An integral taper end mill machining method and end mill based on discretization

Abstract

The present invention relates to the technical field of milling cutter processing, and particularly to a processing method for an integral taper end mill based on discretization. An integral taper end mill parameter expression and its workpiece coordinate system based on a numerically controlled grinding machine are established, and a mathematical model and its coordinate system of a conical grinding wheel for processing are established; the taper end mill is discretized into a finite number of cylindrical end mills by a discretization method; a grinding kinematic model of a single discretized cylindrical end mill is established, and a chip flute expression of the cylindrical end mill is constructed; an optimization algorithm is used to solve the chip flute expression to obtain the ideal position and attitude of the grinding wheel; the processing results of several discretized cylindrical end mills are combined to obtain the complete processing path of the taper end mill; the present invention can be applied to any type of integral taper end mill, effectively solve the interference phenomenon in the processing process, and improve its processing accuracy and processing efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of milling cutter processing, and particularly relates to a processing method and a milling cutter for an integral taper end mill based on discretization. Background Art

[0002] The integral taper end mill is a rotary multi-edge cutting tool with one or more cutting teeth for cutting processing. Due to its good cutting performance and complex profile, it is mainly used for face milling, groove milling, profiling milling, and free-form surface milling. Its processing process is that the grinding wheel cuts the rod stock along the cutting path in space to obtain the chip flutes part of the milling cutter, and then controls the grinding wheel to grind the end face of the milling cutter to obtain the final product.

[0003] The processing difficulties of the integral taper end mill mainly focus on the chip flutes part. Due to the complex structure of the integral taper end mill, the tool radius is constantly changing, and the tool parameters are not fixed, the processing of its cutting part is very difficult and prone to interference phenomena such as over-cutting and under-cutting, which will affect the processing quality at least and may lead to the damage of the tool and the processing equipment at worst.

[0004] The existing manufacturing methods of integral taper end mills include the empirical method and the analytical method. The empirical method often relies on the processing experience of workers to process the milling cutter, approximates the grinding path of the grinding wheel, is prone to errors and cannot guarantee the processing accuracy, and requires multiple trial grindings, resulting in large processing errors. The analytical method obtains the grinding path of the grinding wheel through mathematical derivation by establishing a mathematical model of the milling cutter. This method has high processing accuracy, but it has great limitations on the milling cutter and can only process special types such as integral taper end mills with equal helix angles, and has a small application range. Summary of the Invention

[0005] The purpose of the present invention is to provide a processing method for an integral taper end mill based on discretization, which can effectively solve the interference phenomenon in the processing of the integral taper end mill and is applicable to the processing of any type of integral taper end mill. To achieve the above purpose, the present invention is solved by the following technical solutions:

[0006] In the first aspect, the present invention provides a processing method for an integral taper end mill based on discretization, including the following steps:

[0007] Establish the parameter expression of the integral taper end mill and its workpiece coordinate system based on the CNC grinding machine, and establish the mathematical model and its coordinate system of the conical grinding wheel for processing;

[0008] Discretize the taper end mill into a finite number of cylindrical end mills by the discretization method;

[0009] Establish the grinding kinematic model of a single discrete cylindrical end mill, and construct the chip flute expression of the cylindrical end mill;

[0010] Solve the chip pocket expression using an optimization algorithm to obtain the ideal grinding wheel position and attitude;

[0011] Combine the machining results of several discretized cylindrical end mills to obtain the complete machining path of the tapered end mill.

[0012] As a further technical solution, the genetic algorithm in the optimization algorithm is used to solve the grinding wheel position and attitude of a single cylindrical end mill.

[0013] As a further technical solution, the solution process using the genetic algorithm includes: inputting the initial machining parameters of the i-th cylindrical end mill to generate the initial grinding wheel position and attitude; substituting the machining parameters and initial data into the genetic algorithm for optimization, and the optimization goal is to make the machined groove shape closest to the design requirements; obtaining the optimal position and attitude through iterative optimization; repeating the above process until all discretized cylindrical end mills are calculated.

[0014] As a further technical solution, if Δβ is the difference in the grinding wheel attitude between two adjacent cylindrical end mills, set β r as a limit value. When two adjacent cylindrical end mills do not satisfy Δβ ≤ β r , substitute it into the optimization algorithm for recalculation.

[0015] As a further technical solution, the machining results of several discretized cylindrical end mills need to be smoothed after combination.

[0016] As a further technical solution, the smoothing process uses a fitting strategy based on a cubic polynomial regression function to smooth the grinding wheel machining path.

[0017] As a further technical solution, the chip pocket expression of the cylindrical end mill is constructed using envelope theory.

[0018] As a further technical solution, the CNC grinding machine based on which the parameter expression of the integral tapered end mill and its workpiece coordinate system are established is a five-axis CNC grinding machine.

[0019] In a second aspect, the present invention provides an end mill machined by the method for machining an integral tapered end mill based on discretization as described in the first aspect.

[0020] In a third aspect, the present invention provides a computer-readable storage medium storing multiple instructions, characterized in that: the instructions are adapted to be loaded and executed by a processor of a terminal device for the method for machining an integral tapered end mill based on discretization.

[0021] The beneficial effects of the present invention are as follows:

[0022] (1) The present invention establishes a method for generating a grinding wheel trajectory for five-axis CNC taper end mills based on the discretization idea, transforming the problem of grinding the flute of a taper end mill into a series of sub-problems of grinding a cylindrical end mill. It solves the problems of the complex structure of the taper end mill and the variation of the chip flute cross-section parameters during the machining process.

[0023] (2) By combining and processing the grinding wheel trajectories of multiple cylindrical end mills obtained through solution, the present invention obtains a machining trajectory for the taper end mill with higher precision. Compared with the previous traditional methods, this method has a wide range of applicability and is no longer limited to special types of taper end mills, and its machining precision and efficiency have also been greatly improved.

[0024] (3) To avoid the discontinuity on the surface of the chip flute of the end mill during machining, the present invention proposes corresponding constraint conditions for the grinding wheel in the generated machining trajectory, effectively eliminating the interference phenomenon that may occur during machining. Brief Description of the Drawings

[0025] The accompanying drawings forming a part of the present invention are used to provide a further understanding of the present invention. The schematic embodiments and descriptions thereof of the present invention are used to explain the present invention and do not constitute a limitation to the present invention. It should also be understood that these drawings are shown for simplicity and clarity and are not necessarily drawn to scale. The present invention will now be described and explained with additional features and details by using the drawings, wherein:

[0026] Figure 1 Shows the flowchart of the machining method for the integral taper end mill in the embodiment of the present invention;

[0027] Figure 2 Shows the schematic structural diagram of the integral taper end mill in the embodiment of the present invention;

[0028] Figure 3 Shows the schematic diagram of the grinding wheel for end mill machining in the embodiment of the present invention;

[0029] Figure 4 Shows the schematic diagram of the discretization process of the integral taper end mill in the embodiment of the present invention;

[0030] Figure 5 Shows the schematic diagram of machining a single cylindrical grinding wheel after discretization in the embodiment of the present invention.

[0031] In the figure: 1. Tool shank part; 2. Large end face of the end mill; 3. Chip flute; 4. Cutting part; 5. Small end face of the end mill. Detailed Embodiments

[0032] The following will clearly and completely describe the technical solutions in the typical embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention.

[0033] Embodiment 1

[0034] As Figure 1 shown, this embodiment provides a machining method for an integral taper end mill based on discretization, including the following steps:

[0035] S101: Establish the parameter expression of the integral taper end mill and its workpiece coordinate system based on a five-axis CNC grinding machine, and establish the mathematical model and coordinate system of the conical grinding wheel for machining.

[0036] As Figure 2 shown, the structure of the integral taper end mill is mainly divided into a cutting part 4 and a tool shank part 1. The end face far from the tool shank part 1 is the small end face 5 of the milling cutter, and the one close to the tool shank part 1 is the large end face 2 of the milling cutter. The established workpiece coordinate system is O T . Let r 0 be the radius of the small end face, r e be the radius of the large end face, and L be the total length of the milling cutter. Then the expression of the tool radius r of the integral taper end mill is:

[0037]

[0038] As Figure 3 shown, establish the grinding wheel coordinate system O G of the conical grinding wheel. Let the thickness of the grinding wheel be H, the radius of the grinding wheel be R, and the taper angle of the grinding wheel be α. Then the grinding wheel can be expressed as:

[0039]

[0040] The normal vector of the grinding wheel is:

[0041]

[0042] S102: Discretize the taper end mill into a finite number of cylindrical end mills by the discretization method, and transform the problem of solving the machining path of the taper end mill into the problem of solving the machining path of a traditional cylindrical end mill.

[0043] As Figure 4 shown, in order to accurately solve the grinding wheel machining trajectory of the taper end mill, this embodiment uses the idea of discretization to discretize the taper end mill into several thin slices. The grinding of each discretized thin slice can be regarded as the machining of a cylindrical end mill with a corresponding radius. Therefore, this method simplifies the grinding wheel machining trajectory of the taper end mill into a series of sub-problems for solving the machining of a cylindrical end mill. It solves the problems of the complex structure of the taper end mill and the change of the chip flute cross-section parameters during the machining process.

[0044] S103: Establish the grinding kinematic model of a single discretized cylindrical end mill, and obtain the chip flute expression of the cylindrical end mill using the envelope theory.

[0045] To solve the chip pocket 3 of the discretized cylindrical end mill, a grinding kinematic model of the cylindrical end mill is established, as Figure 5 shown. In the i-th discrete cylindrical end mill, the position and orientation of the grinding wheel can be represented by [x i , y i , z i , β i , where [x i , y i , z i represents the position of the grinding wheel and β i represents the orientation of the grinding wheel. The practical significance of the grinding kinematic model of the cylindrical end mill is the movement of the grinding wheel to grind the end mill in the workpiece coordinate system O T . Therefore, coordinate transformation is required to transform the grinding wheel model established in S102 into the workpiece coordinate system. This machining process is carried out on a five-axis machine tool. Therefore, the grinding wheel has five movement directions in the workpiece coordinate system, namely the movement along the XYZ axes [x i , y i , z i , the rotation along the Y axis β i , and the workpiece rotation v along the Z axis. Therefore, the coordinate transformation formula of the grinding wheel is divided into the translation formula M 1 and the rotation formula M 2 .

[0046] Let the machining time be t, then the grinding kinematic model of the cylindrical end mill can be expressed as:

[0047]

[0048] The above kinematic model represents the movement surface of the grinding wheel in the workpiece coordinate system. The chip pocket 3 is a part of the movement surface. The chip pocket consists of two parts. The first part is generated by the edge of the grinding wheel and is solved using the envelope theory. The envelope theory can be expressed as:

[0049] T N· T V = 0 (5)

[0050] where T N = M 2 ·M 1 · G N,

[0051] * By the above envelope formula, an identity of the parameter variables θ, h, and t can be obtained. Using this identity, the variable θ can be expressed in terms of h and t, denoted as θ

[0052] ​

[0053] The above equation expression is the first part of the chip pocket generated by grinding the workpiece with the edge of the grinding wheel. The other part of the chip pocket is generated by grinding the large end face of the grinding wheel on the workpiece, which can be obtained by setting h = 0 in Formula 4. The two parts together constitute the complete expression of the chip pocket of the cylindrical end mill, and the chip pocket of the end mill can be solved and represented through the groove type expression.

[0054] S104: Use an optimization algorithm to solve the expression of the chip pocket of the cylindrical end mill obtained in S103 to obtain the ideal position and attitude of the grinding wheel.

[0055] When the parameters [x, y, z, β] in the chip pocket expression of S103 are determined, the chip pocket of the cylindrical end mill can be solved. Therefore, for a traditional cylindrical end mill, only the position and attitude of the grinding wheel need to be determined to complete the machining of the end mill. However, the tool parameters (such as the radius) of the taper end mill will continuously change during the machining process, and a series of positions and attitudes of the grinding wheel are required to form the grinding wheel machining path [x 1 ...x n , y 1 ...y n , z 1 ...z n , β 1 ...β n of the taper end mill.

[0056] In this embodiment, the genetic algorithm in the optimization algorithm is used to solve the position and attitude of the grinding wheel of a single cylindrical end mill. The solving process is as follows: 1) Input the initial machining parameters of the i-th cylindrical end mill to generate the initial position and attitude of the grinding wheel [x 0 , y 0 , z 0 , β 0 ; 2) Substitute the machining parameters and initial data into the genetic algorithm for optimization, and the optimization goal is to make the machined groove type closest to the design requirements; 3) Obtain the optimal [x i , y i , z i , β i through the iterative optimization of the genetic algorithm; 4) Repeat the above process until all discretized cylindrical end mills are calculated.

[0057] S105: Combine the machining results of several discretized cylindrical end mills and perform fairing processing to obtain the complete machining path of the taper end mill.

[0058] In S104, the machining paths of all discretized cylindrical end mills are obtained, but they cannot be simply connected to obtain the final machining path of the tapered end mill grinding wheel. During the discretization process, there is a discontinuity in the chip flutes of two adjacent cylindrical end mills. If the adjacent machining paths are simply connected, the surface of the chip flutes of the tapered end mill will be very rough, greatly reducing the performance and accuracy of the chip flutes. In addition, if the difference in the grinding wheel postures β i of two adjacent cylindrical end mills is too large, it will cause a drastic change in the grinding wheel direction during the machining process, thereby leading to the occurrence of interference phenomena.

[0059] To solve the above problems, this embodiment first proposes a constraint condition for the grinding wheel posture, as shown in Equation 7. Let Δβ be the difference in the grinding wheel postures of two adjacent cylindrical end mills, and β r be a limit value. When two adjacent cylindrical end mills do not satisfy Equation 7, the latter is brought into the optimization algorithm in S104 for recalculation.

[0060] Δβ ≤ β r (7)

[0061] Subsequently, to solve the problem of discontinuous chip flute surfaces, this embodiment performs fairing processing after connecting all the discretized grinding wheel positions and postures. The fairing processing uses a fitting strategy based on a cubic polynomial regression function to smooth the grinding wheel machining path, obtaining a sufficiently fair cubic regression function representing the grinding wheel machining path of the tapered end mill. This method can effectively eliminate the discontinuity of the chip flutes and improve the machining accuracy of the tapered end mill. Finally, the grinding wheel is controlled to machine the end face of the tapered end mill to complete the overall machining process of the tapered end mill.

[0062] Embodiment 2

[0063] This embodiment provides a milling cutter processed by using the discretization-based integral tapered end mill machining method described in Embodiment 1.

[0064] Embodiment 3

[0065] This embodiment provides a computer-readable storage medium storing multiple instructions adapted to be loaded and executed by a processor of a terminal device for the discretization-based integral tapered end mill machining method described above.

[0066] Although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by using the disclosed methods and technical contents without departing from the spirit and scope of the present invention. Therefore, any simple modification, equivalent change, and modification made to the above embodiments based on the technical essence of the present invention without departing from the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

Claims

1. A machining method for an integral taper end mill based on discretization, characterized in that, it includes the following steps: Establish the parameter expression of the integral taper end mill and its workpiece coordinate system based on a numerical control grinding machine, and establish the mathematical model of the conical grinding wheel for machining and its coordinate system; Discretize the taper end mill into a finite number of cylindrical end mills by the discretization method; Establish the grinding kinematic model of a single discretized cylindrical end mill, and construct the chip flute expression of the cylindrical end mill; Solve the chip flute expression using an optimization algorithm to obtain the ideal grinding wheel position and attitude; Combine the machining results of several discretized cylindrical end mills to obtain the complete machining path of the taper end mill.

2. The machining method for an integral taper end mill based on discretization according to claim 1, characterized in that, the genetic algorithm in the optimization algorithm is used to solve the grinding wheel position and attitude of a single cylindrical end mill.

3. The machining method for an integral taper end mill based on discretization according to claim 2, characterized in that, the solution process using the genetic algorithm includes: inputting the initial machining parameters of the i-th cylindrical end mill to generate the initial grinding wheel position and attitude; bringing the machining parameters and initial data into the genetic algorithm for optimization, and the optimization goal is to make the machined groove shape closest to the design requirements; obtaining the optimal position and attitude through iterative optimization; repeating the above process until all the discretized cylindrical end mills are calculated.

4. The machining method for an integral taper end mill based on discretization according to claim 1, characterized in that, If Δβ ​​is the difference in grinding wheel posture between two adjacent cylindrical milling cutters, set β r is a limit value. When two adjacent cylindrical milling cutters do not satisfy Δβ≤β r , it is brought into the optimization algorithm and recalculated.

5. The machining method for an integral taper end mill based on discretization according to claim 1, characterized in that, after combining the machining results of several discretized cylindrical end mills, fairing treatment is required.

6. The machining method for an integral taper end mill based on discretization according to claim 5, characterized in that, the fairing treatment uses a fitting strategy based on a cubic polynomial regression function to smooth the grinding wheel machining path.

7. The machining method for an integral taper end mill based on discretization according to claim 1, characterized in that, the chip flute expression of the cylindrical end mill is constructed using the envelope theory.

8. The machining method for an integral taper end mill based on discretization according to claim 1, characterized in that, the numerical control grinding machine based on which the parameter expression of the integral taper end mill and its workpiece coordinate system are established is a five-axis numerical control grinding machine.

9. An end mill, characterized in that, it is machined by using the machining method for an integral taper end mill based on discretization according to any one of claims 1-8.

10. A computer-readable storage medium, in which multiple instructions are stored, characterized in that: the instructions are adapted to be loaded and executed by a processor of a terminal device to perform the machining method for an integral taper end mill based on discretization.

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