Application of Neural Network Prediction in the Optimization of Forming Process of Magnetic Ceramic/Rare Earth Alloy Composite Magnets

In order to ensure that magnet materials have higher mechanical properties and magnetic properties at the same time, magnetic ceramics and rare earth alloys are combined to form composite magnets by bonding and pressing. The nonlinear relationship from input (pressing pressure and holding time) to output (coercivity, density and compressive strength) was established by neural network platform, and the optimization of pressing process was studied. The results show that the density, compressive strength and coercivity of the material increase with increasing pressure. When the pressing pressure exceeds a certain value, the density and compressive strength of the material increase slowly, but the coercivity of the material will decrease. The reason for the decrease of coercivity is related to the crushing of the fast quenched rare earth alloy powders in the form of scales due to excessive pressure and long holding time. The experimental results show that the optimum process parameters with high compressive strength and high coercivity can be found by the prediction of neural network.


Introduction
An artificial neural network consists of a large number of neurons that are widely connected to each other to mimic the structure of the human brain.Its imitation function includes good behavior, memory, association, judgment and so on.Therefore, neural networks have been widely used in many fields.At present, this technique can establish nonlinear correlations between output results and input parameters directly by means of experimental data samples without existing models.This platform is particularly suitable for predicting the nonlinear correlation between product performance and product preparation process parameters in production practice to guide production practice [1] .The composite magnet material is a kind of very important functional material which is formed and cured by mixing the magnetic powder with the binder.Magnetic powder can be fast quenched rare earth alloy powder or/and ferrite magnetic ceramic powder.Ferrite magnets are strong and durable, but they are weak in magnetic strength and fragile in mechanical strength.There are many types of fast quenched rare earth alloy powders, among which nano dual-phase NdFeB permanent magnet powder is composed of nano scale hard magnetic phase and nano scale soft magnetic phase, so in theory, its magnetic properties are very superio [2][3][4] .At present, the most used composite magnet molding methods are injection molding and press molding.In the injection molding method, thermoplastic resin material is mainly used for mixed granulation.In the press molding, thermosetting resin (such as epoxy resin, etc.) is mainly used.The composite magnet material obtained by pressing has higher magnetic properties, higher magnetic powder integral number and density, and has good impact resistance and compressive strength, which are conducive to the further application of composite magnet materials.By pressing, various products with precise size, low shrinkage can be prepared.When the binder content is constant, the magnetic properties and strength of the composite magnet both increase with the increase of density, and the density of the composite magnet is determined by the molding pressure, so the selection of the molding pressure is one of the key issues in the production of composite magnets [5][6][7] .In order to ensure that magnet materials have higher mechanical properties and magnetic properties at the same time, the magnetic ceramics with harder properties and the fast quenched rare earth alloys with higher magnetic properties are combined to form composite magnets by bonding and pressing.With the help of BP neural network prediction platform, the relationship between the pressing process parameters of composite magnet materials and the mechanical properties and magnetic properties of materials is studied.

Experimental Method
The main raw materials in the test are magnetic ceramic powder and fast quenched rare earth alloy magnet powder.The magnetic ceramic is barium ferrite containing strontium and bismuth.The nominal composition of the fast quenched rare earth alloy magnet material is RExFe77B6Cox-1Nb1, where x=6-9, RE are neodymium, samarium and cerium and so on.The metal raw materials were weighed according to the nominal composition of the material before melting and preparation, and the purity of each raw material is greater than 99.9%.The raw materials were put into a vacuum induction furnace to melt into alloy liquid, melting temperature was 1570-1690℃.Then the melt was hold for 5-7 minutes before being cast to form a master alloy.The master alloy was then melted in another melting furnace to produce an alloy liquid, which was then poured on a rotating roller under the iron outlet of the melting furnace to rapidly solidify into an amorphous fast quenched thin strip.The powder of permanent magnet material was obtained by grinding thin strip.Then the obtained powder material is placed in a tubular vacuum heat treatment furnace for crystallization heat treatment.The crystallization heat treatment temperature is set in the range of 500-700℃, and the holding time is 5-30 minutes.After crystallization, the rare earth alloy magnetic powder was mixed with strontium barium ferrite powder and binder in a certain proportion, and then the cylindrical composite magnet material sample with a diameter of 10mm and a height of 10mm were prepared by pressure molding.Finally, the properties of the composite magnet cylinder samples were measured by a multifunctional magnetic measuring instrument and corresponding mechanical properties testing machine.The mass ratio of rare earth alloy magnet material to magnetic ceramic powder is 3:1, and the binder is 4% of the weight of the magnet.The binder is epoxy resin and corresponding curing agent.The range of molding pressure for test is 100-700MPa, and the holding time is 2-32 seconds.After measuring the properties of the material samples, BP neural network platform was used to predict the pressing process parameters.The BP model based on MATLAB has many different topologies, which will interfere with the complexity of its prediction calculation.Therefore, it is necessary to adjust the controllable parameters in the neural network model to make the error between the predicted value and the training value less than the preset error in order to train the network with the test data.In the neural network prediction, the pressure W and pressing holding time Q were taken as input parameters, and the measured coercive force, density and compressive strength were taken as output parameters, so as to predict the changing trend of the influence of the forming pressure parameters on the properties of the test material.

Experimental Results and Discussion
The mean square error of BP neural network training is set to 1e-8.In order to achieve this accuracy, different biases and system weights are applied in the training process of BP neural network.In order to improve the operation speed, various transfer equations such as tansig, purelin and logsig were tested at the hidden layer and output layer.In addition, different training methods such as trainrp, traingd and trainlmtrainbfg were also tested.And various learning equations such as learngd, learngdm, Learning have been tried.The experimental results show that when the accuracy and stability of prediction and training speed are measured, trainlm is used as the training function, the working quality of BP neural network platform shows excellent properties.The linear regression fitting states between the predicted value and the corresponding experimental value are given in Figure 1, Figure 2, and Figure 3.As can be seen, the dotted lines (Y=T) in Figure 1, Figure 2 and Figure 3 are very close to the solid lines(Fit), indicating that the degree of prediction of the model is consistent with the actual situation.Where R is the regression value.For coercivity, density and compressive strength, the Rvalues are 0.97141, 0.99184 and 0.99951, respectively.As can be seen from the prediction surfaces in Figure 4, Figure 5 and Figure 6, the performance data on the prediction surfaces gradually change smoothly.Figure 4 shows the coercive force of composite magnet materials as a function of molding pressure W (100-700 MPa) and holding time Q (2-32 s).The surface in Figure 4 (a) is the predicted surface of the neural network, and the points on the surface are the experimental verification points, indicating that the predicted coercivity value is consistent with the experimental value.Figure 4(b) shows the degree of agreement between the predicted coercivity value and the experimental value, and the value of the relevant parameters reaches 0.94603, indicating that the predicted value and the experimental value are in good agreement.Figure.5 shows the variation trend of the density of composite magnet materials with molding pressure and holding time.The surface in Figure5 (a) is a prediction surface, and the points on the surface are experimental verification points, indicating that the predicted density values are also consistent with the experimental values.Figure 5 (b) shows the degree of agreement between the predicted density value and the experimental value, and the correlation parameter value is 0.98282, indicating that the predicted value and the experimental value also have a high degree of agreement.Figure.6 shows the variation trend of compressive strength of composite magnet materials with pressing pressure and holding time.The surface in Figure 6 (a) is the prediction surface, and the points on the surface are the experimental verification points.Figure 6 (b) shows the degree of agreement between the predicted compressive strength value and the experimental value, and the value of the relevant parameters reaches 0.98775, indicating that the predicted value and the experimental value also have a higher degree of agreement.As can be seen from the prediction surface in Figure 4, when the pressing pressure is 600MPa and the holding time is 20s, the coercivity of the material is higher than that of other process parameters, and its value is 746 kAm -1 .Deviating from this range of optimization process parameters, the coercivity of the material will decrease.It can also be seen from Figure 5 that the density of the alloy increases with the increase of pressing pressure and holding time.However, when the pressing pressure is 600MPa and the holding time is 20s, the density of the alloy reaches 5.85g /cm3.With increasing pressing pressure and holding time, the density of the material increases very little.It can also be seen from Figure 6 that the compressive strength of the material increases with the increase of pressing pressure and holding time.However, when the pressing pressure is 600MPa and the holding time is 20s, the compressive strength of the material is 47.2MPa.With increasing pressing pressure and holding time, the compressive strength of the material is not much improved.It can be seen from Figure 5 and Figure 6 that the density of the material changes with the pressing pressure and holding time, and the overall change trend is consistent with the compressive strength.When the pressing pressure is lower than 600MPa, the density and compressive strength of the material increases with the increase of the pressing pressure and the pressure holding time, which results in the reduction of the void of the composite magnet compact.In the composite magnet, under the action of pressure, the magnetic ceramic particles are easy to fill the gap of the rare earth alloy magnetic powder, and increase the density of the magnet.As the pressure increases and the void decreases, the magnetic ceramics and rare earth alloy magnets are in close contact with each other, and the compressive strength increases.Because magnetic ceramics are hard strong phases, they have a greater contribution to compressive strength.In addition, due to the increase of compact density, a large number of defects and internal stresses are generated in the crystal of the magnet, the dislocation density in the crystal increases, the resulting lattice distortion increases, the stress field increases, and the compressive strength is improved.However, there is no maximum density and compressive strength of the material within the set range of test parameters.When the pressing pressure and holding time exceed a certain value (the pressing pressure 600MPa and the holding time 20s) , the density and compressive strength of the material increase very little.This shows that the increase in density will increase the contact area of the powder particles, which is conducive to the improvement of the mechanical properties of the material.When the density reaches a certain level, it is very difficult to reduce the void due to the increase of mechanical friction.It can be seen from Figure 4 that the coercivity of the material has a maximum value with the change of pressing pressure and holding time.The reason is that, on the one hand, according to the nucleation field theory, with the increase of pressure, the pores between the powder particles are reduced, the magnetic ceramic particles are in close contact with rare earth alloy magnet powder particles, and the coupling between the main magnetic phase and the weak magnetic phase and the non-main magnetic phase in the powder material is enhanced.On the other hand, the larger the lattice distortion, the more defects, the stronger the stress field, and according to the pinning theory of coercive force, the greater the hindering motion to the domain wall movement.These effects all lead to an increase in the coercive force of the magnet [8- 10] .However, when the pressure exceeds a certain value, it is very difficult to reduce the void inside the magnets, so the space for increasing the density value is reduced, and the improvement of the compressive strength is also limited.At this time, if the external pressure continues to increase, the scaly particles in the rare earth alloy magnet will be broken during the pressing process, and the magnetic domain interface will be damaged, so the magnetic properties begin to decline.According to the test results, when the pressing pressure is 600MPa and the holding time is 20 seconds, the magnetic properties of the magnet reach the best state.Therefore, the selection of pressing pressure parameters should not only improve the density of pressing magnets, but also suppress the fragmentation of magnetic particles under the action of excessive pressure or excessive pressure holding time.It can be seen from the test that the pressing pressure and the holding time play an important role in affecting the magnetic properties of the material.In addition, it can also be seen that the prediction surface can not only directly display the trend of material properties with the pressing process parameters, show the optimized process parameters, but also provide a data set of the relationship between the properties of materials and process parameters that can not be obtained by limited experiments.Figure 7 shows the morphology of the pressed magnetic ceramic/rare earth alloy composite magnet.The magnetic ceramic powders and rare earth alloy powders are well fused, and the organization is full and dense.

Conclusion
The experimental results show that with the increase of pressing pressure and holding time, the density, compressive strength and coercivity of the material are increased, which is because the gap of the compact is greatly reduced with the increase of pressure.The density of the compact is increased, resulting in the increase of compressive strength.In addition, the density of magnet increases, the particles of magnetic ceramic and rare earth alloy magnet are in close contact, and the coupling between the main magnetic phase and the weak magnetic phase and the non-main magnetic phase in the magnet powders is enhanced, which is conducive to the improvement of the coercivity of the material.When the pressing pressure exceeds a certain value, some scaly fast-quenching permanent magnet powders are crushed during the pressing process, the magnetic domain interface is damaged, and the magnetic properties begin to decline.The optimized process parameters predicted by the trained neural network are in agreement with the experimental data.The trained neural network platform successfully predicted the trend of the properties of materials with the change of process parameters, and also provided the reference data set of process parameters that could not be achieved by limited experiments.The experimental results show that the optimum process parameters with high compressive strength and high coercivity can be found by the prediction of neural network platform.

Figure 1 .
Figure 1.Relationship of linear regression fitting state between predicted coercivity value and corresponding experimental value.

Figure 2 .
Figure 2. Relationship of linear regression fitting state between predicted density value and corresponding experimental value.

Figure 3 .
Figure 3. Relationship of linear regression fitting state between predicted compressive strength value and corresponding experimental value.

Figure 4 .Figure 5 .Figure 6 .
Figure 4. Prediction and test verification of coercivity of materials (a) Experimental relationship between coercivity and pressing parameters； (b) Predictive relationship between coercivity and pressing parameters.

Figure 7 .
Figure 7.The morphology of the pressed magnetic ceramic/rare earth alloy composite magnet material.