Milling cutter core thickness-based grinding wheel tool path calculation method and system during milling cutter slotting

Abstract

The invention relates to the technical field of milling cutter slotting, and particularly discloses a milling cutter core thickness-based grinding wheel tool path calculation method and system during milling cutter slotting, and the method comprises the following steps: S1, inputting three customizable parameters of the core thickness, the cutting guide surface and the cutting angle of a to-be-processed milling cutter for different types of grinding wheels, and calculating the grinding wheel tool path during milling cutter slotting; s2, in the milling cutter grooving process, only the fillet part of the grinding wheel participates in grinding, and the grinding wheel model in the milling cutter grooving process is simplified into a circular ring body; s3, establishing a grinding wheel tool path calculation model according to the shape parameters of the ring body, the core thickness of the milling cutter, the cutting guide surface, the cutting angle, the tangent condition of the ring body and the core thickness and the tangent condition of the ring body and the cutting guide surface; and S4, the grinding wheel tool path calculation model is analyzed according to a similar conjugate gradient optimization method, and a dynamic grinding wheel tool path during milling cutter grooving is obtained. The method can calculate and simulate to restore the dynamic grinding wheel tool path when the milling cutter is slotted under the condition close to real machining.

Description

Technical Field

[0001] The present invention relates to the technical field of milling cutter grooving, and particularly relates to a calculation method and system for the grinding wheel tool path during milling cutter grooving based on the core thickness of the milling cutter. Background Art

[0002] Solid end mills are widely used in industries such as aerospace, automotive, and mold manufacturing. As a key geometric structure of the solid end mill, its grinding process directly determines multiple important parameters including the helix angle, core diameter, rake angle, and groove width. These parameters have a significant impact on cutting performance such as chip evacuation efficiency, rigidity, and sharpness.

[0003] With the increase in the complexity of machining materials, the refinement of structural design, and the improvement of product performance requirements, the requirements for the geometric structure of cutting tools have become increasingly strict. However, the complexity of the grinding process brought about by this special geometric structure greatly limits the practical application of such tools.

[0004] Current research and practice mostly focus on the spiral groove grinding of solid end mills with constant parameters, that is, when the helix angle, tool radius, and core thickness remain constant, obtaining the grinding wheel tool path during milling cutter grooving to groove the milling cutter to be processed. In this way, not only is the variety of grooved milling cutters single, but when milling with this milling cutter, in the recognized field, its overall vibration resistance, anti-deformation ability, and milling stability are poor.

[0005] There are also a few other existing technologies. For example, in a variable parameter spiral groove grinding trajectory calculation and optimization method with the patent application number CN202410054841.4, through geometric analysis, with the rake angle, helix angle, and core diameter as constraints, a solution model for the grinding wheel position and direction parameters is established, and at the same time, a variable parameter spiral groove grinding trajectory calculation and optimization method is proposed, so as to achieve a constant rake angle or a change according to the design requirements when the helix angle and core diameter change.

[0006] In the above-mentioned existing technologies, these technical methods either perform milling cutter grooving based on the constant parameters of their fixed geometric structures. Although the calculation is simple, when the grooved milling cutter is processed, under high-speed cutting or heavy-load conditions, it is easy to generate large vibrations, which not only affect the machining accuracy but also shorten the tool life. For other existing technologies, although variable parameter spiral grooves are proposed to solve the disadvantages of the aforementioned constant parameter solid end mills, the grinding wheel and the milling cutter spiral groove parameters are isolated from each other, and the reproduced grinding wheel tool path is relatively fuzzy, and it is necessary to separately analyze the geometric structure of each grinding wheel. The geometric structure of the grinding wheel is complex, which not only easily increases the calculation amount but also easily results in rough calculation of the grinding wheel pose. Summary of the Invention

[0007] The present invention aims to provide a calculation method and system for the grinding wheel tool path during the slotting of a milling cutter based on the core thickness of the milling cutter, so as to quickly calculate and simulate and restore the real and applicable grinding wheel tool path for the slotting of various types of milling cutters while ensuring accuracy.

[0008] To achieve the above object, the present invention adopts the following technical solutions: First solution, a calculation method for the grinding wheel tool path during the slotting of a milling cutter based on the core thickness of the milling cutter, including: S1: For different types of grinding wheels, input three customizable parameters of the core thickness, cutting guide surface, and cutting angle of the milling cutter to be processed, and calculate the grinding wheel tool path during the slotting of the milling cutter; wherein, the core thickness is defined by the milling cutter rotation axis and an arbitrary curve in the same plane, the cutting guide surface is defined by the milling cutter blade line and the normal direction, and the cutting angle is defined by the included angle between the grinding wheel rotation axis and the normal direction of the milling cutter blade line; S2: During the slotting of the milling cutter, only the rounded part of the grinding wheel participates in grinding. Simplify the grinding wheel model during the slotting of the milling cutter into a torus, and the torus is used to represent the rounded part of the grinding wheel. Analyze the grinding wheel pose based on the pose of the torus during the slotting process of the milling cutter; wherein, the major radius of the torus is r z =R - r, where, the rotation radius of the grinding wheel is R, and the minor radius r of the torus is equal to the grinding wheel fillet radius; S3: Establish a grinding wheel tool path calculation model based on the shape parameters of the torus, the core thickness of the milling cutter, the cutting guide surface, the cutting angle, the tangency condition between the torus and the core thickness, and the tangency condition between the torus and the cutting guide surface; wherein, when the grinding wheel is tangent to the milling cutter during the slotting process of the milling cutter, for any point on the milling cutter blade line, establish a coordinate system with as the origin, where the X-axis is the cutting point direction of the point , the Z-axis is the normal direction of the point , and ; wherein, when the torus is tangent to the cutting guide surface, the center of the sphere of the torus, the fillet radius of the grinding wheel is r, and is on the space circle of the radius of the torus; the included angle between the torus rotation axis and is fixed to determine the cutting angle parameter; the torus only has one degree of freedom restricted by the angle , is used as the first solution parameter of the grinding wheel tool path calculation model; S4: Analyze the grinding wheel tool path calculation model according to the conjugate gradient-like optimization method and obtain the dynamic grinding wheel tool path during the slotting of the milling cutter.

[0009] Beneficial effects: Different from the prior art, in this solution, in addition to the two customizable parameters of the cutting guide surface and the cutting angle, a customizable parameter of the core thickness is added. Adding the core thickness parameter makes the calculation of the grinding wheel tool path when milling cutter slots more accurate, but also increases the calculation amount. In order to reduce the corresponding calculation amount, this solution can simplify the geometric structures on different types of grinding wheels as a whole at one time, simplify the rounded corner parts participating in grinding in different types of grinding wheels into torus bodies, and analyze the grinding wheel pose through the pose of the torus body, reducing the corresponding calculation amount. At the same time, establish a grinding wheel tool path calculation model based on the tangency conditions of the torus body equivalent to the grinding of the grinding wheel with the core thickness and the cutting guide surface respectively, that is, combine the torus body with the core thickness and the cutting guide surface of the milling cutter respectively. This is equivalent to considering both the grinding wheel and the milling cutter to be processed, the two important participating objects in the milling cutter slotting process. And after deriving the grinding wheel pose, instead of connecting through the entire grinding wheel pose and the milling cutter, it is to connect between the simplified torus body of the grinding wheel and the milling cutter. This can further reduce the calculation amount while enhancing the accuracy of the grinding wheel tool path, enabling the use of three customizable parameters, simplifying the structure of any type of grinding wheel, and combining the torus body with the milling cutter to quickly calculate and simulate to restore the grinding wheel tool path during actual milling cutter slotting. Finally, the solid end mill designed with this variable spiral groove and variable core thickness surface (equivalent to three customizable parameters) is recognized in this field for its excellent anti-vibration performance, anti-deformation ability, better stability and longer service life, and can be widely used in precision manufacturing industries such as aerospace, automotive and mold manufacturing industries, with extremely high product value.

[0010] Specifically, first, improve the accuracy, authenticity and reliability of the grinding wheel tool path calculation. First, simplify the model and perform precise calculation. By simplifying the grinding wheel model into a torus body and only considering the rounded corner part of the grinding wheel participating in grinding, the calculation process is greatly simplified. This simplified model can quickly determine the geometric characteristics of the grinding wheel while retaining the key information of the interaction between the grinding wheel and the milling cutter, thereby improving the accuracy of the grinding wheel tool path calculation. Second, the calculation results are closer to the actual machining situation. Input the three customizable parameters of the core thickness, cutting guide surface, and cutting angle of the milling cutter to be processed, comprehensively considering various geometric characteristics of the milling cutter, making the calculation results closer to the actual machining situation. Especially for milling cutters with complex structures, this method can more realistically restore the interaction between the grinding wheel and the milling cutter.

[0011] Secondly, it generally adapts to the processing requirements of various complex milling cutter structures. The core thickness surface and the milling cutter spiral groove design can handle milling cutters with variable core thickness surfaces and variable spiral grooves, breaking through the limitations of existing constant parameter end mills. After processing, the overall vibration resistance, deformation resistance, and milling stability of the milling cutter are good, suitable for long-term milling in the precision manufacturing industry, and ensuring the quality stability of the same batch of products milled with the milling cutter.

[0012] Moreover, it improves the calculation efficiency. First, it reduces the amount of calculation. It is clear that the part of the grinding wheel participating in grinding during the milling cutter grooving process is the rounded corner part, and the rounded corner part is simplified into a torus, reducing the number of variables of such a complex geometric mechanism as the grinding wheel in the calculation process, thus simplifying the calculation process.

[0013] At the same time, it improves the machining accuracy and stability. By using the conjugate gradient-like optimization method, it effectively avoids the interference between the grinding wheel and the core thickness of the milling cutter, making the grinding wheel tool path closer to the actual machining path, improving the accuracy and reliability of the grinding wheel tool path calculation, and thus improving the machining accuracy and stability.

[0014] Then, it promotes the practical application of complex structure milling cutters. By accurately calculating the grinding wheel tool path, it can effectively improve the machining accuracy and quality of complex structure milling cutters, and promote their practical application in industries such as aerospace, automotive, and mold manufacturing. At the same time, by optimizing the grinding wheel tool path, it can improve the cutting performance of the milling cutter, such as chip removal efficiency, rigidity, and sharpness, etc., so as to meet the special requirements for the milling cutter under different materials and processing conditions, and improve the cutting performance of the milling cutter under different working conditions.

[0015] Subsequently, in step S2, by clarifying the main radius rz of the torus and the grinding wheel fillet radius equivalent to the minor radius r of the torus, the dimensional characteristics of the grinding wheel simplified model are made more explicit. This simplification method can quickly determine the geometric characteristics of the grinding wheel torus, provide an accurate dimensional basis for subsequent grinding wheel pose analysis, thus improving the accuracy and reliability of the grinding wheel tool path calculation, and ensuring the precise grinding cooperation between the grinding wheel and the milling cutter.

[0016] Immediately afterwards, in step S3, by establishing a coordinate system with any point on the milling cutter edge line as the origin and clarifying that the X-axis is the cutting point direction and the Z-axis is the normal direction, it provides a unified and accurate reference coordinate system for the grinding wheel tool path calculation. The establishment of this coordinate system enables the geometric relationship between the grinding wheel and the milling cutter to be clearly described and analyzed, facilitating the accurate determination of the pose and movement trajectory of the grinding wheel in subsequent calculations. At the same time, this definition method of the coordinate system also simplifies the calculation process, improves the calculation efficiency, and ensures the accuracy and reliability of the grinding wheel tool path calculation, especially significant in the grooving machining of milling cutters with complex geometric shapes.

[0017] In addition, in step S4, the geometric constraint conditions when the torus is tangent to the cutting guide surface are clarified, that is, the center of the sphere of the torus position and its tangency relationship with the cutting guide surface. By restricting the center of the sphere of the torus to be on the space circle and the fixed included angle between its axis of rotation and the cutting angle parameter, the degrees of freedom in the grinding wheel tool path calculation model are effectively controlled, leaving only one degree of freedom restricted by the angle. The setting of such constraint conditions not only simplifies the calculation model and reduces the computational complexity, but also ensures the precise tangency between the grinding wheel and the milling cutter, avoiding interference, thereby improving the machining accuracy and stability, which has important practical application value for the grooving machining of complex helical groove milling cutters.

[0018] Finally, the real machining path can be restored and simulated. By calculating and simulating, the dynamic grinding wheel tool path during the grooving of the milling cutter under the approximation of real machining is restored. This method can help engineers better understand the geometric relationships during the machining process, thereby optimizing the machining process, improving the production efficiency and product quality. At the same time, the test cost is reduced. Through accurate calculation and simulation, the number of tests and costs in actual machining are reduced, the production efficiency is improved, and the production cost is reduced.

[0019] Preferably, the separate surface obtained by separately peeling off the core thickness of the milling cutter is the core thickness surface, and the core thickness surface is used to represent the parameter data of the core thickness of the milling cutter to be machined; specifically, the axis of rotation of the milling cutter and any curve coplanar with the axis of rotation, and a plurality of discrete points are interpolated on the curve to form the core thickness surface of the milling cutter; the core thickness surface of the milling cutter can be geometrically characterized as the surface of the geometric body formed by the curve rotating around the axis of rotation of the milling cutter.

[0020] Beneficial effects: By defining the generation method of the core thickness surface of the milling cutter, that is, formed by the axis of rotation of the milling cutter and any curve coplanar with the axis of rotation, and a plurality of discrete points are interpolated on the curve, the complex geometric shape of the core thickness of the milling cutter can be accurately characterized. This parametric description method enables the geometric features of the core thickness of the milling cutter to be accurately captured and quantified, providing rich input information for the grinding wheel tool path calculation model, so as to more realistically restore the interaction between the grinding wheel and the core thickness during the grooving of the milling cutter, improving the adaptability and accuracy of the grinding wheel tool path calculation, and being applicable to the machining of milling cutters with various complex core thickness designs.

[0021] Preferably, the types of the core thickness surface include sphere, cylinder, cone and solid of revolution.

[0022] Advantageous effects: By covering a variety of common geometric shapes, the method of the present invention can be widely applied to milling cutters of different types and structures. This diverse applicability ensures that the calculation model can accurately handle the core thickness of various complex-shaped milling cutters, thereby improving the versatility and flexibility of the grinding wheel tool path calculation. Whether it is a simple spherical or cylindrical milling cutter, or a complex conical or solid of revolution structure, this method can effectively calculate the corresponding grinding wheel tool path to meet the requirements of different processing scenarios, further enhancing the practicality and universality of this solution in practical applications.

[0023] Preferably, to obtain the parameters of the cutting guide surface, specifically, the coordinates of a series of discrete points on the milling cutter blade edge and the normal vectors at each point are obtained. During the milling cutter slotting process, for a single discrete point on the milling cutter blade edge and the surface formed by the blade edge and the surrounding area, it can be characterized as the tangent point during the grinding wheel cutting process, and the plane formed by a single discrete point and the normal direction of the point can be characterized as the cutting plane during the grinding wheel cutting process.

[0024] Advantageous effects: By obtaining the coordinates and normal vectors of a series of discrete points on the milling cutter blade edge, the parametric description of the cutting guide surface is closely combined with the actual cutting process. This method can accurately characterize the geometric features of the milling cutter blade edge and its surrounding area, enabling each tangent point and its cutting plane to be accurately determined during the grinding wheel cutting process. This not only improves the accuracy of the grinding wheel tool path calculation but also can optimize the cutting path of the grinding wheel according to the geometric relationship in the actual cutting process, thereby improving the processing efficiency and surface quality while reducing tool wear.

[0025] Preferably, when analyzing the grinding wheel tool path calculation model according to the conjugate gradient optimization method of the type, a penalty function is established , when simultaneously = 0, the torus is tangent to the core thickness surface of the milling cutter. Conversely, the torus interferes with or is far from the core thickness surface; , where is the second solution parameter. When is a positive number, does not interfere with the core thickness surface; when is a negative number, interferes with the core thickness surface, where Pt is the center of the torus.

[0026] Beneficial effects: By introducing a penalty function mechanism, setting the condition that the torus is tangent to the core thickness surface of the milling cutter when two solution parameters are both 0, and adjusting the value of the penalty function according to the positive and negative values of the solution parameters, an effective constraint means is provided for the optimization of the grinding wheel tool path calculation model. This method can effectively avoid the interference between the grinding wheel and the core thickness of the milling cutter, ensuring the feasibility of the calculation results. At the same time, by optimizing the solution parameters, the grinding wheel tool path is closer to the actual machining path, improving the accuracy and reliability of the grinding wheel tool path calculation, providing more accurate theoretical guidance for the milling cutter slotting process, and helping to improve the machining efficiency and product quality.

[0027] Preferably, it further includes step S5: for optimizing the target grinding wheel tool path; specifically, calculate the initial values of the first solution parameter and the second solution parameter so that the torus has interference with the core thickness surface and does not cross the axis of the first workpiece; First, change the second solution parameter once. If ≥0, obtain at its minimum value; if there exists , obtain when it is just ; Second, change the first solution parameter once. If exists, obtain when it is just ; where S.T. is the function value of ; Finally, until the values of the first solution parameter and the second solution parameter no longer change, end the operation and obtain the output result, which is the optimized target grinding wheel tool path

[0028] Beneficial effects: By gradually optimizing the solution parameters, starting from calculating the initial value of the first solution parameter, adjusting the second solution parameter and the first solution parameter in turn until the parameter values no longer change, and finally obtaining the optimized target grinding wheel tool path. This gradually optimized strategy not only avoids the sudden change of the output result, ensures the smooth transition of the grinding wheel pose, but also significantly reduces the calculation time of subsequent points, improving the calculation efficiency of the entire milling cutter spiral groove edge line. In addition, starting from the second point, using the calculation result of the previous point as the initial value further optimizes the calculation process, making the entire milling cutter slotting process more efficient and accurate, providing reliable technical support for actual production, especially suitable for large-scale production and processing of complex structure milling cutters.

[0029] Preferably, let the center coordinates of the circular circle in the torus space be , and let the coordinate system of the torus be , The X-axis of Pointing to If the Z-axis is the axial direction of the grinding wheel, then there is:

[0030] Indicates the rotation matrix that rotates around the Z-axis according to the right-hand rule ; Indicates the rotation matrix that rotates around the Y-axis according to the right-hand rule ; The torus coordinate system is obtained by rotating the coordinate system around its own Z-axis according to the right-hand rule , and then rotating around its own Y-axis according to the right-hand rule ; It is defined by the X-axis of and obtained.

[0031] Beneficial effects: By clarifying the center coordinates of the space circle of the torus and establishing the torus coordinate system, the rotation relationship of the torus coordinate system is further defined. Specifically, through the rotation matrices around the Z-axis and Y-axis, the transformation process of the torus coordinate system is described. This mathematical description method enables the pose of the torus to be controlled and calculated through precise geometric transformations.

[0032] Specifically, first, improve the calculation accuracy. Through the accurate description of the rotation matrix, the position and attitude of the torus in space can be determined more accurately, thereby improving the accuracy of the grinding wheel tool path calculation. Second, simplify the calculation process. Utilizing the mathematical properties of the rotation matrix, complex three-dimensional space transformation problems can be decomposed into simple matrix operations, simplifying the calculation process. Third, enhance the adaptability of the grinding wheel tool path calculation model. Through this coordinate system transformation, it can better adapt to milling cutters and grinding wheels of different shapes and sizes, making the calculation model more general and flexible.

[0033] Preferably, when the grinding wheel is tangent to the core thickness of the milling cutter, by traversing all points on the space circle of the torus, there is exactly one second solution parameter , such that the sphere with as the center and the secondary radius r of the torus as the radius is tangent to the core thickness surface of the milling cutter at , is the tangent point of the grinding wheel and the core thickness of the milling cutter at this time, then there must be:

[0034] is the normal corresponding to the point on the core thickness surface of the milling cutter, is the point obtained by moving the tangent point on the core thickness surface of the milling cutter along the normal by a distance of r, and it should be in line with Coincide; the torus obtained by simplifying the grinding wheel is tangent to the core thickness plane of the milling cutter at the tangent point , which is equivalent to a moving point on the space circle of the torus obtained by simplifying the grinding wheel and a point on the core thickness offset plane , the core thickness offset plane can be characterized as a new surface formed by offsetting each point on the core thickness plane by a distance r along the normal direction of the point to the outside of the milling cutter; when two solution parameters have a set of determined values such that coincides with , the unique value of the grinding wheel pose can be determined.

[0035] Beneficial effects: Further clarify the geometric constraint conditions when the grinding wheel is tangent to the core thickness of the milling cutter, that is, by traversing all points on the space circle of the torus, find a unique second solution parameter so that the grinding wheel is tangent to the core thickness plane of the milling cutter at a specific point. At the same time, through the constraint conditions of the normal vector, the accuracy of the tangent point is ensured.

[0036] Specifically, first, ensure the machining accuracy. Through precise geometric constraint conditions, ensure that the grinding wheel is precisely tangent to the core thickness of the milling cutter during machining, avoiding interference and overcutting phenomena, thereby improving the machining accuracy. Second, improve the calculation efficiency. By means of traversal and judgment, the tangent point and the corresponding grinding wheel pose that meet the conditions can be quickly found, avoiding complex global searches and improving the calculation efficiency. Third, enhance the reliability of the grinding wheel tool path calculation model. The clear geometric constraint conditions make the calculation of the grinding wheel tool path calculation model more reliable, can better adapt to complex machining scenarios, and reduce machining errors caused by inaccurate models.

[0037] Preferably, the milling cutter to be machined includes a ball-end milling cutter and a non-ball-end milling cutter.

[0038] Beneficial effects: It is clear that this solution can be applied to the grooving machining of both ball-end milling cutters and non-ball-end milling cutters at the same time, significantly improving the versatility and applicability of the method. There are significant differences in the geometric shapes and machining characteristics between ball-end milling cutters and non-ball-end milling cutters. Ball-end milling cutters are usually used for machining complex curved surfaces, and their cutting edge shape is spherical, while non-ball-end milling cutters are mostly used for machining planes or straight grooves, and their cutting edge shapes are straight lines or cylindrical. This solution can cover both types of milling cutters at the same time, indicating that the calculation method adopted in this solution has high flexibility and a wide range of applications, can meet the needs in different machining scenarios, provides a more comprehensive and efficient solution for milling cutter grooving machining, and further expands the application scope and market value of the technology.

[0039] Second solution: A calculation system for the grinding wheel tool path during milling cutter grooving based on the core thickness of the milling cutter, including a data analysis module. The data analysis module includes an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the electronic device realizes the calculation method for the grinding wheel tool path during milling cutter grooving based on the core thickness of the milling cutter described in the first solution.

[0040] Beneficial effects: The beneficial effects of this system are the same as those of the first solution. Description of the drawings

[0041] Figure 1 Schematic diagram of the calculation method for the grinding wheel tool path during milling cutter grooving based on the core thickness of the milling cutter in the first embodiment; Figure 2 Schematic diagram of the simplified toroid of the grinding wheel; Figure 3 Schematic diagram of the constraint where the grinding wheel is tangent to the tangent point on the helical groove edge line; Figure 4 Schematic diagram of the tangency relationship between a moving point on the space circle on the toroid and the core thickness of the ball-end milling cutter; Figure 5 Schematic diagram of the tangency relationship between a moving point on the space circle on the toroid and the core thickness of the non-ball-end milling cutter; Figure 6 Schematic diagram of the calculation and optimization process of the grinding wheel grinding trajectory in NX software. Among them, subfigure (a) is used to represent the first group of grinding wheel grinding trajectories, subfigure (b) is used to represent the second group of grinding wheel grinding trajectories, subfigure (c) is used to represent the third group of grinding wheel grinding trajectories, and subfigure (d) is used to represent the fourth group of grinding wheel grinding trajectories; Figure 7 Schematic diagram of the structure of the calculation system for the grinding wheel tool path during milling cutter grooving based on the core thickness of the milling cutter in at least one embodiment; Figure 8 Schematic diagram of the electronic device structure of the calculation system for the grinding wheel tool path during milling cutter grooving based on the core thickness of the milling cutter in at least one embodiment.

[0042] The reference numerals in the drawings of the specification include: Calculation system 100 for the grinding wheel tool path during milling cutter grooving based on the core thickness of the milling cutter, processor 101, input device 102, output device 103, memory 104, bus 105, computer program 1041. Detailed implementation manners

[0043] Hereinafter, embodiments of the technical solution of the present invention will be described in detail with reference to the drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, so they are only examples and cannot be used to limit the protection scope of the present invention.

[0044] It should be noted that, unless otherwise specified, the technical terms or scientific terms used in this application shall have the ordinary meanings understood by those skilled in the art to which the present invention pertains.

[0045] Embodiment 1 As Figure 1 shown, this embodiment provides a method for calculating the grinding wheel tool path during milling cutter grooving based on the core thickness of the milling cutter. Specifically, it includes: S1: For different types of grinding wheels, input three customizable parameters of the core thickness, cutting guide surface, and cutting angle of the milling cutter to be processed, and calculate the grinding wheel tool path during milling cutter grooving.

[0046] Specifically, the core thickness is defined by the milling cutter rotation axis and an arbitrary curve on the same plane, the cutting guide surface is defined by the milling cutter edge line and the normal direction, and the cutting angle is defined by the included angle between the grinding wheel rotation axis and the normal direction of the milling cutter edge line. The core thickness surface of the milling cutter refers to the thickness of the milling cutter center plane, that is, the plane where the circle with the smallest radius in the axial cross-section of the milling cutter is located. In this embodiment, there are no special requirements for the core thickness of the milling cutter, that is, it is generally applicable to the processing of various milling cutters with different core thicknesses. For the parameter design of its variable core thickness surface, that is, the variable core thickness of the milling cutter - the core thickness is unevenly distributed in the axial direction of the milling cutter. In this way, by analyzing the actual overall core thickness structure of the milling cutter, the grinding wheel tool path during milling cutter grooving can be more realistically restored.

[0047] Specifically, the separate surface obtained by separating the core thickness of the milling cutter alone is the core thickness surface, and the overall data of the core thickness surface can be used to characterize the overall data of the milling cutter core thickness, that is, the overall data of the milling cutter core thickness can be characterized by obtaining the parameter data of the core thickness surface. The axial cross-section of the core thickness surface is a circle, and the radial cross-section is an arbitrary continuous curve. Therefore, the milling cutter core thickness surface can be formed by a rotation of an arbitrary continuous curve around an axis. The milling cutter core thickness surface can be expressed as a series of discrete points and the normal directions between points in the grinding wheel tool path calculation model. The set of this series of discrete points and the normal directions between points is used as the parameters of the core thickness surface of the milling cutter to be processed. The milling cutter core thickness surface can be geometrically characterized as the surface formed by the curve rotating around the milling cutter rotation axis to form a geometric body.

[0048] The milling cutter spiral groove is one of the main structures of the milling cutter and is controlled by several parameters. In this calculation method, there are no special requirements for the spiral groove, that is, it is generally applicable to the processing of various types of spiral grooves. For the variable parameter design of the milling cutter spiral groove, that is, the spiral angle, rake angle, clearance angle, and cutter body parameters (radius, taper) are all variable. Further, by analyzing the overall structure of the milling cutter spiral groove, the grinding wheel tool path during milling cutter grooving can be more realistically restored.

[0049] Through analysis, it is known that during the milling cutter grooving process, this is a cutting process, and the extremely narrow surface is composed of the cutting edge line of the milling cutter and the area around the edge line. For each single discrete point on the cutting edge line of this milling cutter, it can be characterized as the tangent point during the grinding process of the grinding wheel when grooving the milling cutter. For such a single point and its normal direction, they can be characterized as the cutting plane during the grinding process of the grinding wheel when grooving the milling cutter, that is, the cutting guide surface. That is, during the milling cutter grooving process, the overall structure of the milling cutter spiral groove can be expressed as a series of discrete points on the cutting edge line of the milling cutter and the normal direction of the points through the parameters of the cutting guide surface in the grinding wheel tool path calculation model.

[0050] During the milling cutter grooving process, in order to further reduce the analysis of other parameters of the grinding wheel and make the result of the finally output grinding wheel tool path more accurate, through analysis, it is known that the position, material, rotational speed, and feed rate of the grinding wheel have little influence on the milling cutter grooving. Only the rounded part of the grinding wheel participates in grinding on the structure of the grinding wheel, and the rest does not contact the first workpiece. Therefore, during the milling cutter grooving process, on the structure of the grinding wheel, the influence of the part of the grinding wheel other than the rounded part on cutting can be ignored, and only the rounded part of the grinding wheel is included in the grinding wheel tool path calculation model during the calculation process. In this way, not only can the calculation be simplified and the calculation efficiency be improved, but also the grinding wheel tool path during the milling cutter grooving can be accurately calculated.

[0051] S2: During the milling cutter grooving process, only the rounded part of the grinding wheel participates in grinding. Simplify the grinding wheel model during the milling cutter grooving process into a torus, and the torus is used to represent the rounded part of the grinding wheel. Analyze the grinding wheel pose based on the pose of the torus during the milling cutter grooving process.

[0052] Due to the variety of grinding wheels and their complex shapes, it extremely affects the calculation. Grinding wheels include 1V1 grinding wheels, 1V1 bowl-shaped grinding wheels, 1A1 grinding wheels, and 14E1 grinding wheels. As Figure 2 shown, form simplified tori for different types of grinding wheels, and the simplified tori are only used to represent the pose of the rounded part of the grinding wheel. In this way, other parts that have no influence on the cutting process during the milling cutter grooving can be ignored, greatly simplifying the calculation amount, improving the calculation efficiency, and at the same time ensuring the accuracy of the calculation result. And at least one pose of the grinding wheel can be deduced through the pose of the torus, and then the target pose of the grinding wheel can be obtained through the interference judgment between the grinding wheel and the workpiece, which is the unique solution of the grinding wheel pose, truly restoring that the pose of the torus corresponds to only one grinding wheel pose. Thus, it is proved that the torus can represent the grinding wheel in the grinding wheel tool path calculation model. In this embodiment, the first workpiece includes numerically controlled tools such as milling cutters and forming cutters. When the grinding wheel processes the workpiece, only its rounded part participates in grinding, so the grinding wheel model is simplified into a rounded model - a torus. There are only two poses corresponding to the torus of the grinding wheel, but considering that the grinding wheel and the workpiece must not interfere (when the torus is tangent to the core thickness surface of the milling cutter, one of the situations will obviously cause interference), so there is only one.

[0053] Specifically, the grinding wheel is simplified to a toroid. That is, for any type of grinding wheel with rounded corners, the minor radius r of the toroid is equal to the radius of the rounded corner of the grinding wheel, and the grinding wheel with a rotational radius R can be simplified to a toroid formed by a sphere with a radius r revolving around a space circle with a radius where:

[0054] In the calculation model of the grinding wheel tool path, the toroid after the simplification of the grinding wheel can be expressed as follows: the center of a sphere with a radius r is used as a moving point and moves on a space circle with a radius which is the shape feature of the toroid.

[0055] For the rotational radius R and the radius r of the rounded corner of the grinding wheel, the toroid being tangent to the core thickness plane is equivalent to: the space circle with a radius

[0056] has one and only one tangent point with the core thickness offset plane (each point moves a distance r along its normal direction). This tangent point can be regarded as the pose of the rounded corner of the grinding wheel.

[0057] S3: Establish a calculation model of the grinding wheel tool path according to the shape parameters of the toroid, the core thickness of the milling cutter, the cutting guide surface, the cutting angle, the tangency condition between the toroid and the core thickness, and the tangency condition between the toroid and the cutting guide surface. Figure 3 , Figure 3 In this embodiment, the milling cutter includes a ball-end milling cutter and a non-ball-end milling cutter. The cutting guide surface is represented by discrete points on the cutting edge of the milling cutter and various surfaces formed by arbitrarily combining the normal directions of the points. Since the tangent point between the grinding wheel and the core thickness does not correspond to the tangent point between the grinding wheel and the spiral groove, in order to reduce the degrees of freedom of the grinding wheel and simplify the calculation model of the grinding wheel tool path, the discrete points on the cutting edge and the normal directions of the points are used as the constraints for the toroid after the simplification of the grinding wheel. The combination relationship of this constraint can be referred to the normal direction corresponding to point and the tangential direction corresponding to point ; establish a coordinate system to describe the positional relationship. The origin of the coordinate system is , and the coordinate system is . Among them, the X-axis is the cutting point of any point , and the Z-axis is the normal direction of the point , where:

[0058] The simplified torus of the grinding wheel is tangent to the spiral groove to be machined at , and can be regarded as a sphere with a radius of r and a center of the sphere being tangent to the spiral groove to be machined at and being on the space circle with the radius of the torus . Among them:

[0059] is used to restrict the degrees of freedom of the torus. During the milling cutter grooving process, the cutting angle at which the grinding wheel is tangent to the spiral groove of the milling cutter (the axial direction of the torus, that is, the included angle between the axial direction of the grinding wheel and ) also restricts the degrees of freedom of the torus; at this time, the torus only has the degrees of freedom restricted by an angle, and this is set as the first solution parameter , which is one of the unknowns in the grinding wheel tool path calculation model.

[0060] Let the coordinates of the center of the space circle of the torus be , and let the coordinate system of the torus be . The X-axis of points from , and the Z-axis is the axial direction of the grinding wheel. Then there are:

[0061] refers to the rotation matrix that rotates around the Z-axis by according to the right-hand rule, [[ID=4x]] refers to the rotation matrix that rotates around the Y-axis by according to the right-hand rule; that is, the coordinate system of the torus is obtained by rotating the coordinate system around its own Z-axis by (the first solution parameter) according to the right-hand rule, and then rotating around its own Y-axis by (the cutting angle, a known value); is obtained from the definition of the X-axis of and .

[0062] During the milling cutter grooving process, since the tangent point between the grinding wheel and the core thickness of the milling cutter does not correspond one-to-one with the tangent point on the cutting edge of the milling cutter, for any point on the cutting edge of the milling cutter, when calculating the tangent point between the grinding wheel and the core thickness of the milling cutter at this time, the overall data of the core thickness of the milling cutter, that is, the core thickness plane, needs to be considered.

[0063] Let a moving point on the torus be . has an angular degree of freedom, and this is set as . Then there are:

[0064] Rotating according to the right - hand rule around the Z - axis rotation matrix; when time, coincides with

[0065] Specifically, since the interference determination between entities is relatively complex, to simplify the relationship, it is transformed into the interference determination between a point and an entity. According to the specific properties of the milling cutter, the core - thickness plane of the overall concept of the core thickness of the milling cutter can be regarded as a solid of revolution. Then, in the plane where its axis of rotation lies, the interference determination between a point and an entity can be transformed into the determination of the position relationship between a point and a line. Among them, the determination of the ball - end milling cutter is as shown in Figure 4 shown, and the determination of the non - ball - end milling cutter is as shown in Figure 5 shown. The core - thickness plane is represented by a solid line, and the core - thickness offset plane is represented by a dashed line.

[0066] Specifically, when the grinding wheel is tangent to the core thickness of the milling cutter, all points on the spatial circle of the torus are traversed, and there is exactly one second solution parameter such that the sphere with as the center and radius r is tangent to the core - thickness plane at , is the tangent point of the grinding wheel and the core thickness of the milling cutter at this time. Then, there must be:

[0067] is the normal direction corresponding to the point on the core - thickness plane, is the point obtained by moving the tangent point on the core - thickness plane along the normal direction by a distance of r, and it should coincide with

[0068] Then, the torus obtained by simplifying the grinding wheel is tangent to the core - thickness plane at the tangent point , which is equivalent to - a moving point on the spatial circle of the torus obtained by simplifying the grinding wheel, a new point generated by moving the discrete points on the core - thickness plane along the normal direction of this point by a distance of r plus the original normal direction to form a new surface, that is, a point on the core - thickness offset plane. When a set of definite values of the two solution parameters and makes coincide with , the unique value of the grinding - wheel pose is determined at this time.

[0069] ​​S4: Analyze the grinding wheel tool path calculation model according to the conjugate gradient optimization method of the type, and obtain the dynamic grinding wheel tool path during milling cutter grooving. The dynamic grinding wheel tool path calculated through steps S1, S2, and S3 can restore the grinding wheel tool path in the real scenario to a great extent.

[0070] For a point on the cutting edge of the milling cutter with known input , the normal corresponding to the point and the tangential corresponding to the point ; construct the coordinate system of this point — the X-axis is the cutting direction of the point , and the Z-axis line is the normal of the point .

[0071] The simplified torus of the grinding wheel is tangent to the helical groove of the milling cutter at , which can be characterized as a sphere with a radius r and a center tangent to the helical groove at , that is is on the space circle with the radius of the torus.

[0072] For the known input cutting angle and the first solution parameter , then the origin of the coordinate system corresponding to the simplified torus of the grinding wheel and the coordinate system — the X-axis direction of points from to

[0073] The simplified torus of the grinding wheel can be regarded as a sphere with a radius r and a center moving along the space circle with the radius where the torus is located. The second solution parameter that restricts the position is (when , coincides with ).

[0074] The core thickness surface is composed of a number of first discrete points and the normals of the first discrete points. Move these first discrete points along the normal of this point by a distance r to form first moving points. The normal of the first discrete point before forming the first moving point and the first moving point form the core thickness offset surface of the core thickness surface.

[0075] The point is the projection point of on this core thickness offset surface, and its projection method changes according to the type of the core thickness surface. Among them, the types of the core thickness surface include sphere, cylinder, cone, and surface of revolution. The point and the point For the intersection points of the connection line and its extension line with the core thickness offset plane, there are:

[0076] When two solution parameters have a set of definite values such that the point coincides with the point there are:

[0077] At this time, the two solution parameters and are known values. The tangent point between the grinding wheel and the core thickness of the milling cutter is determined, the pose of the simplified torus of the grinding wheel is determined, the torus represents the position of the grinding wheel fillet, at least one solution of the grinding wheel position can be obtained, and other solutions are excluded through the interference judgment between the grinding wheel and the first workpiece, leaving the only solution. Finally, the pose of the torus determines the only pose of the grinding wheel.

[0078] For a known point on the milling cutter edge line and its normal tangential , the known core thickness of the milling cutter (the first discrete point and its corresponding normal), the known grinding wheel parameters (radius r, rotational radius R), the known machining parameters (tangential angle ); through the two solution parameters , continuously optimize to make it meet the conditions, then there are:

[0079] If and only if when the value is solved, the pose of the torus at this time, the corresponding unique pose of the grinding wheel and the tangent point between the grinding wheel and the core thickness of the milling cutter can be calculated.

[0080] In summary, through the two solution parameters , the tangent points between the simplified torus of the grinding wheel and the tangent points on the milling cutter spiral groove edge line and the core thickness plane abstracted from the overall core thickness of the milling cutter are obtained.

[0081] To avoid the values of the two solution parameters deviating from the correct region during the calculation process, a penalty function is set up:

[0082] At the same time, change the definition of so that it can be negative, and set it as :

[0083] Then the optimization equation is:

[0084] When the function value is far from 0, it indicates deviation from the target; when the function value is close to 0, it indicates approaching the target; when the function value is 0, it indicates that at this time the value meets the condition.

[0085] This optimization method is different from the gradient descent method and the genetic algorithm. It does not solve the grinding wheel tool path calculation model from a mathematical level, but from a geometric relationship. The method based on geometric relationship is usually more intuitive, easy to understand and implement. This method of solving the grinding wheel tool path calculation model directly uses the geometric properties of the objects associated with the grinding wheel tool path (the core thickness surface, the variable spiral groove, and the torus formed by simplifying the grinding wheel) for calculation, without the need for complex mathematical derivations or advanced optimization theory knowledge. At the same time, it can avoid getting stuck in complex numerical calculation processes, such as iterative solutions. For certain specific problems, the geometric algorithm may provide a direct and fast solution, reducing the calculation time, especially suitable for real-time applications or scenarios that require quick responses, especially the calculation of the grinding wheel tool path.

[0086] Moreover, when dealing with shape and path planning, the geometric method can provide high-precision control. For example, in the application of grooving a milling cutter with a grinding wheel, accurately planning the tool path according to the geometric shapes of the workpiece and the grinding wheel can ensure the machining accuracy and surface quality.

[0087] Subsequently, for objects with complex or irregular geometric shapes, the method based on geometric relationship has stronger adaptability than the existing mathematical optimization methods. This is because the geometric method can directly handle the spatial characteristics of the core thickness surface, the variable spiral groove, and the torus formed by simplifying the grinding wheel, without the need to convert them into a form suitable for mathematical optimization.

[0088] Finally, different from the gradient descent method or the genetic algorithm, the geometric-based method usually does not involve problems such as local minima or convergence difficulties that may occur during the optimization process, thus providing a more reliable solution method.

[0089] The first solution parameter changes the pose of the torus formed by simplifying the grinding wheel, and changes the pose of the sphere with radius r and the moving point as the center on the space circle of the torus formed by simplifying the grinding wheel.

[0090] As Figure 6 shown, Figure 6The object on the left is the core thickness surface, and the annular object on the right is the toroid. The black lines connecting the toroid and the core thickness surface are used to represent the milling cutter blade line (excluding the normal direction) in the cutting guide surface. The milling cutter blade line is tangent to the annular body and is used to represent the toroid of the grinding wheel. There are a total of 4 groups of different grinding wheel grinding trajectories in subfigures (a)-(d). Among them, the first solution parameters of subfigures (a)-(d) are 0°, 40°, 50°, and 52° in sequence, and the cutting angle is 10°. The calculation method of the grinding wheel tool path during milling cutter grooving based on the milling cutter core thickness further includes step S5: used to optimize the target grinding wheel tool path. Specifically, according to the definitions of the two solution parameters , —— What changes is the pose of the toroid after the grinding wheel is simplified, What changes is the pose of the sphere with a radius of r and a moving center on the space circle of the toroid after the grinding wheel is simplified at point . Through the geometric relationship between the toroid after the grinding wheel is simplified, the milling cutter spiral groove, and the core thickness surface, an optimization path of the conjugate gradient method is obtained to solve the grinding wheel tool path calculation model, and the optimization process can be simulated through a 3D model.

[0091] The optimization process is simulated through a 3D model. The following are the optimization steps: (1) Calculate the initial values of the first solution parameter and the second solution parameter so that the toroid and the core thickness surface have interference and do not cross the axis of the first workpiece.

[0092] (2) Move once —— if is always ≥ 0, obtain at its minimum value; if exists, obtain at the moment when it is just .

[0093] (3) Move once —— if exists (it must exist), obtain at the moment when it is just .

[0094] (4) Repeat (2) and (3) until the values of do not change, then end the operation and obtain the output result. This output result is the target grinding wheel tool path.

[0095] In this way, not only is the mutation of the output result avoided, the smooth transition of the grinding wheel pose is ensured, and the output result is made more accurate. Secondly, the calculation time of the second point and all subsequent points is reduced, and the calculation time of the entire milling cutter spiral groove blade line is greatly reduced.

[0096] Beneficial effects of this embodiment First, this embodiment details the specific methods for obtaining the core thickness surface, cutting guide surface, and the shape characteristics of the grinding wheel. Through these parameters, the tangency conditions between the grinding wheel and the milling cutter spiral groove and core thickness are comprehensively analyzed. At the same time, the process of simplifying the tangency model between the grinding wheel and the milling cutter step by step, in the order of body and surface - sphere and surface - point and offset surface, further simplifies the calculation, and then constructs an accurate and fast-calculating grinding wheel tool path calculation model. When establishing the coordinate system to describe the positional relationship of points and determining the tangency conditions between the torus and the spiral groove and core thickness, various geometric characteristics of the milling cutter and the grinding wheel are fully considered. Solving the model by combining the conjugate gradient optimization method of various types can highly restore the actual grinding wheel tool path during milling cutter slotting, providing precise theoretical guidance for milling cutter slotting processing and helping to improve the accuracy and quality of milling cutter slotting.

[0097] Second, the variable parameter design is adopted for the core thickness and spiral groove of the milling cutter, breaking through the limitations of the existing constant parameter end mill. When facing complex milling cutters with variable spiral grooves and variable core thickness designs, their parameters can be effectively obtained and analyzed and calculated. For milling cutters with unequal core thicknesses, parameters are obtained through the discretization process of the core thickness surface, truly restoring their structures; for spiral grooves with variable helix angles, rake angles, etc., parameters can also be accurately obtained for research. This enables the method to meet the special requirements for milling cutters under different materials and processing conditions, promotes the application of complex structure milling cutters in actual production, and improves the cutting performance of milling cutters under different working conditions.

[0098] Moreover, the grinding wheel is simplified to a torus that only represents the fillet pose, ignoring other parts that do not participate in grinding, greatly reducing the amount of calculation. During the analysis of the tangency conditions and the establishment of the model, the unknowns and constraint conditions are reasonably set, simplifying the calculation process. For example, by determining the degrees of freedom when the torus is tangent to the spiral groove, the number of variables is reduced. When optimizing the target grinding wheel tool path, the calculation result of the previous point is used as the initial value starting from the second point, significantly reducing the calculation time for subsequent points, greatly improving the calculation efficiency of the entire milling cutter spiral groove edge line, and improving the production efficiency.

[0099] Finally, during the process of optimizing the target grinding wheel tool path, by reasonably setting the initial value, gradually moving the variables, and obtaining the corresponding values according to the conditions until the variable values no longer change, the sudden change of the output result is avoided, ensuring the smooth transition of the grinding wheel pose. The penalty function is set up and the interference judgment function is adjusted to effectively avoid the interference between the grinding wheel and the core thickness of the milling cutter, ensuring that the calculation results meet the actual processing requirements. Through the 3D model simulation of the optimization process, the optimization path is intuitively displayed, further improving the accuracy and reliability of the calculation results, and providing reliable technical support for actual milling cutter slotting processing.

[0100] Experimental example 1 When using the calculation method of the grinding wheel tool path for milling cutter grooving based on the core thickness of the milling cutter described in Embodiment 1, calculate the initial position and calculation results of the torus pose during non-ball-end milling cutter grooving, the initial position and calculation results of the torus pose during non-ball-end milling cutter grooving.

[0101] The position of the torus after simplifying the grinding wheel represents the fillet position on the side where the grinding wheel participates in the grinding process of milling cutter grooving. Combining with the interference judgment with the workpiece, the pose of the torus can obtain the only correct pose of the grinding wheel, that is, the pose of the torus represents the pose of the grinding wheel.

[0102] Table 1 Results table of UG 3D model simulation data for the calculation experiment of the grinding wheel tool path based on flat-end milling cutter grooving

[0103] Table 2 Results table of the output of the C++ calculation program for the calculation experiment of the grinding wheel tool path based on flat-end milling cutter grooving

[0104] Specifically, as shown in Table 1 and Table 2, the origin is the center of the spatial circle after simplifying the grinding wheel model; the Z-axis is defined as the axial direction of the grinding wheel rotation axis, and the direction is on the same side as the normal direction of the rake face point; the X-axis is defined as the point that points from the center of the spatial circle to the rake face point and moves along its normal direction by the fillet radius.

[0105] Table 1 and Table 2 calculate the pose of the grinding wheel when calculating a point on the helical groove edge line of the milling cutter. When calculating the entire helical groove edge line of the milling cutter, several points need to be calculated (the set value is 200 or more, and the larger the number, the higher the accuracy of the discrete points). Since each point has two solutions, it is controlled by the initial value. In order to avoid the sudden change of the solutions of adjacent points, that is, the taken solutions are not on the same side, and at the same time, the calculation time of one point (20 - 30 ms) is too long, which will delay the calculation of the entire helical groove edge line of the milling cutter.

[0106] Therefore, starting from the second point, its initial value follows the calculation result of the previous point. After practical tests, on the one hand, it avoids the sudden change of the output result and ensures the smooth transition of the grinding wheel pose; on the other hand, it reduces the calculation time of the second point and all subsequent points (about 2 ms), greatly reducing the calculation time of the entire helical groove edge line of the milling cutter. The calculation of one thousand point data in the C++ program only takes about 1.8 s. It can be seen that using the method of Embodiment 1 can greatly improve the calculation efficiency.

[0107] From the calculation method of the grinding wheel tool path for milling cutter grooving based on the core thickness of the milling cutter described in Embodiment 1 through the C++ calculation program, when arranging from the first tool path coordinate point to the eleventh tool path coordinate point in sequence, the calculation results of C++ are in agreement with the UG 3D model simulation data (the accurate value is 0.01), that is, during the milling cutter grooving process, the grinding wheel is tangent to the helical groove of the milling cutter, the grinding wheel is tangent to the core thickness of the milling cutter, and the grinding wheel tool path based on flat-end milling cutter grooving is accurate.

[0108] Test Example 2 Different from Test Example 1, this test example is used to calculate the grinding wheel tool path when slotting the ball-end milling cutter. In this test, the C++ calculation program outputs the first calculation result, and then the corresponding verification is carried out through the data of the UG 3D model. The test data is as follows: Table 3 UG 3D Model Simulation Data Result Table for the Calculation Test of the Grinding Wheel Tool Path when Slotting the Ball-end Milling Cutter

[0109] Table 4 Output Result Table of the C++ Calculation Program for the Calculation Test of the Grinding Wheel Tool Path when Slotting the Ball-end Milling Cutter

[0110] Specifically, as shown in Table 3 and Table 4, the origin is the center of the spatial circle after simplifying the grinding wheel model; the Z-axis is defined as the axial direction of the grinding wheel rotation axis, and the direction is on the same side as the normal direction of the rake face point; the X-axis is defined as the point that points from the center of the spatial circle to the rake face point and moves along its normal direction by the fillet radius.

[0111] Table 3 and Table 4 calculate the grinding wheel pose when milling a point on the spiral groove edge of the milling cutter. When calculating the entire spiral groove edge of the milling cutter, several points need to be calculated (the set value is 200 or more, and the larger the number, the higher the accuracy of the discrete points). Since each point has two solutions controlled by the initial value, in order to avoid the sudden change of the solutions of adjacent points, that is, the solutions taken are not on the same side, and at the same time, the calculation time of one point (20 - 30 ms) is too long, which will delay the calculation of the entire spiral groove edge of the milling cutter.

[0112] Therefore, starting from the second point, its initial value uses the calculation result of the previous point. After practical tests, on the one hand, it avoids the sudden change of the output result and ensures the smooth transition of the grinding wheel pose; on the other hand, it reduces the calculation time of the second point and all subsequent points (about 2 ms), greatly reducing the calculation time of the entire spiral groove edge of the milling cutter. The calculation of one thousand point data in the C++ program only takes about 1.8 s.

[0113] From the calculation method of the grinding wheel tool path when slotting the milling cutter based on the core thickness of the milling cutter described in Example 1 through the C++ calculation program, when arranging from the first tool path coordinate point to the eleventh tool path coordinate point in sequence, the calculation result of C++ is consistent with the UG 3D model simulation data (the exact value is 0.01), that is, during the milling cutter slotting process, the grinding wheel is tangent to the spiral groove of the milling cutter, and the grinding wheel is tangent to the core thickness of the milling cutter, and the grinding wheel tool path based on the flat-bottom milling cutter slotting is accurate.

[0114] Example 2 Different from the foregoing embodiments, this embodiment provides a calculation system for the grinding wheel tool path when slotting the milling cutter based on the core thickness of the milling cutter, as Figure 7As shown in the figure, a calculation system for the grinding wheel tool path during milling cutter grooving based on the core thickness of the milling cutter includes a data analysis module. The data analysis module includes an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the electronic device implements the calculation method for the grinding wheel tool path during milling cutter grooving according to any one of the above embodiments.

[0115] Specifically, as Figure 8 shown in the figure, the electronic device may include: one or more processors 101, one or more input devices 102, one or more output devices 103, one or more memories 104, and a computer program stored in the memory 104 and executable on the processor. The above-mentioned processor 101, input device 102, output device 103, and memory 104 are interconnected through a bus 105. The memory 104 is used to store the computer program, and the computer program includes program instructions. The processor 101 is configured to call the program instructions to execute the method steps described in the above method embodiments.

[0116] It should be understood that in this embodiment, the so-called processor 101 may be a central processing unit (CPU), and this processor may also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or this processor may also be any conventional processor, etc.

[0117] The input device 102 may include a keyboard, etc., and the output device 103 may include a display (such as an LCD), a speaker, etc.

[0118] The memory 104 may include a read-only memory and a random access memory, and provide instructions and data to the processor 101. A part of the memory 104 may also include a non-volatile random access memory. For example, the memory 104 may also store information about the device type.

[0119] In specific implementation, the processor 101, input device 102, and output device 103 described in the embodiments of the present invention may execute the implementation manners described in the relevant embodiments of a calculation method and system for the grinding wheel tool path during milling cutter grooving based on the core thickness of the milling cutter provided by the embodiments of the present invention, which will not be elaborated herein.

[0120] It should be noted that for a more specific description of the working process of the electronic device and the calculation method of the grinding wheel tool path when performing milling cutter grooving based on the core thickness of the milling cutter, please refer to the method embodiment part described above and will not be elaborated here.

[0121] Embodiment III Different from the foregoing embodiments, in this embodiment, the memory should be understood in a broad sense. It can not only be a hardware component for temporarily storing data in a computer system, but also a physical medium capable of storing digital information and being read by a computer. These media can be permanent or temporary, including but not limited to hard disks and solid-state drives.

[0122] Specifically, the memory can be an internal storage unit of the electronic device described in any embodiment, such as the hard disk or memory of the system. The memory can also be an external storage device of the system, such as a plug-in hard disk equipped on the system, a Smart Media Card (SMC), a Secure Digital (SD) card, a Flash Card, etc. Further, the memory can also include both the internal storage unit of the system and the external storage device. The memory is used to store the computer program and other programs and data required by the system. The memory can also be used to temporarily store the data that has been output or will be output.

[0123] The memory includes various media that can store program codes, such as USB flash drives, mobile hard disks, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical discs.

Claims

1. A calculation method for the grinding wheel tool path during milling cutter grooving based on the core thickness of the milling cutter, characterized in that, Including: S1: For grinding wheels of different models, input three customizable parameters of the core thickness, cutting guide surface, and cutting angle of the milling cutter to be processed, and calculate the tool path of the grinding wheel during milling cutter slotting; among them, the core thickness is defined by the milling cutter rotation axis and an arbitrary curve in the same plane, the cutting guide surface is defined by the milling cutter edge line and the normal direction, and the cutting angle is defined by the included angle between the grinding wheel rotation axis and the normal direction of the milling cutter edge line; S2: During the milling cutter slotting process, only the rounded part of the grinding wheel participates in grinding. Simplify the grinding wheel model during the milling cutter slotting process into a torus, and the torus is used to represent the rounded part of the grinding wheel. Analyze the grinding wheel pose based on the pose of the torus during milling cutter slotting processing; among them, the major radius of the torus is rz = R - r, where R is the rotation radius of the grinding wheel, and the minor radius r of the torus is equal to the grinding wheel rounded radius; S3: Establish a grinding wheel tool path calculation model based on the shape parameters of the torus, the core thickness of the milling cutter, the cutting guide surface, the cutting angle, the tangency condition between the torus and the core thickness, and the tangency condition between the torus and the cutting guide surface; when the grinding wheel is tangent to the milling cutter during the milling cutter grooving process, for any point on the milling cutter edge , establish a coordinate system with as the origin, where the X-axis is the cutting point direction of point , the Z-axis is the normal direction of point , and ; when the torus is tangent to the cutting guide surface, the center of the sphere of the torus , the fillet radius of the grinding wheel is r, and is on the space circle with the radius of the torus; the included angle between the torus rotation axis and is fixed to determine the cutting angle parameter; the torus only has one degree of freedom restricted by the angle , is used as the first solution parameter of the grinding wheel tool path calculation model; S4: Analyze the grinding wheel tool path calculation model according to the conjugate gradient-like optimization method, and obtain the dynamic grinding wheel tool path during milling cutter slotting.

2. The calculation method of the grinding wheel tool path during milling cutter slotting based on the core thickness of the milling cutter according to claim 1, characterized in that The separate surface obtained by separating the core thickness of the milling cutter alone is the core thickness surface, and the core thickness surface is used to represent the parameter data of the core thickness of the milling cutter to be processed; specifically, the milling cutter rotation axis and an arbitrary curve in the same plane as the rotation axis, and a core thickness surface of the milling cutter is formed by interpolating a number of discrete points on the curve; the core thickness surface of the milling cutter can be geometrically characterized as the surface of the geometric body formed by the curve rotating around the milling cutter rotation axis.

3. The calculation method of the grinding wheel tool path during milling cutter grooving based on the core thickness of the milling cutter according to claim 2, characterized in that, The types of the core thickness surface include spheres, cylinders, cones, and solids of revolution.

4. The calculation method of the grinding wheel tool path during milling cutter grooving based on the core thickness of the milling cutter according to claim 1, characterized in that, Obtain the parameters of the cutting guide surface, specifically, obtain the coordinates of a series of discrete points on the milling cutter edge line and the normal vectors at each point. During the milling cutter slotting process, for a single discrete point, the surface formed by the milling cutter edge line and the surrounding area of the edge line can be characterized as the tangent point during grinding wheel cutting processing, and the plane formed by a single discrete point and the normal direction of the point can be characterized as the tangent plane during grinding wheel cutting processing.

5. The calculation method of the grinding wheel tool path during milling cutter grooving based on the core thickness of the milling cutter according to claim 1, characterized in that When analyzing the grinding wheel tool path calculation model according to the conjugate gradient optimization method of different types, a penalty function is established , when simultaneously 0, the toroid is tangent to the core thickness plane of the milling cutter; conversely, the toroid interferes with or moves away from the core thickness plane; , where is the second solution parameter. When is a positive number, does not interfere with the core thickness plane; When is negative, it interferes with the core thickness plane, where P t is the center of the torus.

6. The calculation method of the grinding wheel tool path during milling cutter grooving based on the core thickness of the milling cutter according to claim 5, characterized in that, It further includes step S5: for optimizing the tool path of the target grinding wheel; specifically, calculating the first solution parameter and the second solution parameter initial values, such that the torus interferes with the core thickness surface and does not cross the axis of the first workpiece; First, change the second solution parameter once , if ≥0, obtain the second solution parameter when its minimum value is obtained ; if there exists , obtain the second solution parameter when it is exactly ;​ Secondly, change the first solution parameter once , if exists, obtain the first solution parameter when it is exactly ; where S.T. is the function value of ; ​ Finally, until the first solution parameter and the second solution parameter no longer change in value, the operation is terminated to obtain the output result, which is the optimized target grinding wheel tool path.

7. The calculation method of the grinding wheel tool path during milling cutter slotting based on the core thickness of the milling cutter according to claim 5, characterized in that Set the center coordinates of the circular space of the torus , set the coordinate system of the torus , The X-axis of points to . The Z-axis is the axial direction of the grinding wheel. Then we have: The rotation matrix for rotation about the Z-axis according to the right-hand rule , The rotation matrix for rotation about the Y-axis according to the right-hand rule ; Torus coordinate system is obtained by rotating the coordinate system by the right-hand rule about its own Z-axis , and then rotating by the right-hand rule about its own Y-axis ; it is defined by the X-axis of and obtained.

8. The calculation method of the grinding wheel tool path during the grooving of the milling cutter based on the core thickness of the milling cutter according to claim 5, characterized in that, When the grinding wheel is tangent to the core thickness of the milling cutter, traversing all points on the spatial circle of the torus, there is exactly one second solution parameter , such that the sphere with as the center and the secondary radius r of the torus as the radius is tangent to the core thickness surface of the milling cutter at , is the tangent point of the grinding wheel and the core thickness of the milling cutter at this time, then there must be: For the point on the core thickness surface of the milling cutter The corresponding normal direction For the tangent point on the core thickness surface of the milling cutter Along the normal direction The point after moving a distance of r, and it should coincide with Coincide; The torus after simplifying the grinding wheel is tangent to the core thickness plane of the milling cutter at the tangent point , which is equivalent to a moving point on the space circle of the torus after simplifying the grinding wheel , and a point on the core thickness offset plane , and the core thickness offset plane can be characterized as a new surface formed by offsetting each point on the core thickness plane by a distance r along the normal direction of this point towards the outside of the milling cutter; When two solution parameters have a set of definite values such that coincides with the unique value of the grinding wheel pose can be determined.

9. The calculation method of the grinding wheel tool path during the grooving of the milling cutter based on the core thickness of the milling cutter according to claim 1, wherein, The milling cutter to be processed includes ball-end milling cutters and non-ball-end milling cutters.

10. A calculation system for the grinding wheel tool path during milling cutter grooving based on the core thickness of the milling cutter, characterized in that, Including a data analysis module, the data analysis module includes an electronic device, the electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the electronic device realizes the calculation method of the grinding wheel tool path during milling cutter slotting based on any one of claims 1-9.

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