Method for reducing mass eccentricity of variable pitch variable helix solid end mill

Abstract

The application relates to the technical field of computer-aided manufacturing end mills, in particular to a variable-pitch variable-helix integral end mill quality eccentricity reduction method. On the basis of setting the length of each chip flute of the end mill and the grinding path, the end mill quality eccentricity is optimized through cyclic iteration, and the end mill quality eccentricity meets the required requirements. Compared with the prior art, the end mill quality eccentricity is calculated based on the actual grinding process of the chip flute, the calculation result of the quality eccentricity is more accurate, and the end mill is consistent with the actual production. Moreover, the quality eccentricity reduction is realized by optimizing and adjusting the length of each chip flute. In the actual production process of the end mill, the grinding wheel path of each chip flute is extended to different degrees, so that the method does not need to add an extra grinding wheel path, the end mill quality eccentricity when the helix angle continuously changes along the cutting edge can be accurately controlled, the number of tool paths and the idle stroke are reduced, and the production efficiency is improved.

Description

Technical Field

[0001] This application relates to the field of computer-aided manufacturing end mill technology, and in particular to a method for reducing mass eccentricity of a variable pitch and variable helix integral end mill. Background Technology

[0002] In milling, conventional end mills (typically designed with equal tooth pitch and equal helix angle) are prone to generating regenerative chatter. This self-excited vibration not only reduces the surface quality of the workpiece but also accelerates end mill wear. In contrast, variable pitch and variable helix end mills (hereinafter referred to as dual variable pitch end mills) break the periodicity of cutting forces through an asymmetric cutting edge design, altering the dynamic response characteristics of the system and significantly suppressing chatter. However, the variable pitch and variable helix characteristics result in uneven mass distribution and significant mass eccentricity in these tools. Without eccentricity reduction measures, the resulting dynamic imbalance under high-speed milling conditions will severely affect the surface finish of the workpiece. Therefore, reducing mass eccentricity in dual variable pitch end mills is crucial to ensuring the cutting performance of these high-end tools.

[0003] In the geometry of end mills, the chip groove, due to its largest volume proportion, becomes the main factor affecting tool mass eccentricity. Studies have shown that in the process of reducing mass eccentricity in double-variable end mills, the influence of the end face and flank face of the cutter can be ignored; therefore, it is only necessary to focus on optimizing the structure of the chip groove.

[0004] The main shortcomings of existing eccentricity reduction methods are:

[0005] Currently, the reduction of mass eccentricity in double-variable end mills mainly relies on design-stage optimization, i.e., adjusting the profile of the chip flute to achieve a uniform distribution of mass across the cross-section. However, this method has significant limitations in practical application: on the one hand, machining a chip flute profile that meets design requirements requires the use of specially shaped grinding wheels or the addition of extra grinding paths, which not only increases manufacturing costs but also reduces production efficiency; on the other hand, for tools with helix angles that gradually change along the cutting edge, the actual profile of the chip flute will gradually deviate from the design value with the axial position, resulting in a large eccentricity in the actually manufactured tool even if the mass eccentricity is close to zero during the design stage, thus greatly reducing the reduction effect.

[0006] Therefore, there is a need to provide an improved technical solution that addresses the shortcomings of the existing technology. Summary of the Invention

[0007] The purpose of this application is to provide a method for reducing mass eccentricity of a variable pitch and variable helix integral end mill, so as to solve or alleviate the problems existing in the prior art.

[0008] To achieve the above objectives, this application provides the following technical solution:

[0009] A method for reducing mass eccentricity of a variable pitch, variable helix integral end mill, the method comprising the following steps:

[0010] Step 1: Given the geometric parameters and initial cutting length of each chip groove in the end mill, determine the grinding path of each chip groove;

[0011] Step 2: Based on the surface of the grinding wheel and the grinding path for machining the chip grooves, predict the actual machining surface of each chip groove, and then calculate the centroid coordinates and mass eccentricity value of the end mill.

[0012] Step 3: Connect the centroid coordinates of the end mill, the highest point on the intersection line between the grinding wheel and the end mill at the end of the grinding path, and the center point of the end mill end face, and the projection point on the end mill end face to obtain the minimum angle corresponding to the chip groove, which is the target chip groove.

[0013] Step 4: Extend the cutting length of the target chip groove. For each extension of the set length, repeat Step 2 to recalculate the coordinates of the centroid of the end mill and the mass eccentricity value until the mass eccentricity value reaches the minimum value, then stop extending the chip groove.

[0014] If the mass eccentricity value of the end mill meets the requirements at this time, the optimization will stop and the optimized chip groove cutting length and grinding path will be output.

[0015] If the mass eccentricity value of the end mill does not meet the requirements at this time, then repeat steps 3 and 4 based on the minimum mass eccentricity value reached in step 4; repeat this cycle until the chip groove cutting length and grinding path that meet the requirements are output.

[0016] The preferred method for reducing mass eccentricity of a variable pitch, variable helix integral end mill, as described above, involves establishing a coordinate system S in step 1. t (O t -x t ,y t ,z t ), where the origin O t Coinciding with the center point of the end mill face, z t The axis coincides with the axis of the end mill, and x t axis, y t axis, z t The axes are perpendicular to each other;

[0017] The cutting length of the chip flute is the endpoint A of the cutting edge curve. i Vertical distance L to the end face of the end mill i The subscript i indicates the i-th chip groove.

[0018] In the above-described method for reducing mass eccentricity of a variable pitch and variable helix integral end mill, preferably, in step 2, the actual machined surface of the chip groove includes the grinding process portion and the grinding endpoint portion;

[0019] The grinding process consists of a family of instantaneous contact lines between the grinding wheel and the end mill during the grinding process;

[0020] The grinding endpoint is the contact surface between the grinding wheel and the end mill at the end of the grinding path.

[0021] In the above-described method for reducing mass eccentricity of a variable pitch and variable helix integral end mill, preferably, in step 2, the end mill is discretized into a series of thin slices along the axial direction;

[0022] Then, the profile of each chip groove on each thin sheet is discretized by triangulation, where the area of ​​the cross-sectional profile of the i-th chip groove on the j-th thin sheet is:

[0023]

[0024] In the above-described method for reducing mass eccentricity of a variable pitch, variable helix integral end mill, preferably, the number of triangles formed after the chip flute profile is triangulated and discretized is set to p. Let be the area of ​​the k-th triangle of the chip groove profile; the centroid coordinates of the chip groove profile can be obtained from the formula for calculating the centroid of the combined shape:

[0025]

[0026] in, and The coordinates of the centroid of the k-th triangle of the chip groove profile are given.

[0027] In the above-described method for reducing mass eccentricity of a variable pitch, variable helix integral end mill, preferably, the volume of the i-th chip groove is:

[0028]

[0029] Where n is the number of thin slices formed after the end mill is discretized along the axial direction, and Δh j Let be the thickness of the j-th slice.

[0030] The preferred method for reducing mass eccentricity of a variable pitch, variable helix integral end mill, as described above, is derived from the formula for the centroid of the composite body, where the coordinates of the centroid of the i-th chip groove are:

[0031]

[0032] The preferred method for reducing mass eccentricity of a variable pitch, variable helix integral end mill, as described above, allows for the further determination of the coordinates of the end mill's centroid E based on the volume of the i-th chip groove and its centroid coordinates:

[0033]

[0034] Where m is the number of chip grooves, V t The volume enclosed by the rotating surface of the end mill;

[0035] The mass eccentricity value of the end mill is:

[0036]

[0037] In the above-described method for reducing mass eccentricity of a variable pitch, variable helix integral end mill, preferably, in step 3, the end mill end face is located at x t -y t In a plane, the centroid E of the end mill is at x t -y t The projection of the plane is point E′, and the highest point D is on the intersection line between the grinding wheel and the end mill at the end of the grinding path. i In x t -y t The projection on the plane is D i The projection of the center point of the end mill's end face onto the plane is O. t Then the vector and The included angle is angle θ i ;

[0038] Let {θ1,θ2,L,θ} m The chip groove corresponding to the smallest included angle in the} is the target chip groove.

[0039] In the above-described method for reducing mass eccentricity of a variable pitch and variable helix integral end mill, preferably, in step 4, the cutting length of the target chip groove is extended by a certain step size ΔL. For each extension of ΔL, step 2 is repeated to recalculate the coordinates of the centroid of the end mill and the mass eccentricity value. The mass eccentricity value will show a trend of first decreasing and then increasing as the cutting length is extended. When the mass eccentricity reaches its minimum value, the extension of the target chip groove is stopped.

[0040] Compared with the closest prior art, the technical solution of this application has the following beneficial effects:

[0041] This reduction method, based on setting the cutting edge length of each chip groove in the end mill and the grinding path, optimizes the mass eccentricity of the end mill through iterative optimization to achieve the required level. Moreover, this reduction method does not require adding an extra grinding wheel path, and can precisely control the mass eccentricity of the end mill when the helix angle changes continuously along the cutting edge, reducing the number of passes and idle strokes, and improving production efficiency.

[0042] In addition, this reduction method has no restrictions on the shape of the grinding wheel used when grinding chip grooves, thus reducing production costs. This reduction method also has a wide range of applications, not only applicable to general variable pitch and variable helix angle end mills, but also applicable to end mills where the helix angle of a single chip groove gradually changes along the cutting edge curve. Attached Figure Description

[0043] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. Wherein:

[0044] Figure 1 This is a flowchart illustrating the reduction method according to some embodiments of this application;

[0045] Figure 2 This is a schematic diagram of an end mill provided according to some embodiments of this application in a coordinate system;

[0046] Figure 3 This is a schematic diagram of an end mill axially discretized into thin sheets according to some embodiments of this application;

[0047] Figure 4 This is a triangular discrete schematic diagram of the chip groove profile in a sheet provided according to some embodiments of this application.

[0048] Figure 5 This is a schematic diagram illustrating the determination of a target chip groove according to some embodiments of this application.

[0049] Explanation of reference numerals in the attached figures:

[0050] 1. Grinding process section; 2. Grinding endpoint section; 3. Tool edge curve. Detailed Implementation

[0051] The present application will now be described in detail with reference to the accompanying drawings and embodiments. Various examples are provided by way of explanation and not by way of limitation. In fact, those skilled in the art will recognize that modifications and variations can be made to the present application without departing from the scope or spirit thereof. For example, a feature shown or described as part of one embodiment may be used in another embodiment to produce yet another embodiment. Therefore, it is desirable that the present application encompass such modifications and variations that fall within the scope of the appended claims and their equivalents.

[0052] In the following description, the terms "first / second / third" are used merely to distinguish similar objects and do not represent a specific order of objects. It is understood that "first / second / third" may be interchanged in a specific order or sequence where permitted, so that the embodiments of this application described herein can be implemented in an order other than that illustrated or described herein.

[0053] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. The terminology used herein is for the purpose of describing embodiments of this disclosure only and is not intended to limit this disclosure.

[0054] In the description of this application, the terms "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," and "bottom," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this application and do not require that this application be constructed and operated in a specific orientation, and therefore should not be construed as limiting this application. The terms "connected," "linked," and "set up" used in this application should be interpreted broadly. For example, they can refer to fixed connections or detachable connections; direct connections or indirect connections through intermediate components; wired connections, radio connections, or wireless communication signal connections. Those skilled in the art can understand the specific meaning of the above terms according to the specific circumstances.

[0055] The present application will now be described in detail with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in the embodiments of the present application can be combined with each other.

[0056] According to specific embodiments of this application, such as Figure 1-5 As shown, this application provides a method for reducing mass eccentricity of a variable pitch, variable helix integral end mill. The reduction method includes the following steps:

[0057] Step 1: Given the geometric parameters and initial cutting length of each chip groove in the end mill, determine the grinding path of each chip groove.

[0058] Step 2: Based on the surface of the grinding wheel and the grinding path for machining the chip grooves, predict the actual machining surface of each chip groove, and then calculate the centroid coordinates and mass eccentricity value of the end mill.

[0059] Step 3: Connect the centroid coordinates of the end mill, the highest point on the intersection line between the grinding wheel and the end mill at the end of the grinding path, and the projection point of the end mill's end face onto the end mill's end face to obtain the minimum angle of the chip groove, which is the target chip groove.

[0060] Step 4: Extend the cutting length of the target chip groove. For each extension of the set length, repeat Step 2 to recalculate the coordinates of the centroid of the end mill and the mass eccentricity value until the mass eccentricity value reaches the minimum value, then stop extending the chip groove.

[0061] If the mass eccentricity value of the end mill meets the requirements at this time, the optimization will stop, and the optimized chip groove cutting length and grinding path will be output.

[0062] If the mass eccentricity value of the end mill does not meet the requirements at this time, then repeat steps 3 and 4 based on the minimum mass eccentricity value reached in step 4; repeat this cycle until the chip groove cutting length and grinding path that meet the requirements are output.

[0063] This reduction method, based on setting the cutting length of each chip groove in the end mill and the grinding path, optimizes the mass eccentricity of the end mill through iterative optimization to achieve the required level. In this embodiment, the reduction method can reduce the mass eccentricity of the end mill to below 1μm.

[0064] Compared with existing technologies, this reduction method calculates the end mill's mass eccentricity based on the actual grinding process of the chip grooves. The calculation results are more accurate and consistent with the end mills actually produced. Moreover, this reduction method achieves mass eccentricity reduction by optimizing and adjusting the cutting edge length of each chip groove. In the actual production process of the end mill, this means that the grinding wheel path of each chip groove is extended to different degrees. This eliminates the need to add an extra grinding wheel path and can precisely control the end mill's mass eccentricity when the helix angle changes continuously along the cutting edge, reducing the number of tool passes and idle strokes, and improving production efficiency.

[0065] In addition, this method has no restrictions on the shape of the grinding wheel used when grinding chip grooves. Standard 1A1 and 1V1 grinding wheels can be used to grind chip grooves, reducing production costs. This method also has a wide range of applications. It is not only suitable for general variable pitch and variable helix angle end mills, but also for end mills where the helix angle of a single chip groove gradually changes along the cutting edge curve.

[0066] In step 1, coordinate system S is established. t (O t -x t ,y t ,z t ), where the origin O t Coinciding with the center point of the end mill face, z t The axis coincides with the axis of the end mill, and x t axis, y t axis, z t The axes are perpendicular to each other.

[0067] The geometric parameters of the chip groove and the initial cutting edge length are substituted into the coordinate system, and the grinding path of the chip groove is determined.

[0068] Among them, the cutting length of the chip groove is the endpoint A of the cutting edge curve 3. i Vertical distance L to the end face of the end mill i The subscript i indicates the i-th chip groove.

[0069] In this embodiment, the geometric parameters of the chip flute include the helix angle, rake angle, core diameter, and flute width angle; the cutting edge length of the chip flute determines the length of the grinding path; the cutting edge length of the chip flute is the endpoint A of the cutting edge curve 3. i Vertical distance L to the end face of the end mill i The subscript i indicates the i-th chip groove.

[0070] In this embodiment, the grinding path of the chip groove can be calculated based on the geometric parameters of the chip groove and the initial cutting edge length. The method for obtaining the grinding path of the chip groove is prior art. Here, we will give an example. The grinding path of the chip groove can be determined according to the inventors' published paper, "Ren L, Zhang Z, Li Y, et al. Wheelpathplanning for flute grinding of non-cylindrical solid end-mills based on circular arc projection[J]. Journal of Manufacturing Processes, 2024, 129: 261-272.". In other embodiments, the grinding path of the chip groove can also be generated by computer-aided manufacturing software. This is not specifically limited here.

[0071] In step 2, the actual machined surface of the chip groove includes the grinding process part 1 and the grinding endpoint part 2; the grinding process part 1 is composed of the instantaneous contact line family between the grinding wheel and the end mill during the grinding process; the grinding endpoint part 2 is the contact surface between the grinding wheel and the end mill at the end position of the grinding path.

[0072] In this embodiment, given the known grinding wheel surface and grinding path, the instantaneous contact line family between the grinding wheel and the end mill can be obtained based on the principle of curved envelope, thus obtaining the grinding process part 1 of the actual machined surface of the chip groove.

[0073] In the established coordinate system, the contact surface between the grinding wheel and the end mill can be defined by the inner boundary A. i B i C i and outer boundary C i D i A i Confirmed. Inner boundary A i B i C i The outer boundary C is the instantaneous contact line between the grinding wheel and the end mill at the end of the grinding path. i D i A i D is the intersection line between the grinding wheel's rotating surface and the end mill's rotating surface at the end of the grinding path. iThe point on the intersection line that is furthest from the end face of the milling cutter (i.e., the highest point on the intersection line) is the grinding endpoint of the actual machined surface of the chip groove, thus obtaining part 2.

[0074] In step 2, the end mill is discretized into a series of thin slices along the axial direction. In this embodiment, the end face profile of each slice is composed of the intersection lines of the actual machined curved surfaces of multiple chip grooves and the plane where the slice is located. Since the thickness of each slice is very thin, the thickness of each slice can be considered constant in the thickness direction.

[0075] Then, the profile of each chip groove on each thin sheet is discretized by triangulation, where the area of ​​the cross-sectional profile of the i-th chip groove on the j-th thin sheet is:

[0076]

[0077] In this embodiment, the end mill is first discretized into multiple thin slices in the axial direction, and then the area of ​​each chip groove on each thin slice is calculated.

[0078] Let p be the number of triangles formed after the chip groove profile is discretized by triangulation. Let be the area of ​​the k-th triangle of the chip groove profile; using the formula for calculating the centroid of a composite figure, the coordinates of the centroid of the chip groove profile are:

[0079]

[0080] in, and Let be the centroid coordinates of the k-th triangle of the chip groove profile.

[0081] The volume of the i-th chip groove is:

[0082]

[0083] Where n is the number of thin slices formed after the end mill is discretized along the axial direction, and Δh j Let be the thickness of the j-th slice.

[0084] From the formula for the centroid of the composite body, the coordinates of the centroid of the i-th chip groove are:

[0085]

[0086] Based on the volume and centroid coordinates of the i-th chip groove, the coordinates of the centroid E of the end mill can be further calculated as follows:

[0087]

[0088] Where m is the number of chip grooves, V tV represents the volume enclosed by the rotating surface of the end mill; in this embodiment, the end mill has a cylindrical base structure. t =Hπr 2 H is the length of the end mill, and r is the radius of the end mill.

[0089] The mass eccentricity value of the end mill is:

[0090]

[0091] In this embodiment, the mass eccentricity value of the end mill is the absolute value of the distance between the centroid coordinate of the end mill and the center point of the coordinate system.

[0092] In this embodiment, in step 3, the end mill face is located at x t -y t In a plane, the centroid E of the end mill is at x t -y t The projection of the plane is point E′, and the highest point D is on the intersection line between the grinding wheel and the end mill at the end of the grinding path. i In x t -y t The projection on the plane is D i The projection of the center point of the end mill's end face onto the plane is O. t Then the vector and The included angle is angle θ i Take {θ1,θ2,L,θ} m The chip groove corresponding to the smallest included angle in the} is the target chip groove.

[0093] In this embodiment, in step 4, the cutting length of the target chip groove is extended by a certain step size ΔL. For each extension of ΔL, step 2 is repeated to recalculate the centroid coordinates and mass eccentricity value of the end mill. The mass eccentricity value will show a trend of first decreasing and then increasing as the cutting length is extended. When the mass eccentricity reaches the minimum value, the extension of the target chip groove is stopped. If the mass eccentricity value of the end mill meets the requirements at this time, the optimization is stopped, and the optimized chip groove cutting length and grinding path are output. If the mass eccentricity value of the end mill does not meet the requirements at this time, steps 3 and 4 are repeated based on the minimum mass eccentricity value reached in step 4. This process is repeated until the chip groove cutting length and grinding path that meet the requirements are output.

[0094] Taking a variable pitch, variable helical, three-groove right-hand cylindrical end mill as an example, the process for reducing mass eccentricity is as follows:

[0095] The end mill has a diameter of 16mm, a length of H=100mm, and an initial cutting edge length of L1=L2=L3=40mm. The geometric parameters of each chip groove are shown in Table 1. The helix angle and the groove width angle gradually change along the cutting edge curve. For example, the helix angle of groove 1 gradually changes linearly from 34° at the end face of the end mill to 38° at the end of the cutting edge curve, and the groove width angle gradually changes linearly from 105° at the end face of the end mill to 89° at the end of the cutting edge curve.

[0096] The allowable mass eccentricity of the end mill was set to 1 μm. The results of the mass eccentricity reduction are shown in Table 2. Initially, the mass eccentricity of the end mill was as high as 31.89 μm. Among the included angles θ1, θ2, and θ3, θ1 had the smallest value. Extending its cutting edge length in increments of 0.01 mm, the mass eccentricity reached its minimum of 7.56 μm when the cutting edge length L1 = 42.94 mm. This is still greater than the set allowable value and requires further optimization. At this point, θ3 had the smallest value, so chip groove #3 was selected as the target chip groove. Extending its cutting edge length, the mass eccentricity reached its minimum of 3.21 μm when the cutting edge length L3 = 40.49 mm. This is still greater than the set allowable value and requires further optimization. Continuing optimization, the value of θ1 is now at its minimum. Therefore, chip groove #1 is selected as the target chip groove, and its cutting length is extended. When the cutting length L1 = 43.23 mm, the end mill mass eccentricity reaches its minimum of 1.26 μm, which is greater than the set allowable value, so further optimization is needed. At this point, the value of θ3 is now at its minimum. Therefore, chip groove #3 is selected as the target chip groove, and its cutting length is extended. When the cutting length L3 = 40.57 mm, the end mill mass eccentricity reaches its minimum of 0.51 μm, which is less than the set allowable value, thus achieving the goal of reducing mass eccentricity. The optimized cutting length and grinding path are then output.

[0097] Table 1. Geometric parameters of chip flutes for variable pitch and variable helical three-groove cylindrical end mills.

[0098]

[0099] Table 2 Results of Mass Eccentricity Reduction

[0100]

[0101] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for reducing mass eccentricity of a variable pitch, variable helix integral end mill, characterized in that, The reduction method includes the following steps: Step 1: Given the geometric parameters and initial cutting length of each chip groove in the end mill, determine the grinding path of each chip groove; Step 2: Based on the surface of the grinding wheel and the grinding path for machining the chip grooves, predict the actual machining surface of each chip groove, and then calculate the centroid coordinates and mass eccentricity value of the end mill. Step 3: Connect the centroid coordinates of the end mill, the highest point on the intersection line between the grinding wheel and the end mill at the end of the grinding path, and the center point of the end mill end face, and the projection point on the end mill end face to obtain the minimum angle corresponding to the chip groove, which is the target chip groove. Step 4: Extend the cutting length of the target chip groove. For each extension of the set length, repeat Step 2 to recalculate the coordinates of the centroid of the end mill and the mass eccentricity value until the mass eccentricity value reaches the minimum value, then stop extending the chip groove. If the mass eccentricity value of the end mill meets the requirements at this time, the optimization will stop and the optimized chip groove cutting length and grinding path will be output. If the mass eccentricity value of the end mill does not meet the requirements at this time, then repeat steps 3 and 4 based on the minimum mass eccentricity value reached in step 4; repeat this cycle until the chip groove cutting length and grinding path that meet the requirements are output.

2. The method for reducing mass eccentricity of a variable pitch, variable helix integral end mill according to claim 1, characterized in that, In step 1, coordinate system S is established. t (O t -x t ,y t ,z t ), where the origin O t Coinciding with the center point of the end mill face, z t The axis coincides with the axis of the end mill, and x t axis, y t axis, z t The axes are perpendicular to each other; The cutting length of the chip flute is the endpoint A of the cutting edge curve. i Vertical distance L to the end face of the end mill i The subscript i indicates the i-th chip groove.

3. The method for reducing mass eccentricity of a variable pitch, variable helix integral end mill according to claim 2, characterized in that, In step 2, the actual machined surface of the chip groove includes the grinding process portion and the grinding endpoint portion; The grinding process consists of a family of instantaneous contact lines between the grinding wheel and the end mill during the grinding process; The grinding endpoint is the contact surface between the grinding wheel and the end mill at the end of the grinding path.

4. The method for reducing mass eccentricity of a variable pitch, variable helix integral end mill according to claim 3, characterized in that, In step 2, the end mill is discretized into a series of thin slices along the axial direction; Then, the profile of each chip groove on each thin sheet is discretized by triangulation, where the area of ​​the cross-sectional profile of the i-th chip groove on the j-th thin sheet is:

5. The method for reducing mass eccentricity of a variable pitch, variable helix integral end mill according to claim 4, characterized in that, Let p be the number of triangles formed after the chip groove profile is triangulated and discretized. Let be the area of ​​the k-th triangle of the chip groove profile; the centroid coordinates of the chip groove profile can be obtained from the formula for calculating the centroid of the combined shape: in, and Let be the centroid coordinates of the kth triangle of the chip groove profile.

6. The method for reducing mass eccentricity of a variable pitch, variable helix integral end mill according to claim 5, characterized in that, The volume of the i-th chip groove is: Where n is the number of thin slices formed after the end mill is discretized along the axial direction, and Δh j Let be the thickness of the j-th slice.

7. The method for reducing mass eccentricity of a variable pitch, variable helix integral end mill according to claim 6, characterized in that, From the formula for the centroid of the composite body, the coordinates of the centroid of the i-th chip groove are:

8. The method for reducing mass eccentricity of a variable pitch, variable helix integral end mill according to claim 6. Its features are, Based on the volume and centroid coordinates of the i-th chip groove, the coordinates of the centroid E of the end mill can be further calculated as follows: Where m is the number of chip grooves, V t The volume enclosed by the rotating surface of the end mill; The mass eccentricity value of the end mill is:

9. The method for reducing mass eccentricity of a variable pitch, variable helix integral end mill according to claim 8, characterized in that, In step 3, the end mill face is located at x t -y t In a plane, the centroid E of the end mill is at x t -y t The projection of the plane is point E′, and the highest point D is on the intersection line between the grinding wheel and the end mill at the end of the grinding path. i In x t -y t The projection on the plane is D i The projection of the center point of the end mill's end face onto the plane is O. t Then the vector and The included angle is angle θ i ; Let {θ1,θ2,L,θ} m The chip groove corresponding to the smallest included angle in the} is the target chip groove.

10. The method for reducing mass eccentricity of a variable pitch, variable helix integral end mill according to claim 9, characterized in that, In step 4, the cutting length of the target chip groove is extended by a certain step size ΔL. For each extension of ΔL, step 2 is repeated to recalculate the coordinates of the centroid of the end mill and the mass eccentricity value. The mass eccentricity value will show a trend of first decreasing and then increasing as the cutting length is extended. When the mass eccentricity reaches the minimum value, the extension of the target chip groove is stopped.

Images