Method and system for determining milling tool helical flute grinding trajectory based on two-dimensional particle swarm

Abstract

The application belongs to the technical field of numerical control milling cutter grinding processing, and discloses a milling cutter helical groove grinding track determination method and system based on a two-dimensional particle swarm, which comprises the following steps: establishing an expression of an installation angle and a contact angle for a grinding wheel pose in a workpiece coordinate system; establishing a correlation relationship formula among the installation angle, a grinding wheel contact angle and a workpiece contact angle according to a rake angle machining feature; establishing a constraint equation of the installation angle and the contact angle about milling cutter helical groove parameters; and generating grinding wheel pose parameters meeting machining requirements based on a particle swarm algorithm iteration. The application realizes the conversion from three-dimensional search to two-dimensional search, reduces the search difficulty and improves the efficiency.

Description

Technical Field

[0001] This invention belongs to the field of CNC milling cutter grinding technology, and particularly relates to a method and system for determining the grinding trajectory of milling cutter helical grooves based on two-dimensional particle swarms. Background Technology

[0002] In the manufacturing process of milling cutters, the machining of helical grooves on the cutting edge is highly challenging due to the complex forming principle. The helical groove is formed by grinding the outer contour of a grinding wheel onto the workpiece, and the grinding trajectory of the wheel determines the shape and size of the helical groove. Since the surface of the helical groove is actually an envelope formed by the movement of the grinding wheel, the forming principle is complex and cannot be directly calculated using interferometry. Therefore, accurately calculating the grinding trajectory that meets the machining requirements is crucial.

[0003] In the machining of helical grooves on a milling cutter, the grinding wheel undergoes a relative helical motion around the workpiece axis, and the actual grinding trajectory is determined by the mounting posture of the grinding wheel. Currently, the problem of inversely determining the grinding wheel mounting posture based on the shape of the target helical groove on the milling cutter mainly employs an iterative algorithm. First, a predictive model of the helical groove shape is established. Then, during the iterative process, the posture parameters are adjusted based on the prediction results, ultimately ensuring that the helical groove shape meets the requirements. Prediction algorithms for the shape of the helical groove on the milling cutter can be divided into point cloud-based graphical methods and envelope-based analytical methods. The accuracy of point cloud-based graphical algorithms depends on the accuracy of the point cloud, resulting in low computational efficiency. Analytical algorithms based on the envelope principle obtain the helical groove profile by establishing the envelope condition between the grinding wheel profile and the surface of the helical groove. This method is highly efficient and reliable, and is widely used. This invention also employs this method to obtain the helical groove prediction model. To improve the accuracy and efficiency of solving grinding process parameters during the iterative process, some researchers have selected an appropriate optimization objective function and used an optimization search algorithm to find the optimal solution. Ning et al. (Ning Yangcheng. Research on Precision Grinding Process Algorithm for Helical Grooves of CNC Tools. 2022. Southwest Jiaotong University, MA thesis.) used the grinding wheel pose parameters as optimization variables and the geometric parameter error of the helical groove as the optimization objective function, and adopted an optimization search algorithm to solve the grinding wheel pose.

[0004] Based on the above analysis, the problems and shortcomings of the existing technology are as follows:

[0005] (1) Existing algorithms directly use the installation position of the grinding wheel as the search object, making it difficult to determine the boundary of the search space. This makes it easy for the results to fall into unreasonable processing positions, resulting in problems such as negative core diameter and overcutting.

[0006] (2) Existing algorithms often establish a constraint model relating the front angle, core diameter, and slot width to three process parameters, and then search for the optimal process parameters in three-dimensional space through the three constraint models. This search is difficult and inefficient. Summary of the Invention

[0007] To address the problems existing in the prior art, this invention provides a method and system for determining the grinding trajectory of a milling cutter's helical groove based on two-dimensional particle swarm optimization.

[0008] This invention is implemented as follows: a method for determining the grinding trajectory of a milling cutter's helical groove based on two-dimensional particle swarm optimization, comprising:

[0009] Step 1: Establish the expressions for the installation angle and contact angle with respect to the grinding wheel pose in the workpiece coordinate system;

[0010] Step 2: Establish the correlation formula between the mounting angle, grinding wheel contact angle, and workpiece contact angle based on the machining characteristics of the front angle;

[0011] Step 3: Establish constraint equations for the installation angle and contact angle with respect to the milling cutter helical groove parameters;

[0012] Step 4: Iteratively generate grinding wheel pose parameters that meet the processing requirements based on the particle swarm optimization algorithm.

[0013] Furthermore, in step one, a workpiece coordinate system is established. Initially, the zero points of the workpiece coordinate system and the grinding wheel coordinate system coincide. After determining the grinding wheel mounting posture, the grinding wheel coordinate system is rotated α around the x-axis, and then moved α along the x-axis, y-axis, and z-axis of the workpiece coordinate system, respectively. x a y and a z Any point on the grinding wheel profile can be represented by θ in the workpiece coordinate system as follows:

[0014]

[0015] Any point on the workpiece contour can be represented by ω:

[0016]

[0017] Where R(h) is the outer radius of the grinding wheel at a distance h from the front end face, and θ and ω are the angle parameters of the grinding wheel and the workpiece, respectively. For ease of calculation, we will choose a as the angle parameter. z Analyzing and solving for the case where the value is 0, once the grinding wheel's mounting position is determined, the grinding wheel and the workpiece contact at point A. At this point, the mounting angle and contact angle are known. Given α, θ, and ω, the mounting position of the grinding wheel can be represented as follows:

[0018]

[0019] Furthermore, in step two, after determining the installation position of the grinding wheel, any point on the grinding wheel can be represented by equation (1). When the contact point between the end face of the grinding wheel and the workpiece is B, the coordinates of point B in the workpiece coordinate system are:

[0020]

[0021] The grinding wheel position parameter in the formula can be expressed in terms of contact angle:

[0022]

[0023] When the front end of the grinding wheel contacts the workpiece at point B, the coordinates of the grinding wheel center on the Z-axis of the workpiece coordinate system are:

[0024] z B =R(h)sinθ B sinα (6)

[0025] Similarly, at grinding wheel contact point A, the coordinates of the grinding wheel center on the Z-axis of the workpiece coordinate system are:

[0026] z A =R(h)sinθ A sinα (7)

[0027] The angle of workpiece rotation when the grinding wheel grinds point B can be calculated based on the Z-axis coordinates of points A and B:

[0028]

[0029] Where β is the helix angle of the milling cutter, R w Given the workpiece radius, the coordinates of A' are calculated based on the workpiece rotation angle:

[0030]

[0031] but,

[0032]

[0033] The smaller the angle between points A and B on the end face of the grinding wheel, the smaller the length of A'B. When θ is taken... A =θ B When +0.01, ∠A'O w B is approximately equal to the rake angle of the cutting edge, which can be expressed using the mounting angle and the contact angle as follows:

[0034] γ=f(α,θ,ω) (11)

[0035] Where γ is the rake angle of the peripheral edge.

[0036] Furthermore, in step three, depending on the position of the grinding wheel center on the workpiece center coordinate axis, the core diameter calculation can be divided into two cases:

[0037] (1) When the center of the grinding wheel is located to the left of the center of the workpiece, the core diameter is formed by grinding the end face of the grinding wheel. The grinding point of the core diameter should satisfy the following formula:

[0038]

[0039] Combining equation (1), within the range of θ values Within the core, there exists only one minimum value, therefore the core diameter can be obtained using the bisection method;

[0040] (2) When the grinding wheel is on the right side of the workpiece, it is necessary to calculate and compare the core diameter values ​​of the grinding wheel end face and the grinding wheel side. The calculation process of the core diameter value of the grinding wheel end face is the same as when the center of the grinding wheel end face is on the left side of the workpiece. The envelope equation can be solved by the envelope discriminant. At this time, the core diameter of the milling cutter is obtained by comparing the minimum distance from the front end face of the grinding wheel and the envelope line to the center of the workpiece. The groove width is the angle formed by the line connecting the starting point, the ending point and the center of the workpiece of the spiral groove cutting. Therefore, after determining the contact angle, it is necessary to calculate the angle corresponding to the ending point. At the grinding ending point, the coordinates of the point on the outer circle of the grinding wheel are the same as the coordinates of the point on the workpiece. Therefore, the following relationship exists:

[0041]

[0042] Because the ellipse formed by the projection of the outer circle of the grinding wheel at point T is tangent to the outer diameter of the workpiece, the following relationship holds:

[0043]

[0044] By combining equations (13) and (14), the angles of the grinding end point on the workpiece and grinding wheel, as well as the distance from the corresponding grinding wheel section to the grinding wheel end face, can be obtained. The position of the grinding end point on the z-axis of the workpiece coordinate system at this point can then be calculated.

[0045] z T =R(h) T sinθ T sinα+h T cosα (15)

[0046] Calculate the rotation angle of the starting point when grinding reaches the end point of the plane:

[0047]

[0048] Therefore, the width of the helical groove of the milling cutter can be calculated, i.e., ∠A'O w T.

[0049] Furthermore, in step four, based on the established constraint relationships, the optimal mounting angle and contact angle are searched using a particle swarm optimization algorithm. The mounting angle and grinding wheel contact angle are treated as two-dimensional particles (α, θ). To avoid overcutting, the search space for the mounting angle is set to (0, 95° - β]. The search space for the grinding wheel contact angle is set according to the processing requirements. The algorithm flow for searching the optimal installation angle and contact angle based on particle swarm optimization is as follows:

[0050] (1) Input the grinding wheel model and geometric parameters, and the spiral groove design parameters, including the peripheral cutting angle γ.t Core diameter r ct and groove width φ t ;

[0051] (2) Set the relevant parameters of the particle swarm optimization algorithm, including population size, number of iterations, etc.;

[0052] (3) Initialize the particle swarm position x ij and velocity v ij , where j represents the dimension of the particle and i represents the i-th particle;

[0053] (4) Substitute the initialized particle position, i.e., the mounting angle and the grinding wheel contact angle, into the front angle constraint formula to calculate the corresponding workpiece contact angle, and then calculate the corresponding core diameter r according to the core diameter and groove width calculation model. c and groove width φ;

[0054] (5) Substitute the core diameter and slot width generated by each particle into the fitness function to record the individual best value (pbest) for each particle. ij and the global optimum of the population (gbest) j :

[0055]

[0056] (6) Update the particle swarm position and velocity based on equations (18) and (19). The velocity update equation is:

[0057] v ij (t+1)=ωv ij (t)+c1r1[pbest ij (t)-v ij (t)]+c2r2[gbest j (t)-v ij (t)] (18)

[0058] The position update formula is:

[0059] x ij (t+1)=v ij (t)+v ij (t+1) (19)

[0060] Where t represents the current iteration number, c1 and c2 are acceleration constants, and r1 and r2 are two independent random numbers with values ​​in the range [0,1].

[0061] (7) Calculate the core diameter and cutting edge width generated at the current position, and update the individual optimal fitness and the global optimal fitness. Terminate the algorithm when the optimal fitness meets the accuracy requirements or reaches the maximum number of iterations.

[0062] Another object of the present invention is to provide a milling cutter spiral groove grinding trajectory calculation system based on two-dimensional particle swarm optimization, the milling cutter spiral groove grinding trajectory calculation system based on two-dimensional particle swarm optimization includes:

[0063] The workpiece coordinate system establishment module is used to establish the workpiece coordinate system and, within the workpiece coordinate system, establish the expressions for the installation angle and contact angle with respect to the grinding wheel pose.

[0064] The correlation equation establishment module is used to establish the correlation equation between the mounting angle, grinding wheel contact angle and workpiece contact angle based on the front angle machining characteristics;

[0065] The constraint equation establishment module is used to establish constraint equations for the installation angle and contact angle with respect to the milling cutter helical groove parameters;

[0066] The parameter generation module iteratively generates grinding wheel pose parameters that meet the machining requirements based on the particle swarm optimization algorithm.

[0067] Another object of the present invention is to provide a computer device including a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the method for determining the milling trajectory of a helical groove based on two-dimensional particle swarm optimization.

[0068] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the method for determining the milling trajectory of a helical groove based on two-dimensional particle swarm optimization.

[0069] Another objective of this invention is to provide an information data processing terminal for implementing the milling cutter spiral groove grinding trajectory calculation system based on two-dimensional particle swarm optimization.

[0070] Another object of the present invention is to provide a milling cutter helical groove grinding trajectory calculation system based on two-dimensional particle swarm optimization, the system comprising:

[0071] 1. Coordinate system establishment module, used to establish the expressions for the installation angle and contact angle with respect to the grinding wheel pose in the workpiece coordinate system, and initialize the workpiece coordinate system and the grinding wheel coordinate system;

[0072] 2. The correlation module is used to establish the correlation formula between the mounting angle, grinding wheel contact angle, and workpiece contact angle based on the front angle machining characteristics;

[0073] 3. Constraint equation module, used to establish constraint equations for the mounting angle and contact angle with respect to the milling cutter helical groove parameters, including calculation models for the core diameter and groove width;

[0074] 4. Particle Swarm Optimization Module: Based on the particle swarm algorithm, iteratively generates grinding wheel pose parameters that meet the processing requirements, including the mounting angle and grinding wheel contact angle, and optimizes the grinding trajectory by searching for the optimal solution.

[0075] Another objective of this invention is to provide a milling cutter helical groove grinding trajectory calculation system based on two-dimensional particle swarm optimization, the system comprising the following functional modules:

[0076] 1. Data input module, used to input grinding wheel model, geometric parameters and spiral groove design parameters, such as peripheral rake angle, core diameter and groove width;

[0077] 2. Particle swarm initialization module, used to set relevant parameters of the particle swarm algorithm, including population size, number of iterations, etc., and initialize the position and velocity of the particle swarm;

[0078] 3. The calculation and evaluation module is used to substitute the initialized particle position into the front angle constraint formula to calculate the corresponding workpiece contact angle, and calculate the corresponding core diameter and groove width according to the core diameter and groove width calculation model. Then, the quality of each particle is evaluated based on the fitness function.

[0079] 4. Optimization and Iteration Module: This module iteratively updates the position and velocity of the particle swarm based on the velocity and position update formulas of the particle swarm algorithm. It records the individual optimality of each particle and the global optimality of the swarm. The algorithm terminates when the optimal fitness meets the accuracy requirements or reaches the maximum number of iterations, and outputs the optimal grinding wheel pose parameters.

[0080] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0081] First, this invention characterizes the relative pose of the workpiece and grinding wheel by measuring the angles of the contact points on the workpiece and grinding wheel cross-sections, thereby determining the boundary of the parameter search. Based on the forming characteristics of the peripheral cutting edge rake angle, a correlation model between the grinding wheel mounting angle and the two contact angles is established. After determining the grinding wheel mounting angle and grinding wheel contact angle, the workpiece contact angle that meets the rake angle accuracy can be calculated, realizing the conversion from three-dimensional search to two-dimensional search and reducing the search difficulty. Finally, the optimal solution is searched in two-dimensional space using the particle swarm optimization algorithm to efficiently calculate the grinding trajectory.

[0082] Secondly, the method proposed in this invention can accurately and efficiently calculate the grinding trajectory of the helical groove of the milling cutter, and is applicable to the machining process of helical grooves of milling cutters of different specifications, possessing good versatility. The method proposed in this invention can quickly determine the grinding trajectory before machining the milling cutter, helping to shorten the milling cutter machining and debugging process, improve production efficiency, reduce the consumption of trial grinding materials, and lower trial grinding costs.

[0083] Improved machining accuracy: Through precise mathematical models and optimization algorithms, the control of the grinding wheel position is more accurate, which greatly improves the machining accuracy of the helical groove of the milling cutter.

[0084] Improved processing efficiency: Particle swarm optimization algorithm can quickly find the optimal grinding wheel pose, reducing processing time and improving processing efficiency.

[0085] Reduced human error: Automated trajectory calculation reduces reliance on operator experience, lowers the risk of human error, and improves the stability and repeatability of the process.

[0086] Wide range of applications: This method is not only applicable to the grinding of helical grooves on milling cutters, but can also be extended to the precision machining of other types of tools and parts.

[0087] Third, the expected benefits and commercial value of the technical solution of this invention after transformation are as follows: With the advancement of science and technology and the development of society, the manufacturing industry is shifting towards intelligence and automation, and the requirements for the precision and efficiency of production are also increasing. Milling cutters, as a commonly used metal cutting tool, are widely used in various fields of manufacturing. The helical groove forming principle of milling cutters is complex, the machining difficulty is high, and the machining trajectory is difficult to determine. Often, experience and extensive trial grinding and adjustments are needed to machine a helical groove that meets the requirements. The grinding trajectory calculation method provided by this invention can quickly calculate a trajectory that meets the accuracy requirements, shorten the helical groove machining and debugging process, improve production efficiency, and thus generate significant commercial value.

[0088] The technical solution of this invention solves a long-standing but unsolved technical problem: the grinding trajectory of a milling cutter's helical groove is actually determined by the mounting posture of the grinding wheel and the workpiece. Current methods mainly search for the optimal mounting posture through optimization algorithms, but these methods suffer from difficulties in determining the search boundary and low search efficiency. This invention characterizes the relative posture relationship between the grinding wheel and the workpiece by the angle of the initial contact point between the grinding wheel and the workpiece, and establishes a constraint relationship for the helical groove rake angle. This reduces the number of unknown parameters that need to be calculated, determines the search boundary, and improves search efficiency.

[0089] Fourth, the technological advancements demonstrated by the milling cutter helical groove grinding trajectory determination method based on two-dimensional particle swarm optimization provided by this invention are mainly reflected in the following aspects:

[0090] 1. High-precision trajectory calculation: By establishing expressions for the mounting angle and contact angle with respect to the grinding wheel pose, and associating them with the rake angle machining feature, this method enables high-precision calculation of the milling cutter's helical groove grinding trajectory. This method considers the influence of multiple angles, including the mounting angle, grinding wheel contact angle, and workpiece contact angle, thereby ensuring the accuracy of the trajectory calculation.

[0091] 2. Automated Optimization: By introducing the particle swarm optimization (PSO) algorithm, this method can automatically and iteratively generate grinding wheel pose parameters that meet machining requirements. PSO is an optimization algorithm that finds the optimal solution to a problem by simulating the foraging behavior of bird flocks. The application of this method makes the optimization process of grinding wheel pose parameters more automated and efficient.

[0092] 3. High adaptability: This method can adapt to different processing needs by adjusting the grinding wheel posture parameters to meet specific processing requirements. This flexibility makes the method more widely applicable in practical applications.

[0093] 4. Improved Machining Efficiency and Quality: By accurately calculating and optimizing the grinding wheel pose parameters, this method is expected to improve the machining efficiency and quality of helical grooves on milling cutters. Accurate trajectory calculation can reduce errors during the machining process, thereby improving machining accuracy; while optimized grinding wheel pose parameters can further improve machining efficiency.

[0094] The milling trajectory determination method for helical grooves based on two-dimensional particle swarm optimization provided by this invention demonstrates significant technological advancements in trajectory calculation accuracy, automation optimization, adaptability, and machining efficiency and quality. These advancements not only improve the controllability and stability of the machining process but also contribute to enhancing the quality and competitiveness of the machined products.

[0095] Fifth, this invention provides a method for determining the grinding trajectory of a milling cutter helical groove based on a two-dimensional particle swarm optimization (PSO) algorithm. This method is used to optimize the installation angle and contact angle of the grinding wheel to ensure that the required milling cutter helical groove can be accurately machined during the grinding process.

[0096] 1) Establish coordinate system and initial conditions:

[0097] The workpiece coordinate system and the grinding wheel coordinate system coincide at the initial moment.

[0098] The position of the grinding wheel is determined based on its rotation and displacement.

[0099] The mathematical model of the grinding wheel pose is represented by formula (3).

[0100] 2) Calculations after determining the grinding wheel installation position:

[0101] Calculate the coordinates of the contact point B between the grinding wheel end face and the workpiece (Formula 4).

[0102] The grinding wheel position parameters are represented by formulas (5) and (6).

[0103] Calculate the Z-axis coordinates of the grinding wheel contact points A and B, as well as the workpiece rotation angles (Formula 7) and (8).

[0104] 3) Core diameter calculation:

[0105] The calculation methods differ depending on whether the grinding wheel center is located to the left or right of the workpiece center.

[0106] The core diameter is determined using the dichotomy method and the envelope discriminant.

[0107] 4) Calculation of groove width:

[0108] Calculate the angle corresponding to the end point and the position of the grinding end point on the Z-axis of the workpiece coordinate system (Formulas 13)(14)(15).

[0109] This allows us to calculate the width of the helical groove on the milling cutter.

[0110] 5) Applications of Particle Swarm Optimization Algorithm:

[0111] Set the parameters for the particle swarm optimization algorithm, such as the population size and the number of iterations.

[0112] Initialize particle position and velocity.

[0113] Calculate the core diameter and slot width for each particle, and substitute the results into the fitness function (Equation 17).

[0114] Update particle position and velocity (Equation 18)(19).

[0115] Iterate until the accuracy requirement is met or the maximum number of iterations is reached.

[0116] The significance of technological progress is reflected in the following aspects:

[0117] Optimized efficiency: The two-dimensional particle swarm optimization algorithm can find the optimal installation angle and contact angle, improving grinding efficiency and accuracy.

[0118] Improved precision: The optimized algorithm ensures the precision of the grinding trajectory, which helps to improve the machining quality of the helical groove of the milling cutter.

[0119] High adaptability: The method is applicable to grinding wheels and workpieces of different models and parameters, and has strong universality.

[0120] High degree of automation: Particle swarm optimization reduces human intervention, improves automation, and reduces human error in the grinding process.

[0121] This grinding trajectory calculation method utilizes the global search capability of the particle swarm optimization algorithm, combined with specific constraints and fitness functions, to optimize the grinding process of helical grooves on milling cutters, thereby improving machining efficiency and accuracy. Attached Figure Description

[0122] Figure 1 This is a flowchart of the method for determining the grinding trajectory of a milling cutter helical groove based on two-dimensional particle swarm analysis provided in an embodiment of the present invention.

[0123] Figure 2 This is a schematic diagram of the established grinding wheel coordinate system provided in an embodiment of the present invention;

[0124] Figure 3 This is a schematic diagram of the relative pose relationship between the grinding wheel and the workpiece provided in an embodiment of the present invention;

[0125] Figure 4 This is a schematic diagram of the helix angle peripheral cutting of a milling cutter provided in an embodiment of the present invention;

[0126] Figure 5 This is a schematic diagram of core diameter grinding when the grinding wheel center is located to the left of the workpiece center coordinate axis, provided in an embodiment of the present invention.

[0127] Figure 6 This is a schematic diagram of the grinding core diameter at the front end face of the grinding wheel when the center of the grinding wheel is located to the right of the workpiece center coordinate axis, provided in an embodiment of the present invention.

[0128] Figure 7 This is a schematic diagram of the grinding wheel side grinding core diameter when the grinding wheel center is located to the right of the workpiece center coordinate axis, provided in an embodiment of the present invention;

[0129] Figure 8 This is a schematic diagram of the milling cutter spiral groove width grinding provided in an embodiment of the present invention;

[0130] Figure 9 This is a block diagram of the milling cutter spiral groove grinding trajectory calculation system based on two-dimensional particle swarm analysis provided in an embodiment of the present invention;

[0131] Figure 10 This is a simulation result diagram provided by an embodiment of the present invention. Detailed Implementation

[0132] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0133] Two specific application embodiments of the present invention are as follows:

[0134] Example 1: Grinding helical grooves with a standard spur milling cutter

[0135] Helical groove grinding was performed on a standard spur milling cutter. First, expressions for the grinding wheel's mounting angle and contact angle, as well as a contact model between the grinding wheel and the workpiece, were established in the workpiece coordinate system. By establishing the correlation between the mounting angle, grinding wheel contact angle, and workpiece contact angle, the rake angle of the milling cutter during grinding was ensured to meet design requirements.

[0136] Next, using a particle swarm optimization algorithm, the optimal grinding wheel pose parameters are iteratively calculated based on the specific parameters of the helical groove of the milling cutter (such as helix angle and depth). These parameters ensure that the grinding wheel maintains optimal contact with the ideal trajectory of the helical groove of the milling cutter during the grinding process, thereby achieving high-precision and high-efficiency helical groove machining.

[0137] Parameter settings: Set initial parameters for the particle swarm algorithm, including the number of particles, number of iterations, etc.

[0138] Iterative optimization: The algorithm begins to iterate, and each iteration evaluates and updates the position of the particles (i.e., the grinding wheel pose parameters) to find the optimal solution.

[0139] Grinding execution: The grinding wheel is set according to the optimized pose parameters, and the grinding operation is performed. The grinding wheel moves according to the calculated optimal trajectory to complete the machining of the helical groove of the milling cutter.

[0140] This invention addresses the following problems and deficiencies in existing technologies, achieving significant technological advancements: In traditional milling cutter helical groove grinding methods, the position control of the grinding wheel often relies on the operator's experience and intuitive judgment, which not only reduces machining accuracy but also limits machining efficiency. Furthermore, the lack of an effective mathematical model to describe and optimize the grinding trajectory makes it difficult to precisely control the contact point between the grinding wheel and the workpiece, thus affecting machining quality.

[0141] To address the problems existing in the prior art, the technical solution adopted in this invention is as follows:

[0142] Establishing coordinate system and expressions: First, establish expressions for the installation angle and contact angle with respect to the grinding wheel pose in the workpiece coordinate system, which provides a mathematical basis for subsequent optimization.

[0143] Establishing the correlation formula: Based on the machining characteristics of the front angle, establish the correlation formula between the mounting angle, the grinding wheel contact angle and the workpiece contact angle to ensure the accuracy during the machining process.

[0144] Establishment of constraint equations: By establishing constraint equations for the installation angle and contact angle with respect to the milling cutter helical groove parameters, constraint conditions are provided for the optimization of the grinding wheel pose.

[0145] Application of Particle Swarm Optimization: Finally, the particle swarm optimization algorithm is used to iteratively generate grinding wheel pose parameters that meet the machining requirements in order to optimize the grinding trajectory.

[0146] like Figure 1 As shown, the method for determining the grinding trajectory of a milling cutter helical groove based on two-dimensional particle swarm analysis provided in this embodiment of the invention includes the following steps:

[0147] S101, Establish the expressions for the installation angle and contact angle with respect to the grinding wheel pose in the workpiece coordinate system;

[0148] S102, Establish the correlation formula between the mounting angle, grinding wheel contact angle and workpiece contact angle based on the front angle machining characteristics;

[0149] S103, Establish constraint equations for the installation angle and contact angle with respect to the parameters of the milling cutter helical groove;

[0150] S104, based on the particle swarm optimization algorithm, iteratively generates grinding wheel pose parameters that meet the processing requirements.

[0151] The milling cutter helical groove grinding trajectory determination method based on two-dimensional particle swarm optimization (PSO) algorithm provided in this invention is an intelligent algorithm designed to optimize the grinding wheel's pose parameters to achieve efficient and accurate milling cutter helical groove grinding. The detailed working principle of this method is as follows:

[0152] S101: Establish grinding wheel pose expression

[0153] First, establish the pose expression of the grinding wheel in the workpiece coordinate system. This includes the grinding wheel's mounting angle and contact angle. The mounting angle refers to the angle at which the grinding wheel is mounted on the grinding machine, while the contact angle refers to the angle at the contact point between the grinding wheel and the helical groove of the milling cutter. These two angles together determine the relative position and orientation of the grinding wheel and the workpiece (the helical groove of the milling cutter).

[0154] S102: Establish Relationships

[0155] Next, based on the rake angle machining characteristics of the milling cutter, a correlation formula is established between the mounting angle, the grinding wheel contact angle, and the workpiece contact angle. The purpose of this step is to ensure that the grinding wheel can grind according to the predetermined rake angle characteristics during the machining process, thereby guaranteeing the geometric accuracy and surface quality of the milling cutter's helical groove.

[0156] S103: Establish constraint equations

[0157] Then, constraint equations are established for the mounting angle and contact angle with respect to the parameters of the helical groove on the milling cutter. These parameters include, but are not limited to, the depth, width, and helix angle of the helical groove. The purpose of the constraint equations is to ensure that, during the optimization process, all pose parameters can meet the machining requirements and geometric characteristics of the helical groove on the milling cutter.

[0158] S104: Iterative Optimization of Particle Swarm Optimization Algorithm

[0159] Finally, the grinding wheel pose parameters are iteratively optimized based on a two-dimensional particle swarm optimization algorithm. Particle swarm optimization is a swarm intelligence-based optimization technique that finds the optimal solution by simulating the foraging behavior of bird flocks. In this invention, each "particle" represents a set of grinding wheel pose parameters (installation angle and contact angle). The position of the particle (i.e., the grinding wheel pose parameters) is continuously updated through an iterative process to search for the optimal pose that satisfies the constraints. In each iteration, the particle adjusts its flight direction and distance based on its own experience and the collective experience until it finds the optimal pose parameters, thereby achieving efficient and precise grinding of the helical groove of the milling cutter.

[0160] This optimization method based on two-dimensional particle swarm optimization can automatically and intelligently determine the optimal position of the grinding wheel, significantly improving the efficiency and machining quality of helical groove grinding.

[0161] like Figure 2 As shown, a grinding wheel coordinate system is established on the front face of the grinding wheel.

[0162] like Figure 3 As shown, in step one of the embodiments of the present invention, a workpiece coordinate system is established. Initially, the zero points of the workpiece coordinate system and the grinding wheel coordinate system coincide with the coordinate system. After determining the grinding wheel mounting posture, the grinding wheel coordinate system is rotated α around the x-axis, and then moved α along the x-axis, y-axis, and z-axis of the workpiece coordinate system, respectively. x a y and a z .

[0163] Any point on the grinding wheel profile can be represented by θ in the workpiece coordinate system as follows:

[0164]

[0165] Any point on the workpiece contour can be represented by ω:

[0166]

[0167] Where R(h) is the outer radius of the grinding wheel at a distance h from the front end face, and θ and ω are the angle parameters of the grinding wheel and the workpiece, respectively.

[0168] Because the cross-sectional shape of the helical groove of the milling cutter is completely consistent in any axial direction, and the offset a in the Z direction z Without affecting the cross-sectional shape, for ease of calculation, we will choose a below. z We will analyze and solve for the case where the value is 0.

[0169] Once the grinding wheel's mounting position is determined, the grinding wheel and the workpiece contact at point A, at which point the mounting angle and contact angle are known. Given α, θ, and ω, the grinding wheel's mounting position can be represented as follows:

[0170]

[0171] Analyze the process of front angle grinding, such as Figure 4 As shown, point A, the contact point between the grinding wheel tip and the workpiece, is the apex of the helical groove cutting edge of the milling cutter. As the grinding wheel continues machining, the end face of the grinding wheel contacts the workpiece at point B. At this point, because the workpiece is constantly rotating around its axis, point A rotates to A'. When the distance between A and B is sufficiently close, A'B approximates the tangent at the apex of the helical groove cutting edge of the milling cutter, then ∠A'O w B is the rake angle of the grinding wheel.

[0172] Step two of this embodiment of the invention, after determining the installation posture of the grinding wheel, can represent any point on the grinding wheel according to equation (1). When the contact point between the end face of the grinding wheel and the workpiece is B, the coordinates of point B in the workpiece coordinate system are:

[0173]

[0174] The grinding wheel position parameter in the formula can be expressed in terms of contact angle:

[0175]

[0176] When the front end of the grinding wheel contacts the workpiece at point B, the coordinates of the grinding wheel center on the Z-axis of the workpiece coordinate system are:

[0177] z B =R(h)sinθ B sinα (6)

[0178] Similarly, at grinding wheel contact point A, the coordinates of the grinding wheel center on the Z-axis of the workpiece coordinate system are:

[0179] z A =R(h)sinθ A sinα (7)

[0180] In the machining of helical grooves with a milling cutter, a helix angle is required. While the workpiece rotates around its axis, the grinding wheel moves linearly along the workpiece's axis. Therefore, based on the Z-axis coordinates of points A and B, the angle of workpiece rotation when the grinding wheel grinds point B can be calculated.

[0181]

[0182] Where β is the helix angle of the milling cutter, R w Where is the workpiece radius.

[0183] The coordinates of A' are calculated based on the workpiece rotation angle:

[0184]

[0185] but,

[0186]

[0187] The smaller the angle between points A and B on the end face of the grinding wheel, the smaller the length of A'B. When θ is taken... A =θ B When +0.01, ∠A'O w B is approximately equal to the rake angle of the circumferential cutting edge.

[0188] Therefore, the rake angle of the peripheral cutting edge can be expressed using the mounting angle and the contact angle as follows:

[0189] γ=f(α,θ,ω) (11)

[0190] Where γ is the rake angle of the peripheral edge.

[0191] Based on this relationship, given the peripheral cutting edge angle γ, the mounting angle α, and the grinding wheel contact angle θ, the corresponding workpiece contact angle ω can be calculated. This establishes the correlation between the mounting angle, the grinding wheel contact angle, and the workpiece contact angle, reducing the grinding wheel mounting pose parameters that need to be searched from three dimensions to two dimensions.

[0192] Step three provided in this embodiment of the invention can be divided into two cases based on the different positions of the grinding wheel center on the workpiece center coordinate axis: (1) the grinding wheel center is located to the left of the workpiece center; (2) the grinding wheel center is located to the right of the workpiece center.

[0193] When the center of the grinding wheel end face is on the left side of the workpiece, such as Figure 5 As shown, the core diameter is formed by grinding the end face of the grinding wheel.

[0194] Since the core diameter is actually the shortest distance from the spiral groove profile to the workpiece center, the grinding point of the core diameter should satisfy the following formula:

[0195]

[0196] Combining equation (1), within the range of θ values Within the core, there exists only one minimum value, so the core diameter can be obtained using the bisection method.

[0197] When the grinding wheel is on the right side of the workpiece, the core diameter is formed by machining the end face or side edge of the grinding wheel. The grinding profile of the side edge is actually the envelope of the grinding wheel's projection onto the workpiece plane. For example... Figure 6 , 7 As shown, the core diameters are respectively machined from the end face of the grinding wheel and from the side of the grinding wheel. Therefore, it is necessary to calculate and compare the core diameter values ​​obtained by grinding from the end face and the side of the grinding wheel.

[0198] The calculation process for the core diameter of the grinding wheel end face is the same as when the center of the grinding wheel end face is on the left side of the workpiece. The envelope equation can be solved by the envelope discriminant. At this time, the core diameter of the milling cutter is obtained by comparing the minimum distance from the front end face of the grinding wheel and the envelope line to the center of the workpiece.

[0199] The groove width is the angle formed by the lines connecting the starting point, ending point, and center of the workpiece in the spiral groove cutting process. Therefore, after determining the contact angle, it is necessary to calculate the angle corresponding to the ending point. For example... Figure 8 As shown, point A is the starting point of the spiral groove cutting, and T is the ending point of the spiral groove profile.

[0200] At the end of the grinding process, the coordinates of a point on the outer circle of the grinding wheel are the same as the coordinates of a point on the workpiece. Therefore, the following relationship holds:

[0201]

[0202] Because the ellipse formed by the projection of the outer circle of the grinding wheel at point T is tangent to the outer diameter of the workpiece, the following relationship holds:

[0203]

[0204] By combining equations (13) and (14), we can obtain the angles of the grinding end point on the workpiece and the grinding wheel, as well as the distance from the corresponding grinding wheel section to the grinding wheel end face.

[0205] Calculate the position of the grinding end point on the z-axis of the workpiece coordinate system at this point:

[0206] z T =R(h) T sinθ T sinα+h T cosα (15)

[0207] Because the workpiece rotates during the machining process, calculate the rotation angle of the starting point when grinding reaches the end point of the plane.

[0208]

[0209] Therefore, the width of the helical groove of the milling cutter can be calculated, i.e., ∠A'O w T.

[0210] Step four of this embodiment of the invention involves searching for the optimal mounting angle and contact angle using a particle swarm optimization algorithm based on the established constraint relationships. The mounting angle and grinding wheel contact angle are treated as two-dimensional particles (α, θ). To avoid overcutting, the search space for the mounting angle is set to (0, 95° - β]. The search space for the grinding wheel contact angle is set according to the processing requirements.

[0211] The algorithm flow for searching the optimal installation angle and contact angle based on particle swarm optimization is as follows:

[0212] (1) Input the grinding wheel model and geometric parameters, and the spiral groove design parameters, including the peripheral cutting angle γ. t Core diameter r ct and groove width φt .

[0213] (2) Set the relevant parameters of the particle swarm algorithm, including population size, number of iterations, etc.

[0214] (3) Initialize the particle swarm position x ij and velocity v ij , where j represents the dimension of the particle and i represents the i-th particle.

[0215] (4) Substitute the initialized particle position, i.e., the mounting angle and the grinding wheel contact angle, into the front angle constraint formula to calculate the corresponding workpiece contact angle, and then calculate the corresponding core diameter r according to the core diameter and groove width calculation model. c And the groove width φ.

[0216] (5) Substitute the core diameter and slot width generated by each particle into the fitness function to record the individual best value (pbest) for each particle. ij and the global optimum of the population (gbest) j .

[0217]

[0218] (6) Update the particle swarm position and velocity based on equations (18) and (19).

[0219] The speed update formula is:

[0220] v ij (t+1)=ωv ij (t)+c1r1[pbest ij (t)-v ij (t)]+c2r2[gbest j (t)-v ij (t)] (18)

[0221] The position update formula is:

[0222] x ij (t+1)=v ij (t)+v ij (t+1) (19)

[0223] Where t represents the current iteration number, c1 and c2 are acceleration constants, and r1 and r2 are two independent random numbers with values ​​in the range [0,1].

[0224] (7) Calculate the core diameter and cutting edge width generated at the current position, and update the individual optimal fitness and the global optimal fitness. Terminate the algorithm when the optimal fitness meets the accuracy requirements or reaches the maximum number of iterations.

[0225] like Figure 9As shown, the milling trajectory calculation system for helical grooves based on two-dimensional particle swarm optimization provided in this embodiment of the invention includes:

[0226] The workpiece coordinate system establishment module is used to establish a coordinate system based on the grinding wheel model and workpiece size, and to establish expressions for the installation angle and contact angle with respect to the grinding wheel pose in the workpiece coordinate system;

[0227] The correlation equation establishment module is used to establish the correlation equation between the mounting angle, grinding wheel contact angle and workpiece contact angle based on the front angle machining characteristics;

[0228] The constraint equation establishment module is used to establish constraint equations for the installation angle and contact angle with respect to the milling cutter helical groove parameters;

[0229] The parameter generation module iteratively generates grinding wheel pose parameters that meet the machining requirements based on the particle swarm optimization algorithm.

[0230] The method for determining the grinding trajectory of a milling cutter spiral groove based on two-dimensional particle swarm optimization, provided in the application embodiment of the present invention, is applied to a computer device. The computer device includes a memory and a processor. The memory stores a computer program. When the computer program is executed by the processor, the processor performs the steps of the method for determining the grinding trajectory of a milling cutter spiral groove based on two-dimensional particle swarm optimization.

[0231] The milling cutter spiral groove grinding trajectory determination method based on two-dimensional particle swarm optimization provided in the application embodiment of the present invention is applied to an information data processing terminal, which is used to implement the milling cutter spiral groove grinding trajectory calculation system based on two-dimensional particle swarm optimization.

[0232] It should be noted that embodiments of the present invention can be implemented using hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented using hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or using software executed by various types of processors, or using a combination of the above-described hardware circuitry and software, such as firmware.

[0233] To verify the effectiveness of the grinding trajectory calculation method provided by this invention, a corresponding simulation module was built in Vericut for research. A 1A1 grinding wheel with a radius of 60mm and a width of 10mm was selected for the simulation model. The helical groove of the milling cutter to be machined has a peripheral rake angle of 0.1745rad, a core diameter of 3.2mm, and a groove width of 1.745rad. The grinding trajectory is calculated using the method provided by this invention. The grinding wheel model, workpiece size, and helical groove size parameters are input. After establishing a coordinate system, the optimal grinding wheel mounting angle and the angle corresponding to the grinding wheel contact point are searched in two-dimensional space based on the particle swarm optimization algorithm. The grinding trajectory is calculated based on the results, and simulation machining is performed. The simulation results are as follows: Figure 10 As shown, the milling cutter spiral groove machined using the grinding trajectory generated by this method has a peripheral cutting edge rake angle of 0.1743 rad, a core diameter of 3.1929 mm, and a groove width of 1.7452 rad. Simulation results show that the milling cutter spiral groove parameters machined using the grinding trajectory calculated by the method provided in this invention have small errors and meet machining requirements.

[0234] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for determining the grinding trajectory of a milling cutter's helical groove based on two-dimensional particle swarm optimization, characterized in that, include: Step 1: Establish the expressions for the installation angle and contact angle with respect to the grinding wheel pose in the workpiece coordinate system; Step 2: Establish the correlation formula between the mounting angle, grinding wheel contact angle, and workpiece contact angle based on the machining characteristics of the front angle; Step 3: Establish constraint equations for the installation angle and contact angle with respect to the milling cutter helical groove parameters; Step 4: Iteratively generate grinding wheel pose parameters that meet the processing requirements based on the particle swarm optimization algorithm; Step three, depending on the position of the grinding wheel center on the workpiece center coordinate axis, can be divided into two cases for core diameter calculation: (1) When the center of the grinding wheel is located to the left of the center of the workpiece, the core diameter is formed by grinding the end face of the grinding wheel. The grinding point of the core diameter should satisfy the following formula: Combining equation (1), within the range of θ values Within the core, there exists only one minimum value, therefore the core diameter can be obtained using the bisection method; (2) When the grinding wheel is on the right side of the workpiece, it is necessary to calculate and compare the core diameter values ​​of the grinding wheel end face and the grinding wheel side. The calculation process of the core diameter value of the grinding wheel end face is the same as when the center of the grinding wheel end face is on the left side of the workpiece. The envelope equation can be solved by the envelope discriminant. At this time, the core diameter of the milling cutter is obtained by comparing the minimum distance from the front end face of the grinding wheel and the envelope line to the center of the workpiece. The groove width is the angle formed by the line connecting the starting point, the ending point and the center of the workpiece of the spiral groove cutting. Therefore, after determining the contact angle, it is necessary to calculate the angle corresponding to the ending point. At the grinding ending point, the coordinates of the point on the outer circle of the grinding wheel are the same as the coordinates of the point on the workpiece. Therefore, the following relationship exists: Because the ellipse formed by the projection of the outer circle of the grinding wheel at point T is tangent to the outer diameter of the workpiece, the following relationship holds: By combining equations (13) and (14), the angles of the grinding end point on the workpiece and grinding wheel, as well as the distance from the corresponding grinding wheel section to the grinding wheel end face, can be obtained. The position of the grinding end point on the z-axis of the workpiece coordinate system at this point can then be calculated. z T =R(h T )sinθ T sinα+h T cosα (15) Calculate the rotation angle of the starting point when grinding reaches the end point of the spiral groove cutting: Therefore, the width of the helical groove of the milling cutter can be calculated, i.e., ∠A'O w T; In step four, based on the established constraint relationships, the optimal mounting angle and contact angle are searched using a particle swarm optimization algorithm. The mounting angle and grinding wheel contact angle are treated as two-dimensional particles (α, θ). To avoid overcutting, the search space for the mounting angle is set to (0, 95° - β]. The search space for the grinding wheel contact angle is set according to the processing requirements. The algorithm flow for searching the optimal installation angle and contact angle based on particle swarm optimization is as follows: (1) Input the grinding wheel model and geometric parameters, and the spiral groove design parameters, including the peripheral cutting angle γ. t Core diameter r ct and groove width φ t ; (2) Set the relevant parameters of the particle swarm optimization algorithm, including population size, number of iterations, etc.; (3) Initialize the particle swarm position x ij and velocity v ij , where j represents the dimension of the particle and i represents the i-th particle; (4) Substitute the initialized particle position, i.e., the mounting angle and the grinding wheel contact angle, into the front angle constraint formula to calculate the corresponding workpiece contact angle, and then calculate the corresponding core diameter r according to the core diameter and groove width calculation model. c and groove width φ; (5) Substitute the core diameter and slot width generated by each particle into the fitness function to record the individual best value (pbest) for each particle. ij and the global optimum of the population (gbest) j : (6) Update the particle swarm position and velocity based on equations (18) and (19). The velocity update equation is: v ij (t+1)=ωv ij (t)+c1r1[pbest ij (t)-v ij (t)]+c2r2[gbest j (t)-v ij (t)] (18) The position update formula is: x ij (t+1)=v ij (t)+v ij (t+1) (19) Where t represents the current iteration number, c1 and c2 are acceleration constants, and r1 and r2 are two independent random numbers with values ​​in the range [0,1]. (7) Calculate the core diameter and cutting edge width generated at the current position, and update the individual optimal fitness and the global optimal fitness. Terminate the algorithm when the optimal fitness meets the accuracy requirements or reaches the maximum number of iterations.

2. The method for determining the grinding trajectory of a milling cutter helical groove based on two-dimensional particle swarm optimization according to claim 1, characterized in that, In step one, a workpiece coordinate system is established. Initially, the zero points of the workpiece coordinate system and the grinding wheel coordinate system coincide. After determining the grinding wheel mounting posture, the grinding wheel coordinate system is rotated α around the x-axis, and then moved α along the x-axis, y-axis, and z-axis of the workpiece coordinate system, respectively. x a y and a z Any point on the grinding wheel profile can be represented by θ in the workpiece coordinate system as follows: Any point on the workpiece contour can be represented by ω: Where R(h) is the outer radius of the grinding wheel at a distance h from the front end face, and θ and ω are the angle parameters of the grinding wheel and the workpiece, respectively. For ease of calculation, we will choose a as the angle parameter. z Analyzing and solving for the case where the value is 0, once the grinding wheel's mounting position is determined, the grinding wheel and the workpiece contact at point A. At this point, the mounting angle and contact angle are known. Given α, θ, and ω, the mounting position of the grinding wheel can be represented as follows:

3. The method for determining the grinding trajectory of a milling cutter helical groove based on two-dimensional particle swarm optimization according to claim 1, characterized in that, In step two, after determining the installation position of the grinding wheel, any point on the grinding wheel can be represented by equation (1). When the contact point between the end face of the grinding wheel and the workpiece is B, the coordinates of point B in the workpiece coordinate system are: The grinding wheel position parameter in the formula can be expressed in terms of contact angle: When the front end of the grinding wheel contacts the workpiece at point B, the coordinates of the grinding wheel center on the Z-axis of the workpiece coordinate system are: z B =R(h)sinθ B sinα (6) Similarly, at grinding wheel contact point A, the coordinates of the grinding wheel center on the Z-axis of the workpiece coordinate system are: z A =R(h)sinθ A sinα (7) The angle of workpiece rotation when the grinding wheel grinds point B can be calculated based on the Z-axis coordinates of points A and B: Where β is the helix angle of the milling cutter, R w Given the workpiece radius, the coordinates of A' are calculated based on the workpiece rotation angle: but, The smaller the angle between points A and B on the end face of the grinding wheel, the smaller the length of A'B. When θ is taken... A =θ B When +0.01, ∠A'O w B is approximately equal to the rake angle of the cutting edge, which can be expressed using the mounting angle and the contact angle as follows: γ=f(α,θ,ω) (11) Where γ is the rake angle of the peripheral edge.

4. A milling cutter helical groove grinding trajectory calculation system based on two-dimensional particle swarm optimization, implementing the method as described in any one of claims 1-3, characterized in that, The milling cutter spiral groove grinding trajectory calculation system based on two-dimensional particle swarm optimization includes: The workpiece coordinate system establishment module is used to establish the workpiece coordinate system and, within the workpiece coordinate system, establish the expressions for the installation angle and contact angle with respect to the grinding wheel pose. The correlation equation establishment module is used to establish the correlation equation between the mounting angle, grinding wheel contact angle and workpiece contact angle based on the front angle machining characteristics; The constraint equation establishment module is used to establish constraint equations for the installation angle and contact angle with respect to the milling cutter helical groove parameters; The parameter generation module iteratively generates grinding wheel pose parameters that meet the machining requirements based on the particle swarm optimization algorithm.

5. A milling cutter helical groove grinding trajectory calculation system based on two-dimensional particle swarm optimization, implementing the method as described in any one of claims 1-3, characterized in that, The system includes: The coordinate system establishment module is used to establish the expressions for the installation angle and contact angle with respect to the grinding wheel pose in the workpiece coordinate system, and to initialize the workpiece coordinate system and the grinding wheel coordinate system. The correlation module is used to establish the correlation formula between the mounting angle, grinding wheel contact angle and workpiece contact angle based on the front angle machining characteristics; The constraint equation module is used to establish constraint equations for the mounting angle and contact angle with respect to the milling cutter helical groove parameters, including calculation models for the core diameter and groove width; The particle swarm optimization module iteratively generates grinding wheel pose parameters that meet the machining requirements based on the particle swarm algorithm, including the mounting angle and grinding wheel contact angle, and optimizes the grinding trajectory by searching for the optimal solution.

6. A milling cutter helical groove grinding trajectory calculation system based on two-dimensional particle swarm optimization, implementing the method as described in any one of claims 1-3, characterized in that, The system includes the following functional modules: The data input module is used to input the grinding wheel model, geometric parameters, and spiral groove design parameters, such as the peripheral rake angle, core diameter, and groove width. The particle swarm initialization module is used to set relevant parameters of the particle swarm algorithm, including population size, number of iterations, etc., and to initialize the position and velocity of the particle swarm. The calculation and evaluation module is used to substitute the initialized particle position into the front angle constraint formula to calculate the corresponding workpiece contact angle, and calculate the corresponding core diameter and groove width according to the core diameter and groove width calculation model. Then, it evaluates the merits of each particle based on the fitness function. The optimization and iteration module is used to iteratively update the position and velocity of the particle swarm based on the velocity and position update formulas of the particle swarm algorithm, and to record the individual optimality of each particle and the global optimality of the population. The algorithm terminates when the optimal fitness meets the accuracy requirements or reaches the maximum number of iterations, and outputs the optimal grinding wheel pose parameters.

7. A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the method for determining the milling trajectory of a helical groove based on two-dimensional particle swarm optimization as described in any one of claims 1-3.

8. An information data processing terminal, characterized in that, The information data processing terminal is used to implement the milling cutter spiral groove grinding trajectory calculation system based on two-dimensional particle swarm as described in claim 4.

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