A theoretical prediction method for 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 theoretical prediction method for residual stress on a ground surface of a silicon carbide substrate, which is based on the depth of abrasive particle cutting and the silicon carbide material removal mechanism, divides the loading events into five categories of sliding, plowing, cutting, brittle removal and rolling, establishes a grinding force model for each category, and establishes a set of discrete trajectory points of abrasive particles based on the kinematics of a planetary differential gear train, so that the random motion characteristics of the abrasive particles and the normal force and tangential force generated under different loading categories can be more truly reflected. Then, the normal force generated by the loading event is input into a sliding blister field analytical model to solve the stress tensor increment, and the Von Mises yield criterion is used to perform loading-unloading calculation on each grid element to update the cumulative stress tensor, so that the stress evolution process caused by the multiple contacts between the abrasive particles and the workpiece can be more truly restored, and the physical mechanism of the theoretical prediction method is more accurate.

Description

Technical Field

[0001] This invention relates to the field of precision machining technology for semiconductor materials, and in particular to a theoretical prediction method for 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, silicon carbide has 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] For predicting residual stress on silicon carbide polished surfaces, there are two main categories: simulation prediction and theoretical prediction. Simulation prediction offers higher accuracy but requires longer computation time, while theoretical prediction has slightly lower accuracy but less computation. Current theoretical prediction methods primarily rely on single-grain indentation / scraping models, estimating residual stress distribution by analyzing the mechanical response of a single contact. While these models are valuable in revealing the formation mechanism, they do not consider the coupling effect of multiple abrasive grains and struggle to reflect the stress accumulation effect caused by the random distribution of numerous abrasive grains, rolling (three-body wear), and micro-cutting (two-body wear) in actual processing, resulting in incomplete theoretical modeling. Furthermore, during polishing, equipment performance, polishing pad wear, and abrasive grain state dynamically evolve with processing time, exhibiting time-varying and complex characteristics. However, traditional theoretical prediction methods often rely on experiments and static verification to obtain model parameters, failing to incorporate dynamic data from the processing process, making it difficult to effectively describe time-varying characteristics and leading to incomplete and inaccurate modeling. All of these factors contribute to insufficient accuracy in theoretical prediction.

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

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

[0006] To achieve the above objectives, this invention provides a theoretical prediction method for residual stress on the polished surface of a silicon carbide substrate, comprising the following steps: S1, establishing a discrete trajectory point set of abrasive particles: Based on the polishing process parameters, a motion trajectory model of the abrasive particles relative to the silicon carbide substrate is established based on the kinematics of a planetary differential gear train. A polishing random coefficient is introduced to characterize the random drift characteristics of the abrasive particles. The motion trajectory model is repeatedly run, 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 points of the effective abrasive particles relative to the substrate coordinate system during the polishing process. The silicon carbide substrate surface is divided into mesh elements, and all loading events on each mesh element are recorded. S2, Loading category classification: Based on the silicon carbide material removal mechanism, and according to the constraints and penetration depth of the abrasive particles, the loading events are classified into five categories: two-body wear (slippage, tilling, cutting, brittle removal) and three-body wear (rolling). Each loading event corresponds to only one loading category. Grinding force models are established for different loading categories to solve for the normal and tangential forces generated by each loading category. S3, Calculation of a single mesh element... Residual stress in a grid element: For any grid element, traverse each loading event on that grid element in a time sequence; determine the loading category based on the abrasive grain constraints and penetration depth corresponding to each loading event, and call the grinding force model corresponding to that loading category to calculate the normal and tangential forces generated by that loading event; input the normal force into the Blister field analytical model to solve for the stress tensor increment of that loading event; perform loading-unloading calculations for that loading event according to the VonMises yield criterion, deducting the elastic recovery portion and retaining the plastic portion during unloading, and then performing the subsequent loading... The stress tensor increment of the load is superimposed on the cumulative stress tensor retained after the previous unloading, thereby updating the cumulative stress tensor of the grid cell; after traversing n loading events of the grid cell, the final retained cumulative stress tensor is substituted into the VonMises equivalent stress formula to synthesize a single scalar value, thus obtaining the residual stress of the grid cell; S4, calculate the residual stress distribution across the entire field: traverse all grid cells, calculate the residual stress of each grid cell, and then smooth the residual stress of the entire polishing surface to obtain the theoretical prediction result of the residual stress on the polishing surface of the silicon carbide substrate.

[0007] Furthermore, the loading category is classified as follows: when abrasive grains embed into the grinding disc, it belongs to two-body wear. Under two-body wear, the loading category is determined by comparing the abrasive grain penetration depth with three critical depths: the critical depth for elastoplastic transition, the critical depth for tilling-cutting transition, and the critical depth for ductile-brittle transition. The critical depth for elastoplastic transition is determined based on Hertz contact theory and the yield criterion; the critical depth for tilling-cutting transition is determined by multiplying an empirical coefficient by the critical depth for elastoplastic transition; and the critical depth for ductile-brittle transition is determined based on the benchmark value of the Bifano model and... The load type is determined by the product of the radius and curvature correction coefficients of the abrasive grains; when the abrasive grain penetration depth is less than the critical depth of the elastic-plastic transition, the load type is sliding friction; when the abrasive grain penetration depth is greater than or equal to the critical depth of the elastic-plastic transition and less than the critical depth of the tilling-cutting transition, the load type is tilling; when the abrasive grain penetration depth is greater than or equal to the critical depth of the tilling-cutting transition and less than the critical depth of the ductile-brittle transition, the load type is cutting; when the abrasive grain penetration depth is greater than or equal to the critical depth of the ductile-brittle transition, the load type is brittle removal; when the abrasive grains are in a free state not embedded in the grinding disc, the corresponding load type is rolling of three-body wear.

[0008] Furthermore, when the loading category is slip, the normal force and tangential force The calculation method is as follows:

[0009] ,

[0010] ,

[0011] In the formula, The elastic modulus of silicon carbide; Poisson's ratio for silicon carbide; For the first The actual indentation depth of each abrasive grain; For the first The diameter of the circumscribed circle of an aggregated diamond; Wear rate, which describes the proportion of change in abrasive grain height after agglomerated diamond is subjected to force; For the first The cutting edge inclination angle of each abrasive grain; Let be the coefficient of friction during the sliding phase, where satisfy:

[0012] ,

[0013] In the formula, The contact coefficient of silicon carbide; The contact coefficient of diamond; This represents the contact area between silicon carbide and the abrasive grains. satisfy:

[0014] .

[0015] Furthermore, when the loading category is plowing, the tangential force is calculated first. Calculate the normal force again:

[0016] ,

[0017] ,

[0018] In the formula, The scratch hardness is calculated through a contact scratch test. For the first The actual indentation depth of each abrasive grain; Wear rate, which describes the proportion of change in abrasive grain height after agglomerated diamond is subjected to force; For the first The diameter of the circumscribed circle of an aggregated diamond; For the first The cutting edge inclination angle of each abrasive grain; The coefficient of friction during the plowing stage. satisfy:

[0019] ,

[0020] In the formula, For contact width, satisfy:

[0021] .

[0022] Furthermore, when the loading category is cutting, the normal force and tangential force The calculation method is as follows:

[0023] ,

[0024] ,

[0025] In the formula, This is the grinding force coefficient per unit cutting area; For the first The tangential contact area between the abrasive grain and the workpiece; For the first The normal contact area between each abrasive grain and the workpiece; These are geometric coefficients related to the shape of the abrasive grains; The coefficient of cutting friction is determined based on contact scratch experiments; The average pressure in the contact area, satisfy:

[0026] ,

[0027] In the formula, , These are dimensionless constants determined by the properties of silicon carbide materials; The average velocity in the contact area; For reference strain rate; The scratch hardness is calculated through a contact scratch test. The elastic modulus of silicon carbide; For contact width, satisfy:

[0028] , In the formula, Wear rate, which describes the proportion of change in abrasive grain height after agglomerated diamond is subjected to force; For the first The diameter of the circumscribed circle of an aggregated diamond; For the first The actual indentation depth of each abrasive grain; For the first The cutting edge inclination angle of each abrasive grain.

[0029] Furthermore, when the loading category is brittle removal, the normal force and tangential force The calculation method is as follows:

[0030] ,

[0031] ,

[0032] In the formula, This is a constant related to the shape of the diamond abrasive grains; The fracture toughness of silicon carbide; The scratch hardness is calculated through a contact scratch test. σ is the elastic modulus of silicon carbide; fl The flow stress of silicon carbide; Let be the normal contact area between the i-th abrasive grain and the workpiece; These are geometric coefficients related to the shape of the abrasive grains; The coefficient of cutting friction is determined based on contact scratch experiments; The average pressure in the contact area, satisfy:

[0033] ,

[0034] In the formula, , These are dimensionless constants determined by the properties of silicon carbide materials; The average velocity in the contact area; For reference strain rate; The elastic modulus of silicon carbide; For contact width, satisfy:

[0035] , In the formula, Wear rate, which describes the proportion of change in abrasive grain height after agglomerated diamond is subjected to force; For the first The diameter of the circumscribed circle of an aggregated diamond; For the first The actual indentation depth of each abrasive grain; For the first The cutting edge inclination angle of each abrasive grain.

[0036] Furthermore, when the loading type is rolling, the normal force and tangential force The calculation method is as follows:

[0037] ,

[0038] ,

[0039] In the formula, The indentation angle of the abrasive grains into the workpiece; The depth of the abrasive roller-rolled workpiece; The hardness of silicon carbide; The indentation angle of the abrasive grains into the grinding pad; The depth of the abrasive roller grinding pad; The hardness of the abrasive pad; This refers to the gap between the workpiece and the grinding disc; For the size of the load particles, take , The average diameter of the abrasive grains; Equivalent hardness, satisfy:

[0040] .

[0041] Further, in step S3, the method for obtaining the stress tensor increment of the loading event is as follows: the normal force generated by the loading event, the abrasive geometric parameters, and the elastic modulus and Poisson's ratio of the silicon carbide substrate are used as input parameters and substituted into the sliding Blister field analytical model to obtain the stress tensor increment caused by the loading event. The stress tensor increment contains 3 independent normal stress components and 3 independent shear stress components. In step S3, the method for obtaining the residual stress of the mesh element is as follows: n loading events are executed sequentially; the stress tensor increment of the k-th (k=1, 2, 3…n) loading event is superimposed on the cumulative stress tensor retained after the (k-1)-th unloading event to obtain the updated temporary stress tensor; based on the updated temporary stress tensor… The Von Mises equivalent stress is calculated using six independent components. When the Von Mises equivalent stress is greater than or equal to the yield strength of silicon carbide, plastic yielding is determined. During unloading, the elastic recovery portion is deducted, and the plastic portion is retained, which is used as the cumulative stress tensor after the k-th unloading. When the Von Mises equivalent stress is less than the yield strength of silicon carbide, it is determined to be purely elastic deformation, and the cumulative stress tensor remains in the state after the (k-1)-th unloading. After traversing n loading events of the mesh element, a stress tensor matrix is ​​constructed using the six independent components of the finally retained cumulative stress tensor. The three eigenvalues ​​of the stress tensor matrix are solved, and the three eigenvalues ​​are substituted into the Von Mises equivalent stress formula to synthesize a single scalar value, thus obtaining the residual stress of the mesh element.

[0042] Furthermore, in step S1, the method for dividing the silicon carbide substrate surface into grid cells is as follows: the grid cells are square, and the outer circle size of all grid cells is smaller than the spacing between adjacent discrete trajectory points.

[0043] Furthermore, steps S5 and S6 are also included; S5: Establishing a residual compensation model: A grinding experiment is performed on the silicon carbide substrate to obtain the experimental measured value of residual stress; Theoretical predictions from steps S1 to S4 are carried out using the process parameters of the grinding experiment to obtain the experimental static theoretical prediction value of residual stress; Acoustic emission signals and vibration signals are collected during the experiment, and the acoustic emission signals and vibration signals are preprocessed and feature extracted to screen out sensitive features with high sensitivity to residual stress. The process parameters and sensitive features form an input vector, and the residual between the experimental measured value and the experimental static theoretical prediction value is used as the input vector. To output labels, a training sample set is constructed, and a bidirectional gated recurrent unit network optimized by the Grey Wolf optimization algorithm is used to train the GWO-BiGRU residual compensation model; S6, Online dynamic prediction: During the production line grinding of silicon carbide substrates, theoretical predictions are carried out in steps S1 to S4 based on the grinding process parameters to obtain online static theoretical prediction values. Acoustic emission signals and vibration signals during the production process are collected simultaneously, and residuals are output through the GWO-BiGRU residual compensation model. The residuals are superimposed and compensated on the online static theoretical prediction values ​​to obtain the online dynamic theoretical prediction results.

[0044] The present invention provides a theoretical prediction method for residual stress on the polished surface of a silicon carbide substrate. Compared with existing technologies, this method has the following advantages: Based on the abrasive penetration depth and the silicon carbide material removal mechanism, the present invention classifies loading events into five categories: sliding, plowing, cutting, brittle removal, and rolling, and establishes a grinding force model for each category. Furthermore, based on the kinematics of a planetary differential gear train, a discrete trajectory point set of abrasive particles is established. This method can more realistically reflect the random motion characteristics of abrasive particles and the normal and tangential forces generated under different loading categories. It overcomes the problem that single-particle indentation / scraping models cannot reflect the random distribution of abrasive particles, rolling, and micro-cutting in actual polishing, thus improving the prediction accuracy of residual stress. Then, the normal force generated by the loading event is input into the sliding Blister field analytical model to solve for the stress tensor increment. Loading-unloading calculations are performed successively on each grid cell according to the VonMises yield criterion to update the cumulative stress tensor. This more realistically restores the stress evolution process caused by multiple contacts between the abrasive particles and the workpiece, unlike the simplified method of repeated accumulation of the same loading state in existing technologies, making the physical mechanism of this theoretical prediction method more accurate. Attached Figure Description

[0045] Figure 1 This is a flowchart of the theoretical prediction method for residual stress on the polished surface of a silicon carbide substrate according to the present invention;

[0046] Figure 2 The image shows the trajectory of the abrasive particles after 200 seconds.

[0047] Figure 3 This is a schematic diagram of loading events within a discrete trajectory point set and grid cell. Detailed Implementation

[0048] The embodiments of the present invention will be described in detail below.

[0049] This embodiment provides a theoretical prediction method for residual stress on the polished surface of a silicon carbide substrate, such as... Figure 1 As shown, it includes steps S1 to S4: S1 establishes the discrete trajectory point set of abrasive particles, S2 divides the loading categories, S3 calculates the residual stress of a single mesh element, and S4 calculates the overall residual stress distribution. The specific implementation methods of each step are further described in detail below with reference to the accompanying drawings.

[0050] Step S1: Establish the discrete trajectory point set of abrasive particles

[0051] The purpose of this step is to: establish a motion trajectory model of the abrasive particles relative to the silicon carbide substrate based on the kinematics of the planetary differential gear train; obtain the discrete trajectory point set of the effective abrasive particles relative to the substrate coordinate system by introducing a grinding random coefficient and repeatedly running the motion trajectory model and taking the statistical mean; then divide the silicon carbide substrate surface into grid cells and record all loading events on each grid cell. During the grinding process, a large number of abrasive particles act randomly on the workpiece surface, and their motion trajectories have no obvious pattern. The single trajectory of a single abrasive particle cannot reflect the random distribution of a large number of abrasive particles in actual processing. Therefore, it is necessary to introduce a grinding random coefficient to characterize the random drift characteristics of the abrasive particles. By repeatedly running the motion trajectory model multiple times (more than 50 times in this embodiment) and taking the statistical mean, the trajectory length distribution converges, making the result normally distributed, thus using the statistical mean to characterize the motion law of the abrasive particles. Meanwhile, by discretizing the continuous motion trajectory into trajectory points and recording these trajectory points on the grid cells divided on the surface of the silicon carbide substrate, each discrete trajectory point corresponds to one loading event. This transforms the continuous abrasive trajectory into loading events that can be recorded sequentially on each grid cell, laying the foundation for subsequent calculations of stress increments.

[0052] In a typical grinding apparatus, a grinding 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 simultaneously revolving around the planetary gear. Abrasive grains in the grinding slurry, under grinding pressure, are positioned between the grinding pad and the substrate surface, moving with the grinding pad and exerting pressure and scratches on the substrate surface. Based on the kinematics of the planetary differential gear train, the kinematic equations for any point on the substrate (and the abrasive grains relative to that point) in a global coordinate system can be established. The trajectory of the abrasive grains relative to the silicon carbide substrate is determined by the rotational speed of the grinding disc, the rotational speed of the sun gear, the transmission ratio of the planetary gear, the radial position of the abrasive grain, and the slippage of the abrasive grains relative to the grinding pad. By establishing a substrate coordinate system and solving the equations for the relative motion trajectory of the abrasive grains in this coordinate system, the complete motion path of a single abrasive grain relative to the substrate during the grinding time can be obtained. The model for establishing the trajectory of the abrasive grains relative to the silicon carbide substrate based on the kinematics of the planetary differential gear train is existing technology; therefore, its specific process will not be elaborated in this application.

[0053] 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:

[0054] ;

[0055] 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 be the angular velocity of the workpiece (silicon carbide substrate) as it rotates. 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; Let be the eccentricity between the center of the grinding disc and the center of the workpiece. A grinding random coefficient γ is introduced to characterize the randomness of abrasive grain movement. This is achieved by multiplying γ by the angles of the cosine and sinine functions. The trajectory equation of the abrasive grain at point O relative to the silicon carbide substrate is then:

[0056] .

[0057] Assuming 50 effective abrasive grains are randomly distributed in the grinding pad, based on the method of this embodiment, the motion trajectory of these abrasive grains after 200 seconds is as follows. Figure 2 As shown, by Figure 2 As can be seen, after introducing the grinding random coefficient, the overall abrasive grain trajectory has no obvious texture, which is more in line with the motion characteristics of the actual random motion of abrasive grains.

[0058] Then, the temporal position of the effective abrasive grains relative to the substrate coordinate system is sampled frame by frame and the statistical mean is taken. The statistical mean is then integrated to obtain a set of discrete trajectory points of the effective abrasive grains relative to the substrate coordinate system during the grinding process. Each discrete trajectory point corresponds to one loading event. In specific operation, the spacing between adjacent discrete trajectory points is determined by both the theoretical time step and the abrasive grain movement speed. By reasonably configuring the theoretical time step (based on grinding process parameters such as grinding disk speed, sun gear speed, and gear ring speed), a balance is struck between computational accuracy and computational load. In each run, the temporal position of the effective abrasive grains relative to the substrate coordinate system (i.e., the coordinates of the abrasive grains in the substrate coordinate system at each time step) is sampled frame by frame, and the statistical mean is taken for all positions running at the same time step to smooth out random disturbances. After multiple repeated runs and statistical mean calculations, a set of discrete trajectory points of the effective abrasive grains relative to the substrate coordinate system during the grinding process is obtained. In this set of discrete trajectory points, each discrete trajectory point corresponds to one loading event. Figure 3 As shown, there are a total of 3 loading events within a certain grid cell.

[0059] The silicon carbide substrate surface is divided into mesh cells. To ensure reliable characterization of the residual stress state within each mesh cell, the mesh cell division criterion must satisfy the condition that the circumcircle size of all mesh cells is smaller than the spacing between adjacent discrete trajectory points (to avoid miscounting of loading counts due to two adjacent discrete trajectory points falling into the same mesh cell, since two adjacent discrete trajectory points actually correspond to only one scratch, which is actually a single loading). Preferably, the mesh cells are square. Figure 3 As shown, the three loading events correspond to discrete trajectory points within the three abrasive particle motion trajectories.

[0060] 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.

[0061] Step S2: Divide the loading categories

[0062] In this step, based on the silicon carbide material removal mechanism, the loading events are divided into five loading states according to the constraints and penetration depth of the abrasive grains. A grinding force model is established for each loading state to solve for the normal and tangential forces generated by each loading event. The contact states of two-body wear and three-body wear differ, resulting in different stress field distributions and contributions to surface residual stress. Different penetration depths of the abrasive grains into the silicon carbide correspond to different loading mechanisms such as sliding, plowing, cutting, and brittle removal. The normal force is the direct input for solving the stress tensor increment in the subsequent Blister field solution. Therefore, it is essential to classify each loading event according to the constraints and penetration depth of the abrasive grains and establish a corresponding grinding force model for each state to accurately obtain the normal force for each loading event.

[0063] In this embodiment, the loading category is classified as follows: when abrasive grains are embedded in the grinding disc, it belongs to two-body wear. Under two-body wear, the loading category is determined by comparing the abrasive grain penetration depth with three critical depths: the critical depth for elastic-plastic transition, the critical depth for tilling-cutting transition, and the critical depth for ductile-brittle transition. The critical depth for elastic-plastic transition is determined based on Hertz contact theory and the yield criterion; the critical depth for tilling-cutting transition is determined based on the product of an empirical coefficient and the critical depth for elastic-plastic transition; and the critical depth for ductile-brittle transition is based on the baseline value of the Bifano model. The loading category is determined by multiplying the abrasive grain's radius curvature correction coefficient; when the abrasive grain penetration depth is less than the critical depth of the elastic-plastic transition, the loading category is sliding friction; when the abrasive grain penetration depth is greater than or equal to the critical depth of the elastic-plastic transition and less than the critical depth of the tilling-cutting transition, the loading category is tilling; when the abrasive grain penetration depth is greater than or equal to the critical depth of the tilling-cutting transition and less than the critical depth of the ductile-brittle transition, the loading category is cutting; when the abrasive grain penetration depth is greater than or equal to the critical depth of the ductile-brittle transition, the loading category is brittle removal; when the abrasive grain is in a free state not embedded in the grinding disc, the corresponding loading category is rolling of three-body wear.

[0064] Specifically, the critical depth of the elastoplastic transition is determined based on Hertz contact theory and the yield criterion. :

[0065] ;

[0066] When the abrasive depth reaches the critical condition for the formation of chips due to plastic shear of the material, an empirical coefficient is obtained based on experiments. Critical depth of elastoplastic transition The product determines the critical depth of the tillage-cutting transition. :

[0067] ;

[0068] Based on the baseline values ​​of the Bifano model Correction factor for the radius curvature of abrasive grains The product of these factors determines the critical depth of the ductile-brittle transition. :

[0069] ;

[0070] In the above formula, The radius of the abrasive grain; The yield strength of silicon carbide; This is the equivalent elastic modulus of the abrasive grain. , The Poisson's ratio for silicon carbide. The Poisson's ratio of the abrasive grains; The value is 2.5; It is a dimensionless empirical constant. The value is 0.15. The elastic modulus of silicon carbide; The elastic modulus of the abrasive grain; The hardness of silicon carbide; The fracture toughness of silicon carbide;

[0071] When the loading category is friction (elastic deformation under two-body wear), the interaction between the abrasive grains and the workpiece can be considered as elastic contact between a rigid cone and an elastic body. Under this category, the normal force and tangential force can be solved using elasticity mechanics. and tangential force The calculation method is as follows:

[0072] ,

[0073] ,

[0074] In the formula, The elastic modulus of silicon carbide is expressed in MPa. Poisson's ratio for silicon carbide; For the first The actual indentation depth of each abrasive grain, in μm; For the first The circumscribed diameter of an aggregated diamond, in μm; Wear rate, which describes the proportion of change in abrasive grain height after agglomerated diamond is subjected to force; For the first The inclination angle of the cutting edge of each abrasive grain affects the direction of the force exerted on the interaction between the abrasive grain and the workpiece; Let be the coefficient of friction during the sliding phase, where satisfy:

[0075] ,

[0076] In the formula, The contact coefficient of silicon carbide is given in this embodiment. =8Gpa; The contact coefficient of diamond is given in this embodiment. =0.1; This represents the contact area between silicon carbide and the abrasive grains. satisfy:

[0077] .

[0078] When the loading category is plowing (plastic deformation under two-body wear), plastic deformation will occur inside the workpiece. The tangential force can be calculated first. Then, calculate the normal force in the reverse direction based on the friction coefficient. :

[0079] ,

[0080] ,

[0081] In the formula, The scratch hardness is calculated through a contact scratch test. ; The scratch hardness coefficient is determined experimentally. The strain rate sensitivity index is experimentally calibrated. The scratch speed during the experiment; The length of the scratch during the experiment; For the first The actual indentation depth of each abrasive grain, in μm; Wear rate, which describes the proportion of change in abrasive grain height after agglomerated diamond is subjected to force; For the first The circumscribed diameter of an aggregated diamond, in μm; For the first The inclination angle of the cutting edge of each abrasive grain affects the direction of the force exerted on the interaction between the abrasive grain and the workpiece; The coefficient of friction during the plowing stage. satisfy:

[0082] ,

[0083] In the formula, For contact width, satisfy:

[0084] .

[0085] When the loading category is cutting (cutting removal under two-body wear), when the abrasive grains enter the cutting state, the resistance of the abrasive grains can be divided into the sum of the force caused by chip deformation and the force caused by sliding, and the normal force. and tangential force The calculation method is as follows:

[0086] ,

[0087] ,

[0088] In the formula, , The first The normal and tangential components of the force on each abrasive grain caused by chip deformation, in N; , The first The normal and tangential components of the force on each abrasive grain caused by sliding friction, in N; The grinding force coefficient per unit cutting area is determined by the mechanical properties of the material, and its unit is N / mm. 2 ; For the first The tangential contact area between the abrasive grain and the workpiece; For the first The normal contact area between each abrasive grain and the workpiece; These are geometric coefficients related to the shape of the abrasive grains; The friction coefficient during the cutting stage is determined based on contact scratch tests; in this embodiment, K = 55.331 N / mm was obtained through contact scratch tests between silicon carbide and diamond. 2 , . The average pressure in the contact area is expressed in MPa. satisfy:

[0089] ,

[0090] In the formula, , These are dimensionless constants determined by the properties of silicon carbide materials; The average velocity in the contact area; The reference strain rate is set to 1 s. -1 ; The scratch hardness is calculated through a contact scratch test. ; The scratch hardness coefficient is determined experimentally. The elastic modulus of silicon carbide; For contact width, satisfy:

[0091] .

[0092] When the loading category is brittle removal (brittle removal under two-body wear), the abrasive grains enter brittle removal. At this time, the resistance of the abrasive grains can still be divided into the sum of the force caused by cutting deformation and the force caused by sliding. Compared with cutting removal, the removal mode of the workpiece material will change from ductile removal to brittle removal. At this time, brittle fracture becomes the dominant mechanism of material removal. When the stress caused by the abrasive grains exceeds the yield limit of the material, mid-center cracks and transverse cracks will be generated in the contact area. The former will cause subsurface damage, while the latter will extend in the transverse direction parallel to the workpiece surface, thereby causing the material to peel off / strip. In this stage, the interaction between the diamond abrasive grains and the silicon carbide substrate surface can be divided into two parts: (1) extrusion: promotes the formation of chips and cracks; (2) relative sliding on the substrate surface: generates friction. The former generates chip deformation force ( and The latter generates friction ( and On the one hand, the contact conditions in the chip shear zone during the brittle stage differ from those during the ductile stage, leading to a change in the calculation method for chip deformation force. On the other hand, during brittle removal, the interfacial friction between the abrasive cutting edge and the groove surface still exists and can be considered the same as the friction generated during the ductile removal stage. The normal force during brittle removal... and tangential force The calculation method is as follows:

[0093] ,

[0094] ,

[0095] In the formula, This is a constant related to the shape of the diamond abrasive grains; The fracture toughness of silicon carbide is expressed in MPa. The scratch hardness is calculated through a contact scratch test. ; The scratch hardness coefficient is determined experimentally. The elastic modulus of silicon carbide; For silicon carbide, the flow stress is... Take 4.58 MPa; For the first The normal contact area between each abrasive grain and the workpiece; These are geometric coefficients related to the shape of the abrasive grains; The friction coefficient during the brittle removal stage is calibrated based on contact scratch experiments; The average pressure in the contact area, satisfy:

[0096] ,

[0097] In the formula, , These are dimensionless constants determined by the properties of silicon carbide materials; The average velocity in the contact area; The reference strain rate is set to 1 s. -1 ; The elastic modulus of silicon carbide; For contact width, satisfy:

[0098] .

[0099] In the grinding process, in addition to typical two-body wear, as abrasive grains break down, a three-body wear mechanism also forms on the workpiece surface, involving the interaction of the abrasive grains, the workpiece, and the grinding disc. At this time, the abrasive grains in the flow layer exist in a free or semi-constrained state, driven by external loads to roll or embed themselves between the workpiece and the grinding disc, repeatedly producing local indentations on the workpiece surface, i.e., rolling. When the loading type is rolling, the normal force of the abrasive grains during three-body wear can be calculated based on the fact that the force exerted by the abrasive grains on the grinding pad is equal to the force exerted on the workpiece, combined with the geometric relationships during three-body wear. and tangential force The calculation method is as follows:

[0100] ,

[0101] ,

[0102] In the formula, The indentation angle of the abrasive grains into the workpiece; The depth of the abrasive roller-rolled workpiece, in μm; The hardness of silicon carbide is expressed in MPa. The indentation angle of the abrasive grains into the grinding pad; The depth of the abrasive rolling grinding pad, in μm; The hardness of the abrasive pad is expressed in MPa. The gap between the workpiece and the grinding disc, in μm; The particle size is the load size, which is generally taken as... , The average diameter of the abrasive grains is expressed in μm. Equivalent hardness, satisfy:

[0103] .

[0104] when « (Here, the grinding pad is a honeycomb pad.) =0.2, silicon carbide hardness =9), at this time: As shown above, the equivalent hardness is almost entirely controlled by the hardness of the honeycomb pad, indicating that the smaller the hardness of the honeycomb pad, the smaller the normal force. Therefore, when abrasive particles undergo three-body wear, most of the energy of the normal force is absorbed by the honeycomb pad.

[0105] The above-mentioned grinding force models are established for different loading states to solve the normal and tangential forces generated by each loading event, providing input for subsequent residual stress calculation.

[0106] Step S3: Calculate the residual stress of a single mesh element.

[0107] In this step, for any given mesh cell, each loading event on that mesh cell is traversed sequentially, and its cumulative stress tensor is calculated and updated sequentially, ultimately synthesizing the residual stress scalar value of that mesh cell. Each contact of the abrasive grain with the substrate generates a stress increment within the mesh cell, and multiple abrasive grains exhibit a cumulative effect from multiple contacts. Using only the mechanical response of a single contact cannot reflect the actual process of stress accumulation with the number of loading cycles during processing. Therefore, it is necessary to perform load-unloading calculations for each loading based on the Von Mises yield criterion: during loading, it is determined whether the material has undergone plastic yielding; during unloading, the elastic recovery portion is deducted, and the plastic portion is retained; and the stress tensor increment of the subsequent loading is superimposed on the cumulative stress tensor retained after the previous unloading (rather than repeatedly accumulating the same loading state), thereby truly restoring the plastic accumulation process under multiple contacts. Since unidirectional normal stress or shear stress is usually not used as an evaluation index for residual stress, after traversing all loading events of the mesh element, a stress tensor matrix is ​​constructed using the six independent components of the final retained cumulative stress tensor. The three eigenvalues ​​of the stress tensor matrix are solved, and the three eigenvalues ​​are substituted into the Von Mises equivalent stress formula to synthesize a single scalar value, which is used as the residual stress of the mesh element.

[0108] For any given mesh cell, iterate through each loading event on that mesh cell. Determine the loading state based on the constraints and penetration depth of the abrasive grains corresponding to that loading event. Call the grinding force model corresponding to that loading state to calculate the normal and tangential forces generated by that loading event. Input the normal force into the Blister field analytical model to solve for the stress tensor increment of that loading event. Considering the anisotropy of the semiconductor, the residual stress field intensity perpendicular to the j-axis (j=x,y,z) satisfies the Blister field distribution form, determined by parameters such as the normal force, compaction coefficient, dimensionless quantities related to the indenter geometry, and the elastic modulus and Poisson's ratio perpendicular to the j-axis. residual stress field intensity satisfy:

[0109] ,

[0110] In the formula: Normal force, unit: N; This is the compaction coefficient; A dimensionless quantity related to the geometry of the abrasive indenter; The elastic modulus is perpendicular to the j-axis, in MPa. Scratch hardness; Poisson's ratio is perpendicular to the j-axis; It is half the tip angle of the abrasive grain.

[0111] After obtaining the residual stress field strength Then, the six independent components can be calculated using the following formula:

[0112] .

[0113] In the formula, These are spatial coordinate variables; This is the distance parameter from a spatial point to the origin; Corresponding to perpendicular to The intensity of the residual stress field in the axial direction; The materials are perpendicular to Poisson's ratio of the axis.

[0114] Solving using the above formula yields three independent components of normal stress and three independent components of shear stress, resulting in a complete set of six independent components.

[0115] Based on the principle of this embodiment, each grid cell corresponds to the interaction of multiple effective abrasive grains. Mechanical stress is loaded and unloaded according to the Von Mises criterion to obtain the mechanical residual stress. Once a single loading process is completed, a corresponding relaxation process is performed. Since multiple abrasive grain interactions occur within a single grid cell, the above process needs to be repeated n times. Afterward, the process moves to the next grid cell and repeats the same procedure.

[0116] Loading-unloading calculations were performed on this loading event based on the Von Mises yield criterion: The Von Mises equivalent stress was calculated based on the six independent components of the temporary stress tensor. When the Von Mises equivalent stress was greater than or equal to the yield strength of silicon carbide, plastic yielding was determined, and the elastic recovery portion was deducted and the plastic portion retained during unloading. When the Von Mises equivalent stress was less than the yield strength of silicon carbide, it was determined to be purely elastic deformation, and the stress was fully recovered during unloading. The cumulative stress tensor of the mesh element was updated accordingly. The stress tensor increment of each subsequent loading was superimposed on the cumulative stress tensor retained after the previous unloading. That is, the cumulative stress tensor after the k-th loading was the sum of the cumulative stress tensor retained after the (k-1)-th unloading and the stress tensor increment of the k-th loading, rather than repeatedly accumulating for the same loading state.

[0117] After traversing the mesh element through n loading events, the formula for the six independent components of the final retained cumulative stress tensor is as follows (z=0 at the grinding surface, n is the number of loading events):

[0118] .

[0119] This leads to the final retained stress tensor matrix:

[0120] ,

[0121] In the matrix, = , = ; = .

[0122] Solving the stress tensor matrix The three eigenvalues , , ,Will , , Substituting the values ​​into the Von Mises equivalent stress formula, we obtain the equivalent stress, which is the residual stress:

[0123] ,

[0124] In the formula, This is the VonMises equivalent stress.

[0125] Step S4: Calculate the residual stress distribution across the entire field.

[0126] In this step, all mesh elements are traversed, and the scalar value of residual stress for each mesh element is calculated. Then, the residual stress across the entire polished surface is smoothed to obtain the theoretical prediction of the residual stress on the silicon carbide substrate polished surface. The aforementioned calculations are performed discretely, mesh by mesh, resulting in numerical discontinuities in the predicted residual stress values ​​between elements. Smoothing the residual stress across the entire polished surface suppresses numerical fluctuations from the discrete calculations, making the distribution more continuous, thus obtaining a usable full-field residual stress distribution that matches the actual situation. Preferably, Gaussian smoothing is used to suppress the numerical discontinuities introduced by the mesh-by-mesh discrete calculations, making the residual stress more continuous.

[0127] Thus, we can obtain highly accurate theoretical predictions of residual stress on the polished surface of silicon carbide substrates.

[0128] However, actual production line processing has variable characteristics. Therefore, this embodiment also includes the following steps.

[0129] Step S5: Establish a residual compensation model

[0130] This step obtains experimental measurements of residual stress through grinding experiments, and constructs a GWO-BiGRU 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 theoretical prediction results and experimental measurements in step S4.

[0131] 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.

[0132] 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 1.

[0133] Table 1. Pearson Correlation Coefficients between Characteristics and Residual Stress

[0134]

[0135] 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.

[0136] 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:

[0137] ,

[0138] In the formula: (A, B, C, D) are four process parameters of the grinding process, namely grinding pressure, grinding fluid concentration, grinding disc rotation speed, and sun gear rotation speed; (Z i Z j Z k Z v (V) represents the waveform factor, peak value factor, kurtosis factor, and centroid frequency of the Z-axis vibration signal, respectively; i V j V k V v ) represent the waveform factor, peak factor, kurtosis factor, and centroid frequency of the acoustic emission signal, respectively; Represents the total number of samples.

[0139] Then, steps S1 to S4 were carried out using the process parameters of the grinding experiment to obtain the experimental static theoretical prediction value of the residual stress. The results of the experimental measurements and the experimental static theoretical prediction values ​​are shown in Table 2.

[0140] Table 2. Results of Experimental Measurements and Static Theoretical Predictions

[0141]

[0142] The input vector is constructed using process parameters and sensitive features, and the output label is the residual between experimental measurements and experimental static theoretical predictions. Training sample data is constructed, and the established training sample data is shown in Table 3.

[0143] Table 3 Training Sample Data

[0144]

[0145] Bidirectional Gated Recurrent Unit (BiGRU) is a typical recurrent neural network structure derived from Gated Recurrent Unit (GRU), primarily used for modeling temporally correlated sequence data. By simultaneously introducing two GRU networks (one forward and one backward) in the time dimension, BiGRU fully utilizes the contextual information of the sequence at different time points, thereby enhancing its ability to express temporal features. Compared to traditional recurrent neural networks (RNNs), BiGRU effectively alleviates the gradient vanishing problem through its gating mechanism, exhibiting stronger modeling capabilities in tasks such as time series prediction, signal modeling, and regression analysis. BiGRU possesses efficient temporal dependency modeling capabilities, capturing the dynamic evolution characteristics of sequence signals across multiple time scales, reducing reliance on manual feature extraction. It is particularly suitable for regression problems with significant temporal correlation, and the continuous evolution of surface residual stress during grinding aligns with the applicable scenarios for BiGRU. In this embodiment, the hyperparameters of BiGRU are optimized using GWO, and the model is trained using training sample data to obtain the GWO-BiGRU residual compensation model. Both the BiGRU model and the GWO optimization method are existing technologies, so they will not be described in detail in this application.

[0146] Step S6: Online Dynamic Prediction

[0147] After completing the offline training of the residual compensation model in step S5, it is deployed in the online operation phase of the production line.

[0148] During the production line grinding of silicon carbide substrates, steps S1 to S4 are performed using the grinding process parameters to obtain online static theoretical prediction values. Acoustic emission signals and vibration signals during the production process are collected simultaneously, and preprocessing and feature extraction are performed in the same manner as in step S5 to construct an online input vector. This input vector is then input into a trained GWO-BiGRU residual compensation model to output online residuals. The residuals are then superimposed and compensated on the online static theoretical prediction values ​​to obtain online dynamic theoretical prediction results.

[0149] To verify the accuracy of the dynamic theoretical prediction method in this embodiment, four grinding experiments under different process parameters were designed, and then the static theoretical prediction model (M1) and the dynamic theoretical prediction model (M2, based on GWO-BiGRU) were compared with the experimental measurements.

[0150] The residual stress measurement results of the four grinding experiments are shown in Table 4:

[0151] Table 4. Residual stress measurement results from the grinding experiment.

[0152]

[0153] Then, static theoretical predictions (M1 model) for steps S1-S4 and dynamic theoretical predictions (M2 model) for steps S1-S6 were performed respectively. The predicted values ​​and error rates of each model under the four sets of experiments are shown in Table 5:

[0154] Table 5. Predicted values ​​and error rates of each model in the four sets of experiments.

[0155]

[0156] It is evident that the M2 model achieved the best overall prediction performance, with a mean absolute error of 8.70 MPa and a mean error rate of 5.51%, which is approximately 51.5% lower than the mean absolute error of 17.93 MPa of the M1 model. The results indicate that introducing dynamic signals from the processing procedure to compensate for the static theoretical prediction results can, to some extent, correct system biases, thereby improving the overall prediction accuracy of residual stress on the silicon carbide grinding surface.

[0157] Where there is no conflict, the above embodiments and features can be combined with each other.

[0158] 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 theoretically predicting residual stress on the polished surface of a silicon carbide substrate, characterized in that, Includes the following steps: S1. Establish a discrete trajectory point set of abrasive particles: Based on the grinding process parameters, establish a motion trajectory model of abrasive particles relative to the silicon carbide substrate based on the kinematics of the planetary differential gear system. Introduce a grinding random coefficient to characterize the random drift characteristics of abrasive particles. Repeat the motion trajectory model multiple times, sample the temporal position of effective abrasive particles relative to the substrate coordinate system frame by frame and take the statistical mean. Integrate the statistical mean to obtain a discrete trajectory point set of effective abrasive particles relative to the substrate coordinate system during the grinding process. Each discrete trajectory point corresponds to one loading event. The surface of the silicon carbide substrate is divided into grid cells, and all loading events on each grid cell are recorded. S2. Classification of Loading Events: Based on the silicon carbide material removal mechanism, and according to the constraints and penetration depth of the abrasive particles, the loading events are classified into five loading categories: two-body wear (slippage, tilling, cutting, brittle removal) and three-body wear (rolling). Each loading event corresponds to only one loading category. Grinding force models are established for different loading categories to solve for the normal and tangential forces generated by each loading category. S3. Calculate the residual stress of a single mesh element: For any mesh element, traverse each loading event on that mesh element in chronological order; determine its loading category based on the constraint conditions and penetration depth of the abrasive grains corresponding to each loading event, and call the grinding force model corresponding to that loading category to calculate the normal force and tangential force generated by that loading event; input the normal force into the Blister field analytical model to solve for the stress tensor increment of that loading event; perform loading-unloading calculations for that loading event according to the VonMises yield criterion, deducting the elastic recovery part and retaining the plastic part during unloading, and superimposing the stress tensor increment of the subsequent loading on the basis of the cumulative stress tensor retained after the previous unloading, thereby updating the cumulative stress tensor of the mesh element; after traversing n loading events of the mesh element, substitute the finally retained cumulative stress tensor into the VonMises equivalent stress formula to synthesize a single scalar value, thus obtaining the residual stress of the mesh element; S4. Calculate the residual stress distribution across the entire field: Traverse all mesh elements and calculate the residual stress of each mesh element. Then, smooth the residual stress of the entire polished surface to obtain the theoretical prediction results of the residual stress on the polished surface of the silicon carbide substrate.

2. The method for theoretically predicting residual stress on the polished surface of a silicon carbide substrate according to claim 1, characterized in that, The loading category is determined as follows: when abrasive grains are embedded in the grinding disc, it is considered two-body wear. Under two-body wear, the loading category is determined by comparing the abrasive grain penetration depth with three critical depths: the critical depth for elastoplastic transition, the critical depth for tilling-cutting transition, and the critical depth for ductile-brittle transition. The critical depth for elastoplastic transition is determined based on Hertz contact theory and the yield criterion; the critical depth for tilling-cutting transition is determined by multiplying an empirical coefficient with the critical depth for elastoplastic transition; and the critical depth for ductile-brittle transition is determined by multiplying the baseline value of the Bifano model with the abrasive grain radius curvature correction coefficient. When the abrasive grain penetration depth is less than the critical depth for elastoplastic transition, the loading category is slip friction; when the abrasive grain penetration depth is greater than or equal to the critical depth for elastoplastic transition but less than the critical depth for tilling-cutting transition, the loading category is tilling; when the abrasive grain penetration depth is greater than or equal to the critical depth for tilling-cutting transition but less than the critical depth for ductile-brittle transition, the loading category is cutting; and when the abrasive grain penetration depth is greater than or equal to the critical depth for ductile-brittle transition, the loading category is brittle removal. When the abrasive grains are in a free state and not embedded in the grinding disc, the corresponding loading category is rolling for three-body wear.

3. The method for theoretically predicting residual stress on the polished surface of a silicon carbide substrate according to claim 1, characterized in that, When the loading category is friction, the normal force and tangential force The calculation method is as follows: ， ， In the formula, The elastic modulus of silicon carbide; Poisson's ratio for silicon carbide; For the first The actual indentation depth of each abrasive grain; For the first The diameter of the circumscribed circle of an aggregated diamond; Wear rate describes the proportion of change in abrasive grain height after agglomerated diamond is subjected to force; For the first The cutting edge inclination angle of each abrasive grain; Let be the coefficient of friction during the sliding phase, where satisfy: ， In the formula, The contact coefficient of silicon carbide; The contact coefficient of diamond; This represents the contact area between silicon carbide and the abrasive grains. satisfy: 。 4. The method for theoretically predicting residual stress on the polished surface of a silicon carbide substrate according to claim 1, characterized in that, When the load type is plowing, calculate the tangential force first. Recalculate the normal force : ， ， In the formula, The scratch hardness is calculated through a contact scratch test. For the first The actual indentation depth of each abrasive grain; Wear rate describes the proportion of change in abrasive grain height after agglomerated diamond is subjected to force; For the first The diameter of the circumscribed circle of an aggregated diamond; For the first The cutting edge inclination angle of each abrasive grain; The coefficient of friction during the plowing stage. satisfy: ， In the formula, For contact width, satisfy: 。 5. The method for theoretically predicting residual stress on the polished surface of a silicon carbide substrate according to claim 1, characterized in that, When the loading category is cutting, the normal force and tangential force The calculation method is as follows: ， ， In the formula, The grinding force coefficient per unit cutting area; For the first The tangential contact area between the abrasive grain and the workpiece; For the first The normal contact area between each abrasive grain and the workpiece; These are geometric coefficients related to the shape of the abrasive grains; The coefficient of cutting friction is determined based on contact scratch experiments; The average pressure in the contact area, satisfy: ， In the formula, , These are dimensionless constants determined by the properties of silicon carbide materials; The average velocity in the contact area; For reference strain rate; The scratch hardness is calculated through a contact scratch test. The elastic modulus of silicon carbide; For contact width, satisfy: ， In the formula, Wear rate describes the proportion of change in abrasive grain height after agglomerated diamond is subjected to force; For the first The diameter of the circumscribed circle of an aggregated diamond; For the first The actual indentation depth of each abrasive grain; For the first The cutting edge inclination angle of each abrasive grain.

6. The method for theoretically predicting residual stress on the polished surface of a silicon carbide substrate according to claim 1, characterized in that, When the loading category is brittle removal, normal force and tangential force The calculation method is as follows: ， ， In the formula, A constant related to the shape of diamond abrasive grains; The fracture toughness of silicon carbide; The scratch hardness is calculated through a contact scratch test. σ is the elastic modulus of silicon carbide; fl The flow stress of silicon carbide; Let be the normal contact area between the i-th abrasive grain and the workpiece; These are geometric coefficients related to the shape of the abrasive grains; The coefficient of cutting friction is determined based on contact scratch experiments; The average pressure in the contact area, satisfy: ， In the formula, , These are dimensionless constants determined by the properties of silicon carbide materials; The average velocity in the contact area; For reference strain rate; The elastic modulus of silicon carbide; For contact width, satisfy: ， In the formula, Wear rate describes the proportion of change in abrasive grain height after agglomerated diamond is subjected to force; For the first The diameter of the circumscribed circle of an aggregated diamond; For the first The actual indentation depth of each abrasive grain; For the first The cutting edge inclination angle of each abrasive grain.

7. The method for theoretically predicting residual stress on the polished surface of a silicon carbide substrate according to claim 1, characterized in that, When the loading type is rolling, the normal force and tangential force The calculation method is as follows: ， ， In the formula, The indentation angle of the abrasive grains into the workpiece; The depth of the abrasive roller-rolled workpiece; The hardness of silicon carbide; The indentation angle of the abrasive grains into the grinding pad; The depth of the abrasive roller grinding pad; The hardness of the abrasive pad; This refers to the gap between the workpiece and the grinding disc; For the size of the load particles, take , The average diameter of the abrasive grains; Equivalent hardness, satisfy: 。 8. The method for theoretically predicting residual stress on the polished surface of a silicon carbide substrate according to claim 1, characterized in that, In step S3, the method for solving the stress tensor increment of the loading event is as follows: the normal force generated by the loading event, the abrasive geometric parameters, and the elastic modulus and Poisson's ratio of the silicon carbide substrate are used as input parameters and substituted into the sliding Blister field analytical model to solve for the stress tensor increment caused by the loading event. The stress tensor increment contains 3 independent normal stress components and 3 independent shear stress components. In step S3, the method for obtaining the residual stress of the mesh element is as follows: n loading events are executed sequentially; the stress tensor increment of the k-th (k=1, 2, 3…n) loading event is superimposed on the cumulative stress tensor retained after the (k-1)-th unloading event to obtain the updated temporary stress tensor; the VonMises equivalent stress is calculated based on the 6 independent components of the updated temporary stress tensor; when the VonMises equivalent stress is greater than or equal to the yield strength of silicon carbide, plastic yielding is determined, and the elastic recovery part is deducted and the plastic part is retained during unloading, which is used as the cumulative stress tensor after the k-th unloading event; when the VonMises equivalent stress is less than the yield strength of silicon carbide, it is determined to be pure elastic deformation, and the cumulative stress tensor remains in the state after the (k-1)-th unloading event; after traversing the n loading events of the mesh element, a stress tensor matrix is ​​constructed using the 6 independent components of the finally retained cumulative stress tensor, the three eigenvalues ​​of the stress tensor matrix are solved, and the three eigenvalues ​​are substituted into the VonMises equivalent stress formula to synthesize a single scalar value to obtain the residual stress of the mesh element.

9. The method for theoretically predicting residual stress on the polished surface of a silicon carbide substrate according to claim 1, characterized in that, In step S1, the method for dividing the silicon carbide substrate surface into grid cells is as follows: the grid cells are square, and the outer circle size of all grid cells is smaller than the spacing between adjacent discrete trajectory points.

10. The method for theoretically predicting residual stress on the polished surface of a silicon carbide substrate according to any one of claims 1 to 9, characterized in that, It also includes steps S5 and S6; S5. Establish a residual compensation model: Perform a grinding experiment on the silicon carbide substrate and measure the experimental value of residual stress; use the process parameters of the grinding experiment to carry out theoretical predictions of steps S1 to S4 to obtain the experimental static theoretical 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 theoretical prediction value was used as output label to construct a training sample set. The bidirectional gated recurrent unit network optimized by the Grey Wolf optimization algorithm was used to train the GWO-BIGRU residual compensation model. S6. Online Dynamic Prediction: During the production line grinding of silicon carbide substrates, theoretical predictions are carried out in steps S1 to S4 based on the grinding process parameters to obtain online static theoretical prediction values. Acoustic emission signals and vibration signals during the production process are collected simultaneously. The residuals are output through the GWO-BIGRU residual compensation model, and residual superposition compensation is performed on the online static theoretical prediction values ​​to obtain online dynamic theoretical prediction results.

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