A design method of a conical face drill tip with controllable amount of lag

Abstract

The application discloses a design method of a conical face drill tip with controllable lag amount, and belongs to the technical field of metal cutting tools. In view of the problem that the tail root turning point of the existing drill tip relief surface is prone to "warping back" (the lag amount is negative), which leads to interference with the hole bottom, cutting vibration, short tool life and other problems, the application first changes the "lag amount" from an uncontrollable random result into a quantifiable and preset core design parameter. The technical scheme comprises the following steps: establishing a drill tip coordinate system and a relief surface mathematical model; establishing a design parameter and a grinding parameter analytical equation; taking the target lag amount as a core constraint for solving; obtaining a unique grinding parameter through iterative approximation; and performing numerical control machining based on the solved parameter. The application realizes accurate control of the lag amount, eliminates the warping back of the relief surface from the root, and significantly improves the drilling stability, machining quality and tool life, and is particularly suitable for a large-length-diameter-ratio deep hole twist drill.

Description

Technical Field

[0001] This invention relates to the field of metal cutting tool design and manufacturing technology, and to a method for designing a conical drill tip with controllable hysteresis. Background Technology

[0002] In deep hole drilling, the geometry of the twist drill tip has a decisive influence on cutting performance. Conical drill tips are widely used due to their advantages such as good cutting edge strength and reasonable clearance angle distribution. However, when machining conical drill tips with curved cutting edges (especially concave curved cutting edges) on CNC tool grinders, a common problem exists: the machined flank may exhibit a "backward tilt" near the tail root inflection point (i.e., the inflection point on the side closer to the drill core in the intersection of the flank and the outer cylindrical surface of the drill bit), meaning that the axial position in this area is too high.

[0003] The axial position at the tail root pivot point is usually described by a parameter called "hysteresis," which is defined as the backward distance of the tail root pivot point relative to the outer edge pivot point (the outermost point of the main cutting edge) along the drill bit axis. If the hysteresis is too small or even negative (i.e., backlash), it will cause scraping and interference between the tail root pivot point area of ​​the drill bit's flank and the machined hole bottom surface during drilling, especially under conditions of feed error or workpiece elastic deformation. This not only increases cutting resistance and generates additional frictional heat, accelerating tool wear, but also damages the quality of the machined surface and may even cause cutting vibration, severely restricting the efficiency and accuracy of deep hole machining.

[0004] In existing technologies, the mathematical models and grinding parameter solutions for conical drill tips are mainly designed for straight-edged drill tips. For curved-edged drill tips, it is difficult to define a unified structural coordinate system, resulting in a complex and non-unique mapping relationship between design parameters (such as half-apex angle, chisel edge angle, and clearance angle) and machine tool grinding parameters (such as cone shaft angle, half-cone angle, and cone apex offset). Traditional methods often introduce auxiliary parameters such as the "tail gap angle," but the solution process is cumbersome, and it is difficult to intuitively predict and control the hysteresis at the tail root turning point during the design phase. In engineering practice, repeated trial grinding and adjustments are often made based on the operator's experience, which is inefficient and inconsistent.

[0005] Therefore, there is an urgent need for a method that can accurately and intuitively design and control the hysteresis of the curved cutting edge conical surface drill tip, so as to fundamentally solve the problem of back face warping. Summary of the Invention

[0006] The purpose of this invention is to provide a method for designing a conical drill tip with controllable hysteresis to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A method for designing a conical drill tip with controllable hysteresis, characterized by comprising the following steps: S1: Establish a coordinate system and mathematical model. With the center of the drill bit end face as the origin, establish a coordinate system for the drill tip structure, where... The axis coincides with the drill bit axis, defining the drill bit radius. helix angle The central angle corresponding to the blade width semi-apex angle Horizontal blade angle , structural circumference rear angle Blade offset and target lag And establish the spatial surface equation of the conical rake face; S2: Establish the correlation equation between design parameters and grinding parameters, and derive the half-apex angle. Horizontal blade angle Circumferential rear angle With five grinding parameters—the angle between the taper axis and the drill axis. Half cone angle Cone apex offset component , , A system of mathematical equations relating the two; S3: Incorporate hysteresis as a core design objective into the solution system, based on the helix angle. The central angle corresponding to the blade width and target lag Calculate the angle ω between the projections of the tail root turning point B and the outer edge turning point A onto the end plane, and establish the coordinates of the tail root turning point and the hysteresis. Relationship; S4: Solve for the grinding parameters that satisfy the target hysteresis, using the angle between the conical shaft and the drill shaft. Using the above equations as iterative variables, the lag quantity satisfying the target value is obtained by solving the system of equations simultaneously using the iterative approximation method. Five sets of sharpening parameters , , , , ; S5: Based on the solved grinding parameters, CNC machining is performed. The solved grinding parameters are input into the CNC tool grinder to generate the grinding wheel motion trajectory and grind a curved conical back face with a preset hysteresis.

[0008] In the above-mentioned method for designing a conical drill tip with controllable hysteresis, in step S1, the equation of the conical rake face in its own coordinate system is: ; Transform it to the drill tip structure coordinate system through coordinate rotation. In this process, implicit equations are formed.

[0009] In the above-mentioned method for designing a conical drill tip with controllable hysteresis, in step S2, the chisel edge angle... By simultaneously solving the spatial surface equations of the left and right flank faces, the projection curve of their intersection line onto the drill bit end plane is obtained, and the tangent direction of this projection curve at the origin is calculated. The angle between the axes is obtained.

[0010] In the above-mentioned conical drill tip design method with controllable hysteresis, in step S2, the half-apex angle An approximate method is used to solve the problem, namely, using a plane passing through the outer edge turning point A and parallel to the structural base plane (i.e., The half-apex angle is approximately defined by the tangent direction at the intersection line of the blade face and the back face.

[0011] In the above-mentioned conical drill tip design method with controllable hysteresis, in step S2, the axial structural back angle The solution formula is: ; Where A is the outer edge turning point, and the axial structural rear angle is... The rear angle of the structural circumference specified in the design Through geometric transformation relationships Related.

[0012] In the above-mentioned conical drill tip design method with controllable hysteresis, the formula for calculating the angle ω between the projections of the tail root turning point B and the outer edge turning point A onto the end plane in step S3 is as follows: ; The coordinate expression of the tail root turning point B is: ; Where t is the drill tip height. λ represents the actual lag, and λ is the center angle.

[0013] In the aforementioned design method for a conical drill tip with controllable hysteresis, in step S4, when solving for the grinding parameters using an iterative approximation method, the calculated theoretical hysteresis is used. and target lag The difference is used as the convergence criterion, and the iteration terminates when the difference is less than the preset error threshold.

[0014] Compared with the prior art, the beneficial effects of the present invention are: This invention represents a significant breakthrough in the design and manufacturing of conical drill tips. At the theoretical level, it transforms the "hysteresis" from an uncontrollable random result into a quantifiable and pre-defined core design objective for the first time, fundamentally eliminating the industry-wide problem of "back face warping." Furthermore, by establishing a complete mathematical analytical model, it achieves precise conversion between design parameters and grinding parameters. In terms of manufacturing precision, users can directly specify the optimal hysteresis amount according to processing requirements, and quickly obtain unique grinding parameters through iterative solution. The error can be controlled within 0.01mm, ensuring the high consistency and repeatability of the product, and realizing the transformation from "skill-dependent" to "knowledge-driven". In terms of machining performance, the preset positive hysteresis creates a reasonable gap between the back face and the bottom of the hole, which completely avoids scraping, frictional heat and cutting vibration, significantly reduces cutting resistance and extends tool life, while obtaining a smooth hole wall surface, making it particularly suitable for precision machining applications. In terms of application adaptability, this method is applicable to drill bits of different specifications, and provides ample clearance, especially for deep hole machining. Users can also optimize the hysteresis design according to working conditions to achieve performance-driven manufacturing. In terms of economic benefits, this invention reduces trial grinding and adjustments, lowers tool scrap rates, and extends tool life, playing a significant technological role in promoting the field of precision tool manufacturing. Attached Figure Description

[0015] Figure 1 This is the flowchart of the closed-loop algorithm for determining and correcting hysteresis. Figure 2 This is the control flowchart for the implementation of hysteresis CNC; Figure 3 This is a schematic diagram of the effect of the tool face without hysteresis parameters; Figure 4 This is a schematic diagram of the effect on the cutting face after introducing the hysteresis parameter; Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] like Figure 1 As shown, the design method for a conical drill tip with controllable hysteresis includes the following steps: S1: Establish a unified coordinate system for the drill tip structure and a mathematical model for the conical back face. First, define the key design parameters of the drill tip, including: drill bit radius. helix angle The central angle corresponding to the blade width semi-apex angle Horizontal blade angle , structural circumference rear angle Blade offset and core design lag Establish a drill tip structural coordinate system with the center of the drill bit end face as the origin. ,in The axis coincides with the drill bit axis. This is determined by the cutting edge offset. The projection position of the outer edge turning point A onto the structural base surface is determined, thus uniquely fixing the coordinate system. Based on this, a spatial surface equation describing the rake face of the conical surface is established, wherein the conical surface is formed by a line perpendicular to the axis of the cone. The angle is formed by rotating the generatrix of the angle around the cone axis, and its spatial position is determined by the angle between the cone axis and the drill axis. Half cone angle and the offset component of the cone tip relative to the origin of the drill tip structural coordinate system. , , These five grinding parameters determine the shape of the conical surface in its own coordinate system (with the apex of the cone as the origin and the axis of the cone as the coordinate system). The equation in the axis is: ; By rotating the coordinate system, its coordinate system in the drill tip structure can be obtained. Implicit equations in.

[0018] S2: Establish the theoretical correlation equation between design parameters and grinding parameters. Based on the geometric model established in step 1, the macroscopic design parameters of the drill tip (half-apex angle, chisel edge angle, structural circumferential back angle, cutting edge offset, drill tip height) and five grinding parameters are derived. , , , , A system of mathematical equations relating the following: The equation for solving the bevel angle of the transverse blade is as follows: ; This equation solves for the projection curve of the intersection line (i.e., the chisel edge) onto the drill bit end plane by simultaneously solving the spatial surface equations of the left and right flank faces, and then calculates the tangent direction of this projection curve at the origin. This tangent... The included angle of the shaft is the bevel angle of the transverse cutting edge. This equation transforms the design parameter of "the degree of inclination of the cross-blade" into a specific constraint on the position and direction of the grinding wheel; Strictly speaking, the half-apex angle is the angle between the projection of the main cutting edge (the intersection of the helical groove surface and the flank face) onto the structural base surface and the drill axis. To simplify the model and avoid introducing complex helical groove equations, this invention employs a high-precision approximation method: using a plane passing through the outer edge turning point A and parallel to the structural base surface (i.e., The half-apex angle is approximately defined by the tangent direction at the intersection of the intersection point of the blade face and the rake face. For engineering applications, this approximation has sufficient accuracy. The equation for the half-apex angle is as follows: ; Where t is the drill tip height (axial distance from the outer edge turning point A to the center of the chisel edge). ,Will Substituting into the equation for the back face, we obtain a space curve. Find the relationship between this curve and the outer edge turning point A. derivative The negative reciprocal of the derivative is This formula will take the half-vertex angle It is related to the drill radius R, drill center angle λ, drill tip height t, and all grinding parameters; The axial structural back angle is in a plane parallel to the drill axis and perpendicular to the structural base plane (i.e.) Within the drill plane, the angle between the tangent to the profile of the flank face at the outer edge inflection point A and the end plane (perpendicular to the drill spindle). This directly affects the clearance between the flank face and the bottom of the machined hole, and is crucial for avoiding friction and ensuring smooth cutting. By incorporating the equation for the flank face, we obtain the profile of the flank face on that section. Find the relationship between this profile at point A and... derivative The derivative is The formula is as follows: ; Axial structure rear angle The rear angle of the structural circumference specified in the design There are definite geometric transformation relations. Thus It is also included in the equation set. This equation directly controls the sharpness of the cutting edge and the clearance performance of the flank face, and is one of the core equations connecting the design intent (flank angle size) and the machining realization.

[0019] S3: Incorporate hysteresis as a core design objective into the solution system. Crucially, design lag As known input conditions. Based on the helix angle. blade angle and design lag Calculate the angle ω between the projections of the tail root turning point B and the outer edge turning point A onto the end plane: ; This equation describes the functional relationship between the spatial position of the tail root pivot point B on the edge line of the conical rake face and its axial hysteresis (i.e., the hysteresis that can be achieved after actual machining). The coordinates of the tail root pivot point B can be expressed as: , where h is the actual lag calculated under the current parameters.

[0020] S4: Solve for analytical solutions of grinding parameters that satisfy the target hysteresis. Combine the design parameter equations from step 2 with the hysteresis equations from step 3. To find a unique solution for the five grinding parameters, the angle between the cone shaft and the drill shaft is... Designated as the initial adjustable variable. Through mathematical transformations, the final result is obtained when... Given the other four grinding parameters , , , Regarding design parameters ( , , , , )and The explicit analytical expression of σ. Substituting this analytical solution into the hysteresis equation, the theoretical actual hysteresis h corresponding to the current σ value can be calculated; An iterative approximation method is used: the calculated theoretical lag is compared. Lag of target design If the error exceeds the allowable range, adjust accordingly. Values, recalculate a set of sharpening parameters and corresponding values. until and The difference meets the accuracy requirements. Since the core calculations are all explicit analytical expressions, this iterative process converges extremely quickly and can be completed instantaneously.

[0021] S5: Manufacturing and verification based on the solved grinding parameters The final determined target lag amount A set of sharpening parameters ( , , , , The drill bit is fed into a CNC tool grinder, and the movement trajectory of the grinding wheel relative to the drill bit stock is controlled to grind a curved conical rake face with a preset hysteresis. After machining, the actual hysteresis at the drill tip's apex angle, chisel edge angle, circumferential clearance angle, cutting edge offset, and tail root turning point can be detected by a tool measuring instrument to verify its consistency with the design value.

[0022] A twist drill employing the above-described design method has a conical flank face at its drill tip and a curved cutting edge as its main cutting edge. Its key feature is that the drill tip's tail root inflection point possesses a positive hysteresis amount, precisely designed and machined to ensure this hysteresis amount h. The designed value of this hysteresis amount h is preferably 0.2 mm to 2.5 mm, more preferably 0.5 mm to 1.5 mm, to ensure sufficient clearance between the flank face and the bottom of the hole under various feed conditions, thus avoiding interference.

[0023] The complete implementation process is as follows: After the program starts, it first enters the integrated parameter input interface. This interface is the human-machine interaction window of the CNC system of this invention. Its essential difference from the traditional twist drill programming interface is that, in addition to requiring only input of conventional parameters such as the apex angle, clearance angle, and chisel edge angle in the traditional interface, a new input item, "hysteresis h0," is forcibly added. The operator must simultaneously input the drill diameter D and the half-apex angle. Horizontal blade angle Circumferential rear angle Blade offset helix angle blade angle And the target hysteresis h0, which is the core of this invention. The system automatically completes unit unification and basic verification, marking the transformation from traditional empirical design that "ignores hysteresis" to precise and controllable design that "takes hysteresis as the guide"; After parameter input, the system enters the tool grinding parameter calculation stage based on the new geometric model. Traditional CNC systems, when calculating the grinding parameters for conical surfaces, only rely on conventional parameters such as the apex angle, clearance angle, and chisel edge angle. Their internal mathematical models never include hysteresis variables, leading to random fluctuations in the hysteresis of the ground drill tip, sometimes positive and sometimes negative (backward tilt). The core algorithm of this invention's CNC system integrates a new geometric model, as described in the background art, that includes hysteresis constraints. The system calls the embedded solution engine (which encapsulates the logic of functions such as `solveSharpenPara`), using the target hysteresis h0 as a hard constraint, and simultaneously solves other geometric equations to calculate in real time the five grinding parameters that uniquely guarantee the value of h0: inter-axis angle... Conical half-angle and cone apex offset , , This step represents a crucial leap for the invention from "design concept" to "numerical control implementation." Next, the system enters the toolpath generation and post-processing stage. Using the grinding parameters calculated in the previous step, which already contain the target hysteresis information, the system calls the path planning module (whose logic corresponds to the solvePath function) to calculate a series of precise position and orientation coordinates of the grinding wheel center in the machine tool coordinate system. The trajectory formed by these coordinate points is something that traditional methods cannot generate due to the lack of a hysteresis model. Finally, the system uses a dedicated post-processor to convert these coordinate points into G-code programs executable by specific CNC grinding machines (such as five-axis CNC tool grinders). At this point, a machining program with a preset hysteresis as the absolute target is ready. See Figure 2This implementation further details the core algorithm flow for hysteresis control within the CNC system. When the operator inputs the target hysteresis h0 on the interface, the CNC system's core processor does not directly call a fixed grinding subroutine as in traditional systems, but instead initiates a dynamic parameter solving—trajectory planning chain. First, the system calculates the hysteresis based on h0 and the helix angle... blade angle Calculate the theoretical included angle Subsequently, h0, Together with other design parameters, these are substituted into the patented geometric equations of this invention for solution. This process typically converges quickly, directly outputting a set of grinding parameters. Subsequently, the path planner uses these parameters to generate the grinding wheel's motion trajectory. To cope with extreme parameter combinations, the system also integrates an iterative optimizer containing bisection logic as a robustness guarantee, ensuring that feasible motion commands can be calculated for the CNC axis under any circumstances, thereby rigidly guaranteeing the realization of hysteresis at the physical level. Figure 3 and Figure 4 The comparison visually demonstrates the decisive impact of hysteresis control on machining results and tool performance. Figure 3 The diagram shows the profile of the drill tip back face (red dashed line) of a traditional uncontrolled grinding method. Its tail root turning point is obviously "backward" (the hysteresis is negative). When this type of drill is drilling, the back face will interfere with and scrape against the bottom of the hole, resulting in abnormally increased cutting force, severe heat generation, poor hole wall quality and short tool life. Figure 4 The image shows the profile of the drill tip's rake face (solid green line) after grinding using the CNC method of this invention and setting a positive hysteresis. Its tail root pivot point shifts smoothly backward, creating a reasonable chip removal and cooling space. As a result, the drill bit produces a smooth hole wall, stable cutting, and a significantly extended lifespan. The comparison of these two images powerfully demonstrates that introducing and controlling the "hysteresis" parameter into the CNC system is not simply a matter of increasing the parameter, but rather solves a long-standing technical pain point, bringing about a qualitative leap in tool performance.

[0024] Specific numerical calculation examples To fully verify the universality and computational accuracy of the design method of this invention for drill bits of different specifications, a complete design example for large-diameter drill bits is provided. This example demonstrates the entire process from setting design objectives, performing model calculations to verifying results. 1. Setting Design Goals The goal of this example is to design a diameter The core design parameters for the drill bit tip are set as follows: Geometric parameters: diameter (radius helix angle The included angle of the blade; Cutting geometry parameters: half-apex angle Horizontal blade bevel angle, circumferential back angle Blade offset ; Core control objective: Design lag ; 2. Model Calculation Process and Key Intermediate Results The above design parameters are input into the mathematical model and calculation program established in this invention. The calculation process first determines the drill angle based on the cutting edge offset and radius. The axial structural rear angle is obtained by converting the circumferential rear angle and the half-apex angle. Subsequently, based on the design lag... helix angle Angle with blade Calculate the included angle of the projection corresponding to the turning point of the tail root. ; To find a unique set of grinding parameters that satisfies all design conditions, the interaxial angle is... Used as an iteration variable. Initial value set. The program performs its initial calculation. Based on the analytical model of this invention, it instantly completes the solution and outputs the following key results; Calculated sharpening parameters: A set of defined sharpening parameters (including the half-cone angle) was obtained. and three offsets ); Predicted geometric coordinates: The axial coordinates of the outer edge turning point (highest point of the blade) are calculated to be approximately -3.168 mm, and the axial coordinates of the tail root turning point (lowest point of the blade) are approximately -4.119 mm. Actual hysteresis: The difference between the two coordinates is the actual hysteresis predicted by the model, h = 0.951 mm; 3. Results Analysis and Verification Accuracy analysis: The actual hysteresis h = 0.951 mm obtained from the first iteration calculation is consistent with the design target. The absolute error was 0.049 mm, and the relative error was about 4.9%, which shows that even on the first attempt, the model was able to give prediction results that were very close to the design target, verifying the accuracy of the mathematical model itself. Optimization capability: If higher precision is required for engineering applications, the current error can be used as feedback to adjust the inter-axis angle. Fine-tuning is performed (e.g., adjusting to around 6.7°), and the calculation is recalculated. Since the entire calculation process is based on an explicit analytical formula, each iteration is completed within milliseconds, which can quickly bring the predicted hysteresis to converge to arbitrarily close to the design target (e.g., error less than 0.01 mm), fully demonstrating the efficiency and controllability of the method of this invention; Physical meaning verification: The calculated actual hysteresis h=0.951mm is a positive value and the value is significant (greater than 0.2mm). This theoretically ensures that the machining drill tip has sufficient clearance at the tail root turning point, fundamentally avoiding the "backward tilting" phenomenon and meeting the core purpose of the invention. Integration with actual machining: The finalized set of grinding parameters can be directly used to guide CNC grinding. After machining, the axial coordinates of the highest and lowest points of the cutting edge are measured using measuring instruments. The measured difference will closely match the model prediction (approximately 0.951 mm in this example), thus verifying the design objectives at both theoretical and practical levels.

[0025] This example demonstrates the complete "goal setting - model solving - verification and optimization" process of this invention through the design calculation of a 14mm diameter drill bit. The results show that the method established in this invention can efficiently and accurately solve for machining parameters that meet the preset hysteresis requirements for curved-edge conical drill tips of different specifications, achieving precise control of the hysteresis from design intent to finished product, and solving the engineering problem of back face warping.

[0026] The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

[0027] Although this document uses a considerable amount of technical terms, the possibility of using other terms is not excluded. These terms are used merely for the convenience of describing and explaining the essence of the invention; interpreting them as any additional limitation would be contrary to the spirit of the invention.

Claims

1. A method for designing a conical drill tip with controllable hysteresis, characterized in that, Includes the following steps: S1: Establish a coordinate system and mathematical model. With the center of the drill bit end face as the origin, establish a coordinate system for the drill tip structure, where... The axis coincides with the drill bit axis, defining the drill bit radius. helix angle The central angle corresponding to the blade width semi-apex angle Horizontal blade angle , structural circumference rear angle Blade offset and target lag And establish the spatial surface equation of the conical rake face; S2: Establish the correlation equation between design parameters and grinding parameters, and derive the half-apex angle. Horizontal blade angle Circumferential rear angle With five grinding parameters—the angle between the taper axis and the drill axis. Half cone angle Cone apex offset component , , A system of mathematical equations relating the two; S3: Incorporate hysteresis as a core design objective into the solution system, based on the helix angle. The central angle corresponding to the blade width and target lag Calculate the angle ω between the projections of the tail root turning point B and the outer edge turning point A onto the end plane, and establish the coordinates of the tail root turning point and the hysteresis. Relationship; S4: Solve for the grinding parameters that satisfy the target hysteresis, using the angle between the conical shaft and the drill shaft. Using the above equations as iterative variables, the lag quantity satisfying the target value is obtained by solving the system of equations simultaneously using the iterative approximation method. Five sets of sharpening parameters , , , , ; S5: Based on the solved grinding parameters, CNC machining is performed. The solved grinding parameters are input into the CNC tool grinder to generate the grinding wheel motion trajectory and grind a curved conical back face with a preset hysteresis.

2. The method for designing a conical drill tip with controllable hysteresis according to claim 1, characterized in that, In step S1, the equation of the conical rake face in its own coordinate system is: ; Transform it to the drill tip structure coordinate system through coordinate rotation. In this process, implicit equations are formed.

3. The method for designing a conical drill tip with controllable hysteresis according to claim 1, characterized in that, In step S2, the bevel angle of the transverse blade By simultaneously solving the spatial surface equations of the left and right flank faces, the projection curve of their intersection line onto the drill bit end plane is obtained, and the tangent direction of this projection curve at the origin is calculated. The angle between the axes is obtained.

4. The method for designing a conical drill tip with controllable hysteresis according to claim 1, characterized in that, In step S2, the half-apex angle An approximate method is used to solve the problem, namely, using a plane passing through the outer edge turning point A and parallel to the structural base plane (i.e., The half-apex angle is approximately defined by the tangent direction at the intersection line of the blade face and the back face.

5. The method for designing a conical drill tip with controllable hysteresis according to claim 1, characterized in that, In step S2, the axial structural rear angle The solution formula is: ; Where A is the outer edge turning point, and the axial structural rear angle is... The rear angle of the structural circumference specified in the design Through geometric transformation relationships Related.

6. The method for designing a conical drill tip with controllable hysteresis according to claim 1, characterized in that, In step S3, the formula for calculating the angle ω between the projections of the tail root turning point B and the outer edge turning point A onto the end plane is: ; The coordinate expression of the tail root turning point B is: ; Where t is the drill tip height. λ represents the actual lag, and λ is the center angle.

7. The method for designing a conical drill tip with controllable hysteresis according to claim 1, characterized in that, In step S4, when solving for the grinding parameters using the iterative approximation method, the calculated theoretical hysteresis is used. and target lag The difference is used as the convergence criterion, and the iteration terminates when the difference is less than the preset error threshold.

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