A method for predicting the coverage of shot peening of a spiral bevel gear

Abstract

The application discloses a spiral bevel gear shot peening coverage rate prediction method, comprising the following steps: S1, simulating and calculating actual spiral bevel gear shot peening, and establishing a spiral bevel gear shot peening discrete element model; S2, deriving discrete element calculation results; S3, using software to establish a spiral bevel gear shot peening finite element model, setting various parameters in the finite element model by using the calculation results of step S2, and adopting an import analysis method to carry out target plate surface layer state calculation after projectile impact; S4, extracting finite element calculation results, and establishing a target plate surface node z direction displacement matrix after projectile impact of each group; S5, judging projectile crater coverage of each position by using the node z direction displacement matrix, and taking a percentage of nodes in a projectile crater coverage area and total node numbers as a coverage rate size. The spiral bevel gear shot peening coverage rate prediction method can predict spiral bevel gear shot peening coverage rate, has high prediction accuracy, and can provide guidance for spiral bevel gear shot peening processes.

Description

Technical Field

[0001] This invention relates to the field of shot peening coverage prediction for workpieces, and particularly to a method for predicting the coverage of helical bevel gears through shot peening. Background Technology

[0002] Spiral bevel gears are widely used in aerospace, automotive, and other fields. To improve gear fatigue life and optimize service performance, a shot peening process is typically added at the end of the machining process. Shot peening utilizes high-speed shot to impact the gear surface, inducing uneven plastic deformation, improving the distribution of residual stress on the tooth surface, and increasing surface hardness and wear resistance. Shot peening coverage is an important indicator in the shot peening process, referring to the ratio of the area covered by the shot crater to the surface area of ​​the target area. As a key control parameter of the shot peening process, this value can be used to determine the appropriate shot peening time to achieve optimal surface properties for the parts.

[0003] Improving the accuracy of shot peening coverage prediction can enhance the efficiency of shot peening process parameter optimization and save costs. Traditional prediction methods generally use Avrami's empirical formula, but this method assumes that the crater radius generated by the shot impact is the same. Due to the complex tooth surface of spiral bevel gears, the probability of collision between projectiles is greatly increased, and the actual impact velocity of the projectiles is highly dispersed, resulting in significant differences in the crater radius. Consequently, this deviates greatly from the assumptions of Avrami's empirical formula, leading to low prediction accuracy. Summary of the Invention

[0004] This invention aims to address at least one of the technical problems existing in the prior art. To this end, this invention proposes a method for predicting the shot peening coverage of spiral bevel gears, which can predict the shot peening coverage of spiral bevel gears with high accuracy, thereby providing guidance for the shot peening process of spiral bevel gears.

[0005] The method for predicting the coverage of shot peening of spiral bevel gears according to a first aspect of the present invention includes the following steps:

[0006] S1. Simulation calculations were performed on actual spiral bevel gear shot peening strengthening. A discrete element model of spiral bevel gear shot peening was established using software to simulate the process of shot from the nozzle of the shot peening machine to the tooth surface of the spiral bevel gear.

[0007] S2. Export the discrete element calculation results;

[0008] S3. Use software to establish a finite element model of a spiral bevel gear shot peening, use the calculation results exported in step S2 to set various parameters in the finite element model, and use the import analysis method to calculate the surface state of the target plate after multiple sets of shot impacts.

[0009] S4. Extract the finite element calculation results and establish the z-direction displacement matrix of the target plate surface nodes after each group of projectile impacts;

[0010] S5. Use the node z-direction displacement matrix to determine the crater coverage at each location, and use the percentage of nodes within the crater coverage area to the total number of nodes as the coverage rate.

[0011] The method for predicting the coverage of spiral bevel gear shot peening according to embodiments of the present invention has at least the following beneficial effects:

[0012] In this invention, firstly, a simulation model of shot peening for spiral bevel gears is established using a coupled discrete element method (DEM) and finite element method (FEM). This model is suitable for situations where the complex tooth surface of spiral bevel gears leads to a high probability of collision between projectiles and a large dispersion in the actual impact velocity of the projectiles, thus significantly improving the accuracy of simulation calculations and consequently, the accuracy of determining the shot peening coverage of spiral bevel gears. Secondly, by establishing a z-axis displacement matrix for the nodes on the target plate surface, the coverage of craters at each location is determined using this matrix. The percentage of nodes within the crater coverage area relative to the total number of nodes is used as the coverage rate, further improving the accuracy of determining the shot peening coverage of spiral bevel gears and providing guidance for the shot peening strengthening process of spiral bevel gears.

[0013] According to some embodiments of the present invention, in step S2, the derived discrete element calculation results include, but are not limited to: the time when the projectile impacts the tooth surface, the absolute velocity of the projectile at the time of impact, the coordinates of the impact point of the projectile impacting the tooth surface, the information of the impacted tooth surface element, and the total number of times the tooth surface element is impacted by the projectile.

[0014] According to some embodiments of the present invention, in step S3, the parameters for establishing the finite element model include, but are not limited to:

[0015] The projectile velocity is calculated based on the absolute velocity of the projectile in step S2.

[0016] The number of projectile impacts is calculated based on the total number of projectile impacts on the tooth surface unit in step S2.

[0017] The initial coordinates of the projectile center are calculated based on the projectile velocity, projectile diameter, and the time interval between successive impacts of the projectiles on the tooth surface.

[0018] According to some embodiments of the present invention, the absolute velocity of the projectile in step S2 is... Converted into the relative impact velocity vector between the projectile and the gear. The calculation method is as follows:

[0019] In the geodetic coordinate system, the unit vectors of the new coordinate system's x, y, and z axes are represented as... , , ,but and The relationship is represented as:

[0020]

[0021] Then, taking the four equally divided points on the pitch cone line of the spiral bevel gear tooth surface as the research object, the relative impact velocity vector of all projectiles and gears in this region is denoted as... ;

[0022] Finally in The velocity of the projectile in the finite element model is randomly selected.

[0023] According to some embodiments of the present invention, in step S3, the residual stress on the surface of the gear teeth before shot peening is measured, and the measured residual stress data is used as the prestress field of the target plate to establish a finite element model considering the initial residual stress.

[0024] According to some embodiments of the present invention, in step S3, the finite element model target plate is meshed, and the mesh size of the central region is set to 10. ×10 Furthermore, an infinite unit cell region with a thickness of 0.1 mm was added around the target plate and at its bottom to eliminate the reflection of stress waves at the target plate boundary.

[0025] According to some embodiments of the present invention, in step S4, the first The z-axis displacement matrix of all surface nodes in a representative area of ​​the target plate after the impact of the projectile is denoted as follows: , among which, when At that time, the nodal z-direction displacement matrix generated by the impact of this group of projectiles ,when At that time, the nodal z-direction displacement matrix generated by the impact of this group of projectiles .

[0026] According to some embodiments of the present invention, in step S5, the matrix is... Perform two-dimensional interpolation to obtain the matrix. ,matrix The element in the i-th row and j-th column is represented as , representing the z-direction displacement of the corresponding node, and constructing a zero matrices of the same order ,matrix The element in the i-th row and j-th column is represented as . use Determine the crater coverage at each node and use the matrix. Record the judgment result; if the node is covered by a crater, then the corresponding... Marked as 1, if the node is not covered by the crater, then the corresponding Record it as 0, and then perform the final statistics. The sum of all elements in the matrix, divided by the total number of elements, gives the coverage ratio. .

[0027] According to some embodiments of the present invention, utilizing The process of determining the crater coverage of each node within a representative area of ​​the target plate is as follows: Iteration all elements ,if If the value is negative, it means that the node's displacement in the z-direction is negative, the node is covered by a crater, and the node... It is denoted as 1.

[0028] According to some embodiments of the present invention, for Nodes that are non-negative Perform iterations to determine these nodes. Whether it is covered by shell craters, the specific process is as follows:

[0029] a. Calculation Displacement gradient of its 8 neighboring nodes :

[0030]

[0031] b. Based on the calculation results, determine the nodes. The node with the largest displacement gradient is denoted as _____. ;

[0032] c. Targeting nodes Repeat steps a and b to find the next node as the new node. until the node The iteration stops when the displacement gradients of the eight adjacent nodes are all less than or equal to 0.

[0033] d. After the iteration is complete, the nodes can be found based on the iteration results. corresponding nodes If node If it is negative, it indicates a node. Covered by craters, the node Change to 1.

[0034] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. Attached Figure Description

[0035] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0036] Figure 1 This is a schematic diagram of a discrete element model;

[0037] Figure 2 This is a schematic diagram of the coordinate system transformation for the projectile velocity field;

[0038] Figure 3 Flowchart for the calculation of a finite element model of multiple projectile impacts;

[0039] Figure 4 This is a schematic diagram of the finite element model;

[0040] Figure 5 This is a schematic diagram of the target plate mesh division;

[0041] Figure 6 A schematic diagram showing the measured results of residual stress distribution on unpeeled tooth surfaces;

[0042] Figure 7 Flowchart for coverage determination;

[0043] Figure 8 This is a schematic diagram showing the calculation results of the shot peening surface coverage.

[0044] Figure 9 This is a schematic diagram illustrating the evolution of coverage as a function of the number of projectile impacts. Detailed Implementation

[0045] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0046] In the description of this invention, it should be understood that the orientation descriptions, such as up, down, front, back, inside, outside, top, bottom, etc., are based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0047] In the description of this invention, "multiple" refers to two or more. The use of "first" and "second" is for distinguishing technical features only and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features or their sequential relationship.

[0048] In the description of this invention, unless otherwise explicitly defined, terms such as "set up" and "establish" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this invention in conjunction with the specific content of the technical solution.

[0049] The following is for reference. Figures 1 to 9 A method for predicting the coverage of shot peening reinforcement of spiral bevel gears according to an embodiment of the present invention is described.

[0050] The method for predicting the coverage rate of shot peening of spiral bevel gears according to an embodiment of the present invention includes the following steps: S1. Simulating the actual shot peening of spiral bevel gears, using software to establish a discrete element model of the spiral bevel gear shot peening, simulating the process of the shot from the nozzle of the shot peening machine to the tooth surface of the spiral bevel gear; S2. Exporting the discrete element calculation results; S3. Using software to establish a finite element model of the spiral bevel gear shot peening, using the calculation results exported in step S2 to set various parameters in the finite element model, and using the import analysis method to calculate the surface state of the target plate after multiple sets of shot impacts; S4. Extracting the finite element calculation results, establishing the z-direction displacement matrix of the target plate surface nodes after each set of shot impacts; S5. Using the node z-direction displacement matrix to determine the crater coverage at each location, and using the percentage of nodes within the crater coverage area to the total number of nodes as the coverage rate.

[0051] The method for predicting the coverage rate of shot peening for spiral bevel gears in this invention firstly establishes a simulation model of the spiral bevel gear using a coupled discrete element method (DEM) and finite element method (FEM). This model is adaptable to situations where the complex tooth surface of the spiral bevel gear leads to a high probability of collision between projectiles and a large dispersion in the actual impact velocity of the projectiles, thereby significantly improving the accuracy of simulation calculations and thus enhancing the accuracy of determining the coverage rate of the spiral bevel gear shot peening. Secondly, by establishing a z-axis displacement matrix of the nodes on the target plate surface, the coverage of the crater at each location is determined using this matrix. The percentage of nodes within the crater-covered area relative to the total number of nodes is used as the coverage rate, further improving the accuracy of determining the coverage rate of the spiral bevel gear shot peening and providing guidance for the shot peening process of spiral bevel gears.

[0052] The steps S1 to S5 of the spiral bevel gear shot peening reinforcement coverage prediction method according to the present invention will be described in more detail below.

[0053] Step S1: Perform simulation calculations on the actual shot peening strengthening of spiral bevel gears. Use ABAQUS software or other suitable software to establish a discrete element model of spiral bevel gear shot peening to simulate the process of shot from the nozzle of the shot peening machine to the tooth surface of the spiral bevel gear.

[0054] Figure 1 This is a schematic diagram of discrete element model calculation. A particle generator is used to simulate the nozzle of a shot peening machine to produce projectiles. The normal direction of the particle generator is set to be perpendicular to the tooth root of the spiral bevel gear, and it moves from the small end of the gear to the large end of the gear along the tooth width direction.

[0055] This embodiment takes a spiral bevel gear made of 9310 steel after carburizing and quenching as the research object. The basic mechanical properties of 9310 steel after carburizing and quenching are as follows: Yield strength 1600MPa. ASH110 type shot was selected for shot peening. According to SAE standards, the shot diameter was determined to be 0.30mm. Its basic mechanical properties are: elastic modulus... =210GPa, Poisson's ratio v=0.3, yield strength .

[0056] The parameters for establishing the discrete element model include, but are not limited to: projectile diameter, initial projectile velocity, friction coefficient between the projectile and the gear, friction coefficient between projectiles, and the coefficient of restitution after the collision between the projectile and the gear. The initial projectile velocity refers to the initial velocity of the projectile generated by the particle generator. This velocity corresponds to the velocity of the projectile ejected from the nozzle of the shot peening machine in actual processing. The velocity value is determined according to the formula for calculating the initial projectile velocity, which is expressed as:

[0057]

[0058] In the formula, The average diameter of the projectile is in mm. The flow rate of the pellets is expressed in kg / min. This refers to the nozzle air pressure, expressed in bar.

[0059] The remaining parameters in the discrete element model are set according to the spiral bevel gear shot peening process. The parameter settings of the discrete element model in this embodiment are shown in Table 1.

[0060] Table 1. Some parameters of the discrete element model

[0061]

[0062] Step S2: Export the discrete element calculation results. The exported results include, but are not limited to: the time of impact between the projectile and the tooth surface, the absolute velocity of the projectile at the time of impact, the coordinates of the impact point of the projectile impact on the tooth surface, the information of the impacted tooth surface element, and the total number of times the tooth surface element is impacted by the projectile.

[0063] Specifically, the absolute velocity of the projectile colliding with the tooth surface and the coordinates of each node on the tooth surface impacted by the projectile are exported using ABAQUS software or other suitable software. For example... Figure 2 As shown, surface ABCD represents a local region on the tooth surface, which can be simplified to quadrilateral ABCD. According to the right-hand rule of spatial coordinate systems, with A as the origin and AB as... axis, AD is Establish a Cartesian coordinate system based on the axes. In the geodetic coordinate system, the unit vectors of each coordinate axis are... , , The velocity vector of the projectile m is expressed as In the new coordinate system, it is represented as According to the principle of axis transformation:

[0064]

[0065] Then, taking the four equally divided points on the pitch cone line of the spiral bevel gear tooth surface as the research object, the relative impact velocity vector of all projectiles and gears in this region is denoted as... .

[0066] The total number of projectile impacts on a given tooth surface element and the area of ​​that element are derived using ABAQUS software or other suitable software. The number of projectile impacts per unit area N at that tooth surface element is then calculated using the following formula:

[0067]

[0068] Step S3: Use ABAQUS software or other suitable software to establish a finite element model of the spiral bevel gear shot peening considering the initial residual stress on the tooth surface. Specifically, use the calculation results exported from step S2 to set the shot velocity and shot impact number in the finite element model, and set the initial coordinates of each shot center in combination with the shot velocity. Simplify the quadrilateral ABCD in step S2 into a planar region, take this planar region as the research object, establish the target plate in the finite element model, and use the import analysis method to calculate the surface state of the target plate after multiple sets of shot impacts.

[0069] The process of establishing a finite element model is as follows: Figure 3 As shown. The number of projectile impacts per unit area calculated in step S2 is used to determine the number of projectile impacts in the finite element model, and the projectile velocity calculated in step S2 is used to determine the number of projectile impacts per unit area using a random principle. The projectile velocity is randomly selected as the i-th impact target plate in the finite element model. The center of impact of the projectile is located in a representative area on the target plate surface (e.g., Figure 5 The projectile is randomly distributed within the area shown in the diagram. This is implemented using the `random` function in Python. The initial coordinates of the projectile's center are determined using the following formula. , , :

[0070]

[0071]

[0072]

[0073] Where i represents the impact sequence of the projectile. , , For the speed of the projectile The components in the x, y, and z directions, where d is the diameter of the projectile and t is the time interval between successive impacts of the projectile.

[0074] The import analysis method was used to calculate the surface state of the target plate after multiple sets of projectile impacts. In this case, multiple projectiles, for example, ten projectiles, were used as a group. The *IMPORT function of ABAQUS software was used to use the strain field, stress field, and surface morphology after the previous set of impacts as the initial conditions for the next set of impacts. The target plate state after each set of projectile impacts was calculated sequentially. The model is as follows: Figure 4 As shown.

[0075] Finite element model target plate mesh generation as follows Figure 5 As shown. Except for the infinite element mesh, the target plate size is 2mm × 2mm × 0.5mm, and this part is meshed using C3D8R type elements. To improve computational accuracy, the mesh size in the mesh refinement region is set to 10. ×10 An infinite unit cell region with a thickness of 0.1 mm was added around the target plate and at its bottom, and the cells were divided using a CIN3D8 type mesh to eliminate the reflection of stress waves at the target plate boundary.

[0076] When measuring the residual stress on the surface of unpeeled wheel teeth using X-ray diffraction, and obtaining the residual stress at depth, an electrochemical etching process using an electropolishing machine is required to perform electrochemical etching on the area to be tested. The measured residual stress data (such as...) Figure 6 As shown in the figure, a finite element simulation model considering the initial residual stress is established as the prestress field of the target plate.

[0077] Step S4: Extract the finite element calculation results and establish the z-direction displacement matrix of the target plate surface nodes after each group of projectile impacts.

[0078] Extracting the finite element calculation results, the z-axis displacement coordinate matrix of all surface nodes in the representative area of ​​the target plate after the impact of the k-th group of projectiles is denoted as... .when At that time, the nodal z-direction displacement caused by the impact of the ten projectiles in this group ,when hour, .

[0079] Step S5: Use the node z-direction displacement matrix to determine the crater coverage at each location, and use the percentage of the number of nodes in the covered area to the total number of nodes as the coverage rate.

[0080] To improve computational accuracy, the matrix... Perform two-dimensional interpolation to obtain the matrix. ,matrix The element in the i-th row and j-th column is represented as , representing the z-direction displacement of the corresponding node. And construct a matrix. zero matrices of the same order ,matrix The element in the i-th row and j-th column is represented as ,use Determine the crater coverage at each node and use the matrix. Record the judgment result; if the node is covered by a crater, then the corresponding... Marked as 1, if the node is not covered by the crater, then the corresponding Record it as 0.

[0081] use Figure 7 The process shown determines whether each node is covered by a crater. The upper left corner is a schematic diagram of a crater cross-section, showing half a crater, the surrounding bulge, and parts of the surface unaffected by shot peening. Regions 1 and 2 in the diagram are uncovered crater areas, while regions 3 and 4 are covered crater areas. Region 4 can be directly determined by the z-axis displacement coordinates of the target plate surface nodes. When the z-axis displacement coordinate of a target plate surface node is negative, it indicates that the node is located in region 4 and is covered by a crater. Regions 2 and 3 are bulges caused by shot impact; in these cases, the z-axis displacement coordinates of the target plate surface nodes are all positive. However, region 3 is also a crater-covered area and therefore requires separate judgment. The overall judgment process is as follows.

[0082] First iterate all elements ,if A negative value indicates that the z-direction displacement of the corresponding node is negative, meaning that the node is covered by a crater, the node has been reinforced by shot peening, and the node... Record it as 1. Then, for the remaining nodes... To iterate, that is, to Nodes that are non-negative Perform iterations to determine Is it located in Figure 7 The specific judgment process for area 3, which is covered by craters, is as follows:

[0083] a. Calculation Displacement gradient of its 8 neighboring nodes :

[0084]

[0085] b. Based on the calculation results, determine the nodes. The node with the largest displacement gradient is denoted as _____. ;

[0086] c. Targeting nodes Repeat steps a and b to find the next node as the new node. until the node The iteration stops when the displacement gradients of the eight adjacent nodes are all less than or equal to 0.

[0087] d. After the iteration is complete, the nodes can be found based on the iteration results. corresponding nodes Specifically, when lie in Figure 7 When within area 3, which is covered by craters, as shown, corresponding nodes Located within region 4, node It is a negative number; when lie in Figure 7 When within area 2, which is not covered by craters, as shown, corresponding nodes If the node is located within region 1, then It is not negative. Therefore, according to the node... That is, the corresponding node can be determined. Is it located in Figure 7 Within region 3, which is covered by craters, if node Covered by craters, the node Change to 1.

[0088] statistics The sum of all elements in the array, divided by the total number of elements, gives the coverage ratio. .

[0089] Figure 8 This is a schematic diagram showing the calculated surface coverage of shot peening, where black represents uncovered areas. For example... Figure 8 As shown, the area covered increases with the number of impacts from the projectile to 300 and 500. When the number of impacts reaches 590, the surface is almost completely covered by craters, with a coverage rate of 98%.

[0090] Figure 9 The diagram illustrates the evolution of coverage rate with the number of projectile impacts. It shows that in the initial stage of shot peening, the coverage rate increases rapidly due to the smaller number of projectile impacts and the limited overlap between craters. As the number of projectile impacts increases, the increase in coverage rate gradually slows down. When the number of projectile impacts is 590 and the shot peening time is 72 seconds, the coverage rate reaches 98%. This is consistent with the results of shot peening experiments, thus verifying the reliability of the invention.

[0091] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method of predicting a shot peening coverage of a spiral bevel gear, characterized by, Comprising the following steps: S1. Simulate shot peening of the actual spiral bevel gear, use software to establish a discrete element model of the spiral bevel gear shot peening, simulate the process of the shot from the nozzle of the shot peening machine to the tooth surface of the spiral bevel gear; S2. Derive the discrete element calculation results; S3. Use software to establish a finite element model of the spiral bevel gear shot peening, set various parameters in the finite element model using the calculation results derived in step S2, and use the import analysis method to carry out calculation of the surface state of the target plate after multiple shot impacts; S4. Extract the finite element calculation results to establish a z-direction displacement matrix of the target plate surface nodes after each group of shot impacts; S5. Use the z-direction displacement matrix to judge the crater coverage at each position, and use the percentage of the number of nodes in the crater coverage area to the total number of nodes as the coverage rate.

2. The spiral bevel gear shot peening coverage ratio prediction method according to claim 1, characterized by, In step S2, the derived discrete element calculation results include but are not limited to: the time of shot impact with the tooth surface, the absolute speed of the shot at the time of impact, the impact point coordinates of the tooth surface impacted by the shot, the tooth surface element information impacted by the shot, and the total number of times of impact of the tooth surface element by the shot.

3. The spiral bevel gear shot peening coverage prediction method according to claim 2, characterized by, In step S3, the parameters for establishing the finite element model include but are not limited to: Shot speed, calculated according to the absolute speed of the shot in step S2; Shot impact times, calculated according to the total number of times of impact of the tooth surface element by the shot in step S2; Initial coordinates of the shot center, calculated according to the shot speed, shot diameter, and time interval of successive impact of the shot on the tooth surface.

4. The spiral bevel gear shot peening coverage prediction method according to claim 3, characterized by, Convert the absolute velocity of the projectile in step S2 to the relative impact velocity vector of the projectile and the gear , the calculation method is: In the terrestrial coordinate system, the unit vectors of the new coordinate system x, y, z axes are expressed as , , , and The relationship is expressed as: After the spiral bevel gear tooth surface pitch cone line on the four equal point position for the study object, the region within all the projectile and gear relative impact velocity vector, recorded as ; Finally in the projectile velocity in the finite element model was randomly selected.

5. The spiral bevel gear shot peening coverage ratio prediction method according to any one of claims 1 to 4, characterized by, In step S3, measure the surface residual stress of the spiral bevel gear without shot peening, use the measured residual stress data as the pre-stress field of the target plate, and establish a finite element model considering the initial residual stress.

6. The spiral bevel gear shot peening coverage prediction method according to claim 5, characterized by, In step S3, the finite element model target plate is meshed, and the center area mesh size is set to 10 × 10 , and an infinite element area with a thickness of 0.1 mm is added around the target plate and at the bottom thereof to eliminate the reflection of stress waves at the boundary of the target plate.

7. The method of claim 1 to 4, wherein In step S4, the node z-direction displacement matrix of all surface nodes in the representative region of the target plate impacted by the group of projectiles is recorded as where, when , the node z-direction displacement matrix of the group of projectiles is . When , the node z-direction displacement matrix of the group of projectiles is .

8. The spiral bevel gear shot peening coverage prediction method according to claim 7, characterized by, In step S5, the matrix is two-dimensionally interpolated to obtain a matrix , and the element in the i-th row and the j-th column of the matrix is expressed as , which represents the z-direction displacement of the corresponding node, and a zero matrix of the same order is constructed , and the element in the i-th row and the j-th column of the matrix is expressed as , the crater coverage of each node is determined by using , and the determination result is recorded by using the matrix , if the node is covered by the crater, the corresponding is recorded as 1, if the node is not covered by the crater, the corresponding is recorded as 0, and finally the sum of all elements in the matrix is counted, and the coverage rate size is obtained by dividing the total number of elements, that is .

9. The spiral bevel gear shot peening coverage prediction method according to claim 8, characterized by, Utilizing The process of determining the crater coverage of each node in the representative area of the target plate is as follows: iterating all elements in If is negative, it indicates that the z-direction displacement of the corresponding node is negative, and the node is covered by the crater. Mark the node as 1.

10. The method of claim 9, wherein the method is characterized by: To nodes that are non-negative Iterate to determine whether these nodes are covered by a crater, the specific process is: a. Compute Displacement gradient of its 8 neighboring nodes : b. According to the calculation result, determine the node with the maximum displacement gradient, and mark the node as the node with the maximum displacement gradient, and mark the node as ; c. For each node Repeat steps a, b, find the next node as new , until the displacement gradient of the node with 8 adjacent nodes are all less than or equal to 0, iteration stops; d.After the iteration, according to the iteration result, the node corresponding to the node , if the node is negative, it means that the node is covered by the crater, and the node is changed to 1.

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