MOLD THERMAL DESIGN AND QUASI STEADY STATE CYCLE TIME ANALYSIS IN INJECTION MOLDING. A Thesis. the Degree Master of Science in the

Transcription

1 MOLD THERMAL DESIGN AND QUASI STEADY STATE CYCLE TIME ANALYSIS IN INJECTION MOLDING A Thesis Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University By Yunior Hioe, B.S. * * * * * The Ohio State University 2006 Master s Examination Committee: Dr. Jose M. Castro, Adviser Dr. Allen Yi Approved by: Adviser Graduate Program in Industrial, Welding and Systems Engineering

2 ABSTRACT Injection molding has been around for several hundred years. It started with a simple plunger forcing molten polymer into a mold cavity, since then many of the mechanical aspects have been improved but the basic technique is still the same. Generally there are two phenomena that are always related to injection molding, flow of material and heat management. In plastic injection molding, heat management plays a critical role to ensure that the process ends up with a satisfactory result. The mold thermal design, determines the cooling time which is the largest part of the cycle time. Thus, a good mold thermal is critical to assure successful process economics. The work described here centers around developing a simple method to predict the steady state cooling time. As the injection molding process proceeds, the mold temperature increases due to the hot melt being injected until the mold reaches a thermal equilibrium. Thus the minimum cooling time for the part to reach a level at which it can be demolded without loosing its shape increases until thermal equilibrium is achieved. We have developed a simple approach using one dimensional heat transfer analysis to predict the increase in minimum required cooling time until as molding proceeds until it reaches the steady value. The method applies to simple parts. We also propose how this method can be use for more complicated parts. Further work is needed to completely extend the analysis to complicated parts. ii

3 Dedicated to my parents, brother and grandma iii

4 ACKNOWLEDGMENTS I would like to thank my adviser, Dr. Jose M. Castro for giving me the privilege of being part of his research group. His guidance and encouragement has been a constant source of inspiration during the course of this work. The freedom of research that he has allowed and the patience that he has shown are gratefully acknowledged. I am also thankful to our research group for their help and support; Narayan Bhagavatula, Chuckaphun Aramphongphun (Oak), Carlos Castro, Rachmat Mulyana (Matt), Kate Olsavsky, Thania Gaido Alberty, and Carlos Castillo, thanks guys! My thanks to all my friends and family that helped me out during the completion of this work. My department faculty and staff, who have been very nice and supportive all these years, thank you. Last but not least, Mr. Cedric Sze; I ve been working with him for the last several years of my study at The Ohio State University. He has been a very understanding supervisor and has granted me a graduate assistantship position. I could not have made it without his help. Thank you. iv

5 VITA July 21 st Born Yogyakarta, Indonesia March B.S. Industrial and Systems Engineering, The Ohio State University April 2003 March Graduate Administrative Associate, Industrial, Welding and Systems Engineering, The Ohio State University FIELDS OF STUDY Major Field: Industrial and Systems Engineering Specialization: Polymer Processing v

6 TABLE OF CONTENTS Page ABSTRACT... ii ACKNOWLEDGMENTS... iv VITA... v LIST OF TABLES... x LIST OF FIGURES... xi 1. INTRODUCTION Introduction The Injection Molding Process Mold Engineering Heat Transfer Research Objectives Thesis Outline LITERATURE REVIEW Introduction... 5 vi

7 2.2 Heat Transfer Analysis Mathematical Modeling The In Mold Coating Process MOLD AND PROCESS ANALYSIS Introduction Mold Mold Cooling Process Analysis Material Analysis Experiment Setup Data Acquisition Thermocouple and IR Output Reading ONE DIMENSIONAL HEAT TRANSFER ANALYSIS Introduction One Dimensional Analysis Governing Formula Cycle Time vii

8 4.5 Simulation Thermal Conductivity and Heat Transfer Value Three Step Manual Ejection and Plastication Time Assumption Made Cycle Predictor How to Handle Real Molds and More Complicated Features TWO DIMENSIONAL HEAT TRANSFER ANALYSIS Introduction Two Dimensional Analysis CONCLUSION AND FUTURE WORK Conclusion Future Work APPENDIX A APPENDIX B viii

9 APPENDIX C APPENDIX D LIST OF REFERENCES ix

10 LIST OF TABLES Table Page Table 3.1: Cycoloy MC1300 material properties Table 3.2: Experiment information Table 4.1: Adjustment summary x

11 LIST OF FIGURES Figure Page Figure 1.1: Injection molding machine [10]... 2 Figure 2.1: Heat exchange in the injection molding process... 6 Figure 2.2 In mold coated experiment part... 8 Figure 3.1: IMC Mold Figure 3.2: Sensor Location [2] Figure 3.3: Uniform thickness and 3 thickness mold thermal comparison Figure 3.4: Cycle Time Breakdown [1] Figure 3.5: IR Camera sample picture Figure 3.6: IR Plot Figure 3.7: IR Plot Figure 3.8: IR Plot Figure 4.1: Heat flow and interfaces for passive cooling Figure 4.2: Mold thickness Figure 4.3: Heat flow and interfaces for active cooling Figure 4.4: Grid points arrangement Figure 4.5: Two material interface xi

12 Figure 4.6: Free air convection heat transfer values Figure 4.7: 3 Step sequence Figure 4.8: 3 Step timing from temperature and pressure data plot Figure 4.9: Thermocouple reading Figure 4.10: Modified 1D software Figure 4.11: Final plot result Figure 4.12: Cooling time prediction using Cycle Predictor Figure 4.13: Mold temperature prediction using Cycle predictor Figure 4.14: Top view of Honda Accord s front bumper blue print Figure 4.15: One dimensional slice of Honda Accord s blue print Figure 4.16: One dimensional slice Figure 4.17: Simplified Honda Accord s front bumper Figure 4.18: Sample feature for ribs and bosses Figure 4.19: Guide lines to form one dimensional line Figure 4.20: Final one dimensional transformation Figure 5.1: Two dimensional time and grid structure Figure 5.1: Cooling channel with different thickness part [2] Figure A.1: One dimensional universal heat transfer program flow chart Figure A.2: One dimensional modified heat transfer program flow chart Figure A.2: One dimensional cycle predictor program flow chart xii

13 Figure D.1: March 30 th IR and thermocouple plot, short cycle Figure D.2: March 30 th IR and thermocouple plot, medium cycle Figure D.3: April 2 nd Simulation and Thermocouple Plot, Short Cycle Figure D.4: April 2 nd Simulation and Thermocouple Plot, Medium Cycle Figure D.5: April 2 nd Simulation and Thermocouple Plot, Long Cycle Figure D.6: April 3 rd Simulation and Thermocouple Plot, Short Cycle Figure D.7: April 3 rd Simulation and Thermocouple Plot, Medium Cycle Figure D.8: April 3 rd Simulation and Thermocouple Plot, Long Cycle Figure D.9: March 30 th Simulation and Thermocouple Plot, Short Cycle Figure D.9: March 30 th Simulation and Thermocouple Plot, Medium Cycle xiii

14 CHAPTER 1 INTRODUCTION 1.1 Introduction Heinrich Heine, an important German poet once said, Experience is a good school, but the tuition is high. This work will try to lower the tuition cost by providing a good alternative to the trial and error method that is not only costly but also far from efficient for both resource and time utilization. The plastic industry is a major player in modern industry; injection molding accounts for more than thirty percent of all polymer processing methods [1]. Thus is a very fertile area of research. Injection molding involves many aspects such as: 1. Processing data: temperature setting, injection, pack-hold pressure settings and drying 2. Rheology: viscosity and flow study of the polymer However, all aspect in the injection molding process, one way or another are affected by heat flow. Because of this reason, the work in this thesis is focused on heat flow in the injection molding process. 1

15 1.2 The Injection Molding Process Injection molding is a net shape polymer manufacturing process. The molding equipment basically consists of a mold, clamp, injector and plunger. The whole purpose of the apparatus is to put positive pressure behind the polymer melt to make it flow into the mold cavity. Because the polymer is normally a solid at room temperature, melting before injection and solidification after mold filling is necessary. When starting the process for a new product, the whole cycle is repeated until the desired part quality is achieved. Figure 1.1: Injection molding machine [10] 2

16 1.3 Mold Engineering The mold usually made from tool steel, is quite expensive and requires long delivery time. A skilled mold maker requires years of training to gain knowledge and understanding about the molding process. Modern machining processes help improve mold making in a big way, precise machining assisted by computer and higher tolerances increase the quality of the mold but mold makers still take a huge role in the manufacturing process. Mold making up to certain point is still regarded as an art instead of engineered feat. [9] 1.4 Heat Transfer Because the nature of polymer processing, particularly in the injection molding process is critically influenced by heat transfer, a brief review of the subject will be part of this work. Most of the work here involves one dimensional heat transfer, as we are looking to develop a simple method to represent the complicated heat transfer phenomena occuring during actual molding. Numerical methods will be used to solve the governing partial differential equation instead of infinite series as they are easier to implement computationally. 3

17 1.5 Research Objectives The main goal of this work is to create simple yet robust software package that can predict steady estate cycle time in injection molding process. There are several general purpose computer packages that can be used to solve the complete mold thermal estate. However in order to predict the steady molding cycle, the heat transfer problem would have to be solved many cycles. This takes a prohibitive large amount of time. The approach developed here, takes advantage of the fact that injection molded plastic parts are thin. Thus, a dominant direction of heat flow can always be identified. 1.6 Thesis Outline This thesis is comprised of five chapters, this being the first one. The second chapter is a review of injection molding heat transfer analysis that has been done previously at the in our group and that form the basis for the work presented here. The third chapter will discusses mold and process analysis. The forth chapter discusses in detail the one dimensional analysis. The fifth chapter will be brief study of how this approach can be extended to complicated parts. Finally, the conclusions of the work presented in this thesis and recommendations for future work will be provided in chapter six. 4

18 CHAPTER 2 LITERATURE REVIEW 2.1 Introduction Several aspect of injection molding including novel work on in mold coatings for injection molding, have been an active area of research in Professor Castro s research group and the Center for Advance Polymer and Composite Engineering (CAPCE). In this chapter we review the part that is relevant to the work presented here. 2.2 Heat Transfer Analysis In general an injection mold process is just a big heat exchanger. From the heat transfer perspective, the whole cycle of injection molding can be categorized into two parts: adding heat and extracting heat. Adding heat into the system happens when molten plastic is injected into the mold and heat extraction happens when heat from the molten plastic is conducted into the mold and then further conducted into the frame of the machine or dissipated by mean of the cooling fluid and or convection into the air. 5

19 Polymer Pellets Molding Process Finished Product Heat Added Heat Extracted Figure 2.1: Heat exchange in the injection molding process 2.3 Mathematical Modeling The heat transfer equation is a partial deferential equation. There are several ways to transform this equation so that it can be easily solved using a computer. In the third chapter of his PhD. dissertation, Zuyev describes how several techniques can be employed to approximate Partial Differential Equations (PDE) [2] such as the unsteady state heat conduction equation: T k x x = ρ c p T t T = temperature k = thermal conductivity ρ = density 6

20 c p = heat capacity And if k is constant: k α = ρc p Where α is the thermal diffusivity, thus we can rewrite the equation as: 2 T α 2 x T = t Further discussion on this topic will be carried over on chapter 4 of this work. 2.4 The In Mold Coating Process In Mold Coating (IMC) is a technique where coating material is applied to the part before the mold opens, thus resulting in a ready to use or ready to paint part. The goal of this technique is to reduce the inefficiencies of conventional painting (approximately only 20% of the actual paint actually adheres to the part) by using in mold coating which can have an efficiency of approximately 90%. IMC has been widely used in SMC compression molding, however because the solidification of IMC is based on heat triggered chemical reaction, uniform mold surface temperature is critical for the success of the process. To tackle this inherent problem of using IMC in injection 7

21 molding, software was developed by Zuyev to predict mold surface behavior [2] and this software is the basis of the one developed here. Figure 2.2 In mold coated experiment part 8

22 CHAPTER 3 MOLD AND PROCESS ANALYSIS 3.1 Introduction To study the behavior and model a real world process, first we need to understand and break down all necessary parts of the system that embody it. This chapter is dedicated to address this topic. We will try to understand an injection molding process and later on replicate it or model it using a computer simulation. Mold behavior and process analysis are two major aspects that we need to understand in order to do a good assessment and modeling of the whole process. 3.2 Mold The injection molding machine consists of four sub-systems: feeder, injector, mold and clamp. All four sub-systems are enveloped by the machine frame. The mold is the only part that has direct contact with the molten plastic. Looking from a heat transfer perspective, the mold is a huge chunk of metal that acts as a heat exchanger. Almost all the heat from the plastic is being transfer into the mold and then dispersed into air as free convection or to the cooling media such as oil or water by forced convection. The amount 9

23 of time needed to remove the heat until solidification temperature of the polymer is reached, is known as cooling time. An injection molding mold has to withstand hundreds of heat and pressure cycles during its lifetime. For these reasons, the mold needs to be made using a good quality steel, such as tool steel. It is generally believed that a mold designer is a highly educated engineer. However, that statement is not always true. A skilled draughtsman and sometimes a trained toolmaker needs approximately four years of training before they are capable of producing a complex mold. [9] The experimental mold used in this work, was originally developed for research on In Mold Coating (IMC) of thermoplastics. This mold has three thickness, 0.100, and with no cooling channel. (Figure 3.1) A total of 11 experiments for this study were run using this mold. 10

24 Figure 3.1: IMC Mold Insulation of the mold is done by an insulator pad made from thermosetting polyester. The main reason for this insulating pad is to decrease the heat losses to the injection molding machine. Improved insulation would help in reducing cost for heat management as much as twenty five percent. [8] The mold is equipped with a thermocouple and pressure sensor inside the mold cavity as shown schematically in Figure

25 IMC Nozzle Sensor Location Figure 3.2: Sensor Location [2] Comparison tests shown on Figure 3.3 were run to check if mold temperature measured will be the same for single thickness mold and the three thickness mold setup. This result will be used as an indication that one dimensional analysis is a good approximation to the actual process. 12

26 Long cycle time, 1 thickness Long cycle time, 3 thickness Short cycle time, 1 thickness Short cycle time, 3 thickness temperature, degree C time, seconds Figure 3.3: Uniform thickness and 3 thickness mold thermal comparison As can be seen in Figure 3.3, minimal difference in temperature reading was observed, suggesting that thicknesses difference at the unmeasured spot have a negligible effect and one dimensional analysis can be used. 13

27 3.3 Mold Cooling Mold cooling is critical for a successful injection molding operation and can be broken down into two types: passive and active cooling. Active cooling is by means of conducting heat out by using water or oil (forced convection) and passive cooling is by relying on dissipation of heat by mean of free convection to the air. It is crucial to select the proper cooling method. Although the term cooling implies to reduce temperature, cooling channel temperature is normally set between room temperature and the plastic solidification temperature. Sometimes, a heater can be installed into the mold to raise the mold temperature before the first molding cycle began for process consistency from the first cycle. The reason for this is because polymers have different optimal molding temperatures. For example an amorphous polymer such as ABS has a recommended mold temperature of F or C while a semi-crystalline polymer such as thermoplastic polyester (PET) has a mold temperature of 450 F or 232 C. [8] Almost all engineering polymers requires mold temperatures that are substantially above ambient temperature, thus the term cooling channel could be somewhat less proper for the earlier cycles. If the initial mold temperature is different than the recommended processing temperature, such as too low, a lower quality part may be produced. Some problems that could be associated with low mold temperature are: weaker weld lines than expected, molded part would have more internal stresses, and shrinkage problems. [6] 14

28 The ambient temperature can also have an important role in the injection molding process. A drop or rise in ambient temperature can cause fluctuation in the readings provided by the various temperature control units of the machine. The injection process then becomes unstable for a period of approximately two hours or more. [8] In our case, since the experimental mold depends on passive cooling for heat dissipation, ambient temperature plays even a greater role. 3.4 Process Analysis Injection molding cycle time depends on several steps: clamping speed, fill time, holding and packing, cooling time, mold opening and finally ejection or part removal. Cooling time as shown schematically in Figure 3.4 is by far the longest part of the cycle time. It is known that cooling time can take as much as sixty to eighty percent of the whole cycle time. [1] Clamping speed or closing the mold, opening the mold and part ejection are dictated by the machine specifications. Fill time, holding and packing mostly are dictated by the polymer properties, number of cavity and flow behavior. Cooling time on the other hand is more dependent to how fast heat can be extracted from the polymer. As soon as the polymer reaches the solidification point, the part can be ejected from the mold without risk of deformation. 15

29 Figure 3.4: Cycle Time Breakdown [1] 3.5 Material Analysis Both thermoplastic and thermoset resins can be used in injection molding. A thermoplastic blend by GE Plastic USA, Cycoloy MC1300 consisting of polycarbonate (PC) and acrylonitrile butadiene styrene (ABS) was used for our experiment. MC1300 PC+ABS is an amorphous polymer. Some of the recommended molding parameters are listed in table below. 16

30 Cycoloy MC1300 PC+ABS GE Plastics USA Processing condition: Mold surface temperature 77 C Minimum mold temperature 66 C Maximum mold temperature 88 C Melt temperature 274 C Minimum melt temperature 260 C Maximum melt temperature 288 C Absolute max melt temperature 328 C Ejection temperature 98 C Thermal 275 C Specific heat C p Heat / Cool rate 2090 J/kg C C/s Thermal conductivity k PVT Properties Melt density Solid density 0.23 W/m C g/cm g/cm3 Table 3.1: Cycoloy MC1300 material properties 17

31 3.6 Experiment Setup Multiple experiment were conducted early The first experiment was conducted April 2, 2004, then April 3, 2004, April 28, 2004 then the last one was on March 30, Experiment Date Experiment sequence and cycle length Experiment 1 Experiment 2 April 2, 2004 Medium Short Long April 3, 2004 Medium Short Long Experiment 3 Mold setup Uniform thickness Uniform thickness Info Low Tmelt April 28, 2004 Long Medium Short Three thickness March 30, 2004 Medium Short --- Three thickness Table 3.2: Experiment information Each of the four days, different experiments with different cycle lengths were conducted. For some of the experiments, the part temperature after ejection was measured with an IR camera. Scenario for experiment with IR camera: 1. Molding 2. Manual part ejection 18

32 3. Manual part transport to desk 4. IR camera snap shot 3.7 Data Acquisition Data acquisition was performed using Labview data acquisition software version 6.1 using a National Instrument DAQ board. DAQ PCMCIA I/O card is interfaced with SCXI 1121 and 1321 on SCXI 1000 box to process signal from K type thermocouple into a computer output. Thermocouple and pressure transducer are flush mounted in the mold surface. (Figure 3.2) 3.8 Thermocouple and IR Output Reading There are three outputs available from the experiments: 1. Thermocouple reading 2. Pressure transducer reading 3. Infra red (IR) camera This study is focused on thermal behavior of an injection molding mold, thus the second output was not used explicitly but more as a guideline. All the experiments have the thermocouple reading output recorded by Labview software in a form of comma 19

33 separated value (CSV) which can be imported and processed using Microsoft Office s Excel. The IR camera output has a form of JPG picture with previously defined output point. (Figure 3.5) >120.0 C Spot 2 Spot Spot 1 >120.0 Spot <13.8 C Figure 3.5: IR Camera sample picture 20

34 0.100 inch, IR inch, IR inch, IR Thermocouple temperature, degree C time, seconds Figure 3.6: IR Plot 1 21

35 0.100 inch thick section inch thick section inch thick section Thermocouple 80 temperature, degree C time, seconds Figure 3.7: IR Plot 2 22

36 inch thick section inch thick section inch thick section Thermocouple temperature, degree C time, seconds Figure 3.8: IR Plot 3 As we can see from all three sample plot, IR plots, there is not always perfect agreement with thermocouple reading. The IR camera is less accurate than the thermocouple reading and is used mainly for comparative purposes. We were expecting that IR camera reading would be slightly lower compared to thermocouple reading because of the extra cooling time for the part from transportation. However, it is not always true, for the earlier cycles, part would cool faster inside the relatively cool mold because heat conduction from thermoplastic to the mold is better compared to free air convection by thermoplastic outside the mold. As the mold heating up by continuous cycles, 23

37 temperature difference between cooling part and heated mold will be smaller compared to constant temperature difference for free convection. Because of this, at the later cycles, IR readings are getting closer to thermocouple readings. Thus, we decided not to use IR camera reading as comparison, but using it as trend setter, to compare not point to point base but as overall plot. 24

38 CHAPTER 4 ONE DIMENSIONAL HEAT TRANSFER ANALYSIS 4.1 Introduction It is known and a common practice in order to simplify modeling of a real three dimensional object, to try to reduce it into a two dimensional or even into one dimensional analysis. Because an injection molded part always has a dimension which is much smaller than the others, it is acceptable to analyze it one dimensionally. A step by step analysis and correction will be presented in this chapter. 4.2 One Dimensional Analysis The first step to analyze the heat transfer process is to break down the heat flow during injection molding into several steps. The heat source in an injection molding process is caused by the polymer melt injected into the mold cavity. This heat will be conducted into the cooler material that interfaces with the heat source, metal mold. From the mold, the heat will be dissipated thru active cooling such as cooling channels or passive cooling by means of free air convection. 25

39 Figure 4.1 ill illustrate how heat will flow. The region where two different materials met is referred to interface. In a basic mold system, a passively cooled mold will have four interfaces: 1. polymer to mold 1 2. polymer to mold 2 3. mold 1 to air 4. mold 2 to air Interfaces: 3 Mold 1 2 Thermoplastic Mold 4 Figure 4.1: Heat flow and interfaces for passive cooling 26

40 In our case, the mold parts are treated as two different entities because most of the time mold thicknesses for top and bottom mold halves are not symmetrical. If by any chance the mold thickness is symmetrical, half analysis can be performed by setting a center point of the polymer melt as adiabatic and working the analysis outwards towards the mold. For general rule, mold thickness is the thickness from mold cavity surface up to mold insulator plate in the opposite direction. (Figure 4.2) Mold thickness Figure 4.2: Mold thickness 27

41 Mold with cooling channel will have two extra interfaces for each cooling channel, as illustrated by the figure below. Interfaces: 3 Mold 1 2 Thermoplastic Mold Cooling channel Figure 4.3: Heat flow and interfaces for active cooling In this case, interface 5 and 6 are between mold and cooling material such as water or oil. Please note that the amount of heat transferred represented by red arrows substantially thinner after passing thru the cooling channel, this is true because the cooling channel is capable of dissipating heat in a big percentage from the total heat conducted, thus leaving 28

42 very small or even none afterwards. Preliminary simulation tests using heat transfer coefficient h coolant as high as 2500 W/m C yielded acceptable results. More experiments and simulations will be conducted in the future and are described in the last chapter. 4.3 Governing Formula Resuming the discussion from chapter 2 of mathematical modeling, we will show the technique used to numerically approximate derivatives by finite difference. By Taylor s expansion, assuming ), ( y x u u = with sufficient number of partial derivatives, at two points and ), ( y x ), ( k y h x + + are: n n R y x u y k x h n y x u y k x h y x u y k x h y x u k y h x u = + + ), ( 1)! ( 1... ), ( 2! 1 ), ( ), ( ), ( 1 2 (4.1) With as a reminder term of: R n 1 ),0, (! 1 < < = ξ ξ ξ k y h x u y k x h n R n n (4.2) We can expand the Taylor series into: xxxx xxx xx x j i j i u x u x u x xu u u 4! ) ( 3! ) ( 2! ) ( 4 3 2, 1, + + = (4.3) 29

43 and u ( x) 2! ( x) 3! ( x) 4! i+ 1, j = ui, j + xu x + u xx + u xxx + u xxxx (4.4) Where the grid point ( i, j) or space point ( i x, j y) is surrounded by neighboring grid points. (Figure 4.4) (i-1,j+1) (i,j+1) (i+1,j+1) y (i-1,j) (i,j) (i+1,j) x (i-1,j-1) (i,j-1) (i+1,j-1) Figure 4.4: Grid points arrangement 30

44 2 2, x u u x u u xx x so on and its respective derivatives are evaluated at grid point. ), ( j i Substituting the equations, we can obtain finite-difference formulas for the first and second order derivatives at : ), ( j i ) (, 1, x O x u u x u j i j i + = + forward difference form (4.5) ) ( 1,, x O x u u x u j i j i + = backward difference form (4.6) [ 2 1, 1, ) ( 2 x O x u u x u j i j i + = + ] central difference form (4.7) [ 2 2 1,, 1, 2 2 ) ( ) ( 2 x O x u u u x u j i j i j i + + = + ] (4.8) Same technique can be employed to obtain y u and 2 2 y u. Once we found the finite-difference formulas, we need to use it as replacement for our original partial differential equation. Now for the time derivative: since our original heat transfer equation is: t T x T = 2 2 α with c p k ρ α = 31

45 For the simulation, the final forms of the equation become: t Ti, j = Ti, j 1 + α ( ) T 2 i+ 1, j 1 2Ti, j 1 + Ti 1, j 1 (3.9) z and T i, j 2 t z z and A = Ti, + B j + ( k A z BTi 1, j Ti, j ( k A z B + k B z A + k B z ATi 1, j ) α Aα (3.10) B ) α k z + α k z B A A A B B ( k Ti, j = B T i+ 1, j ) + ( z BhairTair ) k B + z B h air (3.11) Where i is coordinates and j is time step, A is material A and B is material B T i j = temperature = node number = time step A&B = material 1 and 2 z = node width α = k ρc p k ρ = thermal conductivity = density c p = heat capacity 32

46 Equation 4.9 is used for heat conduction with similar material, for example from node 1 to node 2 of the mold and equation 4.10 is used for interfaces where two materials met, for example interface between thermoplastic and mold surface. Medium A Medium B z z i-2 i-1 i i+1 i+2 Figure 4.5: Two material interface The last equation (equation 4.11) is used for modeling free air convection; in the case of active cooling, h air and T air can be replaced by h coolant and T coolant where h value of coolant will be substantially larger. Three finite difference form (equation 4.5, 4.6, and 4.7) forward, backward and central form need to be used according to their purpose; for example: for interface between 33

47 polymer and mold calculation, central form is used with strict requirement that z of steel and thermoplastic has to be the same value. Since we are using an explicit method to approximate the time derivatives, a very important requirement to use this finite-difference form, t 1 λ = has to be fulfilled 2 z 2 to ensure stability of the approximation. [4] 4.4 Cycle Time Cycle time is the main purpose why this study is conducted. It is always a good thing if the cycle time for the whole injection molding process can be decreased. What will be predicted in this study is a Theoretical Minimum Cycle Time, which means it is assignable, admissible or possible in theory only. [9] Mold opening, closing and part ejection time are considered constants since the time requirement is dictated by machine and normally cannot be altered in the process. Packing and holding, and injection speed which controls the fill time are influenced by: quality of finished product, material properties and part geometry. [1] Melt temperature, solidification temperature and mold temperature are related to material properties which are directly related to cooling time. Cooling time depends on how much different is the melt temperature from the solidification temperature and how fast the mold can extract that heat. In the later part of the one dimensional discussion, we will 34

48 discuss how to predict minimum cooling time. The injection molding process usually is not performed under very strictly controlled environment. Ambient temperature, machine controls and heat transfer are treated as a constant; however this is an approximation to actual molding. Ambient temperature, aside from affecting the mold cooling because of changing heat transfer value, it also creates irregularities in machine controls. All these variables in turns affect the cooling time. Usage of hot runners also has a huge impact for cycle time. Hot runner has advantages over cold runners because the runner stay molten and is not ejected during the molding cycle, thus shot size, plasticization time, runner cooling time and required mold opening stroke decreases hence reducing total cycle time.[1] Our study however did not incorporate this feature. 4.5 Simulation One dimensional simulation was run using thermoplastic material properties obtained from Moldflow material database; mold steel can be traced back to its original manufacturer DME Company and passive cooling means free air convection was assumed. Processing conditions such as: melt temperature, packing, hold and cooling time can be obtained directly from machine console or by an external timer. Again, the goal of this simulation is to predict mold thermal behavior in its quasi stable steady state, to achieve that, we need to compare simulation result with the experiments. We know 35

49 that the maximum temperature of the mold cannot exceed the maximum temperature of its heat source, which is the temperature of melted polymer (Tmelt). If we take the temperature of a mold in the beginning of a cycle, then we increase its temperature by introducing heat source by means of a molten polymer; by the end of its cycle, the temperature observed would be higher or equal than at the beginning. Knowing this fact and the heat exchanging nature of the injection molding process, it was decided that comparing minimum temperature for every cycle of an experiment with simulation result would be precise and useful Thermal Conductivity and Heat Transfer Value The first step to begin the simulation is to gather necessary information regarding the material that is to be simulated. Heat transfer value is treated as a fitting parameter in this simulation. Heat conduction for same material and different material (interface) are not a problem. Standard values that can be obtained from material database can be used directly, for example: for our specific PC+ABS blends, thermal conductivity k is 0.23 (W/m C) and specific heat capacity C p = 2090 (J/kg C) can be obtained from many commercially available polymer databases. At the mold top and bottom, that is the interface in contact with the press platens, heat is conducted away through the mold platens. In order to simulate this, the heat transfer in the platens will need to be included. This is too complicated and most likely will be very difficult to obtain a very accurate 36

50 solution. Fro that purpose, this heat transfer was represented by an equivalent heat transfer coefficient which was treated as a fitting parameter. However once determined the same value was used for all experiments. This has been used successfully by Abrams and Castro to simulate SMC compression molds. A value of 200 (W/m 2 C) is used instead of the normal free convection of Air which is between (W/m 2.C). Several simulation tests were used to select the best value possible. (Figure 4.6) Heat Transfer Comparison Temp (degree C) h = 300 h = 250 h = 200 Thermocouple Cycle Figure 4.6: Free air convection heat transfer values 37

51 Several heat transfer values were tested with three final values shown. Heat transfer value simulation plot of 300 W/m 2.C was the closest and as expected the lower value will resulted in higher final temperature at the end of every cycle. However, what we were looking here is not how closely the plot to thermocouple reading but how well the plot trends will mimic the thermocouple reading. A value of 200 W/m 2.C was chosen as simulation value Three Step As discussed previously, the modeling is divided into three steps: 1. Step 1 includes fill time, packing, hold and cooling time. 2. Step 2 starts when the cooling cycle is done and the mold starts opening with the part still sticking into one side of the mold. 3. Step 3 starts immediately as soon as the part is removed and ended when the mold is fully closed. 38

52 Step 1 Step 2 Step 3 Figure 4.7: 3 Step sequence 39

53 Because iteration number of simulation using finite difference analysis (FDA) depends only on the number of nodes and time step, as long the number of nodes or the number of time steps did not change this three-step simulation will not change any simulation time. The number of iteration performed by the computer is the same as assuming one whole cycle of injection molding process as a cooling phase. Timing of every step was set by looking from thermocouple data. (Figure 4.8) Figure 4.8: 3 Step timing from temperature and pressure data plot 40

54 From the figure above, pressure plot data shows the different stages of the molding process. 1. Filling stage with big rise in both pressure and temperature 2. Mold opened, but part still stick at one side 3. Part removed from mold 4. Mold closed and ready for the next cycle By using this, three step simulation, better accuracy and plot fitting is achieved. What happened in these steps are changes of boundary conditions which are handled by changing the interface calculations. For example from step 1 to step 2, the interface between the lower mold half and the thermoplastic is changed into interface between polymer to air and bottom mold half with air. By doing so, the mold will cools at different rate and so does the part Manual Ejection and Plastication Time A fully automated injection molding process has some sort of ejector mechanism and/or part extraction mechanism built into or around it. In our case however, we decided use manual part removal because it was necessary to make sure that there is no external factors that might damage the surface finish of the part. The sequence for our process becomes interrupted once the mold opened. Manual control input to proceed into 41

55 next injection cycle was given once the finished part has been manually retrieved. To compensate for this, aside from cooling time a 10 seconds transportation time was added into the simulation time. To further complicate thing, plastication time that was originally assumed to be done concurrently with cooling time was not sufficient. Because our experiment part uses approximately 80% of the barrel capacity, per shot plastication recovery time was not enough for short cooling time. When we ran our short cycle time, every two cycle the control would freeze the molding process to wait for plastication time. To account for this issue, an extra of 20 second was added on step 3 of the simulation every 2 cycle. 42

56 Thermocouple Reading with Extra Plastication Time Temp (degree C) Cycle Figure 4.9: Thermocouple reading 43

57 Effect of Extra Plastication Time Temp (degree C) Thermocouple Simulation normal 30 Simulation modified Cycle Figure 4.10: Modified 1D software 4.6 Assumption Made There are several issues that we encountered while comparing the simulations with the experimental results. A general approach for modeling injection molding cycle sequence was used. Further test and few modifications were implemented to account for these differences between simulation and experiments. All the adjustment previously described lead to the final simulation runs. To summarize all the adjustment and its respective result, please check the table below. 44

58 Adjustment Summary Heat transfer for free air convection Mold thickness 3 Step Adjustment made Goal Result Testing with multiple heat transfer values Re-measure mold used Separating process into several steps Plot trends more than per point comparison Simulating mold as close as possible Better simulation result Value of 200 From cavity to insulator pad Separation between in and out mold cooling Timing correction Verifying values from machine controls with output data Better simulation result Data from pressure plot Manual ejection Approximate manual part ejection Better simulation result 10 sec after step 2 Plastication time Check plastication time using external timer Fix "Jagged" plot 20 sec after step 3 Table 4.1: Adjustment summary A final plot result shows a very good agreement between simulation results compared to thermocouple reading from the experiments. 45

59 March 30th experiment short cycle Temperature Thermocouple Simulation Cycle Figure 4.11: Final plot result 4.7 Cycle Predictor The cycle Predictor code is a modified one dimensional prediction code that has been discussed before. Like the name indicates, the purpose of this code is to predict a steady state cycle time. With molding process that runs consecutively for more than hundreds of cycles, it would be very useful to know a specific cycle time or cooling time where the system can be carried on indefinitely. In order to analyze this, aside from all the variables needed by the one dimensional code except cooling time, cycle predictor 46

60 requires an ejection temperature. The cycle predictor software will simulate all three steps but at the end of the first step, instead of continuing to the next step, the cooling process will continue until ejection temperature condition has been met. This ejection temperature can be achieved from several sources: 1. Material data sheet from manufacturer 2. Recommendation from R&D department 3. Recommendation from quality control engineer For this study, material data sheet from manufacturer of the polymer is being used. The cycle predictor will be run until the number of specified cycles been reached, once the simulation is completed, several output can be generated, such as: 1. mold temperature at the end of each cycle 2. cooling time required each cycle 3. minimum cooling time From 1, we can see how the mold temperature stabilizes using this method, while 2 can be used if the operator is really trying to save every single second; the third output will be the most useful, because the operator can use this minimum cooling time as guideline to set the process to guarantee that it will run indefinitely. The two figures below show the result of the Cycle Predictor software comparing with standard simulation that has been verified using thermocouple reading. We use the simulation result as comparison, because the experiment was only run for only 70 cycles. 47

61 From figure 4.12 we can see that normal simulation using 14 second cooling time (horizontal line), while adjustable cooling time generated by cycle predictor software showed increasing cooling time needed to compensate for heat buildup in the mold. At molding cycle number 83, the plot intersect, what happened over here was that standard cooling time of 14 second was no longer enough to lower thermoplastic temperature to 98 C at the time of ejection. The cycle predictor suggested that effective cooling time need to be set at minimum seconds or 16 to be even. At 16 second cooling time, the molding process with no external factor interfering, such as sudden big increase in ambient temperature, will be able to run indefinitely will little worry of producing defective parts. In our experiment, we did not see the actual molding result above cycle 70, because we stop at that point. However, some initial surface deterioration was observed after 70 cycles. 48

62 18 16 Time of Step1 (sec) Cycle predictor Experiment cooling time Cycle Figure 4.12: Cooling time prediction using Cycle Predictor The next figure shows the mold thermal behavior at the end of every cycle. At the exact same cycle, 83, cycle predictor curved start to level, which means that mold temperature starting to stabilize. Simulation with standard cooling time in the other hand still showing increase in temperature until cycle 180 and above, where it starting to show stable temperature. With recommended ejection temperature of 98 C we can clearly see some difference in stable temperature. 49

63 C 80 Temp 'C Thermocouple Cycle Predictor Cycle Figure 4.13: Mold temperature prediction using Cycle predictor 4.1 How to Handle Real Molds and More Complicated Features The approach as to how to analyze an actual mold using a one dimensional analysis is explained with the following sketches. The figure below is a top view blueprint of a Honda Accord s front bumper. 50

64 Figure 4.14: Top view of Honda Accord s front bumper blue print 51

65 Now, let us make a vertical slice: Figure 4.15: One dimensional slice of Honda Accord s blue print 52

66 Then a simplified one dimensional look of the slice would be: Cooling Channel Mold TP Figure 4.16: One dimensional slice By repeating this procedure we can have multiple one dimensional slices that can be simulated separately. 53

67 If we take the above slices, simplify to its bare essential and reconstruct it, this is what it will be look like: Figure 4.17: Simplified Honda Accord s front bumper From this reconstruction, more complete analysis can be done. Then the next step would be addressing standard features that are normally present in injection molding parts. Ribs and bosses are normally used to provide structural integrity into thin injection molding part. 54

68 Let us see this sample feature: Cooling channel MOLD TP Figure 4.18: Sample feature for ribs and bosses Then we convert it into one dimension by observing this several guidelines: 1. As much as possible do a straight line perpendicular to both mold surface and general part surface 2. From the center of part feature, take a straight line to closest part surface and the n took another straight line to the closest cooling surface 55

69 3. Active cooling always take priority from passive cooling surface Figure 4.19: Guide lines to form one dimensional line Once the one dimensional guide line is formed, straighten the lines into one straight line. 56

70 Cooling channel Mold TP Figure 4.20: Final one dimensional transformation At this step, one dimensional analysis can be performed. Please note that for feature transformation, the part and mold thickness would look thicker. 57

71 CHAPTER 5 TWO DIMENSIONAL HEAT TRANSFER ANALYSIS 5.1 Introduction Two dimensional heat transfer will be covered briefly, mainly because it was not tested thoroughly as its one dimensional counterpart. This software will be used mainly to verify the rules given at the end of the previous chapter Two Dimensional Analysis The main difference with one dimensional heat transfer is that we have one more space variable that need to be included in the heat transfer equation. The previous i and j variable that corresponds to thickness and time step will be changed to i, j and k, with i and j as coordinates and k as time step. 58

72 X-coordinate Z-coordinate Y-time 2D + time grid structure i-1,j-1,k+1 i,j-1,k+1 i+1,j-1,k+1 i-1,j,k+1 i,j,k+1 i+1,j,k+1 i-1,j-1,k i,j-1,k i+1,j-1,k i-1,j+1,k+1 i,j+1,k+1 i+1,j+1,k+1 i-1,j,k i,j,k i+1,j,k i-1,j+1,k i,j+1,k i+1,j+1,k Figure 5.1: Two dimensional time and grid structure Recall figure 4.3 for one dimensional grid arrangement. The two dimensional software might give a better insight on how features and non-simple part with its relation to mold thermal will behave. A two dimensional 59

73 program could be used to simulate and test cooling channel placement, for example: pitch and distance to the part. Figure 5.1: Cooling channel with different thickness part [2] With two dimensional program simulation data, using slicing scheme explained in chapter 4, we can compare the result with one dimensional simulation. 60

74 CHAPTER 6 CONCLUSION AND FUTURE WORK 6.1 Conclusion We have shown that the one dimensional heat transfer analysis does a good job in predicting the experimental results. The analysis presented here, can be used to estimate the steady state cycle time. An approximate method is suggested for actual molds and parts with complicated features such as ribs and bosses. In cases where cycle time is extremely critical to process economics, the cycle time can initially set short and increased as indicated by the cycle predictor program until steady state. This might be especially more important for short runs, where mold changes occur often. Mold makers can use this software to design and check cooling channel placement, mold thickness, etc. Operator can use this software to troubleshoot and predict mold behavior with different process parameter, for example: molding in winter and summer time will have different ambient temperature, thus different results. 61

75 6.2 Future Work There are several areas of this work that need to be fully tested. In particular the rules to handle actual molds and parts with complicated features such as bosses and ribs, discussed in the last part of chapter 4, need to be tested for accuracy. The implications of the changing thermal environment on physical properties need to be evaluated. In particular, the effects on surface quality for appearance parts need to be tested. As mentioned before, current experiment based only on passively cooled mold using 50 ton Sumitomo injection molding machine. Eighty percent of barrel capacity was used per shot creating plastication delay every two complete cycle. Another mold with more complex cavity and cooling channel is available, this mold could be used efficiently to further conduct more experiment and simulation using bigger tonnage injection molding machine with larger barrel capacity, the 180 tons Sumitomo. Graphical user interface (GUI) or more user friendly interface need to be developed for both one and two dimensional software. 62