2023 年 64 巻 2 号 p. 596-603
The inspection of shrinkage cavities formed inside spheroidal graphite cast iron during the manufacturing process of spheroidal graphite cast products, including large cast structures and machine parts, is considered to be important for quality assurance of cast products. X-ray and ultrasonic methods are generally used for this inspection. However, the former inspection method takes a long time and considerable equipment costs, the latter method requires the use of water as a contact couplant and to polish the surface of the inspection site of the cast iron. In an actual manufacturing factory, there is a demand for a simple and quick method for inspecting shrinkage cavities inside cast iron. In this research, as a simple and high-speed inspection method to evaluate shrinkage cavities inside cast iron by measuring of the vibration of the electromagnetic force is proposed. Three-dimensional electromagnetic field analysis using the finite element method and displacement analysis was performed to analyze the phenomenon, and the usefulness of this method was confirmed by verification experiments.
This Paper was Originally Published in Japanese in J. JFS 94 (2022) 3–10.
Spheroidal graphite cast iron material is used for mechanical components such as crankshafts and turbines as a casting material with excellent tensile strength and toughness. However, spheroidal graphite cast iron may generate shrinkage cavity during manufacturing, which reduces its strength, so it must be inspected for shrinkage cavity.1,2) X-ray, ultrasonic and electromagnetic testing methods have been studied for testing for this shrinkage cavity. The X-ray inspection method transmits radiation into the cast iron to determine the shrinkage cavity, and has the advantage that the shape and location of shrinkage cavity can be distinguished in the image. However, inspection equipment is generally large and may be difficult to apply to large castings. Ultrasonic testing is expected to provide a high degree of accuracy, but requires grinding of the surface area of the cast iron material and contact couplant such as water or glycerin.3) Electromagnetic test methods such as eddy current testing (ECT) usually detect changes in eddy currents generated by the applied alternating current (AC), which makes it difficult to detect shrinkage cavity deep inside the cast iron due to skin effect.4,5) Therefore, this study proposes a test method using vibration measurement by electromagnetic force vibration as a more easier method to evaluate shrinkage cavity inside spheroidal graphite cast iron materials. This is a method of evaluating shrinkage cavity by generating electromagnetic force vibrations in a static magnetic field with permanent magnets and eddy currents generated inside the cast iron material by AC current excitation coils. In this paper, electromagnetic field analysis considering the non-linearity of the magnetic properties of cast iron materials using a three-dimensional finite element method (3D FEM) and displacement analysis caused by electromagnetic force vibration are used to elucidate the test principle and studied through verification experiments.
Figure 1 outlines the test method presented in this study. The proposed electromagnetic sensor consists of an electromagnetic force vibrator and a vibration sensor. The vibrator consists of a square prism-shaped permanent magnet with a hole in the center, around which an AC excitation coil is wound. The vibration sensor detects vibrations by attaching a bar-shaped acrylic contact to the acceleration sensor, inserting it into the hole in the permanent magnet and touching the test material. When an AC current is applied to the AC excitation coil, an AC magnetic field is generated, and eddy currents are produced in the cast iron. These eddy currents and the static magnetic field from the permanent magnets generate Lorentz forces in the cast iron in the ±z-axis direction in Fig. 1. Eddy currents have a steady reversal in direction, and therefore the direction of the Lorentz force reverses in the same way. As a result, vibrations of the same frequency as the excitation current are generated in the cast iron. The shrinkage cavity in the cast iron causes a change in the vibration strength of the cast iron, and this strength is detected by a vibration sensor to assess shrinkage cavity. In this method, instead of applying high-frequency vibrations (several kHz to several GHz) and measuring the ultrasonic wave strength over time (e.g. the electromagnetic acoustic transducer (EMAT) method6)), low-frequency steady-state vibrations (several hundred Hz) are applied to the cast iron material and the displacement of the cast iron material, which varies with the presence of shrinkage cavity at the same timing, is measured. Although this method is expected to be less precise in its probing accuracy than the EMAT and ordinary ultrasonic methods, it is considered useful as a first-stage screening test method in non-destructive testing because of its easier signal processing and faster testing speed. As the effect of magnetostrictive stresses in the low frequency range is minute, only Lorentz forces are considered in this study.
Principle of generation of electromagnetic force vibration.
In this research, the target of the test method was spheroidal graphite cast iron material (FCD600) and the effect of shrinkage cavity on the displacement in the cast iron material was evaluated by electromagnetic field analysis and displacement analysis using the 3D FEM. The method uses a static magnetic field from a permanent magnet and eddy currents from an AC excitation coil to generate Lorentz forces inside the cast iron material. Therefore, the direct current (DC) flux density in the cast iron applied from the permanent magnet is first analyzed by static magnetic field non-linear analysis, which considers the non-linearity of the magnetic character of the cast iron material. Next, the eddy currents in the cast iron generated by the AC excitation coil are analyzed in an AC magnetic field analysis, which also considers the non-linear nature of the magnetic properties of the cast iron material, and the Lorentz force is calculated from the DC flux density and eddy currents. In the low frequency range (several hundred Hz), the effect of magnetostrictive stresses is minute, so only Lorentz forces are considered in this analysis of electromagnetic forces. The Lorentz force changing with the AC excitation frequency was then supplied as a source of applied vibration to the cast iron, and the displacements in the cast iron were analyzed using a 3D FEM displacement analysis, and the displacements obtained from the vibration sensor in the presence or absence of shrinkage cavity were analytically evaluated. Figure 2 shows a summary of the flow of the analysis procedure.
Procedures for electromagnetic field analysis, electromagnetic force analysis, and displacement analysis using 3-D finite element method.
Figure 3 shows the one-half domain of the model used in this analysis. Figure 3(a) shows a bird’s-eye view of the analytical model, Fig. 3(b) shows the x-y plane of the overall model and Fig. 3(c) shows a magnified view of the electromagnetic force vibrator. This vibrator consists of an AC excitation coil wound around the outside of a square-prism-shaped permanent magnet with a hole in it. The dimensions of the permanent magnet are 20 mm wide in the x-direction, 20 mm wide in the y-direction and 15 mm high in the z-direction, modelled on a neodymium magnet with a residual magnetization density of 0.5 T. The size of the central hole is 5 mm wide in the x-direction, 5 mm wide in the y-direction and 15 mm high in the z-direction. The AC excitation coil has 120 turns and carries a sine wave AC current of 500 Hz and 2.0 A. The spheroidal graphite cast iron material was the same size as the cast iron material used in the verification experiments described below, with dimensions of 190 × 30 × 30 mm. The shrinkage cavity area was assumed to be a 20 × 10 × 10 mm rectangle and an electromagnetically vacuum area.
Proposed inspection model for measuring shrinkage cavities in spheroidal graphite cast iron (1/2 domain).
The DC flux distribution from the permanent magnet distributed inside the cast iron material was evaluated by static magnetic field analysis. The initial magnetization curve of the test material, spheroidal graphite cast iron material (FCD600), is considered in this analysis. The basic equations in static magnetic field analysis are shown below.
| \begin{equation} \mathop{\text{rot}}\nolimits(\nu\mathop{\text{rot}}\nolimits\boldsymbol{A}) = \boldsymbol{J}_{0} \end{equation} | (1) |
Initial magnetization curve of spheroidal graphite cast iron (FCD600).
Distribution of DC magnetic flux density inside spheroidal graphite cast iron with shrinkage cavities (residual magnetic flux density of permanent magnet = 0.5 T).
In this section, the eddy currents generated inside the cast iron material are analyzed using a 3D FEM AC electromagnetic field analysis. In the analysis, the following basic equations7) were used, considering the initial magnetization curve of the FCD600 shown in Fig. 4.
| \begin{equation} \mathop{\text{rot}}\nolimits (\nu\mathop{\text{rot}}\nolimits\boldsymbol{A}) = \boldsymbol{J}_{\mathbf{0}} - \sigma \left(\frac{\partial \boldsymbol{A}}{\partial t} + \mathop{\text{grad}}\nolimits{\boldsymbol{\phi}} \right) \end{equation} | (2) |
| \begin{equation} \text{div}\left\{ \sigma - \left(\frac{\partial \boldsymbol{A}}{\partial t} + \mathop{\text{grad}}\nolimits{\boldsymbol{\phi}} \right) \right\} = 0 \end{equation} | (3) |
Distribution of current inside spheroidal graphite cast iron with shrinkage cavities. (excitation frequency = 500 Hz, excitation current = 2.0 A(rms), |Je-max| = 3.25 × 106 A/m2).
Figure 5 shows that the surface layer inside the cast iron has a constant DC magnetic flux density distribution in the ±x direction, and Fig. 6 shows that eddy currents with repeated cyclical reversals in the direction orthogonal to the DC magnetic flux density distribution are generated. Therefore, it is considered that cyclically changing Lorentz forces may be generated inside the cast iron. Then, the Lorentz forces inside the cast iron are calculated from the results of the analysis of the static magnetic field and eddy currents distributed inside the cast iron obtained in Sections 3.3 and 3.4. The basic equation of the Lorentz force is shown below.10)
| \begin{equation} \boldsymbol{F} = \boldsymbol{B}\times \boldsymbol{J}_{\text{e}} \times L \end{equation} | (4) |
Distribution of Lorentz force inside spheroidal graphite cast iron with a shrinkage cavities (excitation frequency = 500 Hz, excitation current = 2.0 A(rms), Fmax = 1.81 × 103 N/m).
The Lorentz force with a steady reversal of the distribution obtained in Section 3.5 causes vibrations at 500 Hz in the surface layer of the cast iron material. Therefore, 3D FEM displacement analysis was used to analyze the displacement inside the cast iron with and without shrinkage cavity when electromagnetic force vibrations due to Lorentz forces were applied to the surface layer of the test cast iron material. The basic equations for 3D displacement analysis are shown below.
| \begin{equation} K\boldsymbol{u} = \boldsymbol{F} \end{equation} | (5) |
Comparison of displacement on the cast iron surface with and without shrinkage cavities inside the cast iron (excitation frequency = 500 Hz, excitation current = 2.0 A(rms)).
Evaluation of presence of shrinkage cavities by frequency spectrum intensity (excitation frequency = 500 Hz, excitation current = 2.0 A(rms)).
Distribution of displacement with and without shrinkage cavities inside the cast iron (excitation frequency = 500 Hz, excitation current = 2.0 A(rms)).
In this study, verification experiments were conducted using spheroidal graphite cast iron material (FCD600) with artificially created actual shrinkage cavity. The spheroidal graphite cast iron specimen with shrinkage cavity evaluated in this experiment was spheroidal graphite cast iron (FCD600) produced by the Japan Foundry Engineering Society, ‘Evaluation Technology of Castings’ Research Subcommittee (ETC-3). Figure 11 shows the position of the vibrator, the spheroidal graphite cast iron material and the electromagnetic force vibrator section of the proposed sensor. Figure 11(a) shows an enlarged view of the electromagnetic force vibrator used in the experiment, Fig. 11(b) shows the dimensions of the vibrator and spheroidal graphite cast iron material in the x-y plane, and Fig. 11(c) shows the same dimensions as in Fig. 11(b) in the x-z plane. The permanent magnet used in the experiment is a neodymium magnet with a surface residual flux density of 0.5 T. It has a square shape with dimensions of 20 × 20 × 15 mm and a ϕ5 through-hole in the center. As shown in Fig. 11(a), an AC excitation coil was wound 120 times around the outside of the permanent magnet to form an electromagnetic force vibrator. A 0.1 mm air gap (Lift-off) is provided between the vibrator and the cast iron material, and AC current is applied to the AC excitation coil. The applied current conditions were 500 Hz and 2.0 A (RMS value). As shown in Fig. 11(c), the vibration sensor uses an acceleration sensor, with a contactor made of acrylic attached to the end of the sensor. It is inserted inside the hole of the permanent magnet and touched to the surface of the test cast iron material to detect vibrations on the surface of the cast iron material. The detected signal is analyzed by FFT and the frequency spectral strength is calculated. In this experiment, the presence or absence of shrinkage cavity is determined by comparing the frequency spectral strength at 500 Hz, the applied frequency. Measurements were taken at 16 points at a pitch of 10 mm in the x-axis direction on the surface of the test cast iron material. Figure 12 shows the evaluation results of measurements carried out using this method. Figure 12(a) shows a transmission diagram taken by X-ray transmission testing of a spheroidal graphite cast iron material with shrinkage cavity in the x-y plane, Fig. 12(b) shows the same X-ray transmission test result diagram as in Fig. 12(a) in the x-z plane and Fig. 12(c) shows the experimental results using this method. The vertical axis of Fig. 12(c) shows frequency spectral strength versus excitation current frequency, while the horizontal axis shows the measurement point. The X-ray transmission test results in Fig. 12(a) and Fig. 12(b) were provided by the Japan Foundry Engineering Society, Research Subcommittee on ‘Evaluation Technology of Castings’ (ETC-3). The displacement analysis results in Fig. 9(b) show that the frequency spectral strength was at a minimum at x = ±10 mm, which is the edge of the shrinkage cavity area. The frequency spectral strength reached a maximum value at x = 0 mm, where the existence of shrinkage cavity is located. The evaluation results in Fig. 12(c) show that the frequency spectral strength reached a minimum value at x = 90 mm and a maximum frequency spectral strength between x = 100 and 140 mm. And the frequency spectral strength was again reduced at x = 150 mm. Comparison of the evaluation results of the above verification experiments with the X-ray transmission test figures shows that the areas of increased frequency spectral strength coincide with the actual areas of shrinkage cavity.
Verification experiment inspection model of spheroidal graphite cast iron with shrinkage cavities (excitation frequency = 500 Hz, excitation current = 2.0 A(rms)).
Verification experiment result for presence of shrinkage cavities by frequency spectrum intensity (excitation frequency = 500 Hz, excitation current = 2.0 A(rms)).
The results of this research are outlined below:
This study is a summary of some of the results obtained by the “Evaluation Technology of Castings” research group (ETC-3) of the Japan Foundry Engineering Society. We would like to express our deepest gratitude to the members of the subcommittee and all the people concerned for their cooperation.
