Convolution-based surface micromorphology prediction method for cylindrical gear internal honing

Abstract

The present application discloses a convolution-based method for predicting the micromorphology of the surface of cylindrical gear internal mesh honing. The method calculates the velocity vector of the abrasive grains on the honing wheel surface at the contact point of the workpiece tooth surface based on the velocity equation of the honing wheel tooth surface relative to the workpiece tooth surface; simulates the process of the abrasive grains sliding and cutting on the workpiece tooth surface along the velocity vector to calculate the abrasive grain cutting characteristics; calculates the total number of abrasive grain cutting times based on the number of revolutions of the workpiece gear and the number of abrasive grains; calculates the number of abrasive grain cutting times at each contact point on the workpiece tooth surface based on the total number of abrasive grain cutting times; performs a convolution calculation based on the abrasive grain cutting characteristics and the number of cutting times at each contact point to obtain a convolution result; and predicts the micromorphology of the workpiece tooth surface during internal mesh honing based on the convolution result. The present application can improve the accuracy of internal mesh honing surface micromorphology prediction and has universal applicability.

Description

Technical Field

[0001] The present application relates to the field of mechanical processing and manufacturing technology, and in particular to a convolution-based method for predicting the micro-morphology of the surface of cylindrical gear internal meshing honing. Background Art

[0002] Faced with the wave of electrification, the transmission systems of high-end equipment have put forward higher index requirements for gears, which urgently requires more advanced gear processing technology to improve the processing quality and manufacturing accuracy of gears to ensure the high reliability service performance of high-end equipment in complex environments and complex working conditions.

[0003] Internal gear honing is a key process in the precision machining of gears and is currently one of the key processes for the precision machining of high-end components for new energy vehicles, high-speed rail, and aerospace. However, due to the unique cross-axis meshing method of internal gear honing and the very complex movement of abrasive particles during machining, the current surface visualization model of internal gear honing can only represent the movement direction of each contact point on a macroscopic scale, and the research on the abrasive honing mechanism and the creation of surface micromorphology is not in-depth enough. Therefore, the existing related technologies are not very accurate in predicting the surface micromorphology of internal gear honing and have poor universality. Summary of the Invention

[0004] This application aims to propose a convolution-based method for predicting the micromorphology of the surface of cylindrical gear internal meshing honing, which can improve the accuracy of the micromorphology prediction of the surface of internal meshing honing and has universal applicability.

[0005] In a first aspect, an embodiment of the present application provides a convolution-based method for predicting the micro-morphology of the surface of cylindrical gear internal meshing honing, the method comprising:

[0006] According to the velocity equation of the honing wheel tooth surface relative to the workpiece tooth surface, the velocity vector of the abrasive grains on the honing wheel surface at the contact point of the workpiece tooth surface is calculated;

[0007] Simulating the sliding cutting process of the abrasive particles on the tooth surface of the workpiece along the motion velocity vector, and calculating the abrasive cutting characteristics;

[0008] Calculate the total number of abrasive cutting times based on the number of revolutions and the number of abrasive grains of the workpiece gear being machined;

[0009] Calculating the number of cutting times of the abrasive particles at each contact point on the tooth surface of the workpiece based on the total number of cutting times of the abrasive particles;

[0010] Performing convolution calculation based on the abrasive cutting characteristics and the number of cutting times of each contact point to obtain a convolution result;

[0011] According to the convolution results, the micromorphology of the tooth surface of the workpiece in internal meshing honing is predicted.

[0012] Compared with the prior art, the first aspect of the present application has the following beneficial effects:

[0013] This method calculates the velocity vector of the abrasive grains on the honing wheel surface at the contact point on the workpiece tooth surface based on the velocity equation for the motion of the honing wheel tooth surface relative to the workpiece tooth surface. The abrasive cutting characteristics are calculated by simulating the sliding cutting process of the abrasive grains on the workpiece tooth surface along the velocity vector. The total number of abrasive grain cuts is calculated based on the number of revolutions of the workpiece gear and the number of abrasive grains. Based on the total number of abrasive grain cuts, the number of abrasive grain cuts at each contact point on the workpiece tooth surface is calculated. A convolution operation is performed based on the abrasive grain cutting characteristics and the number of cuts at each contact point to obtain a convolution result. Based on the convolution result, the micromorphology of the workpiece tooth surface during internal gear honing is predicted. This convolution operation takes into account the cutting range and intensity of the abrasive grains on a three-dimensional surface, enabling accurate prediction of the morphology generation at any local location on the tooth surface. Furthermore, the convolution operation reveals the generation mechanism of the workpiece surface micromorphology through mathematical equations, enabling precise mapping of changes in machining parameters to the workpiece surface micromorphology. Therefore, by performing convolution calculation on the abrasive cutting characteristics and the number of cutting times at each contact point, the accuracy of the prediction of the micromorphology of the internal meshing honing surface can be improved, which is universal.

[0014] In some embodiments, simulating the sliding cutting process of the abrasive particles on the tooth surface of the workpiece along the motion velocity vector and calculating the abrasive cutting characteristics includes:

[0015] Simulating a sliding cutting process of the abrasive particles on the tooth surface of the workpiece along the motion velocity vector, and obtaining the cutting depth of the abrasive particles and the discrete points on the tooth surface contacted during the sliding cutting process;

[0016] Calculating the radius of the abrasive embedded in the tooth surface of the workpiece according to the cutting depth;

[0017] The portion of the abrasive grain embedded in the tooth surface of the workpiece is formed into a spherical cap, the radius of the spherical cap is the radius of the abrasive grain embedded in the tooth surface of the workpiece, and the height of the spherical cap is equal to the cutting depth;

[0018] The vertical distance from the discrete point on the tooth surface to the spherical cap curved surface is used as the abrasive cutting feature, and the discrete point on the tooth surface is a point within the radius of the spherical cap during the sliding cutting process.

[0019] In some embodiments, taking the vertical distance from the discrete point on the tooth surface to the spherical cap surface as the abrasive cutting feature includes:

[0020]

[0021] in, represents a single height removal function, represents the diameter of the abrasive grains, The radius of the point on the bottom of the spherical cap is represented by represents the height of the spherical crown, Represents the radius of the spherical cap.

[0022] In some embodiments, calculating the total number of abrasive cutting times according to the number of revolutions of the workpiece gear and the number of abrasive grains includes:

[0023] Obtain the workpiece gear rotation number and tooth surface processing area required to complete honing;

[0024] According to the abrasive grain size and the honing wheel organization number, the average spacing between the abrasive grains is calculated;

[0025] Calculating the number of abrasive grains based on the average spacing between the abrasive grains and the area of ​​the tooth surface processing region;

[0026] The number of workpiece gear revolutions required to complete the honing is multiplied by the number of abrasive grains to obtain the total number of abrasive grain cutting times.

[0027] In some embodiments, multiplying the number of workpiece gear revolutions required to complete the honing by the number of abrasive grains to obtain a total number of abrasive grain cutting times includes:

[0028]

[0029] in, Indicates the total number of abrasive cutting times, Indicates the number of abrasive particles, Indicates the number of revolutions of the workpiece gear. Indicates the processing time, Indicates the number of workpiece gear revolutions required to complete honing. Indicates the area of ​​the tooth surface processing area, Indicates the abrasive particle size, Indicates the honing wheel organization number.

[0030] In some embodiments, performing convolution calculation based on the abrasive cutting characteristics and the number of cutting times of each contact point to obtain a convolution result includes:

[0031]

[0032] in, represents the convolution result, Indicates the number of cutting times in the matrix Rank Number of cutting times of contact points, represents a single height removal matrix, represents the convolution calculation, Represents the point at the mth row and nth column of the bottom surface of the spherical cap.

[0033] In some embodiments, predicting the micromorphology of the tooth surface of the workpiece of internal meshing honing according to the convolution result includes:

[0034]

[0035] in, represents the predicted internal meshing honing surface micro-topography height matrix, represents the initial tooth surface height matrix, represents the convolution result, Represents the tooth surface normal vector The mold length.

[0036] In a second aspect, an embodiment of the present application further provides a convolution-based system for predicting the micro-morphology of the surface of cylindrical gear internal meshing honing, the system comprising:

[0037] The first calculation unit is used to calculate the motion velocity vector of the abrasive grains on the surface of the honing wheel at the contact point of the tooth surface of the workpiece according to the velocity equation of the motion of the tooth surface of the honing wheel relative to the tooth surface of the workpiece;

[0038] a second calculation unit, for simulating a process in which abrasive particles slide and cut on a tooth surface of a workpiece along the motion velocity vector, and calculating abrasive cutting characteristics;

[0039] a third calculation unit for calculating the total number of abrasive cutting times according to the number of revolutions of the workpiece gear and the number of abrasive grains;

[0040] a fourth calculation unit, configured to calculate the number of cutting times of the abrasive particles at each contact point on the tooth surface of the workpiece based on the total number of cutting times of the abrasive particles;

[0041] a convolution calculation unit, configured to perform convolution calculation based on the abrasive cutting characteristics and the number of cutting times of each contact point to obtain a convolution result;

[0042] The micro-morphology prediction unit is used to predict the micro-morphology of the tooth surface of the workpiece of the internal meshing honing according to the convolution result.

[0043] In a third aspect, an embodiment of the present application further provides an electronic device comprising at least one control processor and a memory for communicating with the at least one control processor; the memory stores instructions that can be executed by the at least one control processor, and the instructions are executed by the at least one control processor so that the at least one control processor can execute the above-mentioned convolution-based method for predicting the micromorphology of the internal meshing honing surface of cylindrical gears.

[0044] In a fourth aspect, an embodiment of the present application further provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are used to enable a computer to execute the above-mentioned convolution-based method for predicting the micromorphology of the internal meshing honing surface of cylindrical gears.

[0045] It can be understood that the beneficial effects of the above-mentioned second to fourth aspects compared with the relevant technologies are the same as the beneficial effects of the above-mentioned first aspect compared with the relevant technologies. Please refer to the relevant description in the above-mentioned first aspect and will not be repeated here. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0047] Figure 1 1 is a flow chart of an embodiment of a convolution-based method for predicting the micro-morphology of the surface of cylindrical gear internal meshing honing provided by the present application;

[0048] Figure 2 This is a schematic diagram of the overall process of the best embodiment of the convolution-based method for predicting the micro-morphology of the surface of cylindrical gear internal meshing honing provided by the present application;

[0049] Figure 3 Schematic diagram of geometric motion of the internal meshing honing process in the best embodiment of the convolution-based cylindrical gear internal meshing honing surface micromorphology prediction method provided by the present application;

[0050] Figure 4 Schematic diagram of the velocity vector of the abrasive grains on the honing wheel surface at the contact point of the workpiece tooth surface in the best embodiment of the convolution-based cylindrical gear internal meshing honing surface micromorphology prediction method provided by the present application;

[0051] Figure 5 This is a schematic diagram of a simulation of sliding cutting of an abrasive particle along a motion velocity vector of the abrasive particle on a workpiece tooth surface in a preferred embodiment of the convolution-based cylindrical gear internal meshing honing surface prediction method provided by the present application;

[0052] Figure 6 Schematic diagram of the number of cuts at each contact point on the tooth surface in the best embodiment of the convolution-based method for predicting the micro-morphology of the internal meshing honing of cylindrical gears provided by the present application;

[0053] Figure 7 Schematic diagram of a rough surface profile obtained by convolutionally removing material in a preferred embodiment of a convolution-based method for predicting the surface micromorphology of internal meshing honing of cylindrical gears provided in the present application;

[0054] Figure 8Schematic diagram of generating surface micromorphology data in a preferred embodiment of the convolution-based surface micromorphology prediction method for cylindrical gear internal meshing honing provided by the present application;

[0055] Figure 9 Schematic diagram of actual abrasive cutting traces in a preferred embodiment of the convolution-based method for predicting the micro-morphology of the surface of cylindrical gear internal meshing honing provided by the present application;

[0056] Figure 10 Schematic diagram of simulated abrasive cutting traces in a preferred embodiment of the convolution-based method for predicting the micro-morphology of the surface of cylindrical gear internal meshing honing provided by the present application;

[0057] Figure 11 2. It is a schematic diagram comparing the two-dimensional profiles of the experimental and simulated micromorphologies in the best embodiment of the convolution-based method for predicting the micromorphology of the surface of the internal meshing honing of cylindrical gears provided by the present application;

[0058] Figure 12 It is a structural schematic diagram of an embodiment of the convolution-based cylindrical gear internal meshing honing surface micromorphology prediction system provided in this application. DETAILED DESCRIPTION

[0059] The following describes in detail embodiments of the present application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present application and are not to be construed as limiting the present application.

[0060] In the description of this application, if there is a description of first, second, etc., it is only for the purpose of distinguishing technical features, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features.

[0061] In the description of this application, it should be understood that descriptions involving orientation, such as the orientation or positional relationship indicated by up, down, etc., are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on this application.

[0062] In the description of this application, it should be noted that, unless otherwise clearly defined, terms such as setting, installing, and connecting should be understood in a broad sense, and technical personnel in the relevant technical field can reasonably determine the specific meaning of the above terms in this application based on the specific content of the technical solution.

[0063] Faced with the wave of electrification, the transmission systems of high-end equipment have put forward higher index requirements for gears, which urgently requires more advanced gear processing technology to improve the processing quality and manufacturing accuracy of gears to ensure the high reliability service performance of high-end equipment in complex environments and complex working conditions.

[0064] Internal gear honing is a key process in the precision machining of gears and is currently one of the key processes for the precision machining of high-end components for new energy vehicles, high-speed rail, aerospace, and other industries. However, due to the unique cross-axis meshing method of internal gear honing and the very complex movement of abrasive particles during machining, the current surface visualization model of internal gear honing can only represent the movement direction of each contact point on a macroscopic scale, and the research on the abrasive honing mechanism and the creation of surface micromorphology is not in-depth enough. Therefore, the existing related technologies are not very accurate in predicting the surface micromorphology of internal gear honing and have poor universality.

[0065] In order to solve the problem that the above-mentioned existing related technologies have low accuracy and poor universality in predicting the micromorphology of the internal meshing honing surface, this application proposes a convolution-based method for predicting the micromorphology of the internal meshing honing surface of cylindrical gears.

[0066] Reference Figure 1 The present invention provides a method for predicting the micro-morphology of the surface of cylindrical gear internal meshing honing based on convolution, the method comprising the following steps:

[0067] Step S100, calculating the velocity vector of the abrasive grains on the honing wheel surface at the contact point of the workpiece tooth surface according to the velocity equation of the honing wheel tooth surface relative to the workpiece tooth surface;

[0068] Step S200, simulating the process of abrasive particles sliding and cutting on the tooth surface of the workpiece along the motion velocity vector, and calculating the abrasive particle cutting characteristics;

[0069] Step S300, calculating the total number of abrasive cutting times according to the number of revolutions of the workpiece gear and the number of abrasive grains;

[0070] Step S400, calculating the number of cutting times of the abrasive grains at each contact point on the tooth surface of the workpiece based on the total number of cutting times of the abrasive grains;

[0071] Step S500: performing convolution calculation based on the abrasive cutting characteristics and the number of cutting times of each contact point to obtain a convolution result;

[0072] Step S600: predicting the microscopic morphology of the tooth surface of the workpiece for internal gear honing according to the convolution result.

[0073] In this embodiment, the velocity vector of the abrasive grains on the honing wheel surface at the contact point on the workpiece tooth surface is calculated based on the velocity equation for the motion of the honing wheel tooth surface relative to the workpiece tooth surface. The abrasive grain cutting characteristics are calculated by simulating the sliding cutting process of the abrasive grains on the workpiece tooth surface along the velocity vector. The total number of abrasive grain cutting times is calculated based on the number of revolutions of the workpiece gear and the number of abrasive grains. Based on the total number of abrasive grain cutting times, the number of abrasive grain cutting times at each contact point on the workpiece tooth surface is calculated. A convolution operation is performed based on the abrasive grain cutting characteristics and the number of cutting times at each contact point to obtain a convolution result. Based on the convolution result, the micromorphology of the workpiece tooth surface for internal gear honing is predicted. In this way, the convolution operation can take into account the cutting range and intensity of the abrasive grains on a three-dimensional curved surface, enabling accurate prediction of the morphology generation at any local location on the tooth surface. Furthermore, the convolution operation reveals the generation mechanism of the workpiece surface micromorphology through mathematical equations, enabling precise mapping of changes in machining parameters to the workpiece surface micromorphology. Therefore, by performing convolution calculation on the abrasive cutting characteristics and the number of cutting times at each contact point, the accuracy of the prediction of the micromorphology of the internal meshing honing surface can be improved, which is universal.

[0074] The above-mentioned calculation of the velocity vector of the abrasive grains on the honing wheel surface at the contact point on the workpiece tooth surface based on the velocity equation for the motion of the honing wheel tooth surface relative to the workpiece tooth surface can be performed by analyzing the geometric motion of the internal mesh honing process to calculate the velocity vector of the abrasive grains on the honing wheel surface at the contact point on the workpiece tooth surface. Since the abrasive grains' position coordinates are necessarily at the contact point on the workpiece tooth surface when they begin cutting the tooth surface, the velocity vector can be obtained by substituting the contact point coordinates into the velocity equation for the motion of the honing wheel tooth surface relative to the workpiece tooth surface. This velocity equation for the motion of the honing wheel tooth surface relative to the workpiece tooth surface can be calculated using existing techniques.

[0075] The above simulation of the abrasive particles sliding and cutting on the workpiece tooth surface along the motion velocity vector calculates the abrasive cutting characteristics. Since the abrasive particles are embedded in the workpiece tooth surface and slide and cut along the motion velocity vector, the part of the abrasive particles embedded in the workpiece tooth surface can be regarded as a radius of , the height is The discrete points on the tooth surface that the spherical cap contacts during the sliding cutting process are points within the radius of the spherical cap. The vertical distances from these discrete points on the tooth surface to the spherical cap surface can be used as abrasive cutting features.

[0076] The number of revolutions of the gear of the above-mentioned workpiece can be obtained by counting how many times the gear rotates per unit time.

[0077] The above calculation of the cutting times of each contact point between the abrasive grain and the tooth surface of the workpiece based on the total cutting times of the abrasive grain can be performed by automatically counting the cutting times of each contact point between the abrasive grain and the tooth surface of the workpiece by a machine, but the sum of the cutting times of each contact point between the abrasive grain and the tooth surface of the workpiece is equal to the total cutting times of the abrasive grain.

[0078] The convolution calculation is performed based on the abrasive cutting characteristics and the number of cutting times of each contact point to obtain the convolution result. The convolution result can be obtained by performing a convolution operation using the number of cutting times of each contact point as the convolved matrix and the abrasive cutting characteristics as the convolution kernel.

[0079] In some embodiments, simulating a process in which abrasive particles slide and cut on a workpiece tooth surface along a motion velocity vector and calculating abrasive cutting characteristics includes:

[0080] The process of abrasive particles sliding and cutting on the workpiece tooth surface along the motion velocity vector is simulated to obtain the cutting depth of the abrasive particles and the discrete points on the tooth surface contacted during the sliding cutting process;

[0081] According to the cutting depth, calculate the radius of the abrasive embedded in the workpiece tooth surface;

[0082] The part where the abrasive is embedded in the tooth surface of the workpiece is regarded as a spherical cap, the radius of the spherical cap is the radius of the abrasive embedded in the tooth surface of the workpiece, and the height of the spherical cap is equal to the cutting depth;

[0083] The vertical distance from the discrete point on the tooth surface to the spherical cap surface is taken as the abrasive cutting feature, and the discrete point on the tooth surface is the point within the radius of the spherical cap during the sliding cutting process.

[0084] In this embodiment, the process of an abrasive particle sliding along a workpiece tooth surface along a velocity vector is simulated to determine the cutting depth of the abrasive particle and the discrete points on the tooth surface it contacts during the sliding cutting process. Based on the cutting depth, the radius of the abrasive particle embedded in the workpiece tooth surface is calculated. The portion of the abrasive particle embedded in the workpiece tooth surface is treated as a spherical cap, with the radius of the cap equal to the radius of the abrasive particle embedded in the workpiece tooth surface and the height of the cap equal to the cutting depth. The perpendicular distance from the discrete point on the tooth surface to the cap surface is used as the abrasive particle cutting feature. In this way, using the abrasive particle cutting feature as a convolution kernel can reflect the weight of the abrasive particle's influence on a specific location on the workpiece tooth surface, laying a solid data foundation for the subsequent accurate prediction of the surface micromorphology of internal gear honing.

[0085] The cutting depth may be the vertical distance between the machined surface and the surface to be machined each time the workpiece is cut.

[0086] In some embodiments, taking the vertical distance from a discrete point on the tooth surface to the spherical cap surface as an abrasive cutting feature comprises:

[0087]

[0088] in, represents a single height removal function, represents the diameter of the abrasive grains, The radius of the point on the bottom of the spherical cap is represented by represents the height of the spherical crown, Represents the radius of the spherical cap.

[0089] In some embodiments, calculating the total number of abrasive cutting times according to the number of revolutions of the workpiece gear and the number of abrasive grains includes:

[0090] Obtain the workpiece gear rotation number and tooth surface processing area required to complete honing;

[0091] According to the abrasive grain size and the honing wheel organization number, the average spacing between the abrasive grains is calculated;

[0092] The number of abrasive grains is calculated based on the average spacing between the abrasive grains and the area of ​​the tooth surface processing area;

[0093] The total number of cuts by the abrasive grains is obtained by multiplying the number of workpiece gear revolutions required to complete the honing by the number of abrasive grains.

[0094] In this embodiment, the distribution of the number of cuts serves as the convolved function, reflecting the contact pattern between the abrasive grains and the workpiece tooth surface. By calculating the total number of cuts per abrasive grain, the number of cuts per contact point is constrained, providing a robust data foundation for accurately predicting the surface micromorphology of internal gear honing.

[0095] In some embodiments, the number of workpiece gear revolutions required to complete honing is multiplied by the number of abrasive grains to obtain the total number of abrasive grain cuts, comprising:

[0096]

[0097] in, Indicates the total number of abrasive cutting times, Indicates the number of abrasive particles, Indicates the number of revolutions of the workpiece gear. Indicates the processing time, Indicates the number of workpiece gear revolutions required to complete honing. Indicates the area of ​​the tooth surface processing area, Indicates the abrasive particle size, Indicates the honing wheel organization number.

[0098] In some embodiments, a convolution calculation is performed based on the abrasive cutting characteristics and the number of cutting times at each contact point to obtain a convolution result, including:

[0099]

[0100] in, represents the convolution result, Indicates the number of cutting times in the matrix Rank Number of cutting times of contact points, represents a single height removal matrix, represents the convolution calculation, Represents the point at the mth row and nth column of the bottom surface of the spherical cap.

[0101] In some embodiments, predicting the micromorphology of the tooth surface of a workpiece for internal gear honing based on the convolution result includes:

[0102]

[0103] in, represents the predicted internal meshing honing surface micro-topography height matrix, represents the initial tooth surface height matrix, represents the convolution result, Represents the tooth surface normal vector The mold length.

[0104] In this embodiment, the convolution operation takes into account the cutting range and intensity of the abrasive particles on a three-dimensional surface, thereby accurately predicting the topography generation at any local location on the tooth surface. Furthermore, the convolution operation reveals the generation mechanism of the workpiece surface microtopography through mathematical equations, accurately mapping changes in machining parameters to the workpiece surface microtopography. This allows for rapid calculation and real-time adjustment, improving the robustness and universality of the prediction.

[0105] To facilitate understanding by those skilled in the art, a set of best embodiments is provided below:

[0106] Faced with the wave of electrification, the transmission systems of high-end equipment have put forward higher index requirements for gears, which urgently requires more advanced gear processing technology to improve the processing quality and manufacturing accuracy of gears to ensure the high reliability service performance of high-end equipment in complex environments and complex working conditions.

[0107] Internal gear honing is a key process in the precision machining of gears and is currently one of the key processes for the precision machining of high-end components for new energy vehicles, high-speed rail, and aerospace. However, due to the unique cross-axis meshing method of internal gear honing and the complex motion of abrasive particles during machining, there is currently little research on predictive models for the microtopography of the machined surface. Current surface visualization models for internal gear honing can only represent the movement direction of each contact point on a macroscopic scale, and research on the abrasive honing mechanism and the creation of surface microtopography is insufficient. This has inhibited the further application and promotion of internal gear honing technology in the field of precision manufacturing.

[0108] Therefore, this embodiment proposes a convolution-based method for predicting the surface micromorphology of cylindrical gear internal meshing honing, which can achieve accurate prediction of the surface micromorphology and microtexture characteristics of the honing workpiece, and is expected to provide practical guidance for the high-precision manufacturing of high-end gears.

[0109] Mathematically speaking, the convolution operation is to combine two functions to produce a new function, which represents the result of one function being processed by another function. and , their convolution is defined as:

[0110]

[0111] The essence of convolution operation can be understood as a weighted summation process, which is highly consistent with the behavior of abrasive particles moving on the workpiece surface and accumulating cutting in grinding. The material removal mechanism of internal meshing honing is similar to that of traditional grinding. The feed motion of the honing wheel presses the surface abrasive particles into the workpiece surface, removing the surface material of the workpiece during relative motion. As the cutting action of a large number of randomly distributed abrasive particles is superimposed on each other, the micromorphology of the workpiece tooth surface after material removal is formed. Through mathematical modeling, the material removal height distribution of honing can be described as the cutting characteristics of a single abrasive particle based on the accumulation of the number of cuts.

[0112] Specifically, the cutting characteristics of the abrasive particles are the cutting marks determined by the cutting direction of the abrasive particles and the depth and radius of the embedded abrasive particles in the workpiece tooth surface. This is abstracted as a convolution kernel, which reflects the weight of the abrasive particle's influence on a certain position on the workpiece tooth surface. The distribution of the number of cuts is used as the convolved function, reflecting the contact form between the abrasive particles and the workpiece tooth surface. The product of the two is the cumulative cutting depth of the abrasive particles. When the abrasive particles cut a certain position on the tooth surface, the adjacent positions will also have a cutting effect on the current position. The degree of influence is defined by the convolution kernel. After the convolution kernel traverses the entire tooth surface, the function after the convolution operation is obtained, that is, the height removal function. Finally, height removal is performed on the initial contour along the normal direction of the tooth surface point to obtain the predicted surface micromorphology data of the internal meshing honing workpiece.

[0113] Reference Figure 2 The technical solution of this embodiment specifically includes the following contents:

[0114] Step 1: Calculate the velocity vector of the abrasive particles. First, we need to analyze the geometric motion of the internal meshing honing process and calculate the velocity vector of the abrasive particles on the honing wheel surface at each contact point on the workpiece tooth surface. Internal meshing honing is a processing method in which the honing wheel is fed back and forth in the axial and radial directions. Figure 3 The coordinate system shown is explained below: is the workpiece gear fixed coordinate system, is the workpiece gear motion coordinate system, For the workpiece gear The angle through which the shaft rotates is ; is the fixed coordinate system of the honing wheel, is the motion coordinate system of the honing wheel, For honing wheel The angle through which the shaft rotates is Since there is an axial angle between the workpiece gear and the honing wheel , so set the transition coordinate system , The distance between the centers is , 、 They are the radial feed speed and axial feed speed of the honing wheel respectively.

[0115] The calculation of the relative speed of each point between the workpiece gear and the honing wheel tooth surface must be performed in the same coordinate system. The following formula can be used to realize the mutual transformation between any coordinate systems:

[0116]

[0117] in, , , , .

[0118] If As the reference coordinate system, through coordinate transformation, the speed of the honing wheel tooth surface relative to the workpiece tooth surface can be expressed as:

[0119]

[0120] like Figure 4 As shown in the figure, the tooth surface of the workpiece is rotated at equal angles along the tooth profile direction from the beginning to the end of meshing, and several contact lines are obtained on the tooth surface. The points on the contact lines are then discretized along the tooth direction, which are called the contact points between the abrasive and the workpiece tooth surface. When the abrasive starts to cut the tooth surface, its position coordinates must be at the contact point. Therefore, the velocity vector of the abrasive can be obtained by substituting the contact point position coordinates ( , , ) is solved into the above formula (2).

[0121] Step 2: Calculate the abrasive cutting characteristics. Assume that the abrasive is of diameter The radius of a single abrasive particle embedded in the workpiece tooth surface can be calculated using the following formula :

[0122]

[0123] in, Indicates the cutting depth.

[0124] Figure 5 The sliding cutting process of the abrasive particles on the workpiece tooth surface along the velocity vector of the abrasive particles is simulated, in which: Figure 5(a) is a schematic diagram showing the process of abrasive particles sliding along the velocity vector of the abrasive particles on the tooth surface of the workpiece and contacting discrete points on the tooth surface. Figure 5 (b) is a schematic diagram showing the cutting process of the abrasive embedded in the workpiece tooth surface. The part of the abrasive embedded in the workpiece tooth surface is regarded as a radius of , the height is The ball crown, , Figure 5 The contact points in (a) represent the discrete points on the tooth surface that the abrasive particles touch when they move a small distance along the velocity vector of the abrasive particles. These discrete points on the tooth surface will be highly removed. The height removed is the vertical distance from each discrete point on the tooth surface to the spherical crown surface, which is expressed as:

[0125]

[0126] in, is a single height removal function. Consider the bottom of the spherical cap as a matrix consisting of m×n points, then the radius corresponding to the point in the mth row and nth column is It can be expressed as , the single height removal amount of this point is D(m,n).

[0127] Step 3: Calculate the number of abrasive cutting times. During the internal meshing honing process, only some abrasive particles perform effective cutting. These particles are called effective abrasive particles, and the abrasive particles that do not participate in cutting are called ineffective abrasive particles. Assume that the amount of material removed by each effective abrasive particle is the same. For any local position on the tooth surface, considering the uneven distribution of abrasive particles and the difference in the height of the cutting edge, the number of cutting times at each contact point can be represented by a discrete matrix, and the following constraints are made:

[0128]

[0129] in, is the total number of abrasive cutting times, It represents the number of cutting times of the abrasive at the contact point of the i-th row and j-th column on the local position of the tooth surface. Since the ineffective abrasive does not participate in the cutting behavior, the number of cutting times at its contact point is 0. Figure 6 The diagram shows the number of cutting times at each contact point on the tooth surface. The calculation process is as follows:

[0130] Assuming that the abrasive grains on the honing wheel surface are evenly distributed, according to the abrasive grain size Organization number of honing wheels , the average spacing between abrasive particles can be calculated for:

[0131]

[0132] Then the number of abrasive grains used to process any tooth surface position can be expressed as:

[0133]

[0134] in, Indicates the area of ​​the tooth surface processing area.

[0135] The contact between the honing wheel and the workpiece tooth surface is a one-way line contact, that is, in each rotation cycle of the workpiece gear, a single abrasive grain will only come into contact with any position of the tooth surface once, and cut the tooth surface along the direction of relative motion. Over multiple cycles, the cutting action of a single abrasive grain continues to accumulate, and the cutting action of all abrasive grains is superimposed to complete the cutting of the entire processing area. Therefore, the product of the number of workpiece gear rotations required to complete honing and the number of abrasive grains is the total number of cuts. Then, the honing processing area is The expression for the total number of cutting times required for the area is:

[0136]

[0137] in, Indicates the number of revolutions of the workpiece gear. Indicates processing time.

[0138] Step 4: Convolution calculates the cumulative height of material removed. Because the surface height matrix is ​​not a continuous function, the convolution should use the summation symbol to convert the cutting number matrix As the convolved matrix, the single height removal matrix As the convolution kernel, perform convolution calculation:

[0139]

[0140] in, represents the convolution calculation, It represents the cumulative height removal matrix, which describes the total height change of the workpiece tooth surface position after honing. The schematic diagram of the rough surface profile obtained by convolution removal of material is shown in Figure 7 shown.

[0141] Step 5: Generate surface micromorphology data. Figure 8 As shown, Added in the normal direction of the corresponding tooth surface point, the predicted micro-morphology data is obtained:

[0142]

[0143] in, represents the initial tooth surface height matrix, Represents the tooth surface normal vector The module length, Represents the predicted surface microtopography height matrix of internal meshing honing gear.

[0144] Figure 9 and Figure 10 The results of the experimental and simulated workpiece tooth surface micromorphology are shown respectively. It can be clearly seen from the figure that the two have the same direction of honing lines. The local enlarged picture of the measured morphology also shows the randomly distributed abrasive marks on the micro tooth surface, reflecting the interaction characteristics between the abrasives on the honing wheel surface and the processed tooth surface during the honing process. This cutting mark is also reflected in the simulated morphology. By comparing the surface height parameters of the experimental and simulated morphologies, the results show that the average height The error is 5.57%, the root mean square height The error is 8.56%, which proves the accuracy of the prediction model. In addition, the two-dimensional profiles of the experimental and simulated micromorphologies are compared, such as Figure 11 As shown in Figure 3, the curve is in the form of random oscillation, which further illustrates that the convolution operation simulates the motion process of the abrasive particles randomly contacting the tooth surface and forming a rough tooth profile.

[0145] In summary, the feasibility and accuracy of the convolution-based surface micromorphology prediction method for internal honing of cylindrical gears are verified.

[0146] Compared with the existing technology, the technical solution of this embodiment has the following advantages:

[0147] (1) Research on abrasive cutting simulation generally simplifies the cutting marks of abrasive particles on the tooth surface into a two-dimensional indentation profile to reduce computational complexity. However, the convolution operation can consider the cutting range and intensity of the abrasive particles on the three-dimensional surface and accurately predict the morphology of any local position on the tooth surface. At the same time, when a large number of random abrasive particles cut at the same or adjacent positions on the tooth surface, the convolution operation can correctly accumulate these effects, which is closer to the actual processing process.

[0148] (2) The prediction model of the micromorphology of the grinding surface is usually extracted and summarized by statistical methods such as neural networks and regression analysis, and then the prediction model is established. Although this type of method has high prediction accuracy, it is easily affected by external factors, cannot be widely applied, and has a long operation cycle. The convolution operation reveals the creation mechanism of the micromorphology of the workpiece surface through mathematical equations. It can accurately map the changes in machining parameters to the micromorphology of the workpiece surface. It has the characteristics of fast calculation and real-time adjustment, which improves the robustness and universality of the prediction model.

[0149] (3) Compared with the method of representing the macroscopic surface texture of the internal meshing honing workpiece by the direction of motion, the convolution operation can simulate the formation process of the honing texture at the micro level and output the microscopic morphology of the workpiece honing surface, accurately reflecting the roughness, waviness, machining traces of the machined tooth surface and the relationship between them and the machining parameters. This provides a method for active control of machining quality and coordinated optimization of process parameters for precision manufacturing of gears, which can effectively reduce the additional costs caused by experimental adjustments and machining errors.

[0150] Reference Figure 12 The present application also provides a convolution-based micro-morphology prediction system for the surface of cylindrical gear internal meshing honing. The system includes a first calculation unit 100, a second calculation unit 200, a third calculation unit 300, a fourth calculation unit 400, a convolution calculation unit 500, and a micro-morphology prediction unit 600, wherein:

[0151] The first calculation unit 100 is used to calculate the motion velocity vector of the abrasive grains on the surface of the honing wheel at the contact point of the workpiece tooth surface according to the velocity equation of the motion of the honing wheel tooth surface relative to the workpiece tooth surface;

[0152] The second calculation unit 200 is used to simulate the sliding cutting process of the abrasive particles on the tooth surface of the workpiece along the motion velocity vector and calculate the abrasive cutting characteristics;

[0153] The third calculation unit 300 is used to calculate the total number of cutting times of the abrasive particles according to the number of revolutions of the workpiece gear and the number of abrasive particles;

[0154] The fourth calculation unit 400 is used to calculate the number of cutting times of the abrasive particles at each contact point on the tooth surface of the workpiece based on the total number of cutting times of the abrasive particles;

[0155] A convolution calculation unit 500 is used to perform convolution calculation based on the abrasive cutting characteristics and the number of cutting times of each contact point to obtain a convolution result;

[0156] The micro-morphology prediction unit 600 is used to predict the micro-morphology of the tooth surface of the workpiece of the internal meshing honing according to the convolution result.

[0157] It should be noted that since the convolution-based cylindrical gear internal meshing honing surface micromorphology prediction system in this embodiment and the above-mentioned convolution-based cylindrical gear internal meshing honing surface micromorphology prediction method are based on the same inventive concept, the corresponding contents in the method embodiment are also applicable to the system embodiment and will not be described in detail here.

[0158] An embodiment of the present application further provides an electronic device, comprising: at least one control processor and a memory for communicating with the at least one control processor.

[0159] The memory, as a non-transient computer-readable storage medium, can be used to store non-transient software programs and non-transient computer executable programs. In addition, the memory may include a high-speed random access memory and may also include a non-transient memory, such as at least one disk storage device, a flash memory device, or other non-transient solid-state storage device. In some embodiments, the memory may optionally include a memory remotely arranged relative to the processor, and these remote memories may be connected to the processor via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0160] The non-transient software program and instructions required to implement the above-mentioned embodiment of a method for predicting the micro-morphology of the surface of the cylindrical gear internal meshing honing based on convolution are stored in the memory. When executed by the processor, the above-mentioned embodiment of a method for predicting the micro-morphology of the surface of the cylindrical gear internal meshing honing based on convolution is executed, for example, the above-mentioned method is executed. Figure 1 Method steps S100 to S600 in.

[0161] The system embodiment described above is merely illustrative. The units described as separate components may or may not be physically separate, i.e., they may be located in one place or distributed across multiple network units. Some or all of these units may be selected based on actual needs to achieve the objectives of this embodiment.

[0162] The present application also provides a computer-readable storage medium storing computer-executable instructions. The computer-executable instructions are executed by one or more control processors to enable the one or more control processors to execute a convolution-based method for predicting the micromorphology of the internal meshing honing surface of a cylindrical gear in the above method embodiment. For example, the above described method is executed. Figure 1 The functions of method steps S100 to S600 in the embodiment of the present invention are as follows:

[0163] Those skilled in the art will appreciate that all or some of the steps and systems disclosed above can be implemented as software, firmware, hardware, or any suitable combination thereof. Some or all of the physical components may be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit. Such software may be distributed on computer-readable media, which may include computer storage media (or non-transitory media) and communication media (or transient media). As is well known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information, such as computer-readable instructions, data structures, program modules, or other data. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disks (DVDs) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to store the desired information and can be accessed by a computer. Furthermore, as is well known to those skilled in the art, communication media typically embodies computer-readable instructions, data structures, program modules, or other data in a modulated data signal such as a carrier wave or other transport mechanism, and may include any information delivery media.

[0164] The above is a specific description of the preferred implementation of the embodiments of the present application, but the embodiments of the present application are not limited to the above-mentioned implementation methods. Technical personnel familiar with the art can also make various equivalent modifications or substitutions without violating the spirit of the embodiments of the present application. These equivalent modifications or substitutions are all included in the scope defined by the claims of the embodiments of the present application.

[0165] The embodiments of the present application are described in detail above in conjunction with the accompanying drawings, but the present application is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by ordinary technicians in the relevant technical field without departing from the purpose of the present application.

Claims

1. A convolution-based method for predicting the micro-morphology of the surface of cylindrical gear internal meshing honing, characterized in that: The method comprises: According to the velocity equation of the honing wheel tooth surface relative to the workpiece tooth surface, the velocity vector of the abrasive grains on the honing wheel surface at the contact point of the workpiece tooth surface is calculated; Simulating the sliding cutting process of the abrasive particles on the tooth surface of the workpiece along the motion velocity vector, and calculating the abrasive cutting characteristics; According to the number of revolutions and the number of abrasive grains of the workpiece gear being machined, the total number of abrasive cutting times is calculated; Calculating the number of cutting times of the abrasive particles at each contact point on the tooth surface of the workpiece based on the total number of cutting times of the abrasive particles; A convolution calculation is performed based on the abrasive cutting characteristics and the number of cutting times of each contact point to obtain a convolution result, including: in, represents the convolution result, Indicates the number of cutting times in the matrix Rank Number of cutting times of contact points, represents a single height removal matrix, represents the convolution calculation, Represents the point at the mth row and nth column on the bottom surface of the spherical cap; Based on the convolution results, the micromorphology of the tooth surface of the workpiece for internal gear honing is predicted, including: in, represents the predicted internal meshing honing surface micro-topography height matrix, represents the initial tooth surface height matrix, represents the convolution result, Represents the tooth surface normal vector The mold length.

2. The convolution-based method for predicting the micro-morphology of the cylindrical gear internal meshing honing surface according to claim 1, characterized in that: The simulating process of sliding cutting of abrasive particles on the tooth surface of the workpiece along the motion velocity vector and calculating the abrasive cutting characteristics includes: Simulating a sliding cutting process of the abrasive particles on the tooth surface of the workpiece along the motion velocity vector, and obtaining the cutting depth of the abrasive particles and the discrete points on the tooth surface contacted during the sliding cutting process; Calculating the radius of the abrasive embedded in the tooth surface of the workpiece according to the cutting depth; The portion of the abrasive grain embedded in the tooth surface of the workpiece is formed into a spherical cap, the radius of the spherical cap is the radius of the abrasive grain embedded in the tooth surface of the workpiece, and the height of the spherical cap is equal to the cutting depth; The vertical distance from the discrete point on the tooth surface to the spherical cap curved surface is used as the abrasive cutting feature, and the discrete point on the tooth surface is a point within the radius of the spherical cap during the sliding cutting process.

3. The convolution-based method for predicting the micro-morphology of the cylindrical gear internal meshing honing surface according to claim 2, characterized in that: The method of using the vertical distance from the discrete point on the tooth surface to the spherical cap surface as the abrasive cutting feature includes: in, represents a single height removal function, represents the diameter of the abrasive particles, The radius of the point on the bottom of the spherical cap is represented by represents the height of the spherical crown, Represents the radius of the spherical cap.

4. The convolution-based method for predicting the micro-morphology of the cylindrical gear internal meshing honing surface according to claim 1, characterized in that: The method of calculating the total number of abrasive cutting times according to the number of revolutions of the workpiece gear and the number of abrasive grains includes: Obtain the workpiece gear rotation number and tooth surface processing area required to complete honing; According to the abrasive grain size and the organization number of the honing wheel, the average spacing between the abrasive grains is calculated; Calculating the number of abrasive grains based on the average spacing between the abrasive grains and the area of ​​the tooth surface processing region; The number of revolutions of the workpiece gear required to complete the honing is multiplied by the number of abrasive grains to obtain the total number of cutting times of the abrasive grains.

5. The convolution-based method for predicting the micro-morphology of the cylindrical gear internal meshing honing surface according to claim 4, characterized in that: The method of multiplying the number of workpiece gear revolutions required to complete the honing by the number of abrasive grains to obtain the total number of abrasive grain cutting times includes: in, Indicates the total number of abrasive cutting times, Indicates the number of abrasive particles, Indicates the number of revolutions of the workpiece gear. Indicates the processing time, Indicates the number of workpiece gear revolutions required to complete honing. Indicates the area of ​​the tooth surface processing area, Indicates the abrasive particle size, Indicates the honing wheel organization number.

6. A convolution-based surface micromorphology prediction system for cylindrical gear internal meshing honing, characterized in that: The system comprises: The first calculation unit is used to calculate the motion velocity vector of the abrasive grains on the surface of the honing wheel at the contact point of the tooth surface of the workpiece according to the velocity equation of the motion of the tooth surface of the honing wheel relative to the tooth surface of the workpiece; a second calculation unit, for simulating a process in which abrasive particles slide and cut on a tooth surface of a workpiece along the motion velocity vector, and calculating abrasive cutting characteristics; a third calculation unit for calculating the total number of abrasive cutting times according to the number of revolutions of the workpiece gear and the number of abrasive grains; a fourth calculation unit, configured to calculate the number of cutting times of the abrasive particles at each contact point on the tooth surface of the workpiece based on the total number of cutting times of the abrasive particles; A convolution calculation unit is used to perform convolution calculation based on the abrasive cutting characteristics and the number of cutting times of each contact point to obtain a convolution result, including: in, represents the convolution result, Indicates the number of cutting times in the matrix Rank Number of cutting times of contact points, represents a single height removal matrix, represents the convolution calculation, Represents the point at the mth row and nth column on the bottom surface of the spherical cap; A micro-morphology prediction unit is used to predict the micro-morphology of the tooth surface of the workpiece of internal meshing honing according to the convolution result, including: in, represents the predicted internal meshing honing surface micro-topography height matrix, represents the initial tooth surface height matrix, represents the convolution result, Represents the tooth surface normal vector The mold length.

7. An electronic device, characterized in that: The invention comprises at least one control processor and a memory for communicating with the at least one control processor; the memory stores instructions that can be executed by the at least one control processor, and the instructions are executed by the at least one control processor to enable the at least one control processor to execute the convolution-based cylindrical gear internal meshing honing surface micromorphology prediction method according to any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are used to enable a computer to execute the convolution-based method for predicting the micro-morphology of the surface of cylindrical gear internal meshing honing according to any one of claims 1 to 5.

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