Study on sinusoidal lapping micro-structured surface by abrasive stone with staggered abrasive particles

In order to manufacture structured surfaces, firstly, the abrasive stone model with staggered abrasive particles is established with mathematical methods. Secondly, the motion of abrasive particles on the abrasive stone is designed. Finally, the surface morphology of the workpiece is simulated. The simulated workpiece morphology under different machining parameters is compared, and the influence of different machining parameters on the workpiece surface morphology is obtained. The results indicate that the microstructured surface can be lapped by using the abrasive stone of staggered abrasive particles. As the amplitude and frequency of the abrasive stone increase, the number of protrusions increases, and the area of individual protrusions decreases.


Introduction
In recent years, biomimetics has discovered that the characteristic structures on biological surfaces can achieve specific functions.For example, the micron-scale convex hull on the surface of lotus leaves can increase the contact angle with water [1][2], causing water droplets on the lotus leaf surface to quickly roll off [3].The grooves on the surface of the shell can reduce resistance to water [4].The structure of the abdomen of a pangolin causes the soil attached to its surface to quickly detach [5].Due to the superior performance of structured surfaces, people machined it with chemical etching, electrochemical etching, and other [6][7] methods, and conducted research on structured surfaces.The drag reduction effect of three different shapes of grooves was compared by Li et al. [8].It was found that the drag reduction effect of V-shaped grooves is better than that of U-shaped and L-shaped grooves.Yousfi et al. [9] machined different surface morphologies on the surface of the engine cylinder with honing, making it more effective in reducing drag.The effects of production time and contact pressure between lapping stones and workpieces on the surface morphology of workpieces during superfinishing were studied by Chang et al. [10].
The above research provides many ways to manufacture micro-structured surfaces, but there are few studies on using lapping methods for structured surfaces.This article introduces the design of abrasive stones with staggered grain patterns, the workpiece morphology is simulated, and the impact of workpiece surface morphology with different machining parameters is analyzed.

Arrangement of abrasive particles
Due to the fact that the machined part is the outer circular surface of the workpiece, the abrasive stone also needs to have a curved surface corresponding to it, so that all the abrasive particles on the abrasive stone participate in lapping, ensuring machining efficiency.The abrasive stone with a staggered arrangement of abrasive particles is shown in Figure 1.Abrasive stone with a staggered arrangement of abrasive particles.When machining the outer circular surface with abrasive stone, the abrasive particles move around the axis of the workpiece.Considering that not all abrasive grains are involved in lapping during abrasive lapping, during the simulation, the abrasive particles are considered hemispherical and evenly divided into equal parts for lapping.In the workpiece coordinate system, the coordinates of the abrasive particle position points for each equal portion obtained from this are as follows: Where D d is the diameter of the workpiece being processed; r k is the radius of the abrasive particle; Ψ is the bisection angle of the abrasive hemisphere; I and J are the number of rows and columns of abrasive particles; a is the arc length of the abrasive stone; k is the average fraction of abrasive particles.

Motion of abrasive particles
During superfinishing [11], the abrasive stone oscillates back and forth along the axis, and the workpiece rotates clockwise along its axis, which can be converted into a counterclockwise rotation of the abrasive stone.The angle of rotation after time t is ω S t, and ω S is the angular velocity of the abrasive stone rotation.The abrasive stone axial harmonic feed is Z=A × Sin(ω S t), where A is the amplitude of the abrasive stone.The motion diagram is shown in Figure 2.

Simulation strategy
The simulation strategy adopted in this article is as follows.Firstly, the shape of the workpiece is constructed.Secondly, machining parameters are input to simulate abrasive motion.Then, the surface of the workpiece is meshed and replaced with the trajectory points of the abrasive particles.Finally, the new workpiece morphology is output.

Analysis of simulation results (1) The Effect of abrasive stone amplitude on the morphology
In morphology simulation, the workpiece speed is set to 25 r/min, the oscillation frequency of the abrasive stone is 405 times/min, the speed ratio is 16.2, and the amplitudes of the abrasive stone are 300, 350, and 400 μm, respectively.The simulation diagram of the workpiece morphology is shown in Figure 3.As shown in Figure 3, as the amplitude of the abrasive stone increases, the area of a single triangular protrusion decreases.According to calculations, the amplitudes are 300, 350, and 400 μm.The average area of a single protrusion of the workpiece at m is 1.35, 1.27, and 1.19 mm 2 , respectively.The influence of different machining parameters on the workpiece morphology is shown in Table 1.(2) Effect of speed ratio on workpiece morphology In morphology simulation, the workpiece speed is set to 25 r/min, and the amplitude of the abrasive stone is selected to be 400 μm.The oscillation frequency of the abrasive stone is 395, 400, and 405 times/min.The ratio of the number of abrasive stone oscillations to the workpiece speed is 15.8, 16, and 16.2.The effect of different speed ratios on the morphology of the workpiece is studied.The simulation diagram of the workpiece morphology is shown in Figure 4. From Figure 4, it can be seen that as the speed ratio increases, the area of a single triangular boss decreases.From the calculation, it can be seen that when the speed ratio is 15.8, 16.0, and 16.2, the area of a single boss on the surface of the workpiece is 1.37, 1.26, and 1.19 mm 2 , respectively.As the speed ratio increases, the surface area of a single platform on the workpiece decreases.The influence of different machining parameters on the workpiece morphology is shown in Table 2.

Conclusion
A micro-structured surface can be machined on the surface of the workpiece by using the abrasive stone with staggered abrasive particles and superfinishing lapping.As the amplitude and oscillation frequency of the abrasive stone increase, the number of protrusions on the surface of the workpiece increases, and the area of individual protrusions decreases.

Figure 1 .
Figure 1.Abrasive stone with a staggered arrangement of abrasive particles.When machining the outer circular surface with abrasive stone, the abrasive particles move around the axis of the workpiece.Considering that not all abrasive grains are involved in lapping during abrasive lapping, during the simulation, the abrasive particles are considered hemispherical and evenly divided into equal parts for lapping.In the workpiece coordinate system, the coordinates of the abrasive particle position points for each equal portion obtained from this are as follows:

Figure 3 .
Workpiece morphology under different abrasive stone amplitudes.
(a) The speed ratio is 15.8.(b) The speed ratio is 16.(c) The speed ratio is 16.2.

Figure 4 .
Workpiece morphology under different speed ratios.

Table 1 .
Effect of different abrasive stone amplitudes on the morphology of workpieces.

Table 2 .
Effect of different abrasive stone frequencies on the morphology of workpieces.