A grinding wheel track calculation method for a numerical control milling cutter helical groove grinding process

Abstract

The application discloses a kind of grinding wheel trajectory calculation methods for numerical control milling cutter helical groove grinding process, specifically: first, the parameterization modeling of the grinding wheel and motion relationship of helical groove grinding process is carried out;Second, the envelope surface formed by the spatial helical motion of grinding wheel is calculated according to the motion trajectory of grinding wheel, and the helical groove profile equation formed by grinding wheel grinding is calculated by the contact condition of space envelope principle;Then, according to the geometric definition of the rake angle, core thickness, groove width parameters of helical groove, the functional relationship of each parameter about grinding wheel pose is established;Finally, the grinding wheel pose solving problem is converted into mathematical optimization problem, and the grinding wheel grinding pose is quickly solved using intelligent algorithm.The application realizes the high-precision, high-efficiency processing of numerical control milling cutter helical groove.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of numerical control milling cutter helical groove grinding, and particularly relates to a grinding wheel track calculation method for a numerical control milling cutter helical groove grinding process. BACKGROUND

[0002] As an important structural feature of an end mill, the helical groove plays a crucial role in the cutting, chip removal, chip breaking and overall rigidity of the tool. To meet the increasingly precise machining requirements and harsh machining conditions of modern manufacturing, the structural design of the helical groove is becoming increasingly complex, and the machining precision requirements are also becoming higher and higher. The existing grinding process has been difficult to meet the helical groove parameter machining precision requirements.

[0003] Karpuschewski et al. used the grinding wheel pose parameters as the optimization variables and the helical groove profile error as the optimization objective function to solve the grinding wheel pose by using the particle swarm algorithm. Li Guochao et al. proposed a helical groove grinding process design method based on the size and pose combination optimization of the double-bevel grinding wheel, selected a specific grinding wheel according to the shape of the helical groove, and established the helical groove structural parameter error and profile error as the optimization objective function. However, the calculation accuracy of the helical groove profile is limited by the discrete step accuracy and is prone to fail to solve. Jia Kang et al. aimed at the accurate and high-quality grinding of the rake face of a broach helical groove, constructed the grinding process constraint conditions to ensure the rake angle, groove bottom arc radius and other elements, formed a grinding wheel pose calculation model and its optimization search method. Liu et al. and Zhan et al. aimed at the grinding wheel wear round corner and solved the grinding wheel grinding pose by using the iteration method. Ren et al. aimed at the grinding process of a 1V1 / 1A1 grinding wheel, established the functional relationship between the rake angle, core thickness and groove width and the grinding wheel pose as a nonlinear equation set of elements, and obtained the grinding wheel pose by solving the equation set, but there is no solution for the transcendental equation. Nguyen et al. simplified the grinding wheel pose parameters, and established the mapping relationship between the helical groove structural parameters and the grinding wheel pose by using the analytic geometry method. Compared with other methods, the solving efficiency is greatly improved, but the algorithm is prone to fail due to the rounding of the end points of the grinding wheel profile.

[0004] At present, the research on the standard grinding wheel grinding process of the helical groove is relatively mature, but there is still a lack of a high-precision and highly versatile calculation method for the formation of the helical groove end face profile, resulting in a contradiction between the solving accuracy and practicality of the grinding wheel pose solving method. SUMMARY

[0005] To overcome the above problems, the present application calculates the accurate mathematical expression of the helical groove radial cross-sectional profile formed by the grinding wheel grinding, constructs the functional relationship between the helical groove structural parameters and the grinding wheel pose, and provides a grinding wheel track calculation method for a numerical control milling cutter helical groove grinding process.

[0006] A method for calculating a grinding wheel trajectory in a CNC milling cutter spiral groove grinding process according to the present invention comprises the following steps:

[0007] Step 1: Establish grinding motion relationship.

[0008] Establish grinding wheel coordinate system O G -X G Y G Z G :Coordinate origin O G Located at the center of the large end circle of the grinding wheel, coordinate axis Z G Coincident with the grinding wheel axis, coordinate plane X G Y G It coincides with the large end circular plane of the grinding wheel; the equation of the grinding wheel rotation surface in the grinding wheel coordinate system is as follows:

[0009]

[0010] Where h is the distance from the point on the rotating surface to the large end face of the grinding wheel, and ψ is the distance from the point on the rotating surface to the coordinate axis Y. G is the rotation angle parameter, and R(h) is the grinding wheel profile equation.

[0011] Establish workpiece coordinate system O W -X W Y W Z W :Coordinate origin O W Located at the center of the tool bar end face, coordinate axis Z W Coincident with the tool bar axis, coordinate plane X W Y W Coincident with the end face of the tool bar.

[0012] Establish grinding wheel grinding posture parameters: center distance a x For two coordinate origins in X W Distance on axis; offset a y For two coordinate origins in Y W Distance on the axis; installation angle α, grinding wheel around X W The angle of axis rotation. Therefore, the transformation matrix between the grinding wheel coordinate system and the workpiece coordinate system is as follows:

[0013]

[0014] The grinding wheel moves along the Z direction W The axis moves forward while rotating around Z W The axis rotates by an angle ξ, and the radius of the spiral edge line is defined as R, which is the same as the radius of the workpiece. The spiral angle is β. Therefore, the transformation matrix M of the grinding wheel coordinate system and the workpiece coordinate system about the angle ξ is e (ξ) is shown in the following formula:

[0015]

[0016] Where, κ = R / tanβ.

[0017] Step 2: Calculate the spiral groove profile formed by grinding wheel.

[0018] The trajectory P of the grinding wheel rotating surface doing spatial spiral motion S (h,ψ,ξ,a x ,a y ,α) is shown as follows:

[0019]

[0020] The motion trajectory equation of the grinding wheel rotating surface P S The partial derivatives of the grinding wheel variables h and ψ are calculated respectively, and the normal vector of the point on the rotation surface is obtained by cross product. The normal vector N(h, ψ) of the point on the rotation surface of the grinding wheel is calculated at the moment ξ = 0, as shown in the following formula:

[0021]

[0022] The motion trajectory equation P of the grinding wheel rotating surface S Find the partial derivative of the motion variable ξ and calculate the velocity vector V(h,ψ) of the point on the grinding wheel rotation surface at the moment ξ=0, as shown in the following formula:

[0023]

[0024] According to the condition that the normal vector and velocity vector of the point on the contact line are perpendicular to each other (N(h,ψ)×V(h,ψ)=0), Equations (5) and (6) are substituted into the calculation of the rotation angle ψ(h) of the point on the contact line of the grinding wheel, which is simplified as follows:

[0025]

[0026] Where B1 = a x cosα+κsinα, B2=(R(h)R′(h)-h)sinα+a y , B3=(κcosα-a x sinα)R′(h).

[0027] Substitute equation (7) back into the motion trajectory equation (4) of the grinding wheel rotating surface to calculate the contact line of the grinding wheel rotating surface, and calculate Z by the contact line through the contact line through the motion transformation. W = 0 in the radial section profile equation of the spiral groove p(h,a x ,a y ,α), as shown below:

[0028]

[0029] In the formula, ξ0=(h cosα-R(h)sin(ψ(h))sinα) / κ.

[0030] Step 3: Establish the grinding wheel posture constraint equation.

[0031] (1) Vector T1 is the tangent vector of p1 at the starting point of the radial cross-section of the spiral groove, and vector P1 is the tangent vector of point O W The vector pointing to point p1 on the radial cross-section of the spiral groove, the rake angle γ is the angle between vector P1 and vector T1, where when the Z of P1×T1 W When the coordinate is positive, the rake angle is positive, and when the coordinate is negative, the rake angle is negative. The functional relationship between the spiral groove rake angle and the grinding wheel posture is f γ As shown in the following formula:

[0032]

[0033] Where h1 is the grinding wheel variable corresponding to point p1, and t r =(0,0,1).

[0034] (2) Core thickness r c Point p2 is the tangent point where the radial cross-section of the spiral groove is tangent to the core thickness circle. The vector P2 is point O. W The vector pointing to point p2 on the radial cross-section of the spiral groove, vector T2 is the tangent vector at point p2, vector P2·T2=0, the functional relationship between the spiral groove core thickness and the grinding wheel posture is f rc As shown in the following formula:

[0035]

[0036] Where h2 is the grinding wheel variable corresponding to point p2, and x′ p (h2,a x ,a y ,α)·y p (h2,a x ,a y ,α)-y′ p (h2,a x ,a y ,α)·x p (h2,a x ,a y ,α)=0.

[0037] (3) Vector P3 is point O W The vector pointing to the end point p3 of the radial section profile of the spiral groove, the groove width φ is the angle between the vector P1 and the vector P3, when the Z of the vector P1×P3 WWhen the coordinate is positive, the groove width is less than 180°, otherwise the groove width is greater than 180°. The functional relationship between the spiral groove core thickness and the grinding wheel posture is f φ As shown in the following formula:

[0038]

[0039] Where h3 is the grinding wheel variable corresponding to point p3, and

[0040] Step 4: Solve the grinding posture of the grinding wheel.

[0041] The objective function of the grinding wheel posture optimization problem is established as follows:

[0042] min Fit=ω1(f γ -γ) 2 +ω2(f φ -φ) 2 +ω3(f rc -r c ) 2 (12)

[0043] Where ω1, ω2, and ω3 are weight coefficients.

[0044] The particle swarm algorithm is used to solve the grinding wheel posture. The grinding wheel posture is regarded as a three-dimensional particle and the grinding wheel posture particle is defined as VecX(a x ,a y ,α); determine the number of particle swarm N, initialize the particle swarm VecX in the grinding wheel posture search space i (a xi ,a yi ,α i ), and initialize the velocity V of each particle i , i=1,2,3,…,N; then iterative calculation is performed, and the particle swarm algorithm iteration rule is as follows:

[0045]

[0046] Where ω is the inertia weight, c1 and c2 are learning factors, r1 and r2 are random numbers in [0,1], and pbest i is the individual optimal, and gbest is the global optimal.

[0047] The calculation process of the particle swarm algorithm is:

[0048] (1) Set the particle swarm algorithm parameters ω, c1, c2, r1, r2, the number of particle swarms N, the maximum number of iterations max_gen and the minimum error allowed for the termination of the iteration;

[0049] (2) Initialize particle swarm: position and velocity Vi and position VecX i ;

[0050] (3) Substitute the initialized particles into formula (12) to calculate the initial fitness value Fit(VecX i ), mark the initial fitness value of each particle as the individual optimal pbest i And mark the best individual as the global optimal gbest;

[0051] (4) Update the position and velocity of the particle swarm according to formula (13);

[0052] (5) Substitute the updated particles into formula (12) to update the fitness value. If Fit(VecX i ) <pbest i , then update the individual optimal pbest i =Fit(VecX i ), if Fit(VecX i ) <gbest,则更新全局最优gbest=Fit(VecX i );

[0053] (6) If the end condition is met, the operation ends; otherwise, return to step (3).

[0054] The closer the value of the objective function is to zero, the more accurate the solution to the above nonlinear equations is.

[0055] The beneficial technical effects of the present invention are:

[0056] The present invention aims at the precise grinding process of parameters such as the rake angle, core thickness, and groove width of the milling cutter spiral groove. By calculating the precise mathematical expression of the radial truncation profile of the spiral groove formed by grinding the grinding wheel, the functional relationship between the spiral groove structural parameters and the grinding wheel posture is constructed, and the grinding wheel posture is quickly solved through an optimization algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 This is a schematic diagram of parametric modeling of 1V1 / 1A1 standard grinding wheel;

[0058] Figure 2 It is a schematic diagram of the motion relationship between the grinding wheel and the workpiece;

[0059] Figure 3 It is the trajectory diagram formed by the grinding wheel in the radial section;

[0060] Figure 4 It is a schematic diagram of the contact line between the grinding wheel and the workpiece bar during grinding;

[0061] Figure 5 It is the geometric definition diagram of the spiral groove structural parameters;

[0062] Figure 6 This is the test result diagram of the rake angle of the experimental processing group I;

[0063] Figure 7 This is the core thickness test result diagram of experimental processing group II;

[0064] Figure 8 This is the test result diagram of the slot width of group III in the experimental processing. DETAILED DESCRIPTION

[0065] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0066] The present invention provides a grinding wheel trajectory calculation method for a CNC milling cutter spiral groove grinding process, specifically:

[0067] Step 1: Establish grinding motion relationship.

[0068] like Figure 1 As shown, establish the grinding wheel coordinate system O G -X G Y G Z G :Coordinate origin O G Located at the center of the large end circle of the grinding wheel, coordinate axis Z G Coincident with the grinding wheel axis, coordinate plane X G Y G It coincides with the large end circular plane of the grinding wheel; the equation of the grinding wheel rotation surface in the grinding wheel coordinate system is as follows:

[0069]

[0070] Where h is the distance from the point on the rotating surface to the large end face of the grinding wheel, and ψ is the distance from the point on the rotating surface to the coordinate axis Y. G is the rotation angle parameter, and R(h) is the grinding wheel profile equation.

[0071] like Figure 2 As shown, establish the workpiece coordinate system O W -X W Y W Z W :Coordinate origin O W Located at the center of the tool bar end face, coordinate axis Z W Coincident with the tool bar axis, coordinate plane X W Y W Coincident with the end face of the tool bar.

[0072] Establish grinding wheel grinding posture parameters: center distance a x For two coordinate origins in X W Distance on axis; offset a y For two coordinate origins in Y WDistance on the axis; installation angle α, grinding wheel around X W The angle of axis rotation. Therefore, the transformation matrix between the grinding wheel coordinate system and the workpiece coordinate system is as follows:

[0073]

[0074] from Figure 2 It can be seen that the spiral groove grinding process can be regarded as the workpiece is fixed and the grinding wheel moves along the spiral edge line. W The axis moves forward while rotating around Z W The axis rotates by an angle ξ, and the radius of the spiral edge line is defined as R, which is the same as the radius of the workpiece. The spiral angle is β. Therefore, the transformation matrix M of the grinding wheel coordinate system and the workpiece coordinate system about the angle ξ is e (ξ) is shown in the following formula:

[0075]

[0076] Where, κ = R / tanβ.

[0077] Step 2: Calculate the spiral groove profile formed by grinding wheel.

[0078] From the kinematic modeling of the grinding wheel, we can see that the grinding wheel first determines the installation position and posture, and then the tool bar rotates around its own axis and moves forward. The relative motion analysis between the grinding wheel and the bar shows that the tool bar can be regarded as fixed. The grinding wheel first determines the installation position and posture, and then performs a spiral motion around the bar axis, such as Figure 3 Therefore, the trajectory P of the grinding wheel rotating surface doing spatial spiral motion S (h,ψ,ξ,a x ,a y ,α) is shown as follows:

[0079]

[0080] The motion trajectory equation of the grinding wheel rotating surface P S The partial derivatives of the grinding wheel variables h and ψ are calculated respectively, and the normal vector of the point on the rotation surface is obtained by cross product. The normal vector N(h, ψ) of the point on the rotation surface of the grinding wheel is calculated at the moment ξ = 0, as shown in the following formula:

[0081]

[0082] The motion trajectory equation P of the grinding wheel rotating surface S Find the partial derivative of the motion variable ξ and calculate the velocity vector V(h,ψ) of the point on the grinding wheel rotation surface at the moment ξ=0, as shown in the following formula:

[0083]

[0084] According to the condition that the normal vector and velocity vector of the point on the contact line are perpendicular to each other (N(h,ψ)×V(h,ψ)=0), Equations (5) and (6) are substituted into the calculation of the rotation angle ψ(h) of the point on the contact line of the grinding wheel, which is simplified as follows:

[0085]

[0086] Where B1 = a x cosα+κsinα, B2=(R(h)R′(h)-h)sinα+a y , B3=(κcosα-a x sinα)R′(h), such as Figure 4 shown.

[0087] Substitute equation (7) back into the motion trajectory equation (4) of the grinding wheel rotating surface to calculate the contact line of the grinding wheel rotating surface, and calculate Z by the contact line through the contact line through the motion transformation. W = 0 in the radial section profile equation of the spiral groove p(h,a x ,a y ,α), as shown below:

[0088]

[0089] In the formula, ξ0=(h cosα-R(h)sin(ψ(h))sinα) / κ.

[0090] Step 3: Establish the grinding wheel posture constraint equation.

[0091] (1) Figure 5 As shown, vector T1 is the tangent vector of p1 at the starting point of the radial section profile of the spiral groove, and vector P1 is point O W The vector pointing to point p1 on the radial cross-section of the spiral groove, the rake angle γ is the angle between vector P1 and vector T1, where when the Z of P1×T1 W When the coordinate is positive, the rake angle is positive, and when the coordinate is negative, the rake angle is negative. The functional relationship between the spiral groove rake angle and the grinding wheel posture is f γ As shown in the following formula:

[0092]

[0093] Where h1 is the grinding wheel variable corresponding to point p1, and t r =(0,0,1).

[0094] (2) Figure 5 As shown, the core thickness r c Point p2 is the tangent point where the radial cross-section of the spiral groove is tangent to the core thickness circle. The vector P2 is point O. WThe vector pointing to point p2 on the radial cross-section of the spiral groove. Vector T2 is the tangent vector at point p2, and vector P2·T2=0. The core thickness may be negative, and such a situation should be discarded. The functional relationship between the spiral groove core thickness and the grinding wheel posture is f rc As shown in the following formula:

[0095]

[0096] Where h2 is the grinding wheel variable corresponding to point p2, and x′ p (h2,a x ,a y ,α)·y p (h2,a x ,a y ,α)-y′ p (h2,a x ,a y ,α)·x p (h2,a x ,a y ,α)=0.

[0097] (3) Figure 5 As shown, vector P3 is point O W The vector pointing to the end point p3 of the radial section profile of the spiral groove, the groove width φ is the angle between the vector P1 and the vector P3, when the Z of the vector P1×P3 W When the coordinate is positive, the groove width is less than 180°, otherwise the groove width is greater than 180°. The functional relationship between the spiral groove core thickness and the grinding wheel posture is f φ As shown in the following formula:

[0098]

[0099] Where h3 is the grinding wheel variable corresponding to point p3, and

[0100] Step 4: Solve the grinding posture of the grinding wheel.

[0101] The objective function of the grinding wheel posture optimization problem is established as follows:

[0102] min Fit=ω1(f γ -γ) 2 +ω2(f φ -φ) 2 +ω3(f rc -r c ) 2 (12)

[0103] Where ω1, ω2, and ω3 are weight coefficients.

[0104] The particle swarm algorithm is used to solve the grinding wheel posture. The grinding wheel posture is regarded as a three-dimensional particle and the grinding wheel posture particle is defined as VecX(a x ,a y ,α); determine the number of particle swarm N, initialize the particle swarm VecX in the grinding wheel posture search space i (a xi ,a yi ,α i ), and initialize the velocity V of each particle i , i=1,2,3,…,N; then iterative calculation is performed, and the particle swarm algorithm iteration rule is as follows:

[0105]

[0106] Where ω is the inertia weight, c1 and c2 are learning factors, r1 and r2 are random numbers in [0,1], and pbest i is the individual optimal, and gbest is the global optimal.

[0107] The calculation process of the particle swarm algorithm is:

[0108] (1) Set the particle swarm algorithm parameters ω, c1, c2, r1, r2, the number of particle swarms N, the maximum number of iterations max_gen and the minimum error allowed for the termination of the iteration;

[0109] (2) Initialize particle swarm: position and velocity V i and position VecX i ;

[0110] (3) Substitute the initialized particles into formula (12) to calculate the initial fitness value Fit(VecX i ), mark the initial fitness value of each particle as the individual optimal pbest i And mark the best individual as the global optimal gbest;

[0111] (4) Update the position and velocity of the particle swarm according to formula (13);

[0112] (5) Substitute the updated particles into formula (12) to update the fitness value. If Fit(VecX i ) <pbest i , then update the individual optimal pbest i =Fit(VecX i ), if Fit(VecX i ) <gbest,则更新全局最优gbest=Fit(VecX i );

[0113] (6) If the end condition is met, the operation ends; otherwise, return to step (3).

[0114] The closer the value of the objective function is to zero, the more accurate the solution to the above nonlinear equations is.

[0115] Test verification:

[0116] A 1A1 grinding wheel was used for processing verification, and the grinding wheel parameters are shown in Table 1.

[0117] Table 1 Grinding wheel geometric parameters

[0118]

[0119] In order to avoid accidental errors, the test was divided into three groups to test the effectiveness of the algorithm in controlling the spiral groove structural parameters of the front angle, core thickness, and groove width. The spiral groove design parameters used in the test are shown in Table 2. The particle swarm algorithm parameter settings for this test are shown in Table 3.

[0120] Table 2 Design parameters of spiral groove in the test

[0121]

[0122] Table 3 Grinding algorithm parameter table setting table

[0123]

[0124] The grinding wheel posture calculated by the method proposed in the present invention is shown in Table 4.

[0125] Table 4 Grinding algorithm parameter settings

[0126]

[0127]

[0128] The grinding wheel postures in Table 4 are simulated and processed in the actual process. Figure 6 、 Figure 7 、 Figure 8 As shown, the experiments show the effectiveness of the method proposed in the present invention.

Claims

1. A method for calculating the grinding wheel trajectory for a CNC milling cutter spiral groove grinding process, characterized in that: The following steps are involved: Step 1: Establish grinding motion relationship: Establish grinding wheel coordinate system O G -X G Y G Z G :Coordinate origin O G Located at the center of the large end of the grinding wheel, coordinate axis Z G Coincident with the grinding wheel axis, coordinate plane X G Y G It coincides with the large end circular plane of the grinding wheel; the equation of the grinding wheel rotation surface in the grinding wheel coordinate system is as follows: Where h is the distance from the point on the rotating surface to the large end face of the grinding wheel, and ψ is the distance from the point on the rotating surface to the coordinate axis Y. G The rotation angle parameter, R(h) is the grinding wheel profile equation; Establish workpiece coordinate system O W -X W Y W Z W :Coordinate origin O W Located at the center of the tool bar end face, coordinate axis Z W Coincident with the tool bar axis, coordinate plane X W Y W Coincident with the end face of the tool bar; Establish grinding wheel grinding posture parameters: center distance a x For two coordinate origins in X W Distance on axis; offset a y For two coordinate origins in Y W Distance on the axis; installation angle α, grinding wheel around X W The angle of axis rotation; therefore, the transformation matrix between the grinding wheel coordinate system and the workpiece coordinate system is as follows: The grinding wheel moves along the Z direction W The axis moves forward while rotating around Z W The axis rotates by an angle ξ, and the radius of the spiral edge line is defined as R, which is the same as the radius of the workpiece. The spiral angle is β. Therefore, the transformation matrix M of the grinding wheel coordinate system and the workpiece coordinate system about the angle ξ is e (ξ) is shown in the following formula: Where, κ = R / tanβ; Step 2: Calculate the spiral groove profile formed by grinding wheel: The trajectory P of the grinding wheel rotating surface doing spatial spiral motion S (h,ψ,ξ,a x ,a y ,α) is shown as follows: The motion trajectory equation of the grinding wheel rotating surface P S The partial derivatives of the grinding wheel variables h and ψ are calculated respectively, and the normal vector of the point on the rotation surface is obtained by cross product. The normal vector N(h, ψ) of the point on the rotation surface of the grinding wheel is calculated at the moment ξ = 0, as shown in the following formula: The motion trajectory equation P of the grinding wheel rotating surface S Find the partial derivative of the motion variable ξ and calculate the velocity vector V(h,ψ) of the point on the grinding wheel rotation surface at the moment ξ=0, as shown in the following formula: According to the condition that the normal vector and velocity vector of the point on the contact line are perpendicular to each other: N(h,ψ)×V(h,ψ)=0, Equations (5) and (6) are substituted into the calculation of the rotation angle ψ(h) of the point on the contact line of the grinding wheel, which is simplified as follows: where B1 = a x cosα + κsinα, B2 = (R(h)R′(h) - h)sinα + a y , B3 = (κcosα - a x sinα)R′(h); Substitute equation (7) back into the motion trajectory equation (4) of the grinding wheel rotating surface to calculate the contact line of the grinding wheel rotating surface, and calculate Z by the contact line through the contact line through the motion transformation. W = 0 in the radial section profile equation of the spiral groove p(h,a x ,a y ,α), as shown below: In the formula, ξ0=(hcosα-R(h)sin(ψ(h))sinα) / k; Step 3: Establish the grinding wheel posture constraint equation: (1) Vector T1 is the tangent vector of p1 at the starting point of the radial cross-section of the spiral groove, and vector P1 is the tangent vector of point O W The vector pointing to point p1 on the radial cross-section of the spiral groove, the rake angle γ is the angle between vector P1 and vector T1, where when the Z of P1×T1 W When the coordinate is positive, the rake angle is positive, and when the coordinate is negative, the rake angle is negative. The functional relationship between the spiral groove rake angle and the grinding wheel posture is f γ As shown in the following formula: Where h1 is the grinding wheel variable corresponding to point p1, and t r =(0,0,1); (2) Core thickness r c Point p2 is the tangent point where the radial cross-section of the spiral groove is tangent to the core thickness circle. The vector P2 is point O. W The vector pointing to point p2 on the radial cross-section of the spiral groove, vector T2 is the tangent vector at point p2, vector P2·T2=0, the functional relationship between the spiral groove core thickness and the grinding wheel posture is f rc As shown in the following formula: Where h2 is the grinding wheel variable corresponding to point p2, and x′ p (h2,a x ,a y ,α)·y p (h2,a x ,a y ,α)-y′ p (h2,a x ,a y ,α)·x p (h2,a x ,a y ,α)=0; (3) Vector P3 is point O W The vector pointing to the end point p3 of the radial section profile of the spiral groove, the groove width φ is the angle between the vector P1 and the vector P3, when the Z of the vector P1×P3 W When the coordinate is positive, the groove width is less than 180°, otherwise the groove width is greater than 180°. The functional relationship between the spiral groove core thickness and the grinding wheel posture is f φ As shown in the following formula: Where h3 is the grinding wheel variable corresponding to point p3, and Step 4: Solve the grinding posture of the grinding wheel: The objective function of the grinding wheel posture optimization problem is established as follows: Where ω1, ω2, and ω3 are weight coefficients; The particle swarm algorithm is used to solve the grinding wheel posture. The grinding wheel posture is regarded as a three-dimensional particle and the grinding wheel posture particle is defined as VecX(a x ,a y ,α); determine the number of particle swarm N, initialize the particle swarm VecX in the grinding wheel posture search space i (a xi ,a yi ,α i ), and initialize the velocity V of each particle i , i=1,2,3,…,N; then iterative calculation is performed, and the particle swarm algorithm iteration rule is as follows: Where ω is the inertia weight, c1 and c2 are learning factors, r1 and r2 are random numbers in [0,1], and pbest i is the individual optimal, and gbest is the global optimal.

2. The method for calculating the grinding wheel trajectory for a CNC milling cutter spiral groove grinding process according to claim 1, wherein: The particle swarm algorithm calculation process is: (1) Set the particle swarm algorithm parameters ω, c1, c2, r1, r2, the number of particle swarms N, the maximum number of iterations max_gen and the minimum error allowed for the termination of the iteration; (2) Initialize particle swarm: position and velocity V i and position VecX i ; (3) Substitute the initialized particles into formula (12) to calculate the initial fitness value Fit(VecX i ), mark the initial fitness value of each particle as the individual optimal pbest i And mark the best individual as the global optimal gbest; (4) Update the position and velocity of the particle swarm according to formula (13); (5) Substitute the updated particles into Equation (12) to update the fitness value. If Fit(VecX i ) < pbest i , then update the individual optimal pbest i = Fit(VecX i ). If Fit(VecX i ) < gbest, then update the global optimal gbest = Fit(VecX i ); (6) If the end condition is met, the operation ends; otherwise, return to step (3).

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