4.1 Cutting force vibration according to depth of cut
Figure 6 shows the machined workpiece, which includes the planar surface, prism pattern, square pyramid, and triangular pyramid pattern. These were generated by the cross number of the cutting tool paths which were -60˚, 0˚, and 60˚. The prism patterns were machined by applied only one of the -60˚, 0˚, and 60˚ cutting paths. The square pyramid patterns were machined by cross machining with two cutting paths among them, and triangular pyramid patterns were machined by the cross of three cutting paths.
Figure 7 shows the measured force signals according to undeformed chip thickness from 3µm to 0.1µm. For each thickness, the cutting signals were measured in x-direction and z-direction. The force of x-direction was cutting force, and the force of z-direction was thrust force. The measuring time of the force signals in the cutting state is about 0.152sec, it was a similar time to the calculated time of 0.15sec that the cutting tool was passed through a workpiece length of 30mm at a feed rate of 200mm/sec. At each cutting condition of undeformed chip thickness, the measured force signals included the machining state of prism, square pyramids, and triangular pyramids. Among these, the signal with a large amplitude is the force measured during the machining of a triangular pyramid. The cause is that the largest area was machined because the cutting tool crosses the center of the previously machined square pyramid, and the vibration was generated by the collision between the cutting tool and workpiece due to interrupted cutting. Typically, since the cutting force is proportional to the cutting area, the value and amplitude of the cutting force were decreasing according to thinning undeformed chip thickness. The thrust force was related to the value of the consuming total cutting energy, it tended to decline as the undeformed chip thickness thinning from 3µm to 1µm. However, with undeformed chip thickness thinner than 500nm, the measured thrust force is difficult to compare a variation. Also, the measured force signals were difficult to analyze quantitatively due to the large variation by interrupted cutting. Therefore, In order to quantitative analysis, the measured force signals were calculated to the value of the root mean square(RMS) by using the equation (2) .
Frms is the RMS value of the measured cutting signal in Fn is the measured force value, and n is the total number of measured force values in cutting time of the triangular pyramid pattern. Figure 8 shows the RMS values of the cutting force and thrust force according to undeformed chip thickness. The RMS value of cutting force was linearly decreased from 0.3726N to 0.0567N according to undeformed chip thickness thinning from 3µm to 0.1µm, but the thrust force was difficult to confirm the tendency that minimum value of 0.0509N at undeformed chip thickness of 2µm and a maximum value of 0.1086N at 0.5µm. From these results, it can be estimated that the influence of the plowing force was increased because the variation in thrust force was small compared to the reduced cutting force. In order to accurately analysis of the size effect using force signal, a specific cutting resistance was applied.
The specific cutting resistance (Ks) is the stress value which is cutting force divided by the cutting area as shown in equation (3), and it can be applied to analyze the cutting characteristic because the Ks has the same unit with specific cutting energy(u) which is calculated by equation (4) .
In equation (3), Fc is the cutting force and A is the cutting area. In equation (4), U is the cutting energy, Vc is the unit volume of metal removal, b is the cutting width, t is the undeformed chip thickness.
Figure 9 shows the variation of the specific cutting resistance and cutting area according to undeformed chip thickness. The specific cutting resistance slightly declines from 1.256GPa to 1.194GPa according to undeformed chip thickness thinning from 3µm to 2µm. However, after a slight increase in the specific cutting resistance up to 1.41GPa at undeformed chip thickness of 1µm, it tended to increase significantly to 5.61GPa at 0.1µm, which was about 4 times as much as specific cutting resistance of undeformed chip thickness 3µm. Even though the cutting area was decreased, the cause of the increase in the specific cutting resistance was analyzed as follows. The rake angle of the cutting tool was significantly decreased where the depth of cut was lower than the edge radius. In this state, the plowing force has a greater effect on the cutting process than the shear force, and the stress by plowing force was concentrated on the edge of the cutting tool . The concentrated stress was showed the increase of the specific cutting resistance, and it can be estimated as a phenomenon due to the size effect. Even though the specific cutting resistance showed an increasing tendency, there is not enough definite reason to determine accurate critical DOC to fabricate the highest quality of machining surface. For this reason, we conducted to the analysis of the cutting state by using the vibration signal of the cutting tool according to vibration direction.
4.2 Cutting vibrations according to depth of cut
Figure 10 shows the results obtained by using the acceleration sensor for measuring the vibration signal of cutting tool according to the variation of undeformed chip thickness. The acceleration of X-direction is the vibration in the cutting direction, and the acceleration in the Z-direction is the vibration of perpendicular direction to the cutting direction. The measured accelerations in the X and Z directions showed similar amplitudes within the respective machining conditions. The maximum value of the acceleration within cutting state was decreased from 2.252m/sec2 to 1.12m/sec2 according to decrease the undeformed chip thickness. Even though this result can indicate the size variation of tool vibration, but it was difficult to indicate the cutting characteristic that was varied by size effect. However, the vibration signal includes many information about characteristic of cutting process, and each information can be confirmed by the frequency domain signal which was converted from time domain signal by using Fourier transform .
The measured acceleration signals were converted to frequency domain signal by using fast Fourier transform (FFT) function of using J-beam(Kistler) which was signal processing software. Hamming window was applied to prevent signal leakage of vibration signal with strong aperiodic during FFT. In addition, FFT-based power spectral density (PSD) with little difference depending on the measuring time was applied. Figure 11 shows results that signal of Fig. 11 converted to FFT-based PSD signal. When the undeformed chip thickness was 3µm, the dominant frequency of the vibration in X-direction was 1135Hz and this PSD amplitude was 0.0025(m/sec2)2/Hz as shown in figure 12 (a). In this machining condition, since the undeformed chip thickness was about 6 times thicker than edge radius of cutting tool, the frequency of 1135Hz can be considered as signal of shearing characteristic. The PSD amplitude of 1135Hz decrease to 0.0006(m/sec2)2/Hz at undeformed chip thickness of 2µm, and it converged almost zero below 1µm. This variation of dominant frequency can be seen that shearing characteristic was gradually decreased. On the other hand, when the undeformed chip thickness was reduced to below than 1µm, the frequency of the vibration signal in Z-direction was concentrated at about 1600Hz. It means that the main machining characteristics have been transferred from the X-direction to the Z-direction, which is analyzed because the influence of the plowing force on the machining process had been increased by size effect. From the above analysis results, the critical DOC may be determined as 1 µm at which the main direction of machining characteristic was converted.
4.3 Machined surface of triangular pyramid pattern according to depth of cut
Above the section 4.1 and 4.2, the critical DOC which occurrence the size effect was determined to by analyzing the force signal and vibration signal. As a result, the variation of the frequency spectrum is effective on the determination of critical DOC more than specific cutting resistance, and it was determined to 1µm. The effectiveness of the determined critical DOC can be verified by the quality of the machined surface because the plastic deformation was generated by the plowing effect.
Figure 12 (a) to (e) show the machined triangular pyramid patterns according to undeformed chip thickness, which was measured by scanning electron microscope(SEM). At the undeformed chip thickness of 3µm, the shape of the exit edge was collapsed due to excessive cutting force, and burrs were formed on the edge of machined pattern as shown in figure 12 (a). The quality of the machined pattern was gradually improved up to critical DOC of 1µm as shown in figure (c). However, when the DOC was shallower than 1µm as shown in figure (d), (e) and (f), the edge of the pattern had been blunted due to the plastic deformation affected by plowing effect. In addition, the material fell off from the edge of the pyramid patterns, which intensified the surface damage and increase in the amount of burrs. From these results, the critical DOC was determined to be 1µm, and this determined value confirmed that same trend as the result of spectral analysis of the vibration signal. Therefore, the frequency spectrum of vibration signal had been verified as an analysis means to determine the optimum depth of cut for machining triangular pyramid pattern with high quality surface and edges. Also, by applying an optimal DOC determined by suggested process, the machined surface and edge quality can be improved, and it can be expected to utilize for mold of advanced optical component required ultra-high brightness retro-reflection.
4.4 Fabrication of the master mold and performance test of retro-reflection film
The optimized DOC through the above experimental results was applied to finish process in manufacturing of the master mold with large area of 250mm by 250mm. Figure 13 shows the machined master mold, and image measured by optical microscope. Because the retro-reflection film has same structures with master mold, the stamper mold having the reverse shape of the master mold using the nickel electroplating replication process was prepared as shown in Fig. 14. The ultra-high luminance retro-reflection film was formed using by press molding process. Figure 15 shows the press molded film and the pyramid pattern on this film. The patterns were well formed without size error compared to master mold. However, the edges were little blunt since the two-replication process for fabrication; i) from master mold to nickel stamper mold, ii) from nickel stamper mold to retro-reflection film.
Figure 15(a) shows the press molded retro-reflection film by using nickel stamper mold which was replicated from master mold. In order to optical performance of retro-reflection, photographs were taken in two states which was the flashlight on and off which are with flashlight and without. Pictures are taken by mobile phone camera (Samsung Galaxy 21 ultra) with distance of 10m and 100m from retro-reflective film. The camera was set to F-number of 1.8, exposure time of 0.1s, and sensitivity of ISO160. When the picture was taken without flashlight, it is difficult to distinguish the presence of retro-reflective film even at a distance of 10m and 100m as shown in Fig. 15 (b) and (d). However, when the flashlight was on, the retro-reflective film can be easily distinguished as shown in Fig. 15 (c) and (e). This result was possible because the emitted light was collected by retro-reflected to the image sensor without being scattered by the triangular pyramid pattern of the retroreflective film. Also, these results mean the optimization of the critical DOC based on the cutting signal analysis can be utilized for manufacturing master mold of superior high luminance retro-reflective film.