A numerical simulation method for shot peening surface reconstruction

Abstract

The present invention discloses a numerical simulation method suitable for shot-peened surface reconstruction. This method uses an autocorrelation function as a constraint parameter, proposes a new autocorrelation function expression based on this, and combines it with a classical linear filter reconstruction model. The FFT method is used to solve the resulting filter coefficients, which are then subjected to a convolution operation to ultimately generate a surface topography with the spatial characteristics of the shot-peened process. According to the present invention, the spatial parameters of the reconstructed shot-peened surface can be adjusted by modifying the τ value in the formula. This method also ensures the stability of the height distribution parameters and spatial parameters on the reconstructed shot-peened surface, and has high accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of shot peening technology, and in particular to a numerical simulation method suitable for shot peening surface reconstruction. Background Art

[0002] Shot peening is one of the effective methods to reduce component fatigue and increase its lifespan. It is currently widely used in surface strengthening processing of key components such as gears. In order to build a digital bridge connecting the service performance of shot peened surfaces, it is necessary to deeply explore its surface morphology characteristics. Surface morphology usually characterizes the microscopic geometric features presented by the surface, and it occupies a vital position in the manufacturing field. At the same time, the surface morphology on the parts significantly affects the various service performances on the surface, among which the areas that have been widely verified are friction, lubrication, wear, contact and fatigue resistance. Therefore, finding the efficiency of the path to obtain the desired surface morphology characteristics has become a problem that needs to be solved. Summary of the Invention

[0003] The present invention aims to solve at least one of the technical problems existing in the prior art. To this end, the present invention proposes a numerical simulation method for shot peening surface reconstruction, which can numerically simulate the surface morphology after shot peening, thereby significantly reducing the cost of various consumables and experimental time.

[0004] A numerical simulation method for shot peening surface reconstruction according to an embodiment of the present invention includes the following steps:

[0005] S1: Given the autocorrelation function matrix R and parameter S q 、S sk 、S ku and μ, the matrix R is set to M rows and N columns;

[0006] S2: Construct symmetric autocorrelation function R Z , substitute the autocorrelation function matrix R into R Z Calculation is performed inside; matrix R Z The size is (2M-1)×(2N-1);

[0007] S3: Generate a normally distributed random height matrix H using a random sequence generator;

[0008] S4: The autocorrelation function R in S2 Z and H are substituted into the transmission matrix C for calculation to generate the initial random height matrix Z C ;

[0009] S5; determine the height matrix Z according to the following formula C Parameter S sk1 With the target parameter S sk The error, Z C Parameter Sku1 With the target parameter S ku The error is calculated as follows:

[0010] ;

[0011] If S obtained by the formula sk1 With S sk The error or S obtained by the formula ku1 With S ku If the error is less than 0.01, execute S6, otherwise execute S7;

[0012] S6; Generate a random matrix Z that conforms to the height distribution using the Johnson transformation system H , and adjust Z H The power spectral density is calculated as follows:

[0013] ;

[0014] Using the time-frequency iteration method, by rearranging Z H The height position is Z C The height sequence to adjust Z C The height distribution of , after iteration, returns S5;

[0015] S7: Adjust Z after final iteration C The mean μ and the root mean square height S q , calculate the final output reconstructed shot peening surface Z, the calculation formula of Z is:

[0016] ;

[0017] Among them, S q is the root mean square height, S sk is the skewness, S ku is the kurtosis, μ is the mean; ifft2() represents the two-dimensional inverse Fourier transform, fft2() represents the two-dimensional Fourier transform, and std2() represents the standard deviation operation.

[0018] The numerical simulation method for shot peening surface reconstruction according to an embodiment of the present invention has at least the following beneficial effects:

[0019] By proposing a new autocorrelation function expression, taking it as a constraint condition, combining it with the classical linear filter reconstruction model, and solving it using the FFT method, the filter coefficient is obtained and then the convolution operation is performed to finally generate the surface morphology with the spatial characteristics of shot peening processing; by modifying the formula The spatial parameters of the reconstructed shot peening surface can be adjusted by adjusting the value. At the same time, this method can ensure the stability of the height distribution parameters and spatial parameters on the reconstructed shot peening surface and has high accuracy.

[0020] According to some embodiments of the present invention, the spatial parameters S of the reconstructed shot peening surface are specified. al With S tr , S al With S tr The calculation formulas are:

[0021] ,

[0022] ;

[0023] Among them, S al is the minimum autocorrelation length, S tr is the aspect ratio of the surface features; tx and ty represent the hysteresis distance in the x and y directions, respectively, which are related to the autocorrelation function (A CF ) are as follows:

[0024] ;

[0025] The autocorrelation function matrix R is determined by the requirements of spatial parameters. The calculation formula of the autocorrelation function matrix R is:

[0026] ;

[0027] Where, Equivalent to the spatial parameter S al , and since the shot peening surface is an isotropic surface, the parameter S tr The default setting is 1 and does not need to be specified; e is the Euler number, and the calculation formulas for parameters a, b, and k are:

[0028] ;

[0029] Among them, rem() means to find the remainder, min() means to take the minimum value in the brackets, and abs() means to take the absolute value.

[0030] According to some embodiments of the present invention,

[0031] ,

[0032] ,

[0033] ;

[0034] Where Q is the defined area, z ( x , y ) represents the height matrix composed of scattered points in Q.

[0035] According to some embodiments of the present invention, the symmetric autocorrelation function R ZThe calculation formula is:

[0036] ;

[0037] Where O is a zero-filled matrix of different specifications, and the matrix P is:

[0038] .

[0039] According to some embodiments of the present invention, the calculation formula of the random height matrix H is:

[0040] ;

[0041] Among them, ifft2() represents the two-dimensional inverse Fourier transform, K i,j The expression is as follows:

[0042] .

[0043] According to some embodiments of the present invention, the calculation formula of the transmission matrix C is:

[0044] ;

[0045] Where fft2() represents the two-dimensional Fourier transform.

[0046] According to some embodiments of the present invention, the random height matrix Z C The calculation formula is:

[0047] .

[0048] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0050] Figure 1 This is a flow chart of shot peening surface reconstruction modeling according to an embodiment of the present invention;

[0051] Figure 2 This is an experimental data table of an embodiment of the present invention;

[0052] Figure 3 Different spatial parameters S are given for the embodiments of the present invention. al Reconstructed 3D image of the shot peening surface;

[0053] Figure 4 Different spatial parameters S are given for the embodiments of the present invention. al Symmetrical autocorrelation function diagram corresponding to the reconstructed shot peening surface. DETAILED DESCRIPTION

[0054] The following describes embodiments of the present invention in detail. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended only to explain the present invention and are not to be construed as limiting the present invention.

[0055] In the description of the present invention, it should be understood that descriptions involving orientation, such as the orientation or positional relationship indicated by up, down, etc., are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0056] In the description of the present invention, "a plurality" refers to more than two. The use of "first" or "second" is solely for the purpose of distinguishing technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of the indicated technical features, or implicitly indicating the order of the indicated technical features.

[0057] In the description of the present invention, unless otherwise clearly defined, terms such as setting, installing, and connecting should be understood in a broad sense, and technicians in the relevant technical field can reasonably determine the specific meanings of the above terms in the present invention based on the specific content of the technical solution.

[0058] Reference Figures 1 to 4 A numerical simulation method for shot peening surface reconstruction according to an embodiment of the present invention comprises the following steps:

[0059] S1: First specify the spatial parameters S of the reconstructed shot peening surface al With S tr Among them, S al is the minimum autocorrelation length, S tr is the aspect ratio of the surface features, and their calculation formula is:

[0060] (1)

[0061] (2)

[0062] Where tx and ty represent the lag distance in the x and y directions respectively, which are related to the autocorrelation function (A CF ) are as follows:

[0063] (3)

[0064] The autocorrelation function matrix R (set to M rows and N columns) is determined by the requirements of the spatial parameters. Its calculation formula is:

[0065] (4)

[0066] Where, Equivalent to the spatial parameter S al , and since the shot peening surface is an isotropic surface, the parameter S tr The default setting is 1 and does not need to be specified. e is the Euler number, and the calculation formula for parameters a, b, and k is:

[0067] (5)

[0068] In the formula, rem() means to find the remainder, min() means to take the minimum value in the brackets, and abs() means to take the absolute value.

[0069] Specify the height distribution parameter S of the target parameter q 、S sk 、S ku and mean μ. Among them, S q is the root mean square height, S sk is the skewness, S ku is the kurtosis, and their calculation formula is as follows:

[0070] (6)

[0071] (7)

[0072] (8)

[0073] Where Q is the defined area, z ( x , y ) represents the height matrix composed of scattered points in Q;

[0074] S2: Construct symmetric autocorrelation function R Z , matrix R Z The size is (2M-1)×(2N-1), and its calculation formula is:

[0075] (9)

[0076] Where O is a zero-filled matrix of different specifications, and the matrix P is:

[0077] (10)

[0078] S3: Generate a random height matrix H, which is calculated as follows:

[0079] (11)

[0080] Among them, ifft2() represents the two-dimensional inverse Fourier transform, K i,j The expression is as follows:

[0081] (12)

[0082] S4: The autocorrelation function R in S2 Z and H are substituted into the transmission matrix C for calculation to generate the initial random height matrix Z C ; The calculation formula of the transmission matrix C is:

[0083] (13)

[0084] Random height matrix Z C The calculation formula is:

[0085] (14)

[0086] Where, fft2() represents two-dimensional Fourier transform, ifft2() represents two-dimensional inverse Fourier transform;

[0087] S5: Determine the height matrix Z according to the following formula C Parameter S sk1 、S ku1 Error and target parameter S sk 、S ku The error is calculated as follows:

[0088] (15)

[0089] Reference Figure 1 As shown, if S obtained by the formula sk1 With S sk The error or S obtained by the formula ku1 With S ku If one of the errors is less than 0.01, execute S7, otherwise execute S6. sk1 is calculated by formula (7), S ku1 is calculated by formula (8), and S sk1 S for comparison sk By artificial given, and S ku1 S for comparison ku through artificial givenness;

[0090] S6: Generate a random matrix Z that conforms to the height distribution using the Johnson transformation system H , and adjust Z HThe power spectral density is calculated as follows:

[0091] (16)

[0092] This method is a time-frequency iteration method, which is implemented by rearranging Z H The height position is Z C The height sequence to adjust Z C The height distribution of , usually after a few iterations, a higher accuracy can be achieved. Figure 1 As shown, that is, by inputting different matrices Z H To calculate different Z C , then calculate the Z C Enter step S5 until jumping to step S7;

[0093] S7: Adjust Z after final iteration C The mean μ and the root mean square height S q , calculate the final output reconstructed shot peening surface Z, the calculation formula of Z is:

[0094] (17)

[0095] Among them, std2() represents the standard deviation operation.

[0096] Reference Figure 1 、 Figure 3 and Figure 4 As shown, given the height distribution parameter μ=0, S q =1,S sk =0.3, S ku =3.3, and then by specifying different values, to form different embodiments:

[0097] In Example 1, The specified value is 20, and the calculated S sk 0.2980, S ku 3.2919, S al 0.9897, S tr is 20.4698;

[0098] In Example 2, The specified value is 50, and the calculated S sk 0.2902, S ku 3.2757, S al 0.9793, S tr is 49.9645;

[0099] In Example 3, The specified value is 80, and the calculated S sk 0.3032, S ku 3.2733, S al 0.9655, S tr It is 77.6793.

[0100] It can be seen from the above three examples that the calculated accuracy is high, and the errors of all parameters are less than 5%. This can ensure the stability of the height parameters and spatial parameters on the reconstructed shot peening surface. Therefore, the surface morphology after shot peening can be numerically simulated, thereby significantly reducing the cost of various consumables and experimental time.

[0101] The embodiments of the present invention are described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the knowledge of ordinary technicians in the relevant technical field without departing from the scope of the present invention.

Claims

1. A numerical simulation method suitable for shot peening surface reconstruction, characterized in that: The following steps are involved: S1: Given the autocorrelation function matrix R and parameter S q 、S sk 、S ku and μ, the matrix R is set to M rows and N columns; S2: Construct symmetric autocorrelation function R Z , substitute the autocorrelation function matrix R into R Z Calculation is performed inside; matrix R Z The size is (2M-1)×(2N-1); S3: Generate a normally distributed random height matrix H using a random sequence generator, where the calculation formula of the random height matrix H is: ； Among them, ifft2() represents the two-dimensional inverse Fourier transform; S4: The autocorrelation function R in S2 Z and H are substituted into the transmission matrix C for calculation to generate the initial random height matrix Z C ; S5; determine the height matrix Z according to the following formula C Parameter S sk1 With the target parameter S sk The error, Z C Parameter S ku1 With the target parameter S ku The error is calculated as follows: ； If S obtained by the formula sk1 With S sk The error or S obtained by the formula ku1 With S ku If the error is less than 0.01, execute S6, otherwise execute S7; S6; Generate a random matrix Z that conforms to the height distribution using the Johnson transformation system H , and adjust Z H The power spectral density is calculated as follows: ； Using the time-frequency iteration method, by rearranging Z H The height position is Z C The height sequence to adjust Z C The height distribution of , after iteration, returns S5; S7: Adjust Z after final iteration C The mean μ and the root mean square height S q , calculate the final output reconstructed shot peening surface Z, the calculation formula of Z is: ； Among them, S q is the root mean square height, S sk is the skewness, S ku is the kurtosis, μ is the mean; ifft2() represents the two-dimensional inverse Fourier transform, fft2() represents the two-dimensional Fourier transform, and std2() represents the standard deviation operation; Specify the spatial parameter S of the reconstructed shot peening surface al With S tr , S al With S tr The calculation formulas are: ， ； Among them, S al is the minimum autocorrelation length, S tr is the aspect ratio of the surface features; tx and ty represent the hysteresis distance in the x and y directions, respectively, which are related to the autocorrelation function A CF The relationship is as follows: ； The autocorrelation function matrix R is determined by the requirements of spatial parameters. The calculation formula of the autocorrelation function matrix R is: ； Where, Equivalent to the spatial parameter S al , and since the shot peening surface is an isotropic surface, the parameter S tr The default setting is 1 and does not need to be specified; e is the Euler number, and the calculation formulas for parameters a, b, and k are: ； Among them, rem() means to find the remainder, min() means to take the minimum value in the brackets, and abs() means to take the absolute value.

2. A numerical simulation method for shot peening surface reconstruction according to claim 1, characterized in that: ， ， ； Where Q is the defined area, z ( x , y ) represents the height matrix composed of scattered points in Q.

3. A numerical simulation method for shot peening surface reconstruction according to claim 1, characterized in that: Symmetric autocorrelation function R Z The calculation formula is: ； Where O is a zero-filled matrix of different specifications, and the matrix P is: 。 4. A numerical simulation method for shot peening surface reconstruction according to claim 1, characterized in that: K i,j The expression is as follows: 。 5. A numerical simulation method for shot peening surface reconstruction according to claim 4, characterized in that: The calculation formula of the transmission matrix C is: ； Where fft2() represents the two-dimensional Fourier transform.

6. A numerical simulation method for shot peening surface reconstruction according to claim 5, characterized in that: Random height matrix Z C The calculation formula is: 。

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