Numerical simulation of single roller melt spinning for NdFeB alloy based on finite element method

Xu-Chao Wang Ming Yue Dong-Tao Zhang Wei-Qiang Liu Ming-Gang Zhu

College of Materials Science and Engineering,Beijing University of Technology

Central Iron and Steel Research Institute

作者简介：*Xu-Chao Wang,e-mail:362577891@qq.com;

收稿日期：26 November 2017

基金：financially supported by the National Natural Science Foundation of China(No.51571064);the National Basic Research Program of China (No.2014CB643701);

Numerical simulation of single roller melt spinning for NdFeB alloy based on finite element method

Xu-Chao Wang Ming Yue Dong-Tao Zhang Wei-Qiang Liu Ming-Gang Zhu

College of Materials Science and Engineering,Beijing University of Technology

Central Iron and Steel Research Institute

Abstract：

The numerical simulation model of single roller melt spinning for rapid quenching process of NdFeB alloy was built,and the vacuum chamber,cooling roller and sample were taken into account as a system.The existing mature technology was in order to verify the correctness of simulation.The rapid quenching ribbons with different roll speeds were used as the simulation objects.The results of the numerical simulation and experiments show that the validity of the model has been testified and the reasons of the formation of complete quenching ribbons and by-product have been explained.The experimental thickness of the ribbons is proportional to the theoretical thickness.In the same spray condition,with the roll speed increasing,the thickness decreases linearly.At the speed range of25-30 m·s^-1,the simulated calculation date is close to the experimental date,which can be considered as an ideal technological parameter.

Keyword：

NdFeB; Melt spinning; Finite element method; Numerical simulation;

Received： 26 November 2017

1 Introduction

Since the outstanding magnetic properties of NdFeB were found in 1983,it has been studied in many ways [ 1, 2, 3, 4, 5] .Fully dense anisotropic NdFeB magnets can be produced by the rapid quenching powders [ 6, 7, 8, 9] ,followed by the hot-pressing process [ 10, 11] .Now,vacuum rapidly quenched technology is a significant method of preparing amorphous and nanocrystalline alloys,which is widely used to prepare NdFeB powders [ 12, 13] .The magnetic fine powders with particle size in an appropriate size have many applications [ 14] .The powders can be used to prepare the bonded magnets [ 15] and the hot-deformed magnets [ 16, 17, 18, 19, 20] .The NdFeB magnets,which were prepared by hot-pressing heat deformation with powders,can have excellent magnetic property of about 432.5 kJ·m^-3 [ 21] .

The process parameters have a direct effect on the magnetic powder performance,and the preparation process of the rapid quenching technique is relatively complex [ 22, 23, 24, 25, 26, 27] ,so we need to accumulate a large amount of experimental data.Therefore,the simulation of the rapid quenching process is necessary and can be helpful to the experiment.Owing to the complexity of the process,it is necessary to take different degrees of simplification [ 28, 29, 30] .But the simulation results are still complicated and the research on the rapid quenching mechanism is not thorough enough.Yang et al. [ 31, 32, 33] have studied the cooling speed of the process with numerical simulation,in which the change of cooling speed along the thickness of the melt-spun ribbons is not considered.In this paper,based on the simplification of the NdFeB rapid quenching process,a preliminary study on the fluid motion of the single-roll rapid quenching process was carried out,and the influence of the rapid quenching process parameters on the preparation of the melt-spun ribbons was discussed.

2 Numerical simulation of rapid quenching process

2.1 Experimental design and numerical model establishment

Figure 1 shows the schematic diagram of the melt spinning.According to the rapid quenching technology and the experimental data,the appropriate process parameter has been defined.The cast ingots were melt-spun to form ribbons,about 40 g,which was conducted by using a vacuum melt spinner with a quartz tube with a nozzle diameter of1 mm,a nozzle height of 3 mm,a roller speed of15-45 m·s^-1 and a vacuum of less than 1×10^-2 Pa at the temperature of 1310℃ [ 34] .The diameter of quartz tube is 21.4 mm,and the ejection pressure is 0.05 MPa.The ejection pressure determines the injection speed of the molten fluid.Some property parameters of the NdFeB alloy were investigated upon experimentation for the numerical simulation of rapid quenching.The density of the NdFeB melt is 6.94 kg2m^-3,and the viscosity is 1.4 Pa-s at the temperature of 1310℃ [ 35] .

When NdFeB was smelted,the melt is forming a curved surface at the nozzle,due to the surface tension.As shown in Fig.2,the nozzle is required to get accurate injection velocity field,and the arc is pided into 16 parts,and the closer to the bottom is,the more compact it is,and in order to ensure the accuracy,FLULID141 and FLULID142 unit were used.Finally,the entire mesh model is pided into1882 nodes.At the top edge of the model,the pressure of0.05 MPa was applied.The velocity of injection at the remaining edges is 0 m·s^-1.

Fig.1 Schematic diagram of rapid quenching

Fig.2 Injection process finite element model

3 Results and discussions

To run the program,the equivalent of NdFeB alloy was the molten state for the liquid jet.Figure 3 clearly shows that speed is focused on the nozzle mouth and the maximum value is 2.2585 m·s^-1.The edge velocity of the nozzle decreases because the edge parts obviously gain resistance by quartz tube.

3.1 Simulation analysis of injection time

In this simulation,the law of conservation of mass is adopted.According to the quality of NdFeB,Eq.(1) can be obtained.

where R_out is the nozzle radius;v_out is the velocity of injection;ρis the density of NdFeB;t is the ending time of the injection;M is the quality of NdFeB.

At last,the simulation calculated the completion time of the injection of 40 g melt;it is 3.24 s,consistent with the time in the actual experiment.

Fig.3 Distribution of velocity at nozzle

3.2 Simulating width of NdFeB ribbons

In the ejection process of the rapid quenching experiments,not all of the molten liquid will shoot vertically.It will also spray on both sides.And the width of the NdFeB ribbons is related to the distance of the nozzle to the rollers.Figure 4is the model for the broadening of the ribbons.

As shown in Fig.5,the speed of 16 nodes is got in the xor y-direction by simulation.And the maximum width of each point is calculated by the following three formulas.

where RM is the width radius of the ribbons;H_y is the distance of the roller;V_y is the initial velocity of the nozzle at each point of the nozzle;V_x is the initial velocity of the injection horizontal direction of the nozzle;L_x is thedistance of the nozzle at each point of the nozzle;H is theheight of the roller wheel at the nozzle center;n is the nthcurve of the jet.

Fig.4 A model for broadening of ribbons

Fig.6 A maximum width of ribbons at nozzle

Fig.7 Comparison of theoretical data and experimental data of ribbons thickness

Fig.5 Velocity curves at nozzle.a y vector and b x vector

As shown in Fig.6,the maximum width of the rapid quenching band is obtained at the 13rd node,2.16 mm.In Fig.3,liquid and spray center vertical velocity is high and consistent,but the edge speed is small,leading to that the center part of melt first reaches the cooling roller and the edge parts of the melt have not reached the roller with the high-temperature condition.The first melt reached the cooling roller,and then condensed quickly.And then the edges melt reached and cooled later.It is called the discontinuous rapid quenching process.The results explain why in the rapid quenching,we get not only the complete rapid quenching ribbons but also the formation of some byproducts,such as round balls or irregular ribbons.

Fig.8 Temperature field cloud picture of ribbons

Fig.9 Curve versus temperature of model at marginal area and central zone

3.3 Simulating quenching speed and ribbon thiclkness

According to the law of conservation of mass,Eq.(5) can be obtained.

where h is the ribbon thickness;v_out is the average velocity of vertical direction of the nozzle;y is the actual width of the belt;v_rotate is the roll speed.

From Fig.7,it can be seen that the experimental thickness of the ribbons,which is prepared by the different quenching speed,is proportional to the theoretical thickness.In the same spray condition,with the roll speed increasing,the thickness decreases linearly.The experimental thickness variation is consistent with Eq.(5).At the speed range of 25-30 m·s^-1,the simulated calculation date is close to the experimental date,which can be considered as an ideal technological parameter.

3.4 Temperature field cloud picture of ribbons

Figure 8 exhibits the temperature field cloud picture of the ribbons at 0.04 s^-1 departure time.With the elongation of the departure time,the temperature in the ribbons is stable,the high temperature distribution of the edge part is reduced,and the whole is presented as a rectangular ring cooling.When the departure time was 0.04 s,the highest temperature of the ribbons is about 272℃

Fig.10 a Thickness and b grain size of ribbons at roll speed of 30 m·s

Fig.11 Hysteresis loops for melt-spun ribbons at roll speed of30 m.s^-1

In Fig.9,with the extension of departure time,the temperature of the edge and the center part of the ribbons are linear.The cooling rate of the rapid quenching band is also changing.The calculated maximum cooling rate at the edge of the area is about 105℃·s^-1.

3.5 Test of micros truc ture and magnetic property of ribbons

From Fig.10,it can be seen that the thickness of the ribbon is about 28.7μm and the average grain size of the ribbons is about 100 nm.The ribbon was prepared by the melt spinning at 30 m·s^-1.In Fig.11,the coercive force of the ribbons is about 1274.3 kA.m^-1,which was test by vibrating sample magnetometer (VSM).

4 Conclusion

In this study,the rapid quenching process was simulated by the Ansys.The simulation shows that the completion time of the injection of 40 g melt is 3.24 s and the maximum speed value is 2.2585 m·s^-1.The results explain why in the rapid quenching,we get not only the complete rapid quenching ribbons but also the formation of some byproducts.The experimental thickness of the ribbons is proportional to the theoretical thickness.In the same spray condition,with the roll speed increasing,the thickness decreases linearly.At the speed range of 25-30 m·s^-1,the simulated calculation date is close to the experimental date,which can be considered as an ideal technological parameter.The thickness of the ribbon is about 28.7μm,and the average grain size of the ribbons is about 100 nm.