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Fractal characterization of surface microtexture of Ti6Al4V subjected to ultrasonic vibration assisted milling
Journal Pre-proofs Fractal characterization of surface microtexture of Ti6Al4V subjected to ultrasonic vibration assisted milling Bo Zhao, Pengtao Li, Chongyang Zhao, Xiaobo Wang PII: DOI: Reference:
S0041-624X(19)30711-5 https://doi.org/10.1016/j.ultras.2019.106052 ULTRAS 106052
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Ultrasonics
Received Date: Revised Date: Accepted Date:
25 March 2019 15 September 2019 21 October 2019
Please cite this article as: B. Zhao, P. Li, C. Zhao, X. Wang, Fractal characterization of surface microtexture of Ti6Al4V subjected to ultrasonic vibration assisted milling, Ultrasonics (2019), doi: https://doi.org/10.1016/ j.ultras.2019.106052
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Fractal characterization of surface microtexture of Ti6Al4V subjected to ultrasonic vibration assisted milling Bo Zhao*, Pengtao Li, Chongyang Zhao, Xiaobo Wang School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo, Henan, China Abstract: The high-frequency tool vibration occurring during ultrasonic vibration cutting results in a formation of unique micromorphology of the machined surface. Different microtextures are known to have a substantial effect on the workpiece service performance. In this study, an attempt is made to assess this effect quantitatively for a more accurate characterization of the processed surface. The dependence between the contour root mean square deviation and fractal dimension is derived via the fractal theory. The concept of characteristic fractal dimension is proposed and successfully applied to Ti6Al4V surfaces subjected to ultrasonic vibration assisted milling (UVAM) with various spindle rotation speeds and vibration amplitudes. The experimental results obtained strongly indicate that smaller characteristic fractal dimensions correspond to more regular surface microtextures and contour curves, which proves the validity of the characteristic fractal dimension representation. Besides, the lower the characteristic fractal dimension of the surface, the shorter the time to reach the stable friction phase during dry friction.
Keywords: Ultrasonic vibration assisted milling (UVAM); Surface characterization method; Characteristic fractal dimension; Friction and wear
*Corresponding author: Bo Zhao, School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo 454000, China, Email: [email protected]
1. Introduction Ultrasonic vibration processing is frequently used in combination with such traditional machining methods as turning, grinding, milling, etc., in order to reduce the cutting force and heat, enhance the tool life, and optimize the chip breaking process [1]. The application of high-frequency vibrations to the machining tool or workpiece changes the cutting mechanism of conventional machining and also results in the formation of a complicated and regularly arranged microtexture of the processed surfaces [2]. Thus, Gao et al. [3] reported that low-frequency ripples appear on the machined surface of aluminum alloy workpieces in ultrasonic vibration turning due to insufficient rigidity of the acoustic system and the improper setting height of the tool tip. The longitudinal stripes mark the feed trace of the tool, while smaller transverse marks are due to the tool vibration. The machined surface reflects rainbow-like streaks. Compared to machined surfaces generated by conventional milling, ultrasonic vibration-assisted milling results in more uniform and finer surface structures [4]. Tao et al. [5-6] established a kinematics model of ultrasonic vibration assisted milling (UVAM) and experimentally proved that the feature curves of the squamous surface could be regarded as the same type of function curve with tool tip trajectories. Based on the machining dynamics, Cheng et al [7-8] predicted the cutting force of two-dimensional vibration-assisted micro-end milling (2D VAMEM) and established the surface topography model through the tool tip trajectory. The model can be used to optimize processing parameters, and the validity of the model is experimentally verified. Bai et al. [9] revealed a similarity between the UVAM surface and typical biological surface topography and proved that UVAM could be applied in the field of bionics for biomimetic purposes. Ma et al. [10] reported that the surface morphology of a titanium alloy after UVAM has a specific regular arrangement of microtexture, which could improve the surface wear resistance. Other studies have also shown that surface microtextures with a particular regular arrangement strongly improve the tribological characteristics of some materials [11-14]. However, to the best of the authors’ knowledge, the main factors controlling the effect of different morphologies on the material friction and wear properties were not quantitatively assessed yet. The surface topography of workpieces refers to various residual heights, textures, and streaks that remain on the workpiece surfaces after their processing [15]. It is generally expressed by roughness, waviness, shape error, spectrum, etc. However, any conventional quantitative description of the rough surface changes with the measurement scale and cannot represent the fundamental characteristics of the surface topography. In this respect, quite promising is the fractal theory that is based on the fractal dimension perspectives and mathematical methods. Being scale-independent, fractal parameters can be used to characterize the surface topography without being affected by the measurement length [16]. Miao et al. [17] reported that higher fractal dimensions correspond to more
complex shapes and more opulent microstructural details. Wang et al. [18] used fractal analysis method to investigate the wear behavior of resin-bonded diamond wheel in Elliptical Ultrasonic Assisted Grinding (EUAG) of monocrystal sapphire, and a series of experiments on EUAG and conventional grinding (CG) are performed. The results show that the fractal dimension of grinding wheel topography is highly correlated to the wear behavior. Gan and Huang [19] applied the fractal theory to the study of the milling surface contour and proved that fractal parameters could quite accurately reflect the fine structure of the surface contour. In summary, the ultrasonic-assisted processing and UVAM, in particular, results in the formation of a certain regular microtexture of the processed surface. However, its degree of regularity has not been adequately described, and the processing results cannot be effectively compared. In this study, the concept of the characteristic fractal dimension is proposed based on the fractal theory. The regularity of the morphology of the ultrasonic milling surface is defined by the characteristic fractal dimension. The Ti6Al4V was selected for the UVAM processing, given its broad application in the aerospace, energy, and biomedical industries [20]. To study the effect of microtextures with different fractal properties on he tribological properties of Ti6Al4V, the respective dry friction tribotests were conducted. Nomenclature l The scan length S(l) The contour root mean square height c The scale factor D The fractal dimension k The line slope Rq The contour root mean square roughness L The measured length Z(x) The surface contour height function ωm The measurement resolution ωs The sample length G The characteristic length γ The modulus of spatial frequency Sq The surface root mean square deviation DC The characteristic fractal dimension fz The feed per tooth ap The cut depth n The spindle rotation speed A The ultrasonic amplitude f The ultrasonic frequency
2. Characteristic fractal dimension of the machined surface
At present, the surface fractal dimensions are assessed using various methods, including the box-counting, power spectrum, structure-function, and variation ones. In this study, the root mean square method (RMSM) is used, due to its known advantages of simple calculation, clear physical meaning, strong surface adaptability, wide zoom area, and good representation effect [21]. The standard procedure for measuring the fractal dimension via RMSM is as follows [22]. Taking the scan length l as the measurement scale and the contour root mean square height S(l) in the scale region as the measure, the following relationship between them is used: S (l ) c l 2 D
(1)
where c is the scale factor and D is the fractal dimension. Equation (1) is also referred to as the measurement standard of multi-scale measurement. Taking logarithm of both parts of Eq. (1), it can be reduced to the following form: log S (l ) log(c) (2 D) log(l )
(2)
Equation (2) implies that the ideal fractal curve exhibits a linear relationship between the measure and the scale in logarithmic coordinates, while its fractal dimension D is negatively proportional to the line slope k, i.e., D=2 - k. However, when RMSM is used, it is necessary to select different measurement scales to obtain various measures, perform the linear regression analysis for the logarithm of the results and, finally, get the slope and fractal dimension of the line segment. When this method is used, it is necessary to measure different scale ranges, which makes the experiment cumbersome and hinders data processing. To simplify the cumbersome steps, the fractal dimension is assessed via the contour root mean square roughness Rq [23]. L
Rq 1 L Z 2 ( x)dx 0
(3)
In Eq. (3), L is the measured length, Z(x)is the surface contour height function. On the other hand, Rq 2 E[ Z 2 ( x)]
(4)
where S
E[ Z 2 ( x)] S ( )d m
G 2( D 1) 1 1 1 42 D 42 D 2 ln 4 2 D s m
(5)
In Eq. (5), ωs is the sample length, ωm is the measurement resolution, and G is the characteristic length, γ is the modulus of spatial frequency. The relationship between Rq and D can be obtained:
Rq
12
G D 1
2 ln(4 2 D)1 2
1 1 42 D 42 D m s
(6)
Since ωs>>ωm, Eq. (6) can be reduced to: Rq
G D 1
(7)
2 ln(4 2 D)1 2 s 2 D
It can be seen from Eq. (7) that the relationship between D and Rq is further simplified: Rq is obtained from a single line profile, while the surface root mean square deviation (SRMSD) Sq reflects the surface topography. To further characterize the machined surface, the concept of characteristic fractal dimension is proposed. A unity value of the characteristic length is always taken, ωs is defined as the sample length, and the relationship between the characteristic fractal dimension (DC) and SRMSD (Sq) is obtained as follows: Sq
1
2 ln(4 2 DC )1 2 s 2 D
(8)
C
3. Experimental setup and trials The experimental platform was built on the VMC850E three-axis vertical machining center. The UVAM experimental setup is depicted in Fig. 1. After the installation, the Ti6Al4V end-milling experiment was carried out. A four-blade spiral carbide milling cutter (8×20×60, 4T, SF20, HRC58) was used in the test. The chemical composition and thermo-mechanical properties of Ti6Al4V are given in Tables 1 and 2, and the size of the workpiece was Φ38 mm×Ф54 mm×h13 mm.
Fig. 1 The UVAM experimental setup
Table 1 Chemical composition of Ti6Al4V (wt%) Ti-Al-4V
Al
V
Fe
O
C
N
H
Si
Balance
6.35
4.1
0.25
0.18
0.06
0.04
0.011
<0.01
Table 2 Thermo-mechanical properties of Ti6Al4V Properties
Value
Density (kg/m3)
4429
Elastic modulus (GPa)
114
Hardness (HV)
340.6
Poisson’s ratio
0.33
Yield strength (MPa)
835
Tensile strength (MPa)
905
Thermal conductivity (W/mK)
6.7
Melting temperature (°C)
1667
The wireless transmission system transmitted energy of ultrasonic generator to the transducer, and the transducer vibrated at a high frequency, but the amplitude was small. The horn amplified the amplitude and transmitted the vibration to the tool. Different surface microtextures were obtained by varying the spindle speed and ultrasonic amplitude. The experimental scheme is shown in Table 3. Table 3 Experimental scheme Test
Spindle rotation
Amplitude
Frequency
number
speed n/(rpm)
A/(μm)
f/(kHz)
1
594
2
35.63
2
1194
2
35.63
3
2388
2
35.63
4
3507
2
35.63
5
4776
2
35.63
6
1194
0
0
7
1194
1
35.68
8
1194
2
35.63
9
1194
3
35.60
10
1194
4
35.56
11
1194
5
35.53
In all tests, the feed per tooth fz =15 μm and the cut depth ap =0.3 mm were used. The surface topography of the workpiece was examined via a VHX-2000 ultra-depth microscope. The contour curve of the workpiece and the surface root mean square deviation (SRMSD) Sq of the surface were measured by a non-contact Talysurf-CCI6000 white light interference surface profiler. The cutting force was obtained using a Kistler-9257B dynamometer.
4. Results, analysis and discussion 4.1 Processing results at different spindle speeds It can be seen from the measurement result depicted in Fig. 2 that at the amplitude A= 2 μm, higher spindle speeds corresponded to more pronounced microtextures of the milling surface. When the speed was 594 rpm, the surface morphology was not uniform and plow-like scratches were noticeable. However, as shown in Fig. 2a, the machined surface had a "ribbed" microtexture under ultrasonic vibration conditions. When the spindle rotation speed reached 1194 rpm, the surface topography was mainly uniform. With the continued speed increase, the surface became more texturized: at a spindle speed of 4776 rpm, an evenly arranged fish scale-like microtexture was observed.
（a）
(b)
(c)
(d)
(e)
Fig.2 Micromorphology of Ti6Al4V workpieces milled at different spindle rotation speeds: (a) 594 rpm; (b) 1194 rpm;(c) 2388 rpm; (d) 3507 rpm; (e) 4776 rpm
The above experimental results strongly indicate that in case of low-amplitude UVAM of Ti6Al4V, with an increase in the spindle speed, the machined surface texture gets more regular and gradually changes from a "riblike" pattern to a "fish scale" one. With the surface topography variation, the surface characterization parameters also vary. The surface root mean square deviation (SRMSD) Sq was obtained, and the characteristic fractal dimension (CFD) DC was calculated for various spindle rotation speeds (Fig. 3).
Sq DC
SRMSD Sq
1.4
1.4 1.2 1.0
1.2
0.8 1.0
0.6
0.8 0.6
CFD DC
1.6
0.4 0
1000
2000
3000
4000
5000
0.2
Spindle speed(rpm) Fig. 3 Milling results at different speeds
As seen in Fig. 3, with an increase in the spindle speed, both the surface SRMSD Sq and the characteristic fractal dimension (CFD) DC of the milling surface exhibit the same decline trends. Combined with the observation results of the machined surface, this implies smaller values of DC correspond to more regular microtextures. To further examine the morphology of the machined surface and verify the above inference, the contour curve of the workpiece surface was obtained with the rotational speeds of 594 and 4776 rpm. As shown in Fig. 4, at the spindle speed of 594 rpm, the contour curve has large fluctuation, and the height of the peak-to-valley can reach 14 μm. The contour curve shows alternative rising and falling trends. When the spindle
speed was raised to 4776 rpm, the fluctuation of the contour curve was significantly reduced, and the peak-to-valley height was about 4 μm. This, the curve became more stable, which further proved that the smaller the characteristic fractal dimension, the more regular the microtexture.
Fig. 4 Contour curve after machining at different speeds
4.2 Processing results at different vibration amplitudes To investigate how the microtexture of the machined surface and the characteristic fractal dimension change at different ultrasonic amplitudes, tests described as 6-11 in Table 1 were carried out.
(a)
(c)
(b)
(d)
(e)
(f)
Fig. 5. Micromorphology of Ti6Al4V subjected to UVAM with different amplitudes: 0 (a), 1 μm (b), 2 μm (c), 3 μm (d), 4 μm (e) and 5 μm (f)
It can be seen in Fig. 5 that in conventional milling, the milling surface has noticeable tool marks, and the surface topography is disorderly. With an increase in the ultrasonic vibration amplitude, the surface microtexture gradually appears. When the amplitude is 2 μm, the microtexture of the surface has the best regularity, as shown in Fig. 5c, the "rib-like" microtexture distribution is relatively uniform. When the amplitude is increased to 3 μm, the regularity of the microtexture of the processing surface is reduced. When the amplitude reaches 4 μm, the regularity of the microtexture is further reduced, and the overall shape of the surface is a ripple, and there are residual burrs. With a further amplitude increase to 5 μm, as shown in Fig. 5f, the degree of the rippled surface is further increased, and burrs get more pronounced. It can be seen from the observation that as the amplitude increases, the regularity of the microtexture of the ultrasonic milling surface first rises and then drops. The surface SRMSD, Sq, and CFD, DC, were calculated and depicted in Fig. 6. 1.50
Sq DC
3.0
1.45 1.40
2.4
CFD DC
CRMSD Sq
2.7
2.1
1.35
1.8
1.30
1.5
1.25
1.2 0
1
2
3
Amplitude(μm)
4
5
1.20
Fig.6 Milling results at different amplitudes
It can be seen from the results in Fig. 6 that both SRMSD and CFD values first decrease with the UVAM amplitude and then gradually increase. This trend is opposite to that of the microtexture regularity. This confirms the earlier finding: the smaller the fractal dimension of the feature, the more uniform the surface microtexture.
Therefore, the regularity of the UVAM-induced microtexture is controlled by the vibration amplitude. When the amplitude is 2 μm, the surface morphology has the best regularity and the most regular shape. When the amplitude is 5 μm, the regularity of the microtexture is significantly broken due to the influence of residual burrs, because the microscopic height of the surface profile gradually increases with the amplitude [24]. Therefore, in the ultrasonic end milling, small-amplitude machining can achieve good processing results. As shown in Fig. 7, the cutting force under different amplitude machining conditions was obtained with Kistler9257B dynamometer, and the sampling frequency was 100 kHz. 60 A=2 μm
A=5 μm
40
40
cutting force (N)
cutting force (N)
50
50 A=0 μm
30 20 10 0 -10 -20
3.8550 3.8555 3.8560 3.8565 3.8570 3.8575
time (s)
30 20 10 0
0
1
2
3
4
5
Amplitude (μm)
(a)
(b) Fig. 7 Cutting forces at different amplitudes
It is seen in Fig. 7a that the amplitude is 0 μm, that is, during conventional machining, the cutting force changes continuously in a sinusoidal direction due to the action of the cutting edge. When the amplitude is 2 μm, the cutting force still changes in a sinusoidal trend, but the peak value decreases, and the cutting force is no longer continuously increased or decreased, and there is a wave phenomenon. Due to the application of ultrasonic vibration, the tool tip and the workpiece to continuously generate impact and separation, which causes the cutting force to abruptly change and does not change continuously. When the amplitude is 5 μm, the tendency of the cutting force to change in a sinusoidal tendency is not obvious and the peak value is further decreased, The force does not change continuously and the value of the instantaneous change in force is obvious. From the results, it can been seen that the larger the amplitude, the better the separation of the tool and the material. The longer the separation time, the smaller the cutting force which is verified from Fig. 7b. However, when the amplitude is too large, the fluctuation of the cutting force increases, which is not conducive to the processed surface. The microtexture formed on the machined surface is broken at large amplitudes, which is consistent with the processing results. To compare the processing results at different amplitudes, the contour curves of workpieces at amplitudes of 0, 2, and 5 μm were obtained. It can be seen in Fig. 8 that the contour curve of the conventional machined surface has
no regularity, the curve is messy, and the wave peaks and trough values differ significantly at different locations. When the amplitude is 2 μm, the contour curve has less fluctuation, the heights of the peaks and troughs at different positions are equal, and the position distribution of the peaks and troughs is relatively uniform, indicating that the microtexture is evenly distributed. When the amplitude is 5 μm, the peak-to-valley height difference of the surface topography is significantly increased to about 16 μm, and the profile height values exhibit multiple rises and drops.
Fig. 8 Contour curves after conventional machining (A=0) and UVAM at different amplitudes (2 and 5 μm).
For further analysis, the three-dimensional topography of the workpiece is obtained by using a white light interferometer. It can be seen from Fig. 9 that the surface of the workpiece has a distinct wave shape. The reason is that the axial separation distance between the tool and the workpiece is too large when the amplitude is large so that the cut material cannot be removed entirely, thereby leaving residual barb-shaped formations. This also increases the height of the contour of the surface topography, and the regularity of the contour curve becomes less apparent.
Fig. 9 3D topography of the milled test piece
The above experimental results prove that the tool speed and axial amplitude have a significant influence on the surface topography, as well as allow one to calculate the characteristic fractal dimension of the workpiece surface
under different processing conditions. They also strongly indicate that smaller characteristic fractal dimensions of the surface correspond to more regular surface microtexture, which implies that it is effective and feasible to use fractal dimension to characterize the surface microtexture regularity. 4.3 Tribological tests Tribological tests of workpieces were carried out using the universal vertical pin-on-disc tribometer (with a dry friction pair composed of a pin and a disc). The friction disc was the workpiece after UVAM. The material of the friction pin was 40 Cr and the size was Ф5 mm×h15 mm. The axial pressure was set to 10 N, the feed speed of the friction pin was 10 mm/s, and the experimental time was set at 900 s. There is an initial running-in phase when the material is rubbed by “squashing” down the height of the highest asperities and increasing the number of asperities in contact. The smoothing mechanism of surfaces during running-in involves the wear of the surface profile peaks and filling of the surface valleys by wear debris [25]. The time of the running-in phase and the friction coefficient under the stable friction conditions have a substantial impact on the tribological and load-carrying characteristics of the material surfaces. The tribological tests were carried out on the specimens used for the conventional milling and UVAM. The respective evolutions of the friction coefficient with time are depicted in Fig. 10. It can be seen in Fig. 10 that after the application of the axial ultrasonic vibration with an amplitude of 2 μm, the friction coefficient of the workpiece sharply increased during the running-in phase, and the stable friction phase could be reached in a shorter time, so
Coefficient of friction
the running-in phase time was reduced, as compared to the conventionally milled specimens.
0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.6 0.5 0.4 0.3 0.2 0.1 0.0
A=0 μm 0
200
400
600
800
time(s)
A=2 μm 0
200
400
600
800
time(s) Fig. 10 Evolution of friction coefficient with and without ultrasonic vibration
To further study the tribological characteristics of the workpiece under different processing conditions, the tribological tests were also carried out on the UVAM specimens processed at different rotation speeds and vibration
amplitudes. The running-in time of the test piece and the average friction coefficient in the steady state were obtained, as shown in Figs. 11 and 12. 500
Coefficient of friction Running-in time
0.49
450
0.48 0.47
400
0.46
350
0.45
300
0.44
250
0.43 0.42
Running-in time(s)
Coefficient of friction
0.50
200
0.41
0
1
2
3
4
5
Amplitude(μm) Fig. 11 Surface parameters for different amplitudes.
Coefficient of friction
Coefficient of friction 260 Running-in time
0.51 0.50
240
0.49
220
0.48 0.47
200
0.46
180
0.45
160
0.44
140
0.43 0
1000
2000
3000
4000
5000
Running-in time(s)
280
0.52
120
Spindle speed(rpm) Fig. 12. Surface parameters for various speeds
It is seen in Figs. 11 and 12 that there is no significant correlation between the friction coefficient, axial amplitude, and spindle rotation speed. The running-in time decreases first with the vibration amplitude, then gradually increases, and as the spindle speed increases, the running-in time is steadily reduced. Noteworthy is that the variation of the running-in time is very similar to that of the characteristic fractal dimension. 4.4 Relationship between characteristic fractal dimension and running-in time To further analyze the correlation between running-in time and characteristic fractal dimension, the relationship between characteristic fractal dimension and running-in time with amplitude and spindle speed is investigated. As seen in Figs. 13 and 14, the characteristic fractal dimension and running-in time exhibit the same variation trend when the amplitude and the spindle speed are changed. The characteristic fractal dimension curve and the runningin time curve are consistent.
500
Running-in time DC
1.45
450
CFD DC
400 1.40
350
1.35
300
1.30
250
Running-in time(s)
1.50
200 1.25
0
1
2
3
Amplitude(μm)
4
5
Fig. 13 Surface properties (CFD, DC) and running-in time values at different UVAM amplitudes
CFD DC
1.2
260 240 220
1.0
200
0.8
180 160
0.6
Run-in time(s)
Running-in time DC
1.4
140
0.4 0
1000
2000
3000
4000
Spindle speed(rpm)
5000
120
Fig. 14 Surface properties (CFD, DC) and running-in time values at different spindle rotation speeds
As shown in Fig. 15, the running-in time is exponentially increased with the characteristic fractal dimension. Therefore, it can be speculated that the change of the characteristic fractal dimension is the fundamental reason forchanging the running-in time. That is to say, the more regular the surface microtexture is, the smaller the characteristic fractal dimension is, and eventually, the stable friction phase can be reached in a shorter time.
Running-in time(s)
450 400 350 300 250 200 150 100 0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
CFD DC Fig. 15 Relationship between fractal dimension and running-in time
5. Conclusions Based on the fractal theory, the surface microtexture regularity of ultrasonic vibration assisted milling (UVAM) of Ti6Al4V was studied. The experimental investigation was carried out, and the following conclusions were obtained. 1. Compared with conventional machining, UVAM can achieve a particular shape of the surface microtexture. An increase in the spindle rotation speed at small vibration amplitudes is shown to increase the microtexture regularity and produce the fish scale-type grid. Under constant spindle speeds, the axial vibration amplitude has a significant influence on the surface micromorphology. If the amplitude is too large, it is not conducive to the formation of a regular surface microtexture, and residual burrs will be formed. The appropriate amplitude value should be selected during UVAM processing. 2. The fractal theory is used in the calculation of the characteristic fractal dimension of the machined surface at different spindle rotation speeds and vibration amplitudes. The higher the spindle speed, the smaller the characteristic fractal dimension of the processed surface. As the amplitude increases, the characteristic fractal dimension first drops and then rises. 3. The lower the fractal dimension of the ultrasonic milling surface, the more regular the surface microtexture. The performed pin-on-disc tribological tests show that smaller characteristic fractal dimension values correspond to shorter running-in times. In actual processing, the running-in time reduction can be achieved by increasing the spindle speed during end milling or by selecting a moderate vibration amplitude.
Declaration of interest The authors declare that no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Acknowledgements This work is supported by the National Natural Science Foundation of China through Grants No.51475148, U1604255.
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Highlights 1. A new method for characterizing surface microtexture has been proposed. 2. The morphology of the machined surface under different spindle speeds and amplitudes were observed. 3. The relationship between characteristic fractal dimension and the surface microtexture regularity was obtained. 4. Effects of characteristic fractal dimension on running-in time were reported.
S0041-624X(19)30711-5 https://doi.org/10.1016/j.ultras.2019.106052 ULTRAS 106052
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Ultrasonics
Received Date: Revised Date: Accepted Date:
25 March 2019 15 September 2019 21 October 2019
Please cite this article as: B. Zhao, P. Li, C. Zhao, X. Wang, Fractal characterization of surface microtexture of Ti6Al4V subjected to ultrasonic vibration assisted milling, Ultrasonics (2019), doi: https://doi.org/10.1016/ j.ultras.2019.106052
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Fractal characterization of surface microtexture of Ti6Al4V subjected to ultrasonic vibration assisted milling Bo Zhao*, Pengtao Li, Chongyang Zhao, Xiaobo Wang School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo, Henan, China Abstract: The high-frequency tool vibration occurring during ultrasonic vibration cutting results in a formation of unique micromorphology of the machined surface. Different microtextures are known to have a substantial effect on the workpiece service performance. In this study, an attempt is made to assess this effect quantitatively for a more accurate characterization of the processed surface. The dependence between the contour root mean square deviation and fractal dimension is derived via the fractal theory. The concept of characteristic fractal dimension is proposed and successfully applied to Ti6Al4V surfaces subjected to ultrasonic vibration assisted milling (UVAM) with various spindle rotation speeds and vibration amplitudes. The experimental results obtained strongly indicate that smaller characteristic fractal dimensions correspond to more regular surface microtextures and contour curves, which proves the validity of the characteristic fractal dimension representation. Besides, the lower the characteristic fractal dimension of the surface, the shorter the time to reach the stable friction phase during dry friction.
Keywords: Ultrasonic vibration assisted milling (UVAM); Surface characterization method; Characteristic fractal dimension; Friction and wear
*Corresponding author: Bo Zhao, School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo 454000, China, Email: [email protected]
1. Introduction Ultrasonic vibration processing is frequently used in combination with such traditional machining methods as turning, grinding, milling, etc., in order to reduce the cutting force and heat, enhance the tool life, and optimize the chip breaking process [1]. The application of high-frequency vibrations to the machining tool or workpiece changes the cutting mechanism of conventional machining and also results in the formation of a complicated and regularly arranged microtexture of the processed surfaces [2]. Thus, Gao et al. [3] reported that low-frequency ripples appear on the machined surface of aluminum alloy workpieces in ultrasonic vibration turning due to insufficient rigidity of the acoustic system and the improper setting height of the tool tip. The longitudinal stripes mark the feed trace of the tool, while smaller transverse marks are due to the tool vibration. The machined surface reflects rainbow-like streaks. Compared to machined surfaces generated by conventional milling, ultrasonic vibration-assisted milling results in more uniform and finer surface structures [4]. Tao et al. [5-6] established a kinematics model of ultrasonic vibration assisted milling (UVAM) and experimentally proved that the feature curves of the squamous surface could be regarded as the same type of function curve with tool tip trajectories. Based on the machining dynamics, Cheng et al [7-8] predicted the cutting force of two-dimensional vibration-assisted micro-end milling (2D VAMEM) and established the surface topography model through the tool tip trajectory. The model can be used to optimize processing parameters, and the validity of the model is experimentally verified. Bai et al. [9] revealed a similarity between the UVAM surface and typical biological surface topography and proved that UVAM could be applied in the field of bionics for biomimetic purposes. Ma et al. [10] reported that the surface morphology of a titanium alloy after UVAM has a specific regular arrangement of microtexture, which could improve the surface wear resistance. Other studies have also shown that surface microtextures with a particular regular arrangement strongly improve the tribological characteristics of some materials [11-14]. However, to the best of the authors’ knowledge, the main factors controlling the effect of different morphologies on the material friction and wear properties were not quantitatively assessed yet. The surface topography of workpieces refers to various residual heights, textures, and streaks that remain on the workpiece surfaces after their processing [15]. It is generally expressed by roughness, waviness, shape error, spectrum, etc. However, any conventional quantitative description of the rough surface changes with the measurement scale and cannot represent the fundamental characteristics of the surface topography. In this respect, quite promising is the fractal theory that is based on the fractal dimension perspectives and mathematical methods. Being scale-independent, fractal parameters can be used to characterize the surface topography without being affected by the measurement length [16]. Miao et al. [17] reported that higher fractal dimensions correspond to more
complex shapes and more opulent microstructural details. Wang et al. [18] used fractal analysis method to investigate the wear behavior of resin-bonded diamond wheel in Elliptical Ultrasonic Assisted Grinding (EUAG) of monocrystal sapphire, and a series of experiments on EUAG and conventional grinding (CG) are performed. The results show that the fractal dimension of grinding wheel topography is highly correlated to the wear behavior. Gan and Huang [19] applied the fractal theory to the study of the milling surface contour and proved that fractal parameters could quite accurately reflect the fine structure of the surface contour. In summary, the ultrasonic-assisted processing and UVAM, in particular, results in the formation of a certain regular microtexture of the processed surface. However, its degree of regularity has not been adequately described, and the processing results cannot be effectively compared. In this study, the concept of the characteristic fractal dimension is proposed based on the fractal theory. The regularity of the morphology of the ultrasonic milling surface is defined by the characteristic fractal dimension. The Ti6Al4V was selected for the UVAM processing, given its broad application in the aerospace, energy, and biomedical industries [20]. To study the effect of microtextures with different fractal properties on he tribological properties of Ti6Al4V, the respective dry friction tribotests were conducted. Nomenclature l The scan length S(l) The contour root mean square height c The scale factor D The fractal dimension k The line slope Rq The contour root mean square roughness L The measured length Z(x) The surface contour height function ωm The measurement resolution ωs The sample length G The characteristic length γ The modulus of spatial frequency Sq The surface root mean square deviation DC The characteristic fractal dimension fz The feed per tooth ap The cut depth n The spindle rotation speed A The ultrasonic amplitude f The ultrasonic frequency
2. Characteristic fractal dimension of the machined surface
At present, the surface fractal dimensions are assessed using various methods, including the box-counting, power spectrum, structure-function, and variation ones. In this study, the root mean square method (RMSM) is used, due to its known advantages of simple calculation, clear physical meaning, strong surface adaptability, wide zoom area, and good representation effect [21]. The standard procedure for measuring the fractal dimension via RMSM is as follows [22]. Taking the scan length l as the measurement scale and the contour root mean square height S(l) in the scale region as the measure, the following relationship between them is used: S (l ) c l 2 D
(1)
where c is the scale factor and D is the fractal dimension. Equation (1) is also referred to as the measurement standard of multi-scale measurement. Taking logarithm of both parts of Eq. (1), it can be reduced to the following form: log S (l ) log(c) (2 D) log(l )
(2)
Equation (2) implies that the ideal fractal curve exhibits a linear relationship between the measure and the scale in logarithmic coordinates, while its fractal dimension D is negatively proportional to the line slope k, i.e., D=2 - k. However, when RMSM is used, it is necessary to select different measurement scales to obtain various measures, perform the linear regression analysis for the logarithm of the results and, finally, get the slope and fractal dimension of the line segment. When this method is used, it is necessary to measure different scale ranges, which makes the experiment cumbersome and hinders data processing. To simplify the cumbersome steps, the fractal dimension is assessed via the contour root mean square roughness Rq [23]. L
Rq 1 L Z 2 ( x)dx 0
(3)
In Eq. (3), L is the measured length, Z(x)is the surface contour height function. On the other hand, Rq 2 E[ Z 2 ( x)]
(4)
where S
E[ Z 2 ( x)] S ( )d m
G 2( D 1) 1 1 1 42 D 42 D 2 ln 4 2 D s m
(5)
In Eq. (5), ωs is the sample length, ωm is the measurement resolution, and G is the characteristic length, γ is the modulus of spatial frequency. The relationship between Rq and D can be obtained:
Rq
12
G D 1
2 ln(4 2 D)1 2
1 1 42 D 42 D m s
(6)
Since ωs>>ωm, Eq. (6) can be reduced to: Rq
G D 1
(7)
2 ln(4 2 D)1 2 s 2 D
It can be seen from Eq. (7) that the relationship between D and Rq is further simplified: Rq is obtained from a single line profile, while the surface root mean square deviation (SRMSD) Sq reflects the surface topography. To further characterize the machined surface, the concept of characteristic fractal dimension is proposed. A unity value of the characteristic length is always taken, ωs is defined as the sample length, and the relationship between the characteristic fractal dimension (DC) and SRMSD (Sq) is obtained as follows: Sq
1
2 ln(4 2 DC )1 2 s 2 D
(8)
C
3. Experimental setup and trials The experimental platform was built on the VMC850E three-axis vertical machining center. The UVAM experimental setup is depicted in Fig. 1. After the installation, the Ti6Al4V end-milling experiment was carried out. A four-blade spiral carbide milling cutter (8×20×60, 4T, SF20, HRC58) was used in the test. The chemical composition and thermo-mechanical properties of Ti6Al4V are given in Tables 1 and 2, and the size of the workpiece was Φ38 mm×Ф54 mm×h13 mm.
Fig. 1 The UVAM experimental setup
Table 1 Chemical composition of Ti6Al4V (wt%) Ti-Al-4V
Al
V
Fe
O
C
N
H
Si
Balance
6.35
4.1
0.25
0.18
0.06
0.04
0.011
<0.01
Table 2 Thermo-mechanical properties of Ti6Al4V Properties
Value
Density (kg/m3)
4429
Elastic modulus (GPa)
114
Hardness (HV)
340.6
Poisson’s ratio
0.33
Yield strength (MPa)
835
Tensile strength (MPa)
905
Thermal conductivity (W/mK)
6.7
Melting temperature (°C)
1667
The wireless transmission system transmitted energy of ultrasonic generator to the transducer, and the transducer vibrated at a high frequency, but the amplitude was small. The horn amplified the amplitude and transmitted the vibration to the tool. Different surface microtextures were obtained by varying the spindle speed and ultrasonic amplitude. The experimental scheme is shown in Table 3. Table 3 Experimental scheme Test
Spindle rotation
Amplitude
Frequency
number
speed n/(rpm)
A/(μm)
f/(kHz)
1
594
2
35.63
2
1194
2
35.63
3
2388
2
35.63
4
3507
2
35.63
5
4776
2
35.63
6
1194
0
0
7
1194
1
35.68
8
1194
2
35.63
9
1194
3
35.60
10
1194
4
35.56
11
1194
5
35.53
In all tests, the feed per tooth fz =15 μm and the cut depth ap =0.3 mm were used. The surface topography of the workpiece was examined via a VHX-2000 ultra-depth microscope. The contour curve of the workpiece and the surface root mean square deviation (SRMSD) Sq of the surface were measured by a non-contact Talysurf-CCI6000 white light interference surface profiler. The cutting force was obtained using a Kistler-9257B dynamometer.
4. Results, analysis and discussion 4.1 Processing results at different spindle speeds It can be seen from the measurement result depicted in Fig. 2 that at the amplitude A= 2 μm, higher spindle speeds corresponded to more pronounced microtextures of the milling surface. When the speed was 594 rpm, the surface morphology was not uniform and plow-like scratches were noticeable. However, as shown in Fig. 2a, the machined surface had a "ribbed" microtexture under ultrasonic vibration conditions. When the spindle rotation speed reached 1194 rpm, the surface topography was mainly uniform. With the continued speed increase, the surface became more texturized: at a spindle speed of 4776 rpm, an evenly arranged fish scale-like microtexture was observed.
（a）
(b)
(c)
(d)
(e)
Fig.2 Micromorphology of Ti6Al4V workpieces milled at different spindle rotation speeds: (a) 594 rpm; (b) 1194 rpm;(c) 2388 rpm; (d) 3507 rpm; (e) 4776 rpm
The above experimental results strongly indicate that in case of low-amplitude UVAM of Ti6Al4V, with an increase in the spindle speed, the machined surface texture gets more regular and gradually changes from a "riblike" pattern to a "fish scale" one. With the surface topography variation, the surface characterization parameters also vary. The surface root mean square deviation (SRMSD) Sq was obtained, and the characteristic fractal dimension (CFD) DC was calculated for various spindle rotation speeds (Fig. 3).
Sq DC
SRMSD Sq
1.4
1.4 1.2 1.0
1.2
0.8 1.0
0.6
0.8 0.6
CFD DC
1.6
0.4 0
1000
2000
3000
4000
5000
0.2
Spindle speed(rpm) Fig. 3 Milling results at different speeds
As seen in Fig. 3, with an increase in the spindle speed, both the surface SRMSD Sq and the characteristic fractal dimension (CFD) DC of the milling surface exhibit the same decline trends. Combined with the observation results of the machined surface, this implies smaller values of DC correspond to more regular microtextures. To further examine the morphology of the machined surface and verify the above inference, the contour curve of the workpiece surface was obtained with the rotational speeds of 594 and 4776 rpm. As shown in Fig. 4, at the spindle speed of 594 rpm, the contour curve has large fluctuation, and the height of the peak-to-valley can reach 14 μm. The contour curve shows alternative rising and falling trends. When the spindle
speed was raised to 4776 rpm, the fluctuation of the contour curve was significantly reduced, and the peak-to-valley height was about 4 μm. This, the curve became more stable, which further proved that the smaller the characteristic fractal dimension, the more regular the microtexture.
Fig. 4 Contour curve after machining at different speeds
4.2 Processing results at different vibration amplitudes To investigate how the microtexture of the machined surface and the characteristic fractal dimension change at different ultrasonic amplitudes, tests described as 6-11 in Table 1 were carried out.
(a)
(c)
(b)
(d)
(e)
(f)
Fig. 5. Micromorphology of Ti6Al4V subjected to UVAM with different amplitudes: 0 (a), 1 μm (b), 2 μm (c), 3 μm (d), 4 μm (e) and 5 μm (f)
It can be seen in Fig. 5 that in conventional milling, the milling surface has noticeable tool marks, and the surface topography is disorderly. With an increase in the ultrasonic vibration amplitude, the surface microtexture gradually appears. When the amplitude is 2 μm, the microtexture of the surface has the best regularity, as shown in Fig. 5c, the "rib-like" microtexture distribution is relatively uniform. When the amplitude is increased to 3 μm, the regularity of the microtexture of the processing surface is reduced. When the amplitude reaches 4 μm, the regularity of the microtexture is further reduced, and the overall shape of the surface is a ripple, and there are residual burrs. With a further amplitude increase to 5 μm, as shown in Fig. 5f, the degree of the rippled surface is further increased, and burrs get more pronounced. It can be seen from the observation that as the amplitude increases, the regularity of the microtexture of the ultrasonic milling surface first rises and then drops. The surface SRMSD, Sq, and CFD, DC, were calculated and depicted in Fig. 6. 1.50
Sq DC
3.0
1.45 1.40
2.4
CFD DC
CRMSD Sq
2.7
2.1
1.35
1.8
1.30
1.5
1.25
1.2 0
1
2
3
Amplitude(μm)
4
5
1.20
Fig.6 Milling results at different amplitudes
It can be seen from the results in Fig. 6 that both SRMSD and CFD values first decrease with the UVAM amplitude and then gradually increase. This trend is opposite to that of the microtexture regularity. This confirms the earlier finding: the smaller the fractal dimension of the feature, the more uniform the surface microtexture.
Therefore, the regularity of the UVAM-induced microtexture is controlled by the vibration amplitude. When the amplitude is 2 μm, the surface morphology has the best regularity and the most regular shape. When the amplitude is 5 μm, the regularity of the microtexture is significantly broken due to the influence of residual burrs, because the microscopic height of the surface profile gradually increases with the amplitude [24]. Therefore, in the ultrasonic end milling, small-amplitude machining can achieve good processing results. As shown in Fig. 7, the cutting force under different amplitude machining conditions was obtained with Kistler9257B dynamometer, and the sampling frequency was 100 kHz. 60 A=2 μm
A=5 μm
40
40
cutting force (N)
cutting force (N)
50
50 A=0 μm
30 20 10 0 -10 -20
3.8550 3.8555 3.8560 3.8565 3.8570 3.8575
time (s)
30 20 10 0
0
1
2
3
4
5
Amplitude (μm)
(a)
(b) Fig. 7 Cutting forces at different amplitudes
It is seen in Fig. 7a that the amplitude is 0 μm, that is, during conventional machining, the cutting force changes continuously in a sinusoidal direction due to the action of the cutting edge. When the amplitude is 2 μm, the cutting force still changes in a sinusoidal trend, but the peak value decreases, and the cutting force is no longer continuously increased or decreased, and there is a wave phenomenon. Due to the application of ultrasonic vibration, the tool tip and the workpiece to continuously generate impact and separation, which causes the cutting force to abruptly change and does not change continuously. When the amplitude is 5 μm, the tendency of the cutting force to change in a sinusoidal tendency is not obvious and the peak value is further decreased, The force does not change continuously and the value of the instantaneous change in force is obvious. From the results, it can been seen that the larger the amplitude, the better the separation of the tool and the material. The longer the separation time, the smaller the cutting force which is verified from Fig. 7b. However, when the amplitude is too large, the fluctuation of the cutting force increases, which is not conducive to the processed surface. The microtexture formed on the machined surface is broken at large amplitudes, which is consistent with the processing results. To compare the processing results at different amplitudes, the contour curves of workpieces at amplitudes of 0, 2, and 5 μm were obtained. It can be seen in Fig. 8 that the contour curve of the conventional machined surface has
no regularity, the curve is messy, and the wave peaks and trough values differ significantly at different locations. When the amplitude is 2 μm, the contour curve has less fluctuation, the heights of the peaks and troughs at different positions are equal, and the position distribution of the peaks and troughs is relatively uniform, indicating that the microtexture is evenly distributed. When the amplitude is 5 μm, the peak-to-valley height difference of the surface topography is significantly increased to about 16 μm, and the profile height values exhibit multiple rises and drops.
Fig. 8 Contour curves after conventional machining (A=0) and UVAM at different amplitudes (2 and 5 μm).
For further analysis, the three-dimensional topography of the workpiece is obtained by using a white light interferometer. It can be seen from Fig. 9 that the surface of the workpiece has a distinct wave shape. The reason is that the axial separation distance between the tool and the workpiece is too large when the amplitude is large so that the cut material cannot be removed entirely, thereby leaving residual barb-shaped formations. This also increases the height of the contour of the surface topography, and the regularity of the contour curve becomes less apparent.
Fig. 9 3D topography of the milled test piece
The above experimental results prove that the tool speed and axial amplitude have a significant influence on the surface topography, as well as allow one to calculate the characteristic fractal dimension of the workpiece surface
under different processing conditions. They also strongly indicate that smaller characteristic fractal dimensions of the surface correspond to more regular surface microtexture, which implies that it is effective and feasible to use fractal dimension to characterize the surface microtexture regularity. 4.3 Tribological tests Tribological tests of workpieces were carried out using the universal vertical pin-on-disc tribometer (with a dry friction pair composed of a pin and a disc). The friction disc was the workpiece after UVAM. The material of the friction pin was 40 Cr and the size was Ф5 mm×h15 mm. The axial pressure was set to 10 N, the feed speed of the friction pin was 10 mm/s, and the experimental time was set at 900 s. There is an initial running-in phase when the material is rubbed by “squashing” down the height of the highest asperities and increasing the number of asperities in contact. The smoothing mechanism of surfaces during running-in involves the wear of the surface profile peaks and filling of the surface valleys by wear debris [25]. The time of the running-in phase and the friction coefficient under the stable friction conditions have a substantial impact on the tribological and load-carrying characteristics of the material surfaces. The tribological tests were carried out on the specimens used for the conventional milling and UVAM. The respective evolutions of the friction coefficient with time are depicted in Fig. 10. It can be seen in Fig. 10 that after the application of the axial ultrasonic vibration with an amplitude of 2 μm, the friction coefficient of the workpiece sharply increased during the running-in phase, and the stable friction phase could be reached in a shorter time, so
Coefficient of friction
the running-in phase time was reduced, as compared to the conventionally milled specimens.
0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.6 0.5 0.4 0.3 0.2 0.1 0.0
A=0 μm 0
200
400
600
800
time(s)
A=2 μm 0
200
400
600
800
time(s) Fig. 10 Evolution of friction coefficient with and without ultrasonic vibration
To further study the tribological characteristics of the workpiece under different processing conditions, the tribological tests were also carried out on the UVAM specimens processed at different rotation speeds and vibration
amplitudes. The running-in time of the test piece and the average friction coefficient in the steady state were obtained, as shown in Figs. 11 and 12. 500
Coefficient of friction Running-in time
0.49
450
0.48 0.47
400
0.46
350
0.45
300
0.44
250
0.43 0.42
Running-in time(s)
Coefficient of friction
0.50
200
0.41
0
1
2
3
4
5
Amplitude(μm) Fig. 11 Surface parameters for different amplitudes.
Coefficient of friction
Coefficient of friction 260 Running-in time
0.51 0.50
240
0.49
220
0.48 0.47
200
0.46
180
0.45
160
0.44
140
0.43 0
1000
2000
3000
4000
5000
Running-in time(s)
280
0.52
120
Spindle speed(rpm) Fig. 12. Surface parameters for various speeds
It is seen in Figs. 11 and 12 that there is no significant correlation between the friction coefficient, axial amplitude, and spindle rotation speed. The running-in time decreases first with the vibration amplitude, then gradually increases, and as the spindle speed increases, the running-in time is steadily reduced. Noteworthy is that the variation of the running-in time is very similar to that of the characteristic fractal dimension. 4.4 Relationship between characteristic fractal dimension and running-in time To further analyze the correlation between running-in time and characteristic fractal dimension, the relationship between characteristic fractal dimension and running-in time with amplitude and spindle speed is investigated. As seen in Figs. 13 and 14, the characteristic fractal dimension and running-in time exhibit the same variation trend when the amplitude and the spindle speed are changed. The characteristic fractal dimension curve and the runningin time curve are consistent.
500
Running-in time DC
1.45
450
CFD DC
400 1.40
350
1.35
300
1.30
250
Running-in time(s)
1.50
200 1.25
0
1
2
3
Amplitude(μm)
4
5
Fig. 13 Surface properties (CFD, DC) and running-in time values at different UVAM amplitudes
CFD DC
1.2
260 240 220
1.0
200
0.8
180 160
0.6
Run-in time(s)
Running-in time DC
1.4
140
0.4 0
1000
2000
3000
4000
Spindle speed(rpm)
5000
120
Fig. 14 Surface properties (CFD, DC) and running-in time values at different spindle rotation speeds
As shown in Fig. 15, the running-in time is exponentially increased with the characteristic fractal dimension. Therefore, it can be speculated that the change of the characteristic fractal dimension is the fundamental reason forchanging the running-in time. That is to say, the more regular the surface microtexture is, the smaller the characteristic fractal dimension is, and eventually, the stable friction phase can be reached in a shorter time.
Running-in time(s)
450 400 350 300 250 200 150 100 0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
CFD DC Fig. 15 Relationship between fractal dimension and running-in time
5. Conclusions Based on the fractal theory, the surface microtexture regularity of ultrasonic vibration assisted milling (UVAM) of Ti6Al4V was studied. The experimental investigation was carried out, and the following conclusions were obtained. 1. Compared with conventional machining, UVAM can achieve a particular shape of the surface microtexture. An increase in the spindle rotation speed at small vibration amplitudes is shown to increase the microtexture regularity and produce the fish scale-type grid. Under constant spindle speeds, the axial vibration amplitude has a significant influence on the surface micromorphology. If the amplitude is too large, it is not conducive to the formation of a regular surface microtexture, and residual burrs will be formed. The appropriate amplitude value should be selected during UVAM processing. 2. The fractal theory is used in the calculation of the characteristic fractal dimension of the machined surface at different spindle rotation speeds and vibration amplitudes. The higher the spindle speed, the smaller the characteristic fractal dimension of the processed surface. As the amplitude increases, the characteristic fractal dimension first drops and then rises. 3. The lower the fractal dimension of the ultrasonic milling surface, the more regular the surface microtexture. The performed pin-on-disc tribological tests show that smaller characteristic fractal dimension values correspond to shorter running-in times. In actual processing, the running-in time reduction can be achieved by increasing the spindle speed during end milling or by selecting a moderate vibration amplitude.
Declaration of interest The authors declare that no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Acknowledgements This work is supported by the National Natural Science Foundation of China through Grants No.51475148, U1604255.
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Highlights 1. A new method for characterizing surface microtexture has been proposed. 2. The morphology of the machined surface under different spindle speeds and amplitudes were observed. 3. The relationship between characteristic fractal dimension and the surface microtexture regularity was obtained. 4. Effects of characteristic fractal dimension on running-in time were reported.