new x abstract - wit press · 2014. 5. 14. · injection molding is a general manufacturing process...

Visualization software for injection molding

F. Trochu, D. Gour, M. AudetX

Mechanical Engineering, Ecole Poly technique,

5%cc.VT, MonWa/, Quebec,

ABSTRACT

Injection molding is a general manufacturing processused in various areas: metal casting, fabrication ofplastic parts and composite materials, etc. Thenumerical simulation of mold filling can help themold designer to properly position the injectionports and air vents so as to ensure an adequatefilling of the mold. As finite elements are usedincreasingly to model the injection flow, the needfor a specialized visualization software has arisento simulate the real-time progression of the flowfront and to display the temperature and pressurefields inside complex three-dimensional molds. Thebasic requirements of such an interface will beexamined in the scope of finite element analysis.As an illustration of these concepts, the computerprogram Visuflot developed for resin transfermolding (RTM) is described. A video showingexamples of real-time simulations will also bepresented.

Transactions on Information and Communications Technologies vol 5, © 1993 WIT Press, www.witpress.com, ISSN 1743-3517

378 Visualization and Intelligent Design

INTRODUCTION

A general software was developed during the summerof 1991 at Ecole Polytechnique[l] to visualize theflow front and pressure field calculated to simulatethe filling of complex three-dimensional molds usedin the manufacturing of composite materials.Although it was initially designed for a particularmanufacturing process, namely resin transfer molding(RTM), its general features make it suitable forapplication to any type of injection moldingsimulation: thermoplastic flow analysis, metalcasting, etc.

The purpose of this paper is to analyze thegeneral software requirements of an injectionmolding simulation and to describe solutions devisedto address these particular needs. An example ofimplementation is provided by program Visuflot,which was developed initially for resin transfermolding. Outputs from Visuflot permit to illustratethis approach, which remains general and can beapplied to any kind of injection process.

The first part of the paper presents theprogramming philosophy of Visuflot and sums up theadvantages of object oriented analysis for thedevelopment of software applications. The secondpart discusses the particular problems of injectionmolding, namely (1) the choice between a fixed gridor a moving mesh to follow the changing shape of theflow front as the fluid fills up the mold and (2)the methodology adopted to advance the flow front ateach time step. Finally, as an illustration ofthese concepts, output results from Visuflot arepresented and the basic requirements of avisualization software for injection molding arestated.

OBJECT ORIENTED DESIGN PHILOSOPHY

This work is part of a trend in software developmentmade possible by the advent of object orientedprogramming[2]. Although it would be difficult todevelop a general purpose program for injectionmolding because each process is governed bydifferent mathematical equations, a great number of


Visualization and Intelligent Design 379

software modules remain identical, in particular themesh generation and visualization modules.

Object oriented programming provides a generalframework for software analysis[3]: the design ofprogram modules is intimately connected with thespecification of data structures, both being"encapsulated", so to say, in what is called asoftware object. Each object can be made completelyindependent from the rest of the system, thecommunication between the various modules beingassured by specialized input-output functions. Thispermits to concentrate on the design of each objectas a whole, without having to worry about itsconnections with other objects.

Object oriented programming has made possiblethe creation of specialized software modules generalenough to be reutilized systematically. Thesoftware is specialized in the sense that itexecutes specific tasks. But at the same time, itis general enough so that the basic componentmodules can be combined easily to create newapplications. An example of a successful objectoriented software is provided by the OSF/Motif userinterface and the X-Window toolkit, which have nowbecome a standard for user interfaces on UNIX basedworkstations. The interface of program Visuflot iswritten with OSF/Motif.

A new generation of application software isbased on object oriented programming. This approachhelps to free end-users from a dependency upon huge"black boxes", i.e., the kind of program designed toincorporate all what the users might need. Theseprograms have progressively grown to become"software monsters", relying heavily on vasthardware resources and highly sensitive to thecomputer system's environment. Everything must beplanned through a complex design procedure by spe-cialized software developers before any new featurecan be added. This kind of program is not flexibleand permits to accomplish only pre-programmed tasks.

On the contrary, the new generation of objectoriented software gives end-users the opportunity todevelop rapidly a specific application, using asbuilding blocks the objects provided by the system'slibrary. In this approach, however, the user musthave a basic knowledge of programming, although heneeds not be a specialist. It is sufficient for himto use the system's library as a tool for the



purpose of his own application. The ACIS system[4]in geometric modelling is a good example of asuccessful software based on object orientedprogramming. The same kind of development is likelyto occur in the field of finite element analysis,graphic applications, animation, etc.

COMPUTER SIMULATION OF INJECTION MOLDING

The main issue in the simulation of mold filling isthe numerical treatment of the transient freesurface or moving boundary. The resin enteringinside the mold is constantly changing shape as itflows, so it is necessary to redefine the geometryof the saturated domain during the simulation. Inthe moving boundary approach, a new mesh is

Figure 1. Example of fixed grid for a subwayseat.



generated at each time step. The mesh generationcould soon become the most tedious part of thesimulation as experienced in [5] for example. Otherproblems occur when this approach is used. Forexample, it is difficult to divide the flow frontinside molds with inserts or to merge the frontscoming from multiple injection ports. In order toovercome these limitations, it is easier to performthe simulation on a fixed grid (figure 1) . But thisrequires the development of a special technique tofollow the progression of the fluid flow on a fixedgrid.

Fill _ factors associated with the elements of themeshThe geometric domain representing the mold isdecomposed into a finite number of solid elements asshown in figure 1 for a subway seat. In the fixedgrid approach, a fill factor f, 0 < f < 1, isassociated to each element in order to track theprogression of the flowfront. These coeffi-cients represent thel e v e l of f l u i dsaturation inside anelement (see figure 2) .If f = 0, the element isempty; when f = 1, it issaturated. The satura-tion coefficients varywith time from 0 to 1inside each element. Atthe end of the fillingprocess, they become 1for all the elements.Note that the fillfactors employed by mostinvestigators [6,7] areassociated with the

with

volumeelement

mdel v°lume element.

The fixed grid approach presents acomputational advantage over moving grid techniquessuch as used in [5-8] because it is no longernecessary to reconstruct the mesh for eachiteration. Moreover, the mesh generation can becomerather complicated in the case of dividing ormerging flow fronts. The drawback of the fixedgrid, however, is a relative loss of accuracy in theshape of the resin front. Nevertheless, this



problem can be overcome by increasing the density ofthe grid and by smoothing the front lines. Therelative loss in accuracy arising from the mesh mustbe contemplated in the scope of the otherapproximations that come into play, namely theapproximation error of the boundary value problemitself.

specifiedflow rateor injectionpressure

Calculation of the flowThe usual strategy tomodel an injectionmolding process is toconsider the domain nfilled up at a giventime by the fluid (seefigure 3). The viscousflow of a Newtonianfluid is described bythe pressure field p andthe velocity vector V ofany fluid particle. Themathematical equationsthat govern the steadystate flow can be solvedinside n for theboundary conditionsindicated in figure 3.At the injection port,either the pressure orthe flow rate isconstant. There is no flow through the impermeablemold walls, i.e., the normal velocity vanishes onthe mold boundary. Finally, along the flow front,the boundary condition is p = 0. The solution of theflow equations yields the pressure and the fluidvelocity everywhere in n.

The knowledge of the pressure distributioninside each element permits to verify the integrityof the mold during the filling process. The fluidvelocity along the flow front gives the fluid massflowing through each element k of the front duringtime increment At (see figure 3)

Figure 3. Solution of theflow problem in the fluidsaturated part of themold.

At (1)

where y* is the velocity vector, n* the outward unitvector normal to the front profile on element k andAI the lateral area of element k on the flow front.



It is important for the numerical scheme toconserve the fluid mass, because this is the basicvariable that can be controlled during a fillingprocess. This can be achieved by using non-conforming finite elements as presented in [1,9].In order to respect also the balance of mass whenmoving the flow front at -each time step, thefollowing simple algorithm was devised.

Progression of the flow frontA new position of the flow front can be deduced ateach time step from the previous one by updating thefill factors of the elements adjacent to n. The waythe algorithm proceeds is indicated in figure 4 inthe simple case of triangles. Two types of boundaryelements are considered: elements with one incomingflow (case 1) and elements with two incoming flows(case 2). Note that this approach based on fluidmass conservation can be generalized to any kind ofmold discretization (prismatic elements, tetra-hedrons, etc.) and applied to any type of injectionprocess.

For the algorithm to work correctly, it isnecessary to allow a temporary overflow inside theelements adjacent to the flow front. Finally, aftereach iteration, a new saturated domain is created.The flow equations can be solved again in this newdomain and the simulation is ready for a newiteration. Note that this algorithm is stable byitself when applied directly to simulate a fillingprocess on a fixed grid. It permits to reproducethe experimental shape of the flow front forisotropic flows[10].

R, R,

case 1: one incoming flow case 2: two incoming flows

R •" A,+ A,

R. • R, + R.

Figure 4. Evacuation of the overflow fromtriangular elements.



The choice of the time step At is important.It must not be too large for the accuracy of thesteady state approximation to remain valid. Itcannot be too small either if the flow front is tomove forward. Actually, when the front becomeslarger, its average velocity V decreases. The beststrategy consists in increasing progessively At sothat the average displacement of the front Ax = 7 Atremains approximately constant throughout thesimulation.

REQUIREMENTS OF A VISUALIZATION SOFTWARE

FOR INJECTION MOLDING

The calculation of the filling process is performedoff-line by program Plot (finite element analysis).At each time step the pressure and velocity arecomputed in the saturated part of the mold and theposition of the flow front is updated accordingly.For a typical three-dimensional mold with 5000degrees of freedom, the computation may last from 45minutes to one hour on a RISC/6000 workstation. Theoutput of Plot is stored on a file, ready forinteractive visualization by program Visuflot.

A visualization software for injection moldingshould be able to represent on the computer thereal-time filling process. This task is not as easyas it might seem, because of the large number ofvolume elements that must be updated in real-time.This capability of program Visuflot will beillustrated by a video. Note that the graphic partof Visuflot is programmed in GL, the "GraphicsLanguage" available either on Silicon Graphics orIBM workstations.

The simulation of the flow can be rendered at arequested speed in direct or reverse mode, i.e., forthe filling or unfilling of the mold. It is notalways possible due to hardware limitations todisplay the filling process with its actualvelocity. Then the program automatically performsthe filling at the maximum possible speed andsignals this limitation to the user via a red lightappearing on the control panel.

Successive positions of the flow front mustalso be recorded on a single image for subsequentanalysis (see figure 5). Since the injection takesplace usually in complex three-dimensional molds, it



is important to posi-tion the object inspace at the sametime as the simula-tion is performed.This can be done withVisuflot via thecontrol panel, amenu-driven interfaceallowing to position,scale and magnify themold.

A sophisticatedvisualization programmust also display thesaturated and/or non-saturated flow frontsbecause this helps toverify and validatethe numerical scheme.The saturated frontis defined as theboundary between the Figure 5 Example offully saturated (f=i) successive positions of theand partly saturated fl°* front.volume elements(0<f<;i) . The non-saturated front is the boundarybetween the partly saturated (0<f<l) and emptyelements (f=0). The real front lies in between thesaturated and non-saturated flow fronts. Byinterpolating the fill factors of each element, itis possible to obtain an estimated position of thereal front. Since all the surfaces representing thefronts are defined in a three-dimensional space, itis important to use shading to display the flowfronts. Examples of shaded fronts will be presentedin the video.

Finally, another important feature is theability to display the pressure field in the mold(see figure 6) . This can be achieved at each timestep either by a color gradation or by assigningdifferent colors on a scale of pressure intervals.Note that if the pressure inside the mold exceeds apreset given value, either a bell is rang or thecorresponding volume element is colored in red.



Figure 6. Example of pressure distribution inthe mold of a subway seat.

CONCLUSION

The analysis is performed on a fixed grid and a fillfactor, representing the fraction of each elementaryvolume occupied by the fluid, is associated witheach element of the mold. This permits to simulatethe case of dividing or merging fronts inside moldscontaining interior obstacles or with multipleinjection ports. An important feature of anumerical scheme for the simulation of an injectionprocess is the ability to conserve the fluid mass.This principle is respected by the algorithmproposed here to advance the flow front on a fixedgrid, which is stable and can be applied to any typeof injection process. A visualization software for



injection molding must be able to simulate the real-time filling of complex three-dimensional molds.Successive positions of the flow front must berecorded also on the same image. The pressure fieldinside the mold must be displayed if requested. Allthese requirements are met by program Visuflot,which was developed to visualize the resin transfermolding process, but can be utilized also for anytype of mold filling simulation.

ACKNOWLEDGEMENTS

The authors wish to thank Jean-Frangois Boudreaultand Dong-Ming Gao for their work on the subway seat.This work was supported by the National ResearchCouncil of Canada who is gratefully acknowledged.

REFERENCES

1. Trochu, F., Gauvin, R. and Zhang, Z.'Simulation of Mold Filling in Resin TransferMolding by Non-conforming Finite Elements'Proceedings of the Conf. on Comp. Aid. Des. forCompos. Mat. (CADCOMP 92), Newark, Delaware,May 1992.

2. Coad, P. and Yourdon, E. Object-OrientedAnalysis, Yourdon Press Computing Series,Prentice Hall, 1990.

3. Hekmatpour, S. C++ A guide for C programmers,Prentice Hall, 1990.

4. ACTS Training Guide, Spatial Technology, Inc.,Boulder, Colorado, 1992.

5. Trochu, F. and Gauvin, R. 'Limitations of aBoundary-Fitted Finite Difference Method forthe Simulation of the Resin Transfer MoldingProcess' Journal of Reinforced Plastics andComposites, July 1991.

6. Bruschke, M.V. and Advani, S.G. 'A FiniteElement/Control Volume Approach to Mold Fillingin Anisotropic Porous Media' Polymer Compo-sites, Vol. 11, No. 6, 1990.



7. Young, W.B., Han, K. , Fang, L.h., Lee, L.J. andLiou, M.J. 'Flow Simulation in Molds withPreplaced Fiber Mats' Polymer Composites, Vol.12, No. 1, pp. 30-38, 1991.

8. Coulter, J.P. and Gugeri, S.I. 'ResinImpregnation During Composites Manufacturing:Theory and Experimentation' Composites Scienceand Technology, 35, pp. 317-330, 1989.

9. Trochu, F. , Gauvin, R. and Gao, D.-M. NumericalAnalysis of the Resing Transfer Molding Processby Non-conforming Finite Elements, submitted toComposites Science and Technology, August 1992.

10. Zhang, Z. Simulation par £l£ments finis duremplissage des moules pour le proc£d£ demoulage par transfert de r£sine (RTM), MAmoirede maltrise, Departement de G&nie mecanique,Ecole Polytechnique, Montreal, Canada, decembre1992.


new x abstract - wit press · 2014. 5. 14. · injection molding is a general manufacturing process...

Documents