- Email: [email protected]
Development of an integrated neural network system for prediction of process parameters in metal injection moulding
Journal of Materials Processing Technology 130–131 (2002) 315–320
Development of an integrated neural network system for prediction of process parameters in metal injection moulding Prasad K.D.V. Yarlagadda School of Mechanical, Manufacturing and Medical Engineering, Queensland University of Technology, Brisbane, Qld 4001 Australia
Abstract In this present work attempts have been made to develop an integrated neural network system for prediction of process parameters such as injection pressure and injection time in metal injection moulding (MIM) process. The current system has been developed by integrating the different aspects of MIM process. The aspects that are addressed in this system are the physical model of MIM filling stage based on governing equations of mould filling, and process parameters for debinding and sintering stages generated by experimentation. In this work the feed forward type of neural network has been used, which was initially trained with the analytical data before incorporating as part of an integrated system. In this work Gauss training method has been incorporated for the usage of function approximation. This integrated system has been implemented in MatLAB environment by using neural networks toolbox. This integrated system was successfully tested to solve the real world problems of MIM process. The analytical algorithm based on governing equations of mould filling process first produces a feasible injection time for the MIM process. Injection time data is then used to train the neural network system. In order to validate the results generated by the neural network system are checked with the simulation results of the ‘‘Moldflow’’ software and found that the results generated by integrated neural network system are not different from the simulated results. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Artificial neural networks; Metal injection moulding; MatLAB; Optimisation; Mould filling
1. Introduction The metal injection moulding (MIM) process is a combined process of injection moulding and powder metallurgy. This process is used to manufacture complex metallic parts at a lower cost than the metal working techniques. The important stages involved in MIM process are plastification, moulding, debinding and sintering. This process consists of mixing ultra-fine particles with a polymeric binder material. The prepared mixture is then made into a granular form and pressed into a mould under higher pressure and appropriate temperature. Subsequent to moulding the green part will be subjected to a debinding process during which the binder is removed. Finally the green part is sintered in a process which is similar to conventional powder metallurgy technique. The main application of this MIM technique is used in economical production of complex parts with high-performance of engineering materials. In the MIM process the most critical
E-mail address: [email protected] (P.K.D.V. Yarlagadda).
step is the moulding phase and more often many problems arising during this stage and lead to various kinds of defects such as voids, sinks, distortion and cracks. These defects can be avoided by proper selection of process parameters such as held pressure, temperature of the mould and melt. High injection pressure is needed to force the melted power mixture of high viscosity into the mould within a short period of time. On the other hand, higher pressure would lead to residual stresses which result distortion or cracking. Even though the increase of melt temperature can reduce viscosity and make mould filling easier, too low a viscosity may result in problems with mould filling such as jetting, splashing or air entrapment. Increasing the mould temperature reduces heat losses and the maximum temperature difference at the end of the mould filling stage. This improves the quality of part, but increases cooling time consequently the production time. Hence it can be realised that the relationship between process parameters for MIM process is very complex and most of these parameters are inter-connected. In this research work attempts have been made to optimise the process parameters in MIM process through a physical model.
0924-0136/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 7 3 8 - 0
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2. Background and current status As mentioned in the previous section the selection of process parameters in the moulding process controls the quality of the finished part, which depends on mould filling analysis during injection state. Several researchers [1–12] attempted to address the problems associated with plastic injection process, which is also referred as MIM process and mould filling analysis. Some researchers Richardson et al. [1], Hieber and Shen [2], and Huilier et al. [3] addressed the mould filling stage problem as a problem of combined energy and transport of momentum and applied to the transient and non-isothermal flow problem. After the mould filling simulation packages became available the researchers Chao and Maul [4] and Pandelidis and Zou [5] tried to optimise the injection cavities, injection velocity and gate locations. The applications of expert systems and neural networks in manufacturing were found in several researchers work [6–11]. Kim and Suh [6] developed a prototype knowledge-based synthesis system for injection moulding. In their work, they mainly focussed on mouldability and mechanical acceptability of the design for plastic parts. Tsang et al. [9] developed an approach for incorporating a knowledge-based system into a computer-aided design system for design of injection moulded parts. The domain of their system is restricted to the appropriate moulding set up, fault detection and shot-to-shot monitoring. Bernhardt and Bertacchi [12] developed an expert system for trouble shooting during moulding. Their system provides guidance to the operator to test and debug the start-up operations and correct problems as they arise in running the system. In 1980s several developments leads to development of interest in neural networks, most notable was the development of a training method for multi-layer networks [9]. This development enabled neural networks to learn functions such as the XOR and development of fully inter-connected networks, which converges with stable outputs. Yarlagadda [10,11] used artificial neural networks for production of process parameters in both die casting and injection moulding processes. In this work the neural network was developed by comparing three different training algorithms: namely error back-propagation algorithm; momentum and adaptive learning algorithm; and Levenberg–Marquardt approximation algorithm. It was found that the Levenberg–Marquardt approximation algorithm was the preferred method for this application as it reduced the sum-squared error to a small value. The accuracy of the developed network was tested by comparing the data generated from the network with that of an expert from a local die casting and injection industry. From the literature review it can be concluded that the moulding stage of MIM process is the most critical for the success of producing the final product with good quality. The MIM parameters such as melt temperature, mould temperature and injection time have to be set for the process can be scientifically obtained from the mould filling simulation. Hence the objectives of the
research work are (1) to develop a mathematical model for the MIM moulding stage in order to identify the correct moulding conditions, and (2) to develop an artificial neural network system to predict optimal moulding conditions.
3. Modelling of MIM process The MIM process begins with the heating of the feedstock to a sufficiently high temperature so that the feedstock Si melted, and then forcing this melt into a cavity where it cools and forms the shape of the part. The objective of this process is to obtain parts which are free of voids or other defects. In order to manufacture satisfactory parts, the temperature of the melt must be within a certain range. If the temperature is too low, the mixture is too viscous and complete mould filling is not possible and if too high, uniform filling becomes difficult, and crack of the part might occur due to large temperature gradient between feedstock and the die. Within the proper melt temperature range, if the setting of the mould temperature is lower level, higher pressure is needed to force the melt into the cavity but the cooling time will be less. On the other hand, increasing the mould temperature will reduce the shear stress and pressure, but the cycle time will be longer. The injection time parameter is the inversion of injection rate. At very injection rates there are high shear rates so that the pressure required to fill cavity is high. On the contrary, when the injection rate is very low, the melt temperature gets very cold towards the end of the flow and will result in higher injection pressure and a higher stress level at the end. In the interest of producing parts at low cost, these contrary constraints necessitate the building of a physical process model for the analysis. 3.1. Modelling of the viscosity The characteristics of feedstock play a key role in MIM mould filling process. The most important is the viscosity, which relates the shear stress to the shear strain rate. The viscosity Z for Newtonian fluid is dependent on temperature and pressure, where as for non-Newtonian fluid, it is a function of temperature, pressure and shear rate. For the MIM feedstock mixture, it not only shows non-Newtonian behaviour but it also further depends upon binder components and the suspension behaviour and behaviour of metal particles that are surrounded by the binder. The two important factors that contribute to the viscosity change by temperature for MIM mixture are thermal activation and thermal expansion and the relation is expressed as E 1 1 Z ¼ Zi exp (1) kT T t0 where Zi and E are material specific constants, k the Boltzman’s constant and E is called the activation energy for viscosity. The temperature dependence of viscosity is further complicated by the fact that the components of
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powder–binder mixture have different melting points. The viscosity behaviour changes with the melting of each component and it is difficult to model this effect in the overall mathematical model. One way to handle this in simulation analysis is to check the temperature and use the appropriate model corresponding to that temperature range. Pressure has relatively small effect on the viscosity of a MIM mixture. Part of this effect is the increase in binder viscosity with pressure. Generally the larger the activation energy E for viscous flow, the larger the sensitivity to pressure changes. Viscosity Z dependence on pressure P which can be expressed in a similar way to the temperature effect as Z ¼ Z0 exp½CðP P0 Þ
(2)
where Z0 is the reference viscosity at a reference pressure P0, which usually is one atmosphere, C the pressure coefficient, which is an effective activation enthalpy for the pressure induced viscosity changes and P the pressure. In practice, the pressure used in MIM moulding changes in the order of a few MPa. Comparing the temperature, the influence of pressure on the viscosity is equal to that caused by the temperature change of approximately 1 K. Therefore, under standard MIM operation, the influence of pressure on the viscosity can be ignored. Overall viscosity model can be arrived by combining Eqs. (1) and (2) under the assumptions; viscosity changes with the pressure is negligible, viscosity is dependent upon the particle size is negligible and the change in solid loading with temperature is negligible. The overall relation is Zm ¼ Zr A 0
1 O 2 E n1 exp g Om kT
(3)
where Zr is binder reference viscosity, n the power law index, E the activation energy for the powder binder system, k the gas constant, Om the maximum solid loading, O the solid loading, g the shear rate and A0 the constant and is approximately equal to 1. 3.2. Modelling of the mould filling stage The MIM process is derived from plastic injection moulding with minor modifications due to the difference in material characteristics. MIM feedstock consists of different components including metal powder and binder, in addition the binder is composed of constituents like polymers, waxes and other wetting materials. Different combinations of these powders and binders, powder size and shape make MIM more complex than simple plastic injection moulding. The governing equations of the flow of MIM melt can be derived from a compressible, viscous fluid. These equations are obtained using the principles of conservation of mass, momentum and energy. In the case of injection moulding, Fig. 1 illustrates a simple mould cavity, which displays the required boundary conditions. There are several surfaces on which boundary conditions exist. By applying the
Fig. 1. Mould filling boundaries considered for simulation model.
momentum and continuity equations, and combining them to obtain: @ @r @ @r Ss Ss þ ¼0 (4) @x @x @y @y where Z S2 ¼
h 2 0
z dz Z
As described above, the rheological response of MIM melt is generally non-Newtonian and non-isothermal. Also the mould filling process in MIM is transient in view of timedependent domain during filling. The governing equations are highly non-linear. Apart from very simple geometry parts, the equations governing the flow of the injection moulding are very difficult to solve. Since usually injection moulds have different and complex geometries, a general method of solution is required. A finite element method has been developed in which triangular elements are used to describe the geometry for calculating the pressure and temperature [2]. In this work the Moldflow numerical techniques have been used for simulating the mould filling stage of MIM process by using the model described in Eqs. (1)–(3) for describing the material behaviour. The effect of moulding conditions on the MIM process has been investigated by using Moldflow simulation program for 17-4PH Stainless steel feedstock, injected into a 150 mm flow length mould with different moulding conditions.
4. Development of hybrid neural network system for MIM process In this work the structure of the feed forward neural network has been used for developing the network to predict MIM process parameters as shown in Fig. 2. For most of the engineering applications, in general, back propagation network in combination with gradient descent optimisation method as learning algorithm. However for current application the gradient descent technique is not suitable due to
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Fig. 2. Neural network for prediction of injection time.
complexity of the MIM process. A more sophisticated optimisation technique namely; Gauss–Newton with Levenberg algorithm was used as a learning algorithm, since it is a powerful tool for the least square problem. More details of the Levernberg learning algorithm and its suitability to similar kind of problems has been explained in detailed in other published work [10,11]. In this research work in order to determine the suitable MIM moulding conditions, the neural network used as a mechanism for mapping the function. As discussed earlier the three moulding conditions need to be identified before setting up the mould are melt temperature, mould temperature and injection time. In this work the melt temperature and mould temperature are established based on Moldflow simulation and these parameters were used as input in the developed feed forward neural network for the prediction of injection time. As discussed earlier the injection time is a reverse of the melt flow rate and it dominates the pressure needed to force the melt into the cavity. The injection time is not only depends on melt and mould temperatures but also on the thickness and flow path of the cavity. Hence the feed forward network is then constructed with four neurons (melt temperature, mould temperature, cavity thickness and flow path length) in the input layer and one neuron (injection time) in the output layer. Establishing the number of neurons in the hidden layer is one of the critical issue while solving problems using multi-layer feed forward networks. The precise solution for this issue is rather difficult because of the complexity of the network mapping and the non-deterministic nature of any successfully completed training procedures. In this MIM system the number of hidden layers are determined by using trial-and-error methods. The procedure adopted for integrating the knowledge base, feed forward neural network and Moldflow simulation system is shown in Fig. 3. When the four input parameters melt temperature, mould temperature, cavity thickness and flow path length are
Fig. 3. Development of artificial neural network system for MIM.
entered into the system, and then the system will predict the suitable injection time. Any neural network will not be able to predict the output parameters accurately unless the network is properly trained with accurate data, hence sufficient care must be taken in the preparation of training data the training data must cover the wide variety of possible ranges. Some of the limitations associated with the current system are; the maximum cavity thickness is 100 mm, the maximum weight of the component is 100 g, the melt temperature must be higher than the material’s freezing temperature (20 8C) and the range of mould temperature is between 30 and 50 8C. The various operating conditions that are used for training the network are given in Table 1. The total data set generated for training the network ð10 5 5 7Þ is 1750 and this forms the neural network’s reasoning domain. After defining the domain, experimental data has been generated from the Moldflow simulation results for each of the 1750 data points and Table 1 The training data used to train the MIM system Process parameter
Operating conditions
Melt temperature (8C)
100, 105, 110,115, 120, 125, 130, 135, 140, 145 30, 35, 40, 45, 50 2, 4, 6, 8, 10 50, 75, 100, 125, 150, 175, 200
Moulding temperature (8C) Cavity thickness (mm) Flow path length (mm)
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Table 2 Simulated injection time for selected data points
Table 3 The data used for testing and predicted results of the neural network
Melt temperature, mould temperature, cavity thickness, flow length
Injection time (s)
Data point
100, 100, 100, 115, 115, 115, 130, 130, 130,
0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.5
Melt temperature (8C)
Mould temperature (8C)
Cavity thickness (mm)
Flow path (mm)
Results/ injection time
1 2 3 4 5 6 7 8 9 10
125 135 140 120 110 105 112 142 137 108
45 48 38 33 35 45 37 40 47 32
6 8 9 7 4 8 5 3 6 8
125 175 190 140 86 175 114 75 108 185
1.5 2.89 3.27 2.07 0.4 2.12 0.9 0.62 1.55 2.26
30, 40, 50, 30, 40, 50, 30, 40, 50,
2, 2, 2, 2, 2, 2, 2, 2, 2,
50 50 50 50 50 50 50 50 50
obtain the best injection time for these points. Some of the results obtained for some of the selected simulation points is shown in Table 2. In this system, the knowledge base system communicate with the user through a built-in interface. By making use of the necessary information, the system reasons out the best choice of melt temperature and mould temperature associated with the cavity thickness and flow length parameters. The system then store these four parameters in a text file and input to the network when the user executes the neural network and predicts the most suitable injection time. Finally the hybrid neural network system yields with the suitable moulding conditions which are based on the reasoning incorporated in the system.
5. Results and discussions After the system has been trained and tested, it was used to predict the moulding conditions for different components and the predicted conditions were compared with both the published results and simulated results from Moldflow system. Before the system was put into full production some tests have been carried out with parts of simple geometries such as rectangular shapes. The tested part dimensions are 76 mm 38 mm 3 mm and is made of metal powder composition 98% Fe and 2% Ni with the wax-based binder. In order to test the accuracy of the developed network, the system performance has been tested with the data which was not included in training of the system. Ten domain points were selected randomly to test the system. The selected domain points, along with input data and predicted results are shown in Table 3. To check the accuracy of the predicted results, the Moldflow simulation program was executed for the selected 10 input points and found that both the simulated results and neural network predicted results are in close agreement with each other. After satisfactory testing of the developed system, the system was used for obtaining moulding parameters for the product made of Fe–Ni material with wax binder. After completion of consulting procedure with the hybrid neural network, the moulding conditions predicted by the network are 125 8C melt temperature, 40 8C mould temperature and 0.7 s injection time. In order to
Table 4 Simulation results obtained from Moldflow software for different injection times Injection time (s)
Pressure needed for injection (MPa)
Temperature at the end of filling (8C)
Maximum stress after moulding (MPa)
0.3 0.5 0.7 0.9 1.1 1.3
2.1 1.6 1.3 1.2 1.1 1.0
123 122 121 119 118 117
0.094 0.074 0.060 0.056 0.051 0.047
check injection times greater and less than the value of 0.7 s were also used as variable inputs to run the Moldflow software. From the simulation, the results of pressure, temperature and maximum stress were recorded for comparison and are shown in Table 4 and Figs. 4–6. In order to obtain the best quality product, the pressure, temperature drop and maximum stress during mould filling should be lower rather than higher, where as while considering cost the injection time should be shorter rather than longer. The variation of pressure with the injection time is shown in Fig. 6. From Fig. 6 it can be clear that the tendency of the pressure to drop before 0.7 s injection time is higher than that after 0.7 s, concluding the optimum injection time as 0.7 s. The variation of the temperature with injection time
Fig. 4. The variation of temperature vs. injection time.
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for the analysis, determining the process parameters from analysis results, introducing a neural network system for function mapping, and building a knowledge base system for manipulating empirical knowledge. The implemented approach strengthened the capability of the system for predicting optimum moulding conditions MIM process. A number of cases have been tested with the developed network and the results obtained were validated with the published results and simulation results with Moldflow simulation system. Fig. 5. The variation of maximum stress vs. injection time.
Acknowledgements The author would like to convey his sincere thanks to Mr. Cheng Wei Chiang and Mr. Cobby NG under graduate students, QUT, for necessary data collection from the local injection moulding industries, Mr. Martin Roth, Emro Products Pty. Ltd., Caloundra, and Mr. Peter Thompson, KJ Precision Engineering Pty. Ltd., Virginia, Queensland, for providing the information and data for the training and testing of the network.
Fig. 6. The variation of pressure vs. injection time.
is shown in Fig. 4. From the plot in Fig. 4 it is clear that the temperature at the end of filling drops more quickly after the 0.7 s injection time. A temperature, which is too low, is unfavourable because of the risk of distortion and higher residual stresses. Therefore the injection time 0.7 s is the optimum duration. Fig. 5 shows the variation of stress with respect to injection time. From Fig. 5 it is evident that the injection time (0.7 s) suggested by system is the optimum choice. From this case study it is evident that the developed hybrid neural network for predicting moulding conditions in MIM process is reasonably accurate in predicting the moulding conditions.
6. Conclusions In this work attempts have been made to develop a hybrid neural network system by integrating a Moldflow analysis system, a knowledge-based system and a neural network system. The current system has been developed by integrating the different aspects of MIM process. The aspects that are addressed in this system are the physical model of MIM filling stage based on governing equations of mould filling, and process parameters for debinding and sintering stages generated by experimentation. In the developed system the various issues addressed are; establishing a physical model
References [1] S.M. Richardson, H.J. Pearson, J.R.A. Pearson, Simulation of injection moulding, Int. J. Plastic Rubber Process. 5 (1980) 55–65. [2] C.A. Hieber, S.F. Shen, A finite element/finite difference simulation of the injection-moulding filling process, J. Non-Newton. Fluid Mech. 12 (1980) 1–32. [3] D. Huilier, C. Leenfant, J. Terrisse, Modelling the package state in injection moulding of thermo plastics, Polym. Eng. Sci. 28 (1988) 1637–1643. [4] O.Y. Chao, G.P. Maul, Optimal injection velocity profiling, Int. J. Prod. Res. 27 (11) (1989) 1917–1934. [5] I. Pandelidis, Q. Zou, Optimisation of injection moulding design— Part ii: moulding conditions optimisation, Polym. Eng. Sci. 30 (15) (1990) 883–893. [6] S.G. Kim, N.P. Suh, Knowledge base system for injection moulding, Robot. Comput. Integr. Manuf. 3 (2) (1987) 181–186. [7] S. Kollias, D. Anastassious, An adaptive least squares algorithm for the efficient training of artificial neural networks, IEEE Trans. Circuits Syst. 36 (1989) 1092–1101. [8] A. Azushima, M. Kim, A PC-based expert system for forming sequence design, Ann. CIRP 39 (1) (1990) 245–248. [9] A.A. Tseng, J.D. Kaplan, Knowledge-based mould design for injection moulding of plastic balls, Proc. ASME Winter Meeting 19 (1990) 19–33. [10] P.K.D.V. Yarlagadda, Prediction of die casting process parameters by using artificial neural network model for zinc alloys, Int. J. Prod. Res. 38 (1999) 119–139. [11] P.K.D.V. Yarlagadda, Prediction of processing parameters for injection moulding by using a hybrid neural network, J. Eng. Manuf. Part-B 215 (2001) 465–1470. [12] E.C. Bernhardt, G. Bertacchi, Expert system for molding frouble shooting, Proc. of ANTEC, (1991) 436–438.
Development of an integrated neural network system for prediction of process parameters in metal injection moulding Prasad K.D.V. Yarlagadda School of Mechanical, Manufacturing and Medical Engineering, Queensland University of Technology, Brisbane, Qld 4001 Australia
Abstract In this present work attempts have been made to develop an integrated neural network system for prediction of process parameters such as injection pressure and injection time in metal injection moulding (MIM) process. The current system has been developed by integrating the different aspects of MIM process. The aspects that are addressed in this system are the physical model of MIM filling stage based on governing equations of mould filling, and process parameters for debinding and sintering stages generated by experimentation. In this work the feed forward type of neural network has been used, which was initially trained with the analytical data before incorporating as part of an integrated system. In this work Gauss training method has been incorporated for the usage of function approximation. This integrated system has been implemented in MatLAB environment by using neural networks toolbox. This integrated system was successfully tested to solve the real world problems of MIM process. The analytical algorithm based on governing equations of mould filling process first produces a feasible injection time for the MIM process. Injection time data is then used to train the neural network system. In order to validate the results generated by the neural network system are checked with the simulation results of the ‘‘Moldflow’’ software and found that the results generated by integrated neural network system are not different from the simulated results. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Artificial neural networks; Metal injection moulding; MatLAB; Optimisation; Mould filling
1. Introduction The metal injection moulding (MIM) process is a combined process of injection moulding and powder metallurgy. This process is used to manufacture complex metallic parts at a lower cost than the metal working techniques. The important stages involved in MIM process are plastification, moulding, debinding and sintering. This process consists of mixing ultra-fine particles with a polymeric binder material. The prepared mixture is then made into a granular form and pressed into a mould under higher pressure and appropriate temperature. Subsequent to moulding the green part will be subjected to a debinding process during which the binder is removed. Finally the green part is sintered in a process which is similar to conventional powder metallurgy technique. The main application of this MIM technique is used in economical production of complex parts with high-performance of engineering materials. In the MIM process the most critical
E-mail address: [email protected] (P.K.D.V. Yarlagadda).
step is the moulding phase and more often many problems arising during this stage and lead to various kinds of defects such as voids, sinks, distortion and cracks. These defects can be avoided by proper selection of process parameters such as held pressure, temperature of the mould and melt. High injection pressure is needed to force the melted power mixture of high viscosity into the mould within a short period of time. On the other hand, higher pressure would lead to residual stresses which result distortion or cracking. Even though the increase of melt temperature can reduce viscosity and make mould filling easier, too low a viscosity may result in problems with mould filling such as jetting, splashing or air entrapment. Increasing the mould temperature reduces heat losses and the maximum temperature difference at the end of the mould filling stage. This improves the quality of part, but increases cooling time consequently the production time. Hence it can be realised that the relationship between process parameters for MIM process is very complex and most of these parameters are inter-connected. In this research work attempts have been made to optimise the process parameters in MIM process through a physical model.
0924-0136/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 7 3 8 - 0
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2. Background and current status As mentioned in the previous section the selection of process parameters in the moulding process controls the quality of the finished part, which depends on mould filling analysis during injection state. Several researchers [1–12] attempted to address the problems associated with plastic injection process, which is also referred as MIM process and mould filling analysis. Some researchers Richardson et al. [1], Hieber and Shen [2], and Huilier et al. [3] addressed the mould filling stage problem as a problem of combined energy and transport of momentum and applied to the transient and non-isothermal flow problem. After the mould filling simulation packages became available the researchers Chao and Maul [4] and Pandelidis and Zou [5] tried to optimise the injection cavities, injection velocity and gate locations. The applications of expert systems and neural networks in manufacturing were found in several researchers work [6–11]. Kim and Suh [6] developed a prototype knowledge-based synthesis system for injection moulding. In their work, they mainly focussed on mouldability and mechanical acceptability of the design for plastic parts. Tsang et al. [9] developed an approach for incorporating a knowledge-based system into a computer-aided design system for design of injection moulded parts. The domain of their system is restricted to the appropriate moulding set up, fault detection and shot-to-shot monitoring. Bernhardt and Bertacchi [12] developed an expert system for trouble shooting during moulding. Their system provides guidance to the operator to test and debug the start-up operations and correct problems as they arise in running the system. In 1980s several developments leads to development of interest in neural networks, most notable was the development of a training method for multi-layer networks [9]. This development enabled neural networks to learn functions such as the XOR and development of fully inter-connected networks, which converges with stable outputs. Yarlagadda [10,11] used artificial neural networks for production of process parameters in both die casting and injection moulding processes. In this work the neural network was developed by comparing three different training algorithms: namely error back-propagation algorithm; momentum and adaptive learning algorithm; and Levenberg–Marquardt approximation algorithm. It was found that the Levenberg–Marquardt approximation algorithm was the preferred method for this application as it reduced the sum-squared error to a small value. The accuracy of the developed network was tested by comparing the data generated from the network with that of an expert from a local die casting and injection industry. From the literature review it can be concluded that the moulding stage of MIM process is the most critical for the success of producing the final product with good quality. The MIM parameters such as melt temperature, mould temperature and injection time have to be set for the process can be scientifically obtained from the mould filling simulation. Hence the objectives of the
research work are (1) to develop a mathematical model for the MIM moulding stage in order to identify the correct moulding conditions, and (2) to develop an artificial neural network system to predict optimal moulding conditions.
3. Modelling of MIM process The MIM process begins with the heating of the feedstock to a sufficiently high temperature so that the feedstock Si melted, and then forcing this melt into a cavity where it cools and forms the shape of the part. The objective of this process is to obtain parts which are free of voids or other defects. In order to manufacture satisfactory parts, the temperature of the melt must be within a certain range. If the temperature is too low, the mixture is too viscous and complete mould filling is not possible and if too high, uniform filling becomes difficult, and crack of the part might occur due to large temperature gradient between feedstock and the die. Within the proper melt temperature range, if the setting of the mould temperature is lower level, higher pressure is needed to force the melt into the cavity but the cooling time will be less. On the other hand, increasing the mould temperature will reduce the shear stress and pressure, but the cycle time will be longer. The injection time parameter is the inversion of injection rate. At very injection rates there are high shear rates so that the pressure required to fill cavity is high. On the contrary, when the injection rate is very low, the melt temperature gets very cold towards the end of the flow and will result in higher injection pressure and a higher stress level at the end. In the interest of producing parts at low cost, these contrary constraints necessitate the building of a physical process model for the analysis. 3.1. Modelling of the viscosity The characteristics of feedstock play a key role in MIM mould filling process. The most important is the viscosity, which relates the shear stress to the shear strain rate. The viscosity Z for Newtonian fluid is dependent on temperature and pressure, where as for non-Newtonian fluid, it is a function of temperature, pressure and shear rate. For the MIM feedstock mixture, it not only shows non-Newtonian behaviour but it also further depends upon binder components and the suspension behaviour and behaviour of metal particles that are surrounded by the binder. The two important factors that contribute to the viscosity change by temperature for MIM mixture are thermal activation and thermal expansion and the relation is expressed as E 1 1 Z ¼ Zi exp (1) kT T t0 where Zi and E are material specific constants, k the Boltzman’s constant and E is called the activation energy for viscosity. The temperature dependence of viscosity is further complicated by the fact that the components of
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powder–binder mixture have different melting points. The viscosity behaviour changes with the melting of each component and it is difficult to model this effect in the overall mathematical model. One way to handle this in simulation analysis is to check the temperature and use the appropriate model corresponding to that temperature range. Pressure has relatively small effect on the viscosity of a MIM mixture. Part of this effect is the increase in binder viscosity with pressure. Generally the larger the activation energy E for viscous flow, the larger the sensitivity to pressure changes. Viscosity Z dependence on pressure P which can be expressed in a similar way to the temperature effect as Z ¼ Z0 exp½CðP P0 Þ
(2)
where Z0 is the reference viscosity at a reference pressure P0, which usually is one atmosphere, C the pressure coefficient, which is an effective activation enthalpy for the pressure induced viscosity changes and P the pressure. In practice, the pressure used in MIM moulding changes in the order of a few MPa. Comparing the temperature, the influence of pressure on the viscosity is equal to that caused by the temperature change of approximately 1 K. Therefore, under standard MIM operation, the influence of pressure on the viscosity can be ignored. Overall viscosity model can be arrived by combining Eqs. (1) and (2) under the assumptions; viscosity changes with the pressure is negligible, viscosity is dependent upon the particle size is negligible and the change in solid loading with temperature is negligible. The overall relation is Zm ¼ Zr A 0
1 O 2 E n1 exp g Om kT
(3)
where Zr is binder reference viscosity, n the power law index, E the activation energy for the powder binder system, k the gas constant, Om the maximum solid loading, O the solid loading, g the shear rate and A0 the constant and is approximately equal to 1. 3.2. Modelling of the mould filling stage The MIM process is derived from plastic injection moulding with minor modifications due to the difference in material characteristics. MIM feedstock consists of different components including metal powder and binder, in addition the binder is composed of constituents like polymers, waxes and other wetting materials. Different combinations of these powders and binders, powder size and shape make MIM more complex than simple plastic injection moulding. The governing equations of the flow of MIM melt can be derived from a compressible, viscous fluid. These equations are obtained using the principles of conservation of mass, momentum and energy. In the case of injection moulding, Fig. 1 illustrates a simple mould cavity, which displays the required boundary conditions. There are several surfaces on which boundary conditions exist. By applying the
Fig. 1. Mould filling boundaries considered for simulation model.
momentum and continuity equations, and combining them to obtain: @ @r @ @r Ss Ss þ ¼0 (4) @x @x @y @y where Z S2 ¼
h 2 0
z dz Z
As described above, the rheological response of MIM melt is generally non-Newtonian and non-isothermal. Also the mould filling process in MIM is transient in view of timedependent domain during filling. The governing equations are highly non-linear. Apart from very simple geometry parts, the equations governing the flow of the injection moulding are very difficult to solve. Since usually injection moulds have different and complex geometries, a general method of solution is required. A finite element method has been developed in which triangular elements are used to describe the geometry for calculating the pressure and temperature [2]. In this work the Moldflow numerical techniques have been used for simulating the mould filling stage of MIM process by using the model described in Eqs. (1)–(3) for describing the material behaviour. The effect of moulding conditions on the MIM process has been investigated by using Moldflow simulation program for 17-4PH Stainless steel feedstock, injected into a 150 mm flow length mould with different moulding conditions.
4. Development of hybrid neural network system for MIM process In this work the structure of the feed forward neural network has been used for developing the network to predict MIM process parameters as shown in Fig. 2. For most of the engineering applications, in general, back propagation network in combination with gradient descent optimisation method as learning algorithm. However for current application the gradient descent technique is not suitable due to
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Fig. 2. Neural network for prediction of injection time.
complexity of the MIM process. A more sophisticated optimisation technique namely; Gauss–Newton with Levenberg algorithm was used as a learning algorithm, since it is a powerful tool for the least square problem. More details of the Levernberg learning algorithm and its suitability to similar kind of problems has been explained in detailed in other published work [10,11]. In this research work in order to determine the suitable MIM moulding conditions, the neural network used as a mechanism for mapping the function. As discussed earlier the three moulding conditions need to be identified before setting up the mould are melt temperature, mould temperature and injection time. In this work the melt temperature and mould temperature are established based on Moldflow simulation and these parameters were used as input in the developed feed forward neural network for the prediction of injection time. As discussed earlier the injection time is a reverse of the melt flow rate and it dominates the pressure needed to force the melt into the cavity. The injection time is not only depends on melt and mould temperatures but also on the thickness and flow path of the cavity. Hence the feed forward network is then constructed with four neurons (melt temperature, mould temperature, cavity thickness and flow path length) in the input layer and one neuron (injection time) in the output layer. Establishing the number of neurons in the hidden layer is one of the critical issue while solving problems using multi-layer feed forward networks. The precise solution for this issue is rather difficult because of the complexity of the network mapping and the non-deterministic nature of any successfully completed training procedures. In this MIM system the number of hidden layers are determined by using trial-and-error methods. The procedure adopted for integrating the knowledge base, feed forward neural network and Moldflow simulation system is shown in Fig. 3. When the four input parameters melt temperature, mould temperature, cavity thickness and flow path length are
Fig. 3. Development of artificial neural network system for MIM.
entered into the system, and then the system will predict the suitable injection time. Any neural network will not be able to predict the output parameters accurately unless the network is properly trained with accurate data, hence sufficient care must be taken in the preparation of training data the training data must cover the wide variety of possible ranges. Some of the limitations associated with the current system are; the maximum cavity thickness is 100 mm, the maximum weight of the component is 100 g, the melt temperature must be higher than the material’s freezing temperature (20 8C) and the range of mould temperature is between 30 and 50 8C. The various operating conditions that are used for training the network are given in Table 1. The total data set generated for training the network ð10 5 5 7Þ is 1750 and this forms the neural network’s reasoning domain. After defining the domain, experimental data has been generated from the Moldflow simulation results for each of the 1750 data points and Table 1 The training data used to train the MIM system Process parameter
Operating conditions
Melt temperature (8C)
100, 105, 110,115, 120, 125, 130, 135, 140, 145 30, 35, 40, 45, 50 2, 4, 6, 8, 10 50, 75, 100, 125, 150, 175, 200
Moulding temperature (8C) Cavity thickness (mm) Flow path length (mm)
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Table 2 Simulated injection time for selected data points
Table 3 The data used for testing and predicted results of the neural network
Melt temperature, mould temperature, cavity thickness, flow length
Injection time (s)
Data point
100, 100, 100, 115, 115, 115, 130, 130, 130,
0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.5
Melt temperature (8C)
Mould temperature (8C)
Cavity thickness (mm)
Flow path (mm)
Results/ injection time
1 2 3 4 5 6 7 8 9 10
125 135 140 120 110 105 112 142 137 108
45 48 38 33 35 45 37 40 47 32
6 8 9 7 4 8 5 3 6 8
125 175 190 140 86 175 114 75 108 185
1.5 2.89 3.27 2.07 0.4 2.12 0.9 0.62 1.55 2.26
30, 40, 50, 30, 40, 50, 30, 40, 50,
2, 2, 2, 2, 2, 2, 2, 2, 2,
50 50 50 50 50 50 50 50 50
obtain the best injection time for these points. Some of the results obtained for some of the selected simulation points is shown in Table 2. In this system, the knowledge base system communicate with the user through a built-in interface. By making use of the necessary information, the system reasons out the best choice of melt temperature and mould temperature associated with the cavity thickness and flow length parameters. The system then store these four parameters in a text file and input to the network when the user executes the neural network and predicts the most suitable injection time. Finally the hybrid neural network system yields with the suitable moulding conditions which are based on the reasoning incorporated in the system.
5. Results and discussions After the system has been trained and tested, it was used to predict the moulding conditions for different components and the predicted conditions were compared with both the published results and simulated results from Moldflow system. Before the system was put into full production some tests have been carried out with parts of simple geometries such as rectangular shapes. The tested part dimensions are 76 mm 38 mm 3 mm and is made of metal powder composition 98% Fe and 2% Ni with the wax-based binder. In order to test the accuracy of the developed network, the system performance has been tested with the data which was not included in training of the system. Ten domain points were selected randomly to test the system. The selected domain points, along with input data and predicted results are shown in Table 3. To check the accuracy of the predicted results, the Moldflow simulation program was executed for the selected 10 input points and found that both the simulated results and neural network predicted results are in close agreement with each other. After satisfactory testing of the developed system, the system was used for obtaining moulding parameters for the product made of Fe–Ni material with wax binder. After completion of consulting procedure with the hybrid neural network, the moulding conditions predicted by the network are 125 8C melt temperature, 40 8C mould temperature and 0.7 s injection time. In order to
Table 4 Simulation results obtained from Moldflow software for different injection times Injection time (s)
Pressure needed for injection (MPa)
Temperature at the end of filling (8C)
Maximum stress after moulding (MPa)
0.3 0.5 0.7 0.9 1.1 1.3
2.1 1.6 1.3 1.2 1.1 1.0
123 122 121 119 118 117
0.094 0.074 0.060 0.056 0.051 0.047
check injection times greater and less than the value of 0.7 s were also used as variable inputs to run the Moldflow software. From the simulation, the results of pressure, temperature and maximum stress were recorded for comparison and are shown in Table 4 and Figs. 4–6. In order to obtain the best quality product, the pressure, temperature drop and maximum stress during mould filling should be lower rather than higher, where as while considering cost the injection time should be shorter rather than longer. The variation of pressure with the injection time is shown in Fig. 6. From Fig. 6 it can be clear that the tendency of the pressure to drop before 0.7 s injection time is higher than that after 0.7 s, concluding the optimum injection time as 0.7 s. The variation of the temperature with injection time
Fig. 4. The variation of temperature vs. injection time.
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for the analysis, determining the process parameters from analysis results, introducing a neural network system for function mapping, and building a knowledge base system for manipulating empirical knowledge. The implemented approach strengthened the capability of the system for predicting optimum moulding conditions MIM process. A number of cases have been tested with the developed network and the results obtained were validated with the published results and simulation results with Moldflow simulation system. Fig. 5. The variation of maximum stress vs. injection time.
Acknowledgements The author would like to convey his sincere thanks to Mr. Cheng Wei Chiang and Mr. Cobby NG under graduate students, QUT, for necessary data collection from the local injection moulding industries, Mr. Martin Roth, Emro Products Pty. Ltd., Caloundra, and Mr. Peter Thompson, KJ Precision Engineering Pty. Ltd., Virginia, Queensland, for providing the information and data for the training and testing of the network.
Fig. 6. The variation of pressure vs. injection time.
is shown in Fig. 4. From the plot in Fig. 4 it is clear that the temperature at the end of filling drops more quickly after the 0.7 s injection time. A temperature, which is too low, is unfavourable because of the risk of distortion and higher residual stresses. Therefore the injection time 0.7 s is the optimum duration. Fig. 5 shows the variation of stress with respect to injection time. From Fig. 5 it is evident that the injection time (0.7 s) suggested by system is the optimum choice. From this case study it is evident that the developed hybrid neural network for predicting moulding conditions in MIM process is reasonably accurate in predicting the moulding conditions.
6. Conclusions In this work attempts have been made to develop a hybrid neural network system by integrating a Moldflow analysis system, a knowledge-based system and a neural network system. The current system has been developed by integrating the different aspects of MIM process. The aspects that are addressed in this system are the physical model of MIM filling stage based on governing equations of mould filling, and process parameters for debinding and sintering stages generated by experimentation. In the developed system the various issues addressed are; establishing a physical model
References [1] S.M. Richardson, H.J. Pearson, J.R.A. Pearson, Simulation of injection moulding, Int. J. Plastic Rubber Process. 5 (1980) 55–65. [2] C.A. Hieber, S.F. Shen, A finite element/finite difference simulation of the injection-moulding filling process, J. Non-Newton. Fluid Mech. 12 (1980) 1–32. [3] D. Huilier, C. Leenfant, J. Terrisse, Modelling the package state in injection moulding of thermo plastics, Polym. Eng. Sci. 28 (1988) 1637–1643. [4] O.Y. Chao, G.P. Maul, Optimal injection velocity profiling, Int. J. Prod. Res. 27 (11) (1989) 1917–1934. [5] I. Pandelidis, Q. Zou, Optimisation of injection moulding design— Part ii: moulding conditions optimisation, Polym. Eng. Sci. 30 (15) (1990) 883–893. [6] S.G. Kim, N.P. Suh, Knowledge base system for injection moulding, Robot. Comput. Integr. Manuf. 3 (2) (1987) 181–186. [7] S. Kollias, D. Anastassious, An adaptive least squares algorithm for the efficient training of artificial neural networks, IEEE Trans. Circuits Syst. 36 (1989) 1092–1101. [8] A. Azushima, M. Kim, A PC-based expert system for forming sequence design, Ann. CIRP 39 (1) (1990) 245–248. [9] A.A. Tseng, J.D. Kaplan, Knowledge-based mould design for injection moulding of plastic balls, Proc. ASME Winter Meeting 19 (1990) 19–33. [10] P.K.D.V. Yarlagadda, Prediction of die casting process parameters by using artificial neural network model for zinc alloys, Int. J. Prod. Res. 38 (1999) 119–139. [11] P.K.D.V. Yarlagadda, Prediction of processing parameters for injection moulding by using a hybrid neural network, J. Eng. Manuf. Part-B 215 (2001) 465–1470. [12] E.C. Bernhardt, G. Bertacchi, Expert system for molding frouble shooting, Proc. of ANTEC, (1991) 436–438.