A modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by small grinding heads

Abstract

This invention relates to a modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head, belonging to the field of optical manufacturing technology. The method includes the following steps: Step i: analyzing the pressure distribution between the grinding disc and the workpiece; Step ii: calculating the abrasive penetration depth based on the maximum pressure distribution value; Step iii: establishing a physical model of surface roughness by combining the abrasive's trajectory length and penetration depth. This method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head is not limited to predicting the roughness of silicon-modified silicon carbide materials polished by robotic small grinding heads, but is also applicable to predicting the roughness of metals or hard and brittle materials processed by other CNC machine tools and other equipment, and guiding actual processing.

Description

Technical Field

[0001] This invention relates to the field of optical manufacturing technology, and in particular to a modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by small grinding heads. Background Technology

[0002] With the continuous advancement of science and technology, space application technology and laser technology are developing rapidly, placing higher demands on the performance of optical systems. As a core component of the system, the surface roughness of optical elements, a key indicator of processing quality, has become particularly important. Various hard and brittle materials used in manufacturing optical elements, such as optical glass, silicon carbide, microcrystalline glass, and single-crystal silicon, often experience brittle removal during polishing, leading to a decrease in surface quality and poor roughness. Therefore, elucidating the evolution of surface roughness during processing, establishing a physical model of roughness, and improving the surface roughness after processing are crucial.

[0003] In mirror polishing, the surface roughness of the workpiece is one of the key indicators for measuring machining quality. Accurately predicting the surface roughness of the workpiece is of great significance for improving manufacturing efficiency and product quality. Surface roughness is affected by many factors; by constructing a surface roughness model, surface roughness can be predicted, thereby controlling machining quality.

[0004] Currently, surface roughness modeling methods are mainly divided into empirical parameter modeling methods, theoretical modeling methods, and artificial intelligence methods. Empirical parameter modeling methods utilize multiple regression, empirical formulas, and various data mining techniques, followed by analysis of large amounts of experimental data, to determine model coefficients and establish a functional relationship between machining parameters and surface roughness. Artificial intelligence methods are based on data signal acquisition and processing; therefore, the accuracy of the acquired data signals and the processing methods both affect the model's prediction accuracy. Model accuracy depends on the training sample data; when the experimental data is within the sample range, the error between the predicted and experimental values ​​is small, and vice versa. Support vector machines, similar to neural networks, require a large amount of dense data obtained from experiments to support the prediction model and make the prediction results more accurate. Artificial neural networks can continuously change the connection weights and topology of the network, making the network output gradually approach the desired output to establish an accurate surface roughness prediction model. Theoretical modeling methods construct surface roughness models by analyzing the surface forming mechanism during different machining processes, studying the influence of tool geometry, process parameters, and other factors affecting the surface roughness of the machined surface on surface formation, and calculating the surface roughness value after machining.

[0005] All three methods have their shortcomings: empirical parameter modeling and artificial intelligence methods do not consider the material removal mechanism, rely on experimental sample data, and the model accuracy will only be continuously improved after training with a large amount of sample data. They are overly dependent on processing conditions and equipment, lack universal applicability, and lack a description of the essence of the processing process. The theoretical modeling method lacks analysis of the physical model of surface roughness after grinding silicon-modified silicon carbide materials. Summary of the Invention

[0006] The present invention aims to solve the technical problems in the prior art by providing a modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by small grinding heads.

[0007] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows:

[0008] A modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head includes the following steps:

[0009] Step i: Analyze the pressure distribution between the grinding disc and the workpiece;

[0010] Step ii: Calculate the penetration depth of the abrasive based on the maximum pressure distribution;

[0011] Step iii: Establish a physical model of surface roughness by combining the length of the abrasive's motion trajectory with the abrasive's penetration depth.

[0012] In the above technical solution, step iii is followed by:

[0013] Step iv: Verify and revise the physical model of surface roughness based on the experimental results.

[0014] In the above technical solution, step i specifically includes the following steps:

[0015] Step (a): Use ANSYS finite element simulation to simulate the pressure distribution between the asphalt grinding disc and the workpiece to obtain the pressure distribution profile curve;

[0016] Step (b): The pressure distribution between the asphalt layer of the grinding disc and the reflector is measured using the Tekscan pressure measurement system. The pressure distribution measurement results between the asphalt grinding disc and the workpiece are obtained by comparing the simulation results with the experimental results.

[0017] The pressure distribution results are obtained by comparing the simulation results obtained in step (a) with the experimental results obtained in step (b).

[0018] In the above technical solution, step ii specifically includes:

[0019] Take a square region at the center of the grinding disc where the pressure is the greatest. Let the pressure in this region be P. The area A of the square region can be determined from the resolution of the pressure sensor. The pressure F in this region is: F = PA.

[0020] Within a square region, there are N1 uniformly distributed spherical abrasive particles. Pressure is uniformly distributed across each abrasive particle. The average pressure F acting on a single abrasive particle is then... avg For: F avg =F / N1;

[0021] The penetration depth d of the abrasive is calculated using the following formula:

[0022]

[0023] Where R is the radius of the abrasive grain, E * It is the equivalent elastic modulus, E p and E w These are the elastic moduli of the abrasive and the workpiece, respectively. p and υ w These are the Poisson's ratios of the abrasive and the workpiece, respectively.

[0024] In the above technical solution, in step iii: the angular velocity of the grinding disc's horizontal rotation is ω, and the length of the abrasive's trajectory within the processing time T is L. total for:

[0025]

[0026] Where v is the feed speed of the grinding disc and e is the eccentricity of the horizontal rotation.

[0027] In the above technical solution, in step iii, the calculation formula for the physical model of surface roughness is:

[0028]

[0029] Among them, L total Let ω be the length of the abrasive's trajectory during processing time T, ω be the angular velocity of the grinding wheel's horizontal rotation, S be the cross-sectional area of ​​the abrasive pressed into the workpiece (shaded area), d be the abrasive's indentation depth, R be the radius of the abrasive, v be the feed rate of the grinding wheel, and e be the eccentricity of the horizontal rotation. a0 R represents the roughness of the original surface. a denoted as the surface roughness after processing, k is the correction factor, N is the amount of abrasive adhering to the grinding wheel, a is the indentation width of the abrasive when it is pressed into the workpiece, and T is the processing time of the grinding wheel.

[0030] In the above technical solution, step iv specifically includes:

[0031] First, the correction coefficient under this condition is obtained by fitting multiple sets of process test data;

[0032] Then, the average of the correction coefficients fitted to all results is taken as the correction coefficients for the physical model of surface roughness.

[0033] The present invention has the following beneficial effects:

[0034] This invention aims to improve the surface roughness after machining. It proposes a physical model for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head, based on the abrasive penetration depth and the abrasive trajectory length. The model established using this invention's method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head has been experimentally verified for its correctness, providing a basis for the rational selection of polishing process parameters.

[0035] The modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head in this invention is not limited to predicting the roughness physical model of silicon-modified silicon carbide material polished by a robot small grinding head, but is also applicable to predicting the roughness physical model of metals or hard and brittle materials processed by other CNC machine tools and other equipment, and guiding actual processing. Attached Figure Description

[0036] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0037] Figure 1 This is a schematic diagram of a three-dimensional structure simulated by ANSYS finite element method.

[0038] Figure 2 This is a schematic diagram of the mesh and boundary conditions in the ANSYS finite element simulation.

[0039] Figure 3 This is a schematic diagram of the ANSYS finite element results.

[0040] Figure 4 This is a schematic diagram of the test results for the Tekscan pressure sensor.

[0041] Figure 5 This is a schematic diagram showing the profile of the Tekscan pressure sensor test results and the ANSYS simulation results.

[0042] Figure 6 This is a schematic diagram of the abrasive grain indentation depth.

[0043] Figure 7 The diagram shows the motion trajectory of a single abrasive grain, where (a) is a schematic diagram of the horizontal rotation motion of the grinding disc, and (b) is a schematic diagram of the fixed-point motion trajectory.

[0044] Figure 8 This is a schematic diagram of the trajectory of a single abrasive grain combined with the feed motion.

[0045] Figure 9This is a schematic diagram of material removal for an ideal surface. Detailed Implementation

[0046] The present invention provides a modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head. This method utilizes the indentation depth and trajectory length of the abrasive grains to establish a physical model of the surface roughness processed by the small grinding head. Specifically, it includes the following steps:

[0047] Step i: Analyze the pressure distribution between the grinding disc and the workpiece;

[0048] Step ii: Calculate the penetration depth of the abrasive based on the maximum pressure distribution;

[0049] Step iii: Establish a physical model of surface roughness by combining the length of the abrasive's motion trajectory with the abrasive's penetration depth;

[0050] Step iv: Verify and correct the established physical model of surface roughness based on the experimental results.

[0051] The method for measuring the pressure distribution between the grinding disc and the workpiece when analyzing the pressure distribution includes the following steps:

[0052] Step (a): Use ANSYS finite element simulation to simulate the pressure distribution between the asphalt grinding disc and the workpiece to obtain the pressure distribution profile curve;

[0053] Step (b): The pressure distribution between the asphalt layer of the grinding disc and the reflector is measured using the Tekscan pressure measurement system. The pressure distribution measurement results between the asphalt grinding disc and the workpiece are obtained by comparing the simulation results with the experimental results.

[0054] The present invention will now be described in detail with reference to the accompanying drawings.

[0055] The modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head in this invention requires the use of a finite element simulation software, a six-degree-of-freedom industrial robot, a flexible pressure sensor testing system, multiple silicon-modified silicon carbide experimental pieces, and polishing slurry, etc. The small grinding head polishing module is integrated on the industrial robot, and the flexible pressure sensor is placed between the grinding head and the workpiece.

[0056] The modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head according to the present invention includes the following steps:

[0057] Step i: Analyze the pressure distribution between the grinding disc and the workpiece; specifically, this includes steps (a) and (b).

[0058] Step (a): Use ANSYS finite element simulation to simulate the pressure distribution between the asphalt grinding disc and the workpiece to obtain the pressure distribution profile curve;

[0059] First, the pressure distribution between the asphalt grinding disc and the workpiece was calculated using ANSYS finite element simulation software. Based on the grinding disc structure and pressure application method in the actual processing, its three-dimensional model is as follows: Figure 1 As shown.

[0060] Table 1 Material parameters for ANSYS finite element simulation:

[0061]

[0062] The structural parameters and material mechanical parameters of the grinding disc are shown in Table 1. Its own weight is added to ensure the accuracy of the simulation. Fixed constraints are set on the bottom surface of the workpiece, such as... Figure 2 As shown in the diagram. When building the model, the lower surface of the grinding disc and the upper surface of the asphalt polishing layer are in bonded contact, while the contact between the asphalt polishing layer and the workpiece is a roughness contact. For example... Figure 3 The figure shown is a simulation result diagram of ANSYS finite element method. The simulation results show that the pressure in the ANSYS finite element simulation results is not uniformly distributed, but shows the characteristics of high pressure in the central region and low pressure in the edge region, similar to a Gaussian distribution.

[0063] Step (b): The pressure distribution between the asphalt layer of the grinding disc and the reflector is measured using the Tekscan pressure sensor measurement system. The pressure distribution measurement results between the asphalt grinding disc and the workpiece are obtained by comparing the simulation results with the experimental results.

[0064] The pressure distribution between the asphalt layer and the reflector on the grinding disc was measured using the Tekscan pressure sensor measurement system. A flexible thin-film pressure sensor was placed between a Φ150mm flat silicon carbide reflector and a Φ50mm diameter asphalt grinding disc for measurement. The measurement results are as follows: Figure 4 As shown. After processing the pressure distribution test results and the pressure distribution results from ANSYS finite element simulation using Matlab, as shown... Figure 5 The measured values ​​and theoretical simulation results are in good agreement in terms of overall trend, and the maximum pressure at the center is almost the same, with a relative error of 11% for the maximum value.

[0065] Step ii: Calculate the penetration depth of the abrasive based on the maximum pressure distribution;

[0066] Take a square region at the center of the grinding disc where the pressure is maximum, and let the pressure in this region be P. Based on the resolution of the pressure sensor, the area A of this square region is 1.27 mm × 1.27 mm. Then, the pressure F within this region is:

[0067] F = PA (1);

[0068] Within this region, there are N1 uniformly distributed spherical abrasive particles. The pressure is uniformly distributed across each abrasive particle. The average pressure F acting on a single abrasive particle is then... avg for:

[0069] F avg =F / N1 (2);

[0070] like Figure 6 As shown, the abrasive will leave an indentation depth on the workpiece under pressure.

[0071] According to Hertz's elastic contact theory, the penetration depth of the abrasive on the workpiece surface can be calculated. For the case of spherical abrasive penetrating a flat surface, the penetration depth d of the abrasive left on the workpiece can be calculated using the following formula:

[0072]

[0073] Where R is the radius of the abrasive grain, E * It is the equivalent elastic modulus, E p and E w These are the elastic moduli of the abrasive and the workpiece, respectively. p and υ w These are the Poisson's ratios of the abrasive and the workpiece, respectively.

[0074] Step iii: Establish a physical model of surface roughness by combining the length of the abrasive's motion trajectory with the abrasive's penetration depth;

[0075] The motion trajectory length of a single abrasive grain during the machining process of a small grinding head is analyzed. The machining method of the small grinding head is horizontal rotation. Taking fixed abrasive as an example, the motion trajectory of the abrasive grain is analyzed by using the horizontal rotation machining method. Figure 7 In (a), O1 is the initial center of the grinding wheel, O2 is the center of the grinding wheel after rotation by an angle θ, r is the radius of the grinding wheel, e is the eccentricity of the translational rotation, and A is the abrasive at a specific point on the grinding wheel. The trajectory of a single abrasive is as follows: Figure 7 As shown in (b), the rotation at a fixed point is a circle with radius e, and the equation of motion for a single abrasive is as follows:

[0076]

[0077] While the grinding wheel rotates horizontally, the position of the abrasive grains relative to the center of the grinding wheel remains fixed on the grinding wheel. Taking the center point of the grinding wheel as the position of the abrasive grain, the grinding wheel also performs a linear feed motion in the x-direction at a speed v. The trajectory of a single abrasive grain at time t can be obtained as shown in formula (6). The following diagram is drawn: Figure 8 The diagram shows the motion trajectory of a single abrasive grain.

[0078]

[0079] The angular velocity of the grinding wheel's horizontal rotation is ω, and the length of the trajectory L of the abrasive grains on the workpiece surface during the machining time T is... total for:

[0080]

[0081] The surface roughness physical model in this embodiment is based on a series of assumptions to describe and predict the surface roughness R after machining. a .

[0082] The basic assumptions include:

[0083] (1) Assume that the abrasive is uniformly distributed on the grinding disc, the abrasive is spherical in shape and has the same particle size, and the abrasive will not fall off during the rotation of the grinding disc;

[0084] (2) Assume that all abrasives do not deform during processing, have the same indentation depth on the workpiece surface, and have the same cross-sectional area;

[0085] (3) It is assumed that the initial surface contour of the workpiece is an equilateral triangle and is evenly distributed on the workpiece surface. However, in reality, the shape of the contour is random.

[0086] The penetration depth d of the abrasive can be obtained from formula (3), and d is related to... Figure 6 The relationship between 'a' and 'a' is shown in the following formula:

[0087]

[0088] Because the grinding wheel is ideally spherical, it will press into the workpiece surface under force, such as... Figure 6 As shown. Figure 6 In the process, the angle between the indented portion of the abrasive and the center of the ball is 2β, and the maximum width of the indented portion of the abrasive is 2a, i.e., 2a.

[0089] according to Figure 6 The geometric relationship shown in the figure indicates that the cross-sectional area of ​​the abrasive indentation into the workpiece surface is the shaded area. That is, the shaded area S:

[0090]

[0091] Combining formulas (8) and (9), the area S of the shaded region can be obtained as:

[0092]

[0093] according to Figure 9 From the geometric relationships in the diagram, we can see that:

[0094] b = (4R) a0 -4R a )tanθ (12);

[0095] c = 4R a tanθ (13);

[0096]

[0097] The volume V1 removed by a single abrasive grain is:

[0098]

[0099] Therefore, the volume V removed by N abrasive particles can be expressed by the following formula:

[0100]

[0101] Considering the randomness and uncertainty of abrasives in the actual polishing process, a correction factor k is added in this embodiment to accurately predict the results, so formula (16) is:

[0102]

[0103] Where b is twice the length of the upper edge of the equilateral triangle after material removal, and c is the distance from the endpoint of the upper edge of the equilateral triangle to the endpoint of the bottom edge of the equilateral triangle after material removal.

[0104] The movement L of the abrasive can be known from the magnetorheological machining method. total The volume removed is:

[0105]

[0106] Combining formulas (17) and (18), we can obtain the calculation formula for the physical model of surface roughness of silicon-modified silicon carbide processed by a small grinding head, as shown in formula (19):

[0107]

[0108] Among them, L total Let ω be the length of the abrasive's trajectory within time T, ω be the angular velocity of the grinding wheel's horizontal rotation, S be the cross-sectional area of ​​the abrasive pressed into the workpiece (shaded area), d be the abrasive's indentation depth, R be the radius of the abrasive, v be the feed speed of the grinding wheel, and e be the eccentricity of the horizontal rotation. a0 denoted as the roughness of the original surface, k as the correction factor, N as the amount of abrasive adhering to the grinding wheel, a as the indentation width of the abrasive when it is pressed into the workpiece, and T as the processing time of the grinding wheel.

[0109] Step iv: Verify and revise the physical model of roughness based on the experimental results;

[0110] First, correction coefficients under this condition are obtained by fitting multiple sets of process test data; then, the average value of the coefficients fitted by all results is taken as the correction coefficients of the roughness physical model.

[0111] The process experiment was completed based on the small grinding head polishing technology. The newly modified silicon carbide experimental piece was polished. Through the experiment of single factor affecting roughness, six correction coefficients were obtained. The results are shown in Table 2. The average of these six coefficients was 0.963.

[0112] Table 2 Results of the single-factor variable comparison experiment:

[0113]

[0114] This invention aims to improve the surface roughness after machining. It proposes a physical model for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head, based on the abrasive penetration depth and the abrasive trajectory length. The model established using this invention's method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head has been experimentally verified for its correctness, providing a basis for the rational selection of polishing process parameters.

[0115] The modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head in this invention is not limited to predicting the roughness physical model of silicon-modified silicon carbide material polished by a robot small grinding head, but is also applicable to predicting the roughness physical model of metals or hard and brittle materials processed by other CNC machine tools and other equipment, and guiding actual processing.

[0116] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head, characterized in that, Includes the following steps: Step i: Analyze the pressure distribution between the grinding disc and the workpiece; Step ii: Calculate the penetration depth of the abrasive based on the maximum pressure distribution; Step iii: Establish a physical model of surface roughness by combining the length of the abrasive's motion trajectory with the abrasive's penetration depth; Step iii is followed by: Step iv: Verify and revise the physical model of surface roughness based on the experimental results; Step i specifically includes the following steps: Step (a): Use ANSYS finite element simulation to simulate the pressure distribution between the asphalt grinding disc and the workpiece to obtain the profile curve of the pressure distribution; Step (b): The pressure distribution between the asphalt layer of the grinding disc and the reflector is measured using the Tekscan pressure measurement system to obtain the pressure distribution measurement results between the asphalt grinding disc and the workpiece; The pressure distribution results are obtained by comparing the simulation results obtained in step (a) with the experimental results obtained in step (b). Step ii specifically includes: Take a square region at the center of the grinding disc where the pressure is greatest; the pressure in this region is... The area of ​​the square region can be determined from the resolution of the pressure sensor. Pressure in this area for: ; Within a square region, there are N1 uniformly distributed spherical abrasive particles. Pressure is uniformly distributed across each abrasive particle. What is the average pressure acting on a single abrasive particle? for: ; abrasive penetration depth Calculated using the following formula: ； ； in, It is the radius of the abrasive grain. It is the equivalent elastic modulus. and These are the elastic moduli of the abrasive and the workpiece, respectively. and These are the Poisson's ratios of the abrasive and the workpiece, respectively.

2. The modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head according to claim 1, characterized in that, In step iii: the angular velocity of the grinding disc's horizontal rotation is Processing time Length of the movement trajectory of the internal abrasive for: ； Where v is the feed speed of the grinding disc. The eccentricity of the rotation is for horizontal rotation.

3. The modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head according to claim 1, characterized in that, In step iii, the calculation formula for the physical model of surface roughness is: ； in, Processing time The length of the movement trajectory of the internal abrasive. The angular velocity of the millstone's horizontal rotation. The shaded area represents the cross-sectional area of ​​the abrasive indented into the workpiece. This refers to the penetration depth of the abrasive. Let the radius of the abrasive be . The feed rate of the grinding disc. For the eccentricity of the rotation, The roughness of the original surface. The surface roughness after processing. As a correction factor, The amount of abrasive material fixed on the grinding wheel. The width of the abrasive pressed into the workpiece. This refers to the processing time of the grinding disc.

4. The modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head according to claim 1, characterized in that, Step iv specifically includes: First, the correction coefficient under this condition is obtained by fitting multiple sets of process test data; Then, the average of the correction coefficients fitted to all results is taken as the correction coefficients for the physical model of surface roughness.

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