Method for solving grinding track of end mill flank surface based on tooth deflection center amount

Abstract

This invention discloses a method for solving the grinding trajectory of an end mill's flank face using a grinding wheel based on tooth offset center. The method includes the following steps: establishing an end mill coordinate system and a grinding wheel coordinate system; adjusting the grinding wheel to be coplanar with the flank face of the end mill's teeth; constructing a first vector related to the cutting edge angle of the end mill's teeth and a second vector related to the clearance angle within the flank face of the end mill's teeth, and performing a cross product operation to obtain the initial grinding wheel vector; then rotating the grinding wheel around the axis containing the first rotation axis vector by a set first swing angle; constructing a third vector related to the tooth offset center within the flank face of the end mill's teeth; obtaining a second rotation axis vector by cross product of the third vector and the second vector; and then rotating the grinding wheel around the axis containing the second rotation axis vector by a set second swing angle to obtain the final grinding wheel vector, thus generating a CNC grinding trajectory for grinding the flank face of the end mill. This invention offers high calculation efficiency and accuracy in grinding trajectory calculation, improving grinding quality.

Description

Technical Field

[0001] This invention relates to the field of milling cutter grinding technology, and in particular to a method for solving the grinding trajectory of the grinding wheel on the back face of an end mill based on the tooth offset center. Background Technology

[0002] End mills are the most widely used core cutting tools in CNC milling. The geometric accuracy of the end mill's flank face, the quality of its cutting edge morphology, and the consistency of its core design parameters directly determine the end mill's cutting performance, part machining accuracy, high-speed cutting stability, and service life. CNC grinding of the flank face is a key process in the end mill manufacturing process, and the precise determination of the grinding wheel's posture and motion trajectory is a core prerequisite for ensuring the grinding quality of the flank face, avoiding machining interference, and improving production efficiency.

[0003] Currently, the industry commonly uses the vector rotation method to solve for the grinding wheel posture and trajectory in end mill flank grinding. However, for end mills with specific tooth offset center values, existing grinding wheel trajectory solution schemes based on the vector rotation method do not incorporate the tooth offset center value into the core vector rotation calculation system. In existing methods, the definition of the rotation axis and the setting of the tilt angle parameters are both set freely without any correlation, completely ignoring the influence of the tooth offset center value on the spatial geometry of the end tooth flank face, and failing to establish a matching relationship between the grinding wheel posture adjustment and the tool tooth offset center value. This freely set posture adjustment method, for end mills with specific tooth offset center values, cannot make the solved grinding wheel posture automatically match the inherent geometry of the tool, which easily leads to inherent deviations between the grinding wheel working vector and the flank face design normal vector, and cannot guarantee the machining accuracy of core design parameters such as end tooth clearance angle and rake angle.

[0004] To compensate for the inherent deviations mentioned above, during on-site machining, operators can only compensate through repeated trial cuts, online measurements, and manual iterative adjustments to the swing angle parameters. This not only significantly extends the tool machining debugging cycle and substantially reduces grinding production efficiency, but also increases manufacturing costs. Furthermore, machining accuracy is highly dependent on the operator's on-site experience, making it difficult to guarantee the machining consistency of the same batch of tools or different end teeth of the same tool. This easily leads to quality problems such as overcutting or undercutting of the flank face, grinding interference between the grinding wheel and the tool substrate, and edge chipping. Therefore, it is necessary to improve the existing technology to overcome its shortcomings. Summary of the Invention

[0005] This invention provides a method for solving the grinding trajectory of the end mill's flank face grinding wheel based on tooth offset center amount. It can integrate the tooth offset center amount into the grinding wheel vector rotation and attitude solution system, automatically match the geometric characteristics of the end mill with tooth offset center amount, eliminate the need for repeated trial and error iteration, achieve high computational efficiency and high solution accuracy, improve grinding quality, and ensure grinding consistency.

[0006] The technical solution adopted by this invention to solve its technical problem is: a method for solving the grinding trajectory of the end mill's flank face grinding wheel based on the tooth offset center, comprising the following steps: S1. Establish the end mill coordinate system O1-X1Y1Z1 and the grinding wheel coordinate system O2-X2Y2Z2; wherein, the relative position of the origin O2 of the grinding wheel coordinate system with the grinding wheel remains constant, and the attitude of the grinding wheel coordinate system is updated synchronously with the attitude adjustment of the grinding wheel. S2, adjust the initial position of the grinding wheel to be coplanar with the back face of the end mill tooth, so that the initial vector of the grinding wheel is consistent with the normal vector of the back face of the end mill tooth; construct a first vector l1 associated with the inclination angle of the end mill tooth and a second vector l2 associated with the clearance angle of the end mill tooth in the back face of the end mill tooth; obtain the normal vector L0 of the back face of the end mill tooth, i.e., the initial vector L0 of the grinding wheel, through the cross product operation of the first vector l1 and the second vector l2. S3, based on the grinding wheel pose determined in step S2, define a first rotation axis vector u2 parallel to the Z2 axis of the grinding wheel coordinate system O2-X2Y2Z2, rotate the grinding wheel around the axis where the first rotation axis vector u2 is located by a set first swing angle β, and obtain the grinding wheel transition vector L1 after one rotation; S4. Based on the grinding wheel pose determined in step S3, a third vector l3 associated with the tooth offset center of the end mill is constructed in the back face of the end mill tooth. The second rotation axis vector u3 is obtained by cross product of the third vector l3 and the second vector l2. The grinding wheel is rotated around the axis where the second rotation axis vector u3 is located by a set second swing angle δ to obtain the final grinding wheel vector L2. S5. Based on the geometric relationship between the final vector L2 of the grinding wheel and the flank face of the end mill tooth, calculate the tool position coordinates of the grinding wheel, transform the tool position coordinates in the grinding wheel coordinate system to the end mill coordinate system O1-X1Y1Z1 through coordinate transformation, and generate the CNC grinding trajectory for grinding the flank face of the end mill.

[0007] As a further improvement of the present invention, in step S1, the origin O1 of the end mill coordinate system O1-X1Y1Z1 is the center of the end mill end face, the X1 axis is the rotation axis of the end mill, the Y1 axis is the direction of the line connecting the origin O1 to the outermost endpoint of the end mill tooth cutting edge, and the Z1 axis is perpendicular to both the X1 axis and the Y1 axis; the origin O2 of the grinding wheel coordinate system O2-X2Y2Z2 is the center of the large end face of the grinding wheel, and the X2 axis, Y2 axis, and Z2 axis correspond to the X1 axis, Y1 axis, and Z1 axis respectively in the same direction.

[0008] As a further improvement of the present invention, the vector along the cutting edge line of the end mill tooth is taken as the end cutting vector, and the first vector l1 is the component vector of the projection of the end cutting vector onto the X1Y1 plane of the end mill coordinate system O1-X1Y1Z1, and its expression is (sinλ, cosλ, 0), where λ is the cutting edge inclination angle of the end mill tooth.

[0009] As a further improvement of the present invention, the second vector l2 is the tangent direction vector of the back face of the end mill tooth, which points behind the cutting edge line of the end mill tooth, and the angle between the second vector l2 and the cutting plane of the end mill tooth is the back angle α.

[0010] As a further improvement of the present invention, in step S3, the first unit rotation axis vector u2' is obtained by calculating the magnitude of the first rotation axis vector u2 and normalizing it, and the grinding wheel transition vector L1 is calculated using the Rodriguez rotation formula, that is: .

[0011] As a further improvement of the present invention, the vector along the end mill tooth cutting edge line is taken as the end cutting edge vector, and the third vector l3 is the component vector of the end cutting edge vector projected onto the Y1Z1 plane of the end mill coordinate system O1-X1Y1Z1, and its expression is (0, cosu, sinu), where sinu=e / r, e is the tooth offset center of the end mill, and r is the bar stock radius of the end mill.

[0012] As a further improvement of the present invention, in step S4, the second unit rotation axis vector u3' is obtained by calculating the magnitude of the second rotation axis vector u3 and performing normalization, and the final grinding wheel vector L2 is calculated using the Rodriguez rotation formula, that is: .

[0013] As a further improvement of the present invention, in step S5, the tool point of the grinding wheel is the geometric center point of the large end circle of the grinding wheel, which coincides with the origin O2 of the grinding wheel coordinate system O2-X2Y2Z2.

[0014] As a further improvement of the present invention, the calculation process of the tool position coordinates includes the following steps: In the end mill coordinate system O1-X1Y1Z1, the parameterized equation of the end mill's cutting edge line is constructed based on the third vector l3 to determine the coordinates of the grinding point Pt on the cutting edge line, where Pt=P0+t×l3, P0 is the starting point of the cutting edge line, t is the position parameter along the cutting edge line, and t satisfies 0≤t≤S, where S is the total length of the cutting edge line. Based on the cross product of the final vector L2 of the grinding wheel and the third vector l3, the direction vector Nt pointing from the grinding point Pt to the tool position is obtained, where Nt = L2 × l3; Based on the coordinates of the grinding point Pt, the direction vector Nt, and the radius Rg of the large end circle of the grinding wheel, the coordinates of the tool position O_g are calculated, where O_g = Pt + Rg × Nt.

[0015] As a further improvement of the present invention, the end tooth cutting edge line is discretized according to a preset step length Δt, and several grinding points Pt are selected in the range of 0~S. The tool position coordinates corresponding to each grinding point Pt are calculated respectively. The ordered set of all tool position coordinates constitutes the CNC grinding trajectory for grinding the back face of the end mill.

[0016] The beneficial effects of this invention are as follows: This invention provides a method for solving the grinding trajectory of a grinding wheel on the flank face of an end mill based on the tooth offset center. By constructing a first vector and a second vector associated with the rake angle and clearance angle respectively within the flank face of the end mill tooth, and performing a cross product operation to obtain the initial grinding wheel vector consistent with the normal of the end mill tooth flank face, the method ensures accurate matching between the initial posture of the grinding wheel and the geometric features of the end mill tooth flank face. Based on this, the progressive adjustment of the grinding wheel posture is completed through two successive vector rotations. The rotation axis of the second rotation is formed by the cross product of a third vector associated with the tooth offset center and a second vector associated with the clearance angle. This allows the grinding wheel's posture adjustment to be directly linked to the tooth eccentricity structure of the end mill, achieving a self-consistent match between the grinding wheel's posture and the end mill's eccentricity structure. This eliminates the need for operators to repeatedly adjust parameters manually through trial and error, effectively improving the calculation efficiency and automation level of the grinding trajectory. Simultaneously, based on the final vector of the grinding wheel, the tool position coordinates are calculated and transformed to generate a suitable CNC grinding trajectory, effectively ensuring the grinding accuracy of the end tooth rake face and the grinding consistency of tools in the same batch. This fundamentally reduces the risk of grinding interference caused by the tooth eccentricity structure and can meet the batch stable grinding requirements of high-precision end mills. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating the steps of the end mill flank grinding wheel trajectory calculation method based on tooth offset center amount in this invention. Figure 2 This is a schematic diagram of the end face where the end teeth of the end mill of the present invention are located; Figure 3 This is a front view of the end mill in this invention; Figure 4 This is a schematic diagram of the structure of the grinding wheel rotating at the first swing angle in this invention; Figure 5A schematic diagram showing the structure of the third vector on the end face where the end teeth of the end mill in this invention are located; Figure 6 This is a schematic diagram of the second swing angle of the grinding wheel in this invention; Figure 7 The image shows a physical drawing of the end mill manufactured according to the set parameters of this invention, where (a) is an enlarged view of the end mill head and (b) is an enlarged view of the end face where the end teeth of the end mill are located.

[0019] Referring to the accompanying drawings, the following explanations are provided: 1. End mill; 101. End tooth cutting edge; 2. Grinding wheel. Detailed Implementation

[0020] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0021] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this application, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number and aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0022] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. The illustrations only show the components related to this application and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the shape, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0023] Additionally, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that practice can be carried out without these specific details.

[0024] The technical solutions provided by the various embodiments of this application are described below with reference to the accompanying drawings.

[0025] See Figures 1 to 6 This invention provides a method for solving the grinding trajectory of an end mill's flank face using a grinding wheel based on tooth offset center, comprising steps S1 to S5: S1. Establish the end mill coordinate system O1-X1Y1Z1 and the grinding wheel coordinate system O2-X2Y2Z2; wherein, the relative position of the origin O2 of the grinding wheel coordinate system with the grinding wheel 2 remains constant, and the attitude of the grinding wheel coordinate system is updated synchronously with the attitude adjustment of the grinding wheel 2.

[0026] S2, adjust the initial position of the grinding wheel to be coplanar with the back face of the end mill tooth, so that the initial vector of the grinding wheel is consistent with the normal vector of the back face of the end mill tooth; construct a first vector l1 associated with the rake angle of the end mill tooth and a second vector l2 associated with the clearance angle of the end mill tooth within the back face of the end mill tooth. Through the cross product operation of the first vector l1 and the second vector l2, obtain the normal vector L0 of the back face of the end mill tooth, that is, the initial vector L0 of the grinding wheel.

[0027] S3. Based on the pose of the grinding wheel 2 determined in step S2, a first rotation axis vector u2 parallel to the Z2 axis of the grinding wheel coordinate system O2-X2Y2Z2 is defined. The grinding wheel 2 is rotated around the axis containing the first rotation axis vector u2 by a set first swing angle β to obtain the grinding wheel transition vector L1 after one rotation. During the rotation, the attitude of the grinding wheel coordinate system is updated synchronously with the pose adjustment of the grinding wheel 2.

[0028] S4. Based on the grinding wheel pose determined in step S3, a third vector l3 associated with the tooth offset center of the end mill 1 is constructed in the back face of the end mill tooth. The second rotation axis vector u3 is obtained by cross product of the third vector l3 and the second vector l2. The grinding wheel 2 is rotated around the axis where the second rotation axis vector u3 is located by a set second swing angle δ to obtain the final grinding wheel vector L2. During the rotation, the orientation of the grinding wheel coordinate system is updated synchronously with the pose adjustment of the grinding wheel 2.

[0029] S5. Based on the geometric relationship between the final vector L2 of the grinding wheel and the flank face of the end mill tooth, calculate the tool position coordinates of the grinding wheel 2. Transform the tool position coordinates in the grinding wheel coordinate system to the end mill coordinate system O1-X1Y1Z1 through coordinate transformation to generate the CNC grinding trajectory for the flank face grinding of the end mill 1.

[0030] This invention constructs a first vector l1 and a second vector l2, associated with the rake angle and clearance angle respectively, within the end mill's tooth relief face. These vectors are then cross-multiplied to obtain an initial grinding wheel vector L0 that aligns with the normal to the end mill's relief face. This ensures a precise match between the initial grinding wheel posture and the geometric features of the end mill's relief face. Based on this, a progressive adjustment of the grinding wheel's posture is achieved through two successive vector rotations. The rotation axis of the second rotation is obtained by cross-multiplying a third vector l3 associated with the tooth offset center and a second vector l2 associated with the clearance angle. This allows the grinding wheel's posture adjustment to be directly correlated with the end mill's relief face geometry. The tooth eccentricity structure of cutter 1 is directly related to the self-consistent matching between the posture of grinding wheel 2 and the eccentricity structure of end mill 1. This eliminates the need for operators to repeatedly adjust parameters manually, effectively improving the calculation efficiency and automation of the grinding trajectory. At the same time, based on the final vector L2 of the grinding wheel, the tool position coordinates are calculated and the coordinate transformation is completed to generate a suitable CNC grinding trajectory. This effectively ensures the grinding accuracy of the end tooth rake face and the grinding consistency of the same batch of tools, fundamentally reducing the grinding interference risk caused by the tooth eccentricity structure. It can meet the batch stable grinding requirements of high-precision end mills.

[0031] In step S1, the grinding wheel 2 is located at the 12 o'clock position of the end mill 1, and the end mill coordinate system O1-X1Y1Z1 and the grinding wheel coordinate system O2-X2Y2Z2 are independent of each other. The origin O1 of the end mill coordinate system O1-X1Y1Z1 is the center of the end mill's end face, the X1 axis is the rotation axis of the end mill, and the Y1 axis is the direction of the line connecting the origin O1 to the outermost endpoint of the end mill's cutting edge line 101 (e.g., ...). Figure 2 As shown, the Z1 axis points from the origin O1 to the 12 o'clock direction and is perpendicular to both the X1 and Y1 axes. The origin O2 of the grinding wheel coordinate system O2-X2Y2Z2 is the center of the large end face of the grinding wheel. The X2, Y2, and Z2 axes correspond to the X1, Y1, and Z1 axes respectively and are in the same direction.

[0032] See Figure 2 and Figure 3 In step S2, the vector along the end mill's end tooth cutting edge line 101 is taken as the end-edge vector, with its direction pointing inward from the outermost endpoint of the end tooth cutting edge line 101. The first vector l1 is the component vector of the projection of the end-edge vector onto the X1Y1 plane of the end mill coordinate system O1-X1Y1Z1, which is directly related to the cutting edge inclination angle of the end tooth, and its expression is (sinλ, cosλ, 0), where λ is the cutting edge inclination angle of the end mill end tooth. The second vector l2 is the tangent direction vector of the relief face of the end mill end tooth, which points behind the end mill's end tooth cutting edge line 101 (away from the machined surface of the workpiece). The second vector l2 is directly related to the relief angle, and the angle between the second vector l2 and the cutting plane of the end mill end tooth is the relief angle α.

[0033] This invention, by clearly defining the specific expressions and spatial attributes of the first vector l1 and the second vector l2, standardizes the precise construction method of the initial vector L0 of the grinding wheel. This ensures that the solution of the initial vector L0 is based entirely on the core geometric parameters of the end mill's end teeth, namely the inclination angle λ and the clearance angle α. This guarantees the complete coincidence of the initial vector L0 of the grinding wheel with the normal of the end tooth's clearance face, avoiding the problem of insufficient grinding accuracy caused by initial posture deviation. It also provides a precise and reliable benchmark for the subsequent progressive adjustment of the grinding wheel's posture.

[0034] Since both the first vector l1 and the second vector l2 are within the flank face of the end mill, the cross product of the first vector l1 and the second vector l2 can be used to obtain the normal vector L0 of the flank face of the end mill, which is the initial vector L0 of the grinding wheel.

[0035] See Figure 4 In step S3, the first unit rotation axis vector u2' is obtained by calculating the magnitude of the first rotation axis vector u2 and normalizing it. The grinding wheel transition vector L1 is then calculated using the Rodriguez rotation formula, i.e.: .

[0036] This invention normalizes the first rotation axis vector u2 and uses the Rodriguez rotation formula to complete the first vector rotation calculation, ensuring the accuracy and stability of the first attitude rotation calculation of the grinding wheel. This effectively simplifies the calculation process of spatial vector rotation and improves the calculation efficiency of grinding wheel attitude adjustment. At the same time, by adjusting the rotation of the first swing angle β, the contact area between the grinding wheel and the end tooth rake face during grinding can be effectively reduced, reducing grinding friction and further improving the grinding surface quality of the end tooth rake face.

[0037] like Figure 5 As shown, the third vector l3 in step S4 is the component vector of the end-edge vector projected onto the Y1Z1 plane of the end mill coordinate system O1-X1Y1Z1, which can be expressed as (0, cosu, sinu), where sinu=e / r, e is the tooth offset center of the end mill, and r is the bar radius of the end mill. By clearly defining the specific expression of the third vector l3 and its relationship with the tooth offset center e, the core construction benchmark of the secondary rotation axis is standardized, so that the spatial direction of the third vector l3 can be determined by the tooth offset center e of the end mill and the bar radius r. This further strengthens the strong correlation between the secondary rotation axis and the tool eccentric structure, ensuring that the secondary attitude adjustment of the grinding wheel can fully adapt to the tooth offset structure of the tool, further improving the self-consistent matching degree between the attitude of the grinding wheel and the geometric features of the tool, and fundamentally avoiding the grinding interference risk caused by the tooth offset structure.

[0038] In step S4, similarly, by calculating the magnitude of the second rotation axis vector u3 and normalizing it, the second unit rotation axis vector u3' is obtained. Then, the final grinding wheel vector L2 is calculated using the Rodriguez rotation formula, i.e.: .

[0039] This invention normalizes vector u3 and uses the Rodriguez rotation formula to complete the second vector rotation calculation, ensuring the accuracy of the second attitude rotation calculation of the grinding wheel. This allows the secondary attitude adjustment of the grinding wheel to be completed entirely based on the rotation axis associated with the tooth offset center amount e, further improving the matching accuracy between the grinding wheel attitude and the tool eccentric structure. At the same time, by adjusting the rotation of the second swing angle δ, the interference risk between the grinding wheel and the end mill tooth structure during grinding can be effectively avoided, improving the safety of the grinding process and the tool yield.

[0040] In step S5, the tool point of the grinding wheel is the geometric center of the large end circle of the grinding wheel, which coincides with the origin O2 of the grinding wheel coordinate system O2-X2Y2Z2.

[0041] The calculation process for the tool position coordinates includes the following steps: S51, in the end mill coordinate system O1-X1Y1Z1, construct the parameterized equation of the end mill's cutting edge line 101 based on the third vector l3, and determine the coordinates of the grinding point Pt on the end mill cutting edge line 101, where Pt=P0+t×l3, P0 is the starting point of the end mill cutting edge line 101, t is the position parameter along the end mill cutting edge line 101, and t satisfies 0≤t≤S, where S is the total length of the end mill cutting edge line 101.

[0042] S52, let Nt be the direction vector pointing from the grinding point Pt to the tool position point (the geometric center point of the large end circle of the grinding wheel). Since Nt is a vector within the end face of the grinding wheel, L2 is the final normal vector of the grinding wheel, and l3 is the tangent vector of the cutting edge that is tangent to the end face of the grinding wheel, Nt satisfies the following relationship: (1) Nt⊥L2; (2) Nt⊥l3; Therefore, Nt can be obtained by the cross product of the final vector L2 of the grinding wheel and the third vector l3, that is: Nt=L2×l3.

[0043] S53. Based on the coordinates of the grinding point Pt, the direction vector Nt, and the radius Rg of the large end circle of the grinding wheel, the coordinates of the tool position O_g are calculated, where O_g = Pt + Rg × Nt.

[0044] S54, along the end tooth cutting edge line 101, discretize the cutting edge at a preset step size Δt, select several grinding points Pt in the range of 0~S, calculate the tool position coordinates corresponding to each grinding point Pt, and the ordered set of all tool position coordinates constitutes the CNC grinding trajectory for grinding the back face of the end mill.

[0045] This invention constructs a parameterized equation for the end mill cutting edge line by using a third vector l3 associated with the tooth offset of the end mill, accurately determining the spatial coordinates of the grinding point Pt on the cutting edge line. This ensures that the selection of the grinding point Pt perfectly matches the actual geometric contour of the end mill cutting edge line with the tooth offset structure. Then, the direction vector Nt pointing from the grinding point Pt to the tool position is obtained through the cross product of the grinding wheel's final vector L2 and the third vector l3. Using this as a reference, combined with the grinding wheel's size parameters, the coordinates of the corresponding tool position are calculated. This guarantees that the tool position corresponding to a single grinding point Pt perfectly matches the grinding requirements of the end mill's flank face and the real-time attitude of the grinding wheel, fundamentally avoiding... This method addresses the issue of over-cutting or under-cutting during grinding caused by tool position deviation. Based on this, it discretizes the end tooth cutting edge along a preset step size Δt, selecting several grinding points Pt within the entire length of the cutting edge and solving for the corresponding tool position coordinates. This orderly set of tool position coordinates forms a complete and continuous CNC grinding trajectory, ensuring that the generated grinding trajectory fully covers the entire contour of the end tooth cutting edge. This guarantees the consistency of grinding accuracy across the entire area of ​​the end tooth's flank face, effectively avoiding incomplete grinding or exceeding accuracy tolerances in localized areas of the cutting edge, and further improving the stability of the grinding process and the machining quality of the end mill finished product.

[0046] Taking a solid flat-end mill with a diameter of 2mm as an example, the effectiveness of the method of the present invention is verified. The geometric parameters of the end mill in this embodiment are as follows: clearance angle α = 12°, tooth offset center e = 0.036mm, cutting edge inclination angle λ = 2°, bar stock radius r = 1mm, first swing angle β is set to 2°, and second swing angle δ is set to 20°. The grinding wheel used is a model 11V9 grinding wheel with a maximum face diameter of 99.3mm, a fillet radius of 0.1mm, and an outer angle of 20°.

[0047] During the actual grinding process of the end tooth rake face, the grinding wheel speed was 4000 rpm, the feed rate was 40 mm / min, and grinding oil was used for cooling during the grinding process.

[0048] Based on the above parameters, the intermediate results obtained by calculating the grinding trajectory of the end mill flank face grinding wheel based on the tooth offset center amount according to steps S1~S5 of the present invention are as follows: The initial vector L0 = (-0.97755174, -0.03413686, 0.20778504); The grinding wheel transition vector L1 = (-0.97579092, -0.0689943, 0.20741076); The second rotation axis vector u3 = (-0.97755174, -0.04161712, 0.20778504); The second unit rotation axis vector u3' = (-0.9773006, -0.04160643, 0.20773166); The final vector of the grinding wheel is L2 = (-0.97780867, -0.0673416, 0.19824901); The coordinates of the tool position point at the final position of the grinding wheel are O_g = (3.8013, 50.4853, 300.5282); A-axis angle (end mill rotation angle) = 18.76169391°; B-axis angle (grinding wheel rotation angle) = -77.91399476°.

[0049] like Figure 7 As shown, the actual grinding of the end mill tooth relief face was completed according to the CNC grinding trajectory generated by the method of this invention, and the core geometric parameters of the machined tool were precisely tested. The test results are shown in Table 1. As can be seen from the data in Table 1, the actual value of the end mill tooth relief angle α obtained by the method of this invention is 12.06°, and the relative error compared with the design value of 12° is only 0.5%; the actual value of the tooth offset center e is 0.0359mm, and the relative error compared with the design value of 0.036mm is only 0.278%. The machining errors of both core parameters are at extremely low levels, far below the industry tolerance requirements for high-precision end mill machining.

[0050] Table 1

[0051] Compared to existing methods that do not consider the tooth offset center value e and require repeated manual trial and error adjustments to the grinding wheel posture, this invention directly integrates the tooth offset center value e into the construction process of the grinding wheel's secondary rotation axis. This achieves geometric self-consistency between the grinding wheel posture and the tool's eccentric structure, significantly reducing manual trial and error and improving the automation and efficiency of grinding trajectory calculation. Furthermore, the solution logic of this invention is clear, the parameter relationships are well-defined, and the input parameters all originate from the tool's own geometric characteristics. This allows it to adapt to the grinding requirements of end mills with different tooth offset center values ​​e, effectively avoiding grinding interference risks caused by the tool's eccentric structure. It also ensures the consistency and stability of the flank grinding of tools in the same batch, demonstrating excellent engineering practicality and batch application value.

[0052] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for solving the grinding trajectory of an end mill's flank face using a grinding wheel based on tooth offset center, characterized in that... Includes the following steps: S1. Establish the end mill coordinate system O1-X1Y1Z1 and the grinding wheel coordinate system O2-X2Y2Z2; wherein, the relative position of the origin O2 of the grinding wheel coordinate system with the grinding wheel remains constant, and the attitude of the grinding wheel coordinate system is updated synchronously with the attitude adjustment of the grinding wheel. S2, adjust the initial position of the grinding wheel to be coplanar with the back face of the end mill tooth, so that the initial vector of the grinding wheel is consistent with the normal vector of the back face of the end mill tooth; construct a first vector l1 associated with the inclination angle of the end mill tooth and a second vector l2 associated with the clearance angle of the end mill tooth in the back face of the end mill tooth; obtain the normal vector L0 of the back face of the end mill tooth, i.e., the initial vector L0 of the grinding wheel, through the cross product operation of the first vector l1 and the second vector l2. S3, based on the grinding wheel pose determined in step S2, define a first rotation axis vector u2 parallel to the Z2 axis of the grinding wheel coordinate system O2-X2Y2Z2, rotate the grinding wheel around the axis where the first rotation axis vector u2 is located by a set first swing angle β, and obtain the grinding wheel transition vector L1 after one rotation; S4. Based on the grinding wheel pose determined in step S3, a third vector l3 associated with the tooth offset center of the end mill is constructed in the back face of the end mill tooth. The second rotation axis vector u3 is obtained by cross product of the third vector l3 and the second vector l2. The grinding wheel is rotated around the axis where the second rotation axis vector u3 is located by a set second swing angle δ to obtain the final grinding wheel vector L2. S5. Based on the geometric relationship between the final vector L2 of the grinding wheel and the flank face of the end mill tooth, calculate the tool position coordinates of the grinding wheel, transform the tool position coordinates in the grinding wheel coordinate system to the end mill coordinate system O1-X1Y1Z1 through coordinate transformation, and generate the CNC grinding trajectory for grinding the flank face of the end mill.

2. The method for solving the grinding trajectory of the end mill's flank face based on tooth offset center as described in claim 1, characterized in that, In step S1, the origin O1 of the end mill coordinate system O1-X1Y1Z1 is the center of the end mill end face, the X1 axis is the rotation axis of the end mill, the Y1 axis is the direction of the line connecting the origin O1 to the outermost endpoint of the end mill tooth cutting edge, and the Z1 axis is perpendicular to both the X1 and Y1 axes; the origin O2 of the grinding wheel coordinate system O2-X2Y2Z2 is the center of the large end face of the grinding wheel, and the X2, Y2, and Z2 axes correspond to the X1, Y1, and Z1 axes respectively.

3. The method for solving the grinding trajectory of the end mill's flank face based on tooth offset center as described in claim 1, characterized in that, The vector along the cutting edge line of the end mill tooth is taken as the end-edge vector. The first vector l1 is the component vector of the projection of the end-edge vector onto the X1Y1 plane of the end mill coordinate system O1-X1Y1Z1, and its expression is (sinλ, cosλ, 0), where λ is the cutting edge inclination angle of the end mill tooth.

4. The method for solving the grinding trajectory of the end mill's flank face based on tooth offset center as described in claim 1, characterized in that, The second vector l2 is the tangent direction vector of the back face of the end mill tooth, which points behind the cutting edge line of the end mill tooth, and the angle between the second vector l2 and the cutting plane of the end mill tooth is the back angle α.

5. The method for solving the grinding trajectory of the end mill's flank face based on tooth offset center as described in claim 1, characterized in that, In step S3, the first unit rotation axis vector u2' is obtained by calculating the magnitude of the first rotation axis vector u2 and normalizing it. The grinding wheel transition vector L1 is then calculated using the Rodriguez rotation formula, i.e.: 。 6. The method for solving the grinding trajectory of the end mill's flank face based on tooth offset center as described in claim 1, characterized in that, The vector along the cutting edge line of the end mill is taken as the end-edge vector. The third vector l3 is the component vector of the projection of the end-edge vector onto the Y1Z1 plane of the end mill coordinate system O1-X1Y1Z1. Its expression is (0, cosu, sinu), where sinu=e / r, e is the tooth offset center of the end mill, and r is the bar stock radius of the end mill.

7. The method for solving the grinding trajectory of the end mill's flank face based on tooth offset center as described in claim 6, characterized in that, In step S4, the second unit rotation axis vector u3' is obtained by calculating the magnitude of the second rotation axis vector u3 and normalizing it. The final grinding wheel vector L2 is then calculated using the Rodriguez rotation formula. 。 8. The method for solving the grinding trajectory of the end mill's flank face based on tooth offset center as described in claim 1, characterized in that, In step S5, the tool point of the grinding wheel is the geometric center of the large end circle of the grinding wheel, which coincides with the origin O2 of the grinding wheel coordinate system O2-X2Y2Z2.

9. The method for solving the grinding trajectory of the end mill's flank face based on tooth offset center as described in claim 8, characterized in that, The calculation process of the tool position coordinates includes the following steps: In the end mill coordinate system O1-X1Y1Z1, the parameterized equation of the end mill's cutting edge line is constructed based on the third vector l3 to determine the coordinates of the grinding point Pt on the cutting edge line, where Pt=P0+t×l3, P0 is the starting point of the cutting edge line, t is the position parameter along the cutting edge line, and t satisfies 0≤t≤S, where S is the total length of the cutting edge line. Based on the cross product of the final vector L2 of the grinding wheel and the third vector l3, the direction vector Nt pointing from the grinding point Pt to the tool position is obtained, where Nt = L2 × l3; Based on the coordinates of the grinding point Pt, the direction vector Nt, and the radius Rg of the large end circle of the grinding wheel, the coordinates of the tool position O_g are calculated, where O_g = Pt + Rg × Nt.

10. The method for solving the grinding trajectory of the end mill's flank face based on tooth offset center as described in claim 9, characterized in that, Discretize along the end tooth cutting edge line according to a preset step size Δt, select several grinding points Pt in the range of 0~S, calculate the tool position coordinates corresponding to each grinding point Pt, and the ordered set of all tool position coordinates constitutes the CNC grinding trajectory for grinding the back face of the end mill.

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