Modeling method for predicting surface roughness of silicon modified silicon carbide processed by small grinding head

Abstract

The invention relates to a modeling method for predicting surface roughness of silicon modified silicon carbide processed by a small grinding head, which relates to the technical field of optical manufacturing and comprises the following steps of: i, analyzing pressure intensity distribution between a grinding disc and a workpiece; step ii, calculating the press-in depth of the grinding material according to the maximum value of the pressure intensity distribution; and iii, establishing a surface roughness physical model by combining the motion trail length of the grinding material and the press-in depth of the grinding material. The modeling method for predicting the surface roughness of the silicon modified silicon carbide processed by the small grinding head is not limited to prediction of a roughness physical model of a silicon modified silicon carbide material polished by the small grinding head of a robot; and the method is also suitable for predicting the roughness physical model of metal or hard and brittle materials processed by equipment such as other numerical control processing machine tools and guiding actual processing.

Description

Technical Field

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

[0002] With the continuous advancement of science and technology, space application technology and laser technology have developed rapidly, which has put forward higher requirements on the performance of optical systems. As the core component of the system, the surface roughness of optical components has become particularly important as a key indicator of processing quality. Various optical glasses, silicon carbide, microcrystalline glass, single crystal silicon and other hard and brittle materials used to manufacture optical components are often accompanied by brittle removal during the polishing process, which will lead to a decrease in surface quality and poor roughness. Therefore, it is very important to clarify the evolution process of surface roughness during processing, establish a physical model of roughness, and improve the surface roughness after processing.

[0003] In mirror polishing, the surface roughness of the workpiece is one of the key indicators to measure the processing quality. Accurately predicting the surface roughness of the workpiece is of great significance to improving manufacturing efficiency and product quality. Surface roughness is affected by many factors. By constructing a surface roughness model, the surface roughness can be predicted and the processing quality can be controlled.

[0004] At present, the modeling methods of surface roughness are mainly divided into empirical parameter modeling method, theoretical modeling method and artificial intelligence method. Among them: the empirical parameter modeling method is to use multiple regression, empirical formulas and various data mining, and then analyze a large amount of experimental data to determine the model coefficients to establish the functional relationship between processing parameters and surface roughness. The artificial intelligence method is based on the acquisition and processing of data signals, so the accuracy of the acquired data signals and the processing methods will affect the prediction accuracy of the model. The model accuracy depends on the sample data of the training. When the experimental data is within the sample range, the error between the predicted value and the experimental value is small. Conversely, the error between the predicted value and the experimental value is large. The support vector machine is similar to the neural network. It requires a large amount of dense data obtained from experiments to support the prediction model to make the prediction result more accurate. The artificial neural network can continuously transform the connection weights and topological structure of the network so that the network output gradually approaches the expected output to establish an accurate surface roughness prediction model. The surface roughness model constructed by the theoretical modeling method is to analyze the forming mechanism of the machined surface during the processing of different processing methods, study the influence of the tool geometry, process parameters and other factors affecting the machining surface roughness on the surface formation, and calculate the surface roughness value after processing.

[0005] The above three methods all have their shortcomings: the empirical parameter modeling method and the artificial intelligence method do not consider the material removal mechanism and rely on experimental sample data. The model accuracy will only continue to improve after a large amount of sample data training. They are overly dependent on processing conditions and equipment, are not universally applicable, and lack a description of the essence of the processing process. The theoretical modeling method lacks analysis of the physical model of the surface roughness after the grinding head processes silicon-modified silicon carbide materials. Summary of the invention

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

[0007] In order to solve the above technical problems, the technical solutions of the present invention are as follows:

[0008] A modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head comprises 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 according to the maximum value of the pressure distribution;

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

[0012] In the above technical solution, after step iii, the method further includes:

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

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

[0015] Step (a): using ANSYS finite element method to simulate the pressure distribution between the asphalt grinding disc and the workpiece, and obtaining a contour curve of the pressure distribution;

[0016] Step (b): using a Tekscan pressure measurement system to measure the pressure distribution between the asphalt layer of the grinding disc and the reflector, obtaining the pressure distribution measurement result between the asphalt grinding disc and the workpiece, and comparing the simulation results with the experimental results to obtain the pressure distribution result;

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

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

[0019] Take a square area at the center of the grinding disc where the pressure is the highest. The pressure on this area is P. The area A of the square area can be known from the resolution of the pressure sensor. The pressure F in this area is: F = PA;

[0020] There are N1 uniformly distributed spherical abrasives in the square area. The pressure is uniformly distributed on each abrasive. The average pressure F acting on a single abrasive is avg For: F avg =F / N1;

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

[0022]

[0023] Where R is the radius of the abrasive particle, E * is the equivalent elastic modulus, E p and E w are the elastic modulus of the abrasive and the workpiece, υ p and w 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 is ω, and the length of the motion track of the abrasive in the processing time T is L total for:

[0025]

[0026] Among them, 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 of the surface roughness physical model is:

[0028]

[0029] Among them, L total is the length of the abrasive's motion trajectory within the processing time T, ω is the angular velocity of the grinding disc's horizontal rotation, S is the cross-sectional area of ​​the shaded part of the abrasive pressed into the workpiece, d is the depth of the abrasive's penetration, R is the radius of the abrasive, v is the feed speed of the grinding disc, e is the eccentricity of the horizontal rotation, and R a0 is the roughness of the original surface, R a is the surface roughness after processing, k is the correction factor, N is the number of fixed abrasives on the grinding disc, a is the width of the abrasive when it is pressed into the workpiece, and T is the processing time of the grinding disc.

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

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

[0032] Then, the average correction coefficient of all the fitting results is taken as the correction coefficient of the surface roughness physical model.

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

[0034] The present invention aims to improve the roughness of the processed surface and proposes a physical model of surface roughness of small grinding head processing based on abrasive indentation depth and abrasive motion track length to predict the surface roughness of silicon-modified silicon carbide processed by small grinding head. The model established by the modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by small grinding head of the present invention has been verified to be correct through experiments, providing a basis for the reasonable selection of polishing process parameters.

[0035] The modeling method of the present invention for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head is not only limited to the prediction of the roughness physical model of silicon-modified silicon carbide materials polished by a small grinding head of a robot, but is also applicable to the prediction of the roughness physical model of metal or hard and brittle materials processed by other CNC machining equipment and the like and to guide actual machining. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0037] Figure 1 This is a schematic diagram of the 3D structure of ANSYS finite element simulation.

[0038] Figure 2 Schematic diagram of ANSYS finite element simulation mesh and boundary conditions.

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

[0040] Figure 4 Schematic diagram of Tekscan pressure sensor test results.

[0041] Figure 5 Schematic diagram of the test results of Tekscan pressure sensor and the outline of ANSYS simulation results.

[0042] Figure 6 Schematic diagram of abrasive penetration depth.

[0043] Figure 7 Schematic diagram of the motion trajectory of a single abrasive particle, 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 Schematic diagram of the motion trajectory of a single abrasive particle combined with feed motion.

[0045] Fig. 9Schematic diagram of material removal from an ideal surface. DETAILED DESCRIPTION

[0046] The modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head of the present invention uses the indentation depth of abrasive particles and the length of the abrasive particle movement trajectory to establish a physical model of the surface roughness processed by a small grinding head, and specifically 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 according to the maximum value of the pressure distribution;

[0049] Step iii: Establishing a surface roughness physical model by combining the motion track length of the abrasive and the penetration depth of the abrasive;

[0050] Step iv: Verify and modify the constructed surface roughness physical model according to the experimental results.

[0051] When analyzing the pressure distribution between the grinding disc and the workpiece, the pressure distribution measurement method of the asphalt grinding disc in contact with the workpiece includes the following steps:

[0052] Step (a): using ANSYS finite element method to simulate the pressure distribution between the asphalt grinding disc and the workpiece, and obtaining a contour curve of the pressure distribution;

[0053] Step (b): Use the Tekscan pressure measurement system to measure the pressure distribution between the asphalt layer of the grinding disc and the reflector to obtain the pressure distribution measurement results between the asphalt grinding disc and the workpiece, and compare the simulation and experimental results to obtain the pressure distribution results.

[0054] The present invention is described in detail below with reference to the accompanying drawings.

[0055] The modeling method of the present invention for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head 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 test pieces and polishing liquid, 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 of the present invention comprises the following steps:

[0057] Step i: analyzing the pressure distribution between the grinding disc and the workpiece; specifically, comprising: step (a) and step (b).

[0058] Step (a): using ANSYS finite element method to simulate the pressure distribution between the asphalt grinding disc and the workpiece, and obtaining a contour curve of the pressure distribution;

[0059] First, the pressure distribution between the asphalt grinding disc and the workpiece was calculated using ANSYS finite element simulation software. According to the grinding disc structure and the way of applying pressure in the actual processing process, the three-dimensional model is as follows: Figure 1 shown.

[0060] Table 1 ANSYS finite element simulation material parameters:

[0061]

[0062] The structural parameters of the grinding disc and the mechanical parameters of the material are shown in Table 1. The self-gravity is added to ensure the accuracy of the simulation. The bottom surface of the workpiece is set with fixed constraints, such as Figure 2 When establishing the model, the lower surface of the grinding disc and the upper surface of the asphalt polishing layer adopt the binding contact mode, while the contact mode between the asphalt polishing layer and the workpiece is the roughness contact. Figure 3 The figure shows the simulation result of ANSYS finite element. The simulation result shows that the pressure in the ANSYS finite element simulation result is not evenly distributed, but shows the characteristics of high pressure in the center area and low pressure in the edge area, which is similar to Gaussian distribution.

[0063] Step (b): Use the Tekscan pressure sensor measurement system to measure the pressure distribution between the asphalt layer of the grinding disc and the reflector to obtain the pressure distribution measurement results between the asphalt grinding disc and the workpiece, and compare the simulation and experimental results to obtain the pressure distribution results.

[0064] The Tekscan pressure sensor measurement system was used to measure the pressure distribution between the grinding disc asphalt layer and the reflector. The flexible film pressure sensor was placed between the Φ150mm flat silicon carbide reflector and the Φ50mm diameter asphalt grinding disc for measurement. The measurement results are shown in Figure 4 After using Matlab to process the pressure distribution test results and the pressure distribution results of ANSYS finite element simulation, as shown in Figure 5 As shown, the measured values ​​are quite consistent with the theoretical simulation results in the overall trend. At the same time, the maximum pressure value at the center is almost the same, and the relative error of the maximum value is 11%.

[0065] Step ii: Calculate the penetration depth of the abrasive according to the maximum value of the pressure distribution;

[0066] Take a square area at the center of the grinding disc where the pressure is the highest. The pressure on this area is P. According to the resolution of the pressure sensor, the area A of the square area is 1.27mm×1.27mm. Then the pressure F in this area is:

[0067] F = PA (1);

[0068] There are N1 uniformly distributed spherical abrasives in this area, and the pressure is uniformly distributed on each abrasive. The average pressure acting on a single abrasive is F avg for:

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

[0070] like Figure 6 As shown, the abrasive will leave a deep penetration into the workpiece under the application of pressure.

[0071] According to the Hertz elastic contact theory, the penetration depth of the abrasive on the workpiece surface can be calculated. For the case where a spherical abrasive is pressed into a plane, the penetration depth d of the abrasive left on the workpiece can be calculated by the following relationship formula:

[0072]

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

[0074] Step iii: Establishing a surface roughness physical model by combining the motion track length of the abrasive and the penetration depth of the abrasive;

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

[0076]

[0077] While the center of the grinding disc is rotating horizontally, the position of the abrasive grains relative to the center of the grinding disc is fixed on the grinding disc. The center point of the grinding disc is taken as the abrasive position. The grinding disc also performs a linear feed motion in the x direction at a speed v. The motion trajectory of a single abrasive at time t can be obtained as shown in formula (6). Figure 8 The motion trajectory of a single abrasive particle is shown.

[0078]

[0079] The angular velocity of the grinding wheel is ω, and the length of the path that the abrasive particles travel on the workpiece surface during the processing time T is L. total for:

[0080]

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

[0082] Basic assumptions include:

[0083] (1) Assume that the abrasive is evenly distributed on the grinding disc, the abrasive is spherical in shape, has the same particle size, and does not fall off as the grinding disc rotates;

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

[0085] (3) Assume 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 abrasive penetration depth d can be obtained from formula (3). Figure 6 The relationship between a and is shown in the following formula:

[0087]

[0088] Since the grinding material is ideally spherical, it will be pressed into the surface of the workpiece under the action of force, such as Figure 6 shown. Figure 6 In the figure, the opening angle of the pressed part of the abrasive relative to the center of the sphere is 2β, and the maximum width of the pressed part of the abrasive is 2a, that is, 2a.

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

[0090]

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

[0092]

[0093] according to Fig. 9 From the geometric relationship in, 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 is:

[0098]

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

[0100]

[0101] Taking into account the randomness and uncertainty of the abrasive in the actual polishing process, in order to accurately predict the results, a correction factor k is added in this embodiment, and then formula (16) is:

[0102]

[0103] Among them, 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 of the equilateral triangle after material removal.

[0104] From the magnetorheological processing method, it can be known that the abrasive movement L total The volume removed is:

[0105]

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

[0107]

[0108] Among them, L total is the length of the abrasive's motion trajectory in time T, ω is the angular velocity of the grinding disc's horizontal rotation, S is the cross-sectional area of ​​the shaded part of the abrasive pressed into the workpiece, d is the depth of the abrasive's penetration, R is the radius of the abrasive, v is the feed speed of the grinding disc, e is the eccentricity of the horizontal rotation, and R a0 is the roughness of the original surface, k is the correction factor, N is the number of fixed abrasives on the grinding disc, a is the width of the abrasive when it is pressed into the workpiece, and T is the processing time of the grinding disc.

[0109] Step iv: verify and modify the roughness physical model based on the experimental results;

[0110] Firstly, the correction coefficient under this condition is obtained based on fitting of multiple sets of process test data; then the correction coefficient of the roughness physical model is taken as the average value of the coefficients of all fitting results.

[0111] The process experiment was completed based on the small grinding head polishing technology. The silicon carbide test piece that had just been modified was polished. Through the experiment of single factor affecting roughness, 6 correction coefficients were obtained. The results are shown in Table 2. The average of these six coefficients is 0.963.

[0112] Table 2 Single factor variable comparison experimental results:

[0113]

[0114] The present invention aims to improve the roughness of the processed surface and proposes a physical model of surface roughness of small grinding head processing based on abrasive indentation depth and abrasive motion track length to predict the surface roughness of silicon-modified silicon carbide processed by small grinding head. The model established by the modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by small grinding head of the present invention has been verified to be correct through experiments, providing a basis for the reasonable selection of polishing process parameters.

[0115] The modeling method of the present invention for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head is not only limited to the prediction of the roughness physical model of silicon-modified silicon carbide materials polished by a small grinding head of a robot, but is also applicable to the prediction of the roughness physical model of metal or hard and brittle materials processed by other CNC machining equipment and the like and to guide actual machining.

[0116] Obviously, the above embodiments are merely examples for the purpose of clear explanation, and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived therefrom are still within the scope of protection of the 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: The following steps are involved: Step i: Analyze the pressure distribution between the grinding disc and the workpiece; Step ii: Calculate the penetration depth of the abrasive according to the maximum value of the pressure distribution; Step iii: Establish a surface roughness physical model by combining the motion trajectory length of the abrasive and the penetration depth of the abrasive.

2. The modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head according to claim 1 is characterized in that: Step iii also includes: Step iv: Verify and modify the surface roughness physical model based on the experimental results.

3. The modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head according to claim 1 or 2, characterized in that: Step i specifically includes the following steps: Step (a): using ANSYS finite element method to simulate the pressure distribution between the asphalt grinding disc and the workpiece, and obtaining a contour curve of the pressure distribution; Step (b): using a Tekscan pressure measurement system to measure the pressure distribution between the asphalt layer of the grinding disc and the reflector to obtain the pressure distribution measurement result between the asphalt grinding disc and the workpiece; The pressure distribution result is obtained by comparing the simulation result obtained in step (a) with the experimental result obtained in step (b).

4. The modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head according to claim 1 or 2, characterized in that: Step ii specifically includes: Take a square area at the center of the grinding disc where the pressure is the highest. The pressure on this area is P. The area A of the square area can be known from the resolution of the pressure sensor. The pressure F in this area is: F = PA; There are N1 uniformly distributed spherical abrasives in the square area. The pressure is uniformly distributed on each abrasive. The average pressure F acting on a single abrasive is avg For: F avg =F / N1; The penetration depth d of the abrasive is calculated using the following relationship: Where R is the radius of the abrasive particle, E * is the equivalent elastic modulus, E p and E w are the elastic modulus of the abrasive and the workpiece, υ p and w are the Poisson's ratios of the abrasive and the workpiece, respectively.

5. The modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head according to claim 1 or 2, characterized in that: In step iii: the angular velocity of the grinding disc is ω, and the length of the abrasive motion trajectory during the processing time T is L total for: Among them, v is the feed speed of the grinding disc and e is the eccentricity of the horizontal rotation.

6. The modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head according to claim 1 or 2, characterized in that: In step iii, the calculation formula of the surface roughness physical model is: Among them, L total is the length of the abrasive's motion trajectory within the processing time T, ω is the angular velocity of the grinding disc's horizontal rotation, S is the cross-sectional area of ​​the shaded part of the abrasive pressed into the workpiece, d is the depth of the abrasive's penetration, R is the radius of the abrasive, v is the feed speed of the grinding disc, e is the eccentricity of the horizontal rotation, and R a0 is the roughness of the original surface, R a is the surface roughness after processing, k is the correction factor, N is the number of fixed abrasives on the grinding disc, a is the width of the abrasive when it is pressed into the workpiece, and T is the processing time of the grinding disc.

7. The modeling method for predicting the surface roughness of silicon-modified silicon carbide processed by a small grinding head according to claim 2, characterized in that: Step iv specifically includes: Firstly, the correction coefficient under this condition is obtained based on fitting of multiple sets of process test data; Then, the average correction coefficient of all the fitting results is taken as the correction coefficient of the surface roughness physical model.

Images