A method for dynamically simulating and predicting residual stress on a ground surface of a silicon carbide substrate

Abstract

The present application relates to the technical field of precision processing of semiconductor materials, and particularly relates to a dynamic simulation and prediction method for residual stress on a ground surface of a silicon carbide substrate, which comprises the following steps: S1, constitutive model correction and simulation result database establishment; S2, modeling of discrete trajectory points of free abrasive particles; S3, residual stress static mapping; S4, residual error compensation model establishment; S5, online dynamic simulation and prediction of grinding. The present application classifies the substrate surface under different loading conditions through the loading times of grid elements, and maps residual stress in different ways for each type of grid element, fully considers the interference effect of the abrasive particle trajectory in actual grinding, and significantly improves the authenticity and accuracy of residual stress prediction; meanwhile, the online features of acoustic emission signals and vibration signals are introduced, and the static simulation and prediction results are dynamically superimposed and compensated by combining the GWO-GPR residual error compensation model, so as to meet the real-time prediction requirements of the production line.

Description

Technical Field

[0001] This invention relates to the field of precision machining technology for semiconductor materials, and in particular to a method for dynamic simulation and prediction of residual stress on the polished surface of a silicon carbide substrate. Background Technology

[0002] Single-crystal silicon carbide, a typical material in third-generation semiconductors, possesses characteristics such as a large bandgap, high breakdown electric field, high saturated electron drift velocity, and high thermal conductivity, and is commonly used in the manufacture of 5G radio frequency devices and high-voltage power devices. To achieve excellent surface flatness and smoothness, planarization processing, such as grinding and polishing, is typically required. However, single-crystal silicon carbide exhibits relatively low fracture toughness and high hardness, making it a typical difficult-to-machine material. This inevitably leads to residual surface stress during processing, significantly affecting material properties and device reliability. Accurately predicting the residual stress on the silicon carbide grinding surface is crucial for improving the production quality and reliability of silicon carbide grinding processes.

[0003] In the prediction of residual stress, the simulation modeling method based on finite element simulation has attracted attention because it can meticulously depict the microscopic process of the interaction between abrasive grains and materials. This type of method usually uses the JH-2 constitutive model to describe the mechanical response of silicon carbide and simulates grinding force, surface stress and crack damage by establishing a finite element model of a single abrasive grain scratch. However, the existing simulation methods have the following shortcomings: (1) The parameters of the JH-2 constitutive model are usually directly taken from empirical values ​​or literature values ​​and are not calibrated for specific grinding conditions, resulting in a systematic deviation between the simulation results and the actual processing; (2) Existing studies are mainly based on the indentation / scraping model of a single abrasive grain, and estimate the residual stress distribution by analyzing the mechanical response of a single contact, without considering the interference effect between the movement trajectories of abrasive grains in actual grinding, which makes it difficult to truly reflect the residual stress distribution; (3) During the grinding process, the equipment performance, grinding pad wear, abrasive grain state and other factors evolve dynamically with the processing time, showing time-varying and complex characteristics; however, traditional simulation models mostly rely on experimental and static verification to obtain model parameters, which makes it difficult to effectively describe time-varying characteristics, resulting in incomplete and inaccurate modeling. All of the above problems have led to a decrease in prediction accuracy.

[0004] Therefore, there is an urgent need for a simulation modeling method with higher prediction accuracy. Summary of the Invention

[0005] The purpose of this invention is to provide a dynamic simulation prediction method for residual stress on the polished surface of a silicon carbide substrate, aiming to solve the problem of low prediction accuracy in the prior art.

[0006] To achieve the above objectives, this invention provides a method for dynamic simulation and prediction of residual stress on the polished surface of a silicon carbide substrate, comprising the following steps: S1, Constitutive model correction and simulation result library establishment: The constitutive model of silicon carbide is corrected using a Bayesian optimization method. The corrected constitutive model is then used to perform explicit Abaqus dynamic simulations of single-grain scratches and dual-grain interference scratches, establishing a simulation result library. The simulation factors in the library include abrasive diameter, abrasive velocity, abrasive loading depth, and interference angle. The simulation results in the library include single-grain residual stress and dual-grain interference residual stress; S2, Modeling of discrete trajectory points of free abrasive particles: Based on the polishing process... Process parameters: Based on the kinematics of the planetary differential gear train, a motion trajectory model of free abrasive particles relative to the silicon carbide substrate is established. A grinding random coefficient is introduced to characterize the random drift characteristics of the free abrasive particles. The motion trajectory model is run repeatedly, and the temporal position of the effective abrasive particles relative to the substrate coordinate system is sampled frame by frame and the statistical mean is taken. The statistical mean is integrated to obtain the discrete trajectory point set of the effective abrasive particles relative to the substrate coordinate system during the grinding process. Each discrete trajectory point corresponds to one abrasive loading. S3, Static mapping of residual stress: The surface of the silicon carbide substrate is divided into mesh cells. The criteria for mesh cell division must meet the requirement that the number of abrasive loading times n in any mesh cell is not greater than 2 and all mesh cells are subjected to abrasive loading times n. The circumcircle size of each grid cell must be smaller than the spacing between adjacent discrete trajectory points. Each grid cell is assigned the number of abrasive loading events *n* during the grinding process based on the discrete trajectory point set. All grid cells are classified and residual stresses are mapped accordingly: n=0 represents non-contact cells, assigned zero residual stress or initial residual stress; n=1 represents single-load cells, where the abrasive diameter, abrasive velocity, and abrasive loading depth of a single abrasive grain within the single-load cell are extracted, and the corresponding residual stress is interpolated from the single abrasive grain residual stress data in the simulation results library and assigned a value; n=2 represents interferential loading cells, where two abrasive loading events within the interferential loading cell are traced. The interference angle is calculated based on the abrasive movement direction corresponding to the two abrasive loading events. The abrasive diameter, abrasive velocity, and abrasive loading depth of the two abrasive grains are extracted and averaged. Combined with the interference angle, the residual stress corresponding to the interference loading unit is obtained by interpolation in the dual abrasive residual stress result data in the simulation result library and assigned a value. Then, the residual stress field of the entire grinding surface is Gaussian smoothed to obtain the static simulation prediction result. S4, Residual compensation model establishment: A grinding experiment is carried out on the silicon carbide substrate, and the experimental measured value of residual stress is obtained. The simulation of steps S1 to S3 is carried out with the process parameters of the grinding experiment to obtain the experimental static simulation prediction value of residual stress.Acoustic emission and vibration signals were collected during the experiment. These signals were preprocessed and feature extracted to identify sensitive features highly sensitive to residual stress. The process parameters and these sensitive features formed an input vector, and the residual between the experimental measurements and the static simulation predictions was used as the output label to construct a training sample set. The kernel function hyperparameter of the Gaussian process regression model was optimized using the Grey Wolf optimization algorithm to train the GWO-GPR residual compensation model. S5. Online dynamic simulation prediction for grinding: During the grinding production of silicon carbide substrates, simulations of steps S1 to S3 were performed using the grinding process parameters to obtain online static simulation predictions. Acoustic emission and vibration signals were simultaneously collected during the production process. The residuals were output through the GWO-GPR residual compensation model, and residual superposition compensation was applied to the online static simulation predictions to obtain the online dynamic simulation prediction results.

[0007] Furthermore, in step S1, the constitutive model of silicon carbide adopts JH-2, and the parameters to be corrected include B, M, D1 and D2. The Bayesian optimization method uses the Metropolis-Hastings sampling strategy to optimize the posterior distribution of the parameters, and the mechanical data obtained from the nanoindentation experiment is used as the calibration basis.

[0008] Furthermore, in step S1, the simulation result library is established by taking the abrasive diameter, abrasive velocity, abrasive loading depth, and interference angle as four input factors, setting each input factor to five levels, and using the L25 orthogonal experimental table to complete the establishment of the simulation result library.

[0009] Further, in step S1, the input factor levels of the simulation result library are set as follows: abrasive diameter ∈ {2,4,6,8,10} μm, abrasive velocity ∈ {0.2,0.4,0.6,0.8,1.0} m / s, abrasive loading depth ∈ {0.2,0.4,0.6,0.8,1.0} μm, and interference angle ∈ {0°,30°,45°,60°,90°}.

[0010] Furthermore, in step S2, the grinding random coefficient is taken as γ∈[0,1], where γ=0 indicates that the abrasive particles are strictly attached to the grinding pad and move, and γ=1 indicates that the abrasive particles are completely free and drift randomly.

[0011] Furthermore, in step S2, the motion trajectory model is run repeatedly at least 50 times.

[0012] Furthermore, in step S3, the method for dividing the silicon carbide substrate surface into grid cells is to use the circumcircle size of the grid cell being smaller than the spacing of adjacent discrete trajectory points by 0.01 mm as a reference, and to decrease the size by 0.01 mm each time. When the number of abrasive loading times n for all grid cells under a certain size is not greater than 2, that size is fixed as the division scale.

[0013] Further, in step S3, the method for dividing the silicon carbide substrate surface into grid cells is as follows: first, the grid cells are initially divided with the outer circle size being smaller than the spacing of adjacent discrete trajectory points by 0.01 mm. Then, it is determined whether the number of abrasive loading n for each grid cell is not greater than 2. For grid cells with abrasive loading n greater than 2, they are further divided until the number of abrasive loading n for all grid cells is not greater than 2.

[0014] Furthermore, in step S3, the abrasive diameter is taken as the average particle size of diamond in the actual polishing fluid; the abrasive velocity is solved by the motion trajectory model; the abrasive loading depth is calculated based on the indentation hardness principle; and the interference angle is obtained by calculating the angle between the directions of the two scratches corresponding to the two abrasive grains.

[0015] Furthermore, in step S4, the process parameters constituting the input vector include grinding pressure, grinding fluid concentration, grinding disc rotation speed, and sun gear rotation speed, and the sensitive features constituting the input vector include the waveform factor, peak factor, kurtosis factor, and centroid frequency of the Z-axis vibration signal, as well as the waveform factor, peak factor, kurtosis factor, and centroid frequency of the acoustic emission signal.

[0016] The present invention provides a method for dynamic simulation and prediction of residual stress on the polished surface of a silicon carbide substrate, which has the following advantages compared with the prior art:

[0017] (1) It uses Bayesian optimization method to correct the constitutive model, eliminates the systematic bias caused by empirical parameters, and makes the simulation results closer to reality.

[0018] (2) It establishes a set of discrete trajectory points of free abrasive particles based on the kinematics of planetary differential gear train, and classifies the substrate surface under different loading conditions by the number of loading times of grid cells. Each type of grid cell maps residual stress in a different way, fully considering the interference effect of abrasive particle trajectory in actual grinding, and significantly improving the authenticity and accuracy of residual stress prediction.

[0019] (3) It introduces the online characteristics of acoustic emission signals and vibration signals, establishes the GWO-GPR residual compensation model, performs dynamic residual superposition compensation on the static simulation prediction results, effectively describes the time-varying characteristics of the grinding process, realizes the leap from static simulation prediction to dynamic simulation prediction, and meets the real-time prediction requirements of the production line. Attached Figure Description

[0020] Figure 1 This is a flowchart of the dynamic simulation prediction method for residual stress on the polished surface of a silicon carbide substrate according to the present invention;

[0021] Figure 2 These are stress cloud diagrams of the second abrasive grain scribing under different interference angles;

[0022] Figure 3 It is a graph of the radial average residual stress predicted by static simulation.

[0023] Figure 4 It is a three-dimensional stress diagram of the residual stress predicted by static simulation;

[0024] Figure 5 This is a flowchart of the online dynamic simulation prediction of grinding in step S5. Detailed Implementation

[0025] The embodiments of the present invention will be described in detail below.

[0026] 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.

[0027] The smooth, flat silicon carbide surface is the result of the abrasive action during grinding. To make the simulation of residual stress more realistic and achievable, this embodiment discretizes the abrasive trajectory into a set of points. When a discrete trajectory point is located at a certain position, it represents that the abrasive has applied residual stress at that position. Simultaneously, this embodiment divides the silicon carbide surface into mesh cells, classifying the effect of the abrasive on the mesh cells into two categories: one where the mesh cell contains only one scratch (corresponding to only one discrete trajectory point, with the abrasive being applied once), thus the mesh cell only contains residual stress caused by a single scratch; the other where the mesh cell contains two scratches (corresponding to two discrete trajectory points, with the abrasive being applied twice), with two abrasives passing through the mesh cell one after the other. In this case, the residual stress generated by the latter abrasive affects the residual stress generated by the former abrasive, i.e., interference exists. This interference is not a simple superposition of the two residual stresses, but rather exhibits a certain superposition rule. This embodiment reveals the superposition rule and uses the obtained superposition rule to predict residual stress. It is easy to understand that during the entire grinding process, the abrasive grains will generate numerous scratches, and a certain area will contain multiple scratches. However, the smaller the grid cell is divided, the fewer scratches are contained in a single grid cell. Until the silicon carbide surface is divided into grid cells with a maximum of only two scratches in each grid cell (0 scratches - 0 abrasive loadings, 1 scratch - 1 discrete trajectory point - 1 abrasive loading, 2 scratches - 2 discrete trajectory points - 2 abrasive loadings), the residual stress in each grid cell can be calculated in a way that is close to reality and feasible. Then, the residual stress data of the entire silicon carbide surface is smoothed to obtain the residual stress field of the silicon carbide surface.

[0028] Based on the above ideas, such as Figure 1 As shown, this embodiment provides a method for dynamic simulation prediction of residual stress on the polished surface of a silicon carbide substrate, including steps S1 to S5: S1 Constitutive model correction and simulation result library establishment, S2 Modeling of discrete trajectory points of free abrasive particles, S3 Static mapping of residual stress, S4 Establishment of residual compensation model, and S5 Online dynamic simulation prediction of polishing. The specific implementation methods of each step are further described in detail below with reference to the accompanying drawings.

[0029] Step S1: Constitutive model correction and simulation result library establishment

[0030] This step aims to establish a lookupable database of simulation results to provide data support for the residual stress mapping in the subsequent step S3.

[0031] This embodiment employs a Bayesian optimization method to modify the constitutive model of silicon carbide. Silicon carbide, as a typical hard and brittle ceramic material, is typically described using the Johnson-Holmquist (JH) constitutive model. In this embodiment, the constitutive model of silicon carbide is JH-2, and the parameters to be modified include damage parameters B (damage constant), M (damage exponent), D1, and D2 (D1 and D2 are parameters related to fracture plastic strain, respectively). These parameters are sensitive to simulation results and vary with silicon carbide crystal form, material batch, and processing conditions. Directly using empirical values ​​from literature would introduce systematic biases. Therefore, this embodiment uses a Bayesian optimization method to perform posterior calibration on parameters B, M, D1, and D2. The core idea of ​​Bayesian optimization is to obtain the posterior distribution of parameters based on the prior distribution of the parameters, combined with observed data (likelihood), and continuously narrow down the posterior distribution through a sampling strategy until it converges to the optimal parameter set. In this embodiment: (1) The parameters to be calibrated {B, M, D1, D2} are used as independent variables, and a prior distribution range (e.g., [0.1, 1.1]) is set for each parameter; (2) The load-displacement curve obtained from the nanoindentation experiment (i.e., discrete data points showing the change of indentation load P with indentation depth h) is used as the calibration basis (observation data / likelihood); (3) The likelihood function is defined, for example, based on the mean square error of the simulated load-displacement curve and the nanoindentation experimental curve; (4) The posterior distribution of the parameters is optimized using the Metropolis-Hastings (MH) sampling strategy. After a sufficient number of iterations, the posterior distribution converges, and the mean value of the converged parameters is taken as the correction result. After correction by the above method, the parameters obtained in this embodiment are: B=0.939, M=0.685, D1=0.809, D2=0.800, all of which are within the set prior range [0.1, 1.1]. The goodness of fit of the model R 2 =0.9839, indicating that the corrected model can explain about 98.39% of the data variance, and the overall consistency is high.

[0032] After obtaining the modified JH-2 constitutive model, Abaqus explicit dynamic simulations of single-grain scratches and dual-grain interference scratches were performed using the modified JH-2 constitutive model, and a simulation result library was established. The single-grain scratch Abaqus explicit dynamic simulation involved only single-grain scratching; while the dual-grain interference scratch Abaqus explicit dynamic simulation involved performing a first scratch followed by a second scratch at a specific angle to the first scratch. The simulation factors in the result library included abrasive diameter, abrasive velocity, abrasive loading depth, and interference angle. The simulation results included single-grain residual stress and dual-grain interference residual stress.

[0033] Specifically, abrasive diameter, abrasive velocity, abrasive loading depth, and interference angle were taken as four input factors, each with five levels. The simulation results database was established using an L25 orthogonal experimental design table. The input factor levels were set as follows: abrasive diameter ∈ {2, 4, 6, 8, 10} μm, abrasive velocity ∈ {0.2, 0.4, 0.6, 0.8, 1.0} m / s, abrasive loading depth ∈ {0.2, 0.4, 0.6, 0.8, 1.0} μm, and interference angle ∈ {0°, 30°, 45°, 60°, 90°}, as shown in Table 1.

[0034] Table 1 Input Factor Level Table

[0035]

[0036] Based on the working conditions arranged in the L25 orthogonal array above, Abaqus finite element models for single abrasive scratches and double abrasive interference scratches were established respectively.

[0037] Figure 2 Stress contour plots for dual abrasive loading at 20 μs, 50 μs, and 200 μs under different interference angles are presented. The figures show that after 20 μs, the stress characteristics of each condition are similar, with stress mainly concentrated at the leading edge of the abrasive grains and the area below it, reflecting the typical high gradient distribution in the contact area during abrasive grain indentation and advancement. After 50 μs, the differences caused by the interference angle become clearer: at smaller interference angles, the two scratch directions are close, and the second abrasive grain is more likely to be repeatedly loaded near the first groove, increasing the continuity of the high stress area and extending towards the bottom and sides of the scratch; as the interference angle increases, the force direction at the scratch intersection changes, the high stress area deflects near the intersection, and the high stress distribution is more concentrated in the intersection area, while the continuous extension along the scratch direction is relatively weakened. After 200 μs, the stress field tends to stabilize, with high stress mainly distributed at the bottom of the scratch and its adjacent side. This area typically corresponds to a higher subsurface stress level and is an important source of residual stress after unloading. In summary, the interference angle primarily alters the geometric relationship of the dual abrasive grain action paths, changing the location of stress concentration and the shape of stress propagation. Smaller angles are more likely to induce repeated loading and strengthen the underlying stress; medium angles are more likely to cause localized stress concentration in the intersection region; when approaching orthogonality, unidirectional superposition is limited, stress distribution is more dispersed, and the residual stress level is relatively low. The simulation results obtained in this embodiment are shown in Table 2:

[0038] Table 2. Simulation Results Database for Four Factors and Five Levels

[0039]

[0040] The residual stress data in this simulation results library will serve as the basis for the subsequent static mapping of residual stress in step S3, and will be used for static simulation.

[0041] Step S2: Modeling the discrete trajectory points of free abrasive particles

[0042] Based on the kinematic relationship of the grinding equipment, this step establishes a motion trajectory model of free abrasive particles relative to the substrate coordinate system. By introducing random coefficients and taking the statistical mean of multiple repeated runs, an effective set of discrete trajectory points of abrasive particles that can reflect the actual grinding conditions is obtained.

[0043] In this embodiment, a motion trajectory model of free abrasive particles relative to a silicon carbide substrate is established based on the kinematics of a planetary differential gear train. In a typical polishing device, a polishing disc, a sun gear, a gear ring, and a planetary gear constitute a planetary differential gear train. The substrate is clamped within the planetary gear, revolving around its own axis while revolving with the planetary gear. Free abrasive particles in the polishing slurry are positioned between the polishing pad and the substrate surface under polishing pressure, moving with the polishing pad and indenting and scratching the substrate surface. Based on the kinematics of the planetary differential gear train, the kinematic equations of any point on the substrate (and the free abrasive particles relative to that point) in a global coordinate system can be established. The motion trajectory of the free abrasive particles relative to the silicon carbide substrate is determined by the rotational speed of the polishing disc, the rotational speed of the sun gear, the transmission ratio of the planetary gear, the radial position of the abrasive particle, and the slippage of the abrasive particle relative to the polishing pad. By establishing a substrate coordinate system and solving the relative motion trajectory equations of the abrasive particles in this coordinate system, the complete motion path of a single abrasive particle relative to the substrate during the polishing time can be obtained. The method of establishing a trajectory model of free abrasive particles relative to a silicon carbide substrate based on the kinematics of a planetary differential gear train is existing technology, therefore its specific process will not be elaborated in this application. Through kinematic analysis of the planetary differential gear train, it can be concluded that... The equation for the motion trajectory of any abrasive grain O on the polishing pad relative to the silicon carbide substrate after time t is:

[0044] ;

[0045] In the above equation, For exercise time; , They are respectively The horizontal and vertical coordinates of any abrasive grain on the grinding pad relative to the silicon carbide substrate in the global coordinate system at any given moment. This represents the initial extreme diameter of the abrasive grain on the grinding pad; This is the initial polar angle of the abrasive grain; Let be the angular velocity of the lower grinding disc. Let ω be the angular velocity of the workpiece (silicon carbide substrate). ω is the angular velocity of the upper grinding disc; Let be the radius of the workpiece. The equivalent radius of the abrasive grain's point of impact relative to the workpiece center; The distance between the center of the grinding pad and the center of the workpiece is denoted as γ. Since free abrasive particles in the grinding fluid are not completely fixed to the grinding pad, but exhibit random drift, tumbling, and position exchange, solving the trajectory using only deterministic kinematics would underestimate the dispersion of the trajectory. Therefore, in this embodiment, a grinding random coefficient is introduced to characterize the random drift characteristics of free abrasive particles. The grinding random coefficient is taken as γ∈[0,1], where γ=0 indicates that the abrasive particles are strictly attached to the grinding pad, and γ=1 indicates that the abrasive particles are completely free and randomly drift. By randomly sampling the γ value at different abrasive particles and different time steps, the trajectory model can be made closer to the actual collective motion behavior of free abrasive particles. The grinding coefficient γ is introduced to characterize the randomness of free abrasive particles. It is introduced by multiplying γ by the angles of the cosine and sinine functions. The trajectory equation of the abrasive particle at point O relative to the silicon carbide substrate is then:

[0046] .

[0047] To eliminate the random fluctuations introduced by the random coefficient γ and obtain a more stable representative trajectory, this embodiment repeatedly runs the motion trajectory model. Preferably, the number of repeated runs is no less than 50. By calculating the total grinding trajectory length L of each run, when the repeated runs are 40-50, the mean of the results converges, and the trajectory length distribution is normally distributed. This indicates that under a certain number of repeated runs, the statistical mean can be used to characterize the motion law of free abrasive particles. Therefore, this embodiment sets the number of repeated runs of the motion trajectory model to be greater than 50 to reduce the randomness brought about by the grinding coefficient γ. Then, the temporal position of the effective abrasive particles relative to the substrate coordinate system is sampled frame by frame and the statistical mean is taken. The statistical mean is integrated to obtain the discrete trajectory point set of the effective abrasive particles relative to the substrate coordinate system during the grinding process. Each discrete trajectory point corresponds to one abrasive loading. In practice, the spacing between adjacent discrete trajectory points is determined by both the simulation time step and the abrasive grain movement speed. By reasonably configuring the simulation time step (based on the grinding process parameters such as the grinding disc speed, sun gear speed, and gear ring speed), this spacing is made larger than the feature size of the subsequent mesh unit division, thereby satisfying the constraint that the outer circle size of the mesh unit is smaller than the spacing between trajectory points.

[0048] In each run, the temporal position of the effective abrasive grains relative to the substrate coordinate system is sampled frame by frame (i.e., the coordinates of the abrasive grains in the substrate coordinate system at each time step), and the statistical average of all positions running at the same time step is taken to smooth out random disturbances. After repeated runs and statistical averaging, a discrete trajectory point set of the effective abrasive grains relative to the substrate coordinate system during the grinding process is obtained. In this discrete trajectory point set, each discrete trajectory point corresponds to one abrasive grain loading (i.e., the abrasive grain exerts a pressing or scratching action on the substrate surface at that position), and the subsequent step S3 is to count the number of loading times n for each grid cell based on this point set.

[0049] Among them, effective abrasive grains refer to abrasive grains that enter the effective radius of the substrate at least once during the entire grinding time; for abrasive grains that do not enter the effective radius of the substrate throughout the entire process, their trajectories are not included in the effective trajectory point set, thereby eliminating invalid trajectories at the source and reducing the amount of computation.

[0050] Step S3, Static mapping of residual stress

[0051] This step is the core of this embodiment. It combines the discrete trajectory point set obtained in step S2 with the simulation result library established in step S1, and realizes the static mapping of residual stress by dividing the substrate surface into grid cells and classifying the loading times.

[0052] First, the surface of the silicon carbide substrate is divided into grid cells. To ensure that the residual stress state in each grid cell can be reliably characterized, the grid cell division criteria must meet the following requirements: the number of abrasive loading times n in any grid cell must not be greater than 2 (i.e., each grid cell can be classified into at most one of the three states: "non-contact, single loading, and double interference loading") and the circumcircle size of all grid cells must be smaller than the distance between adjacent discrete trajectory points (to avoid two adjacent discrete trajectory points falling into the same grid cell and causing miscounting of loading times, because two adjacent discrete trajectory points actually correspond to only one scratch, which is actually a single loading).

[0053] Preferably, the method for meshing the silicon carbide substrate surface is as follows: Based on the circumcircle size of the mesh unit being less than the spacing between adjacent discrete trajectory points (0.01 mm), the mesh unit is decreased by 0.01 mm each time in trial calculations. When the number of abrasive loadings (n) for all mesh units at a certain size is not greater than 2, that size is fixed as the meshing scale. This method is simple to implement, ensures consistent unit sizes, and facilitates parallel computation. Another preferred method for meshing the silicon carbide substrate surface is as follows: Initially, the mesh unit is divided with the circumcircle size being less than the spacing between adjacent discrete trajectory points (0.01 mm). Then, it is determined whether the number of abrasive loadings (n) for each mesh unit is not greater than 2. For mesh units with a number of abrasive loadings (n) greater than 2, further division is performed (e.g., dividing them in half along the geometric midline) until the number of abrasive loadings (n) for all mesh units is not greater than 2. This method maintains large mesh units in sparse trajectory regions and locally densifies them in densely intersecting regions, significantly reducing the total number of mesh units and improving computational efficiency while ensuring the n≤2 constraint. It should be noted that the above two implementation methods are only preferred examples. In this embodiment, the shape of the grid cell is preferably square, but any applicable shape such as rectangle, triangle, regular hexagon or Voronoi cell can also be used.

[0054] Based on the discrete trajectory point set obtained in step S2, assign each mesh element the number of abrasive loading times n during the grinding process, classify all mesh elements and map residual stress to each.

[0055] n=0 represents uncontacted elements, indicating that this region was not traversed by any abrasive particles throughout the grinding process, and is assigned zero residual stress or initial residual stress.

[0056] For units with n=1, a single-load unit is defined, indicating that the region has only undergone one abrasive loading. In this case, the abrasive diameter, abrasive velocity, and abrasive loading depth of a single abrasive grain within the single-load unit are extracted. These are used as lookup keys to interpolate the residual stress corresponding to that single-load unit from the single-abrasive grain residual stress data in the simulation results library and assign a value. For example, if the diameter of a single abrasive grain loaded in a single-load unit is 6 μm, the abrasive velocity is 0.4 m / s, and the abrasive loading depth is 0.2 μm, then the residual stress loaded in that single-load unit is -181.25 MPa (number 12). For cases where completely corresponding data cannot be found in the simulation results library, interpolation is used to obtain the residual stress value.

[0057] The n=2 value represents an interference loading element, indicating that the region has undergone two abrasive loading events with an interference superposition effect between them. In this case, the two abrasive loading events within the interference loading element are traced back. The interference angle is calculated based on the abrasive movement directions corresponding to the two loading events. The abrasive diameter, abrasive velocity, and abrasive loading depth of the two abrasive grains are extracted and averaged. Combined with the interference angle, the residual stress corresponding to this interference loading element is interpolated from the dual-abrasive residual stress data in the simulation results library and assigned a value. For example, within a certain interference loading element, the diameter of each abrasive grain is 6 μm, the abrasive grain velocity is 0.4 m / s and 0.8 m / s, and the abrasive grain loading depth is 0.6 μm. After averaging, the equivalent abrasive grain diameter is 6 μm, the equivalent abrasive grain velocity is 0.6 m / s, and the equivalent abrasive grain loading depth is 0.6 μm. Simultaneously, the interference angle between the two abrasive grains is calculated to be 45°. Using this as a lookup key, the residual stress loaded in this interference loading element is found to be -226.831 MPa (number 13) by searching the simulation results library. For cases where no completely corresponding data can be found in the simulation results library, interpolation is used to obtain the residual stress value.

[0058] The above interpolation can be achieved using any of the following methods: trilinear interpolation, bicubic spline interpolation, radial basis function (RBF) interpolation, or inverse distance weighted interpolation. When the query key happens to match a discrete working condition node in the simulation library, the value can be directly retrieved; when the query key falls between adjacent working conditions, interpolation reconstruction is performed based on the residual stress values ​​of neighboring nodes, thereby obtaining a continuous and smooth residual stress mapping result.

[0059] In this embodiment, the abrasive diameter is taken as the average particle size of diamond in the actual polishing fluid; the abrasive velocity is solved by the motion trajectory model in step S2; the abrasive loading depth is calculated based on the indentation hardness principle; and the interference angle is obtained by calculating the angle between the directions of the two scratches corresponding to the two abrasive grains.

[0060] After assigning residual stress values ​​to all mesh elements, Gaussian smoothing is applied to the residual stress field of the entire silicon carbide substrate polished surface to eliminate local noise and jagged edges caused by discrete mapping, thereby obtaining continuous and smooth static simulation prediction results, such as... Figure 3 and Figure 4 As shown.

[0061] Step S4: Establishing the residual compensation model

[0062] This step obtains experimental measurements of residual stress through grinding experiments, and constructs a GWO-GPR residual compensation model by combining the online characteristics of acoustic emission and vibration signals. This model is used to compensate for the systematic residuals between the static simulation prediction results and experimental measurements in step S3.

[0063] In this embodiment, a grinding experiment was conducted on a silicon carbide substrate to measure the experimental value of residual stress. During the grinding experiment, acoustic emission and vibration signals were simultaneously acquired during the processing. The acoustic emission signal was acquired using an AE sensor attached to the grinding disc or fixture, reflecting microscopic events such as contact between the abrasive grains and the substrate, micro-fracture, and crack propagation. The vibration signal was acquired using an accelerometer positioned on the spindle or worktable, reflecting the macroscopic dynamic state of the processing. After acquiring the raw signals, the acoustic emission and vibration signals were preprocessed and feature extracted. Preprocessing included, but was not limited to, detrending, filtering, and independent noise reduction by process segment using the 3σ criterion. Based on this, the time-domain / frequency-domain features of each signal channel were extracted, and features with a high correlation to residual stress (|r|≥0.6) were selected as sensitive features using the Pearson correlation coefficient as the screening criterion.

[0064] Pearson correlation coefficients were calculated for 100 time-domain and frequency-domain features of the extracted vibration and acoustic emission signals in three directions. The Pearson correlation coefficients between the features and the residual stress are shown in Table 3.

[0065] Table 3. Pearson Correlation Coefficients between Characteristics and Residual Stress

[0066]

[0067] The selection of sensitive features was based on a Pearson correlation coefficient greater than or equal to 0.6. Finally, the sensitive features selected to constitute the input vector included the waveform factor, peak factor, kurtosis factor and centroid frequency of the Z-axis vibration signal, as well as the waveform factor, peak factor, kurtosis factor and centroid frequency of the acoustic emission signal. These features, together with the grinding process parameters, formed a fused input vector.

[0068] To ensure the network can simultaneously learn the mapping relationship between process parameters and residual stress, the process parameters and dynamic features of each sample are concatenated column-wise to construct a fusion input matrix:

[0069] ,

[0070] In the formula, (A,B,C,D) are four process parameters of the grinding process, namely grinding pressure, grinding fluid concentration, grinding disc speed and sun gear speed, respectively; (Zi,Zj,Zk,Zv) represent the waveform factor, peak factor, kurtosis factor and centroid frequency of the Z-axis vibration signal, respectively; (Vi,Vj,Vk,Vv) represent the waveform factor, peak factor, kurtosis factor and centroid frequency of the acoustic emission signal, respectively.

[0071] Then, simulations were performed on steps S1 to S3 using the process parameters of the grinding experiment to obtain the experimental static simulation prediction values ​​of residual stress. The results of the experimental measurements and the experimental static simulation prediction values ​​are shown in Table 4. The experimental measurements were obtained using Raman spectroscopy.

[0072] Table 4. Results of Experimental Measurements and Static Simulation Predictions

[0073]

[0074] The process parameters and sensitive features are used as input vectors, and the residuals between experimental measurements and experimental static simulation predictions are used as output labels to construct training sample data. The established training sample data is shown in Table 5.

[0075] Table 5 Training Sample Data

[0076]

[0077] Simulation residuals mainly originate from time-varying factors such as abrasive particle breakage and dynamic microcrack propagation, inevitably leading to systematic biases in long-term series predictions for simulation models with fixed parameters. Therefore, residual compensation models must possess good adaptability to small samples to capture abrupt changes and drifts in residuals as the process evolves. Gaussian Process Regression (GPR) is suitable for general regression problems, especially time series prediction, and exhibits good generalization ability with small samples. It is suitable for capturing the influence of time-varying factors such as abrasive particle breakage and microcrack propagation; therefore, GPR is suitable for residual modeling and prediction.

[0078] Traditional GPR model conjugate gradient optimization methods use randomly set initial values. If these initial values ​​are improperly set, the search process may get stuck in local optima or even fail to converge, demonstrating a strong dependence on the initial values. Intelligent optimization algorithms can reduce this dependence. The GWO algorithm effectively avoids local optima and is better able to find the global optimum. Therefore, in this embodiment, the hyperparameters of GPR are optimized by GWO, and the model is trained using training sample data to obtain the GWO-GPR residual compensation model. Both the GPR model and the GWO optimization method are existing technologies, and therefore will not be described in detail in this application.

[0079] S5, Online Dynamic Simulation Prediction of Grinding

[0080] After completing the offline training of the residual compensation model in step S4, it is deployed in the online operation phase of the production line.

[0081] During the production line grinding of silicon carbide substrates, simulations are performed in steps S1 to S3 using the grinding process parameters to obtain online static simulation predictions. Acoustic emission and vibration signals from the production process are simultaneously acquired and preprocessed with the same features as in step S4 to construct an online input vector. This input vector is then fed into a trained GWO-GPR residual compensation model to output the online residual. The residual is then superimposed and compensated on the online static simulation predictions to obtain the online dynamic simulation prediction results. The overall process is as follows: Figure 5 As shown.

[0082] Because the GWO-GPR residual compensation model integrates dynamic information such as equipment performance, polishing pad wear, and abrasive grain condition that evolve with processing time, its output residual can compensate for the deviation between static simulation predictions and time-varying operating conditions in real time. This enables online dynamic prediction of residual stress on the polished surface of silicon carbide substrates, meeting the needs of real-time monitoring and process optimization in production lines.

[0083] Experimental verification

[0084] To verify the accuracy of the dynamic simulation prediction method in this embodiment, four sets of grinding experiments under different process parameters were designed, and then the static simulation prediction model (M1) and the dynamic simulation prediction model (M2, based on GWO-GPR) were compared with the experimental values.

[0085] The residual stress measurement results of the four grinding experiments are shown in Table 6:

[0086] Table 6. Residual stress measurement results from the grinding experiment.

[0087]

[0088] Then, static simulation predictions (M1 model) for steps S1-S3 and dynamic simulation predictions (M2 model) for steps S1-S5 were performed respectively. The predicted values ​​and error rates of each model under the four sets of experiments are shown in Table 7.

[0089] Table 7. Predicted values ​​and error rates of each model in the four sets of experiments.

[0090]

[0091] It is evident that the M2 model achieved the best overall prediction performance, with a mean absolute error of 6.55 MPa and an average error rate of 4.20%, which is approximately 53.6% lower than the M1 model's mean absolute error of 14.11 MPa. The results indicate that incorporating dynamic signals from the processing procedure to compensate for static simulation predictions can, to some extent, correct system biases and improve the overall prediction accuracy of residual stress on silicon carbide grinding surfaces. This provides a feasible approach for constructing a more accurate prediction model for residual stress on grinding surfaces.

[0092] In summary, the present invention has the following advantages: (1) It uses the Bayesian optimization method to correct the constitutive model, eliminating the systematic deviation caused by empirical parameters, and making the simulation results closer to reality; (2) It establishes a set of discrete trajectory points of free abrasive particles based on the kinematics of planetary differential gear trains, and classifies the substrate surface under different loading conditions by the number of loading times of grid cells. Various grid cells use different methods to map residual stress, fully considering the interference effect of abrasive particle trajectory in actual grinding, and significantly improving the authenticity and accuracy of residual stress prediction; (3) It introduces the online characteristics of acoustic emission signals and vibration signals, establishes the GWO-GPR residual compensation model, and performs dynamic residual superposition compensation on the static simulation prediction results, effectively describing the time-varying characteristics of the grinding process, realizing the leap from static simulation prediction to dynamic simulation prediction, and meeting the real-time prediction needs of the production line.

[0093] Where there is no conflict, the above embodiments and features can be combined with each other.

[0094] 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 dynamic simulation and prediction of residual stress on the polished surface of a silicon carbide substrate, characterized in that, Includes the following steps: S1. Constitutive Model Correction and Simulation Result Library Establishment: The constitutive model of silicon carbide is corrected using the Bayesian optimization method. The corrected constitutive model is used to perform Abaqus explicit dynamic simulations of single abrasive scratches and double abrasive interference scratches. A simulation result library is established. The simulation factors in the simulation result library include abrasive diameter, abrasive velocity, abrasive loading depth, and interference angle. The simulation results in the simulation result library include single abrasive residual stress and double abrasive interference residual stress. S2. Modeling of Discrete Trajectory Points of Free Abrasive Particles: Based on the grinding process parameters, a motion trajectory model of free abrasive particles relative to the silicon carbide substrate is established based on the kinematics of the planetary differential gear system. A grinding random coefficient is introduced to characterize the random drift characteristics of free abrasive particles. The motion trajectory model is run repeatedly, and the temporal position of the effective abrasive particles relative to the substrate coordinate system is sampled frame by frame and the statistical mean is taken. The statistical mean is integrated to obtain the set of discrete trajectory points of the effective abrasive particles relative to the substrate coordinate system during the grinding process. Each discrete trajectory point corresponds to one abrasive loading. S3. Static Mapping of Residual Stress: The silicon carbide substrate surface is divided into mesh cells. The mesh cell division criteria must meet the following conditions: the number of abrasive loading times (n) within any mesh cell must not exceed 2, and the circumcircle size of all mesh cells must be smaller than the distance between adjacent discrete trajectory points. Each mesh cell is assigned the number of abrasive loading times (n) during the grinding process based on the discrete trajectory point set. All mesh cells are classified and residual stress is mapped to them respectively: n=0 represents uncontacted cells, assigned zero residual stress or initial residual stress; n=1 represents single-load cells, from which the abrasive diameter, abrasive velocity, and abrasive loading depth of a single abrasive grain within the single-load cell are extracted. The residual stress corresponding to the single-load unit is interpolated and assigned a value from the single-abrasive residual stress result data in the simulation result library. For n=2, which is an interference loading unit, the two abrasive loading events within the interference loading unit are traced back. The interference angle is calculated based on the abrasive movement direction corresponding to the two abrasive loading events. The abrasive diameter, abrasive velocity, and abrasive loading depth of the two abrasive grains are extracted and averaged. Combined with the interference angle, the residual stress corresponding to the interference loading unit is interpolated and assigned a value from the dual-abrasive residual stress result data in the simulation result library. Then, the residual stress field of the entire grinding surface is Gaussian smoothed to obtain the static simulation prediction result. S4. Residual Compensation Model Establishment: A grinding experiment is conducted on the silicon carbide substrate to obtain the experimental measured value of residual stress; the process parameters of the grinding experiment are used to carry out simulation of steps S1 to S3 to obtain the experimental static simulation prediction value of residual stress. Acoustic emission and vibration signals were collected during the experiment. The acoustic emission and vibration signals were preprocessed and feature extracted. Sensitive features with high sensitivity to residual stress were selected. The process parameters and sensitive features were used as input vectors. The residual between the experimental measurement value and the experimental static simulation prediction value was used as output label to construct a training sample set. The kernel function hyperparameter of the Gaussian process regression model was optimized by the Grey Wolf optimization algorithm to train the GWO-GPR residual compensation model. S5. Online dynamic simulation prediction for grinding: During the production of silicon carbide substrates, simulations of steps S1 to S3 are carried out using the process parameters of the grinding production to obtain online static simulation prediction values. Acoustic emission signals and vibration signals during the production process are collected simultaneously. The residuals are output through the GWO-GPR residual compensation model, and residual superposition compensation is performed on the online static simulation prediction values ​​to obtain the online dynamic simulation prediction results.

2. The method for dynamic simulation and prediction of residual stress on the polished surface of a silicon carbide substrate according to claim 1, characterized in that: In step S1, the constitutive model of silicon carbide is JH-2, and the parameters to be corrected include B, M, D1 and D2. The Bayesian optimization method uses the Metropolis-Hastings sampling strategy to optimize the posterior distribution of the parameters, and the mechanical data obtained from the nanoindentation experiment is used as the calibration basis.

3. The method for dynamic simulation and prediction of residual stress on the polished surface of a silicon carbide substrate according to claim 1, characterized in that: In step S1, the simulation result library is established by taking the abrasive diameter, abrasive velocity, abrasive loading depth and interference angle as four input factors, setting each input factor to five levels, and using the L25 orthogonal experimental table to complete the establishment of the simulation result library.

4. The method for dynamic simulation and prediction of residual stress on the polished surface of a silicon carbide substrate according to claim 3, characterized in that: In step S1, the input factor levels of the simulation result library are set as follows: abrasive diameter ∈ {2,4,6,8,10} μm, abrasive velocity ∈ {0.2,0.4,0.6,0.8,1.0} m / s, abrasive loading depth ∈ {0.2,0.4,0.6,0.8,1.0} μm, and interference angle ∈ {0°,30°,45°,60°,90°}.

5. The method for dynamic simulation and prediction of residual stress on the polished surface of a silicon carbide substrate according to claim 1, characterized in that: In step S2, the grinding random coefficient is taken as γ∈[0,1]. γ=0 indicates that the abrasive particles are strictly attached to the grinding pad and move, and γ=1 indicates that the abrasive particles are completely free and drift randomly.

6. The method for dynamic simulation and prediction of residual stress on the polished surface of a silicon carbide substrate according to claim 1, characterized in that: In step S2, the motion trajectory model is run repeatedly at least 50 times.

7. The method for dynamic simulation and prediction of residual stress on the polished surface of a silicon carbide substrate according to claim 1, characterized in that: In step S3, the method for dividing the silicon carbide substrate surface into grid cells is as follows: taking the outer circle size of the grid cell as a reference that is smaller than the spacing of adjacent discrete trajectory points by 0.01 mm, the calculation is performed by decreasing the size by 0.01 mm each time. When the number of abrasive loading times n of all grid cells under a certain size is not greater than 2, the size of that size is fixed as the division scale.

8. The method for dynamic simulation and prediction of residual stress on the polished surface of a silicon carbide substrate according to claim 1, characterized in that: In step S3, the method for dividing the silicon carbide substrate surface into grid cells is as follows: first, the grid cells are initially divided with the outer circle size being smaller than the spacing of adjacent discrete trajectory points by 0.01 mm. Then, it is determined whether the number of abrasive loading n for each grid cell is not greater than 2. For grid cells with abrasive loading n greater than 2, they are further divided until the number of abrasive loading n for all grid cells is not greater than 2.

9. The method for dynamic simulation and prediction of residual stress on the polished surface of a silicon carbide substrate according to claim 1, characterized in that: In step S3, the abrasive diameter is taken as the average particle size of diamond in the actual polishing slurry; the abrasive velocity is solved by the motion trajectory model; and the abrasive loading depth is calculated based on the indentation hardness principle. The interference angle is obtained by calculating the angle between the directions of the two scratches corresponding to the two abrasive grains.

10. The method for dynamic simulation and prediction of residual stress on the polished surface of a silicon carbide substrate according to claim 1, characterized in that: In step S4, the process parameters constituting the input vector include grinding pressure, grinding fluid concentration, grinding disc rotation speed, and sun gear rotation speed. The sensitive features constituting the input vector include the waveform factor, peak factor, kurtosis factor, and centroid frequency of the Z-axis vibration signal, as well as the waveform factor, peak factor, kurtosis factor, and centroid frequency of the acoustic emission signal.

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