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Abstract

As a fluid-based precise processing method, soft abrasive flow processing has been widely used in advanced electromechanical systems, complex mold manufacturing, and other engineering fields. Because of the low volume fraction of abrasive particles and micro-force/cutting removal characteristics, there exists a potential improvement in terms of processing efficiency and uniformity. In view of the above problems, this article presents an ultrasonic-assisted soft abrasive flow processing method. Based on the realizable k–ε turbulence model and the mixture flow model, an ultrasonic coupling enhancement dynamic model for soft abrasive flow is set up, and the kinetic energy transport equation of realizable k–ε turbulence model can be revised. Using particle image velocimetry technology, an on-line observation experimental platform for ultrasonic-assisted soft abrasive flow is developed to conduct the real-time acquisition of abrasive flow state and particle distribution in a constrained flow passage. An ultrasonic-assisted soft abrasive flow processing experimental platform is established to complete the processing experiment. The experimental results show that the ultrasonic excitation vibration can effectively enhance the turbulence intensity and distribution uniformity of the abrasive flow, the average processing time can be shortened by more than 6 h, and a better surface quality can be obtained.

Keywords

Fluid-based precise processing ultrasonic-assisted soft abrasive flow multiphase flow mold structured surfaces

Introduction

Mold is not only an important production tool to create a variety of non-metal and metal parts, but also a basic process equipment for an industrial production.^1–3 During the mold manufacturing process, to eliminate the traces left by cutting tools, electric sparks, and other processing tools, polishing is an important procedure of the mold surface engineering. It is the key process of post-processing in the mold manufacturing process, which takes about half of the circle in the entire mold manufacturing.^4–7 There are many small mold holes, narrow grooves, slots, pyramids, prisms, and other complex shaped structures, which are the so-called structured surface, as shown in Figure 1.^8–10 With the increasing demand for product accuracy and surface integrity, the mold manufacturing industry has more stringent requirements on the roughness of the structured surface. For example, the roughness of the surface of an injection molded part needs to reach the precision of the mirror grade.^11–13 Then, the structured surface roughness of the corresponding precision injection mold will be at least 1–2 magnitude higher to meet the requirements.^14–16 Therefore, taking the structured surface as a research object and then performing new approaches of mold structured surface finishing are of great significance.

Figure 1.

Complex structured surfaces of the molds.^17,18

It is well known that fluid physical properties make it changeable and pervasive, so that no matter how complex the structured surface of the part is, the fluid fully reaches the surface of the part being machined to achieve full finishing.^19–22 In recent years, related researchers made full use of the fluid flexible-profiling property to develop some fluid-based processing methods, including abrasive water jet polishing, abrasive flow machining, magnetorheological polishing, and elastic launch processing.^23–27

With respect to the processing mechanism, the abrasive flow in the abrasive water jet polishing and abrasive flow machining methods has a strong impact or high viscosity by exerting a strong jet force or squeeze pressure, in which the workpiece surface is strongly cut by the abrasive particles.^28–30 In this article, the abrasive flow in these processing methods is referred to as “hard” abrasive flow. Although the processing method of using “hard” abrasive flow has high processing efficiency, it is difficult to get the satisfactory surface roughness because it may leave clear and directional machining marks on the surface of the workpiece by the strong circulation and strong pressure reciprocation to drive abrasive flow. So the strong circulation and intensive pressure reciprocation can only be used for the rough polishing of workpieces. New finishing methods are needed to achieve the finishing of the mirror-level roughness in order to solve the problem of precision or even ultra-precision finishing of structured surfaces of molds.

To resolve the problems of “hard” abrasive flow processing methods, Ji et al.^31–33 proposed a new processing method based on “soft” abrasive flow (SAF). The so-called SAF refers to a solid–liquid two-phase abrasive flow with weak viscosity, which has good flow characteristics and is prone to form the turbulent flow. The working principle of SAF processing method for the structural surfaces of the mold is shown in Figure 2. First, a SAF constrained flow passage is constructed. According to the characteristics of the workpiece structured surface, a reasonable restraining module is designed to be installed near the structured surface of the workpiece. The surface of the workpiece to be processed is the wall of the constrained passage. Then the SAF is allocated according to the technical requirements of different workpieces, and the abrasive particles and fluid are mixed to produce the required SAF. Finally, SAF flows to the inlet of constrained flow passage with a certain speed and pressure, and flows through the flow passage to the outlet then backs to the storage tank circularly. Apparently, the SAF processing approach uses a SAF that constrains a weak viscosity fluid in the flow passage to replace the polishing tool, and to perform the finishing of the processed workpiece surface. Different from the “hard” abrasive flow processing, the SAF processing method uses the effect of the micro-cutting force to achieve the gradual surface finishing of the workpiece. This processing method is with the better performance in the turbulent state processing, and the randomness of turbulent flow in the abrasive particle motion determines the disorder of the workpiece surface texture. In view of the above characteristics, SAF processing method can perform mirror-grade machining for the complex structured surfaces of the mold.

Figure 2.

Working principle of SAF processing method: 1—accumulator; 2—stirring motor; 3—high-pressure pump; 4—processing apparatus; 5—contrained module; 6—abrasive flow.

Due to the technical advantages of SAF processing method, it has been widely applied in the mechanical manufacturing area including micro-electro-mechanical components, precise molds, and automobile accessories.^34–36 Li et al.^37,38 conducted theoretical and experimental studies on the distribution of abrasive particles, the dynamic characteristics, the micro-cutting mechanism in the near-wall area, and the control methods of structured surface-constrained flow channels. These studies verify the feasibility and reliability of SAF processing method. In order to improve the processing efficiency, Ji et al.³⁹ studied the inherent relationship between the constrained module structure and the pressure field, velocity field, and abrasive particle volume distribution. A design method of sliding constrained module was proposed and a validation experiment of finishing efficiency was performed. Ji et al.⁴⁰ executed numerical simulation of abrasive flow dynamics in a single-inlet confined flow path and analyzed the movement law of abrasive flow. On the basis of discussing the advantages and disadvantages of finishing, he proposed a dual entrance constrained flow passage design method by combining with the fluid symmetry oblique collision theory. Based on the theory of two-phase turbulence, Ji et al.⁴¹ analyzed the optimized relationship between abrasive particles and fluid in the constrained flow channel and proposed a hedge perturbation control method based on the confined angular flow channel with non-coaxial collision flow structure. Sun et al.⁴² conducted a simulation study of the SAF in the constrained flow channel using the wall function method and the turbulent model and obtained the distribution of the parameters in the flow channel, for instance the turbulent kinetic energy, the velocity, the dynamic pressure, and the wall shear stress of abrasive flow; thus, a method to change the structure of the constrained module was proposed to optimize and regulate the turbulent flow of the abrasive particle in the constrained flow channel. Zhang et al.⁴³ proposed an improved abrasive flow processing method and provided a new material removal model of abrasive flow to reveal the processing regularities for complex geometric surfaces of titanium alloy artificial joints. The numerical and processing experiment results indicated that the proposed material removal model can estimate the processing effects and removal regularities, and the size accuracy and surface quality of the titanium alloy surface are improved.

The turbulence intensity of SAF in the constrained flow passage is the key factor to determine the processing effects. Relevant scholars^34–43 have carried out a series of research works about the designs of the sliding constrained module, dual-inlet constrained flow channel, hedging perturbation flow channel, and the structure of changing confined flow channel, in which the processing efficiency and polishing uniformity have been improved. Obviously, the SAF finishing is a new effective method for precision processing on the complex structured surfaces of the mold. However, the current methods still have such problems as the lower efficient processing, less accurate turbulence regulation or worse surface uniformity, and so on. Therefore, it is necessary to put forward a new SAF processing method to improve the processing efficiency and surface quality.

Related researches^44–46 suggested that the ultrasonic excitation can increase the internal kinetic energy of the fluid medium, and the turbulence intensity will be enhanced. Moreover, ultrasonic can make fluid create remarkable physical variation, that is, the cavitation phenomenon, which can effectively accelerate the motion states of the abrasive particles. Apparently, ultrasonic excitation is a potential approach to resolve the matters of current SAF processing methods. Based on the above analysis, this article introduces the ultrasonic excitation into the SAF processing and proposes an ultrasonic-assisted soft abrasive flow (USAF) processing method for mold structured surfaces.

This article is organized as follows. In section “USAF fluid dynamic model,” the USAF fluid dynamic model is set up, and the kinetic energy transport equation of realizable k–ε turbulence model is revised. In section “Numerical results and discussion,” a numerical USAF model is built up, the boundary conditions of the constrained flow passage are described, and the numerical simulations for USAF processing are performed. In section “Experiment results and discussion,” an observation experimental platform and a processing experimental platform for USAF are developed, the observation and processing experiments are implemented, and the comparative analysis and discussion are presented. In section “Conclusion,” the conclusions are provided.

USAF fluid dynamic model

As presented above, the working principle of SAF processing is that the sparse abrasive flow reaches the turbulent state under the power drive, and the micro-cutting for the workpiece surface can be achieved by the fluidity of the fluid medium. Moreover, the disorder movement of the solid abrasive particle is apt to form more uniform surface quality. Therefore, the primary issue in this study of USAF processing is to set up a two-phase fluid dynamic model under ultrasonic excitation conditions, so that the distribution characteristics and evolution laws of the flow field in constrained flow passage can be obtained.

Particle movement in the abrasive flow is the key issue of this study, especially for the momentum conversion between the solid particle phase and the fluid phase. In the process of two-phase abrasive flow calculation, the fluid medium is a continuous phase, and the abrasive particles are generally regarded as discrete particle units. The initial coordinates before deformation are regarded as an independent variable called the Langrangian coordinates or material coordinates, and the instantaneous coordinates after deformation are viewed as an independent variable called Eulerian coordinates or space coordinates.^47–49 There are mainly two modeling methods involved. The first one is that the particle swarm is treated as a discrete quasi-fluid in the Euler reference system. The hydrodynamic model, based on the above assumptions, is commonly known as a dual-fluid model, which is not suitable for the sparse two-phase particle fluids. The second one, based on the particle trajectory model of Lagrange reference system, Eulerian–Langrangian multiphase flow model is developed to solve the Navier–Stokes (N-S) equation by combining with continuous fluid-phase model.

Based on the above hypothesis, if the flow field distribution laws of continuous-phase fluid are obtained, the particle velocity and affecting force in the flow field can also be obtained, in which the trajectory of each particle is treated as the discrete phase. The volume fraction of discrete particles applied to the above method is generally less than 15%, corresponding to the two-phase composition of the SAF.

Turbulence model

The realizable k–ε turbulence model is designed for the problem of standard k–ε turbulence model that the normal stress may be negative in the case where the average strain rate is very large. In this model, the coefficient in the turbulent viscosity calculation formula is treated as a variable, which is related to the fluid strain rate, and the k equation and $ε$ equation can be described as

$\frac{\partial (ρ k)}{\partial t} + \frac{\partial (ρ k u_{i})}{\partial x_{i}} = \frac{\partial}{\partial x_{j}} [(μ + \frac{μ_{t}}{σ_{k}}) \frac{\partial k}{\partial x_{j}}] + G_{k} - ρ ε + S_{k}$ (1)

$\begin{matrix} \frac{\partial (ρ ε)}{\partial t} + \frac{\partial (ρ ε u_{i})}{\partial x_{i}} = \frac{\partial}{\partial x_{j}} [(μ + \frac{μ_{t}}{σ_{ε}}) \frac{\partial ε}{\partial x_{j}}] \\ + C_{1} E ρ ε - C_{2} ρ \frac{ε^{2}}{k + {(ν ε)}^{\frac{1}{2}}} \\ + C_{1 ε} \frac{ε}{k} C_{3 ε} G_{b} + S_{ε} \end{matrix}$ (2)

where $C_{μ} = 1 / (A_{0} + A_{s} U^{*} (k / ε))$ , $C_{1} = \max {0.43, η / (η + 5)}$ , $A_{0} = 4.0$ , $A_{s} = \sqrt{6} \cos φ$ , $φ = 1 / 3 \arccos (\sqrt{6} W)$ , $W = E_{ij} E_{kj} E_{ki} / (E_{ij} E_{ij})^{1 / 2}$ , $U^{*} = (E_{ij} E_{ij} + Ω_{ij} Ω_{ij})^{1 / 2}$ , $Ω_{ij}$ is the rotation rate tensor, and $S_{k}$ , $S_{ε}$ are the source terms that the user has customized for the model.^50–53

Compared with the standard k–ε turbulence model, the main changes of the realizable k–ε model are as follows: the curvature and rotation are introduced to the formula $C_{μ}$ of turbulent viscosity, which is no longer a constant. In the ε equation, even the k value is small or even 0, there is no possibility that the denominator is 0, so there is not any singularity. The realizable k–ε model has been effectively used for such areas as the flow calculation of rotating uniform shear flow, pipe flow, boundary layer flow, separate flows, and free flow with jets and mixed flows. Based on the above characteristics of the realizable k–ε model, it can be used to describe the flow process of SAF in the boundary layer near the bottom wall of the constrained flow passage.

Mixture multiphase model

Using the relative velocity to describe the discrete phase, the mixture model solves the momentum equation for a mixture, where the continuous equation for the mixed phase is

$\frac{\partial}{\partial t} (ρ_{m}) + \nabla \cdot (ρ_{m} {\overset{⇀}{v}}_{m}) = \dot{m}$ (3)

where $ρ_{m}$ is mixed density, $\nabla = (\partial / \partial x) i + (\partial / \partial y) j + (\partial / \partial z) k$ is a Hamiltonian ( $i$ , $j$ , k are the unit vectors in the axis directions of x, y, z, respectively), ${\overset{⇀}{v}}_{m}$ is the mass average velocity, $\overset{\cdot}{m}$ , which can be zero unless otherwise specified, is a user-defined mass source or the mass transfer caused by cavitation.^54–56

The momentum equation for the mixed phase is

$\begin{array}{l} \frac{\partial}{\partial_{t}} (ρ_{m} {\overset{⇀}{ν}}_{m}) + \nabla \cdot (ρ_{m} {\overset{⇀}{ν}}_{m} {\overset{⇀}{ν}}_{m}) = - \nabla p + \nabla \cdot [μ_{m} (\nabla {\overset{⇀}{ν}}_{m} + \nabla {\overset{⇀}{ν}}_{m}^{T})] + ρ_{m} \overset{⇀}{g} \\ + \overset{⇀}{F} + \nabla \cdot (\sum_{k = 1}^{n} \partial_{k} ρ_{k} {\overset{⇀}{ν}}_{d r, k} {\overset{⇀}{ν}}_{d r, k}) \end{array}$ (4)

where P is the pressure, $μ_{m}$ is the viscosity of the mixed phase, $\overset{⇀}{F}$ is the bulk force, n is the total number of phases, k is a phase of the multiphase flow, $\partial_{k}$ is the volume fraction of phase k, $ρ_{k}$ is the density of the phase k, and ${\overset{⇀}{v}}_{d r, k}$ is the drift speed of the phase k.

The mixture model can describe the multiphase flow with different velocities in each phase, because it is assumed that the coupling between phases is stronger under local equilibrium on a short spatial scale. Obviously, for the research objective of the proposed USAF processing method in this article, it needs to make the abrasive flow produce high-speed turbulent flow in the constrained flow passage so that the abrasive flow can have strong fluid–solid coupling conditions. Therefore, the mixture model can be applied to the numerical calculation for the two-phase abrasive flow under the ultrasonic excitation conditions.

Ultrasonic-coupled SAF dynamic model

The flow field enhancement for SAF by the ultrasonic excitation is performed by the sound power of an ultrasonic sound field, that is, the ultrasonic sound pressure and its various excitation effects. Sound power is the sound energy that passes through a certain area per unit time and is the physical quantity that reflects the energy relationship of the sound field. To obtain the expression of sound power, we need to derive the average acoustic energy density of the sound field. In a sound field of volume V, the energy expression provided by the acoustic vibration for this volume is

$E_{K} = \frac{1}{2} ρ_{0} μ^{2} V$ (5)

where $ρ_{0}$ is the density of the liquid phase; the corresponding cell potential energy expression is

$E_{p} = - \int_{0}^{p} P d V = \frac{p_{2}}{2 ρ_{0} c_{0}^{2}} p^{2}$ (6)

where $d V$ is the amount by which the small volume V is compressed by sound pressure p; the unit of acoustic energy density can be expressed as

$ε = \frac{E_{K} + E_{P}}{v}$ (7)

About 4%–35% of the energy is transferred to the liquid phase by cavitation when the ultrasound field is applied to the liquid. According to the analysis of the particles in the two-phase flow as described above, the sound energy finally acts on the particles of the SAF to enhance the turbulence, thereby improving the efficiency and quality of the finishing process.

According to the realizable k–ε turbulence model, the transport equation for its turbulent kinetic energy is presented as

In equation (8), on the left is the partial derivative of the first turbulent kinetic energy over time in the flow field and the second derivative of the turbulent kinetic energy and velocity vector to the distance.^57–59 Both of the derivatives are the rates at which the turbulent kinetic energy of the flow field is obtained. On the right is the various items of turbulent kinetic energy, the first few have been described in the previous model introduction, the last one $S_{k}$ is the customized correction for the model. Based on the above analysis of the energy transfer in the flow field caused by the ultrasonic pressure fluctuation and the cavitation effect caused by the ultrasonic vibration, and combined with the experimental ultrasonic generator power, the effect of cavitation on the flow field is reflected by the fact that the correction term increases the generation of turbulent kinetic energy.

Then, the transport equation of turbulent kinetic energy dissipation in realizable k–ε turbulence model can be revised as

In equation (9), the dissipation of turbulent kinetic energy on the right is mainly made of the gradient diffusion, eddy energy consumption, and so on. The SAF processing is realized by the collision and friction of the solid particles on the wall surface. During the above course, the massive friction and collision of the particles on the wall surface caused by the turbulence after ultrasonic strengthening consume a large amount of turbulent kinetic energy. However, the friction-induced turbulence dissipation is not reflected in the above transport equation, so we need to modify the dissipation equation through the last term of the equation on the right, that is, the customized term of dissipation.

With respect to the mechanical affecting relationship, the effect of particles on the wall during SAF processing is the particle’s shear stress on the confined flow channel wall. Accordingly, the shear stress of the SAF on the wall in the form of turbulent flow is composed of viscous shear force and inertial shear stress. The viscous shear stress is the force generated by the relative movement of the stratospheric laminar flow. Meanwhile, the inertia shear stress is the additional shear stress which is caused by mixed effect of turbulent pulsation and the upper and lower particles and the momentum exchange. The expression of the shear force is listed below

$τ = τ_{1} + τ_{2} = μ \frac{du}{dy} - ρ u^{*} v^{*}$ (10)

where $μ$ is the viscosity coefficient of fluid, and $u^{*}, v^{*}$ are the instantaneous pulse rates.

Based on the above reduction, the revision of ultrasonic cavitation effect is considered in the turbulent kinetic energy transport equation, and the external friction caused by shear stress $τ$ is added to the turbulent kinetic energy dissipation transport equation so that the realizable k–ε turbulence model can adapt the numerical simulations for SAF under the ultrasonic coupling conditions.

Numerical results and discussion

Numerical model and boundary conditions

SAF processing method is to cover the constrained module on the structured surface to be processed and form a constrained flow channel in combination with the related fixtures. The abrasive flow circulates in the constrained flow channel to realize the micro-cutting of the structured surface. Therefore, the design of the restraint module is of great significance in the SAF finishing, which directly affects the flow field distribution characteristics and the final surface machining quality of the constrained flow path (Figure 3).

Figure 3.

Conventional constrained flow channel: 1—flow passage inlet; 2—turbulence generator; 3—constrained flow passage; 4—flow passage outlet; 5—flow passage upper surface.

In this article, to improve the material removal efficiency of the traditional SAF processing method, the ultrasonic coupling method is used to enhance the turbulence intensity of the abrasive flow in the constrained flow path. And an ultrasonic enhanced numerical model for SAF is established, as shown in Figure 4. The model uses the basic mesh of a conventional constrained flow path, and the ultrasonic pulses are input through a user-defined function (UDF) on the upper surface of the constrained flow path, and a two-phase turbulent field that couples the ultrasonic vibrations is generated within the constrained flow path.

Figure 4.

Mesh division of USAF numerical model.

According to the technical requirements of the USAF, the solid phase is the SiC particle, and the liquid phase is the mixture by a certain proportion of water, cutting fluid, and dispersant. The specific parameters of abrasive particles in constrained flow passage are set as in Table 1.

Table 1.

SAF physical parameters in constrained flow passage.

Parameters	Values
Operating pressure (Pa)	1.51e5
Liquid-phase density (kg m⁻³)	1115.4
Liquid-phase dynamic viscosity (kg/m s)	1.550e–3
Solid-phase density (kg m⁻³)	3170
Liquid-phase dynamic viscosity (kg/m s)	1.32e–5
Abrasive particle diameter (μm)	50
Abrasive particle fraction (%)	10
Abrasive particle temperature (m² s⁻²)	0.0003

SAF: soft abrasive flow.

For the above numerical model of ultrasonic flow field enhancement, the boundary conditions can be defined as follows: the inlet of the circular flow path is set as the velocity inlet boundary and its velocity is 60 m s⁻¹; the right side of the ultrasonic coupling constrained flow passage is set to fully develop the exit boundary. Except for the upper surface, the rest walls of the constrained flow passage are set to be the slip-free wall boundaries. At the same time, in order to simulate the turbulent enhancement caused by the ultrasonic vibration in the flow channel, the upper surface of the constrained flow passage is set as the pressure inlet boundary. The input conditions of pressure fluctuation are set by the UDF. It can be presented by the following sinusoidal variation function

$y = A_{u} \sin k_{u} t$ (11)

where $A_{u}$ is the amplitude of the input ultrasound, $k_{u}$ is the frequency of the input ultrasound, and t is the time variable in Lagrange reference frame.

Numerical results and discussion

As mentioned above, the input of high-frequency vibration wave in the fluid precision processing can improve the processing efficiency and the surface quality. Therefore, with the help of a certain electromechanical actuator, the constrained flow passage is injected with high-frequency vibration energy flow. This is an effective way to enhance the internal energy of the SAF field in the constrained flow passage and then further improve its processing efficiency. Thereby, in order to improve the material removal efficiency of the SAF processing method, the ultrasonic coupling method is used in this article to enhance the turbulence intensity of the abrasive flow in the confined flow passage.

For the above research objectives, numerical simulation for the ultrasonic coupling of SAF flow field is an important research task for the proposed USAF processing method. In order to compare the control effects of ultrasonic excitation in SAF field, the rectangular flow field, under the condition of constant velocity entrance, is first experimented to study the flow field distribution characteristics of the constrained flow passage. For the key parameters of dynamic pressure, velocity, and turbulent kinetic energy, the simulation results are obtained, as shown in Figures 5 –7.

Figure 5.

Pressure distribution of constrained flow passage with constant velocity.

Figure 6.

Velocity distribution of constrained flow passage with constant velocity.

Figure 7.

Turbulent kinetic energy distribution of constrained flow passage with constant velocity.

By the analysis of the pressure distribution in Figure 5, we can find that in the conventional constrained flow passage, although the flow passage has a certain pressure maintaining function, the abrasive flow enters the channel and exists an apparent pressure drop, which is caused by the pressure loss along the flow path and the viscous effect of the inner wall. This distribution will result in a decrease in the removal ability of the SAF in the back stage of the passage; thus, it is difficult to achieve a more balanced surface quality.

Considering the velocity distribution in Figure 6, the velocity of the SAF increases rapidly after entering the constrained flow passage due to the interception of the flow passage inlet. With the gradual reflection of the pressure loss and viscosity in the flow passage, the velocities of the abrasive particles take on a decreasing trend. Due to the roughness of the flow path surface, the viscous effect on the surface is obvious, which leads to the rapid decrease of the abrasive flow velocity in the near-wall area, and this will greatly reduce the removal efficiency of the abrasive flow. It is also one of the key problems to be solved in this article.

According to the results of the turbulent kinetic energy distribution in Figure 7, it can be inferred that in the conventional constrained flow passage, the turbulent flow of abrasive flow can be fully developed due to the lack of turbulence disturbance and excitation. However, the turbulent kinetic energy is decreased because it is limited by the loss of pressure and flow rate, and its reduction amplitude, the velocity, and pressure distribution are more obvious, which shows that the loss of the abrasive flow in the flow path is larger and the disorderly driving ability of the abrasive particles weakens, thereby making negative effects for the surface processing quality.

The constrained flow passage being loaded the ultrasonic vibration, the ultrasonic wave has a cavitation in the abrasive flow. The cavitation effect can disturb the velocity and turbulent kinetic energy distribution in the constrained flow passage, thus strengthening the diffusion of each phase and promoting the disordered distribution of the particles. Therefore, this article focuses on the analysis of the characteristics of the velocity and turbulent kinetic energy distribution in the constrained flow passage after the ultrasonic vibration is loaded. In the calculation, the velocity distributions at different moments on the 100 μm from the bottom in the constrained flow channel are monitored. According to the frequency and phase setting of the UDF, the amplitude of the ultrasonic wave loaded at 0.004 s is close to the maximum, and the amplitude of the ultrasonic wave loaded at 0.0045 is in the middle. The ultrasonic coupling velocity distributions of the above two moments are shown in Figure 8.

Figure 8.

Velocity distributions in the constrained flow passage with ultrasonic excitation: (a) t = 0.0040 s and (b) t = 0.0045 s.

It can be seen from Figure 8 that the velocity distribution in the constrained flow passage is more violent than that in the circular flow passage. By comparing the velocity distributions at two different moments, it can be conclude that discontinuous turbulence is conducive to the intermittent flow field in the constrained flow passage. Local deceleration spots appear randomly in the flow field where the ultrasonic vibration is applied. The main reason for the occurrence of decelerating spots is the ultrasonic cavitation effect caused by the loading ultrasonic excitation, which leads to the local high-pressure and high-temperature in the flow field. As can be seen from the velocity distribution, the entire surface of the workpiece gets more uniform processing; therefore, it can improve the SAF finishing efficiency and processing accuracy.

In order to study the validity of the proposed ultrasonic coupling enhancement method in this article, one point is taken from every 10 mm in the midline near the bottom wall of the flow path (27.5 μm), and the amplitude of velocity is extracted, and then it is compared with the conventional flow path. The results are shown in Figure 9. As can be seen from the curves in the figure, the ultrasonic coupling method can effectively change the velocity distribution in the near wall of the constrained flow path, and the average speed can be doubly increased, which improves the removal efficiency of the abrasive flow in the near wall.

Figure 9.

Velocity distribution comparison in the near wall of constrained flow passage.

As mentioned above, turbulent kinetic energy is the key parameter to characterize the internal energy of constrained passage flow field, and it is closely related to the processing efficiency of abrasive flow. Turbulent kinetic energy reflects the magnitude of turbulent pressure pulsation energy. The larger the turbulent kinetic energy is, the stronger the pressure pulsation is. The increase of turbulent kinetic energy promotes the interaction frequency between the abrasive particles and the surface of the unprocessed workpiece. The disordered movement of abrasive particles improves the processing accuracy and efficiency. Accordingly, the turbulent kinetic energy distribution of the constrained flow passage under ultrasonic coupling is numerically simulated, and the turbulent kinetic energy distribution at different moments is obtained, as shown in Figure 10.

Figure 10.

Turbulent kinetic energy distributions in the constrained flow passage with ultrasonic excitation: (a) t = 0.0040 s, (b) t = 0.0043 s, and (c) t = 0.0045 s.

Referring to the distributions of turbulent kinetic energy, it can be found that the ultrasonic coupling method plays a very significant role in the regulation of the turbulent kinetic energy distribution in the near wall, which is related to the reflection and diffraction of ultrasound in the near wall. The ultrasonic frequency and initial phase set by UDF show that the amplitudes of the ultrasonic waves loaded at three different moments are different, and the distribution of turbulent kinetic energy is unevenly distributed throughout the entire constrained flow passage. It shows different distribution laws at different moments, unlike the regular distribution of the turbulent kinetic energy of the confined flow passage in a steady simulation. Therefore, the SAF after loading the ultrasonic excitation can be fully and evenly processed to all the corners of the workpiece.

To further validate the effectiveness of the ultrasound coupling enhancement in constrained flow passage, we take a point from every 10 mm in the midline near the bottom wall of the flow path (27.5 μm), and the amplitude of velocity is extracted. The results are shown in Figure 11 compared with the conventional flow passage. It can be seen from the curve in the figure that the proposed method in this article can effectively enhance the turbulent kinetic energy distribution in the near-wall region of constrained flow passage, and a five times of average turbulent kinetic energy amplitude can be got.

Figure 11.

Turbulent kinetic energy distribution comparison in the near wall of constrained flow passage.

Experiment results and discussion

Particle image velocimetry–based observation experiments

The movement and distribution of solid abrasive particles in SAF are the core issues in this article. Therefore, an experimental observation platform based on particle image velocimetry (PIV) is set up to capture the abrasive particle trajectories and their related motion parameters in the affecting process of the abrasive flow. The PIV experimental observation platform mainly consists of a high-frequency laser pulse launcher, a high-speed camera, a transparent constrained flow passage, and a PIV post-processing system, as shown in Figure 12.

Figure 12.

PIV experimental observation platform for SAF processing.

The ultra-fast laser pulses of the PIV observation platform enable it to capture the instantaneous details of particle motion in the flow field and provide real-time physical images, real-time vector images of particle movement in flow path, off-line vorticity maps, and other data. It can also provide reliable data for the distribution characteristics of the abrasive flow in the near-wall regions, the distribution characteristics of turbulent kinetic energy in the constrained flow passage, and the particle collision characteristics.

In order to verify the effectiveness of the proposed USAF processing method, a comparative observation experiment is carried out at 50 mm in the near wall of the constrained flow passage. By the observation and experiment, the comparative results are shown in Figures 13 and 14. According to the above results, we can get the following regularities:

In the conventional flow passage, due to the pressure loss along the path and the viscous force of the wall, the movement of the abrasive flow in the near wall is restricted, the distribution of the abrasive particles is not uniform, and the volume fraction is low. The flow velocity vector shows that the velocity trace is relatively sparse and the follow-up characteristics are obvious. The vorticity distribution is obviously controlled by the wall and the overall internal energy is low, taking on a low tendency to dissipate. The volume fraction of the abrasive flow near the wall is low, and the flow field distribution is not uniform. The velocity trace is relatively sparse and has obvious follow-up characteristics. The vorticity energy is low and dissipates. These results are basically consistent with the simulation results in Figures 5 –7 in section “Numerical results and discussion,” such as the pressure and velocity profiles along the channel. The above phenomena will result in negative influence to surface quality, and the material removal efficiency will be limited.

In the ultrasound coupling flow passage, due to the injection of high-frequency pulse energy flow and the ultrasonic reflection and diffraction in the flow path wall, the internal energy of flow field increases rapidly, especially in the near wall. With a relatively high trace density, ultrasonic flow velocity vector reflects the relatively complete vortex flow characteristics. Ultrasonic excitation makes the vorticity distribution improve overall in the near wall of the flow passage. Compared with the vorticity distribution in the trapezoidal constrained flow passage, the vorticity distribution is more uniform. After coupling ultrasonic excitation, the integral number of abrasive fluid near the wall increases and becomes more uniform. The velocity track density increases, and with multiple vortex shapes. Moreover, the energy inside the vorticity is higher and distributed uniformly. These results are in good agreement with the simulation results of Figures 8 and 10 in section “Numerical results and discussion.” The deceleration spots appear in the simulation, and the eddy current is seen in the observation. All of these have confirmed the effect of ultrasonic cavitation can improve the efficiency and accuracy of finishing.

Figure 13.

Flow field distributions in the near-wall region of conventional flow passage: (a) real-time image, (b) velocity vector, and (c) vorticity distribution.

Figure 14.

Flow field distributions in the near-wall region of ultrasonic coupling flow passage: (a) real-time image, (b) velocity vector, and (c) vorticity distribution.

Processing experiment results and discussion

For verifying the effectiveness of the proposed USAF processing method, a processing experimental platform is established, which consists of a SAF mixer, a solid-liquid two-phase diaphragm pump, a workpiece, a constrained flow passage, a valve pipeline, and an ultrasonic vibration exciter. The constrained flow passage is a regular rectangle cross-section flow passage. The particles of solid-phase and the liquid-phase liquid are mixed in a stirring device to form a uniform SAF, which is pressurized and accelerated by the solid–liquid two-phase diaphragm pump to the constrained flow passage. The abrasive particles in the constrained flow passage perform a micro-cutting in the horizontal direction on the structured surface of the workpiece. The SAF is fully developed and flows back to the stirring device through the outlet of the constrained flow passage. Therefore, the abrasive particles in the recycling system can be reused and the utilization rate can be enhanced.

In the above processing system, the chips generated during cutting process are mixed in the SAF, which can block the flow passage and cause negative influence to the processing efficiency. Therefore, in the abrasive flow stirring device, a magnetic device is installed, separating the iron scrap generated from the abrasive flow in cutting.

To evaluate the processing effect of the experimental platform, a rectangular metal strip is selected as the workpiece, which is placed at the bottom of the constrained flow passage for microscopic observation and roughness measurement on the surface. Based on the above design scheme, the USAF processing experiment apparatus is developed, as shown in Figure 15. The power of the ultrasonic generator is 120 W; for the comparative analysis, the frequencies in both the ultrasonic frequency and the numerical simulation are set at 20 kHz. The constrained module is designed with a protruding cylindrical structure for the reliable connection and transmission with the ultrasonic generating device. At the same time, a soft-solid connection is used to enhance the excitation effect. In addition, a partially loaded ultrasonic vibration module is designed at the exit of the constrained flow channel, which can optimize the function of loading position and enhance the fixed point. Moreover, this module can be used to eliminate the surface processing corner of the workpiece and improve the processing uniformity.

Figure 15.

Schematic diagram of USAF processing experiment apparatus: 1—body entity of processing apparatus; 2—constrained module; 3—cover plate of constrained flow passage; 4—ultrasonic exciter; 5—ultrasonci coupling component.

Based on the above design scheme, a USAF processing experiment device is set up, as shown in Figure 16.

Figure 16.

USAF processing experiment device: 1—ultrasonic exciter; 2—flow passage foundation; 3—sample workpiece; 4—lower filling piece; 5—constrained module for ultrasonic loading; 6—upper filling piece; 7—transparent cover plate; 8—assemblled constrained flow passage; 9—ultrasonic transducer.

The ultrasonic wave in the abrasive flow will produce cavitation, which will prompt the tiny bubbles in the abrasive flow to burst instantaneously, and even generate vacuum nucleus and burst, resulting in local high temperature (5000 K), high pressure (1800 atm), and micro-jet. This effect causes the solid–liquid two-phase flow to accelerate and mix uniformly. Meanwhile, the turbulent kinetic energy of the abrasive flow is enhanced and the distribution of the abrasive particles in the abrasive flow is controlled. Therefore, the above phenomenon can improve the abrasive flow finishing effect and processing efficiency.

To check the validity and advancement of the proposed USAF processing method, it is necessary to implement the comparative processing experiments. For the workpieces to be processed, a plurality of rectangular metal strips of the same roughness are provided. The rectangular metal strips are made of 45 # steel, and their length, width, height dimensions are 100, 10, and 5 mm, respectively. The initial surface roughness of the rectangular metal strip is tested by the TR210 roughness tester with an initial value of Ra 0.95. In addition, in order to obtain the details of the surface quality of the workpiece, a KEYENCE-VW-6000 dynamic analysis with three-dimensional display system is used to observe the microscopic surface data.

First, the measurement point on the surface of the workpiece is selected. Considering the fact that the loading method of ultrasonic coupling is generally used in the middle of the flow path, the main influence of ultrasonic energy on both the loading position and the entrance and exit of the flow path is studied. Figure 17 shows the location of measuring points on the surface of the sample workpiece. There are three pairs of test points near the entrance, the middle, and the exit of the sample workpiece.

Figure 17.

Location of measuring points on the surface of sample workpiece: 1—inlet; 2—test points; 3—outlet.

To obtain an accurate surface roughness of the processed workpiece, the TR210 roughness tester is used, and the direction which is perpendicular to the fluid flow in the constrained flow path is used as slip direction (x direction). During the processing experiment, three pairs of test points on the surface of the workpiece are measured for roughness every 2 h, and the measured values are recorded. Each pair of test points are measured for three times with a total of six values, and the average values are taken. There are a total of 10 sets of measuring records during 20 h.

1. Comparative results of surface quality

Based on the USAF processing experiment platform, the comparative processing experiments are performed, in which three pairs of roughness values on the surface of the test workpieces are measured, as shown in Figures 18 –20.

Figure 18.

Roughness variations on the entrance of sample workpiece.

Figure 19.

Roughness variations on the middle of sample workpiece.

Figure 20.

Roughness variations on the exit of sample workpiece.

It can be seen from the figures that when the ultrasonic excitation is unloaded near the entrance to the constrained flow passage, it takes about 12 h for the surface roughness of the sample workpiece to reach 0.2 μm and about 14 h to reach the minimum value of roughness. When the ultrasonic vibration is loaded, it takes only 6 h to reach the roughness of 0.2 μm at the entrance, the roughness reaches the minimum value in only 8 h, and it remains unchanged afterward.

However, the surface roughness of the sample workpiece without ultrasonic vibration increases after 14 h. The weak turbulence of the SAF in the constrained flow passage and the single repetition of the motion are the possible reasons for this phenomenon. When the roughness of the sample workpiece reaches a certain value, the continuous single micro-cutting on the surface will make the surface rougher. After loading the ultrasonic vibration, the surface roughness of the sample workpiece remains the same after the roughness reaches minimum, which indicates that the cavitation effect caused by the loading ultrasonic vibration strengthens the turbulence, and the complex and changeable trajectory of abrasive particles avoids continuous and single cutting for the sample workpiece.

In the middle of the constrained flow passage, after the ultrasonic vibration is loaded, the time which the surface roughness of the sample workpiece reaches the minimum value is about 6 h earlier than that when the ultrasonic vibration is unloaded. In addition, the material removal efficiency increased obviously, and the continuous processing stability of the SAF can be maintained. At the exit of constrained flow passage, the surface roughness of the sample workpiece remains about 0.3 μm after 10 h of ultrasonic vibration. The effect of loaded ultrasonic vibration is still better than that of the unloaded ultrasonic vibration. The above results prove that no matter where the constrained flow passage is, the surface roughness in loaded ultrasonic vibration declines faster than that in unloaded ultrasonic vibration, which shows that the finishing efficiency of the SAF loaded ultrasonic vibration improves significantly.

2. Comparative results of processing efficiency

The key feature of the proposed USAF processing method is that it can effectively increase the internal energy of the abrasive flow field, thus effectively improving the removal efficiency of SAF processing. During the process, we use dynamic three-dimensional system to observe the surface at the entrance; the surface topography at different times which is magnified 500 times is shown in Figure 21. On the left is the unloaded ultrasonic excitation, and on the right shows the loaded ultrasonic vibration.

Figure 21.

Comparative results of sample workpiece surface topography: (a) original topography of workpiece-1, (b) original topography of workpiece-2, (c) processing 8 h without ultrasonic coupling, (d) processing 8 h with ultrasonic coupling, (e) processing 20 h without ultrasonic coupling, and (f) processing 20 h with ultrasonic coupling.

According to the results in Figure 21, after 8 h of processing, the surface of the workpiece becomes smoother, and the original vertical texture is obviously weakened. It can be clearly seen from the analysis and comparison of two figures that the processing effect of USAF processing method is better than that of SAF processing.

After 20 h of processing, some texture slightly parallel to the direction of the SAF appears on the surface of the specimen, and the texture on the left is more obvious, which exactly explains why the surface roughness does not drop after 14 h of processing in Figure 18. However, the texture on the right is not obvious, indicating that loaded ultrasonic vibration can effectively suppress the tailing phenomenon of the SAF processing, which is beneficial to the uniform distribution of abrasive flow turbulence and improve the processing efficiency and quality.

To check the advantages and effectiveness of the proposed method further, the scanning electron microscope (SEM) observation results are conducted. Figure 22 shows a comparison between the USAF processing and conventional SAF processing after 20 h. It can be seen from the figure that the workpiece surface roughness by the USAF processing method is small, the obvious high value area can be removed, and with better surface uniformity. The surface roughness by conventional SAF processing method also decreases, but there is no obvious processing effect compared with ultrasonic coupling. Moreover, there are some regular ordered textures, which indicate that the turbulence degree of abrasive flow and the abrasive motion disorder program are not enough. The above results can fully explain that the ultrasonic coupling strengthening method can not only effectively improve the material removal efficiency of the abrasive flow, but also can get better surface quality.

Figure 22.

SEM comparison of processed surface: (a) conventional SAF processing and (b) USAF processing.

Conclusion

To resolve the problems of processing efficiency and surface uniformity of traditional SAF processing methods, this article proposes an USAF processing method for mold structured surfaces. The required research works have been performed, and the main conclusions are as follows:

Based on the realizable $k - ε$ turbulence model and the mixture multiphase flow model, we set up a fundamental dynamic model of ultrasonic coupling enhancement for SAF. By the sound-flow field coupling theory, the turbulent kinetic energy transport equation of realizable $k - ε$ model is revised. In the dissipative transport equation, the external friction force caused by the shear stress $τ$ is taking into consideration; therefore, the reliability of the modified realizable $k - ε$ model for the simulation of the loaded ultrasonic vibration is improved.

The numerical simulations and online observations show that high-frequency vibration energy flow can excite the coupling of fluid and abrasive particles in constrained flow passage. The high-value cavitation area appears in the abrasive field, which effectively enhances the speed, the pressure, and the distribution of turbulent kinetic energy in the flow passage. The ultrasonic coupling enhancement method can effectively break the viscous force of the fluid in the near wall so that the turbulent kinetic energy in the near wall can be increased more than five times.

We develop the USAF processing experiment platform and its measurement and control system. The relevant processing experiments are completed. The results show that after loading the ultrasonic vibration, the time when the surface roughness of the workpiece reached the minimum is 6 h earlier, and the material removal efficiency improves significantly, and the stability of abrasive flow process can be maintained.

Summarily, the key contribution of the paper is providing an ultrasonic coupling dynamic modeling-solving method for fluid-based precision processing, which can offer useful references to the research works of complex geometric surface machining and ultrasonic-assisted processing methods. The subsequent research works will be performed on the facets of ultrasonic cavitation removal mechanism, dynamical ultrasonic excitation system, and high-frequency pressure pulse monitoring.

Footnotes

Handling Editor: Ismet Baran

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) received no financial support for the research,authorship,and/or publication of this article.

ORCID iD

Jun Li

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