Simulation method for mixed particle size CBN grinding wheel grinding surface morphology

Abstract

The invention relates to the technical field of metal processing, and discloses a simulation method for the grinding surface topography of a mixed-particle-size CBN (Cubic Boron Nitride) grinding wheel. Grinding wheel workpiece motion parameters and abrasive particle geometric parameters are set, a to-be-processed workpiece and a mixed particle size grinding wheel are simulated, and a trajectory equation of a certain abrasive particle under a global coordinate system is determined based on a workpiece surface analysis domain, the grinding wheel workpiece motion parameters and the abrasive particle geometric parameters; according to the trajectory equation, obtaining a trajectory scatter coordinate matrix of the mapping relation between the area where a certain abrasive particle is located and the workpiece surface, and mapping to obtain a minimum coordinate value; the track scatter coordinate matrixes corresponding to all the abrasive particles are mapped repeatedly, and the surface roughness of the workpiece is obtained based on all the coordinate minimum values; and the surface roughness of the workpiece is compared with the preset roughness, the geometrical parameters of the abrasive particles are adjusted based on the comparison result until the obtained surface roughness of the workpiece is smaller than the preset roughness, and the problem that the abrasive particle diameter ratio and the abrasive particle density ratio of an existing mixed particle size grinding wheel are unreasonable in design is solved.

Description

Technical Field

[0001] The invention relates to the technical field of metal processing, and in particular to a method for simulating surface topography of a mixed-grain-size CBN grinding wheel. Background Art

[0002] When grinding titanium microalloyed steel, traditional single-grain superabrasive grinding wheels are prone to abrasive grain passivation, breakage, and even shedding due to uneven grinding stress distribution, seriously affecting the dressing frequency and grinding efficiency of the grinding wheel. Using fine-grain abrasive grinding wheels can produce high-quality surfaces, but the abrasive wears quickly and the grinding wheel requires frequent dressing, resulting in low processing efficiency. Using coarse-grain diamond grinding wheels can increase material removal rates, but the surface uniformity of the abrasive grains on coarse-grain grinding wheels is poor, resulting in poor surface quality of the workpiece, which cannot meet the high surface quality requirements of high-performance devices.

[0003] The existing conventional treatment method is to use the complementary advantages of abrasives of different particle sizes to improve grinding efficiency and processing accuracy. However, based on this, when designing mixed-grain grinding wheels, the effects on workpiece grinding are completely different under the conditions of different abrasive particle size ratios and abrasive density ratios on the surface. Unreasonable abrasive particle size ratios and abrasive density ratios cannot effectively complete the predetermined target workpiece, resulting in unnecessary workpiece loss and energy consumption. Summary of the Invention

[0004] The invention provides a method for simulating the surface topography of a mixed-grain CBN grinding wheel grinding, so as to solve the problem that the abrasive grain size ratio and abrasive grain density ratio of the existing mixed-grain grinding wheel are not designed rationally.

[0005] In order to achieve the above object, the present invention is implemented through the following technical solutions: The present invention provides a method for simulating the surface topography of a mixed-grain-size CBN grinding wheel, comprising the following steps: Step 1: Set the grinding wheel workpiece motion parameters and abrasive geometric parameters, simulate the workpiece to be processed and the mixed-grain grinding wheel composed of coarse-grained and fine-grained abrasives, and obtain the workpiece surface analysis domain. Based on the workpiece surface analysis domain, the grinding wheel workpiece motion parameters, and the abrasive geometric parameters, determine the trajectory equation of an abrasive grain on the mixed-grain grinding wheel surface in the global coordinate system; When simulating a mixed-grain grinding wheel composed of coarse-grained and fine-grained abrasives, the following constraint is included: the distance between the centers of any two abrasive grains is greater than the sum of the radii of the mixed abrasive grains, which is expressed by the following formula: ; in, represents the distance between any two abrasive grain centers; represents the abrasive grain among any two abrasive grains , represents the abrasive grain among any two abrasive grains , The value range is 1 to ; represents the average diameter of coarse-grained abrasive particles, Indicates the average diameter of fine-grained abrasive particles; Specifically, the mixed-size abrasive distribution simultaneously satisfies the following two key conditions: (1) abrasives of different sizes do not interfere with each other in three-dimensional space; and (2) each abrasive can effectively participate in the grinding process. This controllable abrasive arrangement not only avoids the failure of fine-grained abrasives due to coverage, but also improves the overall grinding performance of the grinding wheel.

[0006] Step 2: Obtain a trajectory scatter point coordinate matrix about the mapping relationship between the area where a certain abrasive grain is located on the surface of the mixed-grain grinding wheel and the workpiece surface according to the trajectory equation described in step 1, map the trajectory scatter point coordinate matrix to the workpiece surface analysis domain, and save the lowest coordinate value therein; Step 3: Repeat steps 1 to 2 to map the trajectory scatter coordinate matrix corresponding to all mixed-size grinding wheel surface abrasive grains, and obtain the workpiece surface roughness based on the lowest value of all coordinates; Step 4: Compare the surface roughness of the workpiece with the preset roughness, and adjust the abrasive geometric parameters based on the comparison result until the obtained surface roughness of the workpiece is less than the preset roughness.

[0007] The geometric parameters of the abrasive particles in step 1 and step 4 are the size ratio, density ratio and cutting edge height of the coarse-grained abrasive particles to the fine-grained abrasive particles.

[0008] The above design effectively avoids the problem of abrasive grain overlap failure caused by grain size differences in mixed-grain grinding wheels. By precisely controlling the spatial distribution of the abrasive grains, it is ensured that fine-grained abrasive grains are not completely covered by coarse-grained abrasive grains and thus fail, thereby fully utilizing the synergistic grinding effect of the mixed-grained abrasive grains. The mixed-grained abrasive grains are randomly and evenly arranged on the grinding wheel surface until the specified number of mixed-grained abrasive grains are distributed within a unit area without interfering with each other. This method provides a simulation-based theoretical basis for optimizing the abrasive ratio coefficient of mixed-grain grinding wheels, helping to establish the correlation between grinding process parameters, grinding wheel geometry, and workpiece topography evolution. It transforms traditional empirical trial-and-error grinding wheel design into a precise optimization model based on quantitative indicators. This effectively reduces the experimental trial-and-error costs of mixed-grain grinding wheel abrasive ratio design while providing a reliable mixed-grain grinding wheel processing solution to meet processing needs.

[0009] Furthermore, when executing step 4, the theoretical removal volume of the workpiece surface is calculated based on the lowest values ​​of all saved coordinates, and the material removal efficiency is calculated with the simulated residual volume of the workpiece, and the distribution density ratio of coarse-grained abrasive particles to fine-grained abrasive particles is adjusted according to the material removal efficiency until the material removal efficiency reaches the preset material removal preset value.

[0010] The above design calculates the difference between the theoretical volume of the workpiece after grinding and the residual volume of the simulated workpiece topography, and thus determines the material removal efficiency of the mixed-grit grinding wheel under single-feed conditions. This establishes a quantifiable evaluation benchmark for the machining efficiency of mixed-grit grinding wheels based on material removal efficiency, providing a scientific basis for optimizing the abrasive size ratio parameters used in mixed-grit grinding wheels.

[0011] Furthermore, when simulating a mixed-grain grinding wheel composed of coarse-grained abrasive particles and fine-grained abrasive particles, random shapes of the coarse-grained abrasive particles and the fine-grained abrasive particles are set; The shapes include triangles, quadrilaterals, pentagons, and hexagons.

[0012] Furthermore, when simulating a mixed-grain grinding wheel composed of coarse-grained and fine-grained abrasive particles, a cutting-edge height threshold is set to simulate the surface morphology of the grinding wheel after laser dressing, and the tops of the coarse-grained and fine-grained abrasive particles are intercepted; The setting of the edge height threshold is based on the grinding wheel bond plane and includes the following constraints: ; in, Indicates the set blade height threshold.

[0013] The above design, by introducing the shape difference of abrasive particles, breaks through the limitations of traditional circular or spherical abrasive particle models and more accurately restores the irregular geometric characteristics of actual abrasive particles. By using the set abrasive particle edge height threshold, the mixed-size abrasive particles are processed in a uniform manner, so that as many abrasive particles as possible can be used in the collaborative cutting process, increasing the number of effective abrasive particles per unit area. It ensures that the abrasive clusters are naturally distributed in shape, which is more consistent with the cutting edge characteristics of actual abrasive particles, and is conducive to accurately simulating the material removal mechanism in the grinding process. It effectively improves the degree of fit between the simulated grinding wheel morphology and the actual grinding wheel, laying a reliable geometric foundation for the subsequent accurate simulation of grinding performance.

[0014] Furthermore, the trajectory equation of the abrasive particle in the global coordinate system is obtained by the following steps: A local coordinate system is constructed based on the motion parameters of the grinding wheel workpiece and the geometric parameters of the abrasive particles, and the trajectory equation corresponding to the abrasive particles is obtained based on the local coordinate system. The trajectory equation in the global coordinate system is obtained according to the trajectory equation in the local coordinate system. The construction of the trajectory equation in the local coordinate system specifically includes: constructing the trajectory equation of the circular and translational motion of any abrasive particle on the grinding wheel over time in the local coordinate system based on the grinding wheel workpiece motion parameters and the abrasive particle geometric parameters.

[0015] Through this design, the grinding process of a mixed-grain grinding wheel can be viewed as a superposition of the wheel's rotational motion and the workpiece's feed motion. The cutting paths of the two abrasive grains interfere with each other, and the grooves left by the fine-grained abrasive during grinding may be covered by the coarse-grained abrasive within the same feed path. Therefore, constructing the motion paths of mixed-grained abrasive grains facilitates the precise characterization of the multi-grain synergistic grinding mechanism unique to mixed-grain grinding wheels.

[0016] Furthermore, the trajectory scatter coordinate matrix is ​​obtained by substituting the grinding wheel workpiece motion parameters and the abrasive geometric parameters into the trajectory equation to obtain the trajectory scatter coordinate matrix of the mapping relationship between the area where any abrasive grain is located on the surface of the mixed-grain grinding wheel and the workpiece surface.

[0017] The above design introduces grinding wheel workpiece motion parameters and abrasive geometric parameters to effectively characterize the differences in the motion characteristics of abrasives of different grit sizes during the cutting process. By considering the circumferential distribution characteristics of mixed-size abrasives on the grinding wheel, a functional relationship between "abrasive ratio, circumferential spacing, and surface profile" is established, significantly improving the prediction accuracy of workpiece surface topography.

[0018] Furthermore, the method of obtaining the surface roughness of the workpiece based on all the minimum coordinate values ​​includes: constructing and saving the minimum coordinate values ​​corresponding to all abrasive particles into an analysis domain coordinate matrix, forming workpiece surface morphology data based on the analysis domain coordinate matrix, and obtaining the surface roughness of the workpiece according to the workpiece surface morphology data.

[0019] This design allows for the acquisition of workpiece surface topography data that reflects the microscopic topography of the workpiece surface and the material removal mechanism of mixed-grain abrasives, illuminating the inherent connection between abrasive distribution characteristics and the evolution of cutting marks on the workpiece surface. Based on the acquired surface roughness values ​​and material removal efficiency, a quantitative correlation between the dual objectives of "machining efficiency and surface quality" for mixed-grain grinding wheels has been achieved for the first time.

[0020] Furthermore, the grinding wheel workpiece motion parameters include grinding depth, grinding wheel linear speed and workpiece feed speed; The abrasive particle geometric parameters include abrasive particle shape, abrasive particle size ratio, abrasive particle density ratio and abrasive particle edge height.

[0021] Through the above design, various parameters in the grinding process are systematically set to ensure that the contact state between the abrasive and the workpiece during the simulation process is highly consistent with the actual processing conditions at the grinding mechanism level, thereby more accurately simulating the differentiated cutting behavior of mixed-grain grinding wheels caused by different abrasive geometric parameters. The obtained simulation results can directly guide the regulation and optimization of key ratio parameters in the preparation of mixed-grain grinding wheels.

[0022] Furthermore, the mixed-grain size grinding wheel is evaluated by calculating the peak value of the workpiece surface protrusion, the peak value of the workpiece groove width, and the root mean square value of the height difference based on all the lowest values ​​of the coordinates in step 3; The peak value of the workpiece surface protrusion, the peak value of the workpiece groove width and the root mean square value of the height difference are all evaluated based on a preset threshold value; When the peak value of the protrusion on the workpiece surface exceeds the corresponding preset threshold, adjusting the abrasive particle size ratio or density ratio; When the peak value of the workpiece surface protrusion exceeds the corresponding preset threshold, it means that the abrasive distribution on the grinding wheel surface is too discrete, resulting in uneven removal of workpiece material. The number of fine-grained abrasive grains should be increased or the size of coarse-grained abrasive grains should be reduced to improve the grinding wheel's ability to refine the workpiece surface. When the peak value of the workpiece groove width exceeds the corresponding preset threshold, adjusting the height of the abrasive grains; When the peak value of the workpiece groove width exceeds the preset mean value of the workpiece surface profile, it means that the abrasive edge height is too low, resulting in an increase in the size of the residual grooves formed by grinding. The abrasive edge height should be appropriately increased to reduce the groove width on the workpiece surface. When the root mean square value of the height difference exceeds the corresponding preset threshold, the height of the abrasive particles out of the edge is adjusted.

[0023] When the RMS value of the height difference is greater than the preset value, it means that the workpiece surface has large-scale grinding marks locally and the profile uniformity is worse. The abrasive height should be appropriately reduced to improve the profile flatness of the workpiece surface and increase the material removal efficiency. Through this design, the comprehensive grinding performance of the mixed-grain grinding wheel was evaluated by quantitatively analyzing indicators such as the peak value of the workpiece surface protrusion, the peak value of the workpiece groove width, and the root mean square value of the height difference, combined with the grinding wheel geometry and workpiece surface topography. This study explored the influence of the uniform distribution of mixed-grain abrasives on the workpiece surface topography, summarized the mathematical relationship between the synergistic grinding mechanism of mixed-grain abrasives and surface quality, and established a mathematical relationship between the grinding wheel workpiece motion parameters / abrasive geometry parameters and the ground surface roughness value.

[0024] Beneficial effects: This paper provides a method for simulating surface topography after grinding with a mixed-grain CBN grinding wheel. This method simulates the trajectory equations obtained by simulating the grinding wheel workpiece motion parameters and the abrasive grain geometry. The trajectory equations are then used to map the motion trajectories of the mixed abrasive grains, ultimately yielding simulated results for the workpiece surface profile. This method accurately characterizes the workpiece topography after grinding with the mixed-grain CBN grinding wheel. By adjusting variable parameters, the method explores the impact of the complementary advantages of different grain sizes on machined surface quality and efficiency, providing a theoretical basis for optimizing the mixed-grain grinding wheel process.

[0025] For the first time, the geometric characteristics of mixed-grit grinding wheels were quantified using abrasive ratio coefficients such as grain size ratio, density ratio, and grain height at the edge. Compared to grinding wheels with uniform single-grit abrasives, the inherent correlation between the abrasive ratio parameters, grinding parameters, workpiece material removal, and surface creation mechanisms of mixed-grit grinding wheels was established. This allows for flexible adjustment of mixed-grit grinding wheel processing strategies based on the characteristics of actual grinding conditions and processing requirements. This overcomes the problem that the design of abrasive size ratios and abrasive density ratios for mixed-grit grinding wheels can only be determined through extremely costly trial-and-error methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 This is a flow chart of a method for simulating surface topography grinding by a mixed-grain-size CBN grinding wheel according to an embodiment of the present invention; Figure 2 Schematic diagram of the workpiece morphology of the mixed-grain grinding wheel under the abrasive grain ratio of 0.4 and 0.56 according to an embodiment of the present invention; Figure 3 Schematic diagram of the workpiece morphology of the mixed-grain grinding wheel under the abrasive grain ratio of 0.67 and 0.8 according to an embodiment of the present invention; Figure 4 Schematic diagram of the workpiece morphology of the mixed-grain grinding wheel at abrasive density ratios of 0.5 and 1 according to an embodiment of the present invention; Figure 5 Schematic diagram of the workpiece morphology of the mixed-grain grinding wheel at abrasive density ratios of 1.5 and 2 according to an embodiment of the present invention. DETAILED DESCRIPTION

[0027] The following is a clear and complete description of the technical solutions of the present invention. It should be understood that the embodiments described are only a portion of the embodiments of the present invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0028] Unless otherwise defined, the technical or scientific terms used in the present invention shall have the usual meanings understood by persons of ordinary skill in the field to which the present invention belongs. The words "first", "second" and similar terms used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Similarly, words such as "one" or "a" do not indicate a quantity limitation, but rather indicate the existence of at least one. Words such as "connected" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship also changes accordingly.

[0029] See Figure 1 The embodiment of the present application provides a method for simulating the surface topography of a mixed-grain-size CBN grinding wheel, comprising the following steps: Step 1: Set the grinding wheel workpiece motion parameters and abrasive geometric parameters, simulate the workpiece to be processed and the mixed-grain grinding wheel composed of coarse-grained and fine-grained abrasives, and obtain the workpiece surface analysis domain. Based on the workpiece surface analysis domain, the grinding wheel workpiece motion parameters, and the abrasive geometric parameters, determine the trajectory equation of an abrasive grain on the mixed-grain grinding wheel surface in the global coordinate system; The geometric parameters of abrasive particles include particle shape, particle size ratio, particle density ratio and particle height.

[0030] Among them, the abrasive particle size ratio is It is expressed by the following formula: ; in, represents the average diameter of fine-grained abrasive particles, Indicates the average diameter of coarse-grained abrasive particles; Abrasive density ratio It is expressed by the following formula: ; in, represents the density of fine-grained abrasive particles, Indicates the density of coarse-grained abrasive particles; Specifically, based on the total volume of the abrasive layer Total volume of abrasive particles and the total volume distribution coefficient of the abrasive layer , we can get the following formula: ; Based on this formula, combined with the average volume of coarse-grained abrasive particles , the average volume of fine-grained abrasive particles The derived formula for the number of two-size abrasive particles can be further expressed as the ratio of abrasive particle density. The specific formula is as follows: ; ; in, Indicates the number of coarse-grained abrasive particles, Indicates the number of fine-grained abrasive particles, Indicates the unit volume of mixed-grain grinding wheel, represents the abrasive volume distribution coefficient; Abrasive edge height It means that when setting the height of the abrasive grains, the grinding wheel bond plane is used as a reference to simulate the surface morphology of the grinding wheel after laser dressing, and the tops of the coarse-grained abrasive grains and fine-grained abrasive grains are intercepted; And includes the following constraints: ; Regarding the shape of the abrasive grains, the coarse-grained abrasive grains and the fine-grained abrasive grains are set to random shapes, including triangles, quadrilaterals, pentagons and hexagons.

[0031] When simulating a mixed-grain grinding wheel composed of coarse-grained and fine-grained abrasives, the following constraint is included: the distance between the centers of any two abrasive grains is greater than the sum of the radii of the mixed abrasive grains, which is expressed by the following formula: ; in, represents the distance between any two abrasive grain centers; represents the abrasive grain among any two abrasive grains , represents the abrasive grain among any two abrasive grains , The value range is 1 to ; represents the average diameter of coarse-grained abrasive particles, Indicates the average diameter of fine-grained abrasive particles.

[0032] Grinding wheel workpiece motion parameters include grinding depth, grinding wheel linear speed and workpiece feed speed; The trajectory equation of a certain abrasive particle in the global coordinate system is obtained by the following steps: A local coordinate system is constructed based on the motion parameters of the grinding wheel workpiece and the geometric parameters of the abrasive particles, and the trajectory equation corresponding to the abrasive particles is obtained based on the local coordinate system. The trajectory equation in the global coordinate system is obtained according to the trajectory equation in the local coordinate system. The construction of the trajectory equation in the local coordinate system specifically includes: constructing the trajectory equation of the circular motion of any abrasive particle on the grinding wheel over time in the local coordinate system based on the grinding wheel workpiece motion parameters and the abrasive particle geometric parameters, which is expressed by the following formula: ; in, Indicates any point on the grinding wheel surface Towards coordinates, Indicates any point on the grinding wheel surface Towards coordinates, Indicates the cutting time of the abrasive, Indicates the rotation angle of the grinding wheel per unit time, Indicates the workpiece feed speed, Indicates the linear speed of the grinding wheel. It represents the rotating cutting radius of the abrasive, which is the sum of the radius of the grinding wheel base and the height of the two abrasives on the grinding wheel surface.

[0033] Since the angle of the cutting edge from cutting in to cutting out is very small, there is , so the above formula can be expressed as: ; The contact area between the abrasive and the workpiece is integrated along the cutting direction. Here, the formula for the workpiece material removal volume of a single abrasive particle can be obtained: ; in, and Represent the contact cross-sectional area between abrasive particles of different sizes and the workpiece, is the contact arc length between the abrasive and the workpiece.

[0034] The simulated workpiece in the model is machined using the same process parameters as the target workpiece in actual machining, ensuring that the simulation results accurately reflect the surface topography of the workpiece under real-world machining conditions. Through multi-parameter coupled analysis, the model accurately predicts surface profile characteristics under different abrasive ratios. This model systematically evaluates the impact of different parameter combinations on machining quality, avoiding the limitations of single-variable analysis and significantly reducing R&D costs.

[0035] Step 2: According to the trajectory equation of step 1, obtain the trajectory scatter point coordinate matrix of the mapping relationship between the area where a certain abrasive grain is located on the surface of the mixed-grain grinding wheel and the workpiece surface, map the trajectory scatter point coordinate matrix to the workpiece surface analysis domain, and save the lowest coordinate value; The trajectory scatter coordinate matrix is ​​obtained by substituting the grinding wheel workpiece motion parameters and the abrasive grain geometric parameters into the trajectory equation to obtain the trajectory scatter coordinate matrix of the mapping relationship between the area where any abrasive grain is located on the surface of the mixed-grain grinding wheel and the workpiece surface; Create a mixed grit grinding wheel surface area Any area on the workpiece surface The trajectory scatter coordinate matrix can be expressed by the following formula: ; in, Indicates the surface area of ​​the workpiece The trajectory scatter coordinate matrix, Indicates that the origin of the local coordinate system of the corresponding wear particle and the origin of the global coordinate system are The offset distance in the direction is the difference between the average edge height of the two abrasives on the grinding wheel surface and the grinding depth. Indicates that the local coordinate origin of the trajectory of any cutting point on the grinding wheel to the origin of the global coordinate system is The distance along the axis.

[0036] After mapping the trajectory scatter coordinate matrix and retaining the coordinate value of the lowest point, it can be expressed as: ; in, Represents the analysis domain coordinate matrix that stores the coordinate values ​​of the lowest points.

[0037] Step 3: Repeat steps 1 to 2 to map the trajectory scatter coordinate matrix corresponding to all mixed-size grinding wheel surface abrasive grains, and obtain the workpiece surface roughness based on the lowest value of all coordinates; The lowest coordinate values ​​corresponding to all abrasive particles are constructed and saved in the analysis domain coordinate matrix. The workpiece surface topography data is formed based on the analysis domain coordinate matrix. The workpiece surface roughness is obtained according to the workpiece surface topography data. The workpiece surface roughness is calculated using the following formula: ; In other embodiments, the mixed-grain size grinding wheel may be evaluated by calculating the peak value of the workpiece surface protrusion, the peak value of the workpiece groove width, and the root mean square value of the height difference based on all the lowest values ​​of the coordinates.

[0038] Specifically, when the peak value of the workpiece surface protrusion exceeds the corresponding preset threshold, it means that the abrasive distribution on the grinding wheel surface is too discrete, resulting in uneven removal of workpiece material. The number of fine-grained abrasive grains should be increased or the size of coarse-grained abrasive grains should be reduced to improve the grinding wheel's ability to refine the workpiece surface. When the peak value of the workpiece groove width exceeds the preset mean value of the workpiece surface profile, it means that the abrasive edge height is too low, resulting in an increase in the size of the residual grooves formed by grinding. The abrasive edge height should be appropriately increased to reduce the groove width on the workpiece surface. When the root mean square value of the height difference is greater than the preset value, it means that the workpiece surface locally presents large-scale grinding marks and the contour uniformity is worse. The abrasive height should be appropriately reduced to improve the contour flatness of the workpiece surface and increase the material removal efficiency.

[0039] Step 4: Compare the surface roughness of the workpiece with the preset roughness, and adjust the abrasive geometric parameters based on the comparison result until the obtained surface roughness of the workpiece is less than the preset roughness.

[0040] Specifically, the size ratio of the coarse-grained abrasive particles to the fine-grained abrasive particles is adjusted based on the comparison result between the surface roughness and the preset roughness, until the obtained surface roughness of the workpiece is less than the preset roughness.

[0041] When executing step 4, the theoretical removal volume of the workpiece surface is calculated based on the lowest value of all saved coordinates, and the material removal efficiency is calculated with the simulated residual volume of the workpiece. The distribution density ratio of coarse-grained abrasive particles to fine-grained abrasive particles is adjusted according to the material removal efficiency until the material removal efficiency reaches the preset material removal preset value.

[0042] The volume of the workpiece removed in a single feed is expressed by the following formula: ; in, Indicates the volume removed by a single feed of the workpiece. and represents the distribution function of the two abrasives on the surface of the mixed-grain grinding wheel, represents the overlap coefficient of mixed-size abrasive particles in the cross section, Indicates the unit area of ​​the mixed grain size grinding wheel surface.

[0043] Multiple sets of parameters are selected to predict the grinding results of mixed-grain wheel, which provides a basis for the optimization of mixed-grain abrasive ratio coefficients such as abrasive grain size ratio and abrasive density ratio and the control of surface quality. The specific process parameter group settings are shown in Table 1. Table 1: Grinding parameters under different abrasive particle size ratios

[0044] The appropriate size ratio between mixed-size abrasive particles ensures sufficient mixed abrasive particles per unit area to participate in the grinding process. To ensure that the simulation conditions are highly consistent with the actual grinding process, the theoretical grinding depth was set to 20 μm, the grinding wheel linear speed was set to 30 m / s, and the workpiece feed speed was set to 8 mm / s. This provides a basis for optimizing the design parameters of the mixed-size grinding wheel.

[0045] See Figure 2-5 Under the conditions of different abrasive particle size ratios (0.4, 0.56, 0.67, 0.8) and different abrasive density ratios (0.5, 1, 1.5, 2), the grinding simulation was combined with other conditions in Table 1 to obtain the workpiece surface morphology. It can be seen that when reciprocating grinding with a mixed-grain wheel is performed under specific feed parameter conditions, the surface morphology characteristics of the workpiece can reflect the rationality of the abrasive particle size ratio: (1) When the workpiece surface shows non-uniformly distributed large-scale protrusions and grooves, it indicates that the current mixed abrasive particle size ratio cannot meet the processing requirements. This phenomenon is due to the insufficient participation of fine-grained abrasive particles, resulting in uneven material removal. In this case, the particle size ratio should be appropriately increased or the density ratio should be reduced to enhance the fine-grained abrasive's effect on the refinement of the grinding marks on the workpiece surface.

[0046] (2) If the workpiece surface presents a uniform and dense grinding texture, but the cumulative material removal volume is significantly lower than the theoretical workpiece removal volume, it means that the proportion of coarse-grained abrasive particles is too low. In this case, although the surface quality is good, the material removal efficiency is insufficient. In this case, the particle size ratio should be appropriately reduced or the density ratio should be increased to achieve a balanced optimization of processing efficiency and surface quality.

[0047] The grinding simulation results of the above particle size ratio and density ratio are compared with the actual results, see Table 2 and Table 3; Table 2: Simulation results of mixed-grain wheel grinding

[0048] Table 3: Actual grinding results of mixed grit grinding wheels

[0049] Note: The peak value of protrusion in the table is the peak value of protrusion on the workpiece surface, and the peak value of width in the table is the peak value of groove width of the workpiece.

[0050] As can be seen from the above, the two change trends are exactly the same. The maximum relative error of surface roughness is 24.22%, and the minimum relative error is 0.53%. The maximum relative error of the peak value of the workpiece surface protrusion is 56%, and the minimum relative error is 37.83%. The maximum relative error of the peak value of the workpiece groove width is 50%, and the minimum relative error is 42.5%. Therefore, the simulation method constructed by the present invention has a high accuracy in predicting the results of workpiece grinding surface.

[0051] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A method for simulating surface topography of mixed-grain CBN grinding wheels, characterized in that: The steps include: Step 1: Set the grinding wheel workpiece motion parameters and abrasive geometric parameters, simulate the workpiece to be processed and the mixed-grain grinding wheel composed of coarse-grained and fine-grained abrasives, and obtain the workpiece surface analysis domain. Based on the workpiece surface analysis domain, the grinding wheel workpiece motion parameters, and the abrasive geometric parameters, determine the trajectory equation of an abrasive grain on the mixed-grain grinding wheel surface in the global coordinate system; When simulating a mixed-grain grinding wheel composed of coarse-grained and fine-grained abrasives, the following constraint is included: the distance between the centers of any two abrasive grains is greater than the sum of the radii of the mixed abrasive grains, which is expressed by the following formula: ； in, represents the distance between any two abrasive grain centers; represents the abrasive grain among any two abrasive grains , represents the abrasive grain among any two abrasive grains , The value range is 1 to ; represents the average diameter of coarse-grained abrasive particles, Indicates the average diameter of fine-grained abrasive particles; Step 2: Obtain a trajectory scatter point coordinate matrix about the mapping relationship between the area where a certain abrasive grain is located on the surface of the mixed-grain grinding wheel and the workpiece surface according to the trajectory equation described in step 1, map the trajectory scatter point coordinate matrix to the workpiece surface analysis domain, and save the lowest coordinate value therein; Step 3: Repeat steps 1 to 2 to map the trajectory scatter coordinate matrix corresponding to all mixed-size grinding wheel surface abrasive grains, and obtain the workpiece surface roughness based on the lowest value of all coordinates; Step 4: Compare the surface roughness of the workpiece with the preset roughness, and adjust the abrasive geometric parameters based on the comparison result until the obtained surface roughness of the workpiece is less than the preset roughness.

2. The method for simulating the surface topography of a mixed-grain-size CBN grinding wheel according to claim 1, characterized in that: When executing step 4, the theoretical removal volume of the workpiece surface is calculated based on the lowest value of all saved coordinates, and the material removal efficiency is calculated with the simulated residual volume of the workpiece. The distribution density ratio of coarse-grained abrasive particles to fine-grained abrasive particles is adjusted according to the material removal efficiency until the material removal efficiency reaches the preset material removal preset value.

3. The method for simulating the surface topography of a mixed-grain-size CBN grinding wheel according to claim 1, wherein: When simulating a mixed-grain grinding wheel composed of coarse-grained abrasive particles and fine-grained abrasive particles, the coarse-grained abrasive particles and the fine-grained abrasive particles are randomly shaped. The shapes include triangles, quadrilaterals, pentagons, and hexagons.

4. The method for simulating surface topography of mixed-grain-size CBN grinding wheels according to claim 1, characterized in that: When simulating a mixed-grain grinding wheel composed of coarse-grained and fine-grained abrasive particles, the edge height threshold is set to simulate the surface morphology of the grinding wheel after laser dressing, and the tops of the coarse-grained and fine-grained abrasive particles are intercepted. The setting of the edge height threshold is based on the grinding wheel bond plane and includes the following constraints: ； in, Indicates the set blade height threshold.

5. The method for simulating surface topography of mixed-grain-size CBN grinding wheels according to claim 1, characterized in that: The trajectory equation of the abrasive particle in the global coordinate system is obtained by the following steps: A local coordinate system is constructed based on the motion parameters of the grinding wheel workpiece and the geometric parameters of the abrasive particles, and the trajectory equation corresponding to the abrasive particles is obtained based on the local coordinate system. The trajectory equation in the global coordinate system is obtained according to the trajectory equation in the local coordinate system. The construction of the trajectory equation in the local coordinate system specifically includes: constructing a trajectory equation of the circular motion of any abrasive particle on the grinding wheel over time in the local coordinate system based on the grinding wheel workpiece motion parameters and the abrasive particle geometric parameters.

6. The method for simulating surface topography of mixed-grain-size CBN grinding wheels according to claim 1, characterized in that: The trajectory scatter point coordinate matrix is ​​obtained by substituting the grinding wheel workpiece motion parameters and the abrasive geometric parameters into the trajectory equation to obtain the trajectory scatter point coordinate matrix of the mapping relationship between the area where any abrasive grain is located on the surface of the mixed-grain grinding wheel and the workpiece surface.

7. The method for simulating surface topography of mixed-grain-size CBN grinding wheels according to claim 1, characterized in that: The method of obtaining the workpiece surface roughness based on all the minimum coordinate values ​​includes: constructing and saving the minimum coordinate values ​​corresponding to all abrasive particles into an analysis domain coordinate matrix, forming workpiece surface topography data based on the analysis domain coordinate matrix, and obtaining the workpiece surface roughness according to the workpiece surface topography data.

8. The method for simulating surface topography of mixed-grain-size CBN grinding wheels according to any one of claims 1 to 7, characterized in that: The grinding wheel workpiece motion parameters include grinding depth, grinding wheel linear speed and workpiece feed speed; The abrasive particle geometric parameters include abrasive particle shape, abrasive particle size ratio, abrasive particle density ratio and abrasive particle edge height.

9. The method for simulating the surface topography of a mixed-grain-size CBN grinding wheel according to claim 8, characterized in that: Based on the lowest values ​​of all coordinates in step 3, the peak value of the workpiece surface protrusion, the peak value of the workpiece groove width, and the root mean square value of the height difference are calculated to evaluate the mixed-grain size grinding wheel; The peak value of the workpiece surface protrusion, the peak value of the workpiece groove width and the root mean square value of the height difference are all evaluated based on a preset threshold value; When the peak value of the protrusion on the workpiece surface exceeds the corresponding preset threshold, adjusting the abrasive particle size ratio or density ratio; When the peak value of the workpiece groove width exceeds the corresponding preset threshold, adjusting the height of the abrasive grains; When the root mean square value of the height difference exceeds the corresponding preset threshold, the height of the abrasive particles out of the edge is adjusted.

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