Modeling measurement and characterization method of sine surface roughness template

Abstract

The invention discloses a modeling measurement and characterization method for a sine surface roughness template, and belongs to the technical field of micro-nano geometric quantity measurement and test. According to the method, quantitative measurement and characterization are carried out on parameter indexes of the sine morphology roughness sample plate by utilizing a modeling measurement analysis method and combining an overall angle and a local angle. From the overall perspective, a measurement result of a total distortion parameter is obtained to represent the quality of a sine morphology roughness sample plate, and a measurement result of an amplitude parameter, a measurement result of a periodic parameter and an accurate value of the number of sampling points contained in each cyclic wave are obtained; locally distorted positioning information is obtained from a curve graph of a regression residual error sequence and a measurement sequence, and the roughness sample plate distortion degree is reduced. From a local angle, measurement results of the maximum value, the minimum value, the experimental standard deviation and the range of the single-cycle amplitude of the sine morphology roughness sample plate and measurement results of the maximum value, the minimum value, the experimental standard deviation and the range of the single-cycle period are obtained, and quantitative measurement and characterization are carried out on parameter indexes.

Description

Technical Field

[0001] The invention relates to a modeling measurement and characterization method for a sinusoidal surface roughness sample, and in particular to a measurement and characterization method for various index parameters of a roughness sample that changes in a sinusoidal law, and belongs to the technical field of micro-nano geometric quantity metrology and testing. Background Art

[0002] The peak-to-valley roughness of an uneven surface with a distance of less than 1 mm between two peaks or valleys is called surface roughness. Usually, two parameters are used to evaluate the height characteristics of surface roughness: (1) the arithmetic mean deviation of the profile is the arithmetic mean of the distance between the profile and the reference line; (2) the maximum height of the profile is the maximum drop between the profile peak and the profile valley.

[0003] The average width parameter of the contour unit is defined by the average value of the distance between adjacent peaks (valleys) of the contour within the sampling length, and is used to characterize the distance characteristics of the surface roughness.

[0004] The metrological calibration of the roughness measuring instrument requires the use of roughness standard samples with different parameter specifications. The surface microstructures of these roughness standard samples are usually manufactured to have morphological features that conform to certain rules. In terms of cross-section, there are rectangular pulse waveform grooves, triangular waveform grooves, and sinusoidal waveform grooves.

[0005] The core parameter is the height of the microstructure on the surface of the roughness standard sample, that is, the peak-to-peak value of the cross-sectional waveform, also known as the maximum height of the profile. In addition, people also hope that their microstructure morphology is uniform and consistent, and the peak height and wave width at different positions are uniform and stable. In other words, the cross-sectional waveform is uniform and stable, with low distortion.

[0006] For the three commonly used cross-sectional waveform morphologies mentioned above, it is generally recognized in the industry that the stability of the value, structural uniformity, and application effect of the sinusoidal roughness sample in the application are better than those of the rectangular roughness sample and the triangular roughness sample. Therefore, the sinusoidal roughness sample technology is the key to the metrological calibration of the roughness measuring instrument. People are scrambling to research and develop sinusoidal roughness samples, and this is also the case in my country. However, at present, the cross-sectional sinusoidal waveform distortion of the sinusoidal roughness samples in advanced and developed countries in the world can be better than 1%, while the cross-sectional sinusoidal waveform distortion of the sinusoidal roughness samples in my country is about 5%, and the technical level gap is very obvious. The main reason is that the parameter index measurement of the sinusoidal roughness sample is not fine and comprehensive enough, which makes it impossible for people to find out where the quality problem lies and what technical measures should be taken to solve it. Summary of the invention

[0007] In order to overcome the disadvantage of the large waveform distortion of the above-mentioned sinusoidal morphology roughness template, the purpose of the present invention is to provide a modeling measurement and characterization method for a sinusoidal surface roughness template. Based on the cross-sectional sinusoidal waveform sampling measurement curve sequence of the sinusoidal morphology roughness template, a modeling measurement and analysis method is used to give the cross-sectional sinusoidal waveform index parameters of the sinusoidal morphology roughness template in both overall and local ways, and various parameter indicators affecting the sinusoidal morphology roughness template are quantitatively measured and characterized.

[0008] The objective of the present invention is achieved through the following technical solutions:

[0009] The invention discloses a modeling measurement and characterization method for a sinusoidal surface roughness template. Aiming at the characteristics of the sinusoidal roughness template, an equally spaced sampling measurement sequence is used to first perform an overall analysis and then a local analysis, so as to improve the accuracy of the measurement and characterization results.

[0010] The present invention discloses a method for modeling and characterizing a sinusoidal surface roughness sample, comprising the following steps:

[0011] Step 1: Measurement of cross-sectional morphology.

[0012] Use high-precision roughness testers and other precision measuring instruments to measure and sample the cross-section of the sinusoidal roughness sample at equal intervals. The sampling interval is τ, and the i-th sampling point x i The sampling position t i =i×τ, (i=0,1,…,n-1), and obtain the sinusoidal waveform curve sequence x0,x1,…,x n-1 .

[0013] Using the four-parameter sine wave fitting method, the curve sequence x0,x1,...,x n-1 The least squares waveform fitting is performed, and the function expression of the fitting curve is:

[0014]

[0015] The root mean square value of the fitting residual is:

[0016]

[0017] Where A is the amplitude of the fitted sine waveform; f is the frequency of the fitted sine waveform; To fit the initial phase of the sine waveform, C is the DC offset of the fitted sinusoidal waveform; ρ is the RMS value of the fitting residual.

[0018] Step 2: Locate the peaks and valleys of each local residual through overall calculation.

[0019] The sinusoidal curve fitting method is used to obtain the fitting parameters of the sinusoidal waveform curve sequence of its cross-sectional morphology, and the total distortion D is calculated. T , the number of sampling points per cycle M, the period of each cycle T;

[0020]

[0021] Then, the regression sinusoidal waveform sequence y0, y1, ..., y is calculated. n-1 :

[0022]

[0023] Calculate the regression sequence {y i} and the measurement sequence {x i} between the regression residual sequence z0,z1,...,z n-1 :

[0024] z i =x i -y i (i=0, 1, …, n-1) (7)

[0025] The regression residual sequence z0,z1,...,z n-1 Characterizes the sinusoidal distortion at each sampling point.

[0026] The regression residual series {y i}After the amplitude is appropriately amplified, it is compared with the measurement sequence {x i}Draw on the same curve graph, analyze and find the changing pattern of the regression residuals, and locate the peak and valley values ​​of each local residual.

[0027] Step 3: The cross-sectional sinusoidal waveform index parameters of the sinusoidal roughness sample are given through local calculation, and various parameter indexes affecting the sinusoidal roughness sample are quantitatively measured and characterized.

[0028] The measurement sequence x0,x1,...,x n-1 Divide into N single-cycle subsequences x of length M, connected to each other, covering all measurement data 0,0 ,x 0,1 ,...,x 0,M-1 , x 1,0 ,x 1,1 ,...,x 1,M-1 , …, x N-1,0 ,x N-1,1 ,...,x N-1,M-1 ;

[0029] For a single-cycle subsequence x k,0 ,x k,1 ,...,xk,M-1 , and use the sine curve fitting method to obtain its amplitude A k , frequency f k , DC offset C k , total distortion D k , period T k ;

[0030]

[0031] t kj =j×τ (k=0,1,…,N-1; j=0,1,…,M-1) (9)

[0032] T k =1 / f k (k=0,1,…,N-1) (10)

[0033]

[0034] The fitting parameter results of each single-cycle subsequence are sorted in order, and the amplitude measurement sequence of the roughness sample cross-sectional morphology unit is obtained as A0, A1, ..., A N-1 ; The frequency measurement sequence of the roughness sample cross-sectional morphology unit is f0, f1, ..., f N-1 ; The DC offset measurement sequence of the roughness sample cross-sectional morphology unit is C0, C1, ..., C N-1 ; The total distortion measurement sequence of the roughness sample cross-sectional morphology unit is obtained as D0, D1, ..., D N-1 ; The periodic measurement sequence of the roughness sample cross-sectional morphology unit is T0, T1, ..., T N-1 ;

[0035] Statistical analysis is performed on each parameter sequence to obtain the mean, maximum, minimum, and experimental standard deviation of each parameter, which is used to accurately characterize the parameter index of the measured sinusoidal roughness sample. Among them:

[0036] Single cycle amplitude mean:

[0037]

[0038] Single cycle amplitude experimental standard deviation:

[0039]

[0040] Maximum single-cycle amplitude:

[0041] A max =max{A k} (k=0,1,…,N-1) (15)

[0042] Minimum single-cycle amplitude:

[0043] A min =min{A k} (k=0,1,…,N-1) (16)

[0044] Single cycle amplitude range:

[0045] λ(A k )=A max -A min (17)

[0046] Single cycle frequency mean:

[0047]

[0048] Single-cycle frequency experimental standard deviation:

[0049]

[0050] Maximum single-cycle frequency:

[0051] f max =max{f k} (k=0,1,…,N-1) (20)

[0052] Minimum single-cycle frequency:

[0053] f min =min{f k} (k=0, 1, …, N-1) (21)

[0054] Single cycle frequency error:

[0055] λ(f k ) = f max -f min (twenty two)

[0056] Single cycle DC offset mean:

[0057]

[0058] Single cycle DC offset experimental standard deviation:

[0059]

[0060] Maximum single-cycle DC offset:

[0061] C max =max{C k} (k=0, 1, …, N-1) (25)

[0062] Minimum single-cycle DC offset:

[0063] C min =min{C k} (k=0, 1, …, N-1) (26)

[0064] Single cycle DC offset range:

[0065] λ(C k )=C max -C min (27)

[0066] Single-cycle distortion average:

[0067]

[0068] Single-cycle distortion test standard deviation:

[0069]

[0070] Maximum single-cycle distortion:

[0071] D max =max{D k} (k=0, 1, …, N-1) (30)

[0072] Minimum single-cycle distortion:

[0073] D min =min{D k} (k=0, 1, …, N-1) (31)

[0074] Single-cycle distortion is extremely poor:

[0075] λ(D k )=D max -D min (32)

[0076] Single cycle mean:

[0077]

[0078] Standard deviation of single cycle experiment:

[0079]

[0080] Maximum value of single cycle:

[0081] T max =max{T k} (k=0, 1, …, N-1) (35)

[0082] Minimum single-cycle period:

[0083] T min = min{T k} (k=0, 1, …, N-1) (36)

[0084] Single cycle range:

[0085] λ(T k )=T max -T min (37)

[0086] According to the cross-sectional sinusoidal waveform index parameters of the above-mentioned sinusoidal roughness sample, various parameter indexes affecting the sinusoidal roughness sample are quantitatively measured and characterized.

[0087] As a preferred method, the entire sampling measurement sequence is regarded as a general sinusoidal waveform curve, and the fitting parameters of the sinusoidal waveform curve sequence of its cross-sectional morphology are obtained by using the sinusoidal curve fitting method to calculate the total distortion D T , the number of sampling points per cycle M, the period of each cycle T. And the total distortion D T As an overall quality parameter for the roughness sample.

[0088] The regression residual series {y i}After the amplitude is appropriately amplified, it is compared with the measurement sequence {x i}Draw on the same curve graph, analyze and find the changing pattern of the regression residuals, and locate the peak and valley values ​​of each local residual.

[0089] As a preference, the entire sampling measurement sequence x0, x1, ..., x n-1 Divide into N single-cycle subsequences x of length M, connected to each other, covering all measurement data 0,0 ,x 0,1 ,...,x 0,M-1 , x 1,0 ,x 1,1 ,...,x 1,M-1 , …, x N-1,0 ,x N-1,1 ,...,x N-1,M-1 ;

[0090] For each single-cycle subsequence x k,0 ,x k,1 ,...,x k,M-1 , use the sine curve fitting method to obtain the amplitude A of the single-cycle subsequence k , frequency f k , DC offset C k , total distortion D k , period T k;

[0091] The fitting parameter results of each single-cycle subsequence are sorted in order, and the amplitude measurement sequence of the roughness sample cross-sectional morphology unit is obtained as A0, A1, ..., A N-1 ; The frequency measurement sequence of the roughness sample cross-sectional morphology unit is f0, f1, ..., f N-1 ; The DC offset measurement sequence of the roughness sample cross-sectional morphology unit is C0, C1, ..., C N-1 ; The total distortion measurement sequence of the roughness sample cross-sectional morphology unit is obtained as D0, D1, ..., D N-1 ; The periodic measurement sequence of the roughness sample cross-sectional morphology unit is T0, T1, ..., T N-1 ;

[0092] Statistical analysis is performed on each parameter sequence to obtain the mean, maximum, minimum, experimental standard deviation and range of each parameter, which are used to accurately characterize the parameter indicators of the measured sinusoidal roughness sample.

[0093] The maximum value, minimum value, experimental standard deviation and range of each parameter are used to characterize the uniformity index of each parameter of the measured sinusoidal roughness sample.

[0094] Beneficial effects:

[0095] 1. The present invention discloses a modeling measurement and characterization method for a sinusoidal surface roughness template. Based on the sampling measurement curve sequence of the cross-sectional sinusoidal waveform of the sinusoidal roughness template, the modeling measurement and analysis method is used to give the cross-sectional sinusoidal waveform index parameters of the sinusoidal roughness template in two ways, namely, overall and local, and quantitatively measure and characterize various parameter indexes that affect the sinusoidal roughness template, thereby improving the accuracy and efficiency of quantitative measurement and characterization. Among them, compared with other roughness template evaluation methods, the biggest advantage of the present invention is that the evaluation index is comprehensive and complete. Its overall parameters characterize the macroscopic group characteristics of all sinusoidal morphology units acting together, including overall amplitude, overall period, overall DC offset, overall distortion, etc.; local parameters characterize the microscopic individual characteristics of each single-cycle subsequence in the local unit, including local unit amplitude, local unit period, local unit DC offset, local unit distortion, etc.; the overall uniform characteristics and average effects; the local details and local individual effects are statistically significant and valuable, and provide a reference and basis for the process improvement of the roughness template. Both are indispensable. The overall parameters combined with the local parameters reflect the level of a comprehensive and complete roughness sample.

[0096] 2. The present invention discloses a modeling measurement and characterization method for a sinusoidal surface roughness sample, which combines overall and local angles to quantitatively measure and characterize the parameter index of the sinusoidal roughness sample. Compared with other roughness sample evaluation methods, the special advantage of the present invention is that it uses a four-parameter sinusoidal fitting, which belongs to a modeling measurement method and means. The sinusoidal surface roughness sample evaluation index obtained thereby is accurate and is a least squares optimal estimate.

[0097] From an overall perspective, the measurement result of the total distortion parameter D is obtained. T Characterize the quality of the sinusoidal roughness sample and obtain the measurement results of the amplitude parameter A, the measurement results of the period parameter T, and the precise value M of the number of sampling points contained in each cycle. In addition, from the regression residual sequence {z i} and the measurement sequence {x i}, and obtain the local distortion positioning information from the curve diagram, which provides a basis for improving the manufacturing process of the roughness template, reducing the distortion of the roughness template, and improving its quality, (i=0,1,…,n-1).

[0098] From a local perspective, the maximum single-cycle amplitude A of the sinusoidal roughness sample is obtained. max , minimum value A min , experimental standard deviation s(A k ), range λ(A k ) measurement results, characterizing the amplitude uniformity of its roughness sample;

[0099] Get the maximum value of its single cycle period T max , minimum value T min , experimental standard deviation s(T k ), range λ(T k ) measurement results, characterizing the periodic uniformity of the roughness sample;

[0100] Get the maximum value of its single-cycle distortion D max , minimum value D min , experimental standard deviation s(D k ), range λ(D k ) measurement results, characterizing the uniformity of the distortion of the roughness sample.

[0101] The present invention combines overall and local angles to quantitatively measure and characterize parameter indicators of the sinusoidal roughness sample, can obtain complete quality parameter indicators of the sinusoidal roughness sample, and can provide quantitative analysis and positioning analysis of the characteristics that affect its parameter performance.

[0102] 3. The present invention discloses a modeling measurement and characterization method for a sinusoidal surface roughness sample. The obtained parameter index can be converted into any parameter index defined and reproduced by the surface roughness sample standard. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] Figure 1 It is a schematic diagram of the structure of an actual sinusoidal roughness template embodiment of the present invention.

[0104] Wherein: A-sine waveform amplitude of the cross section of the sinusoidal roughness sample; 2A-peak-to-peak value of the sinusoidal waveform amplitude of the cross section of the sinusoidal roughness sample; T-sine waveform period of the cross section of the sinusoidal roughness sample; C-median height of the sinusoidal waveform of the cross section of the sinusoidal roughness sample; xot coordinate system-the rectangular coordinate system used to characterize the sinusoidal waveform sampling sequence of the cross section of the sinusoidal roughness sample.

[0105] Figure 2 For the present invention Figure 1 Schematic diagram of the cross-section sampling sequence of the actual sinusoidal roughness sample shown.

[0106] Figure 3 It is the waveform of the sampling curve of the sinusoidal roughness sample section and its fitting curve.

[0107] Figure 4 This is the fluctuation of the height parameter Ak of ​​the sinusoidal roughness sample.

[0108] Figure 5 This is the fluctuation of the width parameter Tk of the sinusoidal roughness sample.

[0109] Figure 6 is the frequency parameter f of the sinusoidal roughness sample k Fluctuation situation.

[0110] Figure 7 is the baseline parameter C of the sinusoidal roughness sample k Fluctuation situation.

[0111] Figure 8 is the distortion parameter D of the sinusoidal roughness sample k Fluctuation situation. DETAILED DESCRIPTION

[0112] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below with reference to the accompanying drawings and examples.

[0113] Embodiment 1:

[0114] This embodiment discloses a modeling measurement and characterization method for a sinusoidal surface roughness sample, and the specific implementation steps are as follows:

[0115] Step 1: Measurement of cross-sectional morphology.

[0116] Use high-precision roughness testers and other precision measuring instruments to measure and sample the cross-section of the sinusoidal roughness sample at equal intervals, where T = the designed spatial period is 0.125 mm and the sampling interval τ = 1 μm.

[0117] The i-th sampling point x i The sampling position t i =i×τ, (i=0,1,…,n-1), and obtain the sinusoidal waveform curve sequence x0,x1,…,x n-1 The curve is as follows Figure 3 Series 1 shown.

[0118] Using the four-parameter sine wave fitting method, the curve sequence x0, x1, ..., x n-1 Perform least squares waveform fitting, and the function expression of the fitting curve is:

[0119]

[0120] The root mean square value of the fitting residual is:

[0121]

[0122] Among them, A = 17.619 μm is the amplitude of the fitted sine waveform; f = 8.001 mm -1 To fit the frequency of the sine waveform; To fit the initial phase of the sine waveform, C = -0.005 μm is the DC offset of the fitted sinusoidal waveform; ρ is the RMS value of the fitting residual.

[0123] Step 2: Locate the peaks and valleys of each local residual through overall calculation.

[0124] The sinusoidal curve fitting method is used to obtain the fitting parameters of the sinusoidal waveform curve sequence of its cross-sectional morphology, and the total distortion D is calculated. T =5.1%, number of sampling points per cycle M = 125, period of each cycle T = 124.984μm;

[0125]

[0126] Then, the regression sinusoidal waveform sequence y0,y1,...,y is calculated. n-1 , the regression curve {y i}like Figure 3 Series 2 shown.

[0127]

[0128] Calculate the regression sequence {y i} and the measurement sequence {xi} between the regression residual sequence z0,z1,...,z n-1 , the residual curve {z i}like Figure 3 Series 3 shown.

[0129] z i =x i -y i (i=0, 1, …, n-1) (7)

[0130] The regression residual sequence z0,z1,...,z n-1 Characterizes the sinusoidal distortion at each sampling point.

[0131] The regression residual series {y i}After the amplitude is appropriately amplified, it is compared with the measurement sequence {x i} are drawn on the same curve, analyzing and finding the changing rules of the regression residuals, and locating the peaks and valleys of each local residual. i}After magnification 10 times Figure 3 Series 4. Figure 3 It can be seen from series 4 that the distortion distribution is not uniform, showing a periodic fluctuation feature. The distortion is large at the trough due to processing defects, and the local maximum distortion is about 10%. The deviation curve amplitude shows a distribution feature of low in the middle and high at both ends, which is the fitting effect caused by the uneven width (period) of each sine wave. The local distortion can even be pushed up to 12.6%.

[0132] Step 3: The cross-sectional sinusoidal waveform index parameters of the sinusoidal roughness sample are given through local calculation, and various parameter indexes affecting the sinusoidal roughness sample are quantitatively measured and characterized.

[0133] The measurement sequence x0,x1,...,x n-1 Divide into N single-cycle subsequences x of length M, connected to each other, covering all measurement data 0,0 ,x 0,1 ,...,x 0,M-1 , x 1,0 ,x 1,1 ,...,x 1,M-1 , …, x N-1,0 ,x N-1,1 ,...,x N-1,M-1 ; Select each single-cycle subsequence to be shifted backward by one sampling interval compared to the previous subsequence.

[0134] For each single-cycle subsequence x k,0 ,x k,1 ,...,x k,M-1, and use the sine curve fitting method to obtain its amplitude A k , frequency f k , DC offset C k , total distortion D k , period T k ;

[0135]

[0136] t kj =j×τ (k=0,1,…,N-1; j=0,1,…,M-1) (9)

[0137] T k =1 / f k (k=0,1,…,N-1) (10)

[0138]

[0139] The fitting parameter results of each single-cycle subsequence are sorted in order, and the amplitude measurement sequence of the roughness sample cross-sectional morphology unit is obtained as A0, A1, ..., A N-1 like Figure 4 As shown in the figure, the frequency measurement sequence of the roughness sample cross-sectional morphology unit is f0, f1, ..., f N-1 like Figure 6 As shown; the DC offset measurement sequence of the roughness sample cross-sectional morphology unit is C0, C1, ..., C N-1 like Figure 7 As shown in the figure, the total distortion measurement sequence of the roughness sample cross-sectional morphology unit is D0, D1, ..., D N-1 like Figure 8 As shown; the periodic measurement sequence of the roughness sample cross-sectional morphology unit is T0, T1, ..., T N-1 like Figure 5 As shown;

[0140] Statistical analysis is performed on each parameter sequence to obtain the mean, maximum, minimum, and experimental standard deviation of each parameter, which is used to accurately characterize the parameter index of the measured sinusoidal roughness sample. Among them:

[0141] Single cycle amplitude mean:

[0142]

[0143] Single cycle amplitude experimental standard deviation:

[0144]

[0145] Maximum single-cycle amplitude:

[0146] Amax =max{A k}=18.185μm (k=0,1,…,N-1) (15)

[0147] Minimum single-cycle amplitude:

[0148] A min =min{A k}=16.992μm (k=0,1,…,N-1) (16)

[0149] Single cycle amplitude range:

[0150] λ(A k )=A max -A min =1.193μm (17)

[0151] Single cycle frequency mean:

[0152]

[0153] Single-cycle frequency experimental standard deviation:

[0154]

[0155] Maximum single-cycle frequency:

[0156] f max =max{f k}=8.586μm (k=0, 1, …, N-1) (20)

[0157] Minimum single-cycle frequency:

[0158] f min =min{f k}=7.573μm (k=0, 1, …, N-1) (21)

[0159] Single cycle frequency error:

[0160] λ(f k ) = f max -f min =1.013μm (22)

[0161] Single cycle DC offset mean:

[0162]

[0163] Single cycle DC offset experimental standard deviation:

[0164]

[0165] Maximum single-cycle DC offset:

[0166] C max =max{C k}=0.854μm (k=0, 1, …, N-1) (25)

[0167] Minimum single-cycle DC offset:

[0168] C min =min{C k}=-0.484μm (k=0, 1, …, N-1) (26)

[0169] Single cycle DC offset range:

[0170] λ(C k )=C max -C min =1.338μm (27)

[0171] Single-cycle distortion average:

[0172]

[0173] Single-cycle distortion test standard deviation:

[0174]

[0175] Maximum single-cycle distortion:

[0176] D max =max{D k} =4.92% (k=0, 1, …, N-1) (30)

[0177] Minimum single-cycle distortion:

[0178] D min =min{D k}=1.62% (k=0, 1, …, N-1) (31)

[0179] Single-cycle distortion is extremely poor:

[0180] λ(D k )=D max -D min =3.3% (32)

[0181] Single cycle mean:

[0182]

[0183] Standard deviation of single cycle experiment:

[0184]

[0185] Maximum value of single cycle:

[0186] T max =max{T k}=132.048μm (k=0, 1, …, N-1) (35)

[0187] Minimum single-cycle period:

[0188] T min = min{T k}=116.473μm (k=0, 1, …, N-1) (36)

[0189] Single cycle range:

[0190] λ(T k )=T max -T min =15.575μm (37)

[0191] According to the cross-sectional sinusoidal waveform index parameters of the above-mentioned sinusoidal roughness sample, various parameter indexes affecting the sinusoidal roughness sample are quantitatively measured and characterized.

[0192] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A modeling measurement and characterization method for a sinusoidal surface roughness sample, characterized in that: The following steps are included: Step 1: Measurement of cross-sectional morphology; Use high-precision roughness testers and other precision measuring instruments to measure and sample the cross-section of the sinusoidal roughness sample at equal intervals. The sampling interval is τ, and the i-th sampling point x i The sampling position t i =i×τ, (i=0,1,…,n-1), and obtain the sinusoidal waveform curve sequence x0,x1,…,x n-1 ; Using the four-parameter sine wave fitting method, the curve sequence x0,x1,...,x n-1 The least squares waveform fitting is performed, and the function expression of the fitting curve is: The root mean square value of the fitting residual is: Where A is the amplitude of the fitted sine waveform; f is the frequency of the fitted sine waveform; To fit the initial phase of the sine waveform, C is the DC offset of the fitted sinusoidal waveform; ρ is the RMS value of the fitting residual; Step 2: Locate the peak and valley values ​​of each local residual through overall calculation; The sinusoidal curve fitting method is used to obtain the fitting parameters of the sinusoidal waveform curve sequence of its cross-sectional morphology, and the total distortion D is calculated. T , the number of sampling points per cycle M, the period of each cycle T; Then, the regression sinusoidal waveform sequence y0, y1, ..., y is calculated. n-1 : Calculate the regression sequence {y i } and the measurement sequence {x i } between the regression residual sequence z0,z1,...,z n-1 : z i =x i -y i (i=0, 1, …, n-1) (7) The regression residual sequence z0,z1,...,z n-1 Characterizes the sinusoidal distortion at each sampling point; The regression residual series {y i }After the amplitude is appropriately amplified, it is compared with the measured sequence {x i }Draw on the same curve graph, analyze and find the changing pattern of regression residuals, and locate the peak and valley values ​​of each local residual; Step 3: The cross-sectional sinusoidal waveform index parameters of the sinusoidal roughness sample are given through local calculation, and various parameter indexes affecting the sinusoidal roughness sample are quantitatively measured and characterized; The measurement sequence x0,x1,...,x n-1 Divide into N single-cycle subsequences x of length M, connected to each other, covering all measurement data 0,0 ,x 0,1 ,...,x 0,M-1 , x 1,0 ,x 1,1 ,...,x 1,M-1 , …, x N-1,0 ,x N-1,1 ,...,x N-1,M-1 ; For a single-cycle subsequence x k,0 ,x k,1 ,...,x k,M-1 , and use the sine curve fitting method to obtain its amplitude A k , frequency f k , DC offset C k , total distortion D k , period T k ; The fitting parameter results of each single-cycle subsequence are sorted in order, and the amplitude measurement sequence of the roughness sample cross-sectional morphology unit is obtained as A0, A1, ..., A N-1 ; The frequency measurement sequence of the roughness sample cross-sectional morphology unit is f0, f1, ..., f N-1 ; The DC offset measurement sequence of the roughness sample cross-sectional morphology unit is C0, C1, ..., C N-1 ; The total distortion measurement sequence of the roughness sample cross-sectional morphology unit is obtained as D0, D1, ..., D N-1 ; The periodic measurement sequence of the roughness sample cross-sectional morphology unit is T0, T1, ..., T N-1 ; Statistical analysis is performed on each parameter sequence to obtain the mean, maximum, minimum, and experimental standard deviation of each parameter, which is used to accurately characterize the parameter index of the measured sinusoidal roughness sample; among which: Single cycle amplitude mean: Single cycle amplitude experimental standard deviation: Maximum single-cycle amplitude: A max =max{A k } (k=0, 1, …, N-1) (15) Minimum single-cycle amplitude: A min =min{A k } (k=0, 1, …, N-1) (16) Single cycle amplitude range: λ(A k )=A max -A min (17) Single cycle frequency mean: Single-cycle frequency experimental standard deviation: Maximum single-cycle frequency: f max =max{f k } (k=0, 1, …, N-1) (20) Minimum single-cycle frequency: f min =min{f k } (k=0, 1, …, N-1) (21) Single cycle frequency error: λ(f k )=f max -f min (22) Single cycle DC offset mean: Single cycle DC offset experimental standard deviation: Maximum single-cycle DC offset: C max =max{C k } (k=0, 1, …, N-1) (25) Minimum single-cycle DC offset: C min =min{C k } (k=0, 1, …, N-1) (26) Single cycle DC offset range: λ(C k )=C max -C min (27) Single-cycle distortion average: Single-cycle distortion test standard deviation: Maximum single-cycle distortion: D max =max{D k } (k=0, 1, …, N-1) (30) Minimum single-cycle distortion: D min =min{D k } (k=0, 1, …, N-1) (31) Single-cycle distortion is extremely poor: λ(D k )=D max -D min (32) Single cycle mean: Standard deviation of single cycle experiment: Maximum value of single cycle: T max =max{T k } (k=0, 1, …, N-1) (35) Minimum single-cycle period: T min =min{T k } (k=0, 1, …, N-1) (36) Single cycle range: λ(T k )=T max -T min (37) According to the cross-sectional sinusoidal waveform index parameters of the above-mentioned sinusoidal roughness sample, various parameter indexes affecting the sinusoidal roughness sample are quantitatively measured and characterized.

2. The method for modeling and characterizing a sinusoidal surface roughness sample according to claim 1, characterized in that: The entire sampling measurement sequence is regarded as a general sinusoidal waveform curve, and the sinusoidal curve fitting method is used to obtain the fitting parameters of the sinusoidal waveform curve sequence of its cross-sectional morphology, and the total distortion D is calculated. T , the number of sampling points per cycle M, the period of each cycle T; and the total distortion D T As an overall quality parameter of the roughness sample; The regression residual series {y i }After the amplitude is appropriately amplified, it is compared with the measured sequence {x i }Draw on the same curve graph, analyze and find the changing pattern of the regression residuals, and locate the peak and valley values ​​of each local residual.

3. The method for modeling and characterizing a sinusoidal surface roughness sample according to claim 1, characterized in that: The entire sampling measurement sequence x0,x1,...,x n-1 Divide into N single-cycle subsequences x of length M, connected to each other, covering all measurement data 0,0 ,x 0,1 ,...,x 0,M-1 , x 1,0 ,x 1,1 ,...,x 1,M-1 , …, x N-1,0 ,x N-1,1 ,...,x N-1,M-1 ; For each single-cycle subsequence x k,0 ,x k,1 ,...,x k,M-1 , use the sine curve fitting method to obtain the amplitude A of the single-cycle subsequence k , frequency f k , DC offset C k , total distortion D k , period T k ; The fitting parameter results of each single-cycle subsequence are sorted in order, and the amplitude measurement sequence of the roughness sample cross-sectional morphology unit is obtained as A0, A1, ..., A N-1 ; The frequency measurement sequence of the roughness sample cross-sectional morphology unit is f0, f1, ..., f N-1 ; The DC offset measurement sequence of the roughness sample cross-sectional morphology unit is C0, C1, ..., C N-1 ; The total distortion measurement sequence of the roughness sample cross-sectional morphology unit is obtained as D0, D1, ..., D N-1 ; The periodic measurement sequence of the roughness sample cross-sectional morphology unit is T0, T1, ..., T N-1 ; Statistical analysis is performed on each parameter sequence to obtain the mean, maximum, minimum, experimental standard deviation and range of each parameter to characterize the parameter index of the measured sinusoidal roughness sample; The maximum value, minimum value, experimental standard deviation and range of each parameter are used to characterize the uniformity index of each parameter of the measured sinusoidal roughness sample.

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