A method for simulating workpiece topography and damage in grinding silicon carbide ceramics considering strain rate effect

Abstract

The present application aims to optimize the abrasive grain arrangement and grinding parameters of the grinding wheel to accurately predict the surface topography and damage of silicon carbide ceramic materials during the grinding process. A new mathematical simulation model is established, considering the influence of strain rate effect on material damage, and the grinding process control is realized through the ordered abrasive grain single-layer diamond grinding wheel. A simulation model for predicting the topography and damage of silicon carbide ceramic considering the strain rate effect is successfully established. First, the surface topography model of the ordered abrasive grain single-layer diamond grinding wheel is established, and then the kinematics analysis of the diamond abrasive grain grinding process is carried out to generate the workpiece surface topography model after grinding. Further, considering the damage of silicon carbide ceramic, a damage model considering the strain rate effect is established. This innovation helps to improve the accuracy of grinding workpiece topography prediction, improve the efficiency and precision of grinding process, and promote the development of grinding technology.

Description

Technical Field

[0001] This invention establishes a method for simulating the morphology and damage of silicon carbide ceramic grinding workpieces considering the strain rate effect. By using simulation, a simulation model of the surface morphology and subsurface damage of silicon carbide ceramic material grinding considering the strain rate effect is established, which belongs to the field of simulation technology. Background Technology

[0002] Silicon carbide ceramics have been widely used in the aerospace industry in recent years due to their superior material properties, including good thermal conductivity, high specific stiffness, low coefficient of thermal expansion, high hardness, low density, and strong thermal stability. Grinding is one of the most fundamental methods for processing these materials. The surface integrity of silicon carbide materials (including surface roughness, surface damage, and subsurface damage) has a significant impact on their performance. However, their excellent material properties lead to severe grinding wheel wear, poor surface integrity of the ground workpiece, and high processing costs. Therefore, establishing a simulation model of the workpiece morphology is of great significance for optimizing processing parameters and reducing grinding costs.

[0003] The grinding process of silicon carbide ceramics involves complex interactions between abrasive grains and the workpiece material. Surface and subsurface damage caused by material removal reduces the service life of silicon carbide ceramics. Therefore, a novel numerical simulation model was established to predict the surface morphology of silicon carbide ceramics during precision grinding. The model considers the influence of strain rate on material damage and achieves grinding process control through a single-layer diamond grinding wheel with ordered abrasive grain arrangement. A simulation model for predicting the morphology and damage of silicon carbide ceramics considering strain rate effects was successfully established. Summary of the Invention

[0004] 1. To optimize grinding wheel profile and grinding parameters, predicting the surface morphology of the workpiece is essential. This invention establishes a mathematical simulation model to predict the surface morphology of silicon carbide ceramic materials during the grinding process. The model considers the strain rate effect and utilizes numerical simulation technology to predict the evolution of the surface morphology of the silicon carbide ceramic workpiece through theoretical calculations, aiming to achieve accurate prediction of the surface morphology of the ground ceramic workpiece.

[0005] 2. To achieve the above objectives, the present invention is implemented through the following technical solution:

[0006] The steps for establishing a method for simulating the morphology and damage of silicon carbide ceramic grinding workpieces considering strain rate effects are as follows:

[0007] Step 1: Establish a surface morphology model of a single-layer diamond grinding wheel with ordered abrasive grain arrangement.

[0008] In this study, a single-layer diamond abrasive wheel with ordered abrasive grain arrangement was used. Since the abrasive grains directly remove workpiece material, accurate abrasive grain models are required for modeling the wheel morphology. The abrasive grains used in diamond grinding wheels are mostly irregular hexahedrons and octahedrons; therefore, a truncated octahedron was established to represent the abrasive grains, and the wheel surface was represented as a topological matrix, with the grains on the wheel surface represented by points in the topological matrix. Based on the linear arrangement of the abrasive grains, the angle between the oblique arrangement of the abrasive grains and the wheel circumference was set as α, the distance between two adjacent rows of abrasive grains on the wheel circumference was Δx, and the distance between a row of abrasive grains distributed radially was Δz, ultimately forming a workpiece morphology model of a single-layer diamond grinding wheel with ordered abrasive grain arrangement.

[0009] Step 2: Kinematic Analysis of Diamond Abrasive Grinding Process

[0010] Material removal is caused by the relative motion between the diamond abrasive grains and the workpiece. A single abrasive grain motion model is established, a single abrasive grain is randomly selected, and its trajectory is calculated. Assuming the workpiece surface is planar, the position of the abrasive grain on the z-axis at time point t is calculated based on its position and trajectory. If the z-axis position is less than or greater than the height of the workpiece plane, it indicates that the abrasive grain has interacted with the workpiece surface. In this case, the data is compared with the existing workpiece surface data, and new workpiece surface data is generated.

[0011] Step 3: Establish a surface morphology model of the workpiece after grinding.

[0012] The top surface of an abrasive grain typically contains multiple cutting edges, especially when the abrasive grains are non-uniform. However, during the material removal process, only a small fraction of the cutting edges are actually used for cutting. Therefore, the outermost contour projected onto the grinding normal direction of the abrasive grain is considered the effective cutting edge. To describe the motion of the abrasive grains and the cutting edge information, four coordinate transformation matrices are introduced: m1, m2, m3, and m4. m1 represents the initial point matrix of the effective cutting edge, i.e., the starting coordinates of the cutting edge; m2 considers the position of the abrasive grain on the outer circle of the grinding wheel and the influence of the grinding wheel rotation on the position of the effective cutting edge; m3 considers the influence of the axial position of the grinding wheel on the position of the effective cutting edge; and m4 considers the influence of the workpiece feed rate on the position of the effective cutting edge. Using the above coordinate transformation matrices and other parameters, the spatial position of each abrasive grain at time t is calculated. By combining the existing data of the workpiece surface and the position information of the abrasive grains, the surface morphology data of the workpiece after grinding is generated. For a given data point position (i, j), its corresponding x and y coordinates and the minimum value of the z-axis at that position are calculated.

[0013] Step 4: Considering strain rate effects on silicon carbide ceramic damage

[0014] Grinding silicon carbide ceramics involves complex interactions between abrasive grains and the workpiece material, a process that causes surface and subsurface damage, thus reducing the service life of silicon carbide ceramics. To better understand and predict this damage, a silicon carbide ceramic damage model considering strain rate effects was established. This model allows for more accurate evaluation and optimization of the grinding process of silicon carbide ceramics to extend their service life. During grinding, the material undergoes a brittle-plastic transition, which is related to the critical single-grain cutting thickness. If the single-grain cutting thickness is less than the critical value, the material is removed in a plastic form. If the single-grain cutting thickness exceeds the critical value, the material is removed in a brittle state. At this point, severe damage occurs to the workpiece surface and subsurface. This critical value is related to factors such as grinding speed and the cutting parameters of individual abrasive grains. Analysis and calculation based on relevant formulas help to better understand the changes in brittle and plastic behavior during grinding and to assess the impact of damage. Based on the assumptions of the indentation fracture model, transverse and longitudinal cracks appear below the workpiece surface during grinding. The form of material removal is affected by grinding speed, undeformed chip thickness, and material properties. To select a suitable material removal method, the critical undeformed chip thickness at the brittle-plastic transition is calculated to aid in the decision-making process.

[0015] 3. Compared with the prior art, the beneficial effects of this invention are: (i) Traditional grinding process models often neglect the influence of strain rate effect on the grinding process of silicon carbide ceramics. This invention, by introducing a mathematical model that considers the strain rate effect, more accurately describes the material behavior during the grinding process in simulation prediction, thereby improving the accuracy of morphology prediction; (ii) Through simulation technology, this invention can comprehensively and meticulously simulate the grinding process of silicon carbide ceramics. Simulation analysis can be performed under different process parameters and loading conditions, thus providing more comprehensive prediction results and increasing the reliability of prediction; (iii) Traditional experimental methods require a large amount of time and resources to evaluate the grinding behavior of materials and predict surface morphology, while this invention utilizes mathematical models and simulation technology to perform rapid simulations on computers, greatly saving costs and time; (iv) This invention provides a more accurate prediction tool for the optimization and control of grinding processes. By considering the strain rate effect, this model can be applied to the prediction of grinding processes for different materials, expanding the scope of application and helping to optimize process parameters, improve processing efficiency and quality; (v) The mathematical model and simulation technology provided by this invention provide new methods and tools for the research and development of grinding processes. A deeper understanding of the impact of strain rate on the grinding process can help improve the efficiency and precision of grinding technology and promote its development. Attached Figure Description

[0016] Figure 1 This is a simplified flowchart of a method for simulating the morphology and damage of silicon carbide ceramic grinding workpieces.

[0017] Figure 2 This is a three-dimensional schematic diagram of a single-layer grinding wheel with orderly arranged abrasive grains.

[0018] Figure 3 This is a flowchart of a method for simulating the morphology and damage of silicon carbide ceramic grinding workpieces.

[0019] Figure 4 It is a diagram of the motion trajectory of a single abrasive grain.

[0020] Figure 5 It is a surface morphology image of the workpiece after grinding. Detailed Implementation

[0021] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0022] according to Figure 1 The present invention is described in detail from four aspects: establishing a workpiece morphology model of a single-layer diamond grinding wheel with ordered abrasive grain arrangement, kinematic analysis of the diamond abrasive grinding process, establishing a workpiece surface morphology model after grinding, and considering the strain rate effect on silicon carbide ceramic damage.

[0023] Example 1: A method for simulating the morphology and damage of silicon carbide ceramic grinding workpieces considering strain rate effects, the specific implementation steps are as follows:

[0024] Step 1: Establish a surface morphology model of a single-layer diamond grinding wheel with ordered abrasive grain arrangement.

[0025] 1. Write a graphics drawing program to create a mesh on a 4*4mm workpiece plane (x=4, y=4) with a height of 0. Divide the plane into segments with a distance of dx between adjacent points, ensuring consistent x and y coordinate intervals and point spacing. 2. Draw a matrix of all points on the plane, creating a mesh along the x and y directions, with the z direction representing the height θ. Set the initial workpiece plane as the highest point. 3. Set the grinding wheel parameters (diameter, width, abrasive grain angle, etc.). Due to the linear arrangement of the abrasive grains, the angle between the abrasive grain angle and the grinding wheel circumference is set to α. The distance between two adjacent rows of abrasive grains on the grinding wheel circumference is Δx, and the distance between a row of abrasive grains distributed radially is Δz. 4. Set the abrasive grain diameter and grinding parameters. 5. Set the abrasive grain arrangement matrix, representing abrasive grains as various forms of truncated octahedrons. Irregular abrasive grain shapes are represented by random perturbations placed on the grinding wheel surface, their positions corresponding to the positions where each abrasive grain is generated on the upper wheel. Each perturbation is generated by a matrix containing multiple random parameters, as shown in the figure below:

[0026]

[0027] z(i,j)=min{z1(i,j)|z2(i,j)|z3(i,j)|z4(i,j)|z5(i,j)}

[0028] Where k1 is a random matrix in the x-direction, which helps to modify the height of the abrasive grain in the x-direction; k2 is a random matrix in the y-direction, which helps to adjust the height of the grain in the y-direction; m represents the number of grains; and r0 is the initial radius of the grain.

[0029] Based on the specific positional parameters of the abrasive grains on the grinding wheel surface, the theoretical positions of all abrasive grains dispersed on the grinding wheel surface are initially determined, resulting in a matrix of abrasive grain arrangement. Finally, a three-dimensional schematic diagram of a single-layer textured grinding wheel with ordered abrasive grain arrangement is obtained, as shown below. Figure 2 As shown, the flowchart is as follows Figure 3 .

[0030] Step 2: Kinematic Analysis of Diamond Abrasive Grinding Process

[0031] 1. Establish a single abrasive grain motion model. Randomly select a single abrasive grain and extract the projection data matrix of the cutting edge of the single abrasive grain in the grinding direction. Calculate the workpiece surface at each point on the cutting edge projection during the grinding process. The motion trajectory of a single abrasive grain during the grinding process is as follows: Figure 4 As shown, x and z are the instantaneous coordinates of the abrasive grain, θ is the angle traversed by the rotation of the grinding wheel, t is the time required for the abrasive grain to rotate from its lowest point O to θ, and v is the instantaneous coordinates of the abrasive grain. w h is the workpiece feed rate. g r is the height of the abrasive grain protruding from the surface of the grinding wheel. s Let be the radius of the grinding wheel. The grinding process mainly consists of two motions: the rotation of the grinding wheel and the feed motion of the workpiece. The trajectory of the abrasive can be represented as:

[0032] x = v w ·t+(r s +h g )·sinθ

[0033] z=(r s +h g )·(1-cosθ)

[0034] 2. To ensure material removal from the workpiece, first assume the working surface is a plane z0. Calculate the position of the abrasive grain on the z-axis at time point t, and the z-axis position at the previous time point. If the z-axis is less than the height of the workpiece plane, or if the z-axis is higher than the plane height but the previous point was less than the plane height, it indicates that the abrasive grain has interacted with the workpiece surface, and the calculation can continue. Otherwise, it indicates that the workpiece material cannot be cut at this point. In this case, compare the calculated data with the existing data on the workpiece surface, and regenerate new workpiece surface data.

[0035] Step 3: Establish a surface morphology model of the workpiece after grinding.

[0036] A surface morphology model of the workpiece after grinding is established, and the outermost contour projected along the grinding normal direction of the abrasive grains is used as the effective cutting edge. This method generates a two-dimensional array p, which depicts the effective cutting edge on the top surface of the grains. Then, four coordinate transformation matrices can characterize the spatial position of each abrasive grain at time t as follows:

[0037]

[0038] In the formula, m1 is the initial point matrix of the effective cutting edge, m2 considers the position of the abrasive grains on the outer circle of the grinding wheel and the influence of the grinding wheel rotation on the position of the effective cutting edge, m3 represents the influence of the axial position of the grinding wheel, m4 represents the influence of the workpiece feed rate on the position of the effective cutting edge, a is the angle between the initial position and the perpendicular direction of the grain, q represents the position of the grain diffusion along the grinding wheel axis, p2 represents the data in the y-direction of the two-dimensional array p, and p3 represents the data in the z-axis direction of the two-dimensional array p. The specific surface morphology of the workpiece after machining is as follows: Figure 5 During the grinding process, workpiece material located below the grain position is removed. Finally, the workpiece morphology can be mathematically described using the following formula:

[0039] n i，j = [x, y, min(z)]

[0040] Step 4: Considering strain rate effects on silicon carbide ceramic damage

[0041] Brittle materials undergo a brittle-plastic transition during grinding, a process related to the critical single-grain cutting thickness. If the single-grain cutting thickness is less than the critical thickness, the material is removed in a plastic form. If the single-grain cutting thickness exceeds the critical value, the material is removed in a brittle state, resulting in surface and subsurface damage and mid-diameter cracks. This value is related not only to the material but also to the grinding speed and the single-grain cutting thickness. The single-grain cutting thickness H can be calculated using the following formula:

[0042]

[0043] Note: Where θ is half of the abrasive grain tip angle, d e Where is the diameter of the grinding wheel, and K is the number of dynamic effective tips.

[0044] Based on the assumptions of the indentation fracture model, transverse and longitudinal cracks will appear beneath the workpiece surface. The material removal method is affected by grinding speed, undeformed chip thickness, and material properties. The critical undeformed chip thickness D for the brittle-plastic transition is given to aid in the selection of material removal methods; the specific formula is as follows:

[0045]

Claims

1. A method for simulating the workpiece topography and damage during grinding of silicon carbide ceramics considering strain rate effects, characterized in that The steps include the following: Step 1: Construct a polyhedral diamond abrasive model with randomized size and shape; Step 2: Construct a single-layer diamond grinding wheel model with ordered abrasive grain arrangement; Step 3: Construct the simulation trajectory of multi-abrasive particle cooperative motion; Step 4: Obtain the depth of cracks on the surface of the ceramic workpiece; Step 5: Obtain the discrete morphology of the ceramic workpiece surface; In step 1, the abrasive particles are constructed using polyhedra with random shapes. The polyhedral abrasive particle model is calculated using the following formula: z1(i,j)=k1(1,m)·[x(i)-x(m)]+k2(1,m)·[y(j)-y(m)]+r0 z2(i,j)=k1(2,m)·[x(i)-x(m)]+k2(2,m)·[y(j)-y(m)]+r0 z3(i,j)=k1(3,m)·[x(i)-x(m)]+k2(3,m)·[y(j)-y(m)]+r0 z4(i,j)=k1(4,m)·[x(i)-x(m)]+k2(4,m)·[y(j)-y(m)]+r0 z5(i,j)=k1(5,m)·[x(i)-x(m)]+k2(5,m)·[y(j)-y(m)]+r0 z(i,j)=min{z1(i,j)|z2(i,j)|z3(i,j)|z4(i,j)|z5(i,j)} Where k1 is a random matrix in the x-direction; k2 is a random matrix in the y-direction; m represents the number of grains; r0 is the initial radius of the grain, which follows a normal distribution with an expected value of μ and a standard deviation of σ. In step 3, the trajectory of the abrasive particles can be represented as: Where x and z are the instantaneous coordinates of the abrasive grain, θ is the angle traversed by the rotation of the grinding wheel, t is the time required for the abrasive grain to rotate from its lowest point O to θ, and v w h is the workpiece feed rate. g r is the height of the abrasive grain protruding from the surface of the grinding wheel. s Where is the radius of the grinding wheel; In step 3, the outermost contour projected by the abrasive along the grinding normal direction is taken as the effective cutting edge, represented by a two-dimensional matrix P. The spatial position of any point on the effective cutting edge of the abrasive grain at time t can be characterized by four coordinate transformation matrices: ； Where m1 is the initial point matrix of the effective cutting edge, m2 is the influence of the circumferential position and the rotation of the grinding wheel on the position of the effective cutting edge, m3 is the influence of the axial position of the grinding wheel, m4 is the influence of the workpiece feed rate on the position of the effective cutting edge, α is the angle between the initial position and the direction perpendicular to the grain, q is the position of the grain along the axial direction of the grinding wheel, p2 is the data of the two-dimensional array p in the y-axis direction, and p3 is the data of the two-dimensional array p in the z-axis direction. In step 4, the cutting thickness H of a single abrasive grain can be obtained using the formula... Calculate, where θ is half the abrasive grain tip angle, d e Where K is the grinding wheel diameter and K is the dynamic effective number of abrasive grains; the critical cutting thickness D of a single abrasive grain in the brittle-plastic transition zone of silicon carbide ceramic can be obtained by formula... Calculate, where E is the elastic modulus, Hv is the microhardness, and K is the microhardness. 1c For fracture toughness; the surface damage SD and subsurface damage SSD of silicon carbide ceramics can be calculated using the following formula: ； In the formula, e, r, g, and h are constant values.

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