Method and system for calculating axial distribution consistency coefficient of concave structured grinding wheel

Abstract

The present disclosure provides a concave structure grinding wheel axial distribution consistency coefficient calculation method and system, relates to the technical field of grinding equipment, defines the grinding wheel parameters, establishes the grinding wheel circumferential development chart coordinate system, discrete grinding wheel circumferential surface, calculates discrete point coordinates;According to the set circular pit diameter and the effective grinding area proportion of grinding wheel, calculate all pit area and circular pit number;Define pit arrangement parameters, calculate the pit series parameters of the grinding wheel along the circumferential direction development chart;Based on the series parameters, calculate the pit center coordinates, establish the numerical analysis model of circular pit grinding wheel, define the misalignment amount, and calculate the center coordinates after misalignment;According to the obtained pit center coordinates, analyze the position of the circular pit, and express the discrete points along the circumferential direction of the circular pit grinding wheel with matrix, calculate the fluctuation uneven coefficient of the consistency coefficient by marking the discrete points.

Description

Technical Field

[0001] This disclosure relates to the field of grinding equipment technology, specifically to a method and system for calculating the axial distribution consistency coefficient of a pit-type structured grinding wheel. Background Technology

[0002] The statements in this section are merely background information relating to this disclosure and do not necessarily constitute prior art.

[0003] Grinding is an indispensable precision machining method for achieving high surface quality and dimensional accuracy, playing a crucial role in manufacturing fields such as aerospace. Creating textures on the grinding wheel is a strategy that can significantly improve grinding operations. During the grinding process, it offers advantages such as reduced internal stress and temperature in the workpiece, leading to improved dimensional accuracy and extended tool life. Research on structured grinding wheels mainly focuses on two aspects: wheel surface structure and manufacturing process. However, structured grinding wheels are characterized by uneven surface structure distribution, resulting in uneven surface quality during workpiece grinding, making it difficult to achieve the required machining accuracy and surface quality.

[0004] Research on the surface structure of grinding wheels is now quite mature. For example, a patent for an ordered microstructured grinding wheel discloses the deposition of a diamond film on the outer circumferential surface of the wheel hub, with sub-millimeter-sized microgrooves, improving chip formation efficiency and surface material removal rate, enhancing cutting performance, and improving surface quality and cutting efficiency. Simultaneously, it effectively enhances the grinding wheel's chip removal capacity, making it less prone to clogging, reducing thermal damage to the machined surface, and further improving surface quality. Another patent for a porous, ordered structured grinding wheel discloses that it is manufactured through pre-pressing and laser processing, achieving enhanced cooling, lubrication, and chip removal during grinding, effectively suppressing grinding burns. A biomimetic grinding wheel based on the scales and leaf arrangement of grass carp discloses a biomimetic groove arrangement that draws inspiration from the scales of grass carp, exhibiting characteristics such as suppressing flow field disturbances, a large average convective heat transfer coefficient, and anti-adhesion properties. By breaking down the air barrier generated when the grinding wheel rotates at high speed, the grinding wheel achieves high utilization of grinding fluid and good heat dissipation during grinding, thereby improving the service life of the grinding wheel and the quality of workpiece processing.

[0005] However, the existing grinding wheels described above all neglect the uniformity of the axial distribution of the surface structure, which leads to increased surface roughness and poor surface quality of the workpiece. Furthermore, due to the unique reflection effect of structured grinding wheels, the overall surface contour of the workpiece exhibits regular undulation characteristics, making it difficult to achieve efficient and precise machining. Summary of the Invention

[0006] To address the aforementioned issues, this disclosure proposes a method and system for calculating the axial distribution consistency coefficient of a pitted structured grinding wheel. By establishing a numerical analysis model of the pitted structured grinding wheel, the surface pits are calculated to form a pitted grinding wheel model driven by the axial distribution consistency coefficient. The surface structure parameters are adjusted to optimize the effective grinding area ratio, thereby achieving high-precision and high-efficiency grinding.

[0007] According to some embodiments, the present disclosure adopts the following technical solutions:

[0008] The method for calculating the axial distribution consistency coefficient of pitted structured grinding wheels includes:

[0009] Define the grinding wheel parameters, establish the coordinate system of the grinding wheel circumferential development diagram, discretize the circumferential surface of the grinding wheel, and calculate the coordinates of the discrete points;

[0010] Based on the set diameter of the circular pits and the effective grinding area ratio of the grinding wheel, calculate the area of ​​all pits and the number of circular pits; define the pit arrangement parameters and calculate the pit series parameters of the grinding wheel along the circumferential direction.

[0011] Based on a series of parameters, the coordinates of the center of the pit are calculated, a numerical analysis model of the circular pit grinding wheel is established, the misalignment amount is defined, and the coordinates of the center after misalignment are calculated. Based on the obtained coordinates of the center of the pit, the position of the circular pit is analyzed, and the discrete points along the circumference on the circular pit grinding wheel are represented by a matrix. By marking the discrete points, the fluctuation non-uniformity coefficient of the consistency coefficient is calculated.

[0012] According to some embodiments, the present disclosure adopts the following technical solutions:

[0013] A system for calculating the axial distribution consistency coefficient of pitted structured grinding wheels includes:

[0014] The initialization definition module is used to define the grinding wheel parameters, establish the coordinate system of the grinding wheel circumferential development diagram, discretize the circumferential surface of the grinding wheel, and calculate the coordinates of discrete points;

[0015] The calculation module is used to calculate the area of ​​all pits and the number of circular pits based on the set diameter of the circular pits and the effective grinding area ratio of the grinding wheel; it also defines pit arrangement parameters and calculates the pit series parameters of the grinding wheel along the circumferential direction.

[0016] Based on a series of parameters, the coordinates of the center of the pit are calculated, a numerical analysis model of the circular pit grinding wheel is established, the misalignment amount is defined, and the coordinates of the center after misalignment are calculated. Based on the obtained coordinates of the center of the pit, the position of the circular pit is analyzed, and the discrete points along the circumference on the circular pit grinding wheel are represented by a matrix. By marking the discrete points, the fluctuation non-uniformity coefficient of the consistency coefficient is calculated.

[0017] Compared with the prior art, the beneficial effects of this disclosure are as follows:

[0018] This invention discloses a method for calculating the axial distribution consistency coefficient of pitted structured grinding wheels. A numerical analysis model is established using MATLAB, and a method for calculating the axial distribution consistency coefficient of circular pitted structured grinding wheels is proposed.

[0019] By continuously changing the misalignment of the circular pits, the consistency coefficient can be calculated, which helps to avoid the problem of uneven axial distribution of the structure on the surface of the structured grinding wheel.

[0020] By changing the surface structure parameters of the grinding wheel, various circular pit-structured grinding wheels with different arrangements based on the consistency coefficient were obtained. This confirmed that the leaf sequence arrangement in the circular pit-structured grinding wheel exhibits a significant characteristic of uneven axial distribution of surface structure. Attached Figure Description

[0021] The accompanying drawings, which form part of this disclosure, are used to provide a further understanding of this disclosure. The illustrative embodiments of this disclosure and their descriptions are used to explain this disclosure and do not constitute an undue limitation of this disclosure.

[0022] Figure 1 This is a schematic diagram of the coordinate system for the circumferential development of the grinding wheel in this embodiment;

[0023] Figure 2 This is a schematic diagram showing the row and column spacing of the circular recesses in this embodiment;

[0024] Figure 3 This is a schematic diagram of the translation of the circular pit on the grinding wheel in this embodiment;

[0025] Figure 4 This is a schematic diagram illustrating the calculation of the upper and lower boundary phase angles in this embodiment;

[0026] in, Figure 4 In (a), the circular indentation extends beyond the lower boundary but the center does not extend beyond the lower boundary;

[0027] (b) is a circular indentation that extends beyond the lower boundary and the center of the circle also extends beyond the lower boundary;

[0028] (c) is a circular indentation that extends beyond the upper boundary but whose center does not extend beyond the upper boundary;

[0029] (d) is a circular indentation that extends beyond the upper boundary and the center of the circle also extends beyond the upper boundary;

[0030] Figure 5 This is a schematic diagram of the calculation results of the pit arrangement as the misalignment amount changes in this embodiment;

[0031] in, Figure 5 (a) is a schematic diagram of the pit arrangement when the diameter of the circular pit is 5, the grinding area ratio is constant, and the misalignment is 0.5.

[0032] (b) is a schematic diagram of the pit arrangement when the diameter of the circular pit is 5, the grinding area ratio is constant, and the misalignment is 1.

[0033] (c) is a schematic diagram of the pit arrangement when the diameter of the circular pit is 5, the grinding area ratio is constant, and the misalignment is 1.5.

[0034] Figure 6 This is a schematic diagram of the pit arrangement with increased pit diameter in this embodiment;

[0035] in, Figure 6 (a) is a schematic diagram of the arrangement of circular pits with a diameter of 6 when the misalignment is 2, the grinding area ratio is constant.

[0036] (b) is a schematic diagram of the arrangement of pits with a diameter of 8 when the diameter of the circular pit is 2 and the grinding area ratio is constant.

[0037] (c) is a schematic diagram of the arrangement of pits with a diameter of 10 when the diameter of the circular pit is 2 and the grinding area ratio is constant.

[0038] Figure 7 This is a schematic diagram of the pit arrangement with an increased effective grinding area in this embodiment;

[0039] in, Figure 7 (a) is a schematic diagram of the pit arrangement with an effective grinding area ratio of 0.7 when the diameter of the circular pit and the misalignment are constant.

[0040] (b) is a schematic diagram of the pit arrangement with an effective grinding area ratio of 0.85 when the diameter of the circular pit and the misalignment are constant.

[0041] (c) is a schematic diagram of the pit arrangement with an effective grinding area ratio of 0.9 when the diameter of the circular pit and the misalignment are constant.

[0042] Figure 8 This is a schematic diagram showing the regular arrangement of circular recesses in this embodiment;

[0043] in, Figure 8 (a) is a schematic diagram of the regular arrangement of pits when the diameter of the circular pit is 3, the effective grinding area ratio is constant, and the pit misalignment is 0.

[0044] (b) is a schematic diagram of the regular arrangement of pits when the diameter of the circular pit is 3, the effective grinding area ratio is constant, and the pit misalignment is half the row spacing.

[0045] Figure 9 This is a schematic diagram showing the variation of the axial distribution consistency coefficient along the width direction when the circular pits are arranged in a regular pattern in this embodiment;

[0046] in, Figure 9(a) in the figure shows the curve of the axial distribution consistency coefficient along the width direction when the misalignment is 0.

[0047] (b) is the curve showing the variation of the axial distribution consistency coefficient along the width direction when the misalignment is half the row spacing;

[0048] Figure 10 This is a schematic diagram of the irregular arrangement of circular pits in this embodiment;

[0049] in, Figure 10 (a) is a schematic diagram of the pit arrangement with a misalignment of 5.5 when the diameter of the circular pit is 3, the grinding area ratio is constant, and the pit diameter is 3.

[0050] (b) When the diameter of the circular pit is 3, the grinding area ratio is constant, and the pit arrangement is 6.

[0051] (c) is a schematic diagram of the pit arrangement with a misalignment of 7 when the diameter of the circular pit is 3, the grinding area ratio is constant.

[0052] Figure 11 In this embodiment, when d m A schematic diagram showing the variation of the axial distribution consistency coefficient along the width direction when the coefficient is 5.5.

[0053] Figure 12 In this embodiment, when d m A schematic diagram showing the variation of the axial distribution consistency coefficient along the width direction when the coefficient is 6.

[0054] Figure 13 In this embodiment, when d m A schematic diagram showing the variation of the axial distribution consistency coefficient along the width direction when the coefficient is 7.

[0055] Figure 14 This is a bar chart comparing the root mean square error of the consistency coefficient between regular and irregular arrangements as the misalignment amount changes in this embodiment.

[0056] Figure 15 This is a schematic diagram illustrating the variation of the axial structural consistency coefficient with the amount of misalignment in this embodiment. Detailed Implementation

[0057] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.

[0058] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains.

[0059] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this disclosure. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0060] Example 1

[0061] One embodiment of this disclosure provides a method for calculating the axial distribution consistency coefficient of a pitted structured grinding wheel, including:

[0062] Define the grinding wheel parameters, establish the coordinate system of the grinding wheel circumferential development diagram, discretize the circumferential surface of the grinding wheel, and calculate the coordinates of the discrete points;

[0063] Based on the set diameter of the circular pits and the effective grinding area ratio of the grinding wheel, calculate the area of ​​all pits and the number of circular pits; define the pit arrangement parameters and calculate the pit series parameters of the grinding wheel along the circumferential direction.

[0064] Based on a series of parameters, the coordinates of the center of the pit are calculated, a numerical analysis model of the circular pit grinding wheel is established, the misalignment amount is defined, and the coordinates of the center after misalignment are calculated. Based on the obtained coordinates of the center of the pit, the position of the circular pit is analyzed, and the discrete points along the circumference on the circular pit grinding wheel are represented by a matrix. By marking the discrete points, the fluctuation non-uniformity coefficient of the consistency coefficient is calculated.

[0065] As one embodiment, a specific implementation of the method for calculating the axial distribution consistency coefficient of a pitted structured grinding wheel disclosed herein includes the following steps:

[0066] S1. Define the grinding wheel parameters, establish the coordinate system of the grinding wheel circumferential development diagram, and discretize the circumferential surface of the grinding wheel;

[0067] Setting b s The width d represents the width of the grinding wheel. s The diameter of the grinding wheel, r s Given the radius of the grinding wheel, we can know l s As shown in formula (1):

[0068] s πd s (1)

[0069] l s This indicates the circumference length of the grinding wheel.

[0070] First, establish the coordinate system for the development of the grinding wheel's circumference. Discretize the circumferential surface of the grinding wheel, as shown below. Figure 1The purpose shown is to accurately calculate the coordinates of each point on the circumferential surface of the grinding wheel.

[0071] S2. Define the distance from the grinding wheel circumference and the number of discrete points, and the distance from the grinding wheel width and the number of discrete points. Calculate the coordinates of the discrete points.

[0072] Let the distance of the grinding wheel in the circumferential direction be dl. s The distance from the step in the width direction is db. s Discretize the grinding wheel, nb s nl represents the number of discrete points in the width direction. s The number of discrete points representing the circumference length is represented by the matrix xd. s (i1,j1) represents the y-coordinate, which is represented by the matrix yd. s (i1,j1) indicates that the range of values ​​for discrete points i1,j1 is as shown in formula (2):

[0073]

[0074] The formula for calculating the coordinates of discrete points is shown in formula (3) below:

[0075]

[0076] S3. Based on the set diameter of the circular pits and the percentage of the effective grinding area of ​​the grinding wheel, calculate the area of ​​all pits and the number of circular pits; set the diameter d of the circular pits. a For a diameter of 5mm, the effective grinding area ratio ρ of a circular pit grinding wheel (e.g., ρ = 85%) can be used to obtain the area v of all pits. d As shown in formula (4):

[0077] vd=lsbs(1-ρ)(4)

[0078] The number of circular pits, n, can be obtained from the area of ​​all the pits. d As shown in formula (5):

[0079]

[0080] It should be noted that the result of calculating the number of pits is rounded down.

[0081] S4. Define the pit layout parameters and calculate the number of pits in a row, the number of pits in a column, the row spacing, and the column spacing of the pits in the circumferential unfolded diagram of the grinding wheel.

[0082] Define the row spacing of the pit arrangement as l row The column spacing is l col The pit arrangement parameter is prc, as shown in formula (6):

[0083]

[0084] In the initial state, the default row spacing is equal to the column spacing, p rc =1. From this, we can obtain the number of rows, columns, row spacing, and column spacing of the pits on the grinding wheel surface.

[0085] The number of rows with indentations (rounded down) is shown in formula (7):

[0086]

[0087] Combining the formulas, we get the following equation (8):

[0088]

[0089] The number of rows of indentations is shown in formula (9):

[0090]

[0091] The row spacing of the recesses is as shown in formula (10):

[0092]

[0093] The column spacing of the dimples is as shown in formula (11):

[0094]

[0095] The number of rows and columns involves a rounding process, therefore the final calculated ratio of row spacing to column spacing will differ from the original p. rc There is some deviation, such as Figure 2 The diagram shows the rows and columns of pits.

[0096] S5. Calculate the coordinates of the center of the indentation;

[0097] Define the x-coordinate of the center of all pits using the matrix x da (i2,j2), the y-coordinates are represented by the matrix y da (i2,j2) indicates that the range of values ​​for variables i2 and j2 is as shown in formula (12):

[0098]

[0099] x-coordinate of the center of the circle da (i2,j2), the y-coordinate of the center of the circle. da (i2, j2), the calculation formula (13) is as follows:

[0100]

[0101] S6. Establish a numerical analysis model of a circular pitted grinding wheel and define the misalignment amount;

[0102] A numerical analysis model of a grinding wheel with circular pits is established. To achieve an irregular arrangement of circular pits on the grinding wheel surface, each row of circular pits is shifted a certain distance in the -y direction compared to the previous row. The first row of pits does not shift in the -y direction. Starting from the second row, the pits shift downwards by a specified distance, defined as the misalignment amount d. m , represents the difference in y-coordinate between the center of the next column of pits and the center of the previous column of pits. Calculate and update the coordinates of the center of the misaligned circular pits to ensure that the pits are located on the grinding wheel surface.

[0103] S7. When the circular indentation is displaced downwards, it will touch the lower boundary. Define the upward displacement of the circular indentation and calculate the coordinates of the center of the circle after the displacement.

[0104] It should be noted that when the circular recess is misaligned downwards, a problem arises: the circular recess may touch the lower boundary, causing it to partially or completely extend beyond the lower boundary of the grinding wheel. Considering grinding uniformity, the following setting is made: when the circular recess touches the lower boundary, the portion of the arc extending beyond the lower boundary is shifted by the width of the grinding wheel in the y-direction, as shown below. Figure 3 The diagram shown illustrates the translation of the circular pit on the grinding wheel.

[0105] When calculating the coordinates of the center of a circular indentation, there are two cases that need to be addressed:

[0106] (1) When the circular indentation extends beyond the lower boundary, but the center does not extend beyond the lower boundary, then matrix x dm (i3,j3) represents the x-coordinate, and the matrix y dm0 (i3,j3) represents the y-coordinate, with the same range as in the above formula. The formula for calculating the center coordinates (14) is as follows:

[0107]

[0108] (2) When the center of the circular indentation extends beyond the lower boundary, then The center of the circle needs to be shifted in the positive y-axis direction by a factor of the grinding wheel width. Let K be a constant, representing the multiple of the grinding wheel width. The calculation formula (15) is as follows:

[0109]

[0110] Where K needs to be rounded down to the nearest integer, the x-coordinate remains unchanged, and the y-coordinate is recalculated. The calculation formula (16) is as follows:

[0111]

[0112] Matrix y dm (i3,j3) represents the recalculation of the center coordinates of the pits generated within the grinding wheel unfolding diagram. Finally, the matrix y... dm0 (i3,j3) are incorporated into matrix y dm In (i3,j3).

[0113] S8. Based on the calculated coordinates of the center of the indentation, calculate half of the central angle corresponding to the arc extending beyond the boundary, and name it angle α. Based on angle α, calculate the phase angles corresponding to the two endpoints of the arc extending beyond the boundary, and discuss four cases.

[0114] Based on the calculated coordinates of the center of the indentation, half of the central angle corresponding to the arc exceeding the boundary is obtained and named as angle α. The calculation formula (17) is as follows:

[0115]

[0116] Where α1 represents half of the central angle of the arc when the circular indentation extends beyond the lower boundary, and α2 represents half of the central angle of the arc when the circular indentation extends beyond the upper boundary.

[0117] Based on angle α, calculate the phase angles corresponding to the two endpoints of the arc. Depending on the different cases where the circular indentation extends beyond the boundary, the formula for calculating the phase angle falls into the following four categories. Let y... dmt =y dm (i3,j3), such as Figure 4 The specific analyses of cases (a), (b), (c), and (d) shown are as follows:

[0118] ①: When the center of the pit is inside the lower boundary of the grinding wheel, y dmt <d a / 2, the phase angle calculation formula (18) is as follows:

[0119]

[0120] ②: When the center of the pit is outside the lower boundary of the grinding wheel, y dmt <d a / 2, the phase angle calculation formula (19) is as follows:

[0121]

[0122] ③: When the center of the pit is within the upper boundary of the grinding wheel, y dmt >b s -d a / 2, the phase angle calculation formula (20) is as follows:

[0123]

[0124] ④: When the center of the pit is outside the upper boundary of the grinding wheel, y dmt >b s -d a / 2, the phase angle calculation formula (21) is as follows:

[0125]

[0126] Based on the analysis of the above four scenarios, the location of the circular pit can be determined by analyzing the coordinates of the pit's center, and the phase angle corresponding to the arc of the extended portion can be calculated using the center coordinates.

[0127] S9, Set S f A matrix is ​​used to represent discrete points along the circumference of a circular pitted grinding wheel, both pitted and non-pitted, and the marked points are stored in S. f In the (i,j) matrix;

[0128] The circular pit grinding wheel was constructed, and the misalignment of the circular pit was calculated. All discrete points of the circular pit grinding wheel in the coordinate system can be accurately represented. Therefore, S is set... f The (i,j) matrix represents discrete points along the circumference of a circular pitted grinding wheel, distinguishing between pitted and non-pitted points. These marked points are stored in the matrix for easy retrieval in subsequent calculations. Matrix S f The number of rows i in (i,j) is the same as the number of discrete elements in the circumferential direction of the grinding wheel, and the number of columns j is the same as the number of discrete elements in the width direction of the grinding wheel.

[0129] When constructing the pit in the numerical modeling of the circular pit grinding wheel, the distance between the coordinates of the discrete point on the grinding wheel and the coordinates of the center of the circular pit is set to d. t d t Less than the radius d of the pit a When d = 2, it indicates that the point is inside the circular recess of the grinding wheel, and this point is marked as 0. t Greater than or equal to the pit radius d a When / 2, it indicates that the discrete point is on the circumferential surface of the grinding wheel, i.e., the non-dimpled area, and this point is marked as 1. By cyclically marking, the marked points are stored in S. f In the (i,j) matrix. S f Each element in the (i,j) matrix is ​​a set of 0s and 1s representing the positions of dents and non-dents. Thus, the positions of dents and non-dents on the circular dent grinding wheel have been marked.

[0130] S10. By marking the discrete points, calculate the consistency coefficient and calculate the matrix x. ds (k,l),y ds The range of values ​​for k and l in (k,l) is discussed in three cases.

[0131] The consistency coefficient is calculated by labeling discrete points. Let x... dd The x-coordinate and y-coordinate of the center of the indentation are represented by... dd The y-coordinate of the center of the indentation is shown in equation (22) below.

[0132]

[0133] x pp Represents the x-coordinate and y-coordinate of a discrete point. pp The y-coordinate of the discrete point is represented by the following equation (23).

[0134]

[0135] It should be noted that, since it is necessary to calculate whether the distance between the discrete point and the center of the pit is less than the radius of the pit, and the circular pit is offset downwards, the range of values ​​for l in the matrix is ​​as shown in equation (24).

[0136]

[0137] Among them l min We need to round down to the nearest integer, l max We need to round up to the nearest integer. For the range of values ​​for k in the matrix, there are three cases that need to be handled, and the Sf matrix values ​​within the upper and lower arc ranges need to be calculated separately:

[0138] (1) When the pit extends beyond the upper boundary, then ydd <da / 2

[0139] ①: Calculate S within the lower arc range f The matrix value, then the range of values ​​for k is as shown in equation (25):

[0140]

[0141] Where k max It needs to be rounded up. To prevent k max If it exceeds the upper boundary, then k max =n bs .

[0142] The distance from the discrete point to the center of the pit is shown in equation (26):

[0143]

[0144] ②: Calculate S within the range of the upper arc. f The matrix value, then the range of values ​​for k is as shown in equation (27):

[0145]

[0146] Where k min It needs to be rounded down. To prevent k min If it exceeds the lower boundary, then k min =1.

[0147] The distance from the discrete point to the center of the pit is shown in equation (28) below:

[0148]

[0149] (2) When the pit extends beyond the upper boundary, then y dd >(b s -d a / 2);

[0150] ①: Calculate S within the range of the upper arc. f The matrix value, then the range of values ​​for k is shown in equation (29):

[0151]

[0152] Where k min It needs to be rounded down. To prevent k min If it exceeds the lower boundary, then k min =1.

[0153] The distance from the discrete point to the center of the pit is shown in equation (30) below:

[0154]

[0155] ②: Calculate S within the lower arc range f The matrix value, then the range of values ​​for k is as shown in equation (31):

[0156]

[0157] Where k max It needs to be rounded up. To prevent k max If it exceeds the upper boundary, then k max =n bs。

[0158] The distance from the discrete point to the center of the pit is shown in equation (32) below:

[0159]

[0160] (3) When the pit does not extend beyond the upper and lower boundaries, then y dd >d a / 2,y dd <(b s -d a / 2);

[0161] For a normal Sf matrix value, the range of values ​​for k is shown in equation (33) below:

[0162]

[0163] Where k min Need to be rounded down, k max It needs to be rounded up. To prevent k minBeyond the lower boundary, k max If it exceeds the upper boundary, then k min =1,k max =n bs。

[0164] The distance from the discrete point to the center of the pit is shown in equation (34) below:

[0165]

[0166] S11, Calculate S f The sum of elements in each row of the matrix is ​​used to define the fluctuation non-uniformity coefficient λ of the consistency coefficient. Analysis yields a distribution plot of λ as a function of width, and the average value λ is calculated. m Calculate the root mean square error σ of λ. λ ;

[0167] The discrete points are marked by calculating the distance from each discrete point to the center of the pit. The range of the misalignment is defined as 0 to 1. row Establish S fsum and S fstd A matrix that stores the calculated results of the uniformity coefficient's fluctuation coefficient and standard deviation. For example... Figure 6 The figure shows the fluctuation curve of the axial structural consistency coefficient of the grinding wheel. When the misalignment d... m =l row When d = 2, the circular pits on the grinding wheel surface are arranged in a leaf-like sequence, and the calculated results of the non-uniformity coefficient and standard deviation are relatively large; when d = 2, the circular pits on the grinding wheel surface are arranged in a leaf-like sequence, and the calculated results of the non-uniformity coefficient and standard deviation are relatively large. m Greater than or less than l row When the ratio is 2, the calculated results for the non-uniformity coefficient and standard deviation are relatively small, indicating that the leaf sequence arrangement in the circular pit grinding wheel is not reasonable. By adjusting different structural parameters, better results are calculated, realizing a parameter-driven numerical analysis model.

[0168] Simulation Experiment

[0169] Example 1: such as Figure 5 As shown, in this embodiment, the default diameter d of the circular indentation is... a =5, effective grinding area ratio ρ = 0.85, the misalignment in the grinding wheel numerical model is varied regularly, i.e., the misalignment d m =0.5, d m =1, d m =1.5. It can be clearly seen from the figure that, with the diameter of the circular pit and the effective grinding area remaining unchanged, changing the misalignment does not change the number of pits in the wheel development diagram.

[0170] Example 2: such as Figure 6 As shown, in this embodiment, the default misalignment amount d of the circular indentation is... m=2, effective grinding area ratio ρ = 0.85, the diameter of the circular pit in the numerical model of the grinding wheel is varied regularly, that is, the diameter of the circular pit d a =6, d a =8, d a =10. It can be clearly seen from the figure that, with the misalignment and effective grinding area remaining unchanged, changing the pit diameter results in a gradual decrease in the number of pits as the diameter of the grinding wheel increases.

[0171] Example 3: For example Figure 7 As shown, in this embodiment, the default misalignment amount d of the circular indentation is... m =2, diameter d of the circular indentation a =3, and the effective grinding ratio in the numerical model of the grinding wheel is varied systematically, that is, the effective grinding area ratio ρ = 0.7, ρ = 0.85, ρ = 0.9. It can be clearly seen from the figure that, with the misalignment and the diameter of the circular pits remaining unchanged, changing the effective grinding area ratio results in a gradual decrease in the number of pits in the developed diagram of the grinding wheel as the effective grinding area ratio increases.

[0172] Example 4: For example Figure 8 , Figure 9 As shown in the figure, this embodiment studies and analyzes the regular arrangement of circular pits, with the default diameter d of the circular pits. a =3, effective grinding area ratio ρ = 0.85. When the misalignment d m =0 and d m =l row The patterns are regular, with the same arrangement method, and the calculated uniformity coefficient has the same fluctuation coefficient and standard deviation. The uniformity coefficient of the uniformity coefficient is 0.596078, and the standard deviation is 0.206581; when d m =l row / 2 represents a regular arrangement, specifically a leaf-sequential arrangement. The calculated uniformity coefficient has a fluctuation coefficient of 0.298039 and a standard deviation of 0.0983033.

[0173] Example 5: For example Figure 10 , Figure 11 , Figure 12 , Figure 13 , Figure 14 As shown, this embodiment studies and analyzes the irregular arrangement of circular pits, with the default diameter d of the circular pits. a =3, effective grinding area ratio ρ = 0.85. Select the misalignment amount d. m =5.5, d m =6, d m When d = 7, the circular pits are irregularly arranged. mWhen d = 5.5, the coefficient of variation of the consistency coefficient is 0.0329412, and the standard deviation is 0.00847628; when d m When d = 6, the coefficient of variation of the consistency coefficient is 0.0396078, and the standard deviation is 0.00831875; when d m When the coefficient of variation is 7, the coefficient of variation for the consistency coefficient is 0.0678431, and the standard deviation is 0.0185712; from Figure 13 It is evident from the data that the root mean square error of the consistency coefficient of the regular arrangement is much greater than that of the irregular arrangement, proving that the axial structural distribution consistency coefficient of the irregular arrangement is better than that of the regular arrangement.

[0174] Example 6: For example Figure 15 As shown, in this embodiment, the range of the misalignment value is 0 to 1. row The mean square error of the consistency coefficient and the average value of the fluctuation non-uniformity coefficient of the consistency coefficient are calculated with a step size of 0.01, and then a waveform is plotted. Figure 14 The diagram shows the variation of the axial structural consistency coefficient with the amount of misalignment. It is clear from the diagram that when the misalignment is 0, l... row , l row When the value is 2, the consistency coefficient is relatively large and the curve fluctuates significantly. When the misalignment is not one of these three values, the consistency coefficient is relatively small and the curve fluctuates less. This further illustrates that the consistency coefficient of the axial structure distribution with irregular arrangement is better than that with regular arrangement.

[0175] Example 2

[0176] One embodiment of this disclosure provides a system for calculating the axial distribution consistency coefficient of a pitted structured grinding wheel, comprising:

[0177] The initialization definition module is used to define the grinding wheel parameters, establish the coordinate system of the grinding wheel circumferential development diagram, discretize the circumferential surface of the grinding wheel, and calculate the coordinates of discrete points;

[0178] The calculation module is used to calculate the area of ​​all pits and the number of circular pits based on the set diameter of the circular pits and the effective grinding area ratio of the grinding wheel; it also defines pit arrangement parameters and calculates the pit series parameters of the grinding wheel along the circumferential direction.

[0179] Based on a series of parameters, the coordinates of the center of the pit are calculated, a numerical analysis model of the circular pit grinding wheel is established, the misalignment amount is defined, and the coordinates of the center after misalignment are calculated. Based on the obtained coordinates of the center of the pit, the position of the circular pit is analyzed, and the discrete points along the circumference on the circular pit grinding wheel are represented by a matrix. By marking the discrete points, the fluctuation non-uniformity coefficient of the consistency coefficient is calculated.

[0180] This disclosure is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0181] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0182] While the specific embodiments of this disclosure have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of this disclosure. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this disclosure are still within the scope of protection of this disclosure.

Claims

1. A method for calculating the axial distribution consistency coefficient of a pitted structured grinding wheel, characterized in that, include: Define the grinding wheel parameters, establish the coordinate system of the grinding wheel circumferential development diagram, discretize the circumferential surface of the grinding wheel, and calculate the coordinates of the discrete points; Based on the set diameter of the circular pits and the effective grinding area ratio of the grinding wheel, calculate the area of ​​all pits and the number of circular pits; define the pit arrangement parameters and calculate the pit series parameters of the grinding wheel along the circumferential direction. Based on a series of parameters, the coordinates of the center of the pit are calculated, a numerical analysis model of the circular pit grinding wheel is established, the misalignment amount is defined, and the coordinates of the center after misalignment are calculated. Based on the obtained coordinates of the center of the pit, the position of the circular pit is analyzed, and the discrete points along the circumference on the circular pit grinding wheel are represented by a matrix. By marking the discrete points, the fluctuation non-uniformity coefficient of the consistency coefficient is calculated. There are two ways to calculate the coordinates of the center of a circular indentation: one is when the circular indentation extends beyond the lower boundary, but the center does not extend beyond the lower boundary; the other is when the center of the circular indentation extends beyond the lower boundary.

2. The method for calculating the axial distribution consistency coefficient of the pitted structured grinding wheel as described in claim 1, characterized in that, Define the grinding wheel parameters, establish the coordinate system of the grinding wheel circumferential development diagram, discretize the circumferential surface of the grinding wheel, define the dispersion step length and number of discrete points in the circumferential direction of the grinding wheel, the dispersion step length and number of discrete points in the width direction, and calculate the coordinate value of each point on the circumferential surface of the grinding wheel.

3. The method for calculating the axial distribution consistency coefficient of the pitted structured grinding wheel as described in claim 1, characterized in that, The effective grinding area ratio ρ of the circular pit grinding wheel is used to obtain the area of ​​all pits. v d , l s Indicates the circumference length of the grinding wheel. b s Let the width of the grinding wheel be the total area of ​​all the pits. The number of circular pits can be determined from the area of ​​all the pits. n d : The result of calculating the number of pits is rounded down.

4. The method for calculating the axial distribution consistency coefficient of the pit-type structured grinding wheel as described in claim 1, characterized in that, Define the pit arrangement parameters and calculate the pit series parameters of the grinding wheel along the circumferential direction. The series parameters include the number of pit rows, the number of pit columns, the pit row spacing, and the column spacing. In the initial state, the default row spacing is equal to the column spacing.

5. The method for calculating the axial distribution consistency coefficient of the pitted structured grinding wheel as described in claim 1, characterized in that, A numerical analysis model of a grinding wheel with circular pits is established to realize the irregular arrangement of circular pits on the grinding wheel surface. Each row of circular pits is moved a certain distance in the -y direction compared to the previous row. The first row of pits does not move in the -y direction. Starting from the second row, the pits move downwards by a specified distance, which is defined as the misalignment amount. The misalignment amount represents the difference in y-coordinate between the center of the next row of pits and the center of the previous row of pits. The coordinates of the center of the circular pits after the misalignment are calculated and updated to ensure that the pits are located on the grinding wheel surface.

6. The method for calculating the axial distribution consistency coefficient of the pitted structured grinding wheel as described in claim 5, characterized in that, When the circular pit is misaligned downwards, it will touch the lower boundary. Define the upward translation amount of the circular pit and calculate the coordinates of the center after misalignment. When the circular pit is misaligned downwards, it will touch the lower boundary, causing the circular pit to partially or completely exceed the lower boundary of the grinding wheel. Considering the grinding uniformity, set the following: when the circular pit touches the lower boundary, the arc part that exceeds the lower boundary will be translated by the width of the grinding wheel in the y direction.

7. The method for calculating the axial distribution consistency coefficient of the pitted structured grinding wheel as described in claim 1, characterized in that, Based on the calculated coordinates of the center of the pit, half of the central angle corresponding to the arc extending beyond the boundary is calculated and named α angle. Based on α angle, the phase angles corresponding to the two endpoints of the arc extending beyond the boundary are calculated, and the calculation is performed in four cases.

8. The method for calculating the axial distribution consistency coefficient of the pitted structured grinding wheel as described in claim 1, characterized in that, set up S f A matrix is ​​used to represent discrete points along the circumference of a circular pitted grinding wheel, both pitted and non-pitted, and the marked points are stored in... S f ( i,j In the matrix, the matrix S f ( i,j ) number of rows i The number of columns is the same as the number of discrete particles in the circumferential direction of the grinding wheel. j The number of discrete particles in the width direction is the same as that of the grinding wheel.

9. A system for calculating the axial distribution consistency coefficient of a pitted structured grinding wheel, characterized in that, Specifically, the method for calculating the axial distribution consistency coefficient of the pitted structured grinding wheel as described in any one of claims 1-8 includes: The initialization definition module is used to define the grinding wheel parameters, establish the coordinate system of the grinding wheel circumferential development diagram, discretize the circumferential surface of the grinding wheel, and calculate the coordinates of discrete points; The calculation module is used to calculate the area of ​​all pits and the number of circular pits based on the set diameter of the circular pits and the effective grinding area ratio of the grinding wheel; it also defines pit arrangement parameters and calculates the pit series parameters of the grinding wheel along the circumferential direction. Based on a series of parameters, the coordinates of the center of the pit are calculated, a numerical analysis model of the circular pit grinding wheel is established, the misalignment amount is defined, and the coordinates of the center after misalignment are calculated. Based on the obtained coordinates of the center of the pit, the position of the circular pit is analyzed, and the discrete points along the circumference on the circular pit grinding wheel are represented by a matrix. By marking the discrete points, the fluctuation non-uniformity coefficient of the consistency coefficient is calculated.

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