Shear-thickening polishing of inner raceway surface of bearing and suppression of edge effect

Shear-thickening polishing is a non-traditional finishing method that uses the shear thickening effect by impacting the non-Newtonian fluid over the machining surface. As a result, it forms a velocity gradient that increases viscosity sharply, producing a flexible fixed abrasive tool to remove the material. Shear-thickening polishing is applied for finishing the outer surface of the rotary workpiece in previous work. The material removal distribution on the inner surface is completely different from those on the outer surface due to the different structures. The thickened slurry tends to form a relatively dense boundary layer on the surface, resulting in a decrease in the polishing quality and efficiency. The present study investigates the effect of the impact angle of slurry and polishing velocity on polishing quality to obtain the uniform surface morphology of the ring’s inner surface by the shear-thickening polishing process. The inner raceway of the outer ring of the tapered roller bearing 30203 was taken as the machining object. The numerical material removal model of the raceway surface was built according to the rheological performance of the shear-thickening slurry. A mathematical geometric model is used to explore the real impact angle of slurry. The model was able to accurately predict the experimental conditions, and the results of the simulation were in good agreement with the model’s predictions. In the fixture, a guide block was introduced to guide the flow of the slurry, ensuring consistent material removal across the whole surface. The optimal experimental results show that the average surface roughness measured by Ra reduces from 300 to 42.9 nm in 30 min, which further drops to 11.16 nm in 90 min with a variance of 0.58 nm2. The conclusion could be drawn from the studies of this paper that a uniform inner raceway surface of the bearing is achievable through a properly designed STP process.


Introduction
Surface quality requirements of key parts are becoming more and more stringent as industrial equipment develops, especially for work surfaces that influence part performance [1][2][3][4][5]. Being a core component of industrial equipment, bearing requires high integrity of surface morphology on raceway [6,7]. The surface roughness not only affects the surface friction coefficient [8] but also extends the bearing life [9], meanwhile the raceway surface roughness has a significant impact on bearing noise and vibration under high-speed conditions [10]. However, the conventional raceway process by oilstone has a limitation of surface roughness of about 100 nm. Moreover, due to the forced plunge honing of abrasive particles under mechanical action, grinding heat and residual tensile stress generated by the machining are inevitable, leading to the generation of raceway surface degradation layer and limitation of surface quality.
Considering the inner concave surface characteristics of the inner raceway, it requires greater skill to achieve a high surface quality than the outer raceway. Researchers have done extensive research on the application of ultraprecision machining technology for such inner surfaces. By using a magnetic polishing tool, Grover and Singh [11,12] reduced the surface roughness of an inner cylinder from 0.371 to 0.193 μm in 60 min and that of a ferromagnetic workpiece from 360 to 90 nm in 100 min [13]. Peng et al. [14] utilized a magnetic polishing tool with a rotating and linear coupled motion to machine the inner surface of a circular tube made of titanium alloy. After 2700 cycles, the surface roughness decreased by 24.7% to a minimum value of 0.197 μm. Umehara et al. [15] developed a special magnetically condensed material, which shows a magnetic fluid at high temperature and can be solidified at room temperature. Umehara used a polishing tool made of this material to polish the brass and obtained a smooth surface that is 1/3 the original surface roughness. Zhang et al. [16,17] polished the optical glass with five-axis equipment assisted with an electrorheological polishing technique and found a reduction in surface roughness up to 10 nm within 30 min. However, neither magnetorheological nor electrorheological equipment/materials are exceptionally expensive. Meanwhile, during the magnetorheological/ electrorheological polishing process, the slurry tends to concentrate at the entry of the polishing zone, leading to a decrease in polishing efficiency and quality [18].
Abrasive flow machining/polishing (AFM/AFP) has a relatively low cost and is widely used in ultra-precision machining of curved surfaces. Wu and Zhang [19] used AFM to process the inner surface of small-diameter pipes. Experiment results revealed that AFM could effectively reduce the roughness and remove surface defects. Zhang and Wu [20] found that the thickness of oxide film affects polishing uniformity when CBN abrasive grains are mixed with AFM to process the hollow bearings. In order to polish the raceway of a large ring, Wu and Gao [21] developed a fixture to guide the slurry's behavior and obtained a surface roughness of 0.1 μm. However, the AFM equipment requires good sealing and the processing efficiency was lower than the magnetorheological polishing method.
In summary, current flexible polishing technologies have various limitations when used for processing inner surfaces. Shear-thickening polishing (STP) method is a novel, flexible, contact polishing method that results in high removal rates and good surface quality. Li et al. [22] obtained surface roughness of 5.1 nm by polishing the Cr12Mo1V1 cylinder in 90 min. Lyu et al. [23] utilized brush-assisted STP for processing the cemented carbide inserts to obtain the surface roughness of 8.13 nm. Wang et al. [24] coupled the STP and electrochemical effect to polish the titanium alloy Ti-6Al-4 V for reducing the surface roughness from 124 to 8.6 nm in 15 min. However, STP is a less explored technique for machining the inner surfaces. The flow field distribution while processing internal surfaces is completely different compared with the external surface. When processing the outer surface, the solidified slurry can easily remove the material by relative movement with the workpiece surface pushed by potential flow. While processing the inner surface, it is difficult for the solidified slurry to slip over the surface. What is more, it tends to gather into a mass and adhere to the surface, depraving the processing efficiency and surface quality. Song et al. [25] developed a new method that uses a special wedge-shaped polishing tool to drive the slurry impacting surface, which could realize deterministic polishing of inner surfaces. This method has a low processing efficiency and needs a specific polishing tool according to the surface of the workpiece.
This paper attempts to realize the ultra-precision machining of the inner surface by the STP method. Taking the inner raceway of the 30203 bearing outer ring as the experimental object, a flow field constraint method was proposed to suppress boundary layer thickness by coupling the impact and flow behavior of the slurry in the paper. The study begins with the investigation of the influence of impact angles on polishing uniformity. It is followed by building a mathematical model to explore the true impact angle and analyze the flow field distribution in the polishing area through numerical analysis. The following sections deal with study of influence of impact velocity on polishing uniformity and remove rate through the numerical model developed above, use of a guide block to avoid the"edge effect" phenomenon, and realize the polishing uniformity on the whole curve surface. This paper provides a new technical approach for the precision polishing of inner raceway surface of bearing.

Experiment details
STP method uses the shear thickening effect by impacting the non-Newtonian fluid over the machining surface. As a result, it forms a velocity gradient that increases viscosity, sharply as shown in Fig. 1, producing a flexible fixed abrasive tool to remove the material.
The principle of the ring's STP process is shown in Fig. 2. The ring is fixed by a special fixture driven by the motor to rotate around its center. The shaft of the motor is inclined at an angle of (90 − ) • from the horizontal plane. At the same time, the polishing disc rotates around at an angular speed, ω, which drives the polishing liquid to rotate and impact the surface of the workpiece. The outer circle and the end face of the ring are protected by fixtures and polyurethane tapes to prevent them from being polished.
The thickened slurry adheres to the outer surface and can easily be peeled off by the potential flow with the rotation of the workpiece, which causes relative motion between thickened slurry and workpiece surface to remove material. In contrast, the flow field distribution of the slurry is closer to that of the pipeline flow when polishing the inner surface. As shown in Fig. 3a, when the velocity vector of the slurry is parallel to the wall, the adhered slurry is not easily removed by the potential flow. The thickness of the boundary layer (l) increases with the length of the wall, leading to the effective length of the abrasive particles l is limited in the inlet area, and the material removal process is difficult and varies from point to point. As shown in Fig. 3b, when the potential flow impacts the surface with a suitable incident angle, the normal velocity component can effectively reduce the thickness of the boundary layer, resulting in the adapted effective length of the abrasive particles l ′ ( l ′ ≫ l ).
The paper attempted to reduce the thickness of the boundary layer on the inner surface by adjusting the incident angle and impact velocity of the slurry, so as to realize the high efficient and uniform polishing result of the inner raceway of bearing. Figure 4 shows the multi-axis STP machine as an experiment platform. The slurry is formulated with deionized water (DI Water) and high hydroxyl polymer as thickening phase in a certain proportion to form a shear thickening liquid, and alumina abrasive particles are mixed as the polishing medium. The rest of the processing parameters are shown in Table 1. The material removal rate was measured by precision balance MSA225S-CE (Sartorius, Germany). The MRR calculation formula is as follows: where Δm (g) is the weight loss of the workpiece after polishing, Δt (h) is the polishing time, and the unit of MRR is  Figure 6 shows the raceway surface morphology after polishing for 30 min duration under the inclination angle of 0°. As seen in the figure, a small portion at the entrance has been finished by STP, while the remaining surface shows the grinding morphology. By processing the datum as shown in Eq. (1), the micro-profile curve of the raceway surface can be obtained. As shown in Fig. 6a, the peak corresponds to the surface micro-morphology formed by grinding, which easily breaks the lubricating film, causing load stress concentration and increasing the risk of fatigue failure. For the bearing raceways, the smooth surface helps retain lubricant, thus improving the lubricating properties of the raceway interface. Figure 6b shows the profile curve and microscopic morphology of the raceway after being polished by STP. The microscopic profile curve is rounded at the corner, which improves frictional and wears performance, as the convex part smoothly joins the concave part [26]. To compare the degree of smoothness of raceway profile curves polished by STP, the uniformity of the polishing results can be qualitatively estimated.

Morphology variation and polishing uniformity with different inclination angles
where, x ′ i is the calculated value of feature points' position, x i is the initial value of feature points' position, and N is the total number of feature points.
STP experiments were carried out on the raceway for different inclination angles. The inclination angle refers to the fixed angle between the axis of rotation of the workpiece and the horizontal plane, which is (90 − ) • shown in Fig. 2.
The polishing results are shown in Fig. 7. For inclination angle of − 12.5°, the surface morphology observes no significant changes and the roughness does not decrease; at 0°, the roughness decreases significantly only at the entry region and the morphology of the remaining area remains unchanged, which illustrates that shear-thickening effect diminishes. The overall surface roughness decreases significantly at inclination angles of 12.5 and 25°, however, the surface profile is relatively smoother at an inclination angle of 25°. Further increase in inclination angle brings uneven surface characteristics, which is an indicator of poor polishing quality. From the above experimental results, the best polishing outcome using the STP process is seen at a 25° inclination angle for a 30203 bearing ring raceway. Figure 2 does not reflect the true impact angle due to processing conditions, so it is necessary to establish an accurate mathematical model in order to determine the true impact angle. Firstly, in order to obtain the true optimal impact angle, the relationship between inclination angle of fixture and true impact angle (90 − ) • is built by establishing the mathematical geometric model between slurry flow field and the workpiece during processing. Secondly, the theoretical optimal impact angle   was obtained through numerical simulation based on the Preston removal function. By comparing the degree of agreement between the two models, the available mathematical geometric model and numerical simulation model are obtained. Figure 8 shows the technical roadmap for the mutual verification process. Figure 9 shows the geometric model of the ring during the STP process. The flow trajectory of the slurry was observed by fixing the ring as shown in Fig. 9a. The red area is the polishing trace, which has a large entrance and a small exit and slopes upward along the wall of the ring. where r 1 is the circular radius of the inlet circle, r 2 is the circular radius of the outlet circle, and the oblique angle of the ring section is β = 12.5° as shown in Fig. 5. The true impact angles of slurry can be obtained by using the cosine value of the angle between the vector ���� ⃗ AB and x-axis. Table 2 shows the corresponding relationship between the inclination angle of the fixture and the true impact angle. It is worth noting   Figure 10 shows the calculation process of the numerical analysis. The flow through the channel is assumed to be a rectilinear flow, and thus it can be simplified as a 2D model. The model is shown in Fig. 11; the gray area shows the cross-section of the outer ring of the 30203 bearings. The shear-thickening slurry enters the flow field from the left inlet and the outlets are set to pressure outlets with zero Gaussian pressure. Other simulation parameters are shown in Table 3 [22], where λ is the viscosity thickening coefficient and n is the viscosity index of the shear-thickening slurry. According to the Preston removal function, MRR (material removal rate) = K.P.v, which reveals that MRR is closely related to polishing pressure and relative motion speed. Thus, the normalized equivalent of the P.v is used to evaluate the MRR of the STP process. Figure 12 shows the evolution of pressure and velocity on the raceway surface profile under different impact angles. At different angles, the distribution has the same tendency to decrease followed by stabilization. According to Fig. 13, the pressure and velocity changes at 29.2° can be divided into three zones. The zone1 is the initial contact area between slurry and ring showing a large decrease in pressure. However, the average P.v value remains the highest, which may lead to a higher removal efficiency. The pressure and velocity changes tend to level off in zone2, resulting in good polishing consistency. Zone3 shows a significant decrease in pressure while velocity increases. The results obtained from the preliminary analysis of the simulations are shown in Fig. 14. Using an impact angle of 45° will provide the highest P.v value and the lowest variance on the ring surface, as well as the best removal efficiency and polishing quality. In general, this is consistent with the experimental data from the previous section.

Evolution of surface roughness and MRR at different speeds
During the shear-thickening polishing process, the polishing speed is an important parameter that not only affects the shear rate, which in turn changes the dynamic viscosity, but also affects the flow energy and boundary layer thickness of the slurry. Figures 15 and 16 reveal that the surface roughness steadily decreases as impact velocity increases. The average surface roughness at points 1, 2, and 3 is found to be 79.9 nm at 47 rpm, which decreases steadily to 42.9 nm at 86 rpm. The average surface roughness was measured to be 40 nm at 100 rpm, which is the minimum value recorded in this experiment. However, it has the highest variance of 8.57 nm 2 at 100 rpm. This unusual finding suggests that the uniformity deteriorates at 100 rpm.
The variation of MRR for different rotation speeds of the disc is shown in Fig. 17. The removal rate increases with increasing speed and attaining a maximum value of 2.39 μm/h at 86 rpm. Further increase in speed decreases Firstly, the theory of hydrodynamic flow implies that the length of the inlet section of the pipe increases as the velocity increases, which leads to the smaller boundary layer thickness. Secondly, the higher velocity of shearthickening slurry brings higher viscosity during the shear-thickening interval, which brings an improvement in removal efficiency. Lastly, the positive proportional relationship between the removal rate and P.v value has the greatest impact. The phenomenon of rapid decrease in MRR with impact velocity at polishing rates of 86-100 rpm can be explained in two ways. The first is a result of changes in the waveform in the slurry flow channel, which results in variations in the impact angles. The second is the result of the abrasive particles experiencing greater centrifugal force at higher rotation speeds, resulting in fewer abrasive particles involved in the polishing process.
In order to understand the variation of MRR, simulation was performed to investigate the normalized datum of P.v value using the mathematical model established in the previous section (assuming that the change in polishing disc speed does not influence the waveform, and the value of impact angle is measured at 60 rpm). Another simulation was performed on the basis of true impact angles derived from polishing traces (waveform profile is changing). The results are shown in Fig. 13, where the normalized P.v value and experiment datum have a highly consistent trend when considering angle change when comparing the MRR datum to the experimental datum. In contrast, the normalized equivalent of the P.v value linearly increases with the impact velocity with no change in the waveform. It is believed that the main factor causing the decrease of MRR at high rotation speed is the change of slurry profiles. Due to the uniform dispersion of slurry, the MRR value is almost independent of the centrifugal forces acting on the abrasive particles.
During the rotation, the slurry surface can be regarded as an equipotential surface. Neglecting the effect of internal friction, the sum of centrifugal potential energy and gravitational potential energy of slurry is assumed constant based on the principle of conservation of energy.  where E c is the centrifugal potential energy, E g is the gravitational potential energy, and z is the height of the slurry surface. Solving the above system of equations, we can get the height of the slurry surface as z = 2 R 2 2g . As shown in Fig. 18, the waveform becomes steeper as the rotation speed increases and the contact area between the slurry and ring decreases, resulting in a lower MRR. It can be assumed that the MRR can be further improved if there is enough slurry in a large enough disc.

The conception of edge effect and its causation
Surface roughness was measured at three points along the line of contact of the roller. If a measurement point 4 is added at the entrance of the ring (Fig. 6) and is compared with the points 1-3 in terms of surface roughness, texture, and MRR after polishing, the machining efficiency of point 4 is much higher than that of point 1-3. The phenomenon of over-polishing at the entrance results in uneven polishing, which is called the edge effect of STP.
In order to investigate the cause of the edge effect, the distribution of the P.v value along the flow direction of the slurry on the workpiece surface is simulated at different speeds. The inclination angle of 25° is selected as the process parameter. As shown in Fig. 19, the P.v value at the entrance is much higher than that at the steady flow section, resulting in a rapid decrease of surface roughness at the entrance and higher processing efficiency. Although at different speeds, the P.v value starts falling at a distance of 2 mm along the axis.

Guide block fixture and validation experiment
Guide block is introduced in the fixture to realize the uniformity of STP. As shown in Fig. 20, the guide block is set at the impact inlet of the slurry. The angle of the block is maintained at the same as that of the crosssection of the ring, while the length of the beveled edge is kept at 2 mm. A new measurement point 0 is added to the block, and point 1 is moved to the entrance. The validation experiment is carried out under the rotation velocity of 86 rpm, which has highest removal rate and relatively lower surface roughness.
The measured surface roughness after the application of STP with added guide block is shown in Fig. 21. A notable difference in the surface roughness can be seen at different measuring points. The initial roughness of each point is around 310 nm. After 30 min of STP operation, the average roughness of points 1, 2, and 3 dropped to 40 nm, while it was 17.87 nm at point 0. The overall datum is close to that obtained without guide blocks, which suggests that the guide block has little influence of MRR on the raceway surface. The surface roughness of point 0 decreases to 12.97 nm in 60 min and 5.77 nm in 90 min, while the corresponding values of average roughness for points 1, 2, and 3 are 23.15 and 11.16 nm, respectively. The optical microscopic morphology of the raceway surface is shown in Figs. 22 and 23. The analysis showed that the variation in surface roughness of points 1, 2, and 3 is less than 0.58 nm 2 , suggesting that the edge effect problem of STP was solved by sacrificing guide block, and hence STP provided a uniformly polished surface (Fig. 24).

Conclusions
The shear-thickening polishing of the outer ring of 30203 bearing has been studied under varied inclination angles and slurry velocities. The optimal value of true impact angle was explored using a mathematical model and numerical analysis approach. Guide block was introduced to suppress the edge effect of the STP.
1. The results show that impact angle has a significant influence on the polishing uniformity of the inner surface of the ring. The surface morphology observed significant changes at different inclination angles, and the smoothest datum was found at a 25° angle. The true impact angles derived from the mathematical model were found consistent with those in simulation data. The impact angle corresponding to the smoothest surface morphology was lying in the range of 45 to 65°. 2. The highest MRR and lowest surface roughness were obtained at 86 rpm. This is due to the more pronounced shear-thickening properties of slurry and higher P.v value at higher rotational speeds. The MRR was further improved with a disc of large diameter and enough slurry. 3. For the edge effect of STP, a guide block was introduced in the fixture to satisfy the uniformity requirement. After 90 min of the STP process, the average surface roughness R a decreased from 310 to 11.16 nm, and the roughness variance was found under 0.58 nm 2 .
This paper demonstrates the feasibility of STP for manufacturing the inner surface of a circular ring workpiece and can be used as a processing method to obtain an ultrasmooth inner surface.