An Investigation into the Multi-Pass Radial-Mode Micro Abrasive Air Jet Turning of Fused-Silica Rods

Abstract

With the increased requirement of miniaturization structures on hard and brittle substrates, micro abrasive air jet turning technology has become a promising machining technology for manufacturing miniaturization structures. This paper presents an investigation on multi-pass radial-mode micro abrasive air jet turning of fused silica. The effect of machining parameters on the depth of cut and materials removal rate was analyzed. The waviness and striation formation mechanisms were studied. It was found that increasing the number of passes significantly increases the depth of cut and materials removal rate. When the surface speed is reduced, the depth of cut and materials removal rate significantly increases. The waviness may be attributed to the intersection and overlap of the adjoint jet footprint. The crossed striations have been found, which may lead to the elimination of the striation. A predictive model of the material removal rate was developed using the dimensional analysis method. The model was assessed and shown to be able to give adequate predictions.

1. Introduction

Hard and brittle materials such as fused silica, monocrystalline silicon, single-crystal quartz and ceramics are important base substrates of miniaturization and functionalization parts applied in microfluidic systems, biomedical systems and micro-electro-mechanical systems (MEMS) [1,2]. It is challenging to manufacture the miniaturization structures on these materials due to their properties of high hardness, high brittleness, high melt point and endured corrosion. Conventional machining technologies have limitations in lower machining efficiency and higher production cost, and even they are unable to process such materials [3]. For example, due to the advantages of high light transmittance, corrosion resistance, high-temperature resistance and good thermal stability, fused silica has been widely employed in the manufacture of micro gyroscopes. Until now, grinding has often been used to reduce the diameter of fused-silica rods into the required dimension. However, the material removal rate (MRR) is low, and the cutting force is large, which can not meet the requirements of high efficiency and low-cost production.

Abrasive jet machining is a non-traditional machining technology that developed rapidly within the last 30 years [4]. A stream of high-velocity jet mixed with abrasive particles is ejected to the workpiece surface during processing. The workpiece material is eroded by a large number of micro abrasive particles [5]. It has the advantages of small cutting forces, negligible heat affected zone, a wide range of machinable materials and high MRR, and is very suitable for single-piece manufacturing mode [3,6]. There are two types of abrasive jet machining, that is abrasive water jet (AWJ) machining and micro abrasive air jet (MAAJ).

As for AWJ machining, the abrasive particles are accelerated by a water jet with a pressure between 200 and 380 MPa commonly. Hence, the impact force of the abrasive water jet is large. The workpiece is prone to deformation and/or breaking under the large impact force during the turning process. The AWJ turning is suitable for rods with large diameters. For example, experiments on rods with diameters between 59 and 75 mm are reported [7,8,9]. Li et al. [7] studied the effect of machining parameters on the average depth of cut h and MRR with single-pass radial-mode abrasive waterjet (AWJ) turning of high-tensile steel. Moreover, the predictive model of h was established based on the dimensional analysis method. The results showed that higher MRR could be obtained by radial-mode turning than offset-mode turning. As for single pass turning, a higher h can be found with higher water pressure, P; higher surface speed, V; lower feed speed, u; and the optimum abrasive flow rate, m_a. Liu et al. [8] carried out AWJ turning on alumina ceramics using response surface methodology (RSM). It was reported that u is the most significant machining parameter on h, followed by m_a and P. Liu et al. [10] proposed that the material removal is caused by the crack coalescence in AWJ turning of alumina ceramics. h was predicted by finite element analysis. It is demonstrated that the predicted h is in good agreement with the experimental results. Yue et al. [11] employed a sequential approximation optimization method to optimize the machining parameters of AWJ turning. Zohourkari et al. [9] conducted experimental investigations to study the influence of machining parameters on MRR with offset-mode AWJ turning of AA2011-T4 alloy. The results showed that P, u, the interactive effect of u and P, the interactive effect of m_a and h, as well as the interactive effect of P and h have a significant effect on MRR, while the influence of V is negligible.

As for MAAJ machining, it uses high-pressured air to accelerate the abrasive particles. The air pressure between 0.2 and 0.9 MPa is usually employed, which is much lower than the pressure of water used in AWJ. The impact force during MAAJ turning is much lower than that during AWJ turning. Therefore, the MAAJ turning is especially suitable for brittle materials with small diameters. For example, experiments on glass rods with diameters between 5 and 10 mm are reported [1,12]. In order to manufacture thread with the controlled depth and width on the glass rods by MAAJ turning, Nouhi et al. [1] employed the helical steel spring attached to the surface of the glass rods as the mask during abrasive air jet turning. Furthermore, the models of the cross-sectional profile of helical grooves and MRR have been established. Kowsari et al. [12] studied the size of the footprint formed by the erosion of MAAJ on the curved surface, and they predicted the erosion footprint size on the curved workpiece surface by the computational fluid dynamics (CFD) method. It is reported that the secondary erosion, caused by the rebounded particles, has a significant effect on the erosive footprint, besides the primary erosion caused by the incident abrasive particles.

Although a large number of efforts have been carried out to investigate abrasive jet turning, there are few studies on the macromechanism of material removal in MAAJ turning. Moreover, the researchers mainly focus on single-pass turning, and little report has been found on the analysis of the influence of the number of turning passes on the formation mechanism of machined surface and MRR. There is also a lack of a quantitative model of MRR involved in the influence of multi-pass turning parameters on machining performance. The research on the multi-pass radial-mode MAAJ turning will help to realize the manufacture of miniaturization structures on hard and brittle materials.

This paper carried out the multi-pass radial-mode MAAJ turning processing experiment based on RSM, and then the influence of machining parameters on h and MRR are analyzed. The macromechanism of material removal is analyzed. Finally, in order to provide the reference for the prediction and control of machining performance under MAAJ turning of hard and brittle materials, the dimensional analysis model of MRR is developed.

2. Experimental Set-Up and Procedure

The experiments were conducted on the MAAJ lathe, equipped with an Accuflo AF10 Micro-Abrasive Blaster (Comco Inc., Burbank, CA, USA), an air compressor, a CNC five-axis guiding system and a cleaner. The CNC five-axis guiding system consists of a CNC rotary table and a CNC slide bench. The cylindrical workpiece was held to the four-jaw chuck of the rotary table. The rotary table and the nozzle were installed on the x-, y- and z-axis CNC slide bench, as shown in Figure 1. The rotary table could move in the x and y directions, and the nozzle could move in the z-direction, under the control of the CNC slide bench. CNC rotary table has A and B axis. The A axis allows the workpiece to be rotated. The B axis controls the tilt of the workpiece. In this experiment, the B axis is kept at 0°, which means that the axis of the workpiece is horizontal.

The workpiece was fused-silica bars whose properties are given in

Table 1. Properties of fused-silica bar used in the experiment.

Shape: round bar	Density: 2.2 g/cm3	Elastic modulus: 70.56 GPa
Diameter: 5 mm	Compressive strength: 9.23 GPa	Poisson’s ratio: 0.16
Length: 10 mm	Fracture toughness: 0.753 MPa·m1/2

. Machining parameters considered in this study included air pressure, P; standoff distance, S_d; feed speed, u; workpiece rotational surface speed, V; and number of passes, N. The air pressures were selected according to the common range of applications and the equipment limit. The feed speed and the surface speed were adjusted to avoid helical grooves with a large pitch on the machined surface on the one hand since large-pitch helical grooves often result in low surface quality. On the other hand, the selected feed speed and the surface speed would ensure that all the combinations of machining parameters selected would produce obvious workpiece material removal and avoid a through-cut of the rods. At the predetermined minimum air pressure, maximum feed speed, maximum surface speed and minimum number of passes, the standoff distance was adjusted for the maximum possible workpiece material removal rate. The number of passes was selected to avoid a through cut of the rods. Levels of each machining parameter are listed in

Table 2. Machining parameters and their levels used in the MAAJ turning tests.

Machining Parameters	Symbol	Units	Factor Level
			−1	0	1
Air pressure	P	MPa	0.3	0.4	0.5
Standoff distance	Sd	mm	15	20	25
Feed speed	u	mm/s	1.12	2.24	3.36
Surface speed	V	mm/s	3.93	7.85	11.78
Number of passes	N		2	3	4

. Based on a three-level five-factor Box–Behnken design (BBD) with six repetitions on the central point, a total of 46 tests were executed.

The boron carbide nozzle with an inner diameter of 760 μm was used. The sharp aluminum oxide abrasive with a nominal diameter of 50 μm was employed. The abrasive flow rate, m_a, was calibrated before carrying out the experiments. The abrasive particles ejected from the nozzle over a time period of 1 min under the air pressure of 0.3, 0.4 and 0.5 MPa were collected. The mass of collected abrasive particles was measured using a balance with a resolution of 0.1 mg. Under each level of air pressure, the mass of collected abrasive particles was measured five times, and the average was taken as the actual abrasive flow rate. The calibrated abrasive flow rate is 0.54 g/min. In radial-mode MAAJ turning, the axis of the nozzle and that of the workpiece meet at right angles, and the nozzle moves along the axial direction of the workpiece. The jet impact angle, α, is kept at 90°, as shown in Figure 2. Nouhi et al. [1] indicated that the impact force during MAAJ turning is small. The influence of impact force on the deformation of the rods is not considered in this work.

Multi-pass turning was considered in this study. For an individual pass of turning, it involves the nozzle moving along the axial direction of the workpiece forth and back once. The nozzle moving forth means that the nozzle is moving in the positive x- direction from the starting point to the end point of the nozzle travel. The nozzle moving back means that the nozzle is moving in the negative direction of the x-axis, returning to the starting point from the end of the travel. During multi-pass turning, the nozzle moves forth and back continuously, with the continuous rotation of the workpiece. The abrasive particles are also continuously ejected from the abrasive jet machine. In order to understand the cutting mechanisms of radial-mode MAAJ turning, lower V and higher u were employed.

The fused-silica rods were mounted on the chuck, which was held on the rotary table. The rotary table has a concentricity of less than 10 μm and an end surface jumpiness of less than 15 μm. It was considered that the center of the rod and the rotation axis were aligned in the experiment since the standoff distance was between 15 and 25 mm.

The machined surface of the specimen was examined under VHX-600 3D digital microscope (Keyence Corp., Osaka, Japan). The workpiece diameter after turning was measured at three evenly distributed positions along the circumference of the machined surface. The depth of cut for the ith measured position, h_i, can be given by

$$h_i=(d_t-d_i)/2=[d_t-(d_i^{top}+d_i^{bot})/2]/2$$

(1)

where d_t is the initial diameter of the workpiece before MAAJ turning, d_i is the workpiece diameter of the ith measured position after MAAJ turning. $d_i^{top}$ is the maximum radius distance between peaks and represents the maximum diameter of the ith measured position after MAAJ turning. $d_i^{bot}$ is the minimum radius distance between valleys represents the maximum diameter of the ith measured position after MAAJ turning, as shown in Figure 3. The average of $h_i$ is taken as h.

MRR can be expressed as [7]

$$MRR=[\frac{1}{4}\pi d_t^2-\frac{1}{4}\pi {(d_t-2h)}^2]u=\pi (d_t-h)hu$$

(2)

3. Results and Discussion

3.1. Waviness on Surface Generated by MAAJ Turning

It has been found that some machined surfaces are flat, with roughness as the primary surface irregular characteristic. Figure 4a shows a representative machined surface with h of 330.85 μm. The depth of cut along the axial direction of the workpiece is nearly constant. The percentage of the number of specimens with flat machined surfaces with respect to the total number of specimens is about 30.4%. While some machined surfaces have been machined non-uniformly, they appeared to be dominated by significant waviness and roughness. A typical severe wavy machined surface with h of 276.81 μm is shown in Figure 4b. The depth of cut along the axial direction of the workpiece varies significantly, leading to the formation of a wavy surface. The percentage of the number of specimens with severe waviness on the machined surface with respect to the total number of specimens is about 58.7%. Correspondingly, the percentage of the number of specimens with slight waviness on the machined surface shown in Figure 4c with respect to the total number of specimens is about 10.9%.

During the nozzle move forth or back, since the workpiece is rotary and the nozzle moves along the axial of the workpiece, the jet footprint on the workpiece surface is a helical groove. The stretch-out view of the formed helical groove for an individual pass of turning is shown in Figure 5.

The pitch of helical groove, λ, can be given by

$$\lambda =u\times T=u\times \frac{60}{n}=u\times \frac{\pi d_t}{V}$$

(3)

where T is the time required for one rotation of the workpiece, and n is the workpiece rotation speed. It can be seen from Equation (3) that λ increases with a decrease in V, while it increases with an increase in u.

With regard to multi-pass turning by MAAJ, during an individual pass of turning, a helical groove is formed when the nozzle moves forth, as shown in Figure 5. Then, another helical groove is produced when the nozzle moves back. It is expected that the helical grooves will intersect. For the following passes of turning, the new helical grooves continue to generate, and they intersect and overlap with the adjoining ones. It is believed that, as for a smaller λ, more intersection and more overlap of helical grooves will occur. This may lead to a decrease in the height of the helical groove sidewall, and shallower helical grooves may be formed. The wavy height is reduced, and the machined surface with slight waviness is generated, as shown in Figure 4c. As for a certain value of λ, the intersection and overlap of the helical grooves may lead to the elimination of the helical grooves, resulting in the formation of a flat machined surface, as shown in Figure 4a. As for a larger λ, fewer intersections and less overlap of the helical grooves occur, and the deeper helical grooves remain on the workpiece surface. Thus, the machined surface with significant waviness is formed, as shown in Figure 4b.

3.2. Striation on Surface Generated by MAAJ Turning

It has been reported that striation is frequently generated on the machined surface under AWJ cutting [13]. Moreover, in the study of Li et al. [7], it is shown that the striations have been produced on the specimen surface by AWJ turning of AISI4340, which is a typical ductile material. However, it is not clear whether the striations will be formed on the surface under MAAJ turning of brittle materials.

In this study, striations have been found on the surfaces generated by the MAAJ turning of fused silica. Typical surfaces with striations are shown in Figure 6. Obviously, the striations have been generated on the surface of hard and brittle material under MAAJ turning.

During the MAAJ turning process, the workpiece material removal is mainly due to the impact of abrasive particles, which have high kinetic energies. It should be noted that the machined surface is rough, and the impressions of plowing and excess lips (elongated flakes) [14] have not been found. A typical machined surface is shown in Figure 7. It demonstrated that the brittle fracture mechanism plays a dominant role in the material removal of multi-pass radial-mode MAAJ turning of fused silica. When the abrasive particle with the normal component of the kinetic energy, which is a component of kinetic energy along the direction normal to the workpiece surface higher than the threshold energy required for destructing the workpiece material, impacts the workpiece, cracks are formed on the workpiece. The propagation and the intersection of the cracks lead to material removal [15,16]. However, when the abrasive particle with a normal component of the kinetic energy lower than the required threshold value to destroy the material impacts the workpiece, the workpiece material removal is a rare occurrence.

Li et al. [17,18] and Jafar. et al. [19] reported that the kinetic energy distribution of abrasive particles is non-uniform across the jet cross-section. The kinetic energy of the abrasive particle close to the jet center is higher than that close to the rim of the jet. In addition, Kowsari et al. [12] proposed that the incident abrasive particles are rebounded after they impinge on the workpiece. The rebounded abrasive particles tend to collide with the incident abrasive particles of the jet. This leads to the reduction in the incident abrasive particle kinetic energy. Thirdly, the particle impact angle, φ, defined as the angle between the velocity direction of the abrasive particle and the workpiece surface close to the periphery of the jet, is small, as shown in Figure 2. Correspondingly, the normal component of the abrasive particle kinetic energy is small. These result in more abrasive particles close to the rim of the jet, with the normal component of kinetic energy lower than the threshold energy required for destroying the workpiece material. When the strong abrasive particles with the higher normal component of the kinetic energy impact the workpiece, the workpiece will be destroyed, leaving micro-grooves on the machining surface. When the weak ones with the lower normal component of kinetic energy impact the workpiece, they may deflect to follow the trace of adjoining strong ones and move along the formed micro-grooves [13]. Then the striations are formed on the surface of the workpiece.

As shown in Figure 6, the drag angles β of the striation, which is the sharp angle between the direction of the stration and the axial direction of the workpiece, are different. The helix angle, γ, of the micro-groove shown in Figure 2 can be expressed as

$$\gamma =\arctan (\frac{\pi d_t}{\lambda })=\arctan (\frac{\pi d_t}{u\frac{\pi d_t}{V}})=\arctan (\frac{V}{u})$$

(4)

β is obviously different from γ. Hence, it is believed that the trace of an abrasive particle with low kinetic energy has deflected, which is consistent with the findings of other studies [13].

The intersection of striations has been found on the machined surface, as shown in Figure 8. The machined surface of MAAJ turning can be differentiated into three zones: (1) pre-processing zone, (2) machining zone and (3) machined zone, as shown in Figure 2. With respect to the pre-processing zone, the workpiece surface is machined by the rim of the jet. As the workpiece rotates, the pre-processing zone becomes the machining zone, and the workpiece surface is machined by the central region of the jet. As the workpiece further rotates, the machining zone becomes the machined zone, and the workpiece surface is machined by the rim of the jet again.

As shown in Figure 9, on the one hand, the drag angles of striations on the front side of the workpiece surface are different from that on the rear side of the workpiece surface. On the other hand, the drag angles of striations for the nozzle feed forward are different from that for the nozzle feeds backward. These lead to the intersection of the striations. It should be noted that the striation formation mechanisms are different from the AWJ cutting, in which the intersection of the striation rarely occurs.

It also can be seen from Figure 9 that the direction of the striation when the nozzle moves back is opposite to that when the nozzle moves forth. The striation-crossed leads to the striation peaks being removed, and the striation is disappeared. It is similar to roller burnishing with the helix crossed, as reported by Rodriguez et al. [20]. Both the FEM simulation and experiments show the elimination of the spiral patterns generated by the turning operation.

Figure 8b presents the elimination of striations due to the intersection of striations. Since the striations can be eliminated by the striation intersection, the machined surface produced by MAAJ turning can be smooth without significant striation. The percentage of the number of samples with significant striations on a machined surface with respect to the total number of samples is about 37%. Therefore, the percentage of the number of samples without significant striations on the machined surface with respect to the total number of samples is about 63%. It demonstrated that the machined surface without striation could be produced by selecting the machining parameters properly.

3.3. Analysis of Variance for h and MRR

In order to investigate the degree of sensitivity of h to the machining parameters, the analysis of variance (ANOVA) was carried out. The results of ANOVA for h are shown in

Table 3. ANOVA for h (after backward elimination with p-value < 0.05).

Source	DF	Sum of Squares	Mean Square	F-Value	p-Value
P	1	92,948	92,948	68.89	0.00
Sd	1	7070	7070	5.24	0.03
V	1	8248	8248	6.11	0.02
N	1	72,590	72,590	53.80	0.00
u	1	189,625	189,625	140.54	0.00
u2	1	44,128	44,128	32.71	0.00
V × N	1	6258	6258	4.64	0.04
Error	38	51,272	1349
Total	45	472,140

, corresponding to a 95% confidence level. The insignificant factors were deleted based on the backward elimination method. It was found that u has the most significant effect on h and is followed by P, N, u², V, S_d and V × N.

The results of ANOVA for MRR are shown in

Table 4. ANOVA for MRR (after backward elimination with p-value < 0.05).

Source	DF	Sum of Squares	Mean Square	F-Value	p-Value
P	1	83.16	83.16	77.77	0.00
Sd	1	5.80	5.80	5.42	0.03
V	1	9.41	9.41	8.80	0.01
N	1	65.56	65.56	61.31	0.00
u	1	60.56	60.56	56.63	0.00
V × N	1	6.64	6.64	6.21	0.02
Error	39	41.70	1.07
Total	45	272.82

, corresponding to a 95% confidence level. It was found that P has the most significant effect on MRR and is followed by N, u, V, V × N and S_d.

3.4. The Effect of Machining Parameters on h and MRR

Figure 10 and Figure 11 show the effect of machining parameters on h and MRR, respectively.

3.4.1. The Main Effect of Machining Parameters

It can be seen from Figure 10 and Figure 11 that increasing P increases h and MRR. The abrasive particles are accelerated by the high-speed air stream. The velocity of the air stream increases with an increase in P. As a result, increasing P increases the velocity of the abrasive particles. Higher-speed abrasive particles lead to more material removal, resulting in larger h and MRR.

It can be seen from Figure 10 that h increases first and then decreases with an increase in S_d. As S_d increases from 15 mm to 20 mm, h increases from 281.23 μm to 291.75 μm. The increase in h is very small. As the S_d increases from 20 mm to 25 mm, h decreases from 291.75 μm to 239.19 μm. The decrease in h is significant.

On the one hand, it is demonstrated that the abrasive particles emanating from the nozzle are accelerated by the high-velocity air flow, and their kinetic energies continuously increase within some ejection distance S [17]. The velocity of the air flow decreases rapidly as the jet ejection distance increases. With a larger ejection distance, abrasive particle velocity decreases due to the dragging effect of the air flow, which velocity is lower than that of abrasive particles. It is reported that S is about 6.2 times the nozzle diameter, d_nozzle [17]. Hence, in this study, S can be given by

$$S\approx 6.2\times d_{nozzle}=6.2\times 0.76=4.71\mathrm{mm}$$

(5)

It can be seen from Equation (5) that S is smaller than S_d. It demonstrated that within the range of S_d selected in this study, the kinetic energies of abrasive particles decrease continuously with an increase in S_d. This leads to a decrease in h.

On the other hand, the jet diameter increases with an increase in S_d. The jet diameter can be expressed as

$$d=d_{nozzle}+2S_d\tan \theta$$

(6)

where θ is the jet divergence angle, as shown in Figure 2. It is reported that θ is about 3.5° [21].

In this study, the jet diameters are 2.59, 3.21 and 3.82 mm, respectively, corresponding to the S_d of 15, 20 and 25 mm. Therefore, with the increase in S_d, the cross-sectional area of the jet increases by 52.7% and 116.5%, respectively. Hence, the interference and collision between abrasive particles within the jet decrease, resulting in the increase in effective kinetic energy of the abrasive jet and the increase in h.

When the S_d increases from 15 mm to 20 mm, the increase in effective kinetic energy of the abrasive jet caused by the interference and collision reduction within the jet has a greater effect, but the decrease in the effective kinetic energy of the abrasive jet caused by the increase in jet ejection distance has a smaller effect. As a result, the effective kinetic energy of the abrasive jet increases, leading to an increase in h. Figure 10 also shows that the increase in the h is very limited. It can be assumed that the effective kinetic energy of the abrasive jet does not increase significantly. When S_d increases from 20 mm to 25 mm, the decrease in the effective kinetic energy of the abrasive jet caused by the increase in jet ejection distance has a greater effect, while the increase in the effective kinetic energy of the abrasive jet caused by the reduction in interference and collision within the jet has a smaller effect. Therefore the effective kinetic energy of the abrasive jet decreases, and h becomes smaller. Since Figure 10 shows that h decreases greatly, it is believed that the effective kinetic energy of the jet decreases significantly.

The MRR almost remains constant at firstly and then decreases significantly as the S_d increases, as shown in Figure 11. When the S_d are 15 and 20 mm, MRR are 8.88 and 8.89 mm³/s, respectively. While, as the S_d increases from 20 mm to 25 mm, MRR decreases from 8.89 mm³/s to 7.70 mm³/s. The significant decrease in MRR may be attributed to the notable decrease in the effective kinetic energy of the abrasive jet.

It can be seen from Figure 10 and Figure 11 that h and MRR decrease with an increase in V. It may be attributed that fewer abrasive particles impinge on the workpiece as V increases, resulting in less material removed. Furthermore, the number of abrasive particles with large impact angle also decreases with an increase in V. Hence, h and MRR decreases with an increase in V.

It can be seen from Figure 10 that h increases with an increase in N. It is believed that more abrasive particles impact the workpiece surface with an increase in N, resulting in more workpiece material removal and h increases. It should be noted that MRR also increases with an increase in N, as shown in Figure 11. It is assumed that the ridges of helical grooves, as illustrated in Figure 5, are more likely to be removed with an increase in N. The ridges are formed by the intersection of the helical grooves. The ridges with isolated convex shapes are easier to be removed than the substrate of the workpiece. As N increases, the intersection of the helical grooves increases, resulting in more ridges generated. As a result, MRR increases with an increase in N. The increase in cutting depth is different as the number of passes increases. As the N increases from 2 to 3, h increases from 185.34 μm to 249.72 μm. While as the N increases from 3 to 4, h increases from 249.72 μm to 319.94 μm. The increasing rate of h increases with an increase in N. Since the amount of ridges increases with an increase in N, and the isolated convex-shaped ridges are easier to be removed, the rate of h increases with an increase in N.

It can be seen in Figure 10 that h decreases with an increase in u. Furthermore, the decreasing rate of h decreases with u. The number of effective abrasive particles decreases with an increase in u. This leads to a decrease in h. With a further increase in u, the interference of abrasive particles in the jet decreases, and the effective kinetic energy of the jet increases. Hence, the decreasing rate of h decreases. It should be noted that MRR increases with an increase in u, as shown in Figure 11. The rebound abrasive particles and workpiece debris are easier to escape from the workpiece. Hence, the probability of collision between incident particles and rebound particles, as well as the probability of collision between incident particles and workpiece debris, decreases. The effective kinetic energy of the abrasive jet increases correspondingly. Moreover, the interference of incident abrasive particles may decrease with an increase in u, and hence the effective kinetic energy of the jet increases. Consequently, MRR keeps increasing with an increase in u.

It should be noted that the difference between the maximum and minimum diameter of the rods has an influence on the machining performance since the abrasive tools can affect the deeper zone, as presented in [22]. However, as for MAAJ turning in this experiment, the standoff distance is 15–25 mm, and the maximum difference between the maximum and minimum diameter of the rods after MAAJ turning is about 300 μm. The difference between the maximum and minimum diameter is considered to have a negligible effect on the machining performance. It should be noted that maximum and minimum diameters should be considered if the difference between the maximum and minimum diameters of the workpiece is large. For example, during the machining of integrally bladed rotors (IBR), the maximum and minimum diameters of the workpiece may have a significant influence on the machining performance.

3.4.2. The Interactive Effect of Machining Parameters

The ANOVA of machining parameters shows that the interactive effects of V and N have a significant effect on h and MRR. As indicated in Figure 12 and Figure 13, h and MRR are larger for a higher V and a larger N.

In summary, in the above discussions, h increases with an increase in P, while h increases with a decrease in u. h increases slightly firstly and then decreases with an increase in S_d. MRR increases with an increase in P and u. MRR almost remains constant at first and then decreases significantly as the S_d increases. Increasing N significantly increases h and MRR. h and MRR significantly increase with a decrease in V. During the radial-mode multi-pass turning, the overlap of helical grooves has a significant effect on MRR. When higher MRR is required, lower V, higher u and multi-pass turning mode is always suggested.

It should be noted that, in this MAAJ turning experiment, the optimal Ra is 6 μm measured by the spectral confocal microscope. The smallest h that can be reached is 98 μm, at an air pressure of 0.4 MPa, standoff distance of 20 mm, feed speed of 2.24 mm/s, surface speed of 11.78 mm/s and number of passes of 2.

In particular, it was found that the ratio of MRR and m_a is around 0.5–1. It is larger than that in MAAJ cutting of glass. During MAAJ turning, the abrasive jet impacts the curve surface of the workpiece. This is different from the MAAJ cutting, in which the abrasive jet impacts the flat workpiece. Thus, the collision probability of the incident abrasive particles with the rebound abrasive particles in turning is less than that in cutting. As a result, more jet energy would be employed to remove the workpiece material. The ratio of MRR and m_a becomes larger for turning than that for cutting. Furthermore, as for multi-pass turning, MRR increases in contrast with that for single-pass turning. It may be because the fact that the ridges on the workpiece surface are formed, which are easier to be removed than the substrate of the workpiece. Thirdly, much damage is formed on the machined surface in the pre-machined zone and machined zone, for example, subsurface micro-cracks. The substrate material with damage is easier to be removed. These lead to the ratio of MRR and m_a becoming larger.

4. Dimensional Analysis Model of MRR

In order to predict and control the MRR of MAAJ turning, the model should be established. In this study, the semi-empirical model is a development based on the dimensional analysis method.

In the process of MAAJ turning, the workpiece material is removed by the impact of a large number of abrasive particles. The MRR is mainly affected by the kinetic energy of the abrasive jet, E_k; workpiece fracture toughness, K_1C; workpiece hardness, H_t; particle hardness, H_d; workpiece diameter, d_t; standoff distance, S_d; abrasive flow rate, m_a; number of passes, N; feed speed, u; and workpiece surface speed, V.

Thus, MRR can be expressed as

$$MRR=f_1(E_k,K_{1C},H_t,H_d,d_t,S_d,m_a,N,u,V)$$

(7)

The set of variables in Equation (7) is expressed in terms of three fundamental dimensions, i.e., length L, mass M and time T. Hence, in order to develop the dimensional analysis model of MRR, three recurring variables should be selected. H_t, d_t and u can represent all of the fundamental dimensions in Equation (7) and are selected as the recurring variables.

According to the π theory [7], the other variables in Equation (7) can be expressed as

$${\pi }_1=f_1({\pi }_2,{\pi }_3,{\pi }_4,{\pi }_5,{\pi }_6,{\pi }_7,{\pi }_8)$$

(8)

where, ${\pi }_1=\frac{MRR}{d_t^{2}u}$, ${\pi }_2=\frac{E_k}{H_t{d}_t^3}$, ${\pi }_3=\frac{K_{1C}}{H_t{d}_t^{1/2}}$, ${\pi }_4=\frac{H_d}{H_t}$, ${\pi }_5=\frac{S_d}{d_t}$, ${\pi }_6=\frac{m_{a}u}{H_t{d}_t^2}$, ${\pi }_7=N$, ${\pi }_8=\frac{V}{u}$.

In Equation (8), $\frac{H_d}{H_t}$ represents the effect of the relative hardness of the workpiece and abrasive particle on MRR. $\frac{K_{1C}}{H_t{d}_t^{1/2}}$ represents the effect of workpiece diameter on the brittleness of the workpiece material.

Equation (8) can be rewritten as

$$\frac{MRR}{d_t^{2}u}=f_1(\frac{E_k}{H_t{d}_t^3},\frac{K_{1C}}{H_t{d}_t^{1/2}},\frac{H_d}{H_t},\frac{S_d}{d_t},\frac{m_{a}u}{H_t{d}_t^2},N,\frac{V}{u})$$

(9)

Equation (9) can be expressed in the exponential form as

$$MRR=C_1(d_t^{2}u){(\frac{E_k}{H_t{d}_t^3})}^{{\alpha }_1}{(\frac{K_{1C}}{H_t{d}_t^{1/2}})}^{{\alpha }_2}{(\frac{H_d}{H_t})}^{{\alpha }_3}{(\frac{S_d}{d_t})}^{{\alpha }_4}(\frac{m_{a}u}{H_t{d}_t^2}{)}^{{\alpha }_5}{N}^{{\alpha }_6}(\frac{V}{u}{)}^{{\alpha }_7}$$

(10)

where C₁ is constant, α_i(i = 1,2,3…7) are constants.

The kinetic energy of an abrasive jet $E_k$ can be expressed as

$$E_k=f_2(m_a,P,d_{nozzle},S_d,\theta ,m_p,r_p)$$

(11)

It involves three dimensions, L, T and M, and P, S_d and m_a can be chosen as the recurring variables.

According to π theorem, the other variables in Equation (11) can be expressed as

$${\pi }_9=f_2({\pi }_{10},{\pi }_{11},{\pi }_{12},{\pi }_{13})$$

(12)

where, ${\pi }_9=\frac{E_k}{P{S}_d^3}$, ${\pi }_{10}=\frac{d_{nozzle}}{S_d}$, ${\pi }_{11}=\theta$, ${\pi }_{12}=\frac{m_p}{m_a}$, ${\pi }_{13}=\frac{r_p}{S_d}$.

Or

$$\frac{E_k}{P{S}_d^3}=f_2(\frac{d_{nozzle}}{S_d},\theta ,\frac{m_p}{m_a},\frac{r_p}{S_d})$$

(13)

Equation (13) can be expressed in the exponential form as

$$E_k=C_2(P{S}_d^3){(\frac{d_{nozzle}}{S_d})}^{{\alpha }_8}{\theta }^{{\alpha }_9}{(\frac{m_p}{m_a})}^{{\alpha }_{10}}{(\frac{r_p}{S_d})}^{{\alpha }_{11}}$$

(14)

where $C_2$ and ${\alpha }_i(i=8,9,\dots ,11)$ are constants.

Substitute Equation (14) into Equation (10) gives

$$MRR=C_3(d_t^{2}u){(\frac{P}{H_t})}^{k_1}{(\frac{d_{nozzle}}{S_d})}^{k_2}{\theta }^{k_3}{(\frac{m_p}{m_a})}^{k_4}{(\frac{r_p}{S_d})}^{k_5}{(\frac{K_{1C}}{H_t{d}_t^{1/2}})}^{k_6}{(\frac{H_d}{H_t})}^{k_7}{(\frac{S_d}{d_t})}^{k_8}(\frac{m_{a}u}{H_t{d}_t^2}{)}^{k_9}{N}^{k_{10}}(\frac{V}{u}{)}^{k_{11}}$$

(15)

where $C_3=C_1{C}_2^{{\alpha }_7}{\theta }^{k_3}{(\frac{m_p}{m_a})}^{k_4}{(\frac{K_{1C}}{H_t{d}_t^{1/2}})}^{k_6}{(\frac{H_d}{H_t})}^{k_7}$ and $k_i(i=1,2,\dots ,11)$ are constants.

The experimental data are employed to obtain the constants in Equation (15) and gives

$$MRR=7.805\times {10}^{-11.8}\times d_t^{2}u\times {(\frac{P}{H_t})}^{0.985}{(\frac{1}{S_d})}^{0.288}(\frac{m_{a}u}{H_t{d}_t^2}{)}^{-1.535}{N}^{0.693}(\frac{V}{u}{)}^{-0.698}$$

(16)

Figure 14 shows the percentage deviation of the model-fitted value with respect to the corresponding experimental results. The average percentage deviation of the model is -9.85%, with a standard deviation of 21.79%. On the one hand, some samples have the waviness characteristic, and h is non-uniform along the circumference of the machined surface. In order to analyze MRR, the average value of h is obtained and employed to calculate MRR, according to Equation (2). On the other hand, the m_a is not very stable and depends on P to some extent. This leads to the deviation of the model-fitted values with respect to the corresponding experimental results.

The verification experiments were carried out. The comparison of MRR predicted by the model, MRR_pre, and those obtained by experiments, MRR, are shown in

Table 5. MRR of prediction and experiment.

No.	P (MPa)	Sd (mm)	u (mm/s)	V (mm/s)	N	MRR (mm3/s)	MRRpre (mm3/s)	Error (%)
1	0.35	17	2.52	11.52	2.5	3.86	4.58	18.65
2	0.45	19	2.52	10.47	3.5	6.43	7.67	19.28

. It demonstrated that the model could be employed to predict and control the MRR.

5. Conclusions

The experiments of multi-pass radial-mode MAAJ turning of fused-silica rod were carried out to investigate the macro cutting mechanism, as well as the effect of machining parameters on h and MRR. The conclusions are as follows:

• h increases with an increase in P, while h increases with a decrease in u. h increases slightly firstly and then decreases with an increase in S_d. MRR increases with an increase in P and u. MRR almost remains constant at first and then decreases significantly as the S_d increases. Increasing N significantly increases h and MRR. h and MRR significantly increase with a decrease in V.
• The machined surfaces, with waviness as the primary surface irregular characteristic, were found. The formation of the wavy surface may be attributed to the intersection and overlap of the adjoint jet footprint. The flat machined surfaces, without waviness characteristics, can be obtained by selecting the machining parameters appropriately.
• The striations were formed on the surface of hard and brittle material under MAAJ turning. The drag angle of the striation is different from the helix angle of the helical groove. The intersection of striations was found, which may lead to the elimination of the striation.
• The predictive model of MRR was developed using the dimensional analysis method. The model was assessed and shown to be able to give adequate predictions.