Analysis of local features of engineering ceramics grinding surface

Measurement xxx (xxxx) xxx

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Analysis of local features of engineering ceramics grinding surface Xiaohu Liang, Bin Lin ⇑, Xuelian Liu School of Mechanical Engineering, Tianjin University, Tianjin 300350, China

a r t i c l e

i n f o

Article history: Received 30 April 2019 Received in revised form 25 September 2019 Accepted 30 September 2019 Available online xxxx Keywords: Surface profile Grinding Deep valleys Wavelet Fractal

a b s t r a c t The power spectrum shows that the zirconia grinding surface has fractal feature, but the local features (deep valleys) cannot be described by fractal method. The deep valleys affect sealing and lubrication and can be applied to monitor the process and predict the performance of the workpiece. This paper will attempt to analyze the deep valleys. Based on the wavelet transform, the grinding surface profiles of steel and engineering ceramics are compared. It is demonstrated that the deep valleys are common local features of engineering ceramics grinding surface. Taking grinding surface and lapping surface of zirconia as examples, the distributions of deep valleys are analyzed. The surface profiles which are very close to the real ones in amplitude, spacing, asymmetry and bearing are simulated. The surface simulation experiments show that the distributions of deep valleys are accurate. The analysis steps and expression of deep valleys are summarized. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Engineering ceramics offer many desirable characteristics such as high temperature tolerance, wear and abrasive resistance, and corrosion resistance, and are widely used in industry and commerce [1]. However, due to the high hardness and brittleness, the machining of ceramics is difficult, and the grinding process is the only economically viable process that produces surfaces of high quality and geometric precision [2]. In order to obtain the desirable machining precision and surface quality, scholars have done a lot of work in optimizing machining parameters and improving lubrication systems [1–4]. There is an important relationship between surface topography and surface functions (such as friction, lubrication, bearing and wear) [5]. Reasonable analysis and characterization of surface topography can be used to predict surface functions and to guide processing to achieve a more desirable surface [6]. Studies show that many machined surfaces exhibit statistical self-similarity or self-affine characteristics, which can be analyzed and characterized by fractal theory. The characterization parameters of fractal theory are scale-independent and can effectively reflect complexity and irregularity of the surface [7]. It is widely used in surface research, such as estimation surface properties, characterization of microstructure, and establishment of surface model [8–12], especially the analysis and characterization of surface topography [13–18].

⇑ Corresponding author. E-mail address: [email protected] (B. Lin).

Whether the power spectrum of the surface profile is in a straight line in the log-log coordinate is an important method to judge the fractal features [19]. Fig. 1 shows the grinding surface profiles of steel and zirconia (in this paper, the surface profiles are measured by Form Talysurf i120 surface profiler, and the data are extracted by the Talymap Gold software), and Fig. 2 shows their power spectrum curves. It can be seen from the Fig. 2 that: the zirconia surface basically has the fractal features, while the steel surface exhibits obvious fractal features. Through observation, the main difference between the surface profiles is that the zirconia surface is asymmetrical due to the deep valleys features. The possible reason for this phenomenon is that the grinding process of metal materials is mainly plastic fracture under the effect of abrasive particles, while the removal of engineering ceramics is mainly brittle fracture, which causes central cracks during grinding and results in deep valleys. Deep valley is an important feature that has important influences on surface functions and cannot be ignored in surface analysis and characterization. For example, deep valleys can store lubricants and change the lubrication performance [20,21]; deep valleys may grow into cracks under pressure, resulting in failure [22,23]. Fractal method is suitable for describing surface topography as a whole, while local feature (deep valleys) need to be analyzed separately. There are many methods for surface topography measurement, such as mechanical probe, optical probe, interference microscopy, scanning probe microscopy and so on. Among them, the surface profiler has a large measuring range and high accuracy, which is a direct and effective method to obtain surface profile. This paper mainly analyzes the local features of the engineering ceramics

https://doi.org/10.1016/j.measurement.2019.107205 0263-2241/Ó 2019 Elsevier Ltd. All rights reserved.

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(a)Steel (metal)

Valley

(b) Zirconia (engineering ceramics) Fig. 1. Grinding surface profile obtained by profiler (a) Steel (metal) (b) Zirconia (engineering ceramics).

(a) Steel

(b) Zirconia

Fig. 2. Power spectrums of different materials surface profiles (a) Steel (b) Zirconia.

grinding surface based on the measurement data of the surface profiler. 2. Analysis method 2.1. Fundamental theory Wavelet transform was firstly used in signal analysis, especially for non-stationary signal. It was later introduced into the analysis of surface topography [24–30]. Discrete wavelet transform is the discretization of scale and the translation of basic wavelet. Binary wavelet is a commonly used discrete wavelet. In the binary wavelet transform, the form of the wavelet base function is [31]: j=2

Wj;k ðtÞ ¼ 2


 W 2j t  n

ð1Þ

where WðtÞ—wavelet function, t—time, and n—position. The corresponding wavelet transform is:

Wf ðj; kÞ ¼ 2j=2

Z

þ1

1


 f ðtÞW 2j t  n dt

ð2Þ

where fðtÞ is a square integrable function, denoted by f(t)2 L2 ðRÞ; W means conjugate, j ¼ 1; 2;    ; N In signal analysis, the frequency is equal to the reciprocal of time. Similarly, in surface topography analysis, the spatial frequency can be defined as the reciprocal of the length. That is, time t is replaced by length x in wavelet transform. Through the wavelet transform, it is possible to remove the main shape and only reconstruct the high frequency part of topography according to the cutoff wavelengths [25]. 2.2. Extraction of deep valleys The difference among the grinding surfaces of the steel and engineering ceramics can be further shown by measuring the surface profile along the texture (in general, the measurement direction is perpendicular to the texture direction). The resolution of the surface profiler used in this paper is 16 nmand the sampling interval of horizontal data is 0.125 lm, and the measuring speed is 0.1 mm=s. The roughness Ra of these samples is in the same level. The measurement results are shown in the Fig. 3. It can be seen from the figure: there are no deep valleys on the steel surface,

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(a) Steel

(b) Alumina

(c) Zirconia

(d) Silicon nitride Fig. 3. Grinding surface profiles of different materials (a) Steel (b) Alumina (c) Zirconia (d) Silicon nitride.

while the engineering ceramics surfaces have deep valleys of different depths. Due to the serious asymmetric distribution of deep valleys, the symmetry of the profile is affected. It is difficult to obtain the distribution by the profile perpendicular to the surface texture, especially when the texture is coarse. We assume that the deep valleys along the texture direction and perpendicular to the texture direction are basically the same, and analyze the deep valleys by the profile along the texture. We take zirconia grinding surface as an example. Through observation, it is found that the deep valleys in the figure are attached to a certain profile, and their distribution cannot be well analyzed based on the absolute depth. In order to facilitate the statistics of the width and depth of the deep valley, the wavelet decomposition and reconstruction are applied to remove the shape of the steel and zirconia surface profiles in Fig. 3. The results are shown in Fig. 4 (wavelet decomposition level is 11). It can be found that the asymmetry of zirconia surface profile is more obvious after wavelet decomposition and reconstruction, while the steel is still symmetrical. 2.3. Analysis of deep valleys The minimum points less than 0.6 lm are considered deep valleys (in order to avoid the normal profile being considered as a deep valley, the negative value of the average of 10 max profile

peak heights is taken as the depth threshold), and the width and depth of the deep valleys are all referenced to the ordinate 0.5 lm (According to the starting coordinates of the deep valleys). Fig. 5 shows the analysis results of the deep valleys distribution in Fig. 4(b). When the significance level is 0.05, the widths of the deep valleys accord with the normal distribution (see Fig. 5(a)). The relationship between the width and depth of the valley is shown in Fig. 5(b), and correlation coefficient is 0.63, the significance level is less than 0.01. In order to further analyze the relationship between width and depth of deep valleys, the depth of deep valleys is expanded by 10 times, and the angle between the line of each point and the zero point and the line y ¼ x is denoted by h, and is calculated respectively (see Fig. 6(a)). When the significance level is 0.05, the angle h obeys the normal distribution (see Fig. 6(b)). Five zirconia samples and five silicon nitride samples with the similar roughness Raare selected, and each sample is measured along the texture direction. The same conclusions as above can be drawn from the analysis of the deep valleys distribution (the depth of deep valleys of silicon nitride is expanded by 15 times). Lapping can further improve the surface quality. Fig. 7 shows the surface profiles of zirconia and silicon nitride that have been grinded and lapped. It can be seen from the figure that the surface profiles still show very obvious deep valley features, and the

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(a) Steel

(b) Zirconia Fig. 4. Surface profiles after removing the shape (a) Steel (b) Zirconia.

Fig. 5. Analysis results of the deep valleys distribution (a) Distribution of the width of deep valleys (b) Relationship between the width and depth.

(a) Relationship between the width and depth

(b) Distribution of angle

Fig. 6. Analysis of relationship between width and depth of deep valleys (a) Relationship between the width and depth (b) Distribution of angle h.

surface after lapping is easy to obtain the deep valleys distribution perpendicular to the texture. The zirconia surface is still taken as an example. Similar to the previous analysis, the effect of the main shape is first removed by the wavelet decomposition and reconstruction, and then the minimum points less than 0.15 lm are considered deep valleys, and the ordinate 0.05 lm is taken as a

reference to determine the depth and width of deep valleys. Fig. 8 shows the normal probability plot that can be used to judge whether the width of the deep valleys follows a normal distribution. The plot will be linear if the data are come from a normal distribution. It can be seen from the figure that the data points are not in a straight line, and there is an inflection point at the position of

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(a) Zirconia

(b) Silicon nitride Fig. 7. Grinding and lapping surface profile (a) Zirconia (b) Silicon nitride.

y ¼ x is calculated as above. The result is shown in the Fig. 9. The anglehalso follows the normal distribution when the significance level is 0.05. Five zirconia samples, and five silicon nitride samples with the roughness level Ra ¼ 0:03  0:06 lmare selected, and each sample is measured perpendicular to the texture. The same analysis results of deep valley distribution as above can be obtained. 3. Further analysis 3.1. Verification of the distributions

Fig. 8. Normal probability plot of the valley width in Fig. 7(a).

Fig. 9. Distribution of angle h of the valleys in Fig. 7(a).

3.5lm. Through verification, with 3.5lmas the boundary point, the data points on both sides are in accordance with the normal distribution when the significance level is 0.05. Next, the relationship between the width and depth of the deep valleys is analyzed. The depth of deep valleys is expanded by 30 times, and the angle h between the line of each point and the zero point and the line

The accuracy of the distribution of deep valleys can be verified by profile simulation experiments. The grinding surface profile of zirconia exhibits fractal features, meanwhile, the profile shows asymmetry due to the deep valleys. Therefore, we can regard the surface profile of zirconia as the superposition of fractal curve and deep valleys. Fig. 10(a), (b) show the simulation process of surface profile in Fig. 1(b). Between them, Fig. 10(a) is a Weierstrass-Mandelbrot (W-M) fractal curve with characteristic length scale A ¼ 3:3  109 m and fractal dimension D = 1.51, and Fig. 10(b) is a surface profile obtained by superimposing the deep valleys in the fractal curve and recalculating the mean line, and deep valleys are approximated by semi-ellipse. The widths of the deep valleys are generated randomly according to the width distribution and are accumulated until close to the total width. The depths are calculated according to the relationship between width and depth, and the deep valleys are randomly added into the height of the reference ordinate of the fractal curve. Table 1 shows the roughness parameters comparison between the real profile and the simulated one. We can see that the maximum deviation of the parameters is only 1.87%. Fig. 11(a) shows a comparison of material ratio curves between the real profile1 and the simulated profile1. It can be seen from the figure that the bearing properties of them are very close. In the same way the surface profile in Fig. 7 (a) was simulated. The process is shown in Fig. 10(c), (d) (the fractal curve with characteristic length scale A ¼ 1:14  109 mand fractal dimension D = 1.67). We can see that the maximum deviation of all the roughness parameters between real profile 2 and simulated profile 2 is 2.5% (see Table 1), and the deviation is small. Fig. 11(b) shows the material ratio curves of real profile 2 and simulated profile 2.

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(a) W-M curve of

(b) Simulated profile 1 of Fig. 1(b)

(c) W-M curve of

(d) Simulated profile 2 of Fig.7 (a) Fig. 10. Simulation process of surface profile (a) W-M curve of D = 1.51 (b) Simulated profile 1 of Fig. 1(b) (c) W-M curve of D = 1.67 (d) Simulated profile 2 of Fig. 7(a).

3.2. Analysis steps and expressions

Table 1 Comparison of calculated roughness values. Roughness parameter

Ra (lm)

Rsm (lm)

Rsk

Real profile 1 Simulated profile 1 Real profile 2 Simulated profile 2

0.597 0.601 0.045 0.044

42.8 43.6 21.6 21.2

0.629 0.632 0.601 0.616

We can see that the upper half of the simulated curve is down compared to the real one. This is because the high peaks (see Fig. 10(d)) of the real surface are removed after lapping. The highest 0.07% point in the simulated profile is removed and the material ratio curves are re-compared. The results are shown in Fig. 11 (c). The two curves almost coincide, indicating that the distribution of the simulated deep valleys is consistent with the real one. By comparing the amplitude, spacing, asymmetry and bearing, it is shown that the grinding profile of zirconia can be simulated effectively by the superposition of fractal curve and deep valleys, and the distribution of deep valleys is accurate.

The analysis steps of deep valleys can be summarized as follows: (1), remove the main shape of the surface profile using the wavelet decomposition and reconstruction; (2), select the reference coordinate, and try not to judge the normal profile as a deep valley; (3), count the number, depth, and width of deep valleys. Profile simulation experiments show that the simulated deep valleys can be used for surface analysis. In this paper, the deep valleys are approximated by semi-ellipse. The width of the deep valley corresponds to the long axis 2a, and the depth corresponds to the short half axisb. For the surface roughnessRagreater than 0.03 lm, we find that there is a relationship betweenaandbby a large number of measurements:

b ¼ k  a  tanð0:25p þ hÞ

ð3Þ

where k is a constant; h  Nð0; r3 Þ and 0:25p < h < 0:25p. A large number of measurement experiments show that the widths of the deep valleys meet different normal distributions on both sides of the boundary point c. Therefore, the expression of zðxÞ can be written as:

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(a)

Comparison between Fig. 1(b) and Fig. 10(b).

(b) Comparison between Fig. 7(a) and Fig. 10(d). (c)

Comparison between Fig. 7(a) and Fig.

10(d) with the highest 0.07% point removed Fig. 11. Comparison of material ratio curves (a) Comparison between Figs. 1(b) and 10(b) (b) Comparison between Figs. 7(a) and 10(d) (c) Comparison between Figs. 7(a) and 10(d) with the highest 0.07% point removed.

zðxÞ ¼ k  tan½0:25p þ h " # m1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X X a21  ðx  xm Þ2 þ a22  ðx  xn Þ2  m¼1

ð4Þ

n¼1

    where a1  N l1 ; r1 and 0 < a1  c=2; a2  N l2 ; r2 and a2 > c=2; m1 and n1 are the number of deep valleys; xm , xn are the abscissas of the random point. When the profile amplitude is large, the small deep valleys (0 < a1  c=2) can be ignored. 4. Conclusion The deep valleys are signature local profile features of engineering ceramics formed under brittle processing conditions, which have important effects on surface functions. Compared with plastic material, the deep valleys of engineering ceramics are more likely to expand into cracks, resulting in failure. Deep valleys also affect sealing and lubrication and can be applied to monitor the process and predict the performance of the workpiece. In addition, the analysis of the deep valleys is a supplement to the fractal method to characterize the engineering ceramics grinding surface. Fractal method can characterize one surface with only two parameters. This is a useful exploration for simplifying the characterization parameters and has been widely used. The fractal method mainly describes a surface as a whole, and the local features of engineering ceramics grinding surface cannot be reflected. The analysis of the deep valleys is a description of local features of the engineering ceramics grinding surface. In this paper, a method of using wavelet transform to analyze the deep valleys is proposed. It is found that the widths of deep valleys of zirconia grinding surface obey normal distribution, and there is a relationship between the width and depth of deep valleys, while the widths of deep valleys of zirconia lapping surface meet different normal distributions on both sides of a certain boundary point. In this paper, the zirconia surfaces are reconstructed by superposition of fractal curves and deep valleys. The results show that this method can obtain surfaces that are very similar to the original ones, indirectly prove the accuracy of the distribution of the deep valleys. The distribution of deep valleys can be used to predict the surface functions and improve processing. The expression of deep valleys is summarized, which can be used to analyze surface properties. As for the material ratio curve (see Fig. 11), its upper half is related to wear, and the lower half reflects the distribution of deep valleys. According to the change in the curve, we can determine the total width, widthdepth ratio and other information of the deep valleys. In this paper,

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