Grinding surface topography modeling method for hard and brittle material bearing ring and computer program

Abstract

The invention relates to the technical field of machining simulation, in particular to a grinding surface appearance modeling method for a hard and brittle material bearing ring. The method comprises the following steps: modeling after observing the surface appearance of the grinding wheel; constructing an overall grinding track of the grinding wheel; performing a nanoindentation experiment, a constant-cutting-depth scribing experiment and a variable-cutting-depth scribing experiment on the workpiece, recording experimental data, and calculating the critical cutting thickness of the workpiece; whether the cutting depth is smaller than the critical cutting thickness of the workpiece or not is judged, if yes, the surface topography is constructed in a plastic topography removal mode, and if not, the surface topography is constructed in a brittle topography removal mode; and obtaining a surface topography data matrix, synthesizing the surface topography data matrix to obtain an overall surface topography, and outputting a surface topography simulation result. The grinding morphology modeling method aims at the silicon nitride ceramic bearing ring and is higher in adaptability, reliability and accuracy.

Description

Technical Field

[0001] This invention relates to the field of machining simulation technology, and in particular to a method and computer program for modeling the surface morphology of grinding bearing rings made of hard and brittle materials. Background Technology

[0002] Silicon nitride ceramic materials are typical hard and brittle materials. They have advantages such as good thermal conductivity, low coefficient of thermal expansion, high hardness, low density, and strong thermal stability. In recent years, they have been widely used in aerospace, national defense, rail transportation and other fields. In particular, the use of silicon nitride ceramic bearing rings is becoming more and more widespread.

[0003] In the production of silicon nitride ceramic bearing rings, grinding is a crucial processing step, and the surface quality of the ground surface is a key indicator for evaluating bearing performance. The essence of grinding is the repeated cutting and overlapping of abrasive grains randomly distributed on the surface of a grinding wheel, resulting in a complex surface morphology formation process that is difficult to derive simply. In particular, silicon nitride is a difficult-to-machine, hard, and brittle material, and the outer surface of the bearing is prone to processing damage during grinding, leading to high surface roughness and uneven surface morphology, which in turn affects the high-speed performance and fatigue life of the bearing. Establishing a surface morphology model of the grinding process using mathematical theories and simulation methods, and analyzing the influence of grinding process parameters on the surface morphology, can provide a theoretical basis and technical support for high-quality grinding of silicon nitride ceramic bearing rings, thereby guiding actual grinding production. To address this, existing technologies use simulation techniques to model the surface morphology of workpieces during grinding. However, these models are generally designed for ordinary metal workpieces. The material properties of silicon nitride ceramic bearing rings differ from those of ordinary metal workpieces. In particular, due to the curvature effect of the bearing rings, and the complex plastic-brittle transition involved in the grinding process, the grinding force distribution is non-uniform and involves many variables, resulting in a very complex grinding mechanism for ceramic outer cylindrical parts. This mechanism is fundamentally different from that of metal materials, making existing modeling methods unsuitable.

[0004] Therefore, it is of great significance to propose a grinding surface morphology modeling method with higher adaptability, reliability and accuracy for bearing rings made of silicon nitride ceramics and other similar hard and brittle materials. Summary of the Invention

[0005] The purpose of this invention is to provide a grinding surface morphology modeling method and computer program for bearing rings made of hard and brittle materials, aiming to solve the problem that existing grinding surface morphology modeling methods are not suitable for silicon nitride ceramic bearing rings.

[0006] To achieve the above objectives, this invention provides a method for modeling the surface morphology of grinding bearing rings made of hard and brittle materials, comprising the following steps: S1, observing the surface morphology of the grinding wheel using a microscope, and modeling the grinding wheel based on the observed results; S2, analyzing the motion trajectory of a single abrasive grain and the motion trajectory of adjacent abrasive grains during grinding, fitting the axial and circumferential abrasive grain motion trajectories to obtain the function of the abrasive grain motion trajectory relative to the grinding time, so as to construct the overall grinding trajectory of the grinding wheel; S3, conducting nanoindentation experiments, constant depth scoring experiments, and variable depth scoring experiments on the workpiece, recording the experimental data, and calculating the critical cutting thickness of the workpiece; S4, starting the simulation after inputting the workpiece data and grinding parameters; during the simulation, the workpiece surface is discretized, multiple sampling points are generated, and the grinding depth is determined according to the grinding time. The abrasive grain trajectory is used to determine the position of the abrasive grain cutting point on the workpiece surface. After the abrasive grain interference sampling point is reached, it is determined whether the cutting depth is less than the critical cutting thickness of the workpiece. If so, the surface morphology is constructed using the plastic morphology removal method; otherwise, the surface morphology is constructed using the brittle morphology removal method. In the plastic morphology removal method, the surface morphology is generated by the interference of the abrasive grain motion trajectory on the workpiece surface. In the brittle morphology removal method, the surface morphology is generated by calculating the median crack depth and transverse crack length based on the interference of the abrasive grain motion trajectory on the workpiece surface. The surface morphology data of a single sampling point is obtained. The above steps in step S4 are repeated until the grinding time ends. In step S5, the surface morphology data matrix is ​​obtained, the overall surface morphology is synthesized, and the surface morphology simulation results are output.

[0007] Further, in step S1, the modeling of the grinding wheel includes modeling the shape, size, cutting edge height, and spatial distribution of the abrasive grains on the grinding wheel surface. The modeling method for shape and size is to use a regular triangular pyramid to simulate the shape of the abrasive grains, and to obtain the equivalent diameter of the abrasive grains by calculating the diameter of the circumscribed sphere of the triangular pyramid. The modeling method for cutting edge height is to first perform statistical analysis on the cutting edge height of the abrasive grains, and then fit the data with a normal distribution model to obtain a numerical model of the cutting edge height of the abrasive grains. The modeling method for spatial distribution is to use a cylindrical coordinate system to define the surface edge equation of the grinding wheel, determine the position and offset distance of the abrasive grains on the surface equation, and use a rotation matrix to obtain the direction of the cutting edge of the abrasive grains, thereby realizing the modeling of spatial distribution.

[0008] Furthermore, in step 2, the method for analyzing the motion trajectory of a single abrasive grain is as follows: a global coordinate system is established with the workpiece rotation as the origin, a grinding wheel coordinate system is established with the grinding wheel rotation center as the origin, and a local coordinate system is established with the contact point between the grinding wheel and the workpiece as the origin; the position of the abrasive grain in the grinding wheel coordinate system is transformed to the global coordinate system using the local coordinate system as an intermediary, and the motion trajectory of a single abrasive grain in the global coordinate system is obtained as a function of the grinding time, which is used to describe the position change of a single abrasive grain in three-dimensional space.

[0009] In step 2, the method for analyzing the motion trajectory of adjacent abrasive grains is as follows: the spacing between abrasive grains on the grinding wheel is set to be uniform and the angle difference between the rotation of two adjacent abrasive grains is equal. Based on the first abrasive grain participating in the actual grinding process, according to the function of the motion path of a single abrasive grain in the global coordinate system and the grinding time, and by relying on the angle difference between the rotation of two adjacent abrasive grains, the motion trajectory of the next adjacent abrasive grain in the global coordinate system and the grinding time are obtained sequentially.

[0010] Furthermore, in step S3, the critical cutting thickness a of the workpiece gc The calculation formula is as follows:

[0011]

[0012] Where H represents the hardness of the workpiece, a fundamental physical property parameter; λ0 represents the initial length of the transverse crack, referring to the initial length of the transverse crack generated at the minimum scoring depth in the constant-cut deep scoring experiment; ξ represents the stable length of the transverse crack, referring to the average length of all transverse cracks obtained in the constant-cut deep scoring experiment; θ represents the tip cone half-angle of the abrasive grain during the experiment, determined by the diamond pen tip selected for the constant-cut deep scoring experiment; K ID K represents the dynamic fracture toughness at a certain moment. ID The calculation formula is as follows:

[0013]

[0014] Where β is a dimensionless constant, ranging from 0.04 to 0.075; E is the elastic modulus of the workpiece, a fundamental physical property parameter; H is the hardness of the workpiece, also a fundamental physical property parameter; F b denoted as , where is the scratching force at a certain moment during the brittle process in the variable shear deep scratch test; c is the transverse crack length at a certain moment during the brittle process in the variable shear deep scratch test.

[0015] Furthermore, in step S5, the method for synthesizing the overall surface morphology is as follows: for the intersection point formed by the intersection of multiple trajectories, if the height value of the next intersection point is smaller than the height value of the current intersection point, then the current surface morphology is skipped, and the next intersection point is an effective intersection point that successfully interferes with the workpiece surface.

[0016] Furthermore, in step S4, the median crack depth l m The calculation formula is as follows:

[0017]

[0018] transverse crack length c t The calculation formula is as follows:

[0019]

[0020] Where λ is a dimensionless constant, ranging from 0.9 to 1.2; E is the elastic modulus of the workpiece, which is a basic physical property parameter of the workpiece; and H is the hardness of the workpiece, which is a basic physical property parameter of the workpiece. The cone half-angle of the abrasive grain obtained from simulation; P is the load measured in the constant depth incision test; K ID The dynamic fracture toughness at a certain moment; ω is a dimensionless constant, ranging from 0.025 to 0.035; t is the experimental duration of the constant-cut depth incision test; A is the stress distribution coefficient, ranging from 2.0 to 4.5; ω is a dimensionless constant, ranging from π / 2; R k The radius of the indentation produced under load W;

[0021] K ID The calculation formula is as follows:

[0022]

[0023] Where β is a dimensionless constant, ranging from 0.04 to 0.075; F b denoted as , where is the scratching force at a certain moment during the brittle process in the variable shear deep scratch test; denoted as c is the transverse crack length at a certain moment during the brittle process in the variable shear deep scratch test.

[0024] R k The calculation formula is as follows:

[0025]

[0026] Where λ is a dimensionless constant with a value of 0.018; W is the load applied in the nanoindentation experiment.

[0027] Furthermore, it also includes step S6, calculating the surface roughness based on the surface morphology simulation results.

[0028] Furthermore, the process includes step S7, calculating the subsurface damage depth. The calculation method involves performing actual grinding on the workpiece, ensuring the grinding parameters are consistent with those input during surface morphology modeling. This yields the ground workpiece. The surface roughness of the ground workpiece is then measured, and the sum of the surface areas where material spalling occurred is calculated. For regions where the surface morphology is constructed using a brittle morphology removal method, the formula for calculating the subsurface damage depth within the corresponding region is as follows:

[0029] SSD = χSR 43 (S e ) A ;

[0030] Where SR is the surface roughness of the corresponding region; χ is the scaling parameter; S eThis represents the sum of the surface areas where material peeling occurred within the corresponding region;

[0031] The formula for calculating χ is,

[0032]

[0033] S e The calculation formula is as follows:

[0034]

[0035] Where r is the radius of the material spalling point, and is obtained by measurement.

[0036] The present invention also provides a computer program for running the method described above.

[0037] The grinding surface morphology modeling method for bearing rings made of hard and brittle materials provided by this invention has the following advantages compared with the prior art:

[0038] First, this method considers the motion trajectories of adjacent abrasive grains when analyzing the abrasive grain motion trajectory, which is used to characterize the multi-abrasive grain cutting path at any processing moment. This helps to reveal the interference, collision and interaction between abrasive grains, and can more accurately simulate the actual grinding process.

[0039] Second, this method involves nanoindentation experiments, constant depth scribing experiments, and variable depth scribing experiments. Through these experiments, the material removal mechanism of silicon nitride ceramics can be understood, and key parameters related to material removal calculations can be collected, providing parameter support for subsequent grinding surface morphology modeling. After obtaining the surface morphology simulation results, the experimental data from these experiments can be used to verify the simulation results, ensuring the accuracy of the simulation results.

[0040] Third, when generating surface morphology, plastic morphology removal method and brittle morphology removal method are used to construct surface morphology according to different cutting depths, which is closer to the actual grinding process. Therefore, the simulation results of the generated surface morphology are more accurate.

[0041] In summary, this method for modeling the grinding surface morphology of bearing rings made of hard and brittle materials is suitable for use in silicon nitride ceramic bearing rings. The simulation results are closer to actual grinding, making it appropriate to provide theoretical basis and technical support for high-quality grinding of silicon nitride ceramic bearing rings. The computer program of this invention also has the above-mentioned advantages. Attached Figure Description

[0042] Figure 1 This is a basic flowchart of the grinding surface morphology modeling method for bearing rings made of hard and brittle materials according to the present invention;

[0043] Figure 2This is a simulation diagram of the surface morphology of the grinding wheel obtained based on the present invention;

[0044] Figure 3 This is a schematic diagram of the experimental equipment used for conducting constant depth scratch tests and variable depth scratch tests.

[0045] Figure 4 It is the curve showing the relationship between scratching force and time during the variable shear depth scratching experiment;

[0046] Figure 5 This is a schematic diagram for calculating the sum of the surface areas of material peeling off;

[0047] Figure 6 It is a comparison between the actual grinding results and the simulation results under the first set of grinding parameters;

[0048] Figure 7 This is a comparison between the actual grinding results and the simulation results under the second set of grinding parameters. Detailed Implementation

[0049] The embodiments of the present invention will be described in detail below.

[0050] In this embodiment, unless otherwise explicitly specified and limited, terms such as "set in," "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 a connection through one or more intermediate media. Those skilled in the art can understand the specific meaning of these terms in this embodiment based on the specific circumstances. The directional terms appearing in this embodiment are for the purpose of better describing the characteristics of the features and the relationships between them. It should be understood that when the placement direction of this embodiment changes, the direction of the characteristics of the features and the relationships between them also changes accordingly. Therefore, directional terms do not constitute an absolute limitation on the characteristics of the features and the relationships between them in space, but only a relative limitation.

[0051] This invention provides a method for modeling the surface morphology of ground bearing rings made of hard and brittle materials, such as... Figure 1 As shown, it includes the following steps.

[0052] S1. Observe the surface morphology of the grinding wheel using a microscope, and model the grinding wheel based on the observed results.

[0053] In this embodiment, ultrasonic cleaning is used to remove impurities from the surface of the grinding wheel. A super depth-of-field three-dimensional microscope is used to observe the abrasive grains of the grinding wheel. The observations include the shape of the abrasive grains, the cutting edge height, the distribution state, and the surface morphology of the grinding wheel. The observed surface morphology of the grinding wheel can be used to verify the accuracy of the simulation results of the surface morphology of the grinding wheel.

[0054] After conducting the above observations, the grinding wheel was modeled using MATLAB. The modeling of the grinding wheel included modeling the shape and size of the abrasive grains on the grinding wheel surface, the cutting edge height, and the spatial distribution.

[0055] The modeling method for shape and size involves defining several abrasive grain shapes, such as pyramids, spheres, and truncated octahedrons. All observed abrasive grains are categorized into these shapes, and the grain shapes are defined in MATLAB according to their distribution ratio. When studying abrasive grains, the equivalent diameter is typically used to represent the size of irregular grains. This method uses a regular triangular pyramid to simulate the abrasive grain shape, and calculates the equivalent diameter of the abrasive grain by measuring the diameter of the circumscribed sphere of the pyramid.

[0056] The modeling method for the blade protrusion height is as follows: First, statistical analysis is performed on the abrasive grain protrusion height. The data is then fitted with a normal distribution model to obtain a numerical model of the abrasive grain protrusion height. Specifically, the grinding wheel is measured using a super depth-of-field microscope. The measured data of the abrasive grain protrusion height are imported into SPSS software for normal distribution verification. The verification shows that the distribution of the abrasive grain protrusion height has a certain regularity and central tendency, and all meet the normal distribution. Therefore, the exposed height of the cutting edge is set to conform to (μ, σ). 2 Normal distribution, i.e., the cutting edge height h of the abrasive grains. Z The distribution function is as follows:

[0057]

[0058] Where μ is the mean of the normal distribution and σ is the variance of the normal distribution, according to the "3σ" criterion, μ and σ take the values ​​as follows:

[0059]

[0060] Among them, h gmax h is the maximum diameter of the abrasive grains on the grinding wheel surface. gmin This is the minimum diameter of the abrasive grains on the surface of the grinding wheel.

[0061] The spatial distribution modeling method involves defining the surface edge equation of the grinding wheel using a cylindrical coordinate system, determining the position and offset distance of the abrasive grains on the surface equation, and using a rotation matrix to obtain the direction of the abrasive grain cutting edge, thus achieving spatial distribution modeling. Specifically, to prevent overlap between abrasive grains during surface topography modeling, the grinding wheel is divided into multiple small cubic spaces, with regular triangular pyramidal abrasive grains positioned at the center of each cubic space. First, the average spacing between abrasive grains, the number of abrasive grains, and the volume of the grinding area are calculated. Then, the position and offset distance of the abrasive grains on the surface edge equation are determined. It is assumed that the offset distance of the abrasive grains is formed by alternating linear path movements. Since the cutting edge direction of the abrasive grains is not perfectly vertical upwards but has an inclination angle, the direction and rotation angle of the abrasive grains are considered, and a rotation matrix is ​​used to describe the orientation of the abrasive grains, resulting in a numerical model of the spatial distribution of the abrasive grains. Assuming that the abrasive grains are uniformly distributed in the cylindrical coordinate system, the position of each abrasive grain can be calculated using its coordinates in the cylindrical coordinate system. Then, the coordinates of each abrasive grain in the radial direction are calculated to determine its position in the grinding area, thereby achieving precise control over the spatial distribution of the abrasive grains. To accurately describe the orientation of the abrasive grains, a rotation matrix is ​​constructed. It is assumed that the initial shape of the abrasive grains is a regular triangular pyramid, and a rotation coordinate system is established based on this shape. In the initial state, the cutting edge direction of the abrasive grains is aligned with the coordinate axis. Then, the orientation of the abrasive grains is adjusted by the rotation matrix to simulate the spatial distribution and cutting behavior of the abrasive grains in the actual grinding process. At this time, the offset angle of the abrasive grain tip in any direction can be obtained.

[0062] Based on the above method, the simulation image of the grinding wheel surface morphology is as follows: Figure 2 As shown.

[0063] S2. Analyze the motion trajectory of a single abrasive grain and the motion trajectory of adjacent abrasive grains during grinding. Fit the axial and circumferential abrasive grain motion trajectories to obtain the function of the abrasive grain motion trajectory relative to the grinding time, so as to construct the overall grinding trajectory of the grinding wheel.

[0064] In this embodiment, the method for analyzing the motion trajectory of a single abrasive grain is as follows: a global coordinate system is established with the workpiece rotation as the origin, a grinding wheel coordinate system is established with the grinding wheel rotation center as the origin, and a local coordinate system is established with the contact point between the grinding wheel and the workpiece as the origin; the position of the abrasive grain in the grinding wheel coordinate system is transformed to the global coordinate system by using the local coordinate system as an intermediary, and the motion trajectory of a single abrasive grain in the global coordinate system as a function of the grinding time is obtained, which is used to describe the position change of a single abrasive grain in three-dimensional space.

[0065] In this embodiment, the method for analyzing the motion trajectory of adjacent abrasive grains is as follows: the spacing between abrasive grains on the grinding wheel is set to be uniform and the angle difference between the rotation of two adjacent abrasive grains is equal. Based on the first abrasive grain participating in the actual grinding process, according to the function of the motion path of a single abrasive grain in the global coordinate system and the grinding time, and by relying on the angle difference between the rotation of two adjacent abrasive grains, the motion trajectory of the next adjacent abrasive grain in the global coordinate system and the grinding time are obtained sequentially.

[0066] S3. Perform nano-indentation, constant depth of cut, and variable depth of cut tests on the workpiece, record the experimental data, and calculate the critical cutting thickness of the workpiece.

[0067] In this embodiment, the nanoindentation experiment involves first grinding and polishing the workpiece surface until its surface roughness is reduced to below 10nm and a mirror-like effect is achieved; then, a high-precision micro / nanoindentation instrument is used to conduct the nanoindentation experiment, and experimental data and indentation morphology are recorded in real time during the experiment.

[0068] In this embodiment, the constant depth scratching experiment involves using a single abrasive diamond pen to scratch the workpiece surface at a uniformly increasing scratching depth (e.g., 10μm, 20μm, 30μm up to 100μm). The scratching drive device is a CNC machine tool, with a force-measuring tool holder installed between the diamond pen and the spindle of the CNC machine tool. During scratching, the scratching force data is acquired in real time and the scratch generation is recorded. After the scratching experiment, the workpiece surface is gold-plated, and then the scratched surface is observed using an SEM microscope.

[0069] In this embodiment, the variable cutting and deep scratching experiment involves using a diamond pen with a single abrasive grain to scratch a tilted workpiece (e.g., at a 5° tilt angle). The scratching drive device is a CNC machine tool. A force measuring tool holder is installed between the diamond pen and the spindle of the CNC machine tool. During scratching, the scratching force data is acquired in real time to record the generation of scratches. After the scratching experiment, the workpiece surface is gold-plated, and then the scratched surface is observed using an SEM electron microscope.

[0070] The experimental equipment used in the constant depth scratch test and the variable depth scratch test is as follows: Figure 3 As shown.

[0071] In this embodiment, the critical cutting thickness a of the workpiece gc The calculation formula is as follows:

[0072]

[0073] Where H represents the hardness of the workpiece, a fundamental physical property parameter that can be obtained from literature or measured through conventional experiments. λ0 represents the initial length of the transverse crack, referring to the initial length of the transverse crack generated at the minimum scratch depth (10 μm) in the constant-cut deep scratch test, obtained through observation of the scratch surface. ξ represents the stable length of the transverse crack, referring to the average length of all transverse cracks obtained in the constant-cut deep scratch test, obtained through observation, statistics, and calculation of the scratch surface. θ represents the tip cone half-angle of the abrasive grain during the experiment, determined by the diamond pen tip selected in the constant-cut deep scratch test; the value of θ changes accordingly when different diamond pens are selected. K ID K represents the dynamic fracture toughness at a certain moment. ID The calculation formula is as follows:

[0074]

[0075] Where β is a dimensionless constant, ranging from 0.04 to 0.075; E is the elastic modulus of the workpiece, a fundamental physical property parameter that can be obtained from literature or measured through conventional experiments; H is the hardness of the workpiece, also a fundamental physical property parameter that can be obtained from literature or measured through conventional experiments; F b The scratching force at a specific moment during the brittle process in the variable depth scratching experiment; throughout the entire variable depth scratching process, the cutting stage will experience as follows: Figure 4 The diagram illustrates the plastic deformation stage OA, the combined plastic and brittle removal stage AB, and the brittle removal stage BC. During the brittle removal stage BC, the material peeling off instantaneously also peels off a portion of the material in front of the peeling point. This causes a sudden decrease in the scribing force required to continue scribing on this front portion. However, as scribing continues, the required scribing force returns to normal once the undamaged surface is reached. Therefore, as... Figure 4 As shown, during the brittle removal stage BC, the scratching force versus time curve exhibits a wavy upward trend. To ensure the accuracy of the selected parameters, the preferred moment is the time corresponding to the peak of the curve. c represents the transverse crack length at a specific moment in the brittle process during the variable shear scratching experiment. At the determined time point (and F... b After selecting the same time point, first determine the position of the diamond pen at that time point, and then observe the scratch at that position to obtain the length of the transverse crack at that time point.

[0076] Using the above formula and the experimental data recorded during the nano-indentation experiment, constant depth of cut and variable depth of cut experiment, the critical cutting thickness of the workpiece can be calculated.

[0077] S4. After inputting workpiece data and grinding parameters, the simulation begins. During simulation, the workpiece surface is discretized, generating multiple sampling points. The abrasive grain trajectory is determined based on the grinding time, and the position of the abrasive grain cutting point on the workpiece surface is determined. When the abrasive grains interfere with the sampling point, it is determined whether the cutting depth is less than the critical cutting thickness of the workpiece. If so, the surface morphology is constructed using the plastic morphology removal method; otherwise, the surface morphology is constructed using the brittle morphology removal method. In the plastic morphology removal method, the surface morphology is generated by the interference of the abrasive grain motion trajectory on the workpiece surface. In the brittle morphology removal method, the surface morphology is generated based on the interference of the abrasive grain motion trajectory on the workpiece surface, and the median crack depth and transverse crack length are calculated. The surface morphology data of a single sampling point are obtained. The above steps in step S4 are repeated until the grinding time ends. Step S4 is run in MATLAB software.

[0078] In this embodiment, the median crack depth l m The calculation formula is as follows:

[0079]

[0080] transverse crack length c t The calculation formula is as follows:

[0081]

[0082] Where λ is a dimensionless constant, ranging from 0.9 to 1.2. E is the elastic modulus of the workpiece, a fundamental physical property parameter that can be obtained from literature or measured through conventional experiments. H is the hardness of the workpiece, also a fundamental physical property parameter that can be obtained from literature or measured through conventional experiments. To simulate the cone half-angle of the abrasive grains, since the abrasive grain shape is set to be a regular triangular pyramid in this embodiment, therefore... The angle is 65°. P is the load measured in the constant depth incision test. K ID This refers to the dynamic fracture toughness at a certain moment. ω is a dimensionless constant, ranging from 0.025 to 0.035; t is the experimental duration of the constant-cut depth incision test. A is the stress distribution coefficient, ranging from 2.0 to 4.5. ω is a dimensionless constant, ranging from π / 2. k Let be the radius of the indentation produced under load W.

[0083] K ID The calculation formula is the same as described above.

[0084] R k The calculation formula is as follows:

[0085]

[0086] Where λ is a dimensionless constant with a value of 0.018; W is the load applied in the nanoindentation experiment.

[0087] Using the above formula, combined with the experimental data recorded during the nanoindentation experiment, constant depth scratch experiment, and variable depth scratch experiment, the median crack depth and transverse crack length can be obtained.

[0088] S5. After the grinding time is completed, the surface morphology data matrix is ​​obtained, the overall surface morphology is synthesized, and the surface morphology simulation results are output.

[0089] In this embodiment, the method for synthesizing the overall surface morphology is as follows: for the intersection points formed by the intersection of multiple trajectories, if the height value of the next intersection point is smaller than the height value of the current intersection point, then the current surface morphology is skipped, and the next intersection point is a valid intersection point that successfully interferes with the workpiece surface.

[0090] S6. Calculate the surface roughness based on the surface morphology simulation results.

[0091] In this embodiment, the method for calculating surface roughness is as follows: for each discrete region, traverse all calculated abrasive cutting edge coordinates, and for a certain coordinate (x... cij ,y cij If (x) is satisfied ij <x cij <x ij +△x) and (y ij <y cij <y ij If +△y), then it belongs to the discrete region. The height of each data point constituting the cutting topography element is calculated using the following formula.

[0092]

[0093] This yields the absolute value of the deviation between the height of each data point and the average value. Summing these absolute values ​​and dividing by the number of data points N, the formula for calculating surface roughness Ra is:

[0094]

[0095] S7. Calculate the subsurface damage depth.

[0096] Subsurface damage depth refers to the depth of the damaged area below the material surface caused by the grinding process. It represents structural damage that is difficult to see and reflects the internal structural changes of the material during processing. If the subsurface damage depth can be calculated, it can provide a significant reference for high-quality grinding processes. Studies have shown that subsurface damage depth is related to surface roughness, median crack depth, transverse crack length, and material spalling from the workpiece surface. The median crack depth and transverse crack length are obtained using the formulas described above; the workpiece surface roughness can be directly measured or calculated as described above; and the material spalling from the workpiece surface can be observed. Although subsurface damage depth can also be measured from the workpiece surface, it is relatively complex, and most measurement methods are destructive. In actual production, it is impossible to damage the product. Measuring surface roughness, calculating the median crack depth and transverse crack length, and observing and calculating the material spalling from the workpiece surface are all non-destructive and easier to implement. Therefore, this embodiment also proposes a method for directly calculating subsurface damage depth.

[0097] In this embodiment, the subsurface damage depth is calculated by performing actual grinding on the workpiece, using grinding parameters consistent with those input during surface morphology modeling. This yields a ground workpiece, which is then measured for surface roughness and the sum of the surface areas where material spalling occurs. Prior to this step, the theoretical surface roughness results have been obtained through previous simulations. A comparison can be made between the simulated theoretical surface roughness and the measured experimental surface roughness after actual grinding to verify the accuracy of the simulation. Once the simulation error values ​​are verified to meet requirements, the subsurface damage depth can be calculated using either the simulated theoretical surface roughness or the measured experimental surface roughness. For regions where the surface morphology is constructed using a brittle morphology removal method, the formula for calculating the subsurface damage depth within the corresponding region is as follows:

[0098] SSD = χSR 43 (S e ) A ;

[0099] Where SR is the surface roughness of the corresponding region; χ is the scaling parameter; S e The sum of the surface areas where material spalling occurred within the corresponding region needs to be calculated after observation.

[0100] The formula for calculating χ is,

[0101]

[0102] Se The calculation formula is as follows:

[0103]

[0104] Where r is the radius of the material spalling point, which is obtained through measurement. For example... Figure 5 As shown, the left side is an image of the area where material spalling occurred, as observed in practice. This image is then transformed into the equivalent image shown on the right, illustrating the calculation of the sum of the surface areas where material spalling occurred within that area. The above formula can be solved in a MATLAB program to obtain the subsurface damage depth within a specified area.

[0105] The present invention also provides a computer program for running the method described above. Specifically, the computer program is a computer with a MATLAB program installed, which is used to execute the method described above.

[0106] To verify the accuracy of this method, the inventors designed multiple grinding experiments and simulations for comparison, and selected two sets of data for illustration. In the first comparison group, the grinding parameters for both actual grinding and simulation were set as follows: grinding wheel linear velocity v s =80m / s, workpiece rotational speed v w =80 r / min, grinding depth a p =15μm. In the second comparison group, the grinding parameters for both actual grinding and simulation were set as follows: grinding wheel linear velocity v s =140m / s, workpiece rotational speed v w =80 r / min, grinding depth a p =25μm. The results of the two control groups are as follows: Figure 6 and Figure 7 As shown in the figure, the experimental results are very close to the simulation results, which shows that the method has high reliability and accuracy for surface morphology simulation.

[0107] Furthermore, in the first comparative group, the experimental surface roughness value of the workpiece obtained from the grinding experiment was 0.125 μm, while the theoretical surface roughness value output by the simulation was 0.119 μm, with an error of 4.8%. In the second comparative group, the experimental surface roughness value of the workpiece obtained from the grinding experiment was 0.081 μm, while the theoretical surface roughness value output by the simulation was 0.073 μm, with an error of 9.88%. All of these errors are within acceptable limits, demonstrating the reliability and accuracy of this method for surface roughness calculation.

[0108] Furthermore, in the first comparative group, the experimental subsurface damage depth of the workpiece obtained from the grinding experiment was 20.467 μm, while the theoretical subsurface damage depth output by the simulation was 18.925 μm, with an error of 7.53%. In the second comparative group, the experimental subsurface damage depth of the workpiece obtained from the grinding experiment was 34.335 μm, while the theoretical subsurface damage depth output by the simulation was 31.963 μm, with an error of 6.91%. All of these errors are within acceptable limits, demonstrating the reliability and accuracy of this method in calculating subsurface damage depth.

[0109] In summary, this method for modeling the surface morphology of grinding bearing rings made of hard and brittle materials is suitable for use in silicon nitride ceramic bearing rings. The simulation results are closer to actual grinding, making it appropriate to provide theoretical basis and technical support for high-quality grinding of silicon nitride ceramic bearing rings.

[0110] Where there is no conflict, the above embodiments and features can be combined with each other.

[0111] Finally, it should be noted that the above embodiments are only used to illustrate the preferred technical solutions of the present invention, and are not intended to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the essence and scope of the present invention.

Claims

1. A method for modeling the surface morphology of ground bearing rings made of hard and brittle materials, characterized in that, Includes the following steps: S1. Observe the surface morphology of the grinding wheel using a microscope, and model the grinding wheel based on the observed results; S2. Analyze the motion trajectory of a single abrasive grain and the motion trajectory of adjacent abrasive grains during grinding. Fit the axial and circumferential abrasive grain motion trajectories to obtain the function of the abrasive grain motion trajectory relative to the grinding time, so as to construct the overall grinding trajectory of the grinding wheel. S3. Perform nano-indentation experiment, constant depth of cut test and variable depth of cut test on the workpiece, record the experimental data and calculate the critical cutting thickness of the workpiece. S4. After inputting workpiece data and grinding parameters, start the simulation. During the simulation, discretize the workpiece surface and generate multiple sampling points. Determine the abrasive grain trajectory based on the grinding time and the position of the abrasive grain cutting point on the workpiece surface. When the abrasive grains interfere with the sampling point, determine whether the cutting depth is less than the critical cutting thickness of the workpiece. If so, use the plastic morphology removal method to construct the surface morphology; otherwise, use the brittle morphology removal method to construct the surface morphology. In the plastic morphology removal method, the surface morphology is generated by the interference of the abrasive particle motion trajectory on the workpiece surface; in the brittle morphology removal method, the surface morphology is generated by calculating the median crack depth and transverse crack length based on the interference of the abrasive particle motion trajectory on the workpiece surface; and the surface morphology data of a single sampling point are obtained. Repeat the above steps in step S4 until the grinding time ends; S5. Obtain the surface morphology data matrix, synthesize the overall surface morphology, and output the surface morphology simulation results.

2. The method for modeling the surface morphology of ground bearing rings made of hard and brittle materials according to claim 1, characterized in that: In step S1, the modeling of the grinding wheel includes modeling the shape, size, tip height, and spatial distribution of the abrasive grains on the grinding wheel surface; The modeling method for shape and size is to use a regular triangular pyramid to simulate the shape of the abrasive grains, and to obtain the equivalent diameter of the abrasive grains by calculating the diameter of the circumscribed ball of the triangular pyramid. The modeling method for the blade extension height is as follows: first, perform statistical analysis on the blade extension height of the abrasive grains, then fit the data with a normal distribution model to obtain a numerical model of the blade extension height of the abrasive grains. The spatial distribution modeling method is to define the surface edge equation of the grinding wheel using a cylindrical coordinate system, determine the position and offset distance of the abrasive grains on the surface equation, and use a rotation matrix to obtain the direction of the abrasive grain cutting edge, thereby realizing the modeling of the spatial distribution.

3. The method for modeling the surface morphology of ground bearing rings made of hard and brittle materials according to claim 1, characterized in that: In step 2, the method for analyzing the motion trajectory of a single abrasive grain is as follows: A global coordinate system is established with the workpiece rotation as the origin, a grinding wheel coordinate system is established with the grinding wheel rotation center as the origin, and a local coordinate system is established with the contact point between the grinding wheel and the workpiece as the origin. Using the local coordinate system as an intermediary, the position of the abrasive grain in the grinding wheel coordinate system is transformed into the global coordinate system, and the motion trajectory of a single abrasive grain in the global coordinate system is obtained as a function of the grinding time, which is used to describe the position change of a single abrasive grain in three-dimensional space.

4. The method for modeling the surface morphology of ground bearing rings made of hard and brittle materials according to claim 3, characterized in that: In step 2, the method for analyzing the motion trajectory of adjacent abrasive grains is as follows: Assuming the abrasive grains on the grinding wheel are evenly spaced and the angular difference between adjacent abrasive grains is equal, based on the first abrasive grain participating in the actual grinding process, and according to the function of the motion path of a single abrasive grain in the global coordinate system and the grinding time, and by relying on the angular difference between adjacent abrasive grains, the motion trajectory of the next adjacent abrasive grain in the global coordinate system and the grinding time are obtained sequentially.

5. The method for modeling the surface morphology of ground bearing rings made of hard and brittle materials according to claim 1, characterized in that: In step S3, the critical cutting thickness a of the workpiece gc The calculation formula is as follows: Where H represents the hardness of the workpiece, a fundamental physical property parameter; λ0 represents the initial length of the transverse crack, referring to the initial length of the transverse crack generated at the minimum scoring depth in the constant-cut deep scoring experiment; ξ represents the stable length of the transverse crack, referring to the average length of all transverse cracks obtained in the constant-cut deep scoring experiment; θ represents the tip cone half-angle of the abrasive grain during the experiment, determined by the diamond pen tip selected for the constant-cut deep scoring experiment; K ID K represents the dynamic fracture toughness at a certain moment. ID The calculation formula is as follows: Where β is a dimensionless constant, ranging from 0.04 to 0.075; E is the elastic modulus of the workpiece, a fundamental physical property parameter; H is the hardness of the workpiece, also a fundamental physical property parameter; F b denoted as , where is the scratching force at a certain moment during the brittle process in the variable shear deep scratch test; c is the transverse crack length at a certain moment during the brittle process in the variable shear deep scratch test.

6. The method for modeling the surface morphology of ground bearing rings made of hard and brittle materials according to claim 1, characterized in that: In step S5, the method for synthesizing the overall surface morphology is as follows: For intersection points formed by the intersection of multiple trajectories, if the height value of the next intersection point is smaller than the height value of the current intersection point, then the current surface topography is skipped, and the next intersection point is a valid intersection point that successfully interferes with the workpiece surface.

7. The method for modeling the surface morphology of ground bearing rings made of hard and brittle materials according to claim 1, characterized in that: In step S4, Median crack depth l m The calculation formula is as follows: transverse crack length c t The calculation formula is as follows: Where λ is a dimensionless constant, ranging from 0.9 to 1.2; E is the elastic modulus of the workpiece, which is a basic physical property parameter of the workpiece; and H is the hardness of the workpiece, which is a basic physical property parameter of the workpiece. The cone half-angle of the abrasive grain obtained from simulation; P is the load measured in the constant depth incision test; K ID The dynamic fracture toughness at a certain moment; ω is a dimensionless constant, ranging from 0.025 to 0.035; t is the experimental duration of the constant-cut depth incision test; A is the stress distribution coefficient, ranging from 2.0 to 4.5; ω is a dimensionless constant, ranging from π / 2; R k The radius of the indentation produced under load W; K ID The calculation formula is as follows: Where β is a dimensionless constant, ranging from 0.04 to 0.075; F b denoted as , where is the scratching force at a certain moment during the brittle process in the variable shear deep scratch test; denoted as c is the transverse crack length at a certain moment during the brittle process in the variable shear deep scratch test. R k The calculation formula is as follows: Where λ is a dimensionless constant with a value of 0.018; W is the load applied in the nanoindentation experiment.

8. The method for modeling the surface morphology of ground bearing rings made of hard and brittle materials according to claim 7, characterized in that: It also includes step S6, calculating the surface roughness based on the surface morphology simulation results.

9. The method for modeling the surface morphology of ground bearing rings made of hard and brittle materials according to claim 8, characterized in that: It also includes step S7, calculating the subsurface damage depth, the calculation method is as follows: The workpiece is subjected to actual grinding, with grinding parameters consistent with those input during surface morphology modeling. The resulting ground workpiece is then measured, and the sum of the surface roughness and material spalling areas is calculated. For regions where the surface morphology is constructed using a brittle morphology removal method, the formula for calculating the subsurface damage depth within the corresponding region is as follows: SSD=χSR 43 (S e ) A ; Where SR is the surface roughness of the corresponding region; χ is the scaling parameter; S e This represents the sum of the surface areas where material peeling occurred within the corresponding region; The formula for calculating χ is, S e The calculation formula is as follows: Where r is the radius of the material spalling point, and is obtained by measurement.

10. A computer program, characterized in that, It is used to perform the method as described in any one of claims 1-9.

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