Cooling+simulation+of+plastic+injection+molding

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1、GUO Zhi-ying， HU Jun-qiao， LI De-qun郭 志 英胡 俊 翘李 德 群(State Key Lab of Mold & Die Technology，Huazhong University of Sci & Tech，Wuhan 430074，China)Abstract： analyses the cooling of mold and plastic part during injection molding and the continued cooling of plastic part after being ejected from mold usi

2、ng the heat transfer theory and Boundary Element Method ( BEM) to predict the temperature distribution in both mold and plastic part，and presents the experiments carried out with plates of ABS ( Acrylonitrile-Butadiene-Styrene) to verify the validity of the cooling analysis software used to simulate

3、 the temperature distribution in ABS plate parts，and concludes that the analysis software agree qualitatively well with actual experimental findings.Key words: cooling simulation； mathematical model； boundary Element methodCLC number: TG241Document code： AArticleID： 1005-9113(2001)01-0030-050 INTROD

4、UCTIONInjection molding is a cyclic process wherein melting polymer is forced into a cold metal mold under high pressure and cooled until it is solid enough to be ejected from the mold. Cooling is a crucial part of the injection molding cycle，because it has a major impact on both the quality of prod

5、uct and the productivity of mold. Many defects such as residual stresses， shrink-age， warpage are caused by non-uniform cooling. These defects are critical for the quality of final part from the points of view of appearance and precision. On the other hand，cooling last more than two-thirds of the wh

6、ole injection cycle. The design of an efficient cooling channel would reduce the cooling time and improve the productivity of injection. Therefore， the de-sign of an optimized cooling system would achieve ( 1 ) minimum cooling time， and ( 2 ) balanced or uniform cooling. In order to have a better un

7、derstanding of the injection molding cooling process，computer aided cooling analysis has been used as a helpful analysis tool for the de-sign of cooling system and the evaluation of cooling conditions.Here is a brief description of the development of simulation of plastic injection molding cooling.

8、The pioneering work of Dusinberre focused on the prediction of temperature and pressure fields on rather simple geometries ，and one-dimensional transient model and Finite Difference Method ( FDM ) was used to calculate the temperature distribution. Later， Keing， Kamai and Singh23 applied two - dimen

9、sional Finite Element Method ( BEM ) to simulate the cooling process. Bar-one， Cauik， Burton and Rezayat4,5 first applied Boundary Element Method ( BEM ) to calculate the temperature field，but it was limited to two - dimensional analysis. Since most injection-molded parts are of three-dimensional co

10、mplex geometrical configuration， in order to calculate temperature distributions based on three-dimensional cooling analysis， some researchers used middle-plane BEM to simulate the cooling of injection molding .The cooling analysis software is developed using the numerical approachBoundary Element M

11、ethod and the theory of heat transfer. From this cooling analysis program， temperature distribution can be computed for parts and molds during injection molding. And ai- so，the program can calculate the temperature profile of the part after being ejected from the mold. Moreover， experiments were car

12、ried out to verify the accuracy of the program. finally numerical predictions and experimental data are discussed.1 THEORETICAL ANALYSISAs we know， the molten polymer in the cavity is cooled and solidified during cooling until it is strong enough to be ejected as a molded part without distortion. Th

13、e cooling process is quite complex as heat transfers among the metal mold，melting polymer and the coolant flowing through cooling channels. There are four types of heat transfer involved: ( a ) heat exchanging within the melting polymer， ( b ) heat flowing from the polymer to the metal mold，(c ) hea

14、t transferringbetween the mold and the coolant，（ d ) heat escaping from the outside surfaces of the mold to the ambient air. A simplified scheme of heat transfer during cooling stage of plastic injection molding is shown in Fig. (a)Heat exchanges within melt polymer ( b)Heat flows from polymer to me

15、tal mold ( c ) Heat transfers between mold and coolant ( d ) Heat es-capes from outside surfaces of mold to ambient air Fig. 1 Sketch map of heat transfer during at cooling stageBasically， the cooling process is a three-dimen -sional conduction of transient heat within convective boundary conditions

16、. Complicated boundary geometry is introduced by the layout of cooling channel. A full analysis of both the transient behavior of the polymer melt temperature and the simultaneous varition of mold temperature requires a very long computer operation. Simplifications and approximations have actually b

17、een performed during cooling analysis to improve efficiency. In this paper， the following assumptions are made for building a mathematical model to describe the heat transfer at the cooling stage.(1 ) Latent heat and viscous heating effects of the melting polymer are negligible，hence there is no inn

18、er heat source in the temperature field.( 2) It can be assumed that heat removal from the polymer during molding largely occurs via heat conduction in a direction perpendicular to the plane of the part. That is to say， heat conduction in the plane of the part is negligible.(3 ) The thermal contact r

19、esistance between the polymer and the mold wall is relatively small and can be neglected，because polymer remains in contact with mold walls at cooling stage.(4 ) There is no fluid flow of melting polymer during cooling. And the material properties (尸，c，K) are independent of temperature.Based on the

20、above assumptions， a three-dimen- sional cooling analysis of the mold begins from the gov-erning equation of heat transfer theorya2 t/ a2 x + a2 t/ a2 y + a2 t/ a2 z = 0，V ( x，）E 月(1 )where T is the mold temperature，x，are the three coordinates of a certain point in the mold，月 denotes the mold area.I

21、n order to solve equation (1 ) using the boundary Element method， some finite conditions inciuding initial condition and convective boundary condition are re-quired. The initial condition for injection molding，isT = T( t = 0)where t denotes time， T。represents initial temperature and can be obtained

22、from data fiie of fiow analysis. And the convective boundary condition is -K( dT/an) = h( T -Tc) where K is the thermal conductivity of mold，indicates the heat transfer coefficient between mold and coolant，and Tc is coolant temperature， which can be considered as a constant for simplicity.As to the

23、cooling of plastic part， the cooling of polymer in the mold is considered as one-dimensional transient heat conduction with constant material proper-ties. So，the mathematical model can be derived from the governing equation of heat conduction theory as shown below.K2 a2 tv ax2 = pcdT/at(2)where p，c

24、and Kare density， heat capacity and thermal conductivity of the polymer， and T is the temperature of part. And its convective boundary condition is -K2( aT/an) = h2( T - T) where h2 is the heat exchange coefficient between polymer and mold.Furthermore， research is also done on the cooling process of

25、 the part after it is ejected from the mold. The part continues to cool after ejection， because its temperature is higher than the ambient temperature. And heat flows from the part to the ambient air by convection and radiation until the part reaches room temperature. So，cooling simulation of part c

26、ooling after ejection is Basically a continuation of its initial cooling process in the mold with different treatment of initial and convective boundary conditions.0 NUMERICAL SOLUTION OF MATHEMATI-CAL MODELWhen Boundary Element Method is applied to the calculation of temperature distribution in par

27、t and mold，correlative area needs to be divided into many discrete meshes. The division has much effect on both calculating speed and accuracy. More meshes can improve the calculating accuracy， but it costs much more calculating time. As a compromise， the part can be divided with triangular mesh Ele

28、ment， and the cooling channels with a linear cylindrical Element. After the area is divided and BEM is applied，equation (1 ) can be expressed as follows:（3)from the outside surfaces of the mold to the ambient air. A simplified scheme of heat transfer during cooling stage of plastic injection molding

29、 is shown in Fig. l.Z hJT = Z gf11hij = J Q * ( 0,，）ds厂jSi = J T*( ，）ds（3)where T* is the basic solution of Eq. ( 1 )，Q is the heat flux，N is the number of mesh element， ! and aresource and destination points in the area respectively.And also，Eguation ( 3 ) can be expressed in an-other form asA X =

30、F(4)where X is the unknown temperature distribution in the mold. If Eg. ( 4 ) is solved， the temperature proxies of mold can be obtained. The combination of implicit Finite Difference Method and explicit Finite Difference Method is applied to the calculation of Eg.2) . And it is thus possible to cal

31、culate the temperature distribution in the part after ejection.0 HSCAE/C，A COOLING SIMULATION SOFTWAREBased on the above heat transfer theory and BEM algorithm， a cooling simulation software HSCAE/C is developed. The flow chart used for the simulation of the cooling process is shown in Fig. 2. After

32、 selecting the material and process parameters and designing the cooling system， cooling analysis is applied to the calculation of the temperature distribution in both the mold and the part. And then， temperature profile can be displayed in several visualized ways， such as equivalent curve and color

33、ized cloud graph.Fig. 2 Flow chart of HSCAE/C for prediction of cooling processBesides the functions mentioned above，cooling analysis software ( HSCAE/C) can also be used to pre-dict the minimum time for the molded part to cool down. Moreover， it can be used to evaluate the flow rate of coolant and

34、the pressure drop in each branch of the cooling channel network so that maximum cooling efficiency can be achieved. In a word， HSCAE/C can simulate how the mold cools over the entire cycle and provide critical information needed to optimize coolant process conditions designs of mold and part.1 APPLI

35、CATIONS AND DISCUSSIONSThe temperature distribution of a plate-type is calculated using HSCAE/C. The geometries of a part and cooling channels are as shown in Fig. 3. The plate are 270 mm X 130 mm X 2 mm. And the diameter and the length of two straight cooling channels are 10 mm and 300 mm respectiv

36、ely. The cooling channels are in parallel connection， which are all on the cavity side of the stationary mold. The main process parameters and material used for this study are summarized in the Appendix.Fig. 3 Geometries shape of part and cooling pipeThe overall temperature distribution of plastic p

37、late before being ejected from mold is as shown in Fig. 4， and this temperature field is not uniformly distributed. The highest temperature goes up to 66. 1 C and appears near the middle of plate. And the lowest temperature goes down to 59. 3 C and occurs at the corners. The results reveal that it i

38、s easier to transfer heat at the corner than in the middle of plate.Fig. 4 Temperature profile of part before ejection from moldFig. 5 shows the variation of temperature during cooling in the injection mold. During cooling，the temperature of part gradually decreases from molten temperature until the

39、 ejection temperature at which it is ejected from the mold. And plastic layers closer to the metal are easier to transfer heat. As a result， they are cooled down faster than the center layer of part.Since the temperature of part is higher than the ambient temperature， the part continues to cool down

40、 after being ejected from the mold. As shown in Fig. 6， the temperature curve rises up to the highest temperature and then declines to the lowest temperature. The reason is complicated. When the part is ejected from the mold，heat from the warm inner regions conducts to the part surfaces with most of

41、 heat going in the direction of cooling surface， thus the temperature goes up. And then the two surfaces begin to cool down simultaneously and eventually reach the ambient temperature as shown in Fig. 6.Fig. 5 Temperature change during coolingt /s Point 1Fig. 6 Temperature change after ejectionIn or

42、der to verify the accuracy of the simulation software used for cooling analysis， experiments were carried out with an ABS plate. The experimental plate was molded on a servo-controlled injection-molding ma-chine ( CJ800-400NC ZHENGDE ) with a clamping force of 350 KN. In order to measure time- and p

43、iace- dependent temperature and pressure in the part during injection molding， four duai functional transducers ofpressure and temperature ( GYY-7A) were used. They are placed along the length of the plate as shown in Fig. 7， and located on the cavity side of the stationary mold. To record these mea

44、sured temperature and pres- sure， a signal sampling system run on a personal computer was used.A- -TV -LiPTIPT2PT3PT4Fig. 7 Positions of four transducers in the cavityMeasured temperatures at the time of the part being ejected from the mold are compared with these temperatures predicted with the coo

45、ling analysis software as shown in Table 1 ， which shows that experimental data and simulation results are relatively close to each other，and the values predicted with the simulation soft-ware are about 7 C higher than those measured values. There are several factors to account for this difference.

46、The temperature measured by the transducer is usually slightly lower than the actual temperature due to heat dissipating and time delaying. Besides， the cooling simulation software HSCAE/C does not take in-to consideration of heat escaping from the mold to the ambient air during the total process cy

47、cle， which may result in a higher predicted temperature. Furthermore， the ignorance of thermal contact resistance between mold and hot polymer may lead to an error. To sum up， all these contribute to a higher simulated temperature than the experimental one.Table 1 Comparison of temperatures measured

48、 at fourpoints during experiment and predicted using cooling simulation softwarePointPT1PT2 PT3PT4experimental Value55.659.l 58.956. lsimulation Value6l.565.9 65.66l.90 CONCLUSTIONSThe cooling analysis of the injection molding is adopted to predict the temperature distribution in both mold and part，

49、 using heat transfer theory and Boundary Element Method ( BEM ) and simulate the cooling of mold and part during injection molding and continued cooling of part after being ejected from mold as well. experimental results obtained with an injection-molded plate of ABS can validate the numerical predi

50、ctions of the cooling analysis software. Although the numerical simulation results are proved to be acceptable，there is still much room for improvement. In order to get more accurate predictions，realistic thermal boundary conditions during cooling， crystalline material and material properties depend

51、ent on temperature and time should be taken into consideration when a theoretical mathematical model is being built.APPENDIX Molding ConditionsInjection pressure: 50 M-Pa Holding pressure ： 50 M-Pa melt temperature: 220 C Ejection temperature: 55 C Injection time: 3 s Holding time: 30 s Cooling Cond

52、itionsAmbient temperature: 23 C coolant temperature: 25 CHeat transfer coefficient between mold and polymer:250 W/(m2 K)Heat transfer coefficient between mold and coolant: 275 W/(m2 K)MaterialsPlastic material: ABSmold material: 45# steel coolant: WaterReferences:1 DUSINBERRE G M. Heat Transfer Calc

53、ulations by Finite Difference M. Scranton: Int Textbook Company，1961. 30-42.2 KEING S，KAMAL M R. Heat transfer in the cooling of thermoplastic melts under pressure J . J Chem Eng， 197(4): 210-219.3 SINGH K J. Computer software for plastic cooling analysisa new approach J. ANTEC，1984,30:962-964.4 BAR

54、ONE J， CAULK D A. experimental verification of an optimal thermal design in a compression mold J . polymer Composites，1986(3): 141-145.5 BURTON T E， REZAYAT M. simulation of heat transfer in injection molds J . ASME Computer in Engineering， 198(7) 54-61.6 REZAYAT M， BURTON T E. Combined boundary eie

55、-ment and finite-difference simulation of cooling and solidification in injection molding A . 5th International Conference on numerical Methods in Thermal Problems C . Juky: Hanser Publisher，1987.7 REZAYAT M. numerical computation of cooling-Induced residual stress and deformed shape for injection-moldedthermoplastics J . ANTEC，1989，35: 341-350.