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##### Particle Flight Velocity Analysis Combining Airflow Analysis and Particle Method Analysis

Koichiro NAMBU

Fig. 1: Nozzle and specimen dimensions

Table 1: Physical properties of air

Table 2: Mechanical properties of Particles

Fig. 2: Air velocity distribution for a nozzle-work distance of 100 mm

Fig. 3: Air velocity distribution for a nozzle-work distance of 150 mm

Fig. 4: Air velocity vector at a distance of 150 mm between nozzle outlet and work for a nozzle outlet diameter of 3 mm

Fig. 5: Air velocity vector at a distance of 150 mm between nozzle outlet and work for a nozzle outlet diameter of 10 mm

(a) Nozzle -work distance 50 mm

(b) Nozzle -work distance 100 mm

(c) Nozzle -work distance 150 mm

(d) Explanation of plots in (a)-(c) Fig. 6: Airflow and particle velocity variation at nozzle center

1. Introduction

Shot peening (SP) and fine particle peening (FPP) are cold forming processes that improve fatigue strength, which are used in a wide range of industries, including automotive and aerospace. SP and FPP are processes in which the shot impinges on the specimen. Work hardening increases the hardness of the specimen surface and improves the fatigue strength of the component.

One method of flying these particles is the air injection method. In this method, shots are ejected from a nozzle by stream of air. The particles are pushed out by the air stream which affects the velocity of the particles. Outside the nozzle, the spread of the airflow causes a spread in the trajectory of the shot. However, few studies have investigated the relationship between airflow and particle velocity.

Nambu et al. showed that the velocity of the shot increased as the nozzle inlet pressure increased and that there was a linear relationship in between. They also proposed the optimum distance between the nozzle outlet and the sample [1]. Maeda et al. showed that the part of the nozzle where the shot was most accelerated was the parallel part of the nozzle, and that the optimum length of the parallel part of the nozzle must be considered to obtain a high-speed shot [2]. Ogawa et al. showed that in direct pressure shot peening, the shot velocity was proportional to the 0.57th power of the nozzle inlet pressure [3].

However, these studies on particle flight behavior have neglected the presence of the work material, and the effect of airflow impinging on the work material was not clarified.

Therefore, this study combines a finite element analysis of the airflow in and out of the nozzle, which takes into account the effect of the work material, with a discrete element analysis of the particle flight behavior. Furthermore, the effects of nozzle diameter on airflow and particle flight behavior were evaluated.[4]

2. Analysis conditions

2. Air flow analysis [4,5]

A three-dimensional finite element method (FEM) steady-state analysis was used to analyze the airflow in and out of the shot peening nozzle. Ansys Fluent was used for the FEM analysis of the airflow. The analytical model used for the airflow analysis was created using CAD. Fig. 1 shows a cross-sectional view of the analytical model. The nozzle model simulated the nozzle used in Fuji Corporation's direct-pressure blasting equipment (P-DSU III type). The dimensions of the substrate were 50 mm wide, 50 mm long, and 5 mm thick. The center axis of the nozzle is the y-axis, and y = 0 was the nozzle exit. The air flow was assumed to be air (ideal gas) and its characteristics are shown in Table 1. For the turbulent viscosity model, the k-ω SST model was used, which correctly captures turbulent flow near the nozzle wall and turbulent flow away from the wall.

The nozzle inlet pressure was 2000 hPa and the distance from the nozzle to the work piece was 50, 100, and 150 mm. The nozzle diameter was varied from 3 mm to 10 mm for each analysis.

2.2 Particle flight analysis model [4]

Next, Particle works, a powder analysis software, was used to simulate scattered particles. The simulation conditions were the same as those described above.

An airflow was introduced into Particle works by inputting the y-coordinates of the airflow region obtained from the aforementioned airflow analysis and the velocity in the y-direction at those coordinates. The density of the airflow was determined by averaging the values parallel to the nozzle. This is because particle velocities are most affected by the airflow at the nozzle parallel [3]. The viscosity coefficient of the airflow was calculated from Sutherland's formula, and the kinematic viscosity coefficient was calculated from the average density at nozzle parallels. The drag coefficient of the airflow was calculated from the equation for the drag coefficient in the compressible dominant region from Loth E.'s paper [6]. Other airflow properties are the same as in Table 1. Gravitational acceleration was assumed to be 9.8 m/s2. The particles were modeled as steel particles with a diameter of 70 µm. The physical and mechanical properties of the particles are shown in Table 2. The nozzle and work were treated as rigid bodies, and the coefficients of static and kinetic friction between all objects were set to 0.3 and 0.2, respectively. The simulation was analyzed for 0.5 s, and the output time range was set to 1 × 10-4 s.

3. Results and Discussion[4, 5]

3.1 Air velocity variation at nozzle center axis

Fig. 2 and 3 show the results of air velocity analysis at the nozzle center for distance between nozzle outlet and specimens of 100 mm and 150 mm, respectively. The figures show that the airflow rapidly accelerates to a speed of about 250 m/s just before the nozzle parallel (y≤-55), accelerates slowly at the nozzle parallel (-55≤y≤0), and reaches its maximum speed (almost the speed of sound) near the nozzle exit (y=0). After the nozzle exit, the airflow decelerates slowly, and then suddenly decelerates just before the substrate. The airflow velocity in front of the substrate is considered to decrease rapidly not only due to air resistance but also due to the bounce of the airflow from the substrate.

3.2 Air velocity distribution inside and outside the nozzle [4]

The velocity vectors of the airflow after the nozzle exit were investigated. Fig. 4 and 5 show the velocity vectors of the airflow after the nozzle exit for nozzle diameters of 3 and 10 mm when the nozzle - work distance is 150 mm, respectively. Figures show that the larger the nozzle diameter, the larger the airflow velocity (300 m/s, indicated in red) spreads from the nozzle exit to a position closer to the work. The red area is also wider. This result also indicates that the nozzle with a larger diameter has a longer potential core.

3.3 Particle flight velocity analysis

Next, a coupled airflow-particle method analysis was performed using the data obtained from the airflow analysis.

Fig. 6 shows the variation of airflow velocity at distances of 50, 100, and 150 mm from the nozzle exit to the work, respectively, and the variation of particle velocity near the average maximum particle velocity under each condition. The lines and white plots in the figures indicate air velocity and particle velocity, respectively. The red plots in (a), (b), and (c) indicate the maximum particle velocity. Because of the complexity of the legend, the plots are summarized in (d).

Fig.6 shows that the particles reach their maximum velocity near the intersection of the y-directional velocity of the airflow and the y-directional velocity of the particles under all conditions. This indicates that the optimum condition for the nozzle-workpiece distance at which the particles reach their maximum velocity depends on the nozzle diameter.

4. Conclusions [5]

The following results were obtained from the airflow analysis by the finite element method and from the particle flight velocity analysis by the discrete element method.

1.The airflow reaches its maximum velocity (approximately 330 m/s) near the nozzle outlet regardless of the nozzle diameter.

2.The maximum particle velocity increases as the nozzle diameter increases.

3.The simulation results suggest that the optimum condition for the nozzle-to-work distance is 100 to 150 mm, similar to previous empirical results.

References

1. K. Nambu., et al., Numerical Calculation of Particles Velocity under the Compressible Fluid in Fine Particle Bombardments, Transactions of JSME(ver.C), Vol. 67, No. 660(2010), pp. 306-312 (in Japanese).

2. H. Maeda., et al., Analysis of Particle Velocity and Temperature Distribution of Struck Surface in Fine Particle Peening, Transactions of JSME(ver.C), Vol. 67, No.660(2001), pp. 306-312 (in Japanese).

3. K. Ogawa., Measurement and analysis of shot velocity in pneumatic shot peening, Transactions of JSME(ver.C), Vol. 60(1994), pp. 1120-1125(in Japanese).

4. K. Nambu et al., Airflow analysis inside and outside the nozzle in shot peening process, Proceedings of the 3rd International Conference on Advanced Surface Enhancement (INCASE) 2023, (2024)

5. K. Nambu, et al., Effect of Nozzle diameter on Particle Flying Velocity in Fine Particle Peening Processes, IFHTSE2023 Special issue of NETSUSHORI, (2024)

6. E. Loth, Compressibility and Rarefaction Effects on Drag of a Spherical Particle, AIAA JOURNAL, 46 (2008) 2219-2228.

Osaka Sangyo University, Faculty of Engineering,

Department of Mechanical Engineering,

Associate Professor

Osaka Sangyo University

3-1-1, Nakagaito, Daito-city, Osaka, Japan

E-mail: knambu.mech@ge.osaka-sandai.ac.jp