Abrasive water jet abrasive grain distribution prediction and uniformity evaluation method for spherical and cylindrical machining

Abstract

The application discloses a kind of abrasive water jet abrasive grain distribution prediction and uniformity evaluation method for spherical and cylindrical processing, according to the type of processing surface to be selected corresponding processing path, the processing path is dispersed into multiple processing points, the fitting parameters of the working condition at each discrete processing point are calculated, the real-time target distance and the incidence angle are used as joint index, the corresponding two-dimensional Gaussian abrasive grain distribution is retrieved from the fitting parameter database, and is mapped to the surface of the processing surface to obtain the surface abrasive grain distribution;The surface abrasive grain distribution corresponding to each discrete processing point is weighted and superimposed to obtain the cumulative abrasive grain distribution, and the surface applicability is judged according to the surface radius and the characteristic size of local abrasive grain distribution;Based on the cumulative abrasive grain distribution, the variation coefficient and uniformity index are calculated, and the prediction result is output.The application constructs the fitting parameter database with target distance and incidence angle as joint index, and is compatible with the unified abrasive grain distribution prediction and reinforced uniformity evaluation of two typical processing paths of spherical surface and cylindrical surface.

Description

Technical Field

[0001] This invention relates to the field of abrasive analysis technology, mainly to abrasive waterjet machining, curved surface machining modeling, abrasive distribution prediction and uniformity control, specifically to a method for predicting and evaluating the abrasive distribution and uniformity of abrasive waterjet machining for spherical and cylindrical surfaces. Background Technology

[0002] Abrasive waterjet machining relies on high-speed water jets carrying abrasive particles to impact the workpiece surface, achieving material removal, surface strengthening, surface modification, and polishing. This machining method has advantages such as low processing load, narrow heat-affected zone, wide range of applicable materials, and adaptability to complex curved surface forming, making it of significant application value in aerospace, automotive manufacturing, mold processing, and surface strengthening of complex curved components.

[0003] In abrasive waterjet surface strengthening processes, the spatial distribution characteristics of abrasive particles impacting the workpiece surface directly determine the degree of plastic deformation, residual compressive stress level, surface roughness, and strengthening uniformity of the material surface. Excessive concentration of abrasive particles can easily lead to localized impact overload; conversely, sparse distribution results in insufficient strengthening in certain areas. Therefore, constructing an abrasive particle distribution prediction model and applying it to curved surface machining path planning is crucial for improving the surface strengthening quality of complex curved surfaces.

[0004] Current research on abrasive particle distribution prediction mostly focuses on planar machining conditions. The abrasive particle distribution at a single stagnation point under planar conditions can be obtained through simulation or fitting experimental data. When the nozzle moves along a straight line, the trajectory can be discretized into several injection points, and the local abrasive particle distribution at each point can be superimposed to complete the prediction. However, curved surfaces such as spheres and cylinders exhibit curvature effects, requiring the abrasive particle positions in the planar coordinate system to be mapped to the surface of the curved solid. Furthermore, the directions of the local tangent planes corresponding to each discrete machining point are different.

[0005] In practical curved surface machining scenarios, nozzle motion paths vary. Cylindrical surface machining can proceed either axially or along the curvature direction; spherical surface machining presents two typical approaches: one is where the nozzle axis follows the movement, always pointing towards the center of the sphere; the other is where the nozzle maintains a vertical orientation and a fixed height, sweeping horizontally above the sphere. When machining spherical surfaces using the latter approach, the target distance and the incident angle of the jet relative to the local tangential plane continuously change with the machining position. In this case, directly using a planar abrasive particle distribution model with a 90° incident angle and a fixed target distance will result in significant prediction errors.

[0006] As abrasive particle distribution data under planar working conditions accumulates, two-dimensional Gaussian distribution parameters can be fitted for different combinations of target distance and incident angle. However, existing methods generally lack a mechanism to dynamically correlate the fitted parameters under multiple working conditions with the real-time geometric state of discrete points on the curved surface path. Therefore, it is urgent to construct a database of fitted parameters with target distance and incident angle as joint indices, and to establish a unified abrasive particle distribution prediction model and a method to enhance uniformity evaluation that is compatible with both spherical and cylindrical typical machining paths. Summary of the Invention

[0007] This invention overcomes the shortcomings of the prior art and provides a method for predicting and evaluating the abrasive particle distribution and uniformity of abrasive waterjet for spherical and cylindrical surface machining. It constructs a fitting parameter database with target distance and incident angle as joint indexes and establishes a unified abrasive particle distribution prediction model and enhanced uniformity evaluation method that is compatible with two typical machining paths: spherical and cylindrical surfaces.

[0008] To achieve the above objectives, the technical solution adopted by this invention is: a method for predicting and evaluating the distribution and uniformity of abrasive particles in waterjet abrasive processes suitable for curved surface machining, comprising: Step S1: Obtain the abrasive waterjet processing parameters, the geometric parameters of the surface to be processed, and the processing path parameters, and select the processing path according to the surface type of the surface to be processed; Step S2: A two-dimensional Gaussian local planar abrasive particle distribution model is established using a two-dimensional Gaussian function, and parameter fitting is performed based on parameter regression of target distance and incident angle using a general two-dimensional Gaussian model. Step S3: Establish the mapping relationship between the local plane coordinates and the surface coordinates of the surface to be processed based on the geometric parameters of the surface to be processed, and map the local plane abrasive points to the surface. Step S4: Discretize the selected processing path into N processing points according to the set path dispersion step length, calculate the nozzle exit position, the intersection of the jet and the surface to be processed, the unit direction of the jet, the unit normal vector of the surface, the real-time target distance and the incident angle corresponding to the i-th processing point; establish the local planar abrasive distribution of the i-th processing point based on the real-time target distance and the incident angle, and obtain the surface abrasive distribution corresponding to the i-th processing point using the mapping relationship in step S3; Step S5: Based on the surface radius and the characteristic size of the local abrasive grain distribution, the applicability of the surface is judged, and the abrasive grain distributions corresponding to the N discrete processing points are weighted and superimposed to obtain the cumulative abrasive grain distribution in the target processing area. Step S6: Calculate the coefficient of variation and uniformity index based on the cumulative abrasive particle distribution, and output the surface abrasive particle distribution prediction result and uniformity evaluation result.

[0009] In a preferred embodiment of the present invention, the abrasive waterjet processing parameters include one or more of the following: jet pressure, target distance, nozzle diameter, abrasive flow rate, abrasive particle size, nozzle moving speed, and path deviation. The geometric parameters of the surface to be processed include one or more of the following: surface type, cylindrical radius, spherical radius, cylindrical axial length, spherical processing area, and surface normal direction. The machining path parameters include one or more of the following: cylindrical axial machining path, spherical machining path, number of discrete points on the path, distance between adjacent discrete points, and nozzle dwell time.

[0010] In a preferred embodiment of the present invention, step S1, selecting the processing path according to the type of surface to be processed, includes the following steps: The surface to be processed includes a cylindrical surface or a spherical surface; When the surface to be processed is a cylindrical surface, select a constant normal path that moves along the axial direction of the cylindrical surface or a constant normal path that moves along the curvature direction of the cylindrical surface and the nozzle rotates synchronously with the curvature. When the surface to be processed is a sphere, select a constant normal path in which the nozzle axis always points to the center of the sphere, or select a fixed posture path in which the nozzle axis keeps a fixed vertical direction, the nozzle outlet keeps a fixed height, and moves at a constant speed in the horizontal direction.

[0011] In a preferred embodiment of the present invention, in step S2, the two-dimensional Gaussian local planar abrasive particle distribution model is: ; in: These are the coordinates of the distribution center; These are the standard deviations in the x and y directions, respectively, reflecting the degree of dispersion of abrasive grains along the x and y axes in the erosion region; is the correlation coefficient between x and y, which measures the strength of the linear relationship between the two variables, and its value ranges from [-1,1]; A is the distribution amplitude, which represents the peak value of the abrasive density in the erosion center region.

[0012] In a preferred embodiment of the present invention, when When x and y are linearly independent, the expression for the two-dimensional Gaussian distribution degenerates into: ; The distribution described here is approximately isotropic and is an axis-aligned Gaussian distribution.

[0013] In a preferred embodiment of the present invention, at the i-th discrete processing point on the sphere Establish a local tangent plane at point (x, y), with local coordinates (x, y). The two mutually orthogonal unit direction vectors of the local tangent plane are... and Then the coordinates of the local planar abrasive point mapped onto the sphere are: ; in, and Let be two mutually perpendicular unit direction vectors within the local tangent plane at that point. The three-dimensional coordinates of the local planar abrasive particles mapped onto the sphere.

[0014] In a preferred embodiment of the present invention, in step S3, the mapping relationship from the local planar abrasive grain coordinates (x, y) to the cylindrical surface includes: The formula for arc length is ; If the local planar coordinate x is the length after unfolding along the arc of the semi-cylinder, then... ; ; ; Where x is the local coordinate along the arc of the semi-cylinder, and y is the local coordinate along the length of the cylinder. The central angle corresponding to the local arc length coordinate x. The three-dimensional coordinates of the local planar abrasive particles mapped onto the surface of the semi-cylinder; And / or, The nozzle axis always points in the constant normal path to the center of the sphere: The nozzle moves along the spherical trajectory, and the nozzle axis changes with the processing point and always passes through the center of the sphere, so that the incident angle at each discrete processing point is kept at 90°, and the real-time target distance is kept at the set target distance H0. In the spherical fixed posture path, let the center of the sphere be located at the origin of the coordinate system and the radius of the sphere be... The nozzle jet unit direction is The nozzle outlet is discretized along a fixed height plane as follows: ; The nozzle outlet has a fixed Z-height, and y0 is the starting coordinate of the Y-axis; The X-axis coordinate of the i-th discrete sampling point, where x0 is the starting X-axis coordinate. This represents the step size of the nozzle's movement along the X direction; The point where the jet axis intersects the upper hemisphere is: ; Real-time target distance H i and the incident angle relative to the local tangent plane for: ; ; ; Where, n id is the unit normal vector of the i-th spherical processing point; d is the jet direction vector; The dot product of the jet direction and the sphere normal vector; And / or, The spherical fixed attitude path is sprayed with a 90° normal direction relative to the local tangent plane only at the spherical vertex; after leaving the spherical vertex, the real-time target distance increases with the increase of horizontal distance, and the incident angle decreases with the increase of horizontal distance; the first unit direction vector of the local tangent plane is taken as the projection direction of the jet direction in the local tangent plane, and the second unit direction vector is orthogonal to the first unit direction vector and the spherical normal vector; when the projection of the spherical vertex degenerates, the path tangent is used as the first unit direction vector.

[0015] In a preferred embodiment of the present invention, in step S4, when the surface to be processed is a cylindrical surface, the constant normal path moving at a constant speed along the axis of the cylindrical surface, the nozzle moving along the axial direction of the cylindrical surface to form an abrasive belt, and the cylindrical surface processing path discretized as follows: i = 0, 1, 2, ..., N-1; in, Let be the axial coordinate of the i-th discrete machining point. The initial axial coordinate. is the axial distance between adjacent discrete machining points, and N is the number of discrete points on the cylindrical path; And / or, When the surface to be processed is a cylindrical surface, the constant normal path moving along the curvature direction of the cylindrical surface is discretized by the arc length of the cylindrical surface, and the radius of the cylindrical surface is assumed to be... ,but: ; , ; in, For cylindrical surface machining points, The unit normal vector of the cylinder. This refers to the nozzle exit position. For the unit direction of the jet, For a constant target distance, The step size is the arc length of the cylinder. Angular step size; the nozzle moves and rotates synchronously along the circumference, so that the nozzle axis always remains at 90° relative to the local tangential plane.

[0016] In a preferred embodiment of the present invention, the cumulative abrasive grain distribution on the curved surface is obtained by superimposing the abrasive grain distributions at each discrete machining point: ; in, This represents the cumulative abrasive grain distribution at point P on the curved surface. The abrasive grain distribution after mapping the i-th discrete machining point to the surface; When the distribution areas of multiple dwelling points overlap, the same surface point P will be affected by multiple factors simultaneously. Contributions; It is the weight coefficient of the i-th discrete processing point, used to represent the processing intensity at the i-th position; When the processing conditions at discrete points are the same, then .

[0017] In a preferred embodiment of the present invention, the surface applicability constraint is as follows: ; Where L is the characteristic size of the local abrasive grain distribution, and R is the radius of the curved surface; When the object being processed is a cylindrical surface ; When the object being processed is a sphere ; when At that time, it is assumed that the current surface radius satisfies the applicability requirement of mapping local planar abrasive grain distribution to the surface; And / or, the uniformity of the cumulative abrasive grain distribution on the surface is evaluated using the coefficient of variation and uniformity index, where the coefficient of variation is: ; in, S represents the average cumulative abrasive particle distribution within the target processing area, and S represents the standard deviation of the cumulative abrasive particle distribution within the target processing area; the uniformity index is: ; Among them, the closer U is to 1, the more uniform the distribution of abrasive particles on the curved surface.

[0018] This invention addresses the deficiencies in the technical background, and the beneficial technical effects of this invention are: A method for predicting and evaluating the abrasive particle distribution and uniformity of abrasive waterjet for spherical and cylindrical surface machining is proposed. A fitting parameter database with target distance and incident angle as joint indexes is constructed, and a unified abrasive particle distribution prediction model and enhanced uniformity evaluation method compatible with two typical machining paths of spherical and cylindrical surfaces are established.

[0019] 1. This invention extends planar abrasive distribution to cylindrical and spherical machined surfaces, enabling the prediction of abrasive distribution from planar to curved surfaces.

[0020] 2. This invention proposes a method for predicting the distribution of abrasive particles moving along the axial direction of the cylindrical surface during cylindrical surface machining, which can simulate the formation process of a single abrasive band on the cylindrical surface.

[0021] 3. This invention proposes a normal jetting path modeling method for spherical surface machining, where the nozzle always points towards the center of the sphere, so that each discrete machining point on the spherical path can be mapped using the normal jetting plane distribution function.

[0022] 4. This invention draws on the idea of ​​discretizing planar motion trajectories to decompose the machining path of cylindrical or spherical surfaces into multiple local spray points, which can obtain the cumulative abrasive distribution of the curved surface by superimposing multiple local abrasive distributions.

[0023] 5. This invention introduces surface radius applicability constraints and uniformity evaluation indicators, which can quantitatively evaluate the predicted results of surface abrasive particle distribution. Attached Figure Description

[0024] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0025] Figure 1 This is a flowchart illustrating a preferred embodiment of the present invention for predicting and evaluating the abrasive particle distribution and uniformity of abrasive waterjet machining for spherical and cylindrical surfaces. Figure 2 This is a schematic diagram of the machining path when the surface to be machined is a cylindrical surface, in a preferred embodiment of the present invention, for predicting and evaluating the distribution and uniformity of abrasive particles in a waterjet abrasive jet for machining spherical and cylindrical surfaces, and the surface to be machined is a cylindrical surface. Figure 3 This is a schematic diagram of the movement path along the curvature direction of a cylindrical surface when the surface to be processed is a cylindrical surface in a preferred embodiment of the present invention for predicting and evaluating the distribution and uniformity of abrasive particles in a waterjet abrasive jet for machining spherical and cylindrical surfaces. Figure 4 This is a preferred embodiment of the present invention, a method for predicting and evaluating the abrasive particle distribution and uniformity of abrasive waterjet for machining spherical and cylindrical surfaces. When the surface to be machined is a spherical surface, a schematic diagram of the fixed pose path of the spherical surface is shown (where H1, H2, H3, and H4 represent the real-time target distance at different positions of the nozzle on the spherical surface). Figure 5 This is a schematic diagram of the path in a preferred embodiment of the present invention, which shows the path of the nozzle always pointing to the center of the sphere during the machining of a spherical surface when the surface to be machined is a spherical surface, in an abrasive waterjet abrasive particle distribution prediction and uniformity evaluation method for machining spherical and cylindrical surfaces. Among them, 1. Nozzle; 2. Abrasive grain; 4. Cylindrical surface; 41. Cylindrical axis; 5. Spherical surface. Detailed Implementation

[0026] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. These drawings are simplified schematic diagrams, which are only used to illustrate the basic structure of the present invention and therefore only show the components relevant to the present invention.

[0027] It should be noted that if directional indicators (such as up, down, bottom, top, etc.) are involved in the embodiments of the present invention, these directional indicators are only used to explain the relative positional relationship and movement of the components in a specific posture. If the specific posture changes, the directional indicators will also change accordingly. The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, features defined with "first" and "second" may explicitly or implicitly include one or more of that feature. Unless otherwise explicitly specified and limited, the terms "set," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal connection of two components. For those skilled in the art, the specific meaning of the above terms in the present invention can be understood according to the specific circumstances.

[0028] Example 1, as Figure 1 , Figure 2 , Figure 3 , Figure 4 , Figure 5 As shown, a method for predicting and evaluating the uniformity of abrasive grain distribution in a waterjet abrasive jets suitable for curved surface machining includes: Step S1: Obtain the abrasive waterjet processing parameters, the geometric parameters of the surface to be processed, and the processing path parameters, and select the processing path according to the surface type of the surface to be processed.

[0029] The abrasive waterjet processing parameters include one or more of the following: jet pressure, target distance, nozzle diameter, abrasive flow rate, abrasive particle size, nozzle moving speed, and path deviation.

[0030] The geometric parameters of the surface to be processed include one or more of the following: surface type, cylindrical radius, spherical radius, cylindrical axial length, spherical processing area, and surface normal direction. The machining path parameters include one or more of the following: cylindrical axial machining path, spherical machining path, number of discrete points on the path, distance between adjacent discrete points, and nozzle dwell time.

[0031] Specifically, when the surface to be processed is a cylindrical surface 4, a constant normal path that moves along the axial direction of the cylindrical surface 4 or a constant normal path that moves along the curvature direction of the cylindrical surface 4 and the nozzle 1 rotates synchronously with the curvature is selected; when the surface to be processed is a spherical surface 5, a constant normal path in which the nozzle axis always points to the center of the sphere is selected, or a fixed posture path in which the nozzle axis keeps a fixed vertical direction, the nozzle outlet keeps a fixed height and moves at a uniform speed in the horizontal direction is selected.

[0032] Step S2: A two-dimensional Gaussian local planar abrasive particle distribution model is established using a two-dimensional Gaussian function, and parameter fitting is performed based on parameter regression of target distance and incident angle using a general two-dimensional Gaussian model.

[0033] The two-dimensional Gaussian local planar abrasive particle distribution model is as follows: ; in: These are the coordinates of the distribution center; These are the standard deviations in the x and y directions, respectively, reflecting the degree of dispersion of the abrasive particles 2 in the erosion region along the x and y axes; is the correlation coefficient between x and y, which measures the strength of the linear relationship between the two variables, and its value ranges from [-1, 1]; A is the distribution amplitude, representing the peak value of the abrasive grain density in the erosion center region. The model input is the local planar coordinates (x, y), and the parameters to be fitted include the distribution amplitude A and the distribution center coordinates. Standard deviation in two directions and correlation coefficient The output is the abrasive particle distribution value f(x,y) at that position. The target distance and incident angle are used to determine the above two-dimensional Gaussian parameters under the corresponding working conditions.

[0034] Furthermore, when When x and y are linearly independent, the expression for the two-dimensional Gaussian distribution degenerates into: The distribution described here is approximately isotropic and is an axis-aligned Gaussian distribution.

[0035] Specifically, parameter fitting is performed by establishing parameter regression for target distance and incident angle based on a general two-dimensional Gaussian model, including: Using target distance and incident angle as a joint index, the fitting parameters corresponding to each combination of working conditions are stored in the fitting parameter database. The fitting parameter database includes: distribution amplitude A, distribution center coordinates, etc. Standard deviation and correlation coefficient The distribution parameters in each working condition record are all obtained by pre-fitting the local planar abrasive particle distribution data under the corresponding target distance and incident angle combination conditions.

[0036] Furthermore, for the i-th discrete processing point, with the real-time target distance H... i and angle of incidence A combined index is constructed, and the parameter set is obtained by direct retrieval from the fitting parameter database. : ; in, Let be the amplitude of the i-th two-dimensional Gaussian. , Let be the coordinates of the planar aggregation center of the i-th abrasive grain cluster, and be the location of the cluster center. , The standard deviation of the positional distribution in the x and y directions controls the expansion range of the cluster in both directions; is the correlation coefficient of the xy coordinates of the i-th cluster, used to control the degree of ellipse rotation. The height of the blades extending from the cluster; The cluster tilt angle.

[0037] The parameter set is then used to construct a local two-dimensional Gaussian abrasive grain distribution for the i-th discrete machining point. That is, for different combinations of target distance and incident angle, a set of parameters is fitted to obtain the result. A database of fitting parameters was established with target distance and incident angle as joint indices.

[0038] Step S3: Establish the mapping relationship between the local planar coordinates and the surface coordinates of the surface to be processed based on the geometric parameters of the surface to be processed, and map the local planar abrasive particles to the surface.

[0039] Specifically, when the surface to be machined is curved, the mapping relationship from the local planar abrasive coordinates (x, y) to the cylindrical surface 4 includes: The formula for arc length is ; If the local planar coordinate x is the length after unfolding along the arc of the semi-cylinder, then... That is, convert the arc length x on the plane into the central angle of the semi-cylinder. ; Where is the radius of the cylinder; ; ; Where x is the local coordinate along the arc of the semi-cylinder, and y is the local coordinate along the length of the cylinder surface. The central angle corresponding to the local arc length coordinate x. The coordinates of the local planar abrasive grain 2 after being mapped onto the semi-cylindrical surface are 3D coordinates.

[0040] Specifically, when the surface to be processed is sphere 5, at the i-th discrete processing point on sphere 5 Establish a local tangent plane at point (x, y), with local coordinates (x, y). The two mutually orthogonal unit direction vectors of the local tangent plane are... and Then the coordinates of the local planar abrasive grain 2 mapped onto the spherical surface 5 are: ; in, and Let be two mutually perpendicular unit direction vectors within the local tangent plane at that point. The coordinates of the local planar abrasive grain 2 after being mapped onto the spherical surface 5 are 3D coordinates.

[0041] Step S4: Discretize the selected processing path into N processing points according to the set path dispersion step length, calculate the nozzle exit position, the intersection of the jet and the surface to be processed, the unit direction of the jet, the unit normal vector of the surface, the real-time target distance and the incident angle corresponding to the i-th processing point; establish the local planar abrasive distribution of the i-th processing point based on the real-time target distance and the incident angle, and obtain the surface abrasive distribution corresponding to the i-th processing point using the mapping relationship in step S3.

[0042] Specifically, when the surface to be processed is cylindrical surface 4, a constant normal path that moves along the axial direction of cylindrical surface 4 (i.e., a constant normal path that moves at a constant speed along the axis 41 of cylindrical surface) is selected. Nozzle 1 moves along the axial direction of cylindrical surface 4 to form an abrasive belt. The processing path of cylindrical surface 4 is discretized as follows: i = 0, 1, 2, ..., N-1; in, Let be the axial coordinate of the i-th discrete machining point. The initial axial coordinate. is the axial distance between adjacent discrete machining points, and N is the number of discrete points on the cylindrical path.

[0043] Furthermore, when the surface to be processed is cylindrical surface 4, a constant normal path is selected that moves along the curvature direction of the cylindrical surface and the nozzle 1 rotates synchronously with the curvature. This constant normal path, moving along the curvature direction of the cylindrical surface, is discretized using the arc length of the cylindrical surface. Let the radius of the cylindrical surface be... ,but: ; , ; in, For cylindrical surface machining points, The unit normal vector of the cylinder. This refers to the nozzle exit position. For the unit direction of the jet, The target distance is constant. The step size is the arc length of the cylinder. Angular step size; Nozzle 1 moves and rotates synchronously along the circumference, so that the nozzle axis always remains at 90° relative to the local tangential plane.

[0044] Specifically, when the surface to be processed is a sphere 5, a constant normal path is selected in which the nozzle axis always points to the center of the sphere; then, the nozzle 1 moves along the trajectory of the sphere 5, the nozzle axis changes with the processing point and always passes through the center of the sphere, so that the incident angle at each discrete processing point is kept at 90°, and the real-time target distance is kept at the set target distance H0. When the surface to be processed is spherical surface 5, a fixed posture path is selected where the nozzle axis remains fixed in the vertical direction, the nozzle 1 outlet remains at a fixed height, and the nozzle moves at a uniform speed in the horizontal direction. In this fixed posture path for spherical surface 5, assuming the center of the sphere is located at the origin of the coordinate system... The radius of the sphere and the unit direction of the nozzle jet are... The nozzle outlet is discretized along a fixed height plane as follows: ; The nozzle outlet has a fixed Z-height, and y0 is the starting coordinate of the Y-axis; The X-axis coordinate of the i-th discrete sampling point, where x0 is the starting X-axis coordinate. This represents the step size of the nozzle's movement along the X direction; The point where the jet axis intersects the upper hemisphere is: ; Real-time target distance H i and the incident angle relative to the local tangent plane for: ; ; ; Where, n i Let be the unit normal vector of the i-th spherical processing point.

[0045] Step S5: Based on the surface radius and the characteristic size of the local abrasive grain distribution, the applicability of the surface is judged, and the abrasive grain distributions corresponding to the N discrete processing points are weighted and superimposed to obtain the cumulative abrasive grain distribution within the target processing area.

[0046] Specifically, the surface applicability constraint is as follows: Where L is the characteristic size of the local abrasive grain distribution, and R is the radius of the curved surface; When the object being processed is cylindrical surface 4 ; When the object being processed is a spherical surface 5 ; when At that time, it is assumed that the current surface radius satisfies the applicability requirement of mapping local planar abrasive grain distribution to the surface.

[0047] Specifically, the cumulative abrasive grain distribution on the curved surface is obtained by superimposing the abrasive grain distributions at each discrete machining point: ;in, This represents the cumulative abrasive grain distribution at point P on the curved surface. The abrasive grain distribution after mapping the i-th discrete machining point to the surface; When the distribution areas of multiple dwelling points overlap, the same surface point P will be affected by multiple factors simultaneously. Contributions; It is the weight coefficient of the i-th discrete processing point, used to represent the processing intensity at the i-th position; When the processing conditions at discrete points are the same, for example: constant nozzle speed, equal discrete spacing, constant abrasive flow rate, and the same equivalent residence time at each discrete point, then .

[0048] Step S6: Calculate the coefficient of variation and uniformity index based on the cumulative abrasive particle distribution, and output the predicted distribution result and uniformity evaluation result of the curved abrasive particle 2.

[0049] Specifically, the uniformity of the cumulative abrasive grain distribution on the curved surface is evaluated using the coefficient of variation and uniformity index. The coefficient of variation is: ;in, S represents the average cumulative abrasive particle distribution within the target processing area, and S represents the standard deviation of the cumulative abrasive particle distribution within the target processing area; the uniformity index is: Where, the closer U is to 1, the more uniform the distribution of abrasive particles on the curved surface.

[0050] Example 2: Based on Example 1, taking a planar working condition with vertical spraying from nozzle 1 and a target distance of 40mm as an example, global parameters are obtained by fitting the plane abrasive particle impact point data: Distribution amplitude: Correlation coefficient: ; Distribution center coordinates: ; Standard deviations in the x and y directions: ; in, This indicates that the distribution of abrasive particles 2 is basically close to an axisymmetric two-dimensional Gaussian, with a very small center offset, close to the origin, and a relatively concentrated distribution. Therefore, the local planar abrasive particle distribution function can be expressed as: .

[0051] Furthermore, the fitting of the planar abrasive particle impact point data described here employs existing techniques such as nonlinear least-squares fitting using a two-dimensional Gaussian function. As long as it can basically achieve the fitting calculations required by this scheme, the specific fitting algorithm will not be elaborated upon here. For example, the impact point data of abrasive particles 2 obtained from the simulation are statistically analyzed according to local planar coordinates to obtain the abrasive particle 2 count at each location; then, a two-dimensional Gaussian function is used to fit the data according to the least-squares criterion to obtain the parameter data. Further details will not be elaborated upon here.

[0052] Example 3: When nozzle 1 moves at a constant speed along the axial direction of cylindrical surface 4, let the radius of the cylindrical surface be... The axial position of the current discrete machining point Now, consider a single abrasive grain point within a local planar abrasive grain distribution. The central angle corresponding to this point is: ; Based on the mapping relationship: ; Substitute the values: ; The calculation yielded: ; Therefore, the x-coordinate in the local plane, after being transformed from arc length to central angle, is mapped to the horizontal and vertical coordinates of the semi-cylinder surface; the y-coordinate in the local plane is related to the current discrete point position Y. k The superimposed layers form the 4 axial positions of the cylindrical surface.

[0053] It should be noted that in the actual abrasive grain distribution, most abrasive grains 2 are concentrated near the distribution center. For example, in Example 1, the standard deviation is approximately: ; If the main scope of action is taken as Therefore, most of the abrasive grains 2 are located within a range of approximately 0.864 mm. This range is much smaller than the radius of the semi-cylinder 30 mm, so the change in the lateral coordinates before and after the actual abrasive grain point mapping is small, which indicates that the local plane approximation is reasonable under this radius of curvature.

[0054] Example 4: When the nozzle axis always points towards the center of the sphere and moves at a constant speed, nozzle 1 at that point maintains a local 90° normal spray. Let the radius of the sphere be: The center of the ball is: ; Take the top point of the sphere as a discrete processing point: ; Take local planar abrasive grain points: ; The coordinates of this point mapped onto sphere 5 are: ; Substitute the values: ; therefore: .

[0055] It can be seen that after the coordinate points in the local plane are projected radially onto the sphere, the X, Y, and Z coordinates all change, and the mapped points are located on the spherical surface with a radius of 50 mm.

[0056] It should be noted that in actual abrasive particle distribution prediction, most abrasive particles are concentrated near the distribution center. When x 、y The value is much smaller than the radius of the sphere. At this time, the changes in X and Y coordinates after mapping from sphere 5 are small, which is a normal phenomenon in the process of mapping from the local plane to sphere 5. This phenomenon also shows that when the effective range of local abrasive particle distribution is much smaller than the radius of the sphere, the local plane approximation has good applicability.

[0057] Example 5: Assume the axial machining length of the cylindrical surface. Discrete spacing Then the number of discrete points along the axial path of the cylinder is: ; The axial coordinates of the discrete point are: ; Right now: ; At each discrete machining point, the planar abrasive distribution function f(x, y) in Example 1 is called, and it is mapped to the cylindrical surface through the cylindrical mapping relationship in Example 2.

[0058] If the weights of each discrete machining point are equal, then the cumulative abrasive grain distribution on cylindrical surface 4 is as follows: ; in, This represents the contribution of the i-th discrete machining point to the surface point P after being mapped onto cylindrical surface 4. Through the above superposition, a cumulative abrasive band can be obtained along the axial direction of cylindrical surface 4.

[0059] Example 6: For a spherical path, the path can be discretized into multiple processing points according to the spherical arc length. Let the total arc length of the spherical path be: ; The discrete arc length spacing is: ; The number of discrete points on the spherical path is: ; For each discrete machining point on the spherical surface, a local tangential plane coordinate system is established, and the local planar abrasive particle distribution function f(x, y) at the same target distance is called. Then, the local planar abrasive particle points are mapped onto the surface of sphere 5, and the contributions of each discrete point are summed. ; Where F(P) is the cumulative abrasive particle distribution value at point P on the spherical surface. Let be the contribution of the i-th discrete spherical processing point to point P after mapping.

[0060] This method is equivalent to extending the idea of ​​"single dwelling point superposition" under planar linear motion trajectory to spherical path, except that the local plane corresponding to each single dwelling point needs to be mapped to sphere 5 first before surface superposition.

[0061] Example 7: For the planar abrasive particle distribution function in Example 1, its standard deviation is: , ; The characteristic size of the local abrasive grain distribution is taken as: ; but: ; Define surface applicability parameters: ; For cylinder 4 with a radius of 30mm: ; For a sphere 5 with a radius of 50mm: ; If the applicability threshold is set as follows: ; but: ; This indicates that under this working condition, the radii of curvature of both cylindrical surface 4 and spherical surface 5 are within a reasonable range, and the mapping of local planar abrasive grain distribution to curved surface has good applicability.

[0062] Example 8: Discretize the target processing area of ​​cylindrical surface 4 or spherical surface 5 into M sampling points: ; Calculate the cumulative abrasive particle distribution value at each sampling point: ; The cumulative average abrasive particle distribution is: ; The cumulative standard deviation of abrasive particle distribution is: ; The coefficient of variation is: ; The uniformity index is: ; If the superposition of paths on a certain surface results in: ;but: ; The closer this value is to 1, the more uniform the abrasive grain distribution on the curved surface. This index allows for comparison of the uniformity of abrasive grain distribution on curved surfaces under different target distances, surface radii, path discrete spacing, and nozzle speed conditions.

[0063] Example 9: A constant normal path for axial movement of a cylindrical surface, with a radius... The outer surface of the semi-cylinder is the object to be machined, and the axis 41 of the cylinder is taken as the Y direction. The abrasive waterjet machining parameters are: jet pressure 5MPa, nozzle 1 diameter 1.5mm, abrasive flow rate 5g / min, and abrasive particle size... Set the target distance to 40mm and the nozzle 1 moving speed. .

[0064] Nozzle 1 moves axially at a constant speed along the generatrix at the top of cylinder 4, with a path range of... to , far from a walk ,but: ; ; ; ; Nozzle jet direction is Therefore, the real-time target distance of each discrete point is 40mm, the incident angle is 90°, and the two-dimensional Gaussian parameter in the common basic parameters is used.

[0065] For example, when At that time, take local planar abrasive grain points. The cylindrical mapping angle is: ; ; ; The surface abrasive distributions of all 151 discrete points were superimposed with equal weights. The effective reinforcement zone with a local arc width of ±0.15 mm and a Y=-12 mm to 12 mm range was used as the evaluation area. The cumulative average abrasive distribution was calculated to be approximately 2541.04, and the standard deviation was approximately 111.06.

[0066] ; ; ; Therefore, under the constant normal path along the cylindrical surface, the local planar abrasive distribution is mapped onto the cylindrical surface, which meets the applicability requirements and can form an abrasive band that is continuous and has good uniformity along the cylindrical surface axis.

[0067] Example 10: A constant normal path in which the cylindrical surface moves in the direction of curvature and the nozzle 1 rotates synchronously, with a radius... The outer surface of the semi-cylindrical part is the object to be machined. Nozzle 1 moves along the circumferential curvature of the cylindrical surface and rotates synchronously with the normal of the machining point, ensuring that the jet axis is always incident along the local normal. Assume the machining arc length range is from s = -18mm to s = 18mm, and the distance from the set distance... .

[0068] ; ; ; ; Nozzle jet direction is Therefore, the target distance at all discrete points is 40mm, and the incident angle is 90°. For example, when s=12mm: ; ; ; .

[0069] If we take the abrasive grain point within the local coordinates of this discrete point... Where u is the coordinate of the cylindrical surface along the arc and v is the coordinate of the cylindrical surface along the axis, the central angle corresponding to the abrasive grain point is: ; ; Using a curved strip region with an arc length of -15mm to 15mm and an axial local width of ±0.15mm as the target region, 181 discrete points were cumulatively superimposed to obtain an average cumulative abrasive particle distribution of approximately 2540.7 and a standard deviation of approximately 112.0.

[0070] ; ; .

[0071] This shows that when nozzle 1 rotates synchronously along the curvature direction of the cylindrical surface, each processing point can call the normal jet plane abrasive distribution parameters, and obtain the cumulative abrasive distribution of the cylindrical surface 4 through arc length-central angle mapping.

[0072] Example 11: The nozzle axis always points to the constant normal path of the sphere's center, with a radius... The outer surface of the upper hemisphere is the object to be processed, and the center of the sphere is... Nozzle 1 moves along a great circular arc path on spherical surface 5, with the nozzle axis always pointing towards the center of the sphere, ensuring that each discrete point is a local normal spray.

[0073] The processing arc length range is from s=-14mm to s=14mm, and the distance from the walking length is... .

[0074] ; ; ; ; The direction of the jet is Therefore, the real-time target distance is always 40mm and the incident angle is always 90°.

[0075] For example, when s = 12 mm: ; ; ; .

[0076] If a local planar abrasive point is taken near the top of sphere 5 Using radial projection mapping, the mapped point can be represented as: ; .

[0077] Using a spherical strip region with an arc length of -10 mm to 10 mm and a lateral local width of ±0.15 mm as the evaluation area, 141 discrete processing points were superimposed to obtain a cumulative abrasive distribution average of approximately 2541.0 and a standard deviation of approximately 111.8.

[0078] ; ; .

[0079] Therefore, in the spherical path where the nozzle axis always points to the center of the sphere, the two-dimensional Gaussian abrasive distribution parameters under the 40mm and 90° working conditions can be directly called at each discrete point, and the cumulative abrasive distribution on the spherical surface can be obtained by mapping the local tangent plane to the spherical surface 5.

[0080] Example 12: Horizontal movement path of a spherical surface in a fixed posture, with a radius... The upper hemisphere is the object of processing, and the center of the sphere is... The nozzle axis remains vertically downward, the nozzle outlet is maintained at a fixed height plane Z=90mm, and moves at a constant speed along the X direction.

[0081] ; ; ; ; ; ; ; Therefore, this path is only possible when The normal direction of the jet is 90° at the apex of the sphere; after leaving the apex, the target distance increases and the incident angle decreases.

[0082] For example, when hour: ; ; ; ; The unit normal vector of the sphere at that point is: ; The projection direction of the jet direction onto the local tangent plane can be taken as the first local coordinate direction, and the second local coordinate direction can be taken as the Y direction: ; Therefore, the local planar abrasive point (x, y) first appears in... The surface is unfolded within the local tangent plane and then radially projected onto the spherical surface to achieve the mapping of abrasive particle distribution on the curved surface under a fixed orientation path.

[0083] The target area with X = -12mm to 12mm and a lateral width of ±0.20mm was sampled, and the contribution of 181 discrete points was accumulated. The cumulative average abrasive particle distribution was calculated to be approximately 2575.89, and the standard deviation was approximately 216.39.

[0084] ; .

[0085] Because the incident angles at both ends of this path decrease, the distribution of abrasive particles 2 is stretched along the inclined direction of the jet, resulting in slightly lower uniformity compared to the spherical constant normal path. However, effective prediction can still be achieved through the joint index database of target distance and incident angle. This embodiment demonstrates that the present invention is applicable not only to ideal normal jet spherical paths but also to actual machining paths where the nozzle attitude is fixed and the real-time target distance and incident angle vary with position.

[0086] The above specific embodiments are specific support for the concept proposed in this invention, and should not be used to limit the scope of protection of this invention. Any equivalent changes or modifications made on the basis of this technical solution in accordance with the technical concept proposed in this invention shall still fall within the scope of protection of this invention.

Claims

1. A method for predicting and evaluating the uniformity of abrasive grain distribution in waterjet abrasive processes suitable for curved surface machining, characterized in that, include: Step S1: Obtain the abrasive waterjet processing parameters, the geometric parameters of the surface to be processed, and the processing path parameters, and select the processing path according to the surface type of the surface to be processed; Step S2: A two-dimensional Gaussian local planar abrasive particle distribution model is established using a two-dimensional Gaussian function, and parameter fitting is performed based on parameter regression of target distance and incident angle using a general two-dimensional Gaussian model. Step S3: Establish the mapping relationship between the local plane coordinates and the surface coordinates of the surface to be processed based on the geometric parameters of the surface to be processed, and map the local plane abrasive points to the surface. Step S4: Discretize the selected processing path into N processing points according to the set path dispersion step length, calculate the nozzle exit position, the intersection of the jet and the surface to be processed, the unit direction of the jet, the unit normal vector of the surface, the real-time target distance and the incident angle corresponding to the i-th processing point; establish the local planar abrasive distribution of the i-th processing point based on the real-time target distance and the incident angle, and obtain the surface abrasive distribution corresponding to the i-th processing point using the mapping relationship in step S3; Step S5: Based on the surface radius and the characteristic size of the local abrasive grain distribution, the applicability of the surface is judged, and the abrasive grain distributions corresponding to the N discrete processing points are weighted and superimposed to obtain the cumulative abrasive grain distribution in the target processing area. Step S6: Calculate the coefficient of variation and uniformity index based on the cumulative abrasive particle distribution, and output the surface abrasive particle distribution prediction result and uniformity evaluation result.

2. The method for predicting and evaluating the abrasive grain distribution and uniformity of abrasive waterjet machining applicable to curved surfaces according to claim 1, characterized in that: The abrasive waterjet processing parameters include one or more of the following: jet pressure, target distance, nozzle diameter, abrasive flow rate, abrasive particle size, nozzle moving speed, and path distance. The geometric parameters of the surface to be processed include one or more of the following: surface type, cylindrical radius, spherical radius, cylindrical axial length, spherical processing area, and surface normal direction. The machining path parameters include one or more of the following: cylindrical axial machining path, spherical machining path, number of discrete points on the path, distance between adjacent discrete points, and nozzle dwell time.

3. The method for predicting and evaluating the abrasive grain distribution and uniformity of abrasive waterjet machining applicable to curved surfaces according to claim 1, characterized in that: In step S1, the processing path is selected according to the type of surface to be processed, including the following steps: The surface to be processed includes a cylindrical surface or a spherical surface; When the surface to be processed is a cylindrical surface, select a constant normal path that moves along the axial direction of the cylindrical surface or a constant normal path that moves along the curvature direction of the cylindrical surface and the nozzle rotates synchronously with the curvature. When the surface to be processed is a sphere, select a constant normal path in which the nozzle axis always points to the center of the sphere, or select a fixed posture path in which the nozzle axis keeps a fixed vertical direction, the nozzle outlet keeps a fixed height, and moves at a constant speed in the horizontal direction.

4. The method for predicting and evaluating the abrasive grain distribution and uniformity of abrasive waterjet machining applicable to curved surfaces according to claim 3, characterized in that: In step S2, the two-dimensional Gaussian local planar abrasive particle distribution model is as follows: ； in: These are the coordinates of the distribution center; These are the standard deviations in the x and y directions, respectively, reflecting the degree of dispersion of abrasive grains along the x and y axes in the erosion region; is the correlation coefficient between x and y, which measures the strength of the linear relationship between the two variables, and its value ranges from [-1,1]; A is the distribution amplitude, which represents the peak value of the abrasive density in the erosion center region.

5. The method for predicting and evaluating the uniformity of abrasive grain distribution in waterjet abrasive flow for curved surface machining according to claim 4, characterized in that: when When x and y are linearly independent, the expression for the two-dimensional Gaussian distribution degenerates into: ; The distribution described here is approximately isotropic and is an axis-aligned Gaussian distribution.

6. The method for predicting and evaluating the abrasive grain distribution and uniformity of abrasive waterjet machining applicable to curved surface processing according to claim 5, characterized in that: At the i-th discrete processing point on the sphere Establish a local tangent plane at point (x, y), with local coordinates (x, y). The two mutually orthogonal unit direction vectors of the local tangent plane are... and Then the coordinates of the local planar abrasive point mapped onto the sphere are: ； in, and Let be two mutually perpendicular unit direction vectors within the local tangent plane at that point. The three-dimensional coordinates of the local planar abrasive particles mapped onto the sphere.

7. The method for predicting and evaluating the uniformity of abrasive grain distribution in waterjet machining according to claim 6, characterized in that: In step S3, the mapping relationship from the local planar abrasive grain coordinates (x, y) to the cylindrical surface includes: The formula for arc length is ; If the local planar coordinate x is the length after unfolding along the arc of the semi-cylinder, then... ; ; ； Where x is the local coordinate along the arc of the semi-cylinder, and y is the local coordinate along the length of the cylinder. The central angle corresponding to the local arc length coordinate x. The three-dimensional coordinates of the local planar abrasive particles mapped onto the surface of the semi-cylinder; And / or, The nozzle axis always points in the constant normal path to the center of the sphere: The nozzle moves along the spherical trajectory, and the nozzle axis changes with the processing point and always passes through the center of the sphere, so that the incident angle at each discrete processing point is kept at 90°, and the real-time target distance is kept at the set target distance H0. In the spherical fixed posture path, let the center of the sphere be located at the origin of the coordinate system and the radius of the sphere be... The nozzle jet unit direction is The nozzle outlet is discretized along a fixed height plane as follows: ; The nozzle outlet has a fixed Z-height, and y0 is the starting coordinate of the Y-axis; The X-axis coordinate of the i-th discrete sampling point, where x0 is the starting X-axis coordinate. This represents the step size of the nozzle's movement along the X direction; The point where the jet axis intersects the upper hemisphere is: ； Real-time target distance H i and the incident angle relative to the local tangent plane for: ； ； ； Where, n i Let be the unit normal vector of the i-th spherical machining point; And / or, The spherical fixed attitude path is sprayed with a 90° normal direction relative to the local tangent plane only at the spherical vertex; after leaving the spherical vertex, the real-time target distance increases with the increase of horizontal distance, and the incident angle decreases with the increase of horizontal distance; the first unit direction vector of the local tangent plane is taken as the projection direction of the jet direction in the local tangent plane, and the second unit direction vector is orthogonal to the first unit direction vector and the spherical normal vector; when the projection of the spherical vertex degenerates, the path tangent is used as the first unit direction vector.

8. The method for predicting and evaluating the uniformity of abrasive grain distribution in waterjet abrasive flow for curved surface machining according to claim 1, characterized in that: In step S4, when the surface to be processed is a cylindrical surface, the constant normal path moving at a constant speed along the axis of the cylindrical surface, and the nozzle moving along the axial direction of the cylindrical surface to form an abrasive belt, the cylindrical surface processing path is discretized as follows: ,i=0,1,2,...,N-1; in, Let be the axial coordinate of the i-th discrete machining point. The initial axial coordinate. is the axial distance between adjacent discrete machining points, and N is the number of discrete points on the cylindrical path; And / or, When the surface to be processed is a cylindrical surface, the constant normal path moving along the curvature direction of the cylindrical surface is discretized by the arc length of the cylindrical surface, and the radius of the cylindrical surface is assumed to be... ,but: ; ， ; in, For cylindrical surface machining points, The unit normal vector of the cylinder. This refers to the nozzle exit position. For the unit direction of the jet, The target distance is constant. The step size is the arc length of the cylinder. Angular step size; the nozzle moves and rotates synchronously along the circumference, so that the nozzle axis always remains at 90° relative to the local tangential plane.

9. The method for predicting and evaluating the uniformity of abrasive grain distribution in waterjet abrasive flow for curved surface machining according to claim 1, characterized in that: The cumulative abrasive grain distribution on the curved surface is obtained by superimposing the abrasive grain distributions at each discrete machining point: ； in, This represents the cumulative abrasive grain distribution at point P on the curved surface. The abrasive grain distribution after mapping the i-th discrete machining point to the surface; When the distribution areas of multiple dwelling points overlap, the same surface point P will be affected by multiple factors simultaneously. Contributions; It is the weight coefficient of the i-th discrete processing point, used to represent the processing intensity at the i-th position; When the processing conditions at discrete points are the same, then .

10. The method for predicting and evaluating the uniformity of abrasive grain distribution in waterjet machining according to claim 1, characterized in that: The surface applicability constraint is: ； Where L is the characteristic size of the local abrasive grain distribution, and R is the radius of the curved surface; When the object being processed is a cylindrical surface ; When the object being processed is a sphere ; when At that time, it is assumed that the current surface radius satisfies the applicability requirement of mapping local planar abrasive grain distribution to the surface; And / or, the uniformity of the cumulative abrasive grain distribution on the surface is evaluated using the coefficient of variation and uniformity index, where the coefficient of variation is: ； in, S represents the average cumulative abrasive particle distribution within the target processing area, and S represents the standard deviation of the cumulative abrasive particle distribution within the target processing area; the uniformity index is: ； Among them, the closer U is to 1, the more uniform the distribution of abrasive particles on the curved surface.

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