Production parameters.
Abstract
Chill block melt spinning is used in industrial processes for the production of metallic glasses. It is a rapid solidification process whereby a liquid metal is ejected at high pressure and temperature via a nozzle onto a rotating wheel solidifying in the form of a ribbon. In this work, starting from an alloy with the composition of Fe78Si9B13 (% at.) reproduces the melt spinning technique to get the amorphous magnetic material. A CFD3D model based on the finite volume method (FVM) is proposed. For this purpose, the OpenFoam® open source code is used. In the ribbon production stage, it has been observed that the turbulence involved in the first reported transient lasts a few milliseconds, enough time to study the process with high-speed cameras. We measure the ejection speed by using optical flow on the melt contour. This enables us to check defects in the ribbons, which are predicted with the computational model, such as the case of cracks caused by irregularities in the first formation of the solid layer. The temperature measurement method relies on the fact that the digital camera is sensitive to electromagnetic radiation between 400 and 1000 nm in wavelength and the fact that the image gray level, which is proportional to the temperature T, provided the background illumination level is negligible.
Keywords
- melt spinning
- magnetic materials
- OpenFoam
- CFD
- finite volume method
1. Introduction
Since the 1980s, the production of magnetic materials has been carried out mainly through the melt spinning process. These materials, obtained in the form of low thickness ribbons, have increased magnetic capacities with the utilization of alloys with amorphization capacity and nanocrystalline. Among these alloys, those of
2. Materials and methods
2.1. Set-up and production
These operations are developed in a 7.5 kW induction furnace
With an argon overpressure, the alloy melted is expulsed through the nozzle at an ejection velocity over the spinning wheel. Our implementation of the process captured with a high-speed camera can be observed in Figure 2(a). It is similar to the one reported by Ames Laboratory, USA in Figure 2(b).
To determine the width (
2.2. Obtained product and results
The cooling rate was estimated according to −2.73 × 106 K/s with a wheel speed (
Speed wheel (m/s) | Gap (mm) | Ejection pressure (bar) |
---|---|---|
5–40 | 2, 3, and 4 | 0.3 |
In Figure 3, the
This effect is indicative of the Newtonian cooling in the solidification process of amorphous ribbons. The features are already reported by Pagnola et al. [4, 5]. For wheel speeds between 5 and 40 m/s, the thickness (
The turbulence involved in the reported solidification times lasts a few milliseconds. Enough time to study the process with high-speed cameras and recreate
The Vickers microhardness
For the tensile test of the ribbons, the device of Figure 8 was used. Average values in 10 different samples were determined in Table 2.
Sample | n |
---|---|
Breakage average load (N) | 11.95 |
Average section (mm2) | 0.063 |
Average resistance to traction (MPa) | 190 |
3. Computational modeling
The work of Bussmann et al. [11] proposes a numerical solution of the equations of momentum and energy to study the condition of stable flow and temperature field in the puddle of the process of melt spinning. The proposed model considers the inertial effects, viscous, the surface tension, and the dependence of the viscosity with the temperature until the solidification of the material to an amorphous state.
In the work of Babei et al. [12], a numerical formulation based on the finite difference method is proposed to model the flow and heat transfer phenomenon transient in melting process. The results are contrasted with experimental models finding high consistency between the results.
In the work of Hui et al. [13], a numerical model is proposed for the study of the process of heat transfer and transient flow in the melt spinning process using the Navier-Stokes equations and the heat transfer equation. The proposed model allows the calculation of the cooling speeds along the thickness of puddle for different wheel speeds. Using experimental models, temperature distributions and cooling velocities were obtained, and similar results to those found in the numerical model were obtained.
Wang and Matthys [14] present a bi-dimensional finite difference semi-implicit numerical model for the study of the flow field and heat transfer with phase change in the casting model process. The boundary-layer theory is used to model these fields during the solidification process of the puddle.
Steen and Karcher [15] present the analysis of casting metals using spinning wheels. This work presents a broad discussion of flow stability, a relevant aspect in non-stable flow phenomena, which influences the movement of the meniscus, final texture, and instability of the morphological type of the solidification front.
Theisen et al. [16] focus their study on the behavior of the melt spinning process in time. The model developed is based on the equations of mass balance in unstable state combined with the Bernoulli equation of the flow. The proposed model allows to establish variations in different time scales, allowing to determine the time scale in which the process can be considered as stable. The evolution of the length of the puddle and the thickness of the produced metal tape indicates that the solidification speed varies over time.
In the work of Sowjanya and Kishen Kumar Reddy [17], they investigate the flow field of molten material in the puddle by determining pressure profiles, flow lines, and current function according to the injection pressure of the material in the nozzle. The proposed model allows to determine the point of separation of the material of the wheel to form the tape.
Sowjanya and Kishen Kumar Reddy [18] propose a bi-dimensional numerical model to model the molten puddle during the melt spinning process by finding stable puddle formation times related to its injection pressure. The comparison of experimental thicknesses with numerical results has a high concordance.
3.1. Governing equations
The numerical model is based on the following assumptions [11]:
The width of the tape is much greater than the height of the gap, then puddle is considered essentially two dimensional.
As the diameter of the wheel is much greater than the length of the puddle, the curvature of the wheel beyond the puddle is negligible. In addition, the lower surface of the puddle is considered flat.
Molten material and the fluid that surrounds the puddle are considered as incompressible and a Newtonian fluid with laminar behavior.
Density, surface tension, and thermal diffusivity of the molten material are considered constant. Kinematic viscosity depends on temperature.
The heat flow between the tape and the wheel is of the convective type. The temperature of the wheel remains constant. The transfer of heat by radiation from the puddle is negligible.
The basic equations that govern the phenomenon of molten metal flow in the melt spinning process are given by the mass balance equation:
where
where
where
In this equation,
3.2. Boundary conditions
On the solid surfaces of the injection and wheel nozzle, a non-slip and non-penetration flow condition is considered. On the surface of the wheel, the fluid moves at the same speed as the wheel. The
where
4. Image-based measurements
4.1. Ejection velocity measurement
The most frequently used technique for studying the
The ejection velocity of the molten alloy is a parameter that is directly linked to the ejection pressure, the fluid viscosity and temperature, and nozzle size. This velocity can be measured using image-based velocimetry. Recently, image-based velocimetry has become more attractive than
On the assumption that the movement is small, the image constraint at
From these equations, it follows that
where
4.2. Temperature measurement
In Eqs. (9)–(11),
As proposed by Bizjan et al. [28], many variables are not directly measured or known, but it is safe to assume that they remain constant during the experiment. The constant
In Figure 10, we show the stable flow of the molten alloy in the
5. Conclusions
In this chapter, we have described the
Acknowledgments
The three authors of this chapter,
Conflict of interest
It is hereby acknowledged that all the authors participating in this work do not present any real or potential conflict of interest, including financial aspects.
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