The micro-triangular pyramid patterns are widely used in advanced optical components with retro-reflection characteristic. The performance of the retro-reflection is affected by an effective area, and it can be maximized by machined surface without defects such as edge blunt, burr, surface roughen. The ultra-precision planing process is well-known that can fabricate superior surface when the depth of cut (DOC) is applied to minimum depth above the critical value to prevent the size effect. However, it was very difficult to determine a DOC without comparing of quality of machined surfaces through the ultra-high magnification measuring instrument such as SEM. In this study, the critical DOC which is key parameter was analyzed using cutting force and tool vibration signals. These signals were converted to specific cutting resistance and frequency spectrum, respectively. As a result, spectrum frequency signal was more effective and accurate than specific cutting energy, and critical DOC was determined to 1µm. This proposed process was validated by comparing the quality variation of the machined surfaces with analysis result based on cutting signals. Finally, a master mold with area of 250mm2 for fabrication of the retro-reflection film was manufactured by applying optimized DOC, and the retro-reflection film was fabricated by press molding process. This retro-reflection film was clearly recognized at a distance of 100m from light source with low power.
Research Article
Study On Cutting Force and Tool Vibration For Optimization of Depth of Cut in Ultra-Precision Planing Process of the Master Mold For Retro-Reflection Film
https://doi.org/10.21203/rs.3.rs-958813/v1
This work is licensed under a CC BY 4.0 License
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Size effect
Critical depth of cut
Cutting force
Tool vibration
Triangular pyramid pattern
retro-reflection
The surfaces with micro-structures can change the optical path of the light propagation. The controlled light propagation can achieve the optical performance such as retro-reflection, light diffusion, concentration, etc. [1–5]. In these optical characteristics, optical retro-reflection is widely used in various industries such as night safety signs, traffic signs, vehicle rear reflectors, display, solar-cell, and advanced optical measuring devices [8–11]. The main parameter of the retro-reflection performance is the brightness of the retroreflected light, it was quantified as the ratio of the reflected light intensity to the incident light. Ultra-high brightness retroreflectors can be fabricated by using micro-triangular pyramid array that returns incident lights by total reflection from three surface of inside the pattern, and it is required to minimize the light scattering by the surface defects for higher efficient retro-reflection.
The manufacturing technologies for fabricating micro-triangular pyramid patterns are including chemical etching process [12, 13], laser machining process [14, 15], and lithography process [16]. Even though these technologies enable to fabricate the various shape and fine structure for the retro-reflection, but fabricated patterns typically have a blunt shape and a rough surface. The blunt edges can reduce efficiency of the total reflection of the incident light by reduced area for reflection, and the rough surface can scatter the light on the incident surface. For these reasons, these problems can deteriorate efficiency of the retro-reflection.
The ultra-precision cutting process using a diamond cutting tool have advantages which can fabricate smooth surface with roughness value less than 10 nm level and shape with sharp edges [17–19]. Typically, the cutting process known to fabricate the high-quality of the machined surface applying cutting conditions which is shallow depth of cut and fast cutting speed [20, 21]. However, there is a critical DOC that was difficult to ignore the force acting on the cutting edge due to the curvature of the cutting tool edge. The force acting on the tool edge and the tool flank do not contribute to removal of the chip that is referred as the plowing force. The existence of the plowing force results in increasing the specific cutting energy for remove a unit volume of metal at low values of undeformed chip thickness, and this phenomenon is called a ‘size effect’ [21]. Because the machined surface has problems such as burr and deformation when a size effect is acting in cutting process, determination and analyzation of the critical DOC which generate the size effect is important. [21–23]. To determine the critical DOC, specific cutting resistance(specific cutting resistance have a same value with specific cutting energy.) is widely applied [22, 23]. However, the specific cutting resistance is calculated as the ratio of the cutting force in the cutting direction and cutting area, it is insufficient to accurately analyze the critical DOC with size effect by plowing force acting on the cutting edge in various direction. In other hands, because the cutting tool vibration has the various information of the characteristics in cutting process, method of analyzing tool vibration can be efficiently applied to determine the critical DOC.
In this study, the specific cutting resistance and vibration of the cutting tool were analyzed according to the uncut chip thickness in the finish machining for Cu electroplated metal mold with micro triangular pyramid pattern array. The critical DOC was determined by the results from variation of the specific cutting resistance and the frequency of tool vibration. An experimental study was carried out for validity of using tool vibration signal to determine the critical DOC. Then, it was adapted to fabrication process as a finish cutting condition, the large area master mold with superior quality of surface and edge was manufactured, and the retro-reflection performance of molded film fabricated by using master mold was evaluated.
Figure 1 shows the schematic of the two-dimensional steady state of the orthogonal cutting process. The resultant tool force (Fr) in metal cutting is distributed over the contact area between tool and workpiece. When a DOC is larger than cutting edge radius, the cutting force has small proportion of the resultant force at large value of undeformed chip thickness as shown in Figure 1(a). In this case, the resultant force can be divided to two components of cutting force (Fc) and thrust force (Ft). However, at the small value of undeformed chip thickness as shown in Figure 1 (b), the cutting tool edges plows the work material during the cutting process because of inevitably generated edge radius by joining two surfaces of flank and clearance. In this case, because the force acting on the cutting edge cannot be neglected, the resultant force can be presented by sum of two component force which are plowing force (Fp) and shearing force (Fr’). The plowing force is act on the flank surface of the cutting tool that do not contribute to removal of the chip, and it generate the important phenomenon so-called size effect. The cause of the size effect is presented by Nakayama, Kazuo and Tamura, Kiyoshi in research of cutting force according to DOC. As a resultant of their study, the main cause of the size effect is the decreasing of shear angle with a decrease in the undeformed chip thickness due to the blunt shape of cutting edge [24].
At the relatively large value of undeformed chip thickness, specific cutting energy is decreasing according to decrease the cutting area. However, at the shallow depth of cut which cannot ignore radius of cutting edge, specific cutting energy increase rapidly with decreasing uncut chip thickness. If the portion of specific cutting energy contributing to chip removal will remain constant, the portion resulting from the plowing force will increase. The plowing force occurs high stress acting near the cutting edge, and it can generate the deformation of the machined surface and remaining the residual stress. Also, plowing force has a problem which generate the burr on the machined surface [21, 24]. Therefore, to fabricate the machining results with high-quality surface, it is required to determine the optimum depth of cut before the plowing effect becomes larger than the cutting property.
3.1 Experimental set-up
In order to determine the critical depth of cut which is generate the size effect in machining of the micro triangular pyramid patterns, the study for analyzing cutting force and acceleration signals according to depth of cut is conducted. Figure 2 shows the schematic of experimental set-up for the collecting cutting signals of cutting force and vibration, and Figure 3 shows the experimental system for fabricating triangular pyramid pattern on the Cu-plated mold. The machine tool was consisted of the three linear stages (X, Y, and Z-axis) with positioning resolution of 5 nm and rotation axis(theta-axis) with a resolution of 0.00001˚. For measuring cutting force, the 3-axis dynamometer (9256C2, Kistler) has sensitivity -26p C/N with direction of Fx and Fz, and -13p C/N with direction of Fy. The analog signal generated by dynamometer is converted to voltage signal with range of ±10V by charge amplifier (5080a, Kistler), and it was transferred to data acquisition board (DAQ, Kidaq, Kistler). In order to measure the tool vibration, an accelerometer sensor (8763B, Kistler) of integrated electronics piezo-electric (IEPE) type was attached to the shank of cutting tool. An accelerometer has sensitivity of 100 mV/g and resonance frequency of 35 kHz. The sampling rate was applied to 10 ks/s for collecting enough data, and high-frequency pass filter of 10 Hz was applied for filtering the noise signals of machine tools. The collected signals were analyzed by using software J-beam (Kistler) which is signal analyzer program.
In the planning process, because the edge radius of cutting tool is affected to generate the size effect, the measurement of the edge radius is important. Figure 4 shows the images of single crystal diamond(SCD) which has sharp edge with shape angle of 75˚ and edge radius of about 500nm measured by scanning electron microscope(SEM).
3.2 Experimental conditions
Figure 4 shows the schematic of the planing process to fabricate a triangular pyramid pattern. This process fabricates triangular pyramid patterns by cross-machining the center of the square pyramid pattern which was fabricated by prior machining paths of -60˚ and 60˚.
Figure 5 shows the cutting area of finishing in planing process of a triangular pyramid pattern with height of Ht. Total cutting area(A) of figure 6 (a) consists of V shaped area(A1) and two triangles(A2) as shown in figure 6 (b) and (c), respectively. Table 1 summarizes the values of cutting areas calculated by equation (1) according to undeformed chip thickness(Hu). From these calculated values, the cutting area A2 does not significantly affect the size of total cutting area.
(1)
|
Uncut chip thickness (µm) |
Cutting area A1 (m2) |
Cutting area A2 (m2) |
Total cutting area A (m2) |
|---|---|---|---|
|
3 |
2.97E-10 |
2.36E-12 |
2.97E-10 |
|
2 |
1.99E-10 |
1.05E-12 |
1.99E-10 |
|
1 |
1.00E-10 |
2.62E-13 |
1.00E-10 |
|
0.5 |
5.03E-11 |
1.66E-13 |
5.03E-11 |
|
0.3 |
3.23E-11 |
2.36E-14 |
3.02E-11 |
|
0.1 |
1.01E-11 |
0.51E-15 |
1.01E-11 |
Table 2 summarizes the machining conditions applied to experiments for analyzing size effect according to the variation of undeformed chip thickness. The depth of cuts was applied to 3, 2, 1, 0.5, 0.3, and 0.1µm in the final machining of triangular pyramid pattern, and the total depth of this machining was 107.5 µm. The cutting speed was fixed to 200mm/sec to consider the effect by undeformed chip thickness.
|
Machine tools |
4-axis ultra-precision planar of X, Y, Z and theta-axis (Movement resolution of 5 nm and rotation resolution of 0.0001˚) |
|---|---|
|
Cutting tool |
Single crystal diamond with sharp edge of 70.5 ˚ |
|
Workpiece |
Cu-plated on the SKD 11 with size of 30x30 mm (Vickers Hardness 227.8) |
|
Cutting speed (mm/sec) |
200 |
|
Depth of cut (µm) |
3, 2, 1, 0.5, 0.3, 0.1 |
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) [25].
(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) [20].
(3)
(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 [26]. 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 [27].
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.
In this paper, determination process for critical DOC was suggested based on analysis of the cutting signals which are cutting force and tool vibration. The signals were converted to cutting resistance and frequency domain. Characteristic of size effect was analyzed by using converted signals, and the frequency variation of the tool vibration was more effective. The optimized critical DOC was applied to fabricate the master mold, and the ultra-high luminance retro-reflection film was fabricated. By the considering the above results and discussions, following conclusions can be drawn.
1) In the finish machining of micro triangular pyramid patterns, the RMS value of the cutting force was decreased linearly from 0.3726N to 0.0567N according to shallowing the undeformed chip thickness from 3µm to 0.1µm, the variance tendency of thrust force was difficult to define for confirming of the size effect by plowing force.
2) The specific cutting resistance was calculated using RMS value of the cutting force and cutting area, it shown trends which are slightly increase at undeformed chip thickness of 1µm and significant increase below 0.5µm that increased. For this reason, determination of accurate critical DOC for high quality machined surface was difficult by using the specific cutting resistance.
3) From the results of analyzing tool vibration, the dominant frequency in the cutting state was 1135 Hz in X-direction, and the power spectrum of this signal decreased when the DOC was shallow. On the other hand, the power spectrums of tool vibration in Z-direction had higher values than X-direction at 1µm. From this result, it was considered to occurrence the transition of the main cutting state from the X-direction to the Z-direction, which can be considered as size effect due to the plowing force. Therefore, the critical DOC can be determined more accurately than using the variation of the specific cutting resistance.
4) The surface quality of the machined triangular pyramid pattern was deteriorated due to plastic deformation and burrs by size effect at below undeformed chip thickness of 1µm. From this result, the validity of the determination of the critical DOC using the tool vibration signal was experimentally verified.
5) A high-performance retroreflective film was molded using a press-molding process and a nickel stamper mold, and performance was verified through a simple light reflection test.
6) This optimizing process was expected to be utilized as a manufacturing process for micro structured mold with high quality surface and accurate edges for advanced optical component with high performance.
Acknowledgement
This work was supported by the Korea Institute of Machinery and Materials (NK232E). This work was also funded by the Technology Innovation Program (20003945, Development of core manufacturing technology of 4-axes ultra-precision machining system and lens module for next-generation mobile lens having about 100nm shape accuracy) funded by the Ministry of Trade, Industry & Energy(MOTIE, Korea).
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No competing interests reported.