Calculation method and system for grinding wheel tool path when milling cutter slots based on milling cutter core thickness

Abstract

The present invention relates to the field of milling cutter slotting technology, specifically disclosing a method and system for calculating a grinding wheel tool path during milling cutter slotting based on the milling cutter core thickness. The method comprises: S1: for different types of grinding wheels, three customizable parameters, namely the core thickness, cutting guide surface, and cutting angle of the milling cutter to be processed, are input to calculate the grinding wheel tool path during milling cutter slotting; S2: during the milling cutter slotting process, only the rounded corner portion of the grinding wheel is involved in grinding, and the grinding wheel model during the milling cutter slotting process is simplified to a torus; S3: a grinding wheel tool path calculation model is established based on the shape parameters of the torus, the milling cutter core thickness, 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; S4: the grinding wheel tool path calculation model is analyzed according to a quasi-conjugate gradient optimization method, and a dynamic grinding wheel tool path during milling cutter slotting is obtained. The present invention can perform computational simulation to restore the dynamic grinding wheel tool path during milling cutter slotting under conditions close to real processing.

Description

Technical Field

[0001] The present invention relates to the technical field of milling cutter slotting, and in particular to a method and system for calculating a grinding wheel tool path when a milling cutter slots based on the milling cutter core thickness. Background Art

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

[0003] With the increasing complexity of processed materials, the refinement of structural designs, and the improvement of product performance requirements, the requirements for cutting tool geometry are becoming increasingly stringent. However, the complexity of the grinding process brought about by this special geometry greatly limits the practical application of such tools.

[0004] Current research and practice are mostly focused on the spiral groove grinding of constant parameter end mills, that is, the grinding wheel tool path is obtained when the milling cutter is grooving while the helix angle, tool radius and core thickness remain constant to groove the milling cutter to be processed. This not only results in a single type of milling cutter after grooving, but also when the milling cutter is used for milling, it is generally recognized in the art that its overall vibration resistance, anti-variability and milling stability are poor.

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

[0006] Among the above-mentioned existing technologies, these technical methods are either based on the constant parameters of their fixed geometric structure to perform milling cutter slotting. Although the calculation is simple, the milling cutter after slotting is prone to large vibrations during processing under high-speed cutting or heavy load conditions, which not only affects the processing accuracy but also shortens the service life of the tool. Other existing technologies, although variable parameter spiral grooves are proposed to address the shortcomings of the aforementioned constant parameter end mills, isolate the grinding wheel and the milling cutter spiral groove parameters from each other, resulting in a relatively vague reproduced grinding wheel tool path and requiring separate analysis of the geometric structure of each grinding wheel. The complex geometric structure of the grinding wheel not only increases the amount of calculation, but also easily leads to rough calculation of the grinding wheel posture. Summary of the Invention

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

[0008] In order to achieve the above object, the present invention adopts the following technical solutions:

[0009] The first scheme is a method for calculating the grinding wheel tool path when the milling cutter is slotting based on the milling cutter core thickness, including: S1: for different types of grinding wheels, three customizable parameters of the milling cutter core thickness, cutting guide surface, and cutting angle are input to calculate the grinding wheel tool path when the milling cutter is slotting; wherein, 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 normal, and the cutting angle is defined by the angle between the grinding wheel rotation axis and the milling cutter edge line normal; S2: during the milling cutter slotting process, only the rounded corner part of the grinding wheel is involved in grinding, and the grinding wheel model during the milling cutter slotting process is simplified to a torus, which is used to represent the rounded corner part of the grinding wheel. The grinding wheel posture is analyzed according to the posture of the torus during the milling cutter slotting process; wherein the main radius of the torus is r z =Rr, where the turning radius R of the grinding wheel and the secondary radius r of the torus are equal to the fillet radius of the grinding wheel; S3: A grinding wheel tool path calculation model is established based on the shape parameters of the torus, the thickness of the milling cutter core, 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; where, when the grinding wheel and the milling cutter are tangent during the milling cutter slotting process, for any point on the milling cutter edge line , established with The coordinate system with the origin , where the X axis is the point Cutting point Direction, Z axis is the point Normal direction, and Wherein, when the annular body is tangent to the cutting guide surface, the center of the annular body , the radius of the grinding wheel is r, and The radius of the torus On the space circle; the rotation axis of the torus The included angle is fixed to determine the cutting angle parameters; the torus only has one angle Restricted degrees of freedom, 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 optimization method, and obtain the dynamic grinding wheel tool path when the milling cutter is grooving.

[0010] Beneficial Effects: Compared to existing technologies, this solution differs in that, in addition to the two customizable parameters of cutting guide surface and cutting angle, this solution also incorporates the customizable parameter of core thickness. The addition of core thickness parameters makes the calculation of the grinding wheel tool path when the milling cutter is slotting more accurate, but it also increases the amount of calculation required. To reduce this amount of calculation, this solution can simplify the geometric structure of different types of grinding wheels at once. The filleted corners involved in grinding of different types of grinding wheels are simplified into torus shapes. The grinding wheel position is analyzed based on the position of the torus shape, thus reducing the amount of calculation required. At the same time, the torus body equivalent to the grinding wheel grinding is respectively connected with the tangent conditions of the core thickness and the cutting guide surface to establish a grinding wheel tool path calculation model, that is, the torus body is respectively combined with the core thickness and the cutting guide surface of the milling cutter, which is equivalent to considering both the grinding wheel and the milling cutter to be processed, which are two important participating objects in the milling cutter grooving process. After the grinding wheel posture is deduced, instead of connecting the entire grinding wheel posture and the milling cutter, the simplified torus body of the grinding wheel and the milling cutter are connected. This can further reduce the amount of calculation while enhancing the accuracy of the grinding wheel tool path. By using three customizable parameters and simplifying any type of grinding wheel structure, the torus body and the milling cutter are combined, which can quickly calculate and simulate and restore the grinding wheel tool path when the real milling cutter is grooving. Finally, the integral end mill designed with this variable spiral groove and variable core thickness surface (equivalent to three custom parameters) is recognized in the field for its excellent vibration resistance, anti-variability, better stability and longer service life. It can be widely used in precision manufacturing industries such as aerospace, automobile and mold manufacturing, and has extremely high product value.

[0011] Specifically, first of all, the accuracy, authenticity and reliability of the grinding wheel tool path calculation are improved. First, the model is simplified and the calculation is precise. By simplifying the grinding wheel model into a torus and only considering the fillet part of the grinding wheel involved 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 processing situation. The three customizable parameters of the core thickness, cutting guide surface and cutting angle of the milling cutter to be processed are input, and the various geometric characteristics of the milling cutter are comprehensively considered, so that the calculation results are closer to the actual processing situation. Especially for milling cutters with complex structures, this method can more realistically restore the interaction between the grinding wheel and the milling cutter.

[0012] Secondly, it is universally adaptable to the processing needs of a variety of complex milling cutter structures. The core thickness surface and 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. The finished milling cutter has excellent overall vibration resistance, anti-variability, and milling stability, making it suitable for long-term milling in the precision manufacturing industry and ensuring the consistent quality of products milled with the milling cutter within the same batch.

[0013] Furthermore, the computational efficiency is improved. First, the amount of calculation is reduced by clarifying that the part of the grinding wheel involved in the milling cutter slotting process is the fillet part, and simplifying the fillet part into a torus. This reduces the number of variables related to the complex geometric structure of the grinding wheel in the calculation process, thereby simplifying the calculation process.

[0014] At the same time, the conjugate gradient optimization method is used to effectively avoid the interference between the grinding wheel and the milling cutter core thickness, making the grinding wheel tool path closer to the actual processing path, improving the accuracy and reliability of the grinding wheel tool path calculation, and thus improving the processing accuracy and stability.

[0015] Next, we will promote the practical application of milling cutters for complex structures. By accurately calculating grinding wheel toolpaths, we can effectively improve the machining accuracy and quality of milling cutters for complex structures, promoting their practical application in industries such as aerospace, automotive, and mold manufacturing. Furthermore, by optimizing grinding wheel toolpaths, we can enhance the cutting performance of milling cutters, such as chip removal efficiency, rigidity, and sharpness. This will meet the specific requirements of milling cutters for different materials and processing conditions, and improve the cutting performance of milling cutters under different working conditions.

[0016] Subsequently, in step S2, the dimensional characteristics of the simplified grinding wheel model are further clarified by clarifying the major radius rz of the torus and the grinding wheel fillet radius, which is equivalent to the minor radius r of the torus. This simplified method can quickly determine the geometric characteristics of the grinding wheel torus, providing an accurate dimensional basis for subsequent grinding wheel posture analysis, thereby improving the accuracy and reliability of grinding wheel tool path calculations and ensuring precise grinding coordination between the grinding wheel and the milling cutter.

[0017] Next, in step S3, a coordinate system is established with any point on the milling cutter edge line as the origin. , and clearly defines the X-axis as the cutting point direction and the Z-axis as the normal direction, providing a unified and precise reference coordinate system for grinding wheel toolpath calculations. The establishment of this coordinate system allows for a clear description and analysis of the geometric relationship between the grinding wheel and milling cutter, facilitating accurate determination of the grinding wheel's position and motion trajectory in subsequent calculations. This coordinate system definition also simplifies the calculation process, improves efficiency, and ensures the accuracy and reliability of grinding wheel toolpath calculations, which is particularly important in milling cutter slotting operations involving complex geometries.

[0018] In addition, in step S4, the geometric constraint condition when the torus is tangent to the cutting guide surface is clarified, that is, the center of the torus is Position and its tangent relationship with the cutting guide surface. By limiting the center of the torus By maintaining a fixed angle between the rotation axis and the cutting angle parameter on the spatial circle, the degrees of freedom in the grinding wheel toolpath calculation model are effectively controlled, leaving only one degree of freedom limited by the angle. This constraint not only simplifies the calculation model and reduces computational complexity, but also ensures precise tangency between the grinding wheel and the milling cutter, avoiding interference, thereby improving machining accuracy and stability. This has important practical application value for slotting complex spiral groove milling cutters.

[0019] Finally, the actual machining path can be simulated. By computing and simulating a dynamic grinding wheel toolpath that approximates the actual machining process, this method helps engineers better understand the geometric relationships during machining, thereby optimizing the machining process and improving production efficiency and product quality. Furthermore, it reduces testing costs. Through precise calculations and simulations, the number and cost of actual machining trials are reduced, improving production efficiency and lowering costs.

[0020] Preferably, the separate surface obtained by 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 processed; specifically, the milling cutter rotary axis and an arbitrary curve coplanar with the rotary axis, and the core thickness surface of the milling cutter formed by interpolation of several discrete points on the curve; the core thickness surface of the milling cutter can be geometrically characterized as a surface of a geometric body formed around the milling cutter rotary axis according to the curve.

[0021] Beneficial Effects: By defining the generation method of the milling cutter core thickness surface, namely, the milling cutter's rotary axis and an arbitrary curve coplanar with the rotary axis, and the interpolation of a number of discrete points on the curve, the complex geometry of the milling cutter core thickness can be accurately characterized. This parametric description method allows the geometric characteristics of the milling cutter core thickness to be accurately captured and quantified, providing rich input information for the grinding wheel toolpath calculation model, thereby more realistically reproducing the interaction between the grinding wheel and the core thickness during milling cutter slotting. This improves the adaptability and accuracy of the grinding wheel toolpath calculation and is suitable for milling cutters with a variety of complex core thickness designs.

[0022] Preferably, the types of core thick surfaces include spheres, cylinders, cones, and solids of revolution.

[0023] Beneficial Effects: By encompassing a variety of common geometric shapes, the method of the present invention is widely applicable to milling cutters of different types and structures. This diverse applicability ensures that the calculation model can accurately handle the core thickness of milling cutters of various complex shapes, thereby improving the versatility and flexibility of grinding wheel tool path calculations. Whether it is a simple spherical or cylindrical milling cutter or a complex conical or revolved structure, this method can effectively calculate the corresponding grinding wheel tool path to meet the needs of different processing scenarios, further enhancing the practicality and versatility of this solution in practical applications.

[0024] Preferably, the parameters of the cutting guide surface are obtained, specifically the coordinates of a series of discrete points on the milling cutter edge line and the normal vector at each point. During the milling cutter grooving process, the curved surface composed of the milling cutter edge line and the area around the edge line can be characterized as the tangent point during the grinding wheel cutting process for a single discrete point, and the plane formed by the single discrete point and the normal of the point can be characterized as the tangent plane during the grinding wheel cutting process.

[0025] Beneficial Effects: By obtaining the coordinates and normal vectors of a series of discrete points on the milling cutter edge line, the parametric description of the cutting guide surface is closely integrated with the actual cutting process. This method can accurately characterize the geometric characteristics of the milling cutter edge line and its surrounding area, allowing each tangent point and its tangent plane to be accurately determined during grinding wheel cutting. This not only improves the accuracy of grinding wheel tool path calculations, but also optimizes the grinding wheel cutting path based on the geometric relationships in the actual cutting process, thereby improving processing efficiency and surface quality while reducing tool wear.

[0026] Preferably, when analyzing the grinding wheel tool path calculation model according to the conjugate gradient optimization method, a penalty function is set up , when at the same time When 0, the torus is tangent to the core thickness surface of the milling cutter; otherwise, the torus interferes with or moves away from the core thickness surface; ,in is the second solution parameter, when When is a positive number, No interference with the core thickness surface; when When it is a negative number, Interference with the core thickness surface, where Pt is the center of the torus.

[0027] Beneficial Effects: By introducing a penalty function mechanism, which sets the condition that the torus and the milling cutter core thickness surface are tangent when both solution parameters are zero, and adjusting the penalty function value based on the positive and negative values ​​of the solution parameters, an effective constraint is provided for optimizing the grinding wheel tool path calculation model. This method can effectively avoid interference between the grinding wheel and the milling cutter core thickness, ensuring the feasibility of the calculation results. At the same time, by optimizing the solution parameters, the grinding wheel tool path is made closer to the actual processing path, improving the accuracy and reliability of the grinding wheel tool path calculation, providing more accurate theoretical guidance for milling cutter slotting processing, and helping to improve processing efficiency and product quality.

[0028] Preferably, the step S5 is further included: for optimizing the target grinding wheel tool path; specifically, calculating the first solution parameter and the second solution parameter Initial value, make the ring body interfere with the core thickness surface and not cross the axis of the first workpiece; first, change the second solution parameter once ,like ≥0, when the minimum value is obtained If it exists , get its just Time ; Secondly, change the first solution parameter once ,like Existence, get its just Time ; Among them, ST is Function value; Finally, until the first solution parameter With the second solver parameter When the values ​​of do not change, the operation ends and the output result is obtained, which is the optimized target grinding wheel tool path.

[0029] Beneficial effects: By gradually optimizing the solution parameters, starting from calculating the initial value of the first solution parameter, the second solution parameter and the first solution parameter are adjusted in sequence until the parameter value no longer changes, and finally the optimized target grinding wheel tool path is obtained. This step-by-step optimization strategy not only avoids sudden changes in the output results and ensures a smooth transition of the grinding wheel posture, but also significantly reduces the calculation time of subsequent points and improves the calculation efficiency of the entire milling cutter spiral groove edge line. In addition, from the second point onwards, the calculation result of the previous point is used as the initial value, which further optimizes the calculation process, making the entire milling cutter grooving process more efficient and accurate, providing reliable technical support for actual production, and is especially suitable for large-scale production and processing of milling cutters with complex structures.

[0030] Preferably, the coordinates of the center of the torus space circle are , suppose the torus coordinate system , The X-axis is composed of point to , Z axis is the grinding wheel axis, then:

[0031]

[0032] Refers to rotation around the Z axis according to the right-hand rule The rotation matrix of Refers to rotation around the Y axis according to the right-hand rule The rotation matrix of the torus coordinate system is The coordinate system rotates around its own Z axis according to the right-hand rule , then rotate around its own Y axis according to the right-hand rule Transformed; Depend on The X-axis definition and get.

[0033] Beneficial Effects: By defining the coordinates of the torus's spatial center and establishing a torus coordinate system, the rotational relationships within the torus coordinate system are further defined. Specifically, the transformation process of the torus coordinate system is described using rotation matrices around the Z and Y axes. This mathematical description enables the torus's position and posture to be controlled and calculated through precise geometric transformations.

[0034] Specifically, first, it improves calculation accuracy. The precise description of the rotation matrix allows for more accurate determination of the torus's position and orientation in space, thereby improving the accuracy of grinding wheel toolpath calculations. Second, it simplifies the calculation process. By leveraging the mathematical properties of the rotation matrix, complex three-dimensional spatial transformation problems can be decomposed into simple matrix operations, simplifying the calculation process. Third, it enhances the adaptability of the grinding wheel toolpath calculation model. This coordinate system transformation allows for better adaptation to milling cutters and grinding wheels of varying shapes and sizes, making the calculation model more versatile and flexible.

[0035] Preferably, when the grinding wheel is tangent to the milling cutter core thickness, all points on the space circle of the torus are traversed, and there is only one second solution parameter , so that The sphere with the secondary radius r of the torus as the center is tangent to the thick surface of the milling cutter core at , is the point of intersection between the grinding wheel and the milling cutter core thickness at this time, then at this time there must be:

[0036]

[0037] Point on the thick surface of the milling cutter core The corresponding normal direction, The cutting point on the thick surface of the milling cutter core Along the normal The point after moving distance r should be Overlap; make the simplified annular body of the grinding wheel tangent to the thick surface of the milling cutter core at the tangent point , which is equivalent to a moving point on the space circle of the simplified torus of the grinding wheel And a point on the core thickness offset surface The core thickness offset surface can be characterized as a new surface formed by offsetting each point on the core thickness surface by a distance r toward the outside of the milling cutter along the normal direction of the point. There is a set of fixed values ​​such that and When they coincide, a unique value of the grinding wheel posture can be determined.

[0038] Beneficial Effects: The geometric constraints for when the grinding wheel and the milling cutter core are tangent are further clarified. This method, by traversing all points on the torus, finds a unique second solution parameter that makes the grinding wheel and the milling cutter core surface tangent at a specific point. Furthermore, the accuracy of the tangent point is ensured by the normal vector constraint.

[0039] Specifically, first, it ensures machining accuracy. Through precise geometric constraints, the grinding wheel and the milling cutter core thickness can be accurately tangent during the machining process, avoiding interference and overcutting, thereby improving machining accuracy. Second, it improves computational efficiency. Through traversal and judgment, it can quickly find the tangent point and the corresponding grinding wheel position that meet the conditions, avoiding complex global searches and improving computational efficiency. Third, it enhances the reliability of the grinding wheel tool path calculation model. Clear geometric constraints make the grinding wheel tool path calculation model more reliable, better able to adapt to complex machining scenarios, and reduce machining errors caused by inaccurate models.

[0040] Preferably, the milling cutter to be processed includes a ball-end milling cutter and a non-ball-end milling cutter.

[0041] Beneficial effects: It is clarified that this solution can be applied to the slotting processing of two different types of milling cutters, ball-end milling cutters and non-ball-end milling cutters, which significantly improves the versatility and applicability of the method. There are large differences in geometric shapes and processing characteristics between ball-end milling cutters and non-ball-end milling cutters. Ball-end milling cutters are usually used to process complex curved surfaces, and their cutting edges are spherical, while non-ball-end milling cutters are mostly used to process planes or straight grooves, and their cutting edges are straight or cylindrical. This solution can cover both types of milling cutters at the same time, which shows that the calculation method adopted in this solution has a high degree of flexibility and a wide range of applications. It can meet the needs of different processing scenarios, provide a more comprehensive and efficient solution for milling cutter slotting processing, and further expand the application scope and market value of the technology.

[0042] The second solution is a system for calculating the grinding wheel tool path when a milling cutter is grooving based on the milling cutter core thickness, 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 implements the method for calculating the grinding wheel tool path when a milling cutter is grooving based on the milling cutter core thickness as described in the first solution.

[0043] Beneficial effects: The beneficial effects of this system are the same as those of the first solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 Schematic diagram of a method for calculating a grinding wheel tool path when a milling cutter is grooving based on the milling cutter core thickness according to the first embodiment;

[0045] Figure 2 It is a simplified diagram of the torus of the grinding wheel;

[0046] Figure 3 It is a schematic diagram of the constraint that the grinding wheel is tangent to the tangent point on the spiral groove edge line;

[0047] Figure 4 It is a schematic diagram of the tangent relationship between a moving point in the space of the torus and the core thickness of the ball-end milling cutter;

[0048] Figure 5 It is a schematic diagram of the tangent relationship between a moving point in space on the torus and the core thickness of the non-spherical end milling cutter;

[0049] Figure 6 Schematic diagram of the grinding wheel grinding trajectory calculation and optimization process in NX software, where sub-image (a) is used to represent the first group of grinding wheel grinding trajectories, sub-image (b) is used to represent the second group of grinding wheel grinding trajectories, sub-image (c) is used to represent the third group of grinding wheel grinding trajectories, and sub-image (d) is used to represent the fourth group of grinding wheel grinding trajectories;

[0050] Figure 7 A schematic diagram of a system for calculating a grinding wheel tool path when a milling cutter is grooving based on the milling cutter core thickness according to at least one embodiment;

[0051] Figure 8 A schematic diagram of the electronic device structure of a system for calculating a grinding wheel tool path when a milling cutter is grooving based on the milling cutter core thickness according to at least one embodiment.

[0052] The reference numerals in the drawings of the specification include:

[0053] A computing system 100 , a processor 101 , an input device 102 , an output device 103 , a memory 104 , a bus 105 , and a computer program 1041 for a grinding wheel tool path when a milling cutter grooves based on a milling cutter core thickness. DETAILED DESCRIPTION

[0054] The following embodiments of the technical solution of the present invention will be described in detail with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention and are therefore only examples and are not intended to limit the scope of protection of the present invention.

[0055] It should be noted that, unless otherwise specified, the technical or scientific terms used in this application should have the common meanings understood by those skilled in the art to which the present invention belongs.

[0056] Example 1

[0057] like Figure 1 As shown, this embodiment provides a method for calculating the grinding wheel tool path when a milling cutter is slotting based on the milling cutter core thickness, specifically including:

[0058] S1: For different types of grinding wheels, input the three customizable parameters of the milling cutter core thickness, cutting guide surface, and cutting angle to calculate the grinding wheel tool path when the milling cutter is grooving.

[0059] Specifically, the core thickness is defined by the milling cutter rotation axis and an arbitrary coplanar curve, the cutting guide surface is defined by the milling cutter edge line and the normal, and the cutting angle is defined by the angle between the grinding wheel rotation axis and the normal of the milling cutter edge line. The core thickness surface of the milling cutter refers to the thickness of the center surface of the milling cutter, that is, the plane where the circle with the smallest radius of 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 milling cutters with various different core thicknesses. 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 taking the real overall core thickness structure of the milling cutter as the analysis, the grinding wheel tool path when the milling cutter is grooving can be more realistically restored.

[0060] Specifically, the separate surface obtained by peeling off the core thickness of the milling cutter is the core thickness surface. The overall data of the core thickness surface can be used to characterize the overall data of the milling cutter core thickness, that is, by obtaining the parameter data of the core thickness surface, the overall data of the milling cutter core thickness can be characterized. The axial cross-section of the core thickness surface is a circle, and the radial cross-section is an arbitrary continuous curve. Therefore, the core thickness surface of the milling cutter can be composed of an arbitrary continuous curve rotated around an axis. The core thickness surface of the milling cutter can be expressed as a series of discrete points and point normals in the grinding wheel tool path calculation model. The set of this series of discrete points and point normals serves as the parameters of the core thickness surface of the milling cutter to be processed. The core thickness surface of the milling cutter can be geometrically characterized as a surface of a geometric body formed according to the curve around the milling cutter rotation axis.

[0061] The spiral groove of a milling cutter is a key component of the milling cutter and is controlled by several parameters. This calculation method does not require specific spiral grooves, making it universally applicable to machining a wide variety of spiral grooves. The milling cutter's spiral groove is designed with variable parameters, including the helix angle, rake angle, relief angle, and cutter body parameters (radius and taper). Furthermore, analyzing the overall structure of the milling cutter's spiral groove allows for a more realistic simulation of the grinding wheel's tool path during groove creation.

[0062] Analysis revealed that during the milling process, the spiral groove forms a very narrow curved surface formed by the milling cutter's edge line and the surrounding area. Each discrete point on this milling cutter's edge line can be characterized as a tangent point during the milling process, and each point and its normal can be characterized as a tangent plane, or cutting guide surface, during the milling process. This means that during the milling process, the overall structure of the milling cutter's spiral groove can be expressed in the grinding wheel toolpath calculation model as a series of discrete points and their normals on the milling cutter's edge line, using the parameters of the cutting guide surface.

[0063] To further reduce the analysis of other grinding wheel parameters during the milling cutter slotting process and to ensure a more accurate final grinding wheel toolpath, analysis revealed that the grinding wheel's position, material, rotational speed, and feed rate have minimal impact on slotting. Due to the grinding wheel's structure, only the rounded corners of the grinding wheel participate in the grinding process, while the remaining portion does not contact the primary workpiece. Therefore, during the milling cutter slotting process, the impact of the grinding wheel's structure other than the rounded corners on cutting can be ignored. Only the rounded corners of the grinding wheel are included in the grinding wheel toolpath calculation model during the calculation process. This not only simplifies the calculation and improves efficiency, but also accurately calculates the grinding wheel toolpath for slotting.

[0064] S2: During the slotting process of the milling cutter, only the rounded corner part of the grinding wheel is involved in grinding. The grinding wheel model during the slotting process of the milling cutter is simplified into a torus. The torus is used to represent the rounded corner part of the grinding wheel. The grinding wheel posture is analyzed based on the posture of the torus during the slotting process of the milling cutter.

[0065] The calculation is greatly affected by the variety and complex shapes of grinding wheels. Grinding wheels include 1V1 grinding wheel, 1V1 bowl grinding wheel, 1A1 grinding wheel and 14E1 grinding wheel. Figure 2As shown, different types of grinding wheels are formed into simplified torus bodies, and the simplified torus bodies are only used to represent the grinding wheel fillet posture. This allows other parts that do not affect the cutting process during the milling cutter slotting process to be ignored, greatly simplifying the calculation amount, improving calculation efficiency, and ensuring the accuracy of the calculation results. The posture of the torus body can be used to deduce at least one posture of the grinding wheel. The target posture of the grinding wheel is then obtained by judging the interference between the grinding wheel and the workpiece, which is the unique solution for the grinding wheel posture. The posture of the torus body is truly restored to correspond to the only grinding wheel posture. This proves that the torus body can represent the grinding wheel in the grinding wheel tool path calculation model. In this embodiment, the first workpiece includes CNC tools such as milling cutters and forming cutters. When the grinding wheel is processing the workpiece, only its fillet part is involved in grinding, so the grinding wheel model is simplified to a fillet model - a torus body. There are only two postures of the torus corresponding to the grinding wheel, but considering that the grinding wheel and the workpiece must not interfere with each other (when the torus is tangent to the core thickness surface of the milling cutter, one of the situations will obviously cause interference), there is only one.

[0066] Specifically, the grinding wheel is simplified into a torus - that is, for any model of grinding wheel with rounded corners, the minor radius r of the torus is equal to the corner radius of the grinding wheel, and the grinding wheel rotation radius R can be simplified to the spherical radius of radius r. The torus is formed by sweeping a circle of the space circle, where:

[0067] The simplified torus of the grinding wheel can be expressed as the center of a sphere with a radius r as the moving point in the grinding wheel tool path calculation model. The motion on the space circle is the shape characteristic of the torus.

[0068] The turning radius R and fillet radius r of the grinding wheel, the torus is tangent to the core thickness surface, which is equivalent to: The space circle has only one tangent point with the core thickness offset surface (each point moves a distance r along its normal). This tangent point can be regarded as the grinding wheel fillet posture.

[0069] S3: A grinding wheel tool path calculation model is established based on the shape parameters of the torus, the milling cutter core thickness, 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.

[0070] 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 the discrete points on the milling cutter edge line and the normal direction of the points can be arbitrarily changed to form various surfaces. Because the intersection point between the grinding wheel and the core thickness does not correspond to the intersection point between the grinding wheel and the spiral groove, in order to reduce the freedom of the grinding wheel and simplify the calculation model of the grinding wheel tool path, the discrete points on the edge line and the normal direction of the points are used as the constraints of the simplified torus of the grinding wheel. The combination relationship of the constraints can be referred to Figure 3 , Figure 3The annular object on the right side is a torus. The black line tangent to the annular object is used to represent the milling cutter edge line (excluding the normal) in the cutting guide surface. The milling cutter edge line is tangent to the annular body. The core thickness surface is a solid line, and the core thickness offset surface is a dotted line. The core thickness offset surface can be represented as the new surface formed by offsetting each point on the core thickness surface by a distance r from the normal to the outside of the milling cutter. This offset distance r is the minor radius of the annular body. For any point on the milling cutter edge line, Normal direction corresponding to the point as well as The tangent direction corresponding to the point ; Establish coordinate system description Position relationship, the origin of the coordinate system is , the coordinate system is . The X axis is the cutting point of any point , the normal direction of the Z axis point ,in:

[0071]

[0072] The simplified annular body of the grinding wheel is tangent to the spiral groove to be machined. , which can be regarded as radius r, center of sphere The ball is tangent to the spiral groove to be machined. and The radius of the torus On the space circle, where:

[0073]

[0074] It is used to limit the degree of freedom of the torus. During the milling process, the cutting angle between the grinding wheel and the spiral groove of the milling cutter is (The axial direction of the ring body, that is, the axial direction of the grinding wheel The angle between the torus and the ring also limits the degree of freedom of the ring. At this time, the torus has only one degree of freedom limited by an angle, which is set as the first solution parameter. , as one of the unknowns in the grinding wheel tool path calculation model.

[0075] Assume that the coordinates of the center of the torus space circle are , suppose the torus coordinate system , The X-axis is composed of point to , Z axis is the grinding wheel axis, then:

[0076]

[0077] Refers to rotation around the Z axis according to the right-hand rule The rotation matrix of Refers to rotation around the Y axis according to the right-hand rule The rotation matrix of the torus coordinate system is The coordinate system rotates around its own Z axis according to the right-hand rule (First solution parameter), then rotate around its own Y axis according to the right-hand rule (Cutting angle, known value) transformation; Depend on The X-axis definition and Got it.

[0078] During the milling process, the tangent point between the grinding wheel and the milling cutter core does not correspond to the tangent point on the milling cutter edge line. Therefore, for any point on the milling cutter edge line, Calculate the tangent point between the grinding wheel and the milling cutter core thickness at this time The overall data of the milling cutter core thickness needs to be considered, that is, the core thickness surface.

[0079] Suppose there is a moving point on the torus , There is one angular degree of freedom, set it to , then:

[0080]

[0081] Refers to rotation around the Z axis according to the right-hand rule The rotation matrix of hour, and coincide.

[0082] Specifically, since the interference judgment between entities is relatively complex, in order to simplify the relationship, it is converted into the interference judgment between points and entities. According to the unique properties of the milling cutter itself, the core thickness surface of the overall concept of the milling cutter core thickness can be regarded as a rotating body, then in the plane where its rotation axis is located, the interference judgment between points and entities can be converted into the position relationship judgment between points and lines. Among them, the ball end milling cutter judgment is as follows Figure 4 As shown, the non-ball end milling cutter is judged as follows Figure 5 As shown, the core thickness surface is represented by a solid line, and the core thickness offset surface is represented by a dotted line.

[0083] Specifically, when the grinding wheel is tangent to the milling cutter core thickness, traversing all points on the space circle of the torus, there is only one second solution parameter , so that The sphere with the center and radius r is tangent to the core thickness surface at , That is the point where the grinding wheel and the milling cutter core are tangent to each other. Then, there must be:

[0084]

[0085] Point on the core thickness surface The corresponding normal direction, The tangent point on the core thickness surface Along the normal The point after moving distance r should be coincide.

[0086] Then, the simplified torus of the grinding wheel is tangent to the core thickness surface at the tangent point , which is equivalent to a moving point on the space circle of the simplified torus of the grinding wheel , the core thickness surface discrete point moves along the normal direction of the point by a distance r, and the new point generated by adding the original normal direction to form a new surface, that is, a point on the core thickness offset surface. , when the two solution parameters and There is a set of fixed values ​​such that and When they coincide, the unique value of the grinding wheel posture is determined.

[0087] S4: Analyze the grinding wheel toolpath calculation model using the conjugate gradient optimization method and obtain the dynamic grinding wheel toolpath during slotting. The dynamic grinding wheel toolpath calculated through steps S1, S2, and S3 can largely reproduce the grinding wheel toolpath in real-world scenarios.

[0088] For a point on the milling cutter edge line with a known input , the normal corresponding to the point And the tangent direction corresponding to the point ; Construct the coordinate system of this point ——Cutting with X-axis as point , the normal direction of the Z axis point .

[0089] The simplified annular body of the grinding wheel is tangent to the spiral groove of the milling cutter. , which can be represented by radius r, center The ball is tangent to the spiral groove at ,Right now The radius of the torus on the space circle.

[0090] For a known input cutting angle and the first solution parameter , then the origin of the coordinate system corresponding to the simplified torus with the grinding wheel is and coordinate system —— The X-axis is point to , Z axis is the axial direction of the grinding wheel.

[0091] The simplified torus of the grinding wheel can be regarded as a sphere with a radius of r and a center of The radius of the sphere around the torus The space circle movement forms the restriction The second solution parameter for the position is ( hour, and coincide).

[0092] The core thickness surface is composed of several first discrete points and the normals of the first discrete points. These first discrete points are moved a distance r along the normals of the points to form first moving points. The normals of the first discrete points before the first moving points are formed and the first moving points form the core thickness offset surface of the core thickness surface.

[0093] point for The projection method of the core thickness offset surface is changed according to the type of core thickness surface. The types of core thickness surface include sphere, cylinder, cone and revolution body. for point and point The intersection of the line connecting and its extension line with the core thickness offset surface is:

[0094]

[0095] When the two solution parameters There is a set of fixed values ​​such that the point with dot If they overlap, then:

[0096]

[0097] At this time, the two solution parameters and is a known value. The point of intersection between the grinding wheel and the milling cutter core thickness The position of the simplified torus of the grinding wheel is determined. The torus represents the position of the grinding wheel corner. At least one solution for the grinding wheel position can be obtained. Then, the interference between the grinding wheel and the first workpiece is judged to eliminate other solutions. Only one solution remains. Finally, the position of the torus determines the only grinding wheel position.

[0098] For a known point on the milling cutter edge line and its normal Tangential , known milling cutter core thickness (first discrete point and its corresponding normal), known grinding wheel parameters (radius r, turning radius R), known machining parameters (tangential angle ); through two solution parameters , and continuously optimize it to meet the conditions, then:

[0099]

[0100] If and only if Solved The value can be used to calculate the torus posture, the corresponding unique grinding wheel posture and the tangent point between the grinding wheel and the milling cutter core thickness. .

[0101] In summary, through two solution parameters The tangent points of the simplified annulus of the grinding wheel and the spiral groove edge line of the milling cutter and the tangent points of the core thickness surface abstracted from the core thickness of the milling cutter were obtained.

[0102] To avoid two solution parameters in the calculation process The value deviates from the correct area, and a penalty function is established:

[0103]

[0104] At the same time, change The definition of , so that it can be negative, is set to :

[0105]

[0106] Then the optimization equation is:

[0107] when When the function value is far away from 0, it means it is deviating from the target; when When the function value is close to 0, it means it is close to the target; when When the function value is 0, it means that The value satisfies the condition.

[0108] This optimization method differs from gradient descent and genetic algorithms in that it solves the grinding wheel tool path calculation model not from a mathematical perspective but from a geometric perspective. Methods based on geometric relationships are generally more intuitive, easier to understand, and easier to implement. This method of solving the grinding wheel tool path calculation model directly utilizes the geometric properties of objects associated with the grinding wheel tool path (the core thickness surface, the variable spiral groove, and the torus formed by the simplified grinding wheel) for calculation, without requiring complex mathematical derivations or advanced optimization theory. At the same time, it avoids becoming entangled in complex numerical calculation processes, such as iterative solutions. For certain specific problems, geometric algorithms may provide a direct and fast solution, reducing calculation time. They are particularly suitable for real-time applications or scenarios requiring fast response, especially for the calculation of grinding wheel tool paths.

[0109] Furthermore, geometric methods offer high-precision control when processing shapes and path planning. For example, in an application where a grinding wheel slots a milling cutter, accurately planning the tool path based on the geometry of the workpiece and grinding wheel ensures machining accuracy and surface quality.

[0110] Next, for objects with complex or irregular geometries, methods based on geometric relationships are more adaptable than existing mathematical optimization methods. This is because geometric methods can directly process the spatial characteristics of the core thickness surface, variable spiral grooves, and the torus formed by the simplified grinding wheel without converting them into a form suitable for mathematical optimization.

[0111] Finally, unlike gradient descent or genetic algorithms, geometry-based methods usually do not involve problems such as local minima or convergence difficulties that may occur during the optimization process, thus providing a more reliable solution.

[0112] The first solution parameter What has changed is the posture of the simplified torus of the grinding wheel. What has changed is the point The position of the ball with radius r and moving center on the torus space circle after the grinding wheel is simplified.

[0113] like Figure 6 As shown, Figure 6 The object on the left is the core thickness surface, and the annular object on the right is the torus. The black lines connected to the torus and the core thickness surface represent the milling cutter edge line (excluding the normal) in the cutting guide surface. The milling cutter edge line is tangent to the annular body and is used to represent the annular body of the grinding wheel. There are 4 different groups of grinding wheel grinding trajectories in sub-graphs (a)-(d). Among them, the first solution parameter of sub-graphs (a)-(d) is The calculation method of the grinding wheel tool path when the milling cutter is slotting based on the milling cutter core thickness also includes step S5: for optimizing the target grinding wheel tool path. Specifically, according to the two solution parameters 、 Definition of—— What has changed is the posture of the simplified torus of the grinding wheel. What has changed is the point The position of a sphere with a radius of r and a moving center on the torus after the grinding wheel is simplified. Based on the geometric relationship between the simplified torus, the milling cutter spiral groove, and the core thickness surface, an optimization path similar to the conjugate gradient method is derived to solve the grinding wheel tool path calculation model. The optimization process can be simulated through a 3D model.

[0114] The optimization process is simulated through the 3D model. The following are the optimization steps:

[0115] (1) Calculate the first solution parameter With the second solver parameter The initial value is such that the annulus interferes with the core thickness surface and does not cross the axis of the first workpiece.

[0116] (2) Move once --like Constant ≥ 0, when the minimum value is obtained ;like Existence, get its just Time .

[0117] (3) Move once --like Existence (must exist), get its just Time .

[0118] (4) Repeat (2) and (3) until When the values ​​of do not change, the operation ends and the output result is obtained. The output result is the target grinding wheel tool path.

[0119] This not only avoids sudden changes in the output results, but also ensures a smooth transition of the grinding wheel position, making the output results more accurate. Secondly, it reduces the calculation time of the second point and all subsequent points, greatly reducing the calculation time of the entire milling cutter spiral groove edge line.

[0120] Beneficial effects of this embodiment

[0121] First, this embodiment describes in detail the specific methods for obtaining the core thickness surface, cutting guide surface, and grinding wheel shape characteristics. These parameters are used to comprehensively analyze the tangency conditions between the grinding wheel and the milling cutter spiral groove and core thickness. At the same time, the tangency model between the grinding wheel and the milling cutter is simplified step by step in the order of body and surface - sphere and surface - point and offset surface, which further simplifies the calculation and constructs an accurate and fast grinding wheel tool path calculation model. When establishing the coordinate system to describe the positional relationship of the points and determining the tangency conditions between the torus and the spiral groove and core thickness, the various geometric characteristics of the milling cutter and the grinding wheel are fully considered. Combining the conjugate gradient optimization method to solve the model, it is possible to highly restore the actual grinding wheel tool path during milling cutter grooving, provide accurate theoretical guidance for milling cutter grooving processing, and help improve the accuracy and quality of milling cutter grooving.

[0122] Secondly, the use of variable parameter designs for the milling cutter core thickness and spiral grooves breaks through the limitations of existing constant parameter end mills. When faced with 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, the parameters are obtained by discretizing the core thickness surface to truly restore their structure; for spiral grooves with variable helix angles, rake angles, etc., the parameters can also be accurately obtained for research. This enables this method to meet the special needs of 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.

[0123] Furthermore, the grinding wheel is simplified into a torus that only represents the fillet position, ignoring other parts that do not participate in grinding, which greatly reduces the amount of calculation. In the process of analyzing the tangent conditions and establishing the model, the unknowns and constraints are reasonably set to simplify the calculation process. For example, by determining the degree 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 from the second point onwards, which significantly reduces the calculation time of subsequent points, greatly improves the calculation efficiency of the entire milling cutter spiral groove edge line, and improves production efficiency.

[0124] Finally, in the process of optimizing the target grinding wheel tool path, by reasonably setting initial values, gradually moving variables, and obtaining corresponding values ​​according to conditions until the variable values ​​no longer change, sudden changes in the output results are avoided and a smooth transition of the grinding wheel posture is ensured. The establishment of a penalty function and adjustment of the interference judgment function effectively avoid interference between the grinding wheel and the milling cutter core thickness, ensuring that the calculated results meet actual processing requirements. The optimization process is simulated through a 3D model, which intuitively displays the optimization path, further improving the accuracy and reliability of the calculation results and providing reliable technical support for actual milling cutter slotting operations.

[0125] Test Example 1

[0126] When using the method for calculating the grinding wheel tool path when a milling cutter is grooving based on the milling cutter core thickness as described in Example 1, the initial position and calculation results of the annular body posture when a non-ball head milling cutter is grooving are calculated.

[0127] The position of the simplified torus of the grinding wheel represents the position of the fillet on the side of the grinding wheel involved in the milling cutter slot grinding process. Combined with the interference judgment with the workpiece, the position of the torus can obtain the only correct grinding wheel position, that is, the position of the torus represents the position of the grinding wheel.

[0128] Table 1 UG 3D model simulation data results based on the calculation test of the grinding wheel tool path when the flat bottom milling cutter is slotting

[0129]

[0130] Table 2 Output results of the C++ calculation program based on the calculation test of the grinding wheel tool path when the flat bottom milling cutter is slotting

[0131]

[0132] Specifically, as shown in Tables 1 and 2, the origin is the center of the space circle after the grinding wheel model is simplified; the Z axis is defined as the rotation axis of the grinding wheel, and its direction is on the same side as the normal direction of the rake face point; the X axis is defined as the point from the center of the space circle to the rake face point along its normal movement of the fillet radius.

[0133] Tables 1 and 2 calculate the grinding wheel position at a single point on the milling cutter's spiral groove edge line. Calculating the entire milling cutter's spiral groove edge line requires calculation of several points (set to 200 or higher; a larger number increases the precision of the discrete points). Because each point has two solutions, controlled by the initial value, to avoid sudden changes in the solutions between adjacent points (i.e., solutions on different sides), excessive calculation time for a single point (20-30ms) can delay the calculation of the entire milling cutter's spiral groove edge line.

[0134] Therefore, starting from the second point, the initial value uses the calculation result of the previous point. After practical verification, on the one hand, it avoids the sudden change of the output result and ensures the smooth transition of the grinding wheel posture; on the other hand, it reduces the calculation time of the second point and all subsequent points (about 2ms), greatly reducing the calculation time of the entire milling cutter spiral groove edge line. The calculation of one thousand point data in the C++ program only takes about 1.8s. It can be seen that the method of Example 1 can greatly improve the calculation efficiency.

[0135] From the calculation method of the grinding wheel tool path when the milling cutter is grooving based on the milling cutter core thickness as described in Example 1 through the C++ calculation program, from the first tool path coordinate point to the eleventh tool path coordinate point, the C++ calculation results are consistent with the UG three-dimensional model simulation data (the accuracy value is 0.01), that is, the tangency between the grinding wheel and the milling cutter spiral groove during the milling cutter grooving process, the tangency between the grinding wheel and the milling cutter core thickness, and the accuracy of the grinding wheel tool path when grooving based on the flat-bottom milling cutter.

[0136] Test Example 2

[0137] Unlike the first test case, this one calculates the grinding wheel path when a ball-end milling cutter is used to create slots. This test uses a C++ program to output the first calculation results, which are then verified using UG 3D model data. The test data is as follows:

[0138] Table 3 UG 3D model simulation data results based on the calculation test of grinding wheel tool path when ball end milling cutter is grooving

[0139]

[0140] Table 4 Output results of the C++ calculation program based on the calculation test of the grinding wheel tool path when the ball end mill is grooving

[0141]

[0142] Specifically, as shown in Tables 3 and 4, the origin is the center of the space circle after the grinding wheel model is simplified; the Z axis is defined as the rotation axis of the grinding wheel, and its direction is on the same side as the normal direction of the rake face point; the X axis is defined as the point from the center of the space circle to the rake face point along its normal moving fillet radius.

[0143] Tables 3 and 4 calculate the grinding wheel position at a single point on the milling cutter's spiral groove edge line. Calculating the entire milling cutter's spiral groove edge line requires calculation of several points (set to 200 or above; a larger number increases the precision of the discrete points). Because each point has two solutions controlled by the initial value, to avoid sudden changes in the solutions of adjacent points (i.e., solutions on different sides), and to avoid excessive calculation time (20-30ms) for a single point, which would delay the calculation of the entire milling cutter's spiral groove edge line.

[0144] Therefore, starting from the second point, the initial value uses the calculation result of the previous point. After practical verification, on the one hand, it avoids the sudden change of the output result and ensures the smooth transition of the grinding wheel posture; on the other hand, it reduces the calculation time of the second point and all subsequent points (about 2ms), greatly reducing the calculation time of the entire milling cutter spiral groove edge line. The calculation of one thousand point data in the C++ program only takes about 1.8s.

[0145] From the calculation method of the grinding wheel tool path when the milling cutter is grooving based on the milling cutter core thickness as described in Example 1 through the C++ calculation program, from the first tool path coordinate point to the eleventh tool path coordinate point, the C++ calculation results are consistent with the UG three-dimensional model simulation data (the accuracy value is 0.01), that is, the tangency between the grinding wheel and the milling cutter spiral groove during the milling cutter grooving process, the tangency between the grinding wheel and the milling cutter core thickness, and the accuracy of the grinding wheel tool path when grooving based on the flat-bottom milling cutter.

[0146] Example 2

[0147] Different from the above embodiment, this embodiment provides a calculation system for the grinding wheel tool path when the milling cutter is slotting based on the milling cutter core thickness, such as Figure 7 As shown, a system for calculating the grinding wheel tool path when a milling cutter is grooving based on the milling cutter core thickness includes 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 runnable on the processor, when the processor executes the computer program, the electronic device implements a method for calculating the grinding wheel tool path when a milling cutter is grooving based on the milling cutter core thickness in any of the above embodiments.

[0148] Specifically, such as Figure 8 As shown, 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 memories 104 and executable on the processors. The processors 101, input devices 102, output devices 103, and memories 104 are interconnected via a bus 105. The memory 104 is used to store the computer program, which includes program instructions. The processor 101 is configured to invoke the program instructions to execute the method steps described in the above method embodiments.

[0149] It should be understood that in this embodiment, the processor 101 may be a central processing unit (CPU), or may be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0150] The input device 102 may include a keyboard, etc., and the output device 103 may include a display (LCD, etc.), a speaker, etc.

[0151] The memory 104 may include a read-only memory and a random access memory, and provides instructions and data to the processor 101. A portion of the memory 104 may also include a non-volatile random access memory. For example, the memory 104 may also store device type information.

[0152] In a specific implementation, the processor 101, input device 102, and output device 103 described in the embodiment of the present invention can execute the implementation method described in the relevant embodiments of the method and system for calculating the grinding wheel tool path when the milling cutter is grooving based on the milling cutter core thickness provided by the embodiment of the present invention, which will not be repeated here.

[0153] It should be noted that for a more specific description of the workflow of the electronic device and a method for calculating the grinding wheel tool path when executing a milling cutter grooving based on the milling cutter core thickness, please refer to the aforementioned method embodiment section, which will not be repeated here.

[0154] Example 3

[0155] Unlike the previous embodiment, the memory described in this embodiment should be understood in a broad sense. It can be not only a hardware component for temporarily storing data in a computer system, but also a physical medium that can store digital information and be read by a computer. These media can be permanent or temporary, including but not limited to hard disks and solid-state drives.

[0156] Specifically, the memory can be an internal storage unit of the electronic device described in any embodiment, such as the system's hard drive or memory. The memory can also be an external storage device of the system, such as a plug-in hard drive, Smart Media Card (SMC), Secure Digital (SD) card, or Flash Card equipped with the system. Furthermore, the memory can include both the system's internal storage unit and an 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 data that has been output or is about to be output.

[0157] The memory includes various media that can store program codes, such as USB flash drives, mobile hard disks, read-only memories (ROM), random access memories (RAM), magnetic disks or optical disks.

Claims

1. A method for calculating the grinding wheel tool path when a milling cutter is slotting based on the milling cutter core thickness, characterized in that: include: S1: For different grinding wheel models, three customizable parameters, namely the core thickness, cutting guide surface, and cutting angle, of the milling cutter to be processed are input to calculate the grinding wheel path when the milling cutter is slotting. The core thickness is defined by the milling cutter rotation axis and a coplanar arbitrary curve, the cutting guide surface is defined by the milling cutter edge line and normal, and the cutting angle is defined by the angle between the grinding wheel rotation axis and the milling cutter edge line normal. S2: During the slotting process of the milling cutter, only the rounded corner of the grinding wheel is involved in the grinding. The grinding wheel model during the slotting process of the milling cutter is simplified to a torus. The torus is used to represent the rounded corner of the grinding wheel. The grinding wheel posture is analyzed according to the posture of the torus during the slotting process of the milling cutter. Among them, the main radius of the torus is , where the radius of gyration of the grinding wheel is R, and the minor radius of the torus is r, which is equal to the corner radius of the grinding wheel; S3: According to the shape parameters of the ring body, the thickness of the milling cutter core, the cutting guide surface, the cutting angle, the tangent conditions between the ring body and the core thickness, and the tangent conditions between the ring body and the cutting guide surface, a grinding wheel tool path calculation model is established; wherein, when the grinding wheel and the milling cutter are tangent during the milling cutter slotting process, for any point on the milling cutter edge line , established with The coordinate system with the origin , where the X axis is the point Cutting point Direction, Z axis is the point Normal direction, and When the torus is tangent to the cutting guide surface, the center of the torus , the radius of the grinding wheel is r, and The radius of the torus On the space circle; the rotation axis of the torus The included angle is fixed to determine the cutting angle parameters; the torus only has one angle Restricted degrees of freedom, angles As the first solution parameter of the grinding wheel tool path calculation model; S4: Analyze the grinding wheel tool path calculation model based on the conjugate gradient optimization method, and obtain the dynamic grinding wheel tool path when the milling cutter is grooving.

2. The method for calculating the grinding wheel tool path when a milling cutter is grooving based on the milling cutter core thickness according to claim 1, characterized in that: The separate surface obtained by peeling off the core thickness of the milling cutter is the core thickness surface, which is used to represent the parameter data of the core thickness of the milling cutter to be processed; specifically, the milling cutter rotary axis and an arbitrary curve coplanar with the rotary axis, and the core thickness surface of the milling cutter formed by interpolation of several discrete points on the curve; the core thickness surface of the milling cutter is geometrically characterized as the surface of a geometric body formed around the milling cutter rotary axis according to the curve.

3. The method for calculating the grinding wheel tool path when a milling cutter is slotting based on the milling cutter core thickness according to claim 2, characterized in that: Core surface types include sphere, cylinder, cone, and solid of revolution.

4. The method for calculating the grinding wheel tool path when a milling cutter is grooving based on the milling cutter core thickness 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 vector at each point. During the milling cutter grooving process, the surface composed of the milling cutter edge line and the area around the edge line is characterized as the tangent point during the grinding wheel cutting process for a single discrete point, and the plane formed by the single discrete point and the normal of the point is characterized as the tangent plane during the grinding wheel cutting process.

5. The method for calculating the grinding wheel tool path when a milling cutter is grooving based on the milling cutter core thickness according to claim 1, characterized in that: When analyzing the grinding wheel tool path calculation model according to the conjugate gradient optimization method, a penalty function is set up. ,when 0, the ring body is tangent to the core thickness surface of the milling cutter; on the contrary, when , the torus interferes with or moves away from the core thick surface; ,when = hour, No interference with the core thickness offset surface; when =- , Interference with the core thickness offset surface; is the second solution parameter, P t is the center of the torus, and the core thickness offset surface is characterized by the new surface formed when each point on the core thickness surface is offset to the outside of the milling cutter by a distance r along the normal direction of the point.

6. The method for calculating the grinding wheel tool path when a milling cutter is slotting based on the milling cutter core thickness according to claim 5, characterized in that: The method further includes step S5: optimizing the target grinding wheel tool path; specifically, calculating the first solution parameter Initial values ​​are set so that the torus interferes with the core thickness surface and does not cross the axis of the first workpiece; First, change the second solver parameter once ,like ≥0, the second solution parameter when its minimum value is obtained If it exists , get its just The second solution parameter when ; Secondly, change the first solution parameter once ,like Existence, get its just The first solution parameter when ; Among them, ST is The function value of ; Finally, until the first solution parameter With the second solver parameter When the values ​​of do not change, the operation ends and the output result is obtained, which is the optimized target grinding wheel tool path.

7. The method for calculating the grinding wheel tool path when a milling cutter is grooving based on the milling cutter core thickness according to claim 5, characterized in that: Assume that the coordinates of the center of the torus space circle are , suppose the torus coordinate system , The X-axis is composed of point to , Z axis is the grinding wheel axis, then: Refers to the rotation angle around the Z axis according to the right-hand rule The rotation matrix of Refers to the rotation angle around the Y axis according to the right-hand rule The rotation matrix of The cutting angle between the grinding wheel and the spiral groove of the milling cutter; Torus coordinate system is The first solution parameter is the right-hand rule rotation of the coordinate system around its own Z axis , and then rotate the cutting angle around its own Y axis according to the right hand rule Transformed; Depend on Definition of the X-axis and the center of the torus get.

8. The method for calculating the grinding wheel tool path when a milling cutter is grooving based on the milling cutter core thickness according to claim 5, characterized in that: When the grinding wheel is tangent to the milling cutter core thickness, traverse all points on the space circle of the torus, and there is only one second solution parameter , so that the center of the torus The sphere with the secondary radius r of the torus as the center is tangent to the thick surface of the milling cutter core at , is the point of intersection between the grinding wheel and the milling cutter core thickness at this time, then at this time there must be: Point on the thick surface of the milling cutter core The corresponding normal direction, The cutting point on the thick surface of the milling cutter core Along the normal The point after moving distance r should be coincide; The simplified annular body of the grinding wheel is tangent to the thick surface of the milling cutter core at the tangent point , which is equivalent to a moving point on the space circle of the simplified torus of the grinding wheel , and a point on the core thickness offset surface , When the two solution parameters There is a set of fixed values ​​so that the center of the torus Tangent point on the thick surface of the milling cutter core When they coincide, the unique value of the grinding wheel posture is determined.

9. The method for calculating the grinding wheel tool path when a milling cutter is grooving based on the milling cutter core thickness according to claim 1, characterized in that: The milling cutters to be processed include ball-end milling cutters and non-ball-end milling cutters.

10. A system for calculating the grinding wheel tool path when a milling cutter is slotting based on the milling cutter core thickness, characterized in that: The method comprises a data analysis module, which comprises an electronic device, which comprises a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, the electronic device implements any one of claims 1-9 for calculating the grinding wheel tool path when a milling cutter is grooving based on the milling cutter core thickness.

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