Effects of a Novel Mechanical Vibration Technology on the Internal Stress Distribution and Macrostructure of Continuously Cast Billets

Abstract

In this paper, a new mechanical vibration technology applied to continuous casting production is studied, which is used to break the dendrite at the solidification front, expand the equiaxed dendrite zone, and improve the center quality of the billet. The exciting force of this vibration technology is provided by a new type of vibration equipment (Vibration roll) independently developed and designed. Firstly, an investigation is conducted into the impacts of vibration acceleration, vibration frequency, and the contact area between the Vibration roll (VR) and the billet surface on the internal stress distribution within the billet shell, respectively. Secondly, the billet with and without vibration treatment was sampled and analyzed through industrial tests. The results show that the area ratio of equiaxed dendrites in transverse specimens treated with vibration technology was 11.96%, compared to 6.55% in untreated specimens. Similarly, for longitudinal samples, the linear ratio of equiaxed dendrites was observed to be 34.56% in treated samples and 22.95% in untreated samples. Compared to the specimens without mechanical vibration, the billet treated with mechanical vibration exhibits an increase in the area ratio and linear ratio of equiaxed dendrite ratio by 5.41% and 11.61%, respectively. Moreover, the probability of bridging at the end of solidification of the billet treated by vibration technology was significantly reduced, and the central porosity and shrinkage cavities of the billet were significantly improved. This study provides the first definitive evidence that the novel mechanical vibration technology can enhance the quality of the billet during the continuous casting process.

1. Introduction

Grain size is one of the key structural factors affecting metal processing and properties [1]. The refined microstructure can improve mechanical properties [2] and enhance product quality. Therefore, many techniques that can refine metal grains have been extensively studied. Numerous scholars [3,4,5] have conducted extensive research on the impact of incorporating inoculants to accomplish grain refinement. Their findings confirm that the addition of inoculants during the metal manufacturing process can indeed refine grains and enhance the overall quality of casting billets. However, this technology is often accompanied by drawbacks, including the formation of particle agglomerations, localized defects, and impurities [1]. Some researchers [6,7] have enhanced cast slab quality and solute microsegregation by adjusting the crystallizer or secondary cooling zone heat transfer, achieving certain success. However, this technology may cause uneven cast slab cooling and induce crack and defect formation [8]. Thus, the process of grain refinement through the introduction of external field forces has attracted extensive research interest. Technologies such as electromagnetic stirring [9,10,11,12], ultrasonic vibration [13,14,15,16,17], pulse magnetic oscillation [18,19,20], and other technologies have been widely used in metal casting. Nevertheless, due to the high cost of the above technologies in terms of initial installation and ongoing maintenance, and in order to save energy, reduce emissions, lower production costs for enterprises, and increase the competitiveness of the product market, mechanical vibration technology due to its simple operation and low equipment cost—has gradually received the attention of researchers for use in the casting process. This technology is effective in refining the grain, expanding the equiaxed dendrite zone, and improving the quality of the casting billets.

Few studies have been carried out on mechanical vibration application in continuous casting. Some researchers [21,22] applied mechanical vibration at the solidification end of continuous casting and found it effective in reducing central segregation and porosity, and lowering carbon content in the cast billet center by impacting the outer arc side of the billet within a reasonable range and using high—momentum impact vibration.

This paper presents a new mechanical vibration technology in the secondary cooling zone’s roll section of continuous casting, addressing a research gap in enhancing cast slab quality at the solidification front. The technology works mainly through stress concentration. During vibration, periodic tensile and compressive stresses act on dendrites at the solidification front. When stress exceeds the dendrites’ strength limit, they fracture. This refines grains, expands the equiaxed dendrite zone, and improves cast billet internal quality. This method utilizes a mechanical vibration device that is independently designed and developed, specifically powered by compressed air and known as the VR. The effect of the mechanical vibration technology on the macrostructure of the billet was analyzed and discussed in the actual production process. The results confirm the viability of utilizing this technology to achieve grain refinement, expand the equiaxed dendrite zone, and enhance the central quality of the billet.

2. Vibration Equipment and Experimental Process

2.1. Vibration Principle of VR

The appearance of the VR is the same as that of the foot roll. As the billet moves down, the VR close to the surface of the billet rotates. There is an eccentric rotor inside the VR, and the eccentric rotor is rotated by compressed air. Its rotation continuously shifts the center of gravity, generating centrifugal force. This force alters the rotor position and direction, creating vibrations. Its structure is shown in the partially enlarged view of the VR in Figure 1a.

2.2. Vibration Parameters of VR

As shown in Figure 1a, the acceleration and frequency of the VR are tested. Both ends of the VR are suspended in parallel using a rubber band, while a magnetic receiver is securely attached to the VR’s central surface. By adjusting the intake pressure of the VR, the acceleration and frequency are measured using acceleration testing software. The local magnification of Figure 1a was tested under different inlet pressures for points 1, 2, and 3, and the results are shown in

Table 1. The results of acceleration and frequency test.

Inlet Pressure (Mpa)	Frequency (Hz)	Acceleration (m/s2)
		1	2	3
0.35	50–65	55–75	57–77	60–80
0.45	70–85	84–113	87–116	90–120
0.55	90–110	123–144	126–147	130–150

. As the distance from the measurement point to the equipment center increases, the acceleration value decreases gradually, but the difference is not significant, with only a slight variation of 2–7 m/s².

2.3. Experimental Procedure

Sufficient thickness of the billet provides reliable support for the safety and smoothness of this experiment. Prior to this, in order to prevent steel breakout, vibration equipment with smaller design specifications than this experiment was used for testing, and there were no steel breakouts and mold level fluctuations, and the experiment was carried out smoothly.

Due to the wide mushy zone at the solidification front, dendritic growth is well-developed in medium—and high—carbon steels. Vibration is more effective in breaking dendrites at the solidification front. Consequently, industrial trials of this technology are mainly conducted on medium—and high—carbon steels. Given the steel mill’s production needs, this trial focuses on the 40Cr medium-carbon steel. The composition was measured by atomic emission spectroscopy (AES), with results presented in

Table 2. Composition content of liquid steel (%).

Composition	Fe	C	Mn	S	P	Si	Nb
Content	Balance	0.382	0.611	0.004	0.017	0.188	0.002
Composition	V	Ti	Mo	Ni	Cu	Cr	Al
Content	0.003	0.001	0.002	0.016	0.014	0.866	0.029

. In AES, atoms or ions in molten steel are excited, causing outer-shell electrons to jump to a high-energy state. When they return to the ground state, characteristic spectral lines are emitted. Element types and contents are determined by the wavelengths and intensities of these lines. This method can simultaneously determine multiple elements with high precision and repeatability, making it suitable for rapidly analyzing major and trace elements in molten steel. The newly manufactured VR was assembled onto the frame of the continuous casting machine, and then the debugging process commenced. The installation position and form of the vibration equipment are shown in Figure 2. The accelerometer was employed to measure the acceleration of the VR on the continuous casting machine. The vibration equipment operates smoothly, and the data recorded in the laboratory matched the expected results. In order to prevent excessive exciting force from resulting in the fluctuation of the liquid level of the mold or the occurrence of steel breakout, the equipment was adjusted before the test. During the gas injection process, the gas was gradually introduced, starting from a small volume and increasing to the maximum atmospheric pressure present at the site. Throughout this procedure, the liquid level fluctuations were closely monitored. The results indicate that there were no observable fluctuations in the liquid level, and no steel breakout occurred. In the absence of S-EMS and F-EMS during the continuous casting process of 40Cr steel, the mold electromagnetic stirring was deactivated during the sampling procedure, and the billets treated with and without vibration were, respectively, sampled and analyzed. Since this test serves as an exploratory assessment of the novel vibration technology, primarily aimed at confirming the feasibility of this technology and upgrading the vibration equipment, the vibration sample was obtained solely under the condition of a maximum inlet pressure of 0.55 Mpa. The continuous caster specifications are shown in

Table 3. Continuous casting process parameters.

Parameters	Value	Unit
Casting speed	1.2	m/min
Cooling water flow rate in mold	126.5	m3/h
Temperature difference between inlet and outlet of mold	5.6	°C
Mold height	900	mm
Effective height of mold	830	mm
Vibration device is apart from meniscus	1140	mm
Pouring temperature	1532	°C
Superheat	35	°C

.

3. Numerical Simulation Calculation

The solidification process of 40Cr steel was meticulously calculated utilizing the fluid heat transfer module within the COMSOL6.2 numerical simulation software. Following this, the precise thickness and temperature distribution of the billet shell at the vibration position were obtained. A two-dimensional solid model was established specifically to determine the thickness of the billet shell. Initially, a solid heat transfer module was employed to ascertain the temperature distribution of the model until it reached the calculated solidification value. Subsequently, a solid mechanics module was utilized to conduct mechanical calculations.

3.1. Basic Assumptions and Control Equations

3.1.1. Basic Assumption

In order to facilitate the calculation, the following assumptions are made about the solidification heat transfer model of casting billet:

(a)

Ignoring the heat transfer in the casting direction, the model is simplified into a two-dimensional heat transfer model.

(b)

Ignoring the heat generated by surface friction caused by mold oscillation.

(c)

Ignoring the change in strand section during solidification.

(d)

Ignoring the short-distance thickness difference in the shell.

3.1.2. Solidification Heat Transfer Control Equation

The differential equation controlling two-dimensional solidification heat transfer of continuous casting billet is as follows:

$$\rho \mathrm{c}{\displaystyle \frac{\partial T}{\partial t}}={\displaystyle \frac{\partial }{\partial x}}(k{\displaystyle \frac{\partial T}{\partial x}})+{\displaystyle \frac{\partial }{\partial y}}(k{\displaystyle \frac{\partial T}{\partial y}}),$$

(1)

where $\rho$ is density (kg/m²), c is specific heat capacity (J/(kg·°C)), k is the thermal conductivity (w(m·°C)), T is temperature (°C), and x and y are the distances in the width and thickness direction on the cross section of the billet (m), respectively.

3.1.3. Control Equations of Solid Mechanics

The differential equation controlling two-dimensional stress propagation of continuous casting billet is as follows:

$$m\ddot{x}=F_0\cos \omega t-\mu \dot{x}-kx,$$

(2)

where m is the mass of forced vibration material (kg), $\ddot{x}$ is the acceleration of vibration (m/s²), $F_0$ is the vibration force (N), $\mu$ is the damping coefficient, $\dot{x}$ is the vibration velocity (m/s), k is the elastic coefficient of the vibrating object (N/m), x is vibration displacement (m), $\omega$ is the vibration frequency (Hz), and t is the vibration time (s).

3.2. Physical Property Parameters and Calculation Formulas

3.2.1. Liquidus and Solidus Temperature

Liquidus and solidus temperature are calculated using the following empirical formula, which has been used in a large number of studies [23,24]:

$$\begin{array}{cc}{T}_{Liq}& =1537-88[\%C]-25[\%S]-5[\%C\mathrm{u}]-8[\%Si]-5[\%Mn]-\hfill \\ & 2[\%Mo]-4[\%Ni]-1.5[\%Cr]-18[\%Ti]-2[\%V]-30[\%P]\hfill \end{array},$$

(3)

$$\begin{array}{cc}{T}_{Sol}& =1535-200[\%C]-12.3[\%Si]-6.8[\%Mn]-124.5[\%P]-\hfill \\ & 183.9[\%S]-4.3[\%Ni]-1.4[\%Cr]-4.1[\%Al]\hfill \end{array}.$$

(4)

3.2.2. Mold Heat Flux Distribution

The main function of the mold is to undertake the molten steel from the tundish, form a hard enough solidified shell, and support the core of the liquid steel as it smoothly enters the secondary cooling zone. Because of the various heat transfer mechanisms involved, the heat transfer calculation in the mold is a very complicated problem, which requires complex analysis. Therefore, a large number of researchers tend to use the general equation to calculate the heat transfer of the mold. In this paper, the findings of Savage and Pritchard [25] are used to derive the calculation formula for transient heat flux distribution:

$$q_m=2680+B\sqrt{t},$$

(5)

where $q_m$ is the transient heat flux density in the crystallizer (w/(m²)), and t is the residence time of molten steel in the crystallizer (s).

In view of the existence of a gas gap in the billet mold, according to Flint [26]’s experience, the following modifications were made to the mold heat flux:

• The close contact zone spanning 0–0.1 m below the meniscus. At this time, the billet is in close contact with the copper mold plate, and the heat flux distribution in the center and corner areas is q.
• The initial gas gap formation zone extends 0.1–0.23 m below the meniscus. The heat flux near the center is still q, and the corner area is 75–80% of the central values.
• The gas gap stabilization zone spanning 0.23–0.8 m below the meniscus. The heat flux near the center is still q, and the corner area is 70% of the central values.

3.2.3. Coefficient of Heat Transfer in Secondary Cooling Systems

The convective heat transfer coefficient in the secondary cooling zone is calculated using Nozaki [27]’s empirical formula, which integrates spray water flux and surface temperature through inverse parameter calibration:

$$h_i={\alpha }_i{w}_i^{0.57}(1-0.0075T_w),$$

(6)

where $h_i$ is the equivalent heat transfer coefficient of the second cooling zone (w/(m²·°C)), ${\alpha }_i$ is the correction coefficient of the second cooling zone, $w_i$ is the water flow density of the second cooling zone ((L/(m²·s)), and $T_w$ is the cold water intake temperature (°C).

3.2.4. Radiation Heat Transfer Coefficient

The radiant heat exchange between the billet surface and ambient environment can be characterized by the following thermal coefficient formula:

$$h_s=\epsilon \sigma (T_{sur}^2+T_{env}^2)(T_{sur}+T_{env}),$$

(7)

where $h_s$ is the radiation heat transfer coefficient (w/(m²·°C)) $\epsilon$ is blackness, with a value of 0.8; $\sigma$ is the Boltzmann constant, which is 5.67 × 10⁻⁸ (W/(m²·°C)), $T_{sur}$ is the surface temperature of the billet (°C), and $T_{env}$ is the ambient temperature (°C).

3.2.5. Solid Fraction

There is a solid–liquid two-phase zone in the solidification process of molten steel, and the two-phase zone has a great influence on physical parameters. In this paper, the following formula is used to determine the relationship between solid fraction and temperature:

$$f_s=\sqrt{{\displaystyle \frac{T_L-T}{T_L-T_S}}}.$$

(8)

3.2.6. Physical Parameters

In this study, 40Cr steel is used as the research object. Its physical properties vary depending on temperature. By referring to other scholars’ studies on these physical parameters of 40Cr steel and referencing their rational mathematical formulas, the solidification heat transfer process can be better simulated to more closely align with the actual production process of 40Cr steel.

The relationship between thermodynamic parameters, mechanical performance parameters, and the temperature used in the simulation calculation process is shown in

Table 4. Physical parameters and values.

Parameter	Value	Unit	Source
Latent heat	242,000	$\mathrm{J}/\mathrm{kg}$	JmatPro7.0
Thermal conductivity	$K_S=18.4+9.6\times {10}^{-3}T$	1	[28]
	$K_{SL}=K_S{f}_s+K_L(1-f_s)$
	$K_L=n{K}_S,n=\left(1,7\right)$
Density	${\rho }_S=7500$	$\mathrm{kg}/{\mathrm{m}}^3$	[29]
	${\rho }_{SL}={\rho }_S{f}_s+{\rho }_L(1-f_s)$
	${\rho }_L=6980$
Specific heat	$C_S=550+9.52\times {10}^{-2}T$	$\mathrm{J}/(\mathrm{kg}\cdot °\mathrm{C})$	[30]
	$c_{SL}={\displaystyle \frac{1}{{\rho }_{SL}}}(7500f_s{c}_S+6980(1-f_s)c_L)+L_{\lambda }{\displaystyle \frac{\partial {\alpha }_m}{\partial T}}$
	$C_L=842$
Young’s modulus	$E_{500\le T\le 900}=347.6525-0.350305T$	Gpa	[31]
	$E_{900<T\le T_L}=968-2.33T+1.9\times {10}^{-3}{T}^2-5.18\times {10}^{-7}{T}^3$
Poisson’s ratio	$\nu =0.278+8.23\times {10}^{-5}T$	1	[32]
Sign: ${\alpha }_m={\displaystyle \frac{6980(1-f_s)-7500f_s}{2(6980(1-f_s)+7500f_s)}}$ The right subscript of the parameter S, L, and SL represent the values in the solid phase, liquid phase and solid–liquid two-phase zone temperature, respectively.

.

3.3. Calculation Results and Establishment of the Solid Mechanics Model

3.3.1. Solidification Calculation Result

To investigate the stress distribution patterns within the shell structure of continuously cast billets subjected to VR excitation, a numerical simulation was conducted using the fluid heat transfer module in COMSOL Multiphysics. This model simulated the solidification and heat transfer behavior of square billets within the 0–30 m range below the meniscus of the mold, thereby obtaining the temperature field evolution and dynamic shell thickness growth during the casting process.

As illustrated in Figure 3a, the simulated surface center temperature and corner temperature of the billet were compared with experimental measurements, with a maximum deviation of 3.3% (below the acceptable threshold of 5%), confirming the accuracy of the fluid heat transfer model in capturing the thermal behavior during continuous casting.

During the advanced stages of solidification, the evolving solid–liquid interface creates a constrained mass transport regime when the solid fraction surpasses a critical threshold. This microstructural transition effectively suppresses solute redistribution through the interdendritic melt, resulting in a thermodynamically closed system where the bulk solute concentration remains invariant during subsequent cooling. The critical solid fraction corresponding to complete solute trapping is operationally defined as the effective solidification front for mechanical modeling purposes. Consistent with the methodology established by Takahashi et al. [33], the present analysis adopts a solid fraction of 0.67 as the constitutive interface for continuum mechanics simulations.

The center temperature of the billet in Figure 3a was calculated using Formulas (3)–(8) to obtain the center solid fraction of the solidification center. As shown in Figure 3b, with solidification, the superheat disappears 5.12 m from the meniscus. When the center solid fraction of the billet reaches 0.67, it is 7.47 m from the meniscus. When the center temperature of the casting reaches the solidus temperature, it is 9.24 m from the meniscus. The thermodynamic calculation results for the VR at the lower end of the mold are shown in Figure 4. The shell thickness corresponding to solid fractions of 1, 0.67, and 0 are 17.4, 21.78, and 29.4 mm, with corresponding temperatures of 1448, 1475, and 1497 °C. The center temperature of the shell surface is 1121 °C.

3.3.2. Establishment of Solid Mechanics Model

Since the VR surface is a circular flat plane, the potential bulging of the billet at the VR position must be taken into account. When the VR tightly adheres to the strand surface, its contact with the billet surface is relatively short in the longitudinal direction, measuring 2 mm. Conversely, in the transverse direction, the contact length is longer, equivalent to the VR length of 160 mm. In the longitudinal direction, the vibration roller has a small contact area (2 mm) with the cast slab. The internal stress distribution in the cast slab mainly concentrates 25 mm above and below the contact area. In the transverse direction, the stress concentrates at the two ends of the contact area. To help readers better understand the stress distribution in the slab shell, the model length is minimized longitudinally and matches the cast slab’s width transversely. As shown in Figure 5, models with widths of 21.78 mm and lengths of 50 mm and 200 mm were established in the longitudinal and transverse directions, respectively.

To ensure the accuracy of solid mechanics simulation results, the coupling function in COMSOL software was used. Firstly, solid heat transfer calculations were performed on the model, with the surface and solid–liquid interface temperatures set to those corresponding to solidification rates of 0 and 0.67 as calculated in Section 3.3.1. After the solid heat transfer outputs reached steady-state results, solid mechanics calculations were then performed in the time domain. The heat transfer results are shown in Figure 5, where Figure 5a,b represent the temperature field distributions of the model in the longitudinal and transverse directions, respectively.

4. Results and Discussion

4.1. Effect of Acceleration on Stress Distribution in Shell

In the solid mechanics model, stress is loaded as a sinusoidal force with a frequency of 50 Hz, the right boundary is a low-reflection boundary, and the calculation results are shown in Figure 6. From left to right, the stress distribution in the shell at half period intervals of 0.001 s; from top to bottom, the stress distribution in the shell when the loading stress acceleration is 100,150 m/s². From a wave perspective, the incident stress wave on the left travels to the right, acting on the dendrite front, causing tensile fracture of the inner surface dendrites, all while following the laws of mass, momentum, and kinetic energy conservation. Over half a period, the loading stress wave is a continuous increment. As shown in Figure 6, with constant loading stress wave acceleration, the wave amplitude and the stress in the shell increase over time, expanding the high-stress area. When the loading time is constant, higher acceleration leads to greater stress wave peaks, increased stress values, and a larger high-stress zone.

Probes were inserted at points A, B, C, and D in Figure 5a to extract stress values under different accelerations and time conditions within half a loading period. The results in Figure 7 show that when the loading time reaches half a period, the stress wave peaks simultaneously at all four points, indicating rapid wave propagation with no significant delay. When acceleration increases from 100 m/s² to 150 m/s², the maximum stress values at points A, B, C, and D rise from 7.03 × 10⁸, 2.65 × 10⁷, 1.4 × 10⁷, and 7.7 × 10⁶ N/m² to 1.06 × 10⁹, 3.98 × 10⁷, 2.1 × 10⁷, and 1.16 × 10⁷ N/m², respectively, all increasing by 33.4%. The stress values follow the order of A > B > C > D under the same conditions. This is mainly due to material damping, which attenuates stress during transmission.

4.2. Effect of Frequency on Stress Distribution in Shell

To enable readers to intuitively understand stress distribution in shells under different frequencies, this section applies a stress wave of 3 × 10⁹ N/m² to the left end of the model. By changing the stress wave frequency, we observe stress distribution at different times, with results shown in Figure 8. As the incident stress wave frequency increases, the time for the shell to reach maximum stress shortens. This means that within the same time frame, higher loading frequencies lead to more stress wave excitations when the casting passes through the VR, increasing the number of exciting force loads and unloads on the dendrites in the shell. This boosts the likelihood of dendrite fragmentation at the solid–liquid interface, effectively expanding the equiaxed dendrite zone.

As shown in Figure 9, when the incident stress wave frequency increases from 50 Hz to 100 Hz, the time for points A, B, C, and D to reach maximum stress decreases from 0.01 s to 0.005 s, doubling the stress wave propagation frequency.

The above studies show that, when other conditions are constant, higher incident stress wave acceleration leads to greater stress wave amplitudes and larger high-stress areas in the shell. Greater frequencies result in more loading and unloading stress wave propagation cycles in the same time, improving vibration effectiveness.

The relationship between vibration acceleration, frequency, and excitation force is shown in Formulas (9) and (10):

$$\left|\mathrm{a}\right|=\left|R\right|{\left(2\pi f\right)}^2=\left|R\right|{\left(\omega \right)}^2,$$

(9)

$$F\approx \left|\mathrm{a}\right|m.$$

(10)

As shown in Formulas (9) and (10), in practice, the VR acceleration and frequency are positively correlated. As the gas pressure at the VR inlet increases, the angular velocity of the rotor inside the VR driven by compressed gas increases, leading to higher frequency, acceleration, and excitation force. The simultaneous increase in acceleration and frequency enhances the conditions for vibrating and breaking dendrites at the solidification front.

4.3. Influence of Contact Area Between VR and Shell on Stress Distribution in Shell

As the VR tightly contacts the billet over a longer area transversely, the loading length equals the VR length. Figure 10a,b show stress distributions under 150 m/s² acceleration at different times and under various accelerations at 0.01 s, respectively. The stress distribution pattern here is similar to that in the longitudinal direction. The only difference is that stress concentrates at the edges of the VR in contact with the shell initially, then spreads towards the solidification front center with increased time and acceleration. From Figure 11 and the four points in Figure 5b, under the same time and acceleration conditions, the stress values follow the order of G > E > H > F.

As the transverse directional VR frequency impact on stress distribution is consistent with that in the longitudinal direction, it is not elaborated in this section. Figure 12 offers a comparative analysis of the maximum stress values at four points in the longitudinal and transverse directions (Figure 5a,b). When the same frequency and acceleration stress waves are applied at the left edge, if the VR has a small contact area with the billet surface, the maximum exciting force on the dendrites at the solidification front decreases with distance from the loading point. Conversely, with a large contact area, this maximum exciting force is smaller than when the contact area is small. This occurs because a larger contact area between the VR and shell spreads the stress concentration to the VR ends, dispersing the work performed on the shell. To enhance the vibration effect, the equipment’s outer shell structure was modified as shown in Figure 1b. The VR’s outer shell was changed from a flat to a convex profile. This reduces the transverse contact area between the VR and the billet, focusing stress near the VR’s center.

In this experiment, the billet was 200 × 200 mm in size, and the length of the VR was 160 mm. When the VR was tightly attached to the surface of the billet, there was a 20 mm gap at each edge of the billet. As mentioned in Section 3.3.1, the shell thickness at the point where the billet reached the VR was 21.78 mm, and the solidified layer had extended beyond the edges of the VR in the transverse direction. Although the stress is highest near the VR edges, the stress wave does not affect the solidified shell. Compared to when there is less contact, the stress at the solidification front’s center is significantly reduced. This not only wastes the VR’s work but also weakens the vibration effect. Moreover, the solid shells formed at both edges hindered the pressing force of the VR on the solidifying shell, thereby reducing the amplitude of the actual incident stress wave. Therefore, to enable the applied stress to be transmitted more efficiently to the solidification front, to increase the exciting force on the dendrites at the solidification front, and to cause their necking and breaking, it is necessary to optimize and modify the structure of the VR.

4.4. Industrial Test Results

The longitudinal and transverse samples were first machined flat on a milling machine and then finely polished to achieve a smooth surface. They were subsequently etched using 50% concentrated hot hydrochloric acid at 75 °C, and then the macrostructure was observed and analyzed.

As indicated by the simulation results in Section 3.3.1, the shell thickness at the VR position has reached 21.78 mm. As can be seen from Figure 13, the solidification front of the inner arc side and the right arc side are both in the columnar crystal zone at this time, providing excellent conditions for the mechanical fracture of dendrites.

As shown in Figure 13 and Figure 14 and

Table 5. Comparison between vibration-treated and untreated results.

Mechanical Vibration	Area Ratio (%)	Linear Ratio (%)
Untreated	6.55	22.95
Treated	11.96	34.56

, a comparison of the macrostructures of vibration technology treated and untreated samples reveals the following:

The area percentage of equiaxed dendrites in transverse sections of the vibrated sample is 11.96%, up by 5.41% from the 6.55% of the untreated sample. For longitudinal sections, the linear ratio of equiaxed dendrites in the vibrated sample is 34.56%, an increase of 11.61% over the untreated sample’s 22.95%.

Untreated billets exhibit developed columnar crystals on the inner arc side. These form a bridging structure at the center, leading to severe and continuous porosity and shrinkage cavities that greatly harm the casting quality. After vibration technology treatment, the excitation force reaches the solidification front, inducing tensile stress on columnar dendrites towards the billet center direction. This increases their bending stress, breaks the dendrites, and forms “crystal drops” under gravity. After remelting and dispersion, multiple nucleation sites grow and hinder columnar crystal growth, expanding the equiaxed dendrite zone and significantly improving center quality.

Macrostructure comparison shows that vibration on the outer arc side does not significantly break dendrites. During the experiment, the flux film clogged the outer arc vibration equipment’s air outlet, reducing its frequency and acceleration, and thus its effectiveness. Perhaps the solidification front on the outer arc side at the VR position is within the fine equiaxed crystal zone. This may explain the less obvious dendrite fracture there. It also offers ideas for subsequent industrial trials and equipment design modifications.

In summary, compared to untreated billets, the application of vibration technology during continuous casting in the mold foot roll zone refines grains, expands the equiaxed dendrite ratio, and improves center quality of the billet.

5. Conclusions

• Numerical simulations confirmed the feasibility of applying mechanical vibration to the mold foot roll zone during continuous casting. The results show that as the acceleration of the applied stress wave increases, the exciting force on dendrites at the solidification front also increases, enhancing their bending stress. An increase in stress wave frequency raises the loading and unloading frequency on columnar dendrites, boosting fracture chances. However, a larger contact area between the VR and shell reduces the exciting force on dendrites at the shell center, diminishing vibration effectiveness.
• Macrostructural comparisons after on-site tests indicate that applying vibration technology during continuous casting significantly expands the equiaxed dendrite ratio, with area and linear ratios increasing by 5.41% and 11.61%, respectively. Vibration also reduces central porosity and shrinkage cavities in castings, improving central quality.
• This research is an exploratory experiment for the novel vibration technology that not only validated its feasibility but also revealed shortcomings. These findings provide a reliable theoretical basis and experimental experience for the design and modification of vibration equipment in future tests.