Polishing machine cooling structure multi-objective optimization method based on heat generation model

Abstract

The invention discloses a polishing machine cooling structure multi-objective optimization method based on a heat generation model, which comprises the following steps: establishing a discrete point temperature variance calculation model in the radial direction of a polishing disk surface and a water channel volume calculation model of the polishing disk; the value range of the width of each water channel of the polishing disc, the value range of the interval width of each water channel, the value range of the number of the water channels, the value range of the interval width inside the cooling water channels, the value range of the interval width outside the cooling water channels and the value range of the depth of the water channels are used as constraint conditions; the minimum temperature variance of discrete points in the radial direction of the polishing disc surface, the maximum water channel volume of the polishing disc and the maximum thickness of the polishing disc serve as optimization targets, and the water channel width and the water channel depth of the polishing disc, the inner interval width of cooling water channels, the outer interval width of the cooling water channels, the interval width of all the water channels, the thickness of the polishing disc and the number of the water channels are optimized; and taking the optimal solution obtained by optimization as the structural parameter of the cooling water channel of the polishing disk.

Description

Technical Field

[0001] The invention belongs to the technical field of semiconductor ultra-precision machining, and in particular relates to a multi-objective optimization method for a polishing machine cooling structure based on a heat generation model. Background Art

[0002] Silicon carbide (SiC) is a widely used semiconductor material with the characteristics of large bandgap, high critical breakdown potential, and high temperature resistance, making it widely used in new energy vehicles, aerospace, electronic equipment, etc. In order to ensure the qualification rate and stability of products in practical applications, the SiC substrate must have an ultra-flat surface, but its high hardness, high brittleness, and stable chemical properties make it extremely difficult to process. These characteristics limit the development and application of SiC materials. Internationally, chemical mechanical polishing (CMP) is considered to be the only effective processing method that can achieve ultra-smooth, damage-free nanoscale surfaces and global flattening. The main mechanism of this technology is to couple the chemical action of the polishing liquid with the friction and cutting action of the polishing pad and abrasive particles, thereby simultaneously achieving a high material removal rate and a low surface roughness.

[0003] At present, the research on polishing temperature field mainly uses mathematical modeling and software finite element analysis. In contrast, there is little research on how to reduce the uneven temperature of the polishing surface in chemical mechanical polishing. Temperature uniformity has an important influence on the polishing of SiC workpieces (uneven temperature of the disk surface will be transmitted to the surface of the SiC workpiece, causing it to warp, thereby causing the precision of the SiC workpiece to decrease, the yield of the polishing machine to decrease, and the production cost of the enterprise to increase and the production efficiency to decrease). It is directly related to the polishing effect and quality, polishing efficiency and stability, and process parameters and equipment requirements. Therefore, it is necessary to conduct in-depth research on how to use the heat generation model of chemical mechanical polishing to optimize the temperature field of the polishing surface. Once this is obtained, the heat generation model can be used to improve the existing structure of the polishing disk to improve the precision and yield of the SiC substrate. Summary of the invention

[0004] The purpose of the present invention is to provide a multi-objective optimization method for the cooling structure of a polishing machine based on a heat generation model, which can optimize the cooling water channel structure of the polishing machine and improve the temperature uniformity of the polishing disk surface.

[0005] The technical solution provided by the present invention is:

[0006] A multi-objective optimization method for a polishing machine cooling structure based on a heat generation model, comprising:

[0007] Establish a temperature variance calculation model for the temperature measurement points in the radial direction of the polishing disk surface:

[0008] as well as

[0009] Calculation model of water channel volume of polishing disc:

[0010]

[0011] In the formula, Q i is the heat of any temperature measuring point i on the polishing disc surface, n is the number of temperature measuring points in the radial direction of the polishing disc; w si is the width of each waterway, w ji is the width of each waterway interval, ε is the number of waterways, w in is the interval width in the cooling water channel, w out is the width of the outer interval of the cooling water channel, d d is the depth of each cooling water channel;

[0012] The value range of each water channel width of the polishing plate, the value range of each water channel interval width, the value range of the number of water channels, the value range of the interval width inside the cooling water channel, the value range of the interval width outside the cooling water channel and the value range of the water channel depth are used as constraints;

[0013] Taking the minimum temperature variance of discrete points in the radial direction of the polishing disc surface, the maximum water channel volume of the polishing disc and the maximum thickness of the polishing disc as the optimization objectives, the polishing disc water channel width, water channel depth, inner interval width of the cooling water channel, outer interval width of the cooling water channel, interval width of each water channel, polishing disc thickness and number of water channels are optimized;

[0014] The optimal solution obtained by optimization is used as the structural parameters of the polishing disk cooling water channel.

[0015] Preferably, the calculation model of the heat at any temperature measuring point on the polishing disc surface is:

[0016]

[0017] Where r is the heat flux distribution coefficient; v is the relative speed between the silicon carbide workpiece and the polishing disc; μ P is the friction coefficient between the workpiece and the polishing pad and abrasive; F is the pressure exerted by the upper and lower polishing discs on the workpiece; h x is the convection heat transfer coefficient between the local silicon carbide workpiece and polishing disc and the air; t w is the surface temperature of silicon carbide workpiece; t f is the air temperature around the polishing machine, A is the surface area contacted by the air, and A xis the contact area between the disk surface and the air; c is the specific heat capacity of the polishing liquid; m is the mass of the polishing liquid flowing into the polishing interface per unit time; t is the polishing time; ΔT1 is the temperature difference between the polishing liquid when flowing in and when flowing out; K is the proportionality coefficient, ΔT2 is the temperature difference between the polishing disk surface and the coolant, λ is the thermal conductivity; l is the plate length, and Nu is the fluid Nusselt number.

[0018] Preferably, the relative speed between any point on the workpiece and the polishing disc is:

[0019]

[0020] Among them, ω P is the angular velocity of the polishing disc, ω w is the angular velocity of the workpiece; is the angle between the line connecting the center of the polishing disk and the center of the workpiece and the X-axis in the workpiece coordinate system, e is the ratio of the distance from a point on the workpiece to the center of the planetary gear to the radius of the outer ring gear, and (x, y) is the motion trajectory of the workpiece.

[0021] Preferably, the motion trajectory model of the workpiece is:

[0022]

[0023] Among them, k is the ratio of the radius of the center wheel to the outer ring gear; m is the speed ratio of the outer ring gear to the center gear; ζ is the speed ratio of the polishing disc to the center wheel, and R is the radius of the outer ring gear.

[0024] Preferably, the polishing plate water channel width, water channel depth, inner spacing width of cooling water channel, outer spacing width of cooling water channel, spacing width of each water channel, polishing plate thickness and number of water channels are optimized by NSGA-II algorithm.

[0025] Preferably, the process of optimization by NSGA-II algorithm comprises the following steps:

[0026] Step 1: Randomly generate an initial population, which includes N pop individuals; each of the individuals is a set consisting of the polishing plate water channel width, water channel depth, cooling water channel inner interval width, cooling water channel outer interval width, each water channel interval width, polishing plate thickness and water channel number;

[0027] Step 2: Update the current population using the crossover and mutation methods to obtain a crossover and mutation population;

[0028] Step 3: Merge the crossover and mutation populations with the current population, perform non-dominated sorting on the merged population to obtain the individual ranks, and calculate the crowding distance of each individual. Sort the population according to the sorting rules of individual ranks in ascending order and crowding distance in descending order, and retain the top N individuals. popIndividuals as a new population;

[0029] Repeat steps 2-3 until the specified number of cycles is reached and the optimal solution set is obtained;

[0030] Step 4: Select a solution that can achieve the minimum temperature variance of discrete points in the radial direction of the polishing disk surface from the optimal solution set as the final solution.

[0031] The beneficial effects of the present invention are:

[0032] The multi-objective optimization method for the cooling structure of a polishing machine based on a heat generation model provided by the present invention can optimize the cooling water channel structure of the polishing machine, improve the temperature uniformity of the polishing disc surface, and thus improve the polishing quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is a schematic diagram of the double-sided high-precision grinding and polishing machine described in the present invention.

[0034] Figure 2 It is a schematic structural diagram of the lower polishing plate described in the present invention.

[0035] Figure 3 This is a diagram showing the position of a SiC workpiece according to the present invention after a period of time t.

[0036] Figure 4 This is a simplified diagram of the velocity model of the SiC workpiece relative to the polishing disk according to the present invention.

[0037] Figure 5 This is a simplified diagram of the motion boundary of the SiC workpiece described in the present invention.

[0038] Figure 6 Schematic diagram of the cooling water channel structure and design variables of the present invention.

[0039] Figure 7 This is the Ansys simulated polishing disk surface temperature distribution diagram before the optimization of the present invention.

[0040] Figure 8 This is the temperature distribution diagram of the polishing disk surface optimized by Ansys simulation of the present invention.

[0041] Fig. 9 This is a radial temperature comparison diagram before and after the optimization of the present invention. DETAILED DESCRIPTION

[0042] The present invention is further described in detail below in conjunction with the accompanying drawings so that those skilled in the art can implement the invention with reference to the description.

[0043] like Figure 1-2As shown, the double-sided high-precision grinding and polishing machine device includes at least one planetary wheel 300 for placing the SiC workpiece 400. The SiC workpiece 400 is held in the planetary wheel 300, and the planetary wheel 300 is meshed with the lower polishing disc 500 and the inner ring gear 200 through gears. The planetary wheel has multiple SiC workpieces built in, and multiple SiC workpieces are distributed on the planetary wheel at equal angles around the center of the planetary wheel. During polishing, the upper polishing disc 100 is driven downward by a cylinder (not shown in the figure) to apply pressure to the SiC workpiece, and the planetary wheel 300 rotates around the inner ring gear 200 through gear meshing.

[0044] During the polishing process of SiC workpiece, the main temperature of the polishing contact surface is generated by the friction between the SiC workpiece and the abrasive, polishing pad, and polishing disc. In the actual polishing process, the polishing disc and the SiC workpiece / planetary wheel can be simplified into two planes that move relative to each other. Since the SiC workpiece is mounted in the planetary wheel, and in order to simplify the mathematical model, the SiC workpiece and the planetary wheel can be regarded as one.

[0045] In view of the operating principle of the SiC workpiece 400 during polishing, the present invention provides a multi-objective optimization method for the cooling structure of a polishing machine based on a heat generation model, such as Figure 3-6 As shown, the specific implementation process is as follows.

[0046] a. Obtain the operating parameters of the double-sided high-precision grinding and polishing equipment

[0047] b. Convert the obtained operating parameters into the planetary wheel motion parameters in the double-sided polishing machine

[0048] c. Establishing the motion trajectory model of SiC workpiece according to the motion parameters

[0049] d. According to the SiC workpiece motion trajectory model, the SiC workpiece motion velocity model can be derived

[0050] e. Establish the SiC workpiece polishing heat generation model based on the SiC workpiece motion velocity model

[0051] f. Establish a multi-objective optimization model for water cooling structure based on SiC polishing heat generation model

[0052] g. Verification using ANSYS software

[0053] Step a, specifically, obtain the operating parameters of the double-sided high-precision grinding and polishing equipment, the operating parameters including the inner ring gear 200 rotation speed ω1, the outer ring gear 600 rotation speed ω3, the inner ring gear 200 radius r and the outer ring gear 600 radius R.

[0054] Step b, converting the obtained operating parameters into the motion parameters of the planetary wheel in the double-sided polishing machine.

[0055] Specifically, the linear velocities of the contact points between the planetary wheel 300 and the inner ring gear 200 and the contact points between the planetary wheel 300 and the outer ring gear 600 are the same. Figure 3 , the corresponding motion parameters can be calculated as follows:

[0056]

[0057] Among them, ω H ω is the angular velocity of the planetary wheel 300, ω2 is the angular velocity of the planetary wheel 300, ω1 is the angular velocity of the inner ring gear 200, and ω3 is the angular velocity of the outer ring gear 600.

[0058] Step c: establishing a motion trajectory model of the SiC workpiece 400 based on the motion parameters and simplifying the planetary wheel 300 and the SiC workpiece 400 as a whole.

[0059] like Figure 3 , the figure shows the position of the SiC workpiece 400 after time t. Based on the set double-sided high-precision grinding and polishing machine model, the movement time t of the planetary wheel 300 is set to obtain the revolution angle and rotation angle of the planetary wheel 300. The calculation method is as follows:

[0060] Since it is a compound motion of revolution and rotation, the vector method is used to analyze and solve the motion trajectory of any point on the workpiece relative to the polishing plate 500, and the coordinate system X is established with the center of the polishing plate as the origin, the horizontal right direction as the positive X direction, and the vertical upward direction as the positive Y direction. P -Y p (Polishing plate coordinate system); after time t, X P -Y p The coordinate system is rotated by angle α to obtain X' P -Y' p Coordinate system.

[0061] From the vector method we know that:

[0062] OP'=OO1'+O1'P'

[0063] Let |O1'P'|=l(0≤L≤r), L is the distance from a point P' on the planetary gear to the center of rotation of the planetary gear 300, which can be expressed in coordinates:

[0064]

[0065] OO1' can be expressed as:

[0066] OO'1=i(Rr)cos(θ-α)+j(Rr)sin(θ-α);

[0067] In the above formula, θ = ∠(i,OO'1); α=∠(X'P ,OX P )(angle of rotation of the polishing disk 500), where i is the unit vector in the x-direction; where j is the unit vector in the y-direction.

[0068] From the above formula, we can get:

[0069]

[0070] Substituting the above formula into the equation, we can get:

[0071]

[0072] The three angles can be expressed as:

[0073]

[0074] Among them, ω P is the rotation speed of the polishing disc 500, θ=∠(i,OO'1); α=∠(X' P ,OX P )(angle of rotation of the polishing disc).

[0075] To simplify the parameters, extract the relationship between related variables:

[0076]

[0077] k represents the radius ratio of the inner ring gear 200 to the outer ring gear 600; m represents the rotational speed ratio of the outer ring gear 600 to the inner ring gear 200; e represents the ratio of the distance from a point P on the workpiece to the center of the planetary wheel 300 to the radius of the outer ring gear 600; n represents the rotational speed ratio of the polishing disc 500 to the inner ring gear 200.

[0078] According to the above-mentioned motion parameters of the planetary wheel 300, the motion trajectory model of the SiC workpiece 400 can be obtained:

[0079]

[0080] In step d, Figure 4 , the figure is a schematic diagram of the velocity model of the SiC workpiece 400 relative to the polishing plate 500. According to the above motion trajectory equation of the SiC workpiece 400, the velocity of any point on the trajectory can be obtained:

[0081] (1) Taking the SiC workpiece 400 as a reference, the radial velocity and circumferential velocity at point P are:

[0082]

[0083] Where V ρ,w For SiC workpiece 400 radial velocity, V θ,wThe circumferential speed of the SiC workpiece is 400.

[0084] (2) Taking the polishing disc 500 as a reference, the radial velocity and circumferential velocity at point P are:

[0085]

[0086] (3) The radial velocity and circumferential velocity of any point P on the SiC workpiece 400 relative to the polishing disk 500 are:

[0087]

[0088] Where V ρ is the radial velocity, V θ is the circumferential velocity, V θ,P V is the circumferential speed of the polishing disc 500 ρ,P The radial speed of the polishing disk is 500.

[0089] (4) With the center of the SiC workpiece 400 as the coordinate origin, the horizontal right direction is the positive direction of the x-axis, and the vertical upward direction is the positive direction of the y-axis. G -Y G Coordinate system (workpiece coordinate system), radial and circumferential speed in X G -Y G The direction components are:

[0090]

[0091] (5) Substituting the above equation into the equation, we can get the velocity of any point P on the workpiece relative to the polishing plate 500 at X G -Y G Direction component V x 、V y :

[0092]

[0093] (6) With the polishing disk 500 as the center, the horizontal right direction is the positive direction of the x-axis, and the vertical upward direction is the positive direction of the y-axis. P -Y P Coordinate system (polishing disc coordinate system), X G -Y G Any point in the coordinate system (workpiece coordinate system) is converted to X P -Y P The relationship in the coordinate system is:

[0094]

[0095] in For X P -Y P Coordinate origin and XG -Y G The line connecting the origin and X P -Y P The angle of the coordinate X axis.

[0096] (7) Convert the coordinates of any point P on the workpiece into X P -Y P The coordinates of the SiC workpiece 400 can be obtained by calculating the speed of any point P on the SiC workpiece 400 relative to the polishing plate 500:

[0097]

[0098] In step e, specifically, during the operation of the double-sided polishing machine, the heat generated on the surface of the polishing disc 500 is mostly caused by the friction between the abrasive, the SiC workpiece 400 and the polishing pad. From the perspective of energy conversion, the SiC workpiece 400 rubs against the polishing pad and the abrasive in the grinding fluid under the pressure of the upper and lower polishing discs 500, converting the mechanical energy of the polishing machine into heat energy. Therefore, the temperature rise of the working surface of the polishing disc is directly related to the pressure applied by the upper and lower polishing discs, the friction coefficient between the workpiece and the polishing pad, the relative speed between the SiC workpiece 400 and the polishing disc 500, and the abrasive in the grinding fluid.

[0099] Using the finite element method, the mechanical energy consumed by friction in a very small area of ​​the polishing pad and the SiC workpiece 400 is calculated as follows:

[0100]

[0101] Wherein, f is the friction force generated in the extremely small area where the workpiece contacts the polishing pad and the abrasive; v is the relative speed between the SiC workpiece 400 and the polishing disk 500 in the extremely small area where the workpiece contacts the polishing pad and the abrasive; t0 is the friction time between the workpiece and the abrasive and the polishing pad in this extremely small area.

[0102] The friction force f generated in the extremely small area where the SiC workpiece 400 contacts the polishing pad and the abrasive is calculated as follows:

[0103] f=μ P ×F

[0104] In the formula, μ P is the friction coefficient between the SiC workpiece 400 and the polishing pad and abrasive; F is the pressure applied by the upper and lower polishing plates 500 to the workpiece.

[0105] During the polishing process of the double-sided polisher, the heat generated by friction is not completely transferred to the polishing disc 500, but is transferred to the SiC workpiece 400 and the polishing disc 500 in a certain proportion. The heat flow distribution coefficient is calculated as follows:

[0106]

[0107] Where r is the heat flow distribution coefficient; λ w is the thermal conductivity of the SiC workpiece 400; p is the thermal conductivity of the polishing pad; D is the thermal diffusion coefficient of the polishing pad; v is the relative speed between the SiC workpiece 400 and the polishing disk 500; r g is the radius of the SiC workpiece 400 .

[0108] According to the above-mentioned motion velocity equation of the SiC workpiece 400, the calculation method of the heat generation at any point on the trajectory is:

[0109]

[0110] Wherein, r is the heat flux distribution coefficient; v is the relative speed between the SiC workpiece 400 and the polishing plate 500; μ P is the friction coefficient between the SiC workpiece 400 and the polishing pad and abrasive; F is the pressure applied by the upper and lower polishing plates 500 to the workpiece; and t is the polishing time.

[0111] In step f, specifically, according to the law of heat transfer, a mathematical model is established by combining the heat generated by polishing in the radial direction of the polishing disc 500 and the cooling of the cooling water channel.

[0112] There are three factors that cause heat dissipation on the polishing disk: air convection heat dissipation, polishing liquid convection heat dissipation and cooling water channel water flow heat dissipation.

[0113] (1) The air heat dissipation is solved as follows:

[0114] According to the local Newton cooling formula, the heat flux density on the surface can be expressed as:

[0115] Q x =h x ·(t w -t f )

[0116] In the formula, h x is the convection heat transfer coefficient between the local silicon carbide workpiece and polishing disc and the air; t w is the surface temperature of silicon carbide workpiece; t f is the air temperature around the polishing machine. Since the polishing disc rotates at a constant speed during the polishing process, the air heat dissipation process is considered to be steady state, and the local surface heat transfer coefficient at each location is considered to be the same value of 10W (m 2 / ℃), the total heat dissipation of air can be obtained by integrating the local heat flux density over the entire heat transfer surface:

[0117]

[0118] Where A is the surface area in contact with air and t is the polishing time.

[0119] (2) According to heat transfer theory, the heat dissipation of the polishing liquid is as follows:

[0120] Q slurry =K·c·m·t·ΔT1

[0121] Where c is the specific heat capacity of the polishing liquid; m is the mass of the polishing liquid flowing into the polishing interface per unit time; t is the polishing time; ΔT1 is the difference between the temperature of the polishing liquid when it flows in and when it flows out; K is the proportionality coefficient, which is used as a correction formula (because not all polishing liquid will flow through the polishing interface, and the temperature rise is not the difference between the initial temperature of the polishing liquid and the temperature of the polishing disk surface). K×c×m is equivalent to the convective heat transfer coefficient between the polishing liquid and the polishing interface.

[0122] (3) The heat dissipation of the cooling water channel is as follows:

[0123] The heat exchange between the coolant and the polishing surface above is a convective heat transfer phenomenon caused by the forced flow of the coolant under the action of external force, and it is a forced convective heat transfer without phase change. The convective heat transfer between the coolant and the top of the polishing plate belongs to the heat transfer of the external swept plate of the constant fluid. The average surface heat transfer coefficient of the entire plate length is:

[0124]

[0125] Where h is the average surface heat transfer coefficient of the entire plate length; λ is the thermal conductivity; l is the plate length, and this paper takes the centerline length of each water channel; Nu is the Nusselt number of the fluid, which is related to the flow state of the fluid and needs to be judged by the Reynolds number Re:

[0126]

[0127] Where ρ is the fluid density; υ is the characteristic velocity of the flow field; L is the characteristic length of the flow field; and μ is the dynamic viscosity coefficient of the fluid.

[0128] Under the condition of fluid sweeping the flat plate, the critical value of the Reynolds number of laminar turbulence in the flow field is Re = 5×10 5

[0129] Since the workpiece is performing a composite friction rotation motion of rotation and revolution, the friction with the polishing disk surface is not uniform in area, which will cause the temperature in different places to be different. The wall temperature through which the coolant flows changes along the way. If the coolant is idealized so that its temperature remains unchanged, then this heat exchange phenomenon is constant heat flow cooling the non-isothermal wall.

[0130] a) When cooling with constant heat flow along the entire length of the water channel, the average Nu number of laminar convection heat transfer is:

[0131] Nu=0.680Re 1 / 2 Pr1 / 3

[0132] b) The average Nu number of turbulent convection heat transfer during constant heat flow cooling along the entire length of the water channel is:

[0133] Nu=0.037Re 4 / 5 Pr 1 / 3

[0134] Where Re is the Reynolds number of the fluid; Pr is the Prandtl number of the fluid

[0135] The heat taken away by the coolant in any cooling water channel of the polishing disc is obtained from the above formula:

[0136]

[0137] In the formula, Q fluid is the heat taken away by the coolant from the polishing disc which is parallel to the cooling water channel and has the same area; h is the average heat transfer coefficient of the heat transfer surface; A is the contact area between the polishing disc and the coolant; t is the polishing time; ΔT2 is the temperature difference between the polishing disc surface and the coolant temperature.

[0138] According to the above analysis of heat dissipation factors, the heat generation model at any point on the polishing disk surface is:

[0139]

[0140] In the formula, Q i is the heat at any point on the disk (i=1,2,……,n); Q is the heat generated by friction per unit time at any point on the disk; Q slurry Q is the heat removed by the polishing fluid at any point on the disk per unit time; Air Q is the heat carried away by the air at any point on the disk per unit time; fluid It is the heat removed by the cooling water channel at any point within the influence range of the cooling water channel.

[0141] According to the heat generation model of the SiC workpiece 400, a multi-objective optimization model of the water cooling structure is established as follows:

[0142]

[0143] Where D is the thickness of the polishing disc 500, w si is the width of each waterway, w ji The width of each waterway interval, ε is the number of waterways, w is the in is the cooling water channel spacing width (the distance from the inner ring of the polishing plate to the first cooling water to the left), w out is the width of the outer interval of the cooling water channel (the distance from the right side of the outermost cooling water channel to the outer ring of the polishing plate), d d is the depth of any water channel d.

[0144] The optimization objective function established is minF = {f1, -f2, -f3};

[0145] in:

[0146]

[0147] f3=D;

[0148] Where, f1 represents objective function 1, i.e., the temperature variance of several points on the polishing disc in the radial direction; f2 represents objective function 2, i.e., the volume of the cooling water channel; f3 represents objective function 3, i.e., the thickness of the polishing disc; D is the thickness of the polishing disc, w si is the width of each waterway, w ji The width of each waterway interval, ε is the number of waterways, w in Width of interval in cooling water channel, w out Cooling water channel outer interval width, d d Depth of waterway.

[0149] In this embodiment, based on the above objective function, the optimal thickness of the polishing disc, the optimal water channel structure parameters of the polishing disc and the optimal water channel structure volume are designed using a multi-objective optimization algorithm based on NSGA-II.

[0150] The specific calculation process is as follows:

[0151] The input parameters are: population size (number of solutions) N pop , the maximum number of iterations t max , the number of crossover elements is N corssover , the number of mutation elements is N mutate , mutation rate mu, objective function.

[0152] The output parameters are: Pareto optimal solution, corresponding parameters of the polishing disk water cooling structure, optimal disk thickness of the polishing disk and optimal water cooling structure volume.

[0153] The basic principle of the algorithm is: based on the crossover and mutation of the genetic algorithm, the non-dominated sorting and crowding distance are used to select the Pareto optimal solution.

[0154] The specific steps of the algorithm are:

[0155] (1) Initialize the solutions in the population. Each solution in the population contains multiple optimization design variables (water channel width of the water cooling structure, water channel depth of the water cooling structure, width of the inner and outer intervals of the water cooling structure, intervals between water channels of the water cooling structure, and thickness of the polishing plate)

[0156] Each solution in the population contains a continuous part and a discrete part. The continuous solution in the population is initialized by a random generation method, namely, the width of the water channel of the water cooling structure, the depth of the water channel of the water cooling structure, the width of the inner and outer intervals of the water cooling structure, the intervals between the water channels of the water cooling structure, and the thickness of the polishing plate:

[0157] X p,q =lb q +(ub q -lb q )·rand

[0158] Where, X p,q represents the q-th dimensional solution of the p-th solution in the population, lb q represents the lower bound of the q-th dimensional solution, ub q It represents the upper bound of the q-th dimensional solution. rand is a random number generated by the system, and its value is between 0 and 1.

[0159] The discrete solution in the population is initialized using a random generation method, that is, the number of cooling channels:

[0160] S = Randbetween(a,b)

[0161] Where S represents the number of cooling water channels, and Randbetween is a function that randomly selects an integer from a to b, where a and b are the upper and lower limits of the number of cooling water channels, respectively.

[0162] (2) Calculate the objective function value based on the current solution.

[0163] (3) For each iteration:

[0164] a. Generate a crossover population. The number of crossover elements generated in each iteration is N. crossover , each time two elements in the population are selected for crossover, a total of N crossovers are required crossover / 2 times.

[0165] The following pair of formulas is used to achieve the intersection of continuous solutions:

[0166]

[0167] Among them, X1 and X2 are the continuous solution parts of two solutions from the population, one row of m dimensions, m represents the dimension of the continuous solution, α is a 1-row m-dimensional random number array, Y1 and Y2 represent the two continuous solutions after the crossover. The multiplication of the two arrays in the formula is the multiplication of the elements in the corresponding positions in the array.

[0168] The crossover of discrete solutions is achieved through partial matching crossover (PMX). The principle of PMX is to take the fragments of the same position of two solutions and exchange them.

[0169] b. Produce mutant populations.

[0170] The mutation method of continuous solution is: first randomly select m·mu elements to be mutated from the m-dimensional continuous solution. Then use the following formula to realize the mutation of continuous solution in the element:

[0171] Y(i)=X(i)+σ·randn

[0172] Among them, σ represents the variable step length of the i-th dimension element in the continuous solution, and randn is a random number generated by the system that follows a normal distribution.

[0173] The variation method of the discrete solution is: randomly select two different numbers from the number of cooling water channels and exchange the positions of these two values.

[0174] c. Combine the original population, crossover population and variant population to form a mixed population.

[0175] d. Perform non-dominated sorting on a mixed population.

[0176] e. Calculate the crowding distance of each particle in the mixed population.

[0177] f. Sort the mixed population according to the non-dominated sorting results and the crowding distance of the particles, and retain the top N pop The solution is used as the basis for the next iteration. The sorting rule is: first sort in ascending order according to the level obtained by non-dominated sorting, and then sort the elements of each same level in descending order according to the crowding distance.

[0178] (4) After reaching the set number of iterations, the final population (optimal solution set) is returned. (At this time, the population contains the optimal solution set for the radial temperature fluctuation of the polishing disk, the thickness of the polishing disk, and the volume of the water cooling structure.)

[0179] Afterwards, the solution that can achieve the minimum temperature fluctuation in the radial direction of the polishing disk in the optimal solution set is selected as the final solution, and the final solution corresponds to the optimal disk thickness, optimal water channel structure parameters and optimal water channel structure volume of the polishing disk.

[0180] In step g, specifically, the double-sided high-precision grinding and polishing process is modeled and simulated using the Ansys / Workbench transient thermal module, such as Figure 5 , the figure is a simplified diagram of the motion boundary of the SiC workpiece 400, which applies pressure in the normal direction to the surface of the SiC workpiece 400 to simulate the pressure exerted on the SiC workpiece 400 by the cylinder-driven upper polishing plate 100, and applies a rotational speed around each Z-axis to the SiC workpiece 400 and the lower polishing plate 500.

[0181] like Figures 7 to 9, which are Ansys simulation temperature before optimization, Ansys simulation temperature after optimization, and Ansys and Matlab radial simulation temperature before and after optimization. Figure 7-9 It can be seen that after the optimization by the method provided by the present invention, the radial temperature fluctuation (variance) of the polishing disc is relatively optimized by 13.4%; the maximum temperature of the disc surface drops from 61.0°C to 58.2°C, and the average temperature drops from 43.5°C to 38.7°C; the maximum radial temperature drops from 52.9°C to 50.7°C, and the average temperature drops from 36.4°C to 34.8°C. This fully demonstrates that the optimization method provided by the present invention can improve the cooling effect of the polishing disc and improve the temperature uniformity of the polishing disc surface.

[0182] The multi-objective optimization method for the cooling structure of a polishing machine based on a heat generation model provided by the present invention obtains the operating parameters of the polishing equipment in advance; obtains the motion parameters of the planetary wheel from the obtained operating parameters; derives the motion trajectory model of the SiC workpiece from the motion parameters of the planetary wheel; and then derives the motion speed of each point on the SiC trajectory from a motion diagram of the SiC workpiece relative to the polishing disk; the total amount of heat generated at each point on the SiC trajectory can be obtained in combination with the motion speed of each point on the SiC trajectory, thereby obtaining the heat generation model of the SiC workpiece; and derives the objective function in combination with a multi-objective optimization algorithm, thereby obtaining the parameters of the water cooling structure of the polishing disk after optimization; and finally, performs comparison and verification before and after optimization by using Ansys software.

[0183] Based on the motion trajectory model of the SiC workpiece, it is possible to predict where the polishing concentration area appears on the polishing disk surface, and to perform targeted optimization to make the polishing contact area uniform; based on the heat generation model of the polishing disk surface, the temperature distribution during the polishing process can be predicted; based on the multi-objective optimization method of NSGA-Ⅱ, the temperature change of the polishing disk can be optimized with targeted water cooling structure, which is more scientific and accurate.

[0184] Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the specification and the implementation modes, and they can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and the illustrations shown and described herein.

Claims

1. A multi-objective optimization method for the cooling structure of a polishing machine based on a heat generation model, characterized in that: include: Establish a temperature variance calculation model for the temperature measurement points in the radial direction of the polishing disk surface: as well as Calculation model of water channel volume of polishing disc: f2=πd d [(w in +w s1 ) 2 -w in 2 +(w in +w s1 +w j1 +w s2 ) 2 -(w in +w s1 +w j1 ) 2 +...... +(in in +in s1 +in j1 +in s2 +in j2 +......+in s(ε-1) +in j(ε-1) +in si ) 2 -(In in +in s1 +in j1 +in s2 +in j2 +......+in s(ε-1) +in j(ε-1) ) 2 ]; In the formula, Q i is the heat of any temperature measuring point i on the polishing disc surface, n is the number of temperature measuring points in the radial direction of the polishing disc; w si is the width of each waterway, w ji is the width of each waterway interval, ε is the number of waterways, w in is the interval width in the cooling water channel, w out is the width of the outer interval of the cooling water channel, d d is the depth of each cooling water channel; The value range of each water channel width of the polishing plate, the value range of each water channel interval width, the value range of the number of water channels, the value range of the interval width inside the cooling water channel, the value range of the interval width outside the cooling water channel and the value range of the water channel depth are used as constraints; Taking the minimum temperature variance of discrete points in the radial direction of the polishing disc surface, the maximum water channel volume of the polishing disc and the maximum thickness of the polishing disc as the optimization objectives, the polishing disc water channel width, water channel depth, inner interval width of the cooling water channel, outer interval width of the cooling water channel, interval width of each water channel, polishing disc thickness and number of water channels are optimized; The optimal solution obtained by optimization is used as the structural parameters of the polishing disk cooling water channel.

2. The multi-objective optimization method for the cooling structure of a polishing machine based on a heat generation model according to claim 1, characterized in that: The calculation model of the heat at any temperature measuring point on the polishing disc surface is: Where r is the heat flux distribution coefficient; v is the relative speed between the silicon carbide workpiece and the polishing disc; μ P is the friction coefficient between the workpiece and the polishing pad and abrasive; F is the pressure exerted by the upper and lower polishing discs on the workpiece; h x is the convection heat transfer coefficient between the local silicon carbide workpiece and polishing disc and the air; t w is the surface temperature of silicon carbide workpiece; t f is the air temperature around the polishing machine, A is the surface area contacted by the air, and A x is the contact area between the disk surface and the air; c is the specific heat capacity of the polishing liquid; m is the mass of the polishing liquid flowing into the polishing interface per unit time; t is the polishing time; ΔT1 is the temperature difference between the polishing liquid when flowing in and when flowing out; K is the proportionality coefficient, ΔT2 is the temperature difference between the polishing disk surface and the coolant, λ is the thermal conductivity; l is the plate length, and Nu is the fluid Nusselt number.

3. The multi-objective optimization method for the cooling structure of a polishing machine based on a heat generation model according to claim 2, characterized in that: The relative speed between any point on the workpiece and the polishing disc is: Among them, ω P is the angular velocity of the polishing disc, ω w is the angular velocity of the workpiece; is the angle between the line connecting the center of the polishing disk and the center of the workpiece and the X-axis in the workpiece coordinate system, e is the ratio of the distance from a point on the workpiece to the center of the planetary gear to the radius of the outer ring gear, and (x, y) is the motion trajectory of the workpiece.

4. The multi-objective optimization method for the polishing machine cooling structure based on the heat generation model according to claim 3 is characterized in that: The motion trajectory model of the workpiece is: Among them, k is the ratio of the radius of the center wheel to the outer ring gear; m is the speed ratio of the outer ring gear to the center gear; ζ is the speed ratio of the polishing disc to the center wheel, and R is the radius of the outer ring gear.

5. The multi-objective optimization method for the cooling structure of a polishing machine based on a heat generation model according to claim 3 or 4, characterized in that: The NSGA-Ⅱ algorithm is used to optimize the polishing plate water channel width, water channel depth, inner interval width of cooling water channel, outer interval width of cooling water channel, interval width of each water channel, polishing plate thickness and number of water channels.

6. The multi-objective optimization method for the cooling structure of a polishing machine based on a heat generation model according to claim 5, characterized in that: The optimization process using the NSGA-Ⅱ algorithm includes the following steps: Step 1: Randomly generate an initial population, which includes N pop individuals; each of the individuals is a set consisting of the polishing plate water channel width, water channel depth, cooling water channel inner interval width, cooling water channel outer interval width, each water channel interval width, polishing plate thickness and water channel number; Step 2: Update the current population using the crossover and mutation methods to obtain a crossover and mutation population; Step 3: Merge the crossover and mutation populations with the current population, perform non-dominated sorting on the merged population to obtain the individual ranks, and calculate the crowding distance of each individual. Sort the population according to the sorting rules of individual ranks in ascending order and crowding distance in descending order, and retain the top N individuals. pop Individuals as a new population; Repeat steps 2-3 until the specified number of cycles is reached and the optimal solution set is obtained; Step 4: Select a solution that can achieve the minimum temperature variance of discrete points in the radial direction of the polishing disk surface from the optimal solution set as the final solution.

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