The technique Implemented in our flexible-body model is based on the contact statement mentioned above. Basically it works as follows: for each of the selected nodes along the sliding path, a force is computed according to equation
That depends on the relative vertical position y and velocity y of the node to the moving platen.
However, the force is only activated when the node and the moving platen effectively overlap. In fad, It is weighted by a function that depends on the horizontal distance x between the node and the moving platen.
The force is ramped up from zero or ramped down to zero In order to guarantee a smooth application and to minimize any discontinuities.
No contact points and contact normals are computed. The distance and velocity of a node relative to the moving platen are taken In the global coordinate system and the contact and friction forces are always collinear with the coordinate system unit vectors.
Nevertheless, this approach gives acceptable results, as the deformation of the damp base is very small. A Coulomb friction force is applied in the same way.
Figure 3: moving platen sliding model
The main disadvantage is that a huge number of Interface nodes are needed to have any sound representation of the moving contact forces. Unfortunately, this gives a huge number of flexible-body DOF and therefore unacceptable computation times. Now, instead of defining these nodes as interface nodes, they remain interior nodes. From a purely theoretical point of view, the accuracy of the results is not guaranteed anymore when using interior nodes as interface nodes. However, choosing more normal modes can reduce the error. The comparison of a model using interior nodes for the moving platen sliding with one using interface nodes shows a very 9000 Compliance Of the results While having a much taster computation time. Therefore we used this model for the following simulations. Other methods were not tested but some of them are presented in (3) and (4).
The flexible bodies are created in ANSYS. Simplified CAD geometries of both platens were imported In the FE program and meshed automatically with tetrahedral SOLID187 elements. The damp base was generated 'manually" with SHELL63 elements and the tie bars are modeled with BEAM4 elements. Stationary platen, clamp base and tie bars were put together b one assembly and the different components connected via spring-damper elements (COMBIN14). A macro for the computation of the modified Craig-Brampton basis is available In ANSYS. It allows the user to specify the Interface nodes and the number of normal modes. The resulting modal basis Is written to a file that has to be imported Into ADAMS.
The ANSYS macro automatically selects the six DOF of each interface node as u}. However, it is not imperative to select all the six DOF. This allows us to furthermore reduce the number of static modes and thus the number of flexible-body DOF. The macro has been changed accordingly to select only the effectively required DOF ua Finally, the moving platen has 29 flexible-body DOF and the stationary platen, clamp base and tie bars assembly has 95 flexible-body DOF.
Figure4:ADAMS flexible-body model
附錄B
注塑機(jī)的動(dòng)態(tài)模擬
Author1, Author2, Author3.
Applied Thermal Engineering, 2016, 8(6):556-568
摘要：討論了充分考慮相關(guān)的參數(shù)是一個(gè)集成的設(shè)計(jì)方法為各子系統(tǒng)優(yōu)化的整體系統(tǒng)，主要由光電—機(jī)械結(jié)構(gòu)CAD，CAE與PDM集成信息平臺(tái)?；诘奶摂M模型的參數(shù)驅(qū)動(dòng)的方法，側(cè)重于模式的轉(zhuǎn)型的設(shè)計(jì)和分析的步驟之間的數(shù)據(jù)共享，所以并行仿的設(shè)計(jì)進(jìn)行優(yōu)化。作為應(yīng)用實(shí)例，綜合設(shè)計(jì)介紹了一種大型光學(xué)機(jī)械結(jié)構(gòu)，包括光學(xué)設(shè)計(jì)，結(jié)構(gòu)設(shè)計(jì)與分析，進(jìn)一步驗(yàn)證了該方法的優(yōu)點(diǎn)。由于分析了基于PDM和CAD和CAE過程的設(shè)計(jì)，集成設(shè)計(jì)達(dá)到結(jié)構(gòu)優(yōu)化效率高。
關(guān)鍵詞：集成設(shè)計(jì)：CAD / CAE：大規(guī)模的結(jié)構(gòu)：光學(xué)儀器
1. 介紹
產(chǎn)品整體不同技術(shù)的分析，例如，機(jī)械、液壓、控制系統(tǒng)，模擬軟件可持續(xù)發(fā)展和更多計(jì)算機(jī)硬件操作變得越來越可行。結(jié)合特殊的軟件程序包是可以和允許對(duì)所謂的機(jī)電一體化系統(tǒng)模擬的。如果在過去這些工具被應(yīng)用與航空和汽車工業(yè)中，那么他們現(xiàn)在會(huì)找到更多應(yīng)用工程技術(shù)的相同點(diǎn)。因此，被研究的是HUSKY注塑機(jī)夾緊裝置的動(dòng)態(tài)特性。ANSYS有限元（FE）程序，ADAMS多維模擬軟件，DSHplus流體動(dòng)力模擬軟件和MATLAB仿真設(shè)計(jì)控制工具都被用于這個(gè)目。結(jié)合這些不同的模擬工具并應(yīng)用它們于合模機(jī)構(gòu)，我們就能分析和理解機(jī)器的動(dòng)態(tài)行為和不同子系統(tǒng)之間的聯(lián)系。這就需要去提高性能，像減少磨損、循環(huán)時(shí)間或噪音，或者避免部件早期的錯(cuò)誤。
合模機(jī)構(gòu)是一個(gè)開啟與合上模具并能夠在注塑和保壓階段有效的緊閉的機(jī)構(gòu)。HUSKY QUADLOCTM合模機(jī)構(gòu)是一個(gè)二板式液壓合模系統(tǒng)。主要由動(dòng)模板，合模工作臺(tái)，定模板和四個(gè)拉桿構(gòu)成。模板鎖定和合模壓力是通過動(dòng)模板整合的合模栓塞實(shí)現(xiàn)的。合模栓塞可以旋轉(zhuǎn)45度去嚙合拉桿螺紋為了保證動(dòng)模板在注塑位置上。合模機(jī)構(gòu)的主要功能是驅(qū)動(dòng)液壓油：液體壓力被施加在合模栓塞上去產(chǎn)生需要的合模壓力并且兩個(gè)油缸被用于動(dòng)模板的移動(dòng)[1]。
分析的焦點(diǎn)集中在兩個(gè)方面：第一，壓力作用在工作臺(tái)之間的襯墊上和為了預(yù)見的基礎(chǔ)并阻止機(jī)器在運(yùn)轉(zhuǎn)中爬行。第二，為了減少總體循環(huán)時(shí)間的最優(yōu)化的噴射控制信號(hào)。因此，模擬模型被限制移動(dòng)模版的注射。
2. 模擬模型
機(jī)械，液壓，控制系統(tǒng)被分別的在ADAMS, DSHplus和MATLAB仿真中模擬。ADAMS可能包括由鏈接FORTRAN書面使用和C程序在模型中引起的不標(biāo)準(zhǔn)的現(xiàn)象。DSHplus利用這個(gè)特點(diǎn)在兩個(gè)可能的程序上建立了一個(gè)co模擬。另外，ADAMS處理插件允許使用者用模擬鏈接MBS模型。因此，鏈接三個(gè)模擬工具和模擬整個(gè)機(jī)器是可能的。這里有兩個(gè)可能估計(jì)：第一。各個(gè)整合它自己不平衡的部分并和其他的部分交換參數(shù)。第二，三個(gè)模型被完全的整合并只有模擬求解整合不同的因素部分。
圖1 HUSKY QUADLOCTM合模機(jī)構(gòu)
此外，柔性的機(jī)械部件可以包括在ADAMS中。我們用ANSYS產(chǎn)生必要的FE模式，并在被納入ADAMS之前降低這些大型模型自由度。
減少自由度方法是基于引用Craig和bampton的組件式合成技術(shù)這是必要的。
圖2 模型的聯(lián)合仿真
2.力學(xué)模型
合模機(jī)構(gòu)的剛性模型很簡(jiǎn)單,只分為兩個(gè)部分: 移動(dòng)模板和固定模板和合模工作臺(tái)還有拉桿（參見圖4）。合模工作臺(tái)是固定在地面上裝有線性彈簧-阻尼單元和滑動(dòng)的動(dòng)模板構(gòu)成報(bào)表式的模型?；旧?，報(bào)表式是一個(gè)穿透深度X和滲透速率X與壓力成正比的非線性彈簧-阻尼單元K和d分別的是接觸剛度和阻尼系數(shù)， e是一個(gè)指數(shù)，由于數(shù)值原因應(yīng)選擇大于1。如果沒有滲透，那么就沒有壓力作用，否則就會(huì)有接觸，正常應(yīng)在接觸點(diǎn)和作用力兩部分之間計(jì)算。該報(bào)表還包括了一個(gè)庫侖摩擦模型。從靜態(tài)到動(dòng)態(tài)的摩擦系數(shù)的變化，是基于相對(duì)速度的兩個(gè)幾何碰撞。最終，在兩個(gè)模板之間定義了兩個(gè)液壓缸的壓力和接觸報(bào)表。為了有一個(gè)更準(zhǔn)確的力學(xué)模型，同時(shí)，鑒于更為實(shí)際的分配作用在合模工作臺(tái)上的力，他的不同部分被列為柔性機(jī)構(gòu)。這些柔性機(jī)構(gòu)是來自在被輸入之前減少了的FE模式。這種在ADAMS里減少方法的實(shí)施是基于組件式頻率合成器( CMS )中的技術(shù)，即變形是被看作是線性組合模式形狀。在ADAMS里，約束模式和固定邊界的正常模式是用來生成組件矩陣模式Ф。這種方法被稱為Craig-Bampton方法。接下來，在ADAMS中基本的原則和柔性體積分的步驟被展示：更詳細(xì)的理論介紹可以在[2]式中看到。一個(gè)FE模型的建立可以足夠詳細(xì)的正確表達(dá)出模型的重要性。操作者這時(shí)可以選擇充當(dāng)MBS模型的邊界作為節(jié)點(diǎn)。被約束的運(yùn)動(dòng)和力被施加在這些邊界節(jié)點(diǎn)上；其余的節(jié)點(diǎn)稱為內(nèi)部節(jié)點(diǎn)。由固定在邊界節(jié)點(diǎn)上的自由度（DOF）和求解特征，我們得到固定邊界常態(tài)模量，這個(gè)正常的設(shè)定模式通常是截?cái)?。約束模量被定義為當(dāng)其余邊界節(jié)點(diǎn)自由度都受約束時(shí)，一個(gè)元件施加在一個(gè)邊界節(jié)點(diǎn)的一個(gè)自由度的靜態(tài)結(jié)構(gòu)的變形。最后組成還原矩陣的模式被解釋為常態(tài)設(shè)定模式和約束設(shè)定模式。實(shí)際位移坐標(biāo)u和組成廣義坐標(biāo)q之間的關(guān)系是
在方程（2）中，普遍的大量的自由度u被徹底的減少到只有少數(shù)混合現(xiàn)實(shí)和虛擬的自由度q。然而，Craig-Bampton的基礎(chǔ)形態(tài)q也有一些毫無疑問的缺點(diǎn),使有時(shí)在多維仿真中難以直接利用它。這套約束模式包含6個(gè)剛體自由度，必須取而代之在ADAMS中主體局部的大位移自由度。它們必須被移除，因此在求解方程中，結(jié)構(gòu)模型的矩陣被轉(zhuǎn)化。
其中k和m在矩陣中分別代表降低的剛度和質(zhì)量。在基礎(chǔ)模量上處理的結(jié)果是；N包含的特征在方程（3）中被表現(xiàn)。
最后一步,是一個(gè)純粹的數(shù)學(xué)方法,并沒有進(jìn)一步減少自由度的數(shù)量。新的基礎(chǔ)模量就沒有了直接的物理意義了,而是針對(duì)上述的問題。
柔性體的運(yùn)動(dòng)模型是與剛性體來自同一方程，即拉格朗日方程。為了計(jì)算動(dòng)能和勢(shì)能，柔性體上任意點(diǎn)的位置和速度是由廣義坐標(biāo)表示的。
x，y，z，Ψ，θ，Φ，為局部參照系附加彈性體和描述六個(gè)剛體模式的坐標(biāo)。最終形式的運(yùn)動(dòng)方程是
其中ξ 為廣義坐標(biāo)，
M 依賴于ξ的廣義質(zhì)量矩陣，
K 只取決于的廣義剛度矩陣，
D 阻尼矩陣定義模態(tài)阻尼§，因此D是對(duì)角線，
Ψ 適用于柔性體運(yùn)動(dòng)學(xué)約束方程，
λ 拉格朗日乘數(shù)，
Q 廣義應(yīng)用的力。
另外，一個(gè)柔性體在ADAMS模式下相當(dāng)?shù)闹苯亓水?dāng)。不過，也有一些力量和關(guān)節(jié)限制，我們可以界定給它們。特別是在一個(gè)柔性體上摩擦力的問題，即動(dòng)模板在工作臺(tái)上滑動(dòng)，是一個(gè)多維動(dòng)力學(xué)的開放性問題。然而，它們制定的標(biāo)準(zhǔn)使得運(yùn)行好并且被證明有用。
在我們的柔性模型中，技術(shù)的執(zhí)行是基于上述的表訴。基本上它的模式如下:對(duì)于每一個(gè)沿滑動(dòng)路徑選定的節(jié)點(diǎn)，一個(gè)力根據(jù)作用在動(dòng)模板上垂直位置和速度的關(guān)系的方程（1）進(jìn)行計(jì)算。然而，力只是在當(dāng)節(jié)點(diǎn)和動(dòng)模板的重疊部分起作用時(shí)才作用。事實(shí)上，重量的函數(shù)是基于節(jié)點(diǎn)和動(dòng)模板之間的水平距離。力從零斜線上升或斜線降低到零是為了保證應(yīng)用能順利和盡量減少任何間斷。沒有接觸點(diǎn)和接觸平均值計(jì)算。節(jié)點(diǎn)的距離和速度相對(duì)于動(dòng)模板應(yīng)采用總的坐標(biāo)系統(tǒng)和適用于矢量單元坐標(biāo)的接觸和摩擦力。不過，這種做法是能夠接受的結(jié)果，正如變形的合?；鶖?shù)很小。庫侖摩擦力適用于同樣的方法。
主要缺點(diǎn)是大量的分界節(jié)點(diǎn)都需要有充分代表性的移動(dòng)接觸力。不幸的是，這有太多的柔性體自由度和并且無法計(jì)算次數(shù)?，F(xiàn)在，并不是把這些節(jié)點(diǎn)作為邊界節(jié)點(diǎn)，他們?nèi)允莾?nèi)部節(jié)點(diǎn)。從純理論的角度看，當(dāng)使用內(nèi)部節(jié)點(diǎn)作為邊界節(jié)點(diǎn)時(shí)結(jié)果的準(zhǔn)確性無法保證。然而，更多的選擇標(biāo)準(zhǔn)模式，可以減少誤差。比較采用內(nèi)節(jié)點(diǎn)的模型對(duì)對(duì)應(yīng)采用表面節(jié)點(diǎn)的滑動(dòng)模板會(huì)有一個(gè)非常一致的結(jié)果，同時(shí)還會(huì)加快計(jì)算速度。因此，我們使用這一模型進(jìn)行模擬后，其他方法都沒有測(cè)試過，但它們中的一些曾在上述中
圖3 動(dòng)模板彈性模型
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