Higher standards have been set for elbow-type parts' inner-surface finish in industrial production. The influence mechanism of inlet velocity, bend ratio, and bending angle on the surface quality of elbows is analyzed to study the surface quality control technology of abrasive flow machining (AFM) elbows, and the surface quality control method of elbows in AFM is established. The results of the numerical simulation demonstrate that a suitable increase in inlet velocity can enhance the machining effect of the abrasive flow; a smaller curvature radius has a higher machining intensity and a larger curvature radius has a better overall machining uniformity; the numerical simulation also confirms that the analysis of the flow state in the 90° elbow applies to elbows with different bending angles, demonstrating the analysis's applicability. The test results of the curvature radius are consistent with the results of the numerical simulation, and for a larger curvature radius, the inlet velocity or inlet pressure can be increased appropriately to achieve better surface quality control. The test results of the inlet pressure show that increasing the inlet pressure can improve the machining effect of the abrasive flow, indicating that the inlet pressure and inlet velocity are proportional to each other. Therefore, the experimental findings confirm the accuracy of the numerical calculations and offer technical support for the elbow AFM quality control system that has been developed.
Research Article
Effectiveness Analysis of Abrasive Flow Machining on Elbow Inner-surface Finish
https://doi.org/10.21203/rs.3.rs-2430779/v1
This work is licensed under a CC BY 4.0 License
Journal Publication
published 22 Sep, 2023
Read the published version in The International Journal of Advanced Manufacturing Technology →
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Inter-surface finish
Abrasive flow machining
Elbow
Surface quality control
Elbow-type parts are widely used in a variety of industrial production and daily life, including evaporators in food processing, sterilizers on heat transfer tubes, pacemaker catheters, drug guide tubes, cars, tanks, and other vehicles used in high-pressure oil pipes, intake and exhaust manifolds, and a variety of tube musical instruments. They are a vital component of modern industry. Elbow-type components are now widely used in manufacturing and industrial operations [1]. It is especially crucial to improve the quality of the inner surface of these elbow-type parts to make them better fit the variety of requirements of practical applications and to decrease the friction suggested in the elbow [2]. The issue of the intricate inner surface of elbow-type parts, which is challenging to manufacture by conventional procedures, has been resolved by the development of AFM technology [3]. AFM, also referred to as squeeze grinding or squeeze honing, is a newly developed machining technique. Its fundamental principle is to squeeze the processing medium containing high-hardness abrasive grains through the pressure produced by the movement of the AFM, causing the abrasive to flow through the inner surface, an outer surface, and the pipe of the workpiece in an erratically [4]. For surface finishing, deburring, polishing, and other requirements, solid-liquid two-phase abrasive particle flow, and workpiece wall impact collision are used, leading to higher workpiece surface accuracy [5, 6]. The required finish/texture is one of the prime requirements in various, finished components through conventional machining, processes like grinding, lapping, polishing, and super finishing processes [7]. The application of abrasive gels with a helical passageway is proposed to create multiple motions of abrasive medium and to obtain the even surface of the complex holes in the AFM process [8].
Numerous academics have investigated the various pipe types and the variables affecting AFM. Singh et al. indicate the amount of finishing stresses and forces generated during the finishing of microholes fabricated on surgical stainless steel (316L) workpieces are computed by using the finite element method [9]. Huang et al. studied the transient flow-gas phase field, as well as the motion, dynamics, and collision properties of the sand, which were computed using the coupled EDEM-FLUENT approach, and the wear of the sandblaster and its wear pattern were computed using the Archard wear model [10]. Wei et al. note a new predictive model for material removal in AFM is proposed based on a combination of a material removal model for single abrasives and a statistical model of active abrasives [11]. With outlet pressure as a variable, Zahoor et al. carried out a numerical analysis to determine the impact of ambient pressure on the performance of microjets by examining the performance for constant liquid and gas flow rates [12]. Singh et al. use an abrasive flow finishing process to finish medical stainless steel pipe, and use the finite element method to determine the finishing force produced by this process in the test process, and obtain the best surface finish [13]. Sankar et al. have studied the convective properties of various media and finishing properties of abrasives in detail [14]. Singh et al. developed an economical abrasive flow polishing medium using viscoelastic polymers. The results show that the nanometer surface finish can be obtained by changing the viscosity of the developer [15]. Chih-Hua et al. have measured the pressure and velocity of AFM media for branch channels with different shapes and diameters to develop and verify the existing numerical models [16]. Petare et al. studied the effects of the AFF process on the wear characteristics, surface finish, and micro-morphology of straight bevel gear (SBG), and determine the optimum value of the AFF process through many experiments [17]. There is currently a dearth of pertinent literature analyzing how elements like bend ratio affect the elbow of AFM.
Currently, more researchers are using numerical simulation techniques in conjunction with real engineering procedures to use numerical simulation techniques to address prevalent turbulence issues in engineering. Taher et al. investigate the unsteady Reynolds-averaged Navier–Stokes simulations of the turbulent cavitating flow around a hydrofoil CLE [18]. Li et al. explore the vortex formation mechanism of a special inner curved surface machined by abrasive flow precision machining, the large eddy simulation method is used to analyze the precision machining behavior of abrasive flow and the effect of vortex clusters on the wall under different inlet pressure [19]. Santos et al. investigate the potential of large-eddy simulation (LES) to assess the influence of turbulent eddies on averaged concentration over short time intervals and, thus, with LES results compared with wind-tunnel data [20]. Koukouvinis et al. capture the complex flow field and cavitation structures forming in the injector, Large Eddy Simulation along with a two-phase homogenous mixture model was employed and compressibility of the liquid was included as well [21]. Bose et al. indicate that large-eddy simulation (LES) has proven to be a computationally tractable approach to simulating unsteady turbulent flows [22]. Li et al. based on the large eddy simulation method, the KET sub-grid model was selected to simulate the abrasive flow polishing S-shaped elbow with side holes, and the processing experiment was carried out [23]. To investigate the AFM of the elbow using the large eddy numerical simulation techniques and the mixing model applied to the solid-liquid two-phase flow model, this paper concentrates on elbow-type parts to produce more compelling simulation findings.
The relationship between variables like bend ratio and bending angle and the surface quality of elbows machined by the abrasive flow is still unclear, despite extensive research in the field. Thus, computational simulations and machining experiments have been conducted. The quality control features of the elbow used in AFM were examined and addressed from several perspectives, including the bend ratio and bending angle of the elbow, which were based on the elbow's distinctive structural properties. The elbow is separated into various sections, as seen in Fig. 1, to allow for a more thorough investigation of the distribution of flow characteristics and the mechanism of micro-cutting surfaces at each section of the AFM elbow to achieve surface quality control.
Due to the transverse pulsation of the particles in the flow, the abrasive's velocity distribution tends to be uniform when it is moving in a turbulent flow. The intensity of the abrasive mixing and the uniformity of the velocity distribution increase with increasing Reynolds number. Figure 2 shows the velocity structure distribution of the abrasive on the cross-section of the circular pipe.
According to Fig. 2, when the abrasive flows through a certain cross-section of the pipe, the velocity is divided into three regions:
(1) Viscous bottom zone. Near the pipe wall, due to the limitation of the transverse pulsation of abrasive particles by the pipe wall, the viscosity of the abrasive plays a leading role, and the abrasive behaves as a laminar flow. The radial velocity of the abrasive in this region has a large gradient, and the velocity at the contact position with the pipe wall is zero.
(2) The core region of turbulence. Due to the effect of turbulence pulsation, the velocity distribution of the abrasive is more uniform between the tube axis and the region not too far away from the tube wall, and the abrasive in this region is in turbulent motion.
(3) Transition zone. This region is located between the turbulent core region and the viscous bottom layer. Generally, the flow state in the transition region is complex and the range is very small, which can be regarded as the treatment of the turbulent core region [24].
In turbulent motion, the thickness of the viscous bottom layer \(\delta\) is mainly related to the thickness of the pipe fitting Reynolds number,\(\operatorname{Re}\) and the friction factor \(\lambda\) of the pipe fitting. The approximate relationship is as follows:
$$\delta \approx 30\frac{d}{{\operatorname{Re} \sqrt \lambda }}$$ (5)
According to the formula, the larger the Reynolds number, the thinner the viscous substrate. When the roughness\(\Delta\)of the pipe fitting is greater than the thickness \(\delta\)of the viscous bottom layer (namely\(\Delta >\delta\)), the burr inside the pipe fitting will be exposed outside the viscous bottom layer, causing the stability of the viscous bottom layer to be destroyed. The fluid in the turbulent core impinges on the burr and bulge of the pipe fitting, thus generating the vortex. As the turbulence intensifies, the energy loss of the fluid in the tube increases, and the polishing performance of the abrasive flow is enhanced.
When the roughness of the pipe fitting\(\Delta\)is less than the thickness of the viscous bottom layer \(\delta\) (namely\(\Delta <\delta\)), the uneven part of the pipe fitting will be covered by the viscous bottom layer. In this case, the roughness has little effect on the distribution of the turbulent structure, the flow state of the abrasive flow in the pipe fitting is relatively stable, and its effect on the polishing of the pipe fitting is small [25].
3.1 Model building and meshing
The 90° elbow is used as the research object in this paper; it has an 8mm inner diameter and was 3D-modeled using SOLIDWORKS and meshed using Gambit. The quality of the grid will have a direct impact on the accuracy of the calculation results during the division meshing process; the neater and more detailed the grid, the more accurate the calculation results. The computation results will have a bigger error if the grid is divided arbitrarily. As a result, a high-quality hexahedral grid was employed for the model by its shape, and the resulting grid model was divided as depicted in Fig. 3.
The grid quality is as close to 1 as possible at the 90° elbow grid quality check, while the FLUENT simulation requires a value greater than 0.1. The grid quality of the 90° elbow can satisfy the computation requirements, as shown in Fig. 3.
3.2 Parameter setting and boundary conditions
To simulate the flow pattern of the abrasive flow in the flow channel of the elbow, the calculation platform is FLUENT, the mixture multiphase flow model, the standardturbulence model, and the three-dimensional double precision and pressure-based solver are chosen. In the material settings, hydraulic oil is used for the liquid phase; hydraulic oil No. 32 is chosen for the liquid phase, and its kinematic viscosity is 38 mm2/s; silicon carbide is chosen for the discrete phase; velocity inlet and free outlet are used for boundary conditions; the angle of entry of the abrasive flow is used for the angle of the vertical elbow inlet cross-section; and the SIMPLE iterative method is chosen for the solution.
4.1 Influence of inlet velocity on machining characteristics
In this simulation, the impact of various inlet velocities on the elbow's response to AFM is examined. Three alternative inlet velocities of 30 m/s, 35 m/s, and 40 m/s were chosen for the flow of abrasive flow in the 90 ° elbow, all other things being equal. According to Fig. 4, the dynamic pressure distribution at various intake velocities gets larger as the inlet velocity gets faster. The dynamic pressure rises most noticeably in the bending section, but it also exhibits an upward trend in the outlet section. The research shows that as inlet velocity increases, the abrasive flow turbulence increases and the impact on the elbow wall becomes more forceful.
In Fig. 5, a comparative investigation of the wall shear forces at various intake velocities reveals that as the inlet velocity rises, so does the wall shear force. However, when the input velocity is increased significantly, the machining process loses its uniformity. This can be changed as needed during the actual machining process.
4.2 Influence of bend ratio on machining characteristics
The bend ratio is the ratio of the elbow's bending section's diameter (D) to its curvature radius (R). The elbow's inlet pressure is 5 MPa, and the elbow's diameter and other conditions are examined. A 90º elbow with a different bend ratio or curvature radius on the elbow's effect from AFM is examined, and the bend ratio R/D for 1, 2, and 4 of the elbows are used for numerical simulation. After the calculations are complete, the dynamic pressure and velocity distribution shown in Fig. 6 is obtained.
As observed in Fig. 6, the smaller the bend ratio, the higher the dynamic pressure and velocity are for the same inlet velocity or inlet pressure. The dynamic pressure distribution for the abrasive flow drops in the input section and increases in the bending section when the bend ratio R/D is 1. It reaches its maximum in the region between 0° and 30°. When it comes to the abrasive flow's velocity distribution, the velocity value in the elbow's bending section is higher than the velocity value in other areas, and the change there is less noticeable. As the abrasive flow approaches the bending section, however, the velocity increases and eventually reaches its maximum value close to the inner wall of the bending section, and it then decreases before increasing again in the outlet section. The dynamic pressure in the exit section grows as the bend ratio rises, while the velocity gradually declines and the velocity distribution becomes more uniform.
As seen in Fig. 7, the difference in wall shear force between the inlet section and the outlet section at the same cross-section of the inner and outer wall is not very large when R/D is 1. This is because, at the same inlet velocity and inlet pressure, the smaller the bend ratio, the greater the wall shear force. For the bending section, as the bend ratio increases, the difference in wall shear force between the inner and outer walls at the same cross-section decreases; for the entrance section, as the bend ratio increases, the wall shear force decreases more gradually. For the exit section, as the bend ratio increases, the wall shear force on the same cross-section starts to differ, and the larger the bend ratio, the larger the area where the difference occurs.
According to numerical simulation results, for a smaller curvature radius and a constant elbow diameter, the dynamic pressure and velocity in the bending section are greater. This will significantly increase the wall shear force and make vortices more likely to appear, but it also means that the frequency and number of abrasive particles impacting the wall in the circumferential direction within a unit of time increase, indicating that the machining is taking place. The dynamic pressure, velocity, and wall shear forces are distributed evenly for larger curvature radiuses, but the relatively low values and lack of eddy current susceptibility suggest better machining uniformity in the bending section as well as generally. Increasing the inlet velocity or inlet pressure as necessary will improve surface quality control if the machining strength needs to be increased. The analysis of the numerical simulation is a very important guide to the results of the test, so to improve the inner-surface finish of the elbow, corresponding methods can be taken according to the trend of the simulation.
4.2 Influence of the bending angle on the machining characteristics
For the bend ratio simulation, the identical inlet conditions and parameter settings were employed, and numerical simulations were run for the four frequently used elbows of 60°, 90°, 120°, and 180° when the bend ratio was rather high. Following the computation, Fig. 8 depicts the dynamic pressure and velocity distribution of the abrasive flow in elbows with various bending angles, and Fig. 9 depicts the force distribution on the wall.
The maximum dynamic pressure value of the abrasive flow in the elbow steadily rises as the bending angle increases, as shown in Fig. 8, and the abrasive flow collides more forcefully against the wall of the bending section. The bending and exit sections are where the abrasive flow's maximum dynamic pressure occurs at all four bending angles. The dynamic pressure near the inner side is greater than the dynamic pressure near the outer side in the first half of the bending section, and the dynamic pressure near the outer side is greater than the dynamic pressure near the inner side in the second half of the bending section and the exit section, which confirms that the analysis of the abrasive flow's dynamics was accurate.
As can be seen from Fig. 9, as the bending angle increases, the wall shear force on the elbow also starts to rise. This is primarily because as the bending angle rises, the abrasive flow and elbow collision become more violent, while the likelihood that the abrasive particles and elbow wall collision rebound to the opposite side of the wall also gradually increases.
As seen in Fig. 10, when the elbow is bent at a 60° angle, no vortex is visible in the bending section. However, at a 180° angle, vortices are visible at several cross-sections, indicating that the larger the bending angle, the more likely it is that a vortex will appear. This is also true for the dynamic pressure at the bending section's cross-section: the larger the bending angle, the higher the dynamic pressure.
The results of numerical simulations demonstrate that, when all other factors remain constant, larger bending angles result in higher dynamic pressure and velocity, which significantly increases the wall shear force and makes vortices more likely to appear. However, it also means that the frequency and number of abrasive particles impacting the wall in the circumferential direction within a unit of time increases, which raises the machining intensity. To create an elbow with a bending angle that is equivalent to the machining effect of the bigger bending angle, the intake pressure or inlet velocity can be properly increased for lesser bending angles. When the bend ratio is carefully examined, it can be seen that it is currently quite high, with the dynamic pressure near the inner side being higher than the dynamic pressure near the outer side in the first half of the bending section and the exit section part, and the dynamic pressure near the outer side being higher than the dynamic pressure near the inner side in the second. The analysis of 90° elbows for different curvature radiuses will become more convincing as a result of the numerical simulation's verification that elbows with different bending angles all follow the trend of 90° elbows and that the analysis of the flow state in 90° elbows applies to elbows with different bending angles. This will also give the analysis and test results of the numerical simulation for different curvature radii a wider analytical foundation.
Both corrosion and heat resistance are good attributes of stainless steel. A stainless steel elbow with an exterior diameter of 10 mm and an internal diameter of 8 mm was used for the test. The most often used abrasive particles are silicon carbide, boron carbide, and aluminum trioxide. The preferred abrasive is silicon carbide, which has an 8µm particle size. The primary abrasive carrier was hydraulic oil, which has a 38 mm2/s kinematic viscosity and a tiny amount of triethanolamine. The final setup included 40% abrasive specimens, and the vertical elbow inlet cross-section was angled according to the angle at which the abrasive flow entered.
5.1 Effect of abrasive flow on the machining of elbows with different angles
This experiment solely looked at the machining effect of the 90° elbow because the numerical simulation showed that the distribution trend of the abrasive flow state was consistent across all elbow angles. The 90° elbow was initially produced using a self-designed AFM machine at an inlet pressure of 5MPa, all other things being equal. After the elbow has been machined, it needs to be wire cut. To see, the wire-cut elbow is set up on the electron microscope. Figure 11 depicts the impact of the elbow's inner surface before and after section machining; as seen in Fig. 11 (a), the elbow's inner surface quality is subpar before machining. The comparative analysis demonstrates that after the AFM, the elbow's inner surface quality increased.
A key determinant of a workpiece's surface quality is roughness. The NT1100 raster surface roughness measurement equipment was used to assess the roughness of several sections of the 90° elbow before and after machining to more precisely and intuitively analyze the impact of abrasive flow on the machining of a 90° elbow. The elbow's 3D internal surface roughness is depicted in Figs. 12 and 13, respectively, before and after machining. Results of the elbow's internal surface roughness before and after machining are shown in Table 1.
The three-dimensional internal surface roughness of the bending section part, the inlet section part, and the outlet section part of the original elbow are depicted in Figs. 12(a), 12(b), and 12(c), respectively. The surface quality has significantly improved after machining since the roughness plots after machining is flatter and more regular than the roughness plots after machining. As observed in Table 1, Fig. 12 demonstrates that the inner surface roughness value for the bending section part, which is 1.54µm, is higher than the inner surface roughness value for the straight section part. This difference is primarily due to the elbow's machining process. The forming process is what caused the inner surface roughness values for the inlet and outflow sections of the straight section region to differ by 1.36µm and 1.34µm, respectively. As seen in Figs. 13(d), 13(e), and 13(f), the inner surface roughness of the machined elbow's bending section, inlet section, and outlet section is 0.447µm, 0.448µm, and 0.451µm, respectively. The inner surface roughness of the bending section is somewhat less than that of the straight section. This is primarily because the dynamic pressure, velocity, and wall shear force in the bending section are higher than those in the straight section. Additionally, the bending section will produce a vortex and more violent particle collisions, which is why the test results are consistent with the trend of numerical simulation analysis. In the case of a straight section, after machining, the inner surface of the inlet section is rougher than the inner surface of the outlet section. This is because, after the bending section, the dynamic pressure of the abrasive flow starts to decline and the machining effect on the elbow wall is diminished.
|
Number |
a |
b |
c |
d |
e |
f |
|---|---|---|---|---|---|---|
|
Ra value(µm) |
1.54 |
1.36 |
1.34 |
0.447 |
0.448 |
0.451 |
A scanning electron microscope was used to examine the surface morphology of the elbow before machining and the surface morphology of the elbow at various locations after machining to further confirm the accuracy of the analysis of the quality of the inner surface of the elbow by the abrasive flow. According to Fig. 14, the elbow's inner surface had some spots and unevenness before the AFM, and the surface quality was subpar. The elbow's inner surface was substantially smoother after the AFM, and the results were in line with those of the surface roughness test.
The test results demonstrate the reasonableness of the trend of the numerical simulation analysis of 90° elbows, demonstrating that elbows with different bending angles exhibit similar test results and the trend's plausibility, as well as confirming the viability of the AFM method.
5.2 Influence of inlet pressure on the machining effect
According to numerical models, increasing the input velocity correctly enhances the abrasive flow's ability to machine. However, excessively raising the entrance velocity of the grain flow reduces the machining process' homogeneity. Different intake velocities can be achieved by changing the value of the inlet pressure parameter during the actual machining process to test this trend. For the comparison of 90° elbows with a 50 mm curvature radius and an 8 mm internal diameter, 3MPa, 5MPa, and 7MPa were used. Here, it was compared and assessed how rough the bending and exit sections were at 3MPa and 7MPa. The test results given in Table 2 were compiled using the roughness values at various elbow locations and inlet pressure ranges.
Table 2 The internal surface roughness of the elbow with the different inlet pressure
According to Table 2, the near outer wall of the elbow's bending section has a roughness value of 0.274µm when the inlet pressure is 7 MPa. Comparing the roughness difference between the inner and outside walls in the same region reveals that when the inlet pressure rises, the roughness difference between the inner and outer walls changes in the bending section area from 0.005µm to 0.011µm to 0.006µm to 0.034µm. The abrasive flow improves the elbow's ability to be machined, but it also widens the disparity in roughness at various points on the elbow. A suitable increase in inlet pressure can enhance the abrasive flow's machining effect. In addition to showing that intake pressure and inlet velocity are proportionate to one another and may be modified as necessary during the actual machining process of the abrasive flow, this is comparable to the numerical simulation of elbows with various inlet velocities.
5.3 Influence of curvature radius on machining effect
Based on the examination of the numerical simulation findings, it can be said that elbows with various bending angles all follow the general pattern of dynamic pressure, velocity, and wall shear force distribution for elbows with a 90° bending angle. It is possible to get a similar machining result to that of an elbow with a bigger bending angle for smaller bending angles by increasing the inlet pressure or inlet velocity. As a result, the input pressure for this test is kept at 5 MPa, and the other parameters are adjusted to the same circumstances for the impact of the various curvature radius on the AFM effect. It should be highlighted that although the tests merely serve to confirm the validity of the trends from the numerical simulations, the curvature radius does not correspond with the numerical simulations. Results for elbows with an inner surface roughness of 30mm, 40mm, and 50mm in the bending section parts and the exit section parts are shown in Figs. 15 to 17. In Figs. 15 to 17, it can be seen that the near outer wall points of the elbow's bending and departure sections are flatter and more regular than the near inner wall points, indicating that the near outer wall surfaces of both have been machined more effectively than the near inner wall surfaces.
The test findings reported in Table 3 are the sum of the roughness values at various elbow locations and at various curvature radiuses.
Table 3 The internal surface roughness of the elbow with the different curvature radius
Table 3 demonstrates that the internal surface roughness value achieved by the AFM decreases with decreasing elbow curvature radius at the same elbow diameter. The structural changes in the elbow's bending section occur more quickly, the flow of abrasive particles is more turbulent inside the elbow, and the effect of the abrasive particles on the wall is larger the lower the curvature radius. The disparities at the near inner and outer walls of various curvature radius elbows at the same cross-section are gathered into a line graph as shown in Fig. 18 to better assess the uniformity of the machining of elbows with varied curvature ratios by the abrasive flow.
From Fig. 18, it is clear that, under the same parameter setting conditions, the bending section part and the exit section part's elbow alterations should be made with greater care. This will improve the machining uniformity of the abrasive flow. This is consistent with the trend of the numerical simulation analysis; the larger the curvature radius, the more uniform the distribution of dynamic pressure, velocity, and wall shear force, but with relatively small values and less susceptible to vortices, and the smaller the difference between the inner surfaces of the near inner and outer walls, improving the overall machining uniformity of the abrasive flow. Better surface quality control can be obtained by raising the inflow velocity or inlet pressure as necessary to increase the machining intensity or inner-surface finish. However, as can be seen from Table 3, the amount of machining required on the tube wall increases with the rate of change in both the bending section and the exit section parts. This is also consistent with the trend of numerical simulation analysis; the smaller the curvature radius, the more uneven the distribution of dynamic pressure, velocity, and wall shear force, the greater the difference between the values of the inner and outer walls, and the more likely it is that a vortex will appear. However, it also means that the quantity and frequency of abrasive particles impacting the wall in the circumferential direction within a unit of time increases, and the greater the difference between the inner and outer wall values. Thus, the experimental results confirm the validity and plausibility of the AFM of elbows as well as the accuracy and reliability of the numerical simulations, thereby providing technical support for the elbow AFM quality control technology that has been proposed. Different parameters should be chosen depending on the real needs while using the abrasive flow to machine elbows.
This study reveals the relationship between elbow characteristics and AFM surface quality. The effectiveness of AFM approaches in improving the surface quality of elbow-type objects has been confirmed by experimental analysis and numerical simulations. The precise results are as follows:
(1) The effects of various inlet velocities, bending ratios or curvature radius, and bending angles on the machining characteristics were first simulated in order to improve the inner-surface finish of elbows machined by abrasive flow and to establish quality control of elbows machined by the abrasive flow. The simulation findings demonstrate that a suitable increase in input velocity enhances the grain flow's machining effect. However, unnecessarily raising the abrasive flow's inlet velocity, which can be changed as needed during the actual AFM process, reduces the process's homogeneity. In terms of the curvature radius, a lower curvature radius leads to much higher machining intensity in the bending section and significantly more surface removal of the material; a larger curvature radius leads to better overall machining uniformity. Increasing the inflow velocity or inlet pressure as necessary will improve surface quality control if the machining intensity is increased. The greater the bending angle, the greater the machining intensity. In order to make the elbow with a bending angle similar to the machining effect of the larger bending angle and to confirm that the analysis of the flow state in the 90° elbow is applicable to different bending angles of the elbow, the smaller bending angle can be appropriately increased by increasing the inlet pressure or inlet velocity. This will give the analysis of the 90° elbow for different curvature radii a wider range and make it more convincing. As a result, the inner-surface finish of the elbow can be improved by adopting the appropriate approach in accordance with the trend of the simulation, and the analysis of the numerical simulation is crucial for directing the test results.
(2) Comparative investigation demonstrates that following the AFM, the elbow's inner surface quality improved. The internal surface roughness of the 90° elbow was measured using the NT1100 raster surface roughness measuring equipment before and after machining in order to examine the impact of the abrasive flow on the elbow. The test results reveal that the machined shape flattens and becomes more regular, which is consistent with the results of the surface roughness test. They also show that the trend of the numerical simulation analysis of the 90° elbow is reasonable, demonstrating that the different bending angles of the elbow have similar test results and the reasonableness of the trend as well as confirming the viability of the AFM method.
(3) To examine the impact of inlet pressure and curvature radius on the machining effect of the elbow, an experimental study was conducted. The machining impact of the abrasive flow is improved for the inlet pressure by a suitable increase in the inlet pressure. Similar to how elbows with varied inlet velocities were numerically simulated, this demonstrates that inlet pressure and inlet velocity are proportionate to one another and may be changed as necessary during the actual AFM process. According to the trend of the numerical simulation analysis, the machining uniformity of the abrasive flow is better for the curvature radius the more softly the elbow changes in the bending section as well as in the exit section. Better surface quality control can be obtained by changing the inflow velocity or inlet pressure as necessary to improve the machining strength or inner-surface finish. The tendency of the numerical simulations is that the intensity of the machining of the tube wall increases with the rate of change in the bending section and the exit section. At this point, the machined finish will improve the further the tube wall is machined. The test outcomes validate the accuracy of the numerical simulation, demonstrate the viability and efficiency of the AFM elbows, and offer technical backing for the proposed quality control method for AFM elbows. Different settings should be chosen when using AFM on the elbow by the real requirements.
Ethical approval Not applicable.
Consent to participate Not applicable.
Consent to publication All presentations of case reports have consent for publication.
Conflict of interest The authors declare they have no conflict of interest.
Funding support This work was supported by [Science and technology development plan project of Jilin province] (Grant numbers [20210201057GX] and [20220201036GX]) and [Science and technology research project of Jilin Provincial Department of Education] (Grant numbers [JJKH20220734KJ])
Acknowledgments
The authors would like to thank Science and technology development plan project of Jilin province No. 20210201057GX and No. 20220201036GX , Science and technology research project of Jilin Provincial Department of Education No. JJKH20220734KJ.
Authors’ contributions
Junye Li designed and performed the manuscript, analyzed the data, and drafted the manuscript. Gongqiang Tian and Yanlu Yin analyzed the data and supervised this study. Guangfeng Shi and Jingran Zhang conceived the project, and Xinming Zhang organized the paper and edited the manuscript. All authors read and approved the manuscript
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