1. Introduction

Rubber products with microstructures on their surfaces, such as microchannel devices ¹ and superhydrophobic rubber sheets ^2,3, have been manufactured mainly through molding processes. The complexity of these microstructures has also increased. For example, tire products with complex microstructures on their sidewalls have been commercialized to provide visual decoration by enhancing light absorption ⁴. In addition, tire products with tiny protrusions or pockets distributed across the entire curved sidewall have been produced to improve cooling performance ^5,6,7. Although the shapes of these small protrusions and pockets are simple, their arrangements on curved surfaces are complex. Certain pressure-sensitive sensor products employ arrays of fine conical micropillars composed of a conductive rubber ⁸. Furthermore, there is a growing demand for devices with increased microchannel complexities ^9,10. However, molding is costly and unsuitable for prototypes or small-lot production owing to expensive mold fabrication. If microstructures can be shaped by machining, low-cost and rapid manufacturing of various rubber products is possible. However, owing to the flexibility of rubber, machining is challenging and achieving high precision is difficult. Various studies have been conducted on rubber-surface machining ^{11,12,13,14,15,16,17,18,19,20,21,22,23}. Jin and Murakawa ¹¹ showed that high-speed milling with a 6-mm-diameter end mill at 40,000 rpm yields accurate and smooth surfaces. Shinozuka and Imakama ¹³ realized smooth surfaces using tools with microgrooved faces for high-speed orthogonal cutting. Teramoto et al. ¹⁴ and Chainawakul et al. ¹⁵ modeled rubber end milling and estimated the cutting forces and errors. Some studies have focused on cooling the rubber workpiece to reduce elastic deformation during machining ^{16,17,18,19,20,21}, and others have focused on heating the tool to improve cutting performance ^22,23. In a study focusing on burr formation, Shih et al. machined grooves 3.81 mm deep, which are considerably deeper than those used in the present study, in an elastomer composed of synthetic and natural rubbers using various woodworking router bits. Among them, downcut end mills achieved burr-free machining ²⁰. Although the tools used by Shih et al. were woodworking tools, they appear to be essentially equivalent to those employed in the present investigation. Accordingly, the up-cut and down-cut tools reported by Shih et al. are designated here as the right-twist and left-twist tools, respectively, because the twist direction and twist angle of the end mill are regarded as key geometrical parameters in this study. However, Shih et al. primarily focused on burr suppression and did not investigate dimensional accuracy, which is also a critical requirement for precise groove milling, in addition to the absence of burrs.

In the present study, we investigated the effects of tool geometry and machining conditions on burr formation and dimensional accuracy in the milling of microstructures, specifically submillimeter-deep stepped micro-grooves, on rubber surfaces. The direct machining of complex surface microstructures on rubber without relying on molding processes is expected to be beneficial for prototyping and small-lot production. Accordingly, as a fundamental investigation into machining-based fabrication of complex surface microstructures, this paper presents the first step toward creating stepped grooves as microstructures through cutting.

2. Experimental Method

A lab-developed numerically controlled (NC) milling machine was used for the experiments. As shown in Fig. 1, the machine consisted of a commercially available XYZ stage, an NC stage controller, a high-speed tool spindle, and a spindle controller. In this configuration, the workpiece was machined by moving it relative to the tool, while the tool was rotated clockwise. An uncoated 5-mm-diameter double-flute square end mill made of cemented carbide was used. Nitrile rubber was used as the workpiece material. It is widely used in industrial applications, particularly for rubber parts that require oil resistance, wear resistance, and mechanical strength. The hardness of the rubber material measured with a Type A durometer was 62. The dimensions of the workpiece were 50 mm \(\times\) 25 mm \(\times\) 10 mm. The target shape of the microgroove is shown in Fig. 2. As shown in Fig. 2, the groove had stepped features at submillimeter depths. One or two micro-grooves were machined on each workpiece. The workpieces were fixed to aluminum plates using double-sided adhesive tape, and the plates were secured to the machine tool stage with screws. Machining was performed as follows. As shown in Fig. 3, the stage was fed at the center of a workpiece in the \(y\)-direction with a cut depth of 200 μm (Stage 1), and then the left step (Stage 2) and right step (Stage 3) were machined in the same manner at a depth of 100 μm. The machined length in the \(y\)-direction was 25 mm, which was the length of the workpiece. After machining, the surfaces were visually observed and closely examined using scanning electron microscopy (SEM). Cross-sectional machined profiles were measured using a laser-type three-dimensional surface profiler (Mitaka Kohki, NH-3) ^24,25 with a laser spot diameter of approximately 1 μm.

3. Investigation of Burr Formation

3.1. Machining Using an End Mill with Rightward-Twisting Cutting Edges

First, the workpieces were machined to the target shape using an end mill with rightward-twisting cutting edges, as shown in Fig. 4(a). The cutting edge was twisted clockwise from top to bottom along the tool axis. This type of end mill is commonly used to machine metal workpieces. Hereafter, this end mill is referred to as the right-twist tool. In this experiment, the twist angle of the cutting edges was 30°. The cutting conditions were a feed rate of 0.20 mm/s and a rotation speed of 5,000 rpm. As shown in Fig. 4(b), burrs were observed on the left edge of the 10-mm-wide groove at a cut depth of 100 μm. Moreover, the right edge contained large residues that covered the center. This result is attributed to removal of the workpiece such that the chips generated from the groove edges bounced out of the groove. Such chips are not broken by elastic deformation at the groove edges, which results in burrs and residues.

To investigate the burr formation shown in Fig. 4(b), Fig. 5 presents a photograph of the side view of a machined single groove. A single groove was formed as part of the process to obtain the stepped-groove target shape, corresponding to the center groove in Stage 1 in Fig. 3. However, this single groove was formed during the machining of a stepped groove, which is different from that shown in Fig. 4, although the machining process was the same. As shown in Fig. 5, burrs appear on both edges of the groove, because the chips remained on the edges as a result of elastic deformation of the edges in the outward direction of the groove. In particular, a large burr was generated on the right edge. When the left and right steps were subsequently machined, the burrs generated during the machining of the center groove did not break up and remained. As a result, the burrs, particularly on the right edge, are considered to have become so large that they cover the center groove, as shown in Fig. 4(b).

(a)(b)

4. Effect of Twist Angle on Burr Formation

As described in the previous section, burr formation was effectively suppressed using the left-twist tool. In the preceding experiment, a tool with a twist angle of 30° was employed as the representative setting. Previous work by Shih et al. demonstrated that down-cut end mills (corresponding to left-twist tools) can achieve burr-free machining in the deep-groove milling of elastomers ²⁰. Motivated by these findings, the influence of the twist angle on burr formation and dimensional accuracy in microstructured machining was investigated in the present study. To this end, machining experiments were conducted using left-twist tools with twist angles of 15°, 30°, and 45°. For comparison, a right-twist tool with a twist angle of 30° was also employed. The feed rate of the workpiece was set to 0.20, 0.50, and 0.80 mm/s, while the tool rotational speed was kept constant at 5,000 rpm. For machining with a right-twist tool, the SEM images of the machined surfaces are shown in the first row of Fig. 8, revealing burrs on the left and right edges. In each SEM image, the burr on the right edge was large and covered the center groove. The burr morphology changed little, even when the feed rate was changed in the range of 0.20 to 0.80 mm/s. Subsequently, machining was performed using left-twist tools with various twist angles. The results are shown in the second, third, and fourth rows of Fig. 8. Each left-twist tool produced only a few burrs, if any. This result was attributed to the left-twist tool’s elastic bending of chips inward and downward along the groove, making them easier to break. As shown in Fig. 8, the edges of the grooves and steps appear not to be straight. This apparent distortion is likely due to the low-magnification observations and is attributable to aberrations in the electron optics of the SEM device. It should be noted that the SEM images shown in Fig. 8 were acquired at low magnification, not to characterize the detailed edge morphology or individual burr shapes, but to evaluate the overall distribution and occurrence tendency of burr formation along the machined edge. A closer look at Fig. 8 shows that burrs were scarcely generated by the left-twist tool at a low feed rate of 0.20 mm/s, regardless of the twist angle. This result is attributed to the reduced chip thickness owing to the low feed rate, which facilitates chip breakage. At a high feed rate of 0.80 mm/s, it was observed that slight burrs gradually appeared as the twist angle decreased. This tendency is likely due to a decrease in the cutting force directed downward into the groove, which, in turn, reduces chip breakage. Additionally, the burrs observed at the right edge were likely caused by down-cut end milling performed at that edge.

5. Evaluation of Dimension Accuracy of Machined Surfaces

The cross-sectional profiles of the machined surfaces were measured using a surface profiler. Large burrs were present on the surfaces machined with the right-twist tool, as described in Sections 3 and 4. These burrs were removed using tweezers before the measurement. Figure 9 shows the cross-sectional profiles of the surfaces machined using a left-twist tool with a twist angle of 30°, a feed rate of 0.2 mm/s, and a rotational speed of 5,000 rpm. The figure presents overlaid profiles measured at different positions along the workpiece length: 6.25 mm, 12.5 mm (the center), and 18.75 mm from the side edge. As shown in Fig. 9, the profiles nearly coincide, indicating that machining was stable along the tool feed direction. This result also indicates that the distortion observed in the SEM images in Fig. 8 was caused by aberrations in the electron optics of the SEM device.

Figure 10 shows the profiles of the surfaces machined at different feed rates using a left-twist tool with a twist angle of 30°, where the measuring position was at the center of the 25 mm length. The depth errors at the center of the profiles increased with the feed rate. Thus, we obtained the depth errors at the center of the central groove and at both side steps for each cutting condition, as shown in Fig. 11. Figs. 11(a), (b), and (c) show the depth errors at the center of the central groove, left step, and right step, respectively. As shown in the insets of Fig. 11, the positive sign on the vertical axis represents insufficient cut depth, and the negative sign represents overcutting. These figures reveal that when the feed rate was low, the depth errors tended to be small at the center of the central groove and at both side steps for any twist angle. As the feed rate increased, the depth errors increased and were affected by the twist angle.

The increase in the depth error with increasing feed rate, as shown in Fig. 11, can be explained as follows. When a cutting edge passes over a workpiece, the cutting force causes elastic deformation of the surface. A positive depth error is considered to result from the elastic recovery that occurs after the cutting edge has passed. On the basis of this interpretation, a higher feed rate increases the chip thickness, which in turn leads to a greater cutting force, and consequently, a larger amount of elastic recovery. Moreover, at all feed rates, the depth error tends to increase with the twist angle. This tendency is attributed to the increase in cutting force with increasing twist angle, which leads to a greater elastic deformation of the workpiece. The depth-direction origin of the machining was determined by placing a block gauge on the workpiece and setting the origin to the point where electrical contact was established between the block gauge and the tool. Consequently, the origin may be set with the workpiece slightly indented, which could lead to overcutting near the origin. Therefore, at a low feed rate (0.2 mm/s), the chip thickness becomes small and the material’s elastic recovery is reduced, which may make the influence of overcutting due to the origin-setting method more apparent.

6. Conclusions

We investigated the milling of microstructures, specifically stepped micro-grooves with submillimeter depths, on a nitrile rubber surface. The experiments were conducted using an NC milling machine and cemented carbide end mills with different twist directions and angles. We compared the left-twist and right-twist tools and evaluated the effects of twist angle and feed rate on burr formation and dimensional accuracy. Burr formation was significantly suppressed using a left-twist tool. In particular, nearly burr-free machining was achieved when either a large twist angle or low feed rate was applied. The depth errors of the grooves were reduced under the conditions of a small twist angle or low feed rate. A possible reason for the deterioration in the depth error with greater twist angles and higher feed rates is the elastic deformation of the workpiece caused by an increase in the vertical cutting force. These findings provide important guidelines for the small-lot, high-mix production of rubber products with microstructured surfaces. This study represents a fundamental first step toward the machining-based fabrication of complex microstructured geometries on rubber surfaces, addressing not only burr suppression but also dimensional accuracy. In the present study, the discussion of the mechanisms of burr formation and suppression was limited to qualitative considerations. In future work, a more detailed mechanistic understanding will be pursued, based on direct observations of the chip flow using a high-magnification, high-speed camera, systematic analyses of the chip morphology, measurements of the cutting forces, and cutting simulations. Furthermore, we plan to extend this study to the machining of finer and more complex microstructured geometries using smaller-diameter tools, which will enable the fabrication of more intricate rubber microstructures.