Grinding wheel grinding pose planning method for chip pocket of taper end mill

Abstract

The invention discloses a tapered end mill chip pocket grinding wheel grinding pose planning method. The method comprises the following steps that a mathematical representation model of a tapered end mill chip pocket and a grinding wheel is established; establishing a kinematic model of the grinding wheel grinding taper end mill chip pocket; solving a kinematic model of the grinding wheel grinding taper end mill chip pocket; calculating an equivalent core thickness error and an equivalent slot width error based on an arc projection method; establishing an optimization model of the grinding wheel grinding pose; and the grinding wheel grinding pose is optimized and solved by using a genetic algorithm. According to the method, the solving precision and solving efficiency of the grinding wheel grinding pose of the taper end mill chip flute can be improved, and the method has important significance in improving the manufacturing precision and cutter quality of high-end end mills in China.

Description

Technical Field

[0001] The invention relates to the field of tool manufacturing, and in particular to a grinding posture planning method for a chip groove grinding wheel of a tapered end mill. Background Art

[0002] Machining is a core component of modern manufacturing, widely used in aerospace, automotive, shipbuilding, rail transportation, healthcare, and other critical sectors crucial to national security and public well-being. Cutting remains an indispensable process in contemporary manufacturing. As the core foundational equipment for cutting, CNC tools directly impact machining accuracy, efficiency, and product quality, playing a vital role in the development of the manufacturing industry. Integral carbide-coated end mills are widely used in modern manufacturing due to their excellent cutting performance, long service life, and good machining stability.

[0003] The structure of an end mill includes a circumferential chip groove, a circumferential flank, an end chip groove, and an end flank, and these structures are typically ground using a grinding wheel. The circumferential chip groove is the most important structure of an end mill, and the grinding wheel grinding path is relatively complex. For cylindrical end mills with a fixed cross-sectional shape, the parameters of the circumferential chip groove are fixed, and effective methods for solving the grinding wheel grinding posture already exist. However, for tapered end mills with variable cross-sectional shapes, the parameters of the circumferential chip groove corresponding to different cross-sections are also different, and the above-mentioned grinding wheel grinding posture solution method is no longer applicable.

[0004] Currently, there is relatively little research on solving the grinding posture of grinding wheels for chip grooves of tapered end mills. Researchers generally use parameter optimization methods to find the optimal solution for the grinding posture of grinding wheels. Some researchers have used the Nelder-Mead algorithm to optimize the grinding posture of grinding wheels with variable parameter chip grooves. However, Nelder-Mead has the following shortcomings: the algorithm depends on the shape and position of the initial simplex. If the initial point is not good, it may converge to a local optimum. The algorithm is also sensitive to parameter settings, such as reflection coefficient and shrinkage coefficient. Improper settings of these parameters may affect the convergence speed and results. The above shortcomings can easily lead to low accuracy of the grinding wheel grinding trajectory obtained, or even incorrect grinding trajectories. Summary of the Invention

[0005] In order to overcome the above-mentioned shortcomings and deficiencies of the prior art, the object of the present invention is to provide a grinding posture planning method for a tapered end mill chip groove grinding wheel.

[0006] The purpose of the present invention is achieved through the following technical solutions:

[0007] A method for planning grinding posture of a tapered end mill chip groove grinding wheel comprises the following steps:

[0008] Establish a mathematical representation model of the chip groove and grinding wheel of the tapered end mill;

[0009] Establish and solve the kinematic model of the chip groove of the tapered end mill with a grinding wheel;

[0010] Calculate the equivalent core thickness error and equivalent slot width error based on the arc projection method;

[0011] Establish a grinding wheel grinding posture planning model;

[0012] The genetic algorithm is used to optimize the grinding wheel grinding posture planning model, and the optimized grinding wheel grinding posture planning model is used to plan the grinding wheel posture.

[0013] Furthermore, the mathematical representation model of the tapered end mill chip groove and the grinding wheel is established as follows:

[0014] The mathematical representation model of the chip groove of the tapered end mill is in the tool coordinate system S t (O t -x t ,y t ,z t ) is established, including a mathematical representation model of the cutting edge curve, the groove width curve and the core surface;

[0015] The mathematical representation model of the grinding wheel is in the grinding wheel coordinate system S w (O w -x w ,y w ,z w ) was established.

[0016] Furthermore, a kinematic model of the chip groove of a tapered end mill with a grinding wheel is established to describe the relative motion between the grinding wheel and the tool. The grinding wheel remains stationary in a certain position, while the end mill performs rotational motion around its own axis and linear motion along its own axis. The specific establishment process is as follows:

[0017] By establishing the reference coordinate system S r (O r -x r ,y r ,z r ), using parameters a, b, c, μ and δ to describe the tool coordinate system S t and the grinding wheel coordinate system S w The relative position relationship between the grinding wheel and the tool is used to describe the position of the grinding wheel relative to the tool during the grinding process.

[0018] Furthermore, the kinematic model of the chip groove of the tapered end mill with a grinding wheel is solved, specifically:

[0019] Calculate the normal vector of the cutting edge curve;

[0020] Calculate the normal vector of the grinding wheel surface;

[0021] Based on the conjugate surface theory, the grinding wheel surface and the cutting edge should have a common normal at the contact point. The kinematic model is solved according to the same coordinates and opposite normal vectors of the contact point.

[0022] Furthermore, the calculation of the equivalent core thickness error and the equivalent slot width error based on the arc projection method is specifically as follows:

[0023] The point in the grinding wheel coordinate system is rotated around the grinding wheel z w Rotate to x w O w z w , and then in x w O w z w The surface generates projection, and the points in the tool coordinate system are converted into points in the grinding wheel coordinate system through matrix transformation;

[0024] Then the calculation is performed, and the process is as follows:

[0025] Solve the expression for circular arc projection;

[0026] Calculate the equivalent core thickness error based on the arc projection of the core surface;

[0027] The equivalent slot width error is calculated based on the arc projection of the slot width curve.

[0028] Furthermore, the establishment of the grinding wheel grinding posture planning model is based on the constraints of avoiding the grinding wheel interfering with the ground part and ensuring that the solution is a real number, taking the sum of the squares of the equivalent core thickness error and the equivalent groove width error as the objective function, and taking the objective function value of zero as the optimization target.

[0029] Furthermore, the genetic algorithm simulates the problem to be solved into a biological evolution process, producing the next generation through operations such as replication, crossover, and mutation. According to the principle of survival of the fittest and survival of the fittest, individuals with better and better genes are evolved from generation to generation, and finally individuals with the best genes are obtained.

[0030] Furthermore, the genetic algorithm comprises the following steps:

[0031] Generate an initial population;

[0032] Perform fitness calculation;

[0033] Perform selection operations on the population;

[0034] Perform crossover operations on the population;

[0035] Perform mutation operations on the population;

[0036] The operations of calculating fitness, selection, crossover, and mutation are repeated until the termination criterion is met, thereby obtaining the optimal individual and solving the optimal end mill chip groove grinding trajectory.

[0037] Furthermore, the arc projection is formed by the point in the grinding wheel coordinate system around z w Axis rotation to x w O w z w Plane formation, based on the definition of circular projection, the expression of circular projection is derived.

[0038] Furthermore, based on the previously solved kinematic model, the expression of the upper envelope of the core arc projection is derived, and the relationship between the grinding wheel profile and the upper envelope at x is calculated. w The minimum distance in the direction is defined as the equivalent core thickness error.

[0039] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0040] This method first establishes a mathematical representation model of the chip flute and grinding wheel of a tapered end mill, and then establishes a kinematic model of the grinding wheel grinding the chip flute of a tapered end mill, describing the relative motion of the grinding wheel and end mill. The kinematic model of the grinding wheel grinding the chip flute of a tapered end mill is solved based on conjugate surface theory. With the help of the solved kinematic model, the equivalent core thickness error and equivalent flute width error are calculated using the circular arc projection method. On this basis, an optimization model for the grinding wheel grinding posture is established, and the grinding wheel grinding posture is optimized and solved using a genetic algorithm. This method can improve the solution accuracy and efficiency of the grinding wheel grinding posture of the chip flute of a tapered end mill, which is of great significance for improving the manufacturing precision and tool quality of high-end end mills in my country. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 The present invention is a flowchart of a method for planning grinding posture of a tapered end mill chip groove grinding wheel.

[0042] Figure 2 It is a schematic diagram of the relative motion between the grinding wheel and the tool.

[0043] Figure 3 It is a schematic diagram of the geometric definition of the chip groove of a tapered end mill.

[0044] Figure 4 It is a schematic diagram of the kinematic model of the chip groove of the tapered end mill with a grinding wheel.

[0045] Figure 5 is a schematic diagram of the equivalent core thickness error.

[0046] Figure 6 is a schematic diagram of the equivalent slot width error. DETAILED DESCRIPTION

[0047] The present invention will be further described in detail below with reference to the examples, but the embodiments of the present invention are not limited thereto.

[0048] Example

[0049] like Figure 1 As shown, a method for planning grinding posture of a tapered end mill chip groove grinding wheel comprises the following steps:

[0050] Step 1: Establish a mathematical representation model of the tapered end mill chip groove and grinding wheel, specifically:

[0051] Establish tool coordinate system S t (O t -x t ,y t ,z t ) and the grinding wheel coordinate system S w (O w -x w ,y w ,z w ),like Figure 2 As shown. The tool coordinate system S t Rigidly connected to the tool, origin O t Coincident with the center of the tool end face, z t The axis is aligned with the tool axis and points into the tool, x t The axis passes through the point on the cutting edge; the grinding wheel coordinate system S w Rigidly connected to the grinding wheel, plane z w =0 coincides with the end face of the grinding wheel, z w The axis is aligned with the axis pointing to the inside of the grinding wheel. The geometric definition of the chip groove of the tapered end mill is as follows Figure 3 As shown in the figure, the chip groove of the tapered end mill is defined by three parts, namely the cutting edge curve, the groove width curve and the core surface. The mathematical representation model of the chip groove of the tapered end mill is in the tool coordinate system S t The mathematical representation model of the grinding wheel is established in the grinding wheel coordinate system S w Establishing a mathematical representation model of the chip groove and grinding wheel of a tapered end mill includes the following steps:

[0052] (1)r t (t) (h1, θ1) = [r1 (h1) cos θ1, r1 (h1) sin θ1, h1] T Describes the outer contour of the tapered end mill, the cutting edge curve is represented by r t (1) (h1)=[r1(h1)cos(θ1(h1)),r1(h1)sin(θ1(h1)),h1] T Indicates that r1(h1) is the radius of the milling cutter corresponding to the point on the cutting edge curve. For a tapered milling cutter, r1(h1) = R + h1tanλ1; θ1(h1) is the angle of rotation of the point on the cutting edge curve around the milling cutter axis. When the helix angle is a fixed value, Where h1 is the z corresponding to the point on the cutting edge curve. t Axis coordinates, R is the radius of the bottom surface of the taper milling cutter, λ1 is the taper, β is the helix angle, label 1 identifies the parameters related to the cutting edge curve, t indicates that the expression is in the tool coordinate system S t defined in;

[0053] (2) The core surface is composed of r t (2) (h2, θ2) = [r2 (h2) cos θ2, r2 (h2) sin θ2, h2] T Indicates that the core surface is a surface of revolution with a radius equal to the core thickness, where h2 is the z-axis corresponding to a point on the core surface. t Axis coordinates, r2(h2) is the radius of the milling cutter corresponding to the point on the core surface, θ2 is the angle of rotation of the point on the core surface around the milling cutter axis, label 2 identifies the parameters related to the core surface, t represents the expression in the tool coordinate system s t defined in;

[0054] (3) The groove width curve is formed by rotating the cutting edge curve clockwise around the milling cutter axis at the groove width angle, so the groove width curve is formed by r t (3) (h3)=M t r t (h3) indicates that, where M t is the rotation transformation matrix, h3 is the z corresponding to the point on the slot width curve t Axis coordinates, label 3 identifies the parameters related to the groove width curve, t represents the expression in the tool coordinate system S t defined in;

[0055] (4) The surface of the grinding wheel is Indicates that, h0 is the z corresponding to the point on the grinding wheel surface w Axis coordinates, r0 (h0) is the radius of the grinding wheel corresponding to the point on the grinding wheel surface, θ0 is the angle of rotation of the point on the grinding wheel surface around the grinding wheel axis, the label 0 identifies the parameters related to the grinding wheel, and w indicates that the expression is in the grinding wheel coordinate system S w Defined in.

[0056] Step 2: Establish the kinematic model of the chip groove of the tapered end mill with a grinding wheel;

[0057] The process of grinding the chip groove of a tapered end mill with a grinding wheel can be described as follows: the grinding wheel remains stationary in a specific posture, while the end mill performs rotational motion around its own axis and linear motion along its own axis. In order to describe the relative motion between the grinding wheel and the tool, a reference coordinate system S is established. r (O r -x r ,y r ,z r ),like Figure 4 As shown, the grinding wheel origin O w Fixed at z r =0 plane, a, b, c determine the position of the grinding wheel relative to the tool, μ determines the direction of the grinding wheel relative to the tool axis; as the grinding progresses, the tool moves around z r The axis rotates by δ, and the position and direction of the grinding wheel relative to the tool gradually change. Therefore, the parameters a, b, c, μ and δ define the position of the grinding wheel relative to the tool during the sharpening process. The position of the grinding wheel relative to the tool is expressed in the grinding wheel coordinate system S w and tool coordinate system S t It is represented by the transformation matrix between them.

[0058]

[0059] M rw is the grinding wheel coordinate system S w To the reference coordinate system S r The transformation matrix of the transform.

[0060]

[0061] M rt From the tool coordinate system S t To the reference coordinate system S r The transformation matrix of the transform.

[0062]

[0063] M tw is the grinding wheel coordinate system S w To the tool coordinate system S t The transformation matrix of the transformation is transformed through the transformation matrix M tw The relative motion of the grinding wheel and the tool can be described.

[0064] Step 3: Solve the kinematic model of the chip groove of the tapered end mill with a grinding wheel;

[0065] Specifically:

[0066] During the grinding process of a grinding wheel grinding a chip groove, the grinding wheel surface contacts the cutting edge curve. Conjugate surface theory shows that the two surfaces have the same normal and curvature at the contact point, so the grinding wheel surface and the cutting edge curve should have a common normal at the contact point. Based on the same contact point coordinates and opposite normal vectors, the kinematic model of grinding a tapered end mill chip groove with a grinding wheel can be solved. It includes the following steps:

[0067] (1) To calculate the normal vector of the cutting edge curve Establish the natural axis system S at the points on the cutting edge curve n (O-ijk), e.g. Figure 3As shown. The i-axis is along the radial direction of the end mill, the j-axis is tangential to the cutting edge curve, the k-axis is perpendicular to the i-axis and the j-axis, and the j-axis unit vector is calculated by the following formula:

[0068]

[0069] The unit normal vector of the rotary surface of the end mill is expressed by the following formula:

[0070]

[0071] Substitute θ1(h1) into i t (h1,θ1) can get the i-axis unit vector i(h1)=[i x ,i y ,i z ] T , and the k-axis unit vector k(h1)=i×j=[k x ,k y ,k z ] T , since the normal vector of the cutting edge curve The angle with the k-axis is the normal angle α n ,therefore It is expressed by the following formula:

[0072]

[0073] In the above formula, α n is the normal rake angle, and is related to the radial rake angle α r There is a geometric relationship, calculated by the following formula:

[0074]

[0075] (2) According to the expression of grinding wheel radius r0(h0), the normal vector n of the grinding wheel surface w The calculation formula is as follows:

[0076]

[0077] In the above formula, r0 ′ Defined as the radius of the grinding wheel r0 relative to z w The derivative of the axis coordinate h0, that is The parameters

[0078] (3) The grinding wheel surface and the cutting edge curve are tangent at the contact point. The point on the grinding wheel surface is expressed in the tool coordinate system as The vector on the grinding wheel surface is expressed in the tool coordinate system as The cutting edge point is represented by r in the tool coordinate system t (1)(h1), the cutting edge normal vector is expressed in the tool coordinate system as According to the same coordinates of the contact points, r t (0) (h0,θ0)=r t (1) (h1); According to the opposite normal vector of the contact point, Solving the above two equations gives the formulas for a, b, c, and δ:

[0079]

[0080] In the above formula, θ0 is the rotation angle of the contact point on the grinding wheel surface around the grinding wheel axis. θ0 is calculated by the following formula:

[0081]

[0082] In the above formula, θ0 must be non-imaginary, so η must satisfy |η| ≤ 1. Based on the obtained parameters a, b, c, μ, and δ, the grinding wheel grinding posture of the tapered end mill chip groove can be solved:

[0083]

[0084] In the above formula, O x , O y , O z are the three components of the coordinates of the center point of the grinding wheel end face in the tool coordinate system, that is, the grinding wheel position; F x 、F y 、F z is the normal direction of the grinding wheel end face in the tool coordinate system, that is, the grinding wheel posture. The grinding wheel posture during grinding is defined by the parameters a, b, c, μ, and δ, and the parameters a, b, c, and δ are defined by h0 and μ. Therefore, the grinding wheel grinding posture is defined by h0 and μ.

[0085] Step 4: Calculate the equivalent core thickness error and equivalent slot width error based on the arc projection method, specifically:

[0086] The parameters of the chip groove include rake angle, helix angle, core thickness radius, and groove width. The kinematic model solved by the above steps can ensure that the chip groove has accurate helix angle and rake angle, that is, the machining helix angle is equal to the designed helix angle, and the machining rake angle is equal to the designed rake angle. However, it cannot guarantee that the chip groove has accurate core thickness radius and groove width. Therefore, the arc projection method is used to solve this problem. The specific method of the arc projection method is to move the point in the grinding wheel coordinate system around the grinding wheel z w Axis rotation to x w O w z w plane, and then in x w O w z w The plane produces a projection, and the points in other coordinate systems want to be on xw O w z w The plane projection needs to be transformed into a point in the grinding wheel coordinate system through matrix transformation. The arc projection method is used to obtain the grinding wheel surface, core surface, and groove width curve in x w O w z w The arc projection of the plane, the shortest distance between the envelope line on the arc projection of the grinding wheel surface and the core surface is defined as the equivalent core thickness error, such as Figure 5 As shown in the figure, the shortest distance between the grinding wheel surface and the arc projection of the groove width curve is defined as the equivalent groove width error, as shown in the figure. Figure 6 As shown in FIG, the equivalent core thickness error and the equivalent slot width error can be used to evaluate the core thickness error and slot width error during the grinding process. The equivalent core thickness error and the equivalent slot width error are calculated based on the arc projection method, which includes the following steps:

[0087] (1) For point r in the grinding wheel coordinate system w =[x w ,y w ,z w ] T , around z w Rotate to x w O w z w The expression of the arc projection is:

[0088]

[0089] In the above formula, the subscript Ψ indicates that the point is rotated to x w O w z w Arc projection of a plane.

[0090] (2) The expression of the core surface in the grinding wheel coordinate system is as follows:

[0091]

[0092] Then the expression of the core arc projection is:

[0093]

[0094] According to the envelope theory, the envelope surface of the core arc projection should satisfy the following formula:

[0095]

[0096] From this, we can solve the expression of θ2 corresponding to the envelope line on the core surface arc projection:

[0097]

[0098] In the above formula, the parameters d, e, f and ρ are calculated by the following formula:

[0099]

[0100] Substituting θ2 into The upper envelope of the core arc projection can be obtained, and the upper envelope is expressed as The equivalent core thickness error Δ1 is defined as the difference between the grinding wheel profile and the upper envelope at x w The minimum distance in the direction, so the calculation formula of Δ1 is as follows:

[0101]

[0102] In the above formula, the value of Δ1 needs to be searched within the h2 interval corresponding to the grinding wheel profile. When Δ1>0, the grinding wheel profile and the upper envelope are separated from each other, indicating that the grinding wheel surface is separated from the core surface, resulting in the actual core thickness radius being larger than the designed radius. When Δ1<0, the grinding wheel profile intersects with the upper envelope, indicating that the grinding wheel surface intersects with the core surface, resulting in the actual core thickness radius being smaller than the designed radius. The value of Δ1 depends on the grinding wheel posture, that is, on the values ​​of h0 and μ. In order to ensure the accuracy of the core thickness radius, it is necessary to optimize h0 and μ to satisfy Δ1=0.

[0103] (3) Calculate the equivalent groove width error based on the arc projection of the groove width curve. The expression of the groove width curve in the grinding wheel coordinate system is as follows:

[0104]

[0105] The expression of the arc projection of the groove width curve is as follows:

[0106]

[0107] The equivalent groove width error Δ2 is defined as the difference between the grinding wheel profile and the groove width curve at x w The minimum distance in the direction, so the calculation formula of Δ2 is as follows:

[0108]

[0109] In the above formula, the value of Δ2 needs to be searched within the h3 interval corresponding to the grinding wheel profile. When Δ2>0, the grinding wheel profile and the groove width curve are separated from each other, indicating that the grinding wheel surface is separated from the groove width curve, resulting in the actual groove width being smaller than the designed groove width. When Δ2<0, the grinding wheel profile and the groove width curve intersect, indicating that the grinding wheel surface intersects with the groove width curve, resulting in the actual groove width being larger than the designed groove width. The value of Δ2 depends on the grinding wheel posture, that is, on the h0 and μ values. To ensure the accuracy of the groove width, it is necessary to optimize h0 and μ to satisfy Δ2=0.

[0110] Step 5: Establish an optimized model of the grinding wheel grinding posture, specifically:

[0111] For each grinding wheel posture, it is necessary to simultaneously satisfy Δ1 = 0 and Δ2 = 0, thereby establishing the optimization model of the grinding wheel grinding posture:

[0112]

[0113] In the above formula, Δ represents the sum of the squares of Δ1 and Δ2. When Δ1 = 0 and Δ2 = 0, Δ is minimized. Solving for h0 and μ, which correspond to the minimum Δ value of 0, ensures that the actual core radius and actual groove width are equal to the designed core radius and groove width. The optimization model must satisfy 0 < μ ≤ π / 2-β to ensure that the grinding wheel does not interfere with the ground area, and |η| ≤ 1 to avoid obtaining imaginary solutions.

[0114] Step 6: Use genetic algorithm to optimize and solve the grinding wheel grinding posture.

[0115] A genetic algorithm is a method for searching for optimal solutions by simulating the natural evolutionary process. This method simulates the problem to be solved as a biological evolutionary process, producing the next generation through operations such as replication, crossover, and mutation. Following the principles of survival of the fittest, each generation evolves to produce individuals with increasingly better genes, ultimately achieving individuals with optimal genes. A population is a collection of a certain number of individuals. Individuals are actually entities with characteristics on their chromosomes, and chromosomes carry several genes. Here, the parameters h0 and μ are considered genes on the chromosomes, and the array containing h0 and μ can be considered a chromosome, representing each individual. Using a genetic algorithm to optimize the grinding wheel's grinding posture includes the following steps:

[0116] (1) The initial population is the population generated at the beginning of the genetic algorithm, and the genes of individual chromosomes are quite different. Generating the initial population of the genetic algorithm involves setting the population size, individual coding, and randomly generating individuals. The population size depends on the complexity of the problem. Here, the population size is set to N; the operation object of the genetic algorithm is a symbol string representing an individual, so the parameters h0 and μ must be encoded as a symbol string. The value range of the parameter h is (0, H), where H is the thickness of the grinding wheel; the value range of μ is (0, π / 2-β), where β is the spiral angle. In order to ensure the accuracy requirements, it is necessary to divide the interval lengths of h0 and μ by the solution accuracy m, thereby obtaining the interval number n1 = H / m, n2 = (π / 2-β) / m, according to and Take the minimum number of binary digits N1 and N2 required to encode h0 and μ. The parameters h0 and μ are thus encoded as binary numbers with N1 and N2 digits. Each bit of the binary encoding of h0 and μ is randomly set to 0 or 1, and thus randomly generated values ​​of h0 and μ can be generated within the range of the independent variable, with each set of values ​​corresponding to one individual.

[0117] (2) Fitness is used to evaluate the quality of each individual, thereby determining the size of their chances of participating in inheritance. Fitness needs to be determined based on the objective function, which is As the objective function, set the fitness function F = 1 / Δ. The smaller the value of the objective function, the greater the fitness. For h0 and μ values ​​that do not meet the constraint condition |η| ≤ 1, the fitness is directly set to 0, that is, the individuals corresponding to the combination of h0 and μ are directly excluded; for h0 and μ values ​​that meet Δ = 0, the fitness is directly set to 10^6, that is, the probability of the individuals corresponding to the combination of h0 and μ participating in inheritance is set to 1, and other individuals are excluded;

[0118] (3) The selection operation selects individuals with higher fitness from the current population as parents to generate the next generation. It includes the following steps: First, calculate the sum of the fitness of all individuals in the population. Second, calculate the selection probability of each individual The value of the selection probability represents the probability of an individual participating in the next generation of inheritance. For an individual with a fitness of 10^6, the selection probability is 1, and all individuals participating in the next generation of inheritance are this individual, and the algorithm converges to the optimal solution. Then, each selection probability forms a probability interval, generates a random number rand∈[0,1), and accumulates the selection probability. Select the one that satisfies C i-1 ≤rand≤C i Individual G i , that is, rand falls on individual G i The corresponding probability interval; finally, the difference in the number of individuals in the population before and after the selection operation is calculated N c , select the N with the highest fitness in the population after the selection operation c Individuals are copied and added to the population after the selection operation. On the one hand, the population size is kept constant at N; on the other hand, the best individuals in the population are not eliminated, thus preserving high-quality genes.

[0119] (4) Crossover operation refers to exchanging some genes of two paired chromosomes in a certain way to form two new individuals. Its purpose is to explore new solutions in the search space while retaining the good characteristics of the parent generation. It includes the following steps: First, set the crossover probability P c ∈[0.001,0.1], so that the gene has a probability P c Crossover occurs; P c Usually a smaller value is taken to avoid destroying high-quality genomes. As the number of iterations increases, P should be gradually reduced. c , thereby retaining an increasing proportion of high fitness individuals; secondly, for each individual G in the population i =(h 0i ,μ i), randomly select individual G in the population j =(h 0j ,μ j ) and cross it, i, j∈[1,N], indicating that individuals G with numbers i and j are selected i and G j For individual G j , generate a random number rand∈[0,1); when rand≤P c Time G j With G i Crossover, when rand>P c Time G j Not with G i Crossover; then, in individual G i and G j Randomly select a gene from the gene sequence for crossover, set a random value, and use the random value to determine the exchange h 0i 、h 0j Or swap μ i 、μ j Finally, the exchanged genes are recombined into new individuals and these new individuals are added to the offspring population.

[0120] (5) Mutation operation refers to randomly selecting an individual in the population and changing its genes with a certain probability, which is used to introduce new genetic diversity into the population and prevent the algorithm from converging to the local optimal solution too early. It includes the following steps: First, set the mutation probability P m ∈[0.001,0.1], so that the gene has a probability P m Mutation occurs; P m Usually a smaller value is taken to avoid destroying high-quality genes. As the number of iterations increases, P should be gradually reduced. m , thereby retaining an increasing proportion of high fitness individuals; secondly, determine whether the gene mutates, generate a random number rand∈[0,1) for each gene, when rand≤P m Participate in mutation when rand>P m does not participate in the mutation; then, the genes involved in the mutation are randomly changed by flipping a bit of the binary code of the gene, changing a bit in the code of h0 and μ from 1 to 0 or from 0 to 1; finally, h0 and μ after the binary code change are recombined into a new individual and added to the offspring population.

[0121] (6) After the fitness calculation, selection operation, chromosome crossover, and chromosome mutation operations, a new generation of populations is generated from the initial population. The above operations are continued on the new generation of populations to continuously generate new populations, and the proportion of individuals with high fitness in the population continues to increase. When the number of iterations reaches a sufficiently large value, the individual with the best fitness can be obtained. At this time, h0 and μ can satisfy Δ = 0. The calculated grinding wheel posture can simultaneously ensure the processing accuracy of the helix angle, rake angle, core thickness radius, and groove width.

[0122] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be considered as equivalent replacement methods and are included in the scope of protection of the present invention.

Claims

1. A method for planning grinding posture of a tapered end mill chip groove grinding wheel, characterized in that: The steps include: Establish a mathematical representation model of the chip groove and grinding wheel of the tapered end mill; Establish and solve the kinematic model of the chip groove of the tapered end mill with a grinding wheel; Calculate the equivalent core thickness error and equivalent slot width error based on the arc projection method; Establish a grinding wheel grinding posture planning model; The genetic algorithm is used to optimize the grinding wheel grinding posture planning model, and the optimized grinding wheel grinding posture planning model is used to plan the grinding wheel posture.

2. The method for planning grinding posture of a tapered end mill chip groove grinding wheel according to claim 1, characterized in that: The mathematical representation model of the chip groove and grinding wheel of the tapered end mill is specifically as follows: The mathematical representation model of the chip groove of the tapered end mill is in the tool coordinate system S t (O t -x t ,y t ,z t ) is established, including a mathematical representation model of the cutting edge curve, the groove width curve and the core surface; The mathematical representation model of the grinding wheel is in the grinding wheel coordinate system S w (O w -x w ,y w ,z w ) was established.

3. The method for planning grinding posture of a tapered end mill chip groove grinding wheel according to claim 1, characterized in that: The kinematic model of the chip groove of a tapered end mill with a grinding wheel is established to describe the relative motion between the grinding wheel and the tool. The grinding wheel remains stationary in a certain position, while the end mill performs rotational motion around its own axis and linear motion along its own axis. The specific establishment process is as follows: By establishing the reference coordinate system S r (O r -x r ,y r ,z r ), using parameters a, b, c, μ and δ to describe the tool coordinate system S t and the grinding wheel coordinate system S w The relative position relationship between the grinding wheel and the tool is used to describe the position of the grinding wheel relative to the tool during the grinding process.

4. The method for planning grinding posture of a tapered end mill chip groove grinding wheel according to claim 1, characterized in that: The kinematic model of the chip groove of the tapered end mill with a grinding wheel is solved as follows: Calculate the normal vector of the cutting edge curve; Calculate the normal vector of the grinding wheel surface; Based on the conjugate surface theory, the grinding wheel surface and the cutting edge should have a common normal at the contact point. The kinematic model is solved according to the same coordinates and opposite normal vectors of the contact point.

5. The method for planning grinding posture of a tapered end mill chip groove grinding wheel according to claim 1, characterized in that: The calculation of the equivalent core thickness error and the equivalent slot width error based on the arc projection method is specifically as follows: The point in the grinding wheel coordinate system is rotated around the grinding wheel z w Rotate to x w O w z w , and then in x w O w z w The surface generates projection, and the points in the tool coordinate system are converted into points in the grinding wheel coordinate system through matrix transformation; Then the calculation is performed, and the process is as follows: Solve the expression for circular arc projection; Calculate the equivalent core thickness error based on the arc projection of the core surface; The equivalent slot width error is calculated based on the arc projection of the slot width curve.

6. The method for planning grinding posture of a tapered end mill chip groove grinding wheel according to any one of claims 1 to 5, characterized in that: The grinding wheel grinding posture planning model is established based on the constraints of avoiding the grinding wheel from interfering with the ground part and ensuring that the solution is a real number, taking the sum of the squares of the equivalent core thickness error and the equivalent groove width error as the objective function, and taking the objective function value of zero as the optimization goal.

7. The method for planning grinding posture of a tapered end mill chip groove grinding wheel according to claim 6, characterized in that: The problem to be solved by the genetic algorithm is simulated into a biological evolution process, which produces the next generation through operations such as replication, crossover, and mutation. According to the principle of survival of the fittest and elimination of the weak, the genetically improved individuals are evolved from generation to generation, and finally the genetically optimized individuals are obtained.

8. The method for planning grinding posture of a tapered end mill chip groove grinding wheel according to claim 7, characterized in that: The genetic algorithm comprises the following steps: Generate an initial population; Perform fitness calculation; Perform selection operations on the population; Perform crossover operations on the population; Perform mutation operations on the population; The operations of calculating fitness, selection, crossover, and mutation are repeated until the termination criterion is met, thereby obtaining the optimal individual and solving the optimal end mill chip groove grinding trajectory.

9. The method for planning grinding posture of a tapered end mill chip groove grinding wheel according to claim 5, characterized in that: The arc projection is formed by the point in the grinding wheel coordinate system around z w Axis rotation to x w O w z w Plane formation, based on the definition of circular projection, the expression of circular projection is derived.

10. The grinding posture planning method for a tapered end mill chip groove grinding wheel according to claim 5, characterized in that: Based on the previously solved kinematic model, the expression of the upper envelope of the core arc projection is derived, and the relationship between the grinding wheel profile and the upper envelope at x is calculated. w The minimum distance in the direction is defined as the equivalent core thickness error.

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