Grinding method for screw tap rear surface based on constant clearance angle and cutting edge line constraint

Abstract

The application discloses a screw tap point tap rear surface grinding method based on constant clearance angle and cutting edge line constraint, and specifically is: a screw tap point tap rear surface geometric parameter model is established, key geometric parameters such as rear surface clearance angle and cutting edge line are defined; the space pose parameters of a standard grinding wheel for grinding the rear surface and the grinding wheel attitude are defined, a translation matrix, a rotation matrix and a grinding wheel kinematics model between the grinding wheel coordinate system and the workpiece coordinate system are established, and unified description of the grinding wheel grinding movement is realized; based on the cutting edge line constraint and the conjugate surface theory, a contact constraint relationship between the grinding wheel surface normal vector and the rear surface normal vector is established, and an analytical solution method of the grinding wheel attitude parameters and the position parameters is derived; under the condition of given swing angle and grinding parameters, the accurate solution of the rear surface grinding wheel grinding pose meeting the constant clearance angle requirement is realized. The application can realize high-precision grinding processing of the screw tap point tap rear surface, and has good accuracy, stability and engineering application value.

Description

Technical Field

[0001] This invention belongs to the field of precision grinding of CNC cutting tools, and specifically relates to a grinding method for the back face of a screw tip tap based on constant back angle and cutting edge line constraint. Background Technology

[0002] Spiral taps possess advantages such as high structural strength, low tapping friction and torque, high machining accuracy, and high efficiency, making them crucial cutting tools for internal thread machining in aerospace, automotive, and equipment manufacturing industries. In their structure, the flank face directly determines the distribution of the cutting edge's clearance angle, the strength of the cutting edge line, and the friction state during cutting, significantly impacting tapping torque, machining accuracy, and tool life. Especially under conditions of high-efficiency precision tapping, a well-designed flank face structure can not only reduce cutting friction and heat but also improve the strength of the cutting edge line and cutting stability. Therefore, the quality of its grinding process is critical to the overall cutting performance of the tap.

[0003] Compared to end mills, taps and other hole-machining tools operate in a narrower and more enclosed cutting space, placing higher demands on tool profile accuracy, clearance angle distribution, and cutting edge quality. High-performance taps not only require reliable chip breaking and removal capabilities but also must ensure the clearance angle accuracy and cutting edge transition quality of the flank face. However, the complex structure of the tap flank face limits the accurate description of its spatial structure and cutting edge morphology. Furthermore, existing grinding processes have limitations in achieving uniform clearance angle distribution and cutting edge integrity, further increasing the difficulty of flank face grinding process design. In addition, the grinding trajectory and grinding posture directly affect the clearance angle distribution and cutting edge quality of the flank face; improper parameter settings can easily lead to grinding interference and damage to adjacent cutting edges. Therefore, establishing a standard grinding wheel kinematic model with the clearance angle and cutting edge as constraints, and accurately solving the grinding wheel posture, is crucial for the precision grinding of screw-tip taps. Therefore, it is necessary to conduct in-depth research on the grinding trajectory and posture design methods of the flank face under complex cutting edge constraints in order to ensure the accuracy of the clearance angle, the quality of the cutting edge, and the smooth transition of the flank face, thereby improving the overall cutting performance and service life of the screw tip tap.

[0004] The flank grinding process mainly refers to the grinding trajectory and posture of the grinding wheel during the flank grinding of cutting tools. It directly affects the clearance angle accuracy, flank surface quality, and cutting edge quality of the tool, thus influencing the overall cutting performance and service life of the tool. It is a crucial step in tool grinding. Currently, scholars both domestically and internationally have conducted extensive research on flank grinding processes for tools with different morphologies, covering aspects ranging from geometric modeling to motion error compensation.

[0005] Regarding the geometric modeling and grinding pose solving of the flank face of end mills, Li Guochao analyzed the structure and grinding process of the flank face of the peripheral cutting edge, established three types of flank faces: planar, eccentric, and concave, and presented grinding pose solving models for the grinding wheel of these three types of flank faces. Subsequently, Liu Jianjun et al. established a mathematical model of the end-cutting edge line of a circular-head end mill and studied the grinding process of the end-cutting flank face. They proposed a method for calculating the motion trajectory of the grinding wheel and the tool axis vector, which can improve the manufacturing accuracy of the tool and reduce the design cycle. Liu Meng et al., combining the kinematic structure of a five-axis CNC grinding machine, realized the mapping from the geometric model to the machine tool interpolation command for the grinding pose of the planar flank face of a right-angle end mill. The above studies respectively focused on the geometric modeling and grinding pose solving of the flank faces of the peripheral and end-cutting edges of end mills, but neglected the problem of the non-smooth connection between the peripheral and end-cutting edge lines and the problem of the flank face not being able to transition smoothly due to drastic changes in grinding posture. To address this issue, Han et al., considering the structural characteristics of the off-center teeth and inwardly inclined ends of arc-head end mills, constructed a cutting line model with a smooth connection between the peripheral and end cutting lines based on the method of intersecting the plane and the arc rotation surface, and derived the tool path for flank grinding. Tang Jun et al. studied the grinding process of the eccentric flank face of the peripheral cutting edge of arc-head and ball-end end mills, and proposed a trajectory calculation method for continuous grinding of the eccentric flank face of end mills using parallel grinding wheels. Kim et al., by studying the mapping relationship between tool geometry and grinding wheel geometry and pose parameters, proposed an iterative search method to obtain the grinding wheel geometry and pose in the grinding of the flank face of end mills, which greatly improved the solution calculation efficiency. For the more complex flank face of conical end mills, Yang et al. discretized the grinding process of the peripheral cutting edge of the conical end mill into a finite cylindrical end mill grinding process, and proposed a grinding wheel trajectory generation method for four-axis grinding of the flank face.

[0006] With increasing demands for grinding precision, error accumulation and dynamic compensation during the grinding process have become a research hotspot for many scholars. Regarding grinding wheel wear error modeling, Ma Yuhao et al. and Zhang Peishuo et al. proposed grinding trajectory compensation methods for grinding wheel wear by analyzing the mapping relationship between grinding wheel profile wear and the geometric errors generated by the cam profile, effectively reducing the impact of grinding wheel wear on the grinding process. Liu et al., focusing on the grinding process of helical grooves on end mills after grinding wheel wear, compensated for the grinding wheel grinding posture by analyzing the boundary conditions affected by grinding wheel wear during helical groove grinding and constructing a functional relationship between helical groove parameters and the worn grinding wheel posture. To further improve the real-time performance and intelligence of compensation, Liu Qingtao et al., based on the structure of the cylindrical grinding machine and the machining characteristics of the grinding wheel, proposed a machine tool interpolation model considering grinding wheel wear, improving machining accuracy by correcting the tool position coordinates. Chen Kang et al., from a data-driven perspective, proposed a grinding wheel wear prediction model based on the grey relational method by recording the changes in the outer diameter of the grinding wheel during the chamfering step, achieving predictive compensation for the chamfering step. These studies have significantly reduced the impact of machining wear on machining accuracy, providing important support for high-precision machining of complex tools.

[0007] In summary, existing flank grinding processes are mainly designed for conventional cutting tools such as end mills and drills, whose cutting edges are mostly helical lines of cylinders or cones. However, the cutting edge of a screw-tip tap is an irregular spatial curve formed by the intersection of the screw tip flute and the cutting cone surface. This makes it impossible for existing flank grinding methods to achieve radial grinding of conical flanks with complex cutting edge constraints, resulting in uneven distribution of the clearance angle. Furthermore, under conditions of dense cutting edge count, interference with adjacent cutting edges cannot be effectively avoided, leading to easy damage to the cutting edge and severely limiting the cutting performance of screw-tip taps. Summary of the Invention

[0008] To address the problems existing in the prior art, this invention provides a method for grinding the back face of a screw tip tap based on a constant back angle and cutting edge line constraint.

[0009] The present invention provides a method for grinding the back face of a screw tip tap based on a constant clearance angle and cutting edge line constraint, comprising the following steps:

[0010] Step 1: Define the grinding posture of the grinding wheel and model its kinematics.

[0011] (1) Define the back face parameters.

[0012] First, define the parameters of the flank face of the screw tap; point P e and P ed These are the starting point and ending point of the flank face profile, respectively, while curve P... e P edThis is called the flank profile curve; the back angle of the flank profile section is defined as α2, where α2 is the angle passing through the starting point P of the flank profile section. e The tangent vector c of the circle t The profile of the flank face at the starting point P e The tangent vector r at point t The angle between them.

[0013] According to the definition of the back face, the back angle α2 is expressed as:

[0014] (1)

[0015] Let point P be the cutting edge line. e Coordinate P e =[x pe , y pe , z pe If point P is an integer, then point P is an integer. e The angle θ between the line connecting the center of the circle and the positive direction of the axis Xw p =arctan(y pe / x pe ), vector c t and r t They are represented as follows:

[0016] (2)

[0017] (3)

[0018] (2) Definition of the tool face posture after grinding with a grinding wheel.

[0019] The flank face is ground by means of the cutting edge line along the cutting cone of the screw tip tap. The grinding position and attitude of the grinding wheel are defined by the pose parameters dx, dy, dz, λ1, δ; dx, dy, dz are the centers O of the grinding wheel coordinate system, respectively. Gr To the tool coordinate system X W Y W Z W The distance is T, then the translation matrix T from the grinding wheel coordinate system to the workpiece coordinate system is... Gr-W Represented as:

[0020] (4)

[0021] Point P e Let P be any point on the cutting edge line; define the grinding edge line point P. e The grinding speed direction vector at point v is t Its direction vector l of the generatrix passing through that point p The included angle is the swing angle λ1, and the grinding speed direction at the grinding point is the grinding wheel axis X. Gr1 The direction, i.e., XGr1 Parallel to v t And Y Gr1 Then it is the point P of the over-grind cutting edge. e The direction of the normal vector of the tangent plane; grinding wheel coordinate system O Gr -X Gr Y Gr Z Gr From coordinate system O Gr1 -X Gr1 Y Gr1 Around the coordinate axis X Gr1 The rotation angle δ is obtained, therefore the grinding wheel coordinate system O Gr -X Gr Y Gr Z Gr The rotation matrix R for transformation to the workpiece coordinate system WCS Gr-W Represented as:

[0022] (5)

[0023] In the formula, κ is the half-cone angle of the cutting cone, and the rotation matrix is... , , , They are respectively:

[0024] (6)

[0025] (7)

[0026] (8)

[0027] (9)

[0028] (3) Modeling of the kinematics of grinding wheel.

[0029] Given the translation matrix T from the grinding wheel coordinate system to the workpiece coordinate system. Gr-W and rotation matrix R Gr-W The transformation matrix M from the grinding wheel coordinate system GCSR to the workpiece coordinate system WCS Gr-W Represented as:

[0030] (10)

[0031] Any point S on the rotating surface of a standard grinding wheel G (h, ψ) is represented as:

[0032] (11)

[0033] According to equations (10) and (11), the motion trajectory of any point on the rotating surface of the grinding wheel in the workpiece coordinate system, i.e., the kinematic model of the grinding wheel, is expressed as:

[0034] (12)

[0035] Step 2: Solve the position of the grinding wheel on the back face.

[0036] Any point P on the cutting edge line of the screw tap e In WCS, this is further represented as:

[0037] (13)

[0038] In the formula:

[0039] (14)

[0040] Based on the vector v t The definition is that the vector v corresponding to any point on the cutting edge line is... t The positive direction unit vector V of the coordinate axis Zw Zw =[0,0,1,0] T In WCS, coordinate transformation is described as follows:

[0041] (15)

[0042] (16)

[0043] In the formula , , These are the coordinate axes Z and Z respectively. W Y W X W The rotation matrix; based on θ p Definition of θ p =arctan(y Pe (u) / x Pe (u)).

[0044] According to equation (2), the cutting edge point P of the flank face profile is... e The back face tangent vector r at the location t The description of the flank normal vector n at the cutting edge point of the flank profile under any axial section. r By r t With v t_W The cross product is obtained, and it is represented in WCS as:

[0045] (17)

[0046] Normal vector nr It is further represented as:

[0047] (18)

[0048] The normal vector of any point on the surface of the grinding wheel is represented as:

[0049] (19)

[0050] In the formula, m = 1 / √(1 + tan 2 (k G ));n G_Gr The subscript Gr indicates that the representation under GCSR is considered;

[0051] Based on equation (19), the normal vector N at any point on the surface of the grinding wheel during the movement of the grinding wheel's tool face after grinding can be further calculated. W In WCS, this is represented as:

[0052] (20)

[0053] Since the standard grinding wheel grinds the flank face along the cutting edge to ensure the integrity of the cutting edge, any point on the cutting edge is a grinding point in contact with the grinding wheel. According to the conjugate surface theory, during the flank face grinding process, the grinding wheel surface and the cutting edge curve should have a common normal at the contact point, i.e., n r =N W (λ1, δ, h, ψ) and G W (dx, dy, dz, λ1, δ, h, ψ)=P e (u), based on the conditions, the following expression is listed:

[0054] (twenty one)

[0055] (twenty two)

[0056] For ease of calculation, equation (22) is further expressed as:

[0057] (twenty three)

[0058] By matrix transformation, the right-hand side of equation (23) is rotated. , , Moving the equation to the left side, we obtain the following equation:

[0059] (twenty four)

[0060] Right now:

[0061] (25)

[0062] The expression for parameter ψ obtained from equation (25) is as follows:

[0063] (26)

[0064] Based on equation (25), the following relationship can be derived:

[0065] (27)

[0066] (28)

[0067] In the formula, V1 and V2 are respectively:

[0068] (29)

[0069] The results are obtained from equations (27) and (28):

[0070] (30)

[0071] According to equation (21), the position parameters dx, dy, and dz of the grinding wheel trajectory are expressed as:

[0072] (31)

[0073] In the formula:

[0074] (32)

[0075] Given the parameters λ1, h, and u, substitute them into equation (26) to obtain the parameter ψ, then substitute the parameter ψ into equation (30) to obtain the parameter δ, substitute the obtained ψ and δ into equation (31), and combine with equation (32) to solve for the grinding wheel position parameters dx, dy, and dz; complete the calculation and solution of the grinding wheel grinding posture of the screw tip tap rake face based on constant back angle and cutting edge line constraint.

[0076] The beneficial technical effects of this invention compared to the prior art are as follows:

[0077] (1) Considering the complexity of the flank face structure and the irregular spatial characteristics of the cutting edge line, this invention constructs a standard grinding wheel kinematic model based on constant flank angle and cutting edge line constraints. This solves the problem that traditional methods cannot simultaneously achieve flank angle consistency and cutting edge line accuracy, reveals the mapping relationship between the grinding wheel posture and flank angle constraints, and improves the modeling and grinding accuracy of the flank face.

[0078] (2) This invention establishes a full integration of the standard grinding wheel kinematic model and the flank face design parameter model. It achieves more reliable and accurate grinding wheel trajectory and attitude calculation, and improves the practicality and machinability of the method.

[0079] (3) Based on the theory of conjugate surfaces, this invention proposes a method for solving the grinding wheel posture considering the back angle of the cross section and the constraints of the cutting edge line. This method can adaptively obtain the corresponding grinding wheel posture according to different back face structural characteristics, which enhances the adaptability of back face grinding, thereby ensuring the integrity of the cutting edge line and the accuracy of the back angle.

[0080] (4) The algorithm was verified through simulation and actual grinding experiments. The results show that the relatively small error is negligible, which ensures the good grinding quality of the back face and proves the accuracy and effectiveness of the proposed algorithm for grinding the back face of the screw tip tap based on constant back angle and cutting edge line constraint. Attached Figure Description

[0081] Figure 1 This is a schematic diagram illustrating the definition of the back face of the screw tip tap of the present invention.

[0082] Figure 2 This is a schematic diagram defining the back face of another type of screw-tip tap.

[0083] Figure 3 This is a schematic diagram of the tool face posture after grinding.

[0084] Figure 4 This defines the standard grinding wheel surface geometry.

[0085] Figure 5 The result is a simulation of the machining of the back face.

[0086] Figure 6 , Figure 7 , Figure 8 Measurements were taken for the simulation experiment of the flank face (wherein, Figure 6 Z W =0 mm measurement section, Figure 7 Z W =2 mm measuring section, Figure 8 Z W =4 mm measurement section).

[0087] Figure 9 , Figure 10 For the actual grinding and testing environment of the screw tip groove (wherein, Figure 9 : Screw tip groove grinding device Figure 10 (Screw tip groove structure parameter measuring device).

[0088] Figure 11 , Figure 12 , Figure 13For actual experimental measurement of the flank face (where, Figure 11 Z W =0 mm measurement section, Figure 12 Z W =2mm measuring section, Figure 13 Z W =4 mm measurement section). Detailed Implementation

[0089] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0090] The present invention provides a method for grinding the back face of a screw tip tap based on a constant clearance angle and cutting edge line constraint, comprising the following steps:

[0091] Step 1: Define the grinding posture of the grinding wheel and model its kinematics.

[0092] (1) Define the back face parameters.

[0093] First, define the flank parameters of the screw tap, point P. e and P ed These are the starting point (cutting edge point) and ending point of the flank face profile, respectively, while curve P... e P ed This is called the flank face curve. In practical engineering applications, the flank face typically has two types of geometric definitions, the first type ( Figure 1 Define the back angle of the flank profile as α2, where α2 is the angle at the starting point P of the flank profile. e The tangent vector c of the circle t The profile of the flank face at the starting point P e The tangent vector r at point t The included angle between them. The second type ( Figure 2 The profile of the flank face is defined by defining the angle μ and the corresponding radial drop dμ. The flank face studied in this invention adopts the first type of definition for the flank face profile.

[0094] According to the definition of the back face, the back angle α2 is expressed as:

[0095] (1)

[0096] Let point P be the cutting edge line. e Coordinate P e =[x pe , y pe , z pe If point P is an integer, then point P is an integer. e The angle θ between the line connecting the center of the circle and the positive direction of the axis Xw p =arctan(y pe / xpe ), vector c t and r t They are represented as follows:

[0097] (2)

[0098] (3)

[0099] (2) Definition of the tool face posture after grinding with a grinding wheel.

[0100] To describe the grinding motion of the rake face of a screw-tip tap, the grinding wheel posture and related posture parameters are defined, such as... Figure 3 As shown.

[0101] The flank face is ground along the cutting edge of the screw-tip tap. The grinding wheel position and orientation are defined by pose parameters (dx, dy, dz, λ1, δ); dx, dy, and dz are the centers O of the grinding wheel coordinate system, respectively. Gr To the tool coordinate system X W Y W Z W The distance is T, then the translation matrix T from the grinding wheel coordinate system to the workpiece coordinate system is... Gr-W Represented as:

[0102] (4)

[0103] like Figure 3 As shown, point P e Let P be any point on the cutting edge line; define the grinding edge line point P. e The grinding speed direction vector at point v is t Its direction vector l of the generatrix passing through that point p The included angle is the swing angle λ1. Since this invention uses a standard grinding wheel to grind the back face, the grinding speed direction at the grinding point is the grinding wheel axis X. Gr1 The direction, i.e., X Gr1 Parallel to v t And Y Gr1 Then it is the point P of the over-grind cutting edge. e The direction of the normal vector of the tangent plane; grinding wheel coordinate system O Gr -X Gr Y Gr Z Gr From coordinate system O Gr1 -X Gr1 Y Gr1 Around the coordinate axis X Gr1 The rotation angle δ is obtained, therefore the grinding wheel coordinate system O Gr -X Gr Y Gr Z GrThe rotation matrix R for transformation to the workpiece coordinate system WCS Gr-W Represented as:

[0104] (5)

[0105] In the formula, κ is the half-cone angle of the cutting cone, and the rotation matrix is... , , , They are respectively:

[0106] (6)

[0107] (7)

[0108] (8)

[0109] (9)

[0110] (3) Modeling of the kinematics of grinding wheel.

[0111] Given the translation matrix T from the grinding wheel coordinate system to the workpiece coordinate system. Gr-W and rotation matrix R Gr-W The transformation matrix M from the grinding wheel coordinate system GCSR to the workpiece coordinate system WCS Gr-W Represented as:

[0112] (10)

[0113] Depend on Figure 4 It can be seen that any point S on the rotating surface of the standard grinding wheel G (h, ψ) is represented as:

[0114] (11)

[0115] According to equations (10) and (11), the motion trajectory of any point on the rotating surface of the grinding wheel in the workpiece coordinate system, i.e., the kinematic model of the grinding wheel, is expressed as:

[0116] (12)

[0117] Step 2: Solve the position of the grinding wheel on the back face.

[0118] Any point P on the cutting edge line of the screw tap e In WCS, this is further represented as:

[0119] (13)

[0120] In the formula:

[0121] (14)

[0122] Based on the vector v t The definition is that the vector v corresponding to any point on the cutting edge line is... t The positive direction unit vector V of the coordinate axis Zw Zw =[0,0,1,0] T In WCS, coordinate transformation is described as follows:

[0123] (15)

[0124] (16)

[0125] In the formula , , These are the coordinate axes Z and Z respectively. W Y W X W The rotation matrix; based on θ p Definition of θ p =arctan(y Pe (u) / x Pe (u)).

[0126] According to equation (2), the cutting edge point P of the flank face profile is... e The back face tangent vector r at the location t The description of the flank normal vector n at the cutting edge point of the flank profile under any axial section. r By r t With v t_W The cross product is obtained, and it is represented in WCS as:

[0127] (17)

[0128] Normal vector n r It is further represented as:

[0129] (18)

[0130] The normal vector of any point on the surface of the grinding wheel is represented as:

[0131] (19)

[0132] In the formula, m = 1 / √(1 + tan 2 (k G ));n G_Gr The subscript Gr indicates that the representation is considered under GCSR;

[0133] Based on equation (19), the normal vector N at any point on the surface of the grinding wheel during the movement of the grinding wheel's tool face after grinding can be further calculated. W In WCS, this is represented as:

[0134] (20)

[0135] Since the standard grinding wheel grinds the flank face along the cutting edge to ensure the integrity of the cutting edge, any point on the cutting edge is a grinding point in contact with the grinding wheel. According to the conjugate surface theory, during the flank face grinding process, the grinding wheel surface and the cutting edge curve should have a common normal at the contact point, i.e., n r =N W (λ1, δ, h, ψ) and G W (dx, dy, dz, λ1, δ, h, ψ)=P e (u), based on the conditions, the following expression is listed:

[0136] (twenty one)

[0137] (twenty two)

[0138] For ease of calculation, equation (22) is further expressed as:

[0139] (twenty three)

[0140] By matrix transformation, the right-hand side of equation (23) is rotated. , , Moving the equation to the left side, we obtain the following equation:

[0141] (twenty four)

[0142] Right now:

[0143] (25)

[0144] The expression for parameter ψ obtained from equation (25) is as follows:

[0145] (26)

[0146] Based on equation (25), the following relationship can be derived:

[0147] (27)

[0148] (28)

[0149] In the formula, V1 and V2 are respectively:

[0150] (29)

[0151] The results are obtained from equations (27) and (28):

[0152] (30)

[0153] According to equation (21), the position parameters dx, dy, and dz of the grinding wheel trajectory are expressed as:

[0154] (31)

[0155] In the formula:

[0156] (32)

[0157] Given the parameters λ1, h, and u, substitute them into equation (26) to obtain the parameter ψ, then substitute the parameter ψ into equation (30) to obtain the parameter δ, substitute the obtained ψ and δ into equation (31), and combine with equation (32) to solve for the grinding wheel position parameters dx, dy, and dz; complete the calculation and solution of the grinding wheel grinding posture of the screw tip tap rake face based on constant back angle and cutting edge line constraint.

[0158] Step 3: Simulation and actual grinding experiments.

[0159] (1) Simulated grinding experiment:

[0160] To verify the accuracy and practicality of the standard grinding process algorithm for the flank face of the screw tip tap proposed in this invention, and to provide a basis for actual machining verification, the grinding process algorithm proposed above will be used here. By inputting the given screw tip structure design parameters, screw tip groove grinding process parameters, and flank face grinding process parameters, the tool position executable file will be calculated and output. This file will then be imported into Vericut simulation software for grinding simulation. The correctness of the algorithm will be verified by measuring the flank face clearance angle parameters.

[0161] This invention uses a certain type of screw tip tap as an example for processing verification. The specific parameters of the tool are shown in Table 1. In order to facilitate experimental observation of the overall contour of the back face and measurement of the back angle parameters, it is necessary to first process the screw tip groove and the straight groove before processing the back face. The grinding process parameters of the screw tip groove are shown in Table 2.

[0162] Table 1 Design parameters of screw tip structure for screw tap

[0163]

[0164] Table 2 Grinding process parameters for screw tip groove

[0165]

[0166] Taking a cylindrical grinding wheel with a thickness of 5 mm as an example, the simulation and actual machining verification of the flank face are carried out. The grinding process parameters of the flank face and the grinding wheel parameters are shown in Table 3.

[0167] Table 3 Grinding process parameters for the flank face

[0168]

[0169] Considering the complexity of the flank face, the machinability of flank face grinding cannot be predicted before actual machining. Simulation machining has the advantages of high efficiency and low cost; therefore, simulation machining verification tests are necessary before actual machining. This invention sets the tool blank and grinding wheel parameters in the VERICUT 9.2 simulation environment, imports the calculated toolpath execution file for simulation machining, and some toolpath codes are shown in Table 4. The simulation machining results are as follows: Figure 5 As shown.

[0170] Table 4. Tool positions for flank grinding (partial)

[0171]

[0172] like Figures 6-8 As shown, it can be seen that the grinding wheel did not interfere with adjacent teeth during the grinding of the flank face. To further facilitate the measurement of whether the clearance angle of the flank face is consistent and whether the cutting edge line is not damaged, the simulated screw tip structure was respectively measured at Z... W =0 mm, Z W =2 mm, Z W The back angle and section radius were measured at a cross-section of 4 mm and compared with the design parameters. The measured cross-section is shown below. Figures 6-8 As shown in Table 5, the measurement comparison results are presented.

[0173] Table 5 Comparison of Simulation Measurement and Design Values ​​of the Back Face

[0174]

[0175] According to the data in Table 5, compared with the design values, the absolute errors of α2 and R in the simulated grinding results are 0.087° and 0.007 mm, respectively, and the relative errors are 0.870% and 0.183%, respectively. The results show that the simulation measurement results are in good agreement with the design parameter values ​​of back angle α2 and cross-sectional radius R, which preliminarily verifies the feasibility and effectiveness of the standard grinding process algorithm for the back face along the cutting edge line of the screw tip tap proposed in this invention.

[0176] (2) Actual grinding experiment:

[0177] To further verify the accuracy and feasibility of the proposed grinding algorithm for the flank face of the screw-tip tap, and to ensure machining precision, actual machining verification is required. Before actual machining, machine tool grinding simulation is also necessary. After confirming the simulation is correct, actual grinding verification of the flank face is performed on the Tianyou Chuangruan MG05 five-axis CNC tool grinder. The internal structure of the machine tool is as follows... Figure 9 As shown, the tool design parameters and process parameters used in the actual machining verification experiment are consistent with those in the flank face simulation experiment. The workpiece is made of high-speed steel, and standard grinding wheels are used for machining. Oil spraying is employed during the machining process, with the grinding wheel linear speed set at 50 m / s and the feed rate at 1500 mm / min. The machine tool NC executable file shown in Table 6 can be calculated using the flank face grinding process algorithm module and the machine tool post-program.

[0178] Table 6. NC Programs for Back Face Grinding (Partial)

[0179]

[0180] After importing the calculated NC values ​​into a CNC tool grinder, actual machining can be performed. After machining, the geometric parameters of the ground screw tip groove are measured using a PG1000 tool measuring instrument. The measuring device is as follows: Figure 10 As shown. To ensure consistency with the simulation experiment and to facilitate the measurement of the clearance angle, after the clearance face is ground, wire EDM is used to adjust the screw tip tap from the screw tip face along the axial Z-axis. W =2 mm and Z W Cut at a point equal to 4 mm. Cut at Z... W =0 mm, Z W =2 mm, Z W The measurement was performed at the cross section at 4 mm, and the measured cross section is as follows: Figures 11-13 As shown in Table 7, the comparison results between the measured values ​​and the design values ​​are as follows.

[0181] Table 7 Comparison of Actual Measurement and Design Values ​​of the Back Face

[0182]

[0183] As shown in Table 7, the absolute errors between the designed values ​​and the actual measured values ​​of α2 and R in the grinding results are 0.059° and 0.063 mm, respectively, and the relative errors are 0.590% and 1.647%, respectively. Since machine tool errors are unavoidable in actual machining experiments, there are certain errors in the back angle and the radius of the cross-section obtained from actual grinding. However, the measurement results are basically consistent with the design values ​​and can meet the accuracy requirements of actual machining, proving the correctness and effectiveness of the algorithm proposed in this invention.

Claims

1. A method for grinding the flank face of a screw tip tap based on a constant clearance angle and cutting edge line constraint, characterized in that, Includes the following steps: Step 1: Define the grinding wheel posture and model the grinding wheel kinematics: (1) Define the flank face parameters: First, define the parameters of the flank face of the screw tap; point P e and P ed These are the starting point and ending point of the flank face profile, respectively, while curve P... e P ed This is called the flank profile curve; the back angle of the flank profile section is defined as α2, where α2 is the angle passing through the starting point P of the flank profile section. e The tangent vector c of the circle t The profile of the flank face at the starting point P e The tangent vector r at point t The angle between them; According to the definition of the back face, the back angle α2 is expressed as: （1） Let point P be the cutting edge line. e Coordinate P e =[x pe , y pe , z pe If point P is an integer, then point P is an integer. e The angle θ between the line connecting the center of the circle and the positive direction of the axis Xw p =arctan(y pe / x pe ), vector c t and r t They are represented as follows: （2） （3） (2) Definition of the tool face posture after grinding with a grinding wheel: The flank face is ground by means of the cutting edge line along the cutting cone of the screw tip tap. The grinding position and attitude of the grinding wheel are defined by the pose parameters dx, dy, dz, λ1, δ; dx, dy, dz are the centers O of the grinding wheel coordinate system, respectively. Gr To the tool coordinate system X W Y W Z W The distance is T, then the translation matrix T from the grinding wheel coordinate system to the workpiece coordinate system is... Gr-W Represented as: （4） Point P e Let P be any point on the cutting edge line; define the grinding edge line point P. e The grinding speed direction vector at point v is t Its direction vector l of the generatrix passing through that point p The included angle is the swing angle λ1, and the grinding speed direction at the grinding point is the grinding wheel axis X. Gr1 The direction, i.e., X Gr1 Parallel to v t And Y Gr1 Then it is the point P of the over-grind cutting edge. e The direction of the normal vector of the tangent plane; grinding wheel coordinate system O Gr -X Gr Y Gr Z Gr From coordinate system O Gr1 -X Gr1 Y Gr1 Around the coordinate axis X Gr1 The rotation angle δ is obtained, therefore the grinding wheel coordinate system O Gr -X Gr Y Gr Z Gr The rotation matrix R for transformation to the workpiece coordinate system WCS Gr-W Represented as: （5） In the formula, κ is the half-cone angle of the cutting cone, and the rotation matrix is... , , , They are respectively: （6） （7） （8） （9） (3) Kinematic modeling of grinding wheel: Given the translation matrix T from the grinding wheel coordinate system to the workpiece coordinate system. Gr-W and rotation matrix R Gr-W The transformation matrix M from the grinding wheel coordinate system GCSR to the workpiece coordinate system WCS Gr-W Represented as: （10） Any point S on the rotating surface of a standard grinding wheel G (h, ψ) is represented as: （11） According to equations (10) and (11), the motion trajectory of any point on the rotating surface of the grinding wheel in the workpiece coordinate system, i.e., the kinematic model of the grinding wheel, is expressed as: （12） Step 2: Solving the position of the grinding wheel on the flank face: Any point P on the cutting edge line of the screw tap e In WCS, this is further represented as: （13） In the formula: （14） Based on the vector v t The definition is that the vector v corresponding to any point on the cutting edge line is... t The positive direction unit vector V of the coordinate axis Zw Zw =[0,0,1,0] T In WCS, coordinate transformation is described as follows: （15） （16） In the formula , , These are the coordinate axes Z and Z respectively. W Y W X W The rotation matrix; based on θ p Definition of θ p =arctan(y Pe (u) / x Pe (u)); According to equation (2), the cutting edge point P of the flank face profile is... e The back face tangent vector r at the location t The description of the flank normal vector n at the cutting edge point of the flank profile under any axial section. r By r t With v t_W The cross product is obtained, and it is represented in WCS as: （17） Normal vector n r It is further represented as: （18） The normal vector of any point on the surface of the grinding wheel is represented as: （19） In the formula, m = 1 / √(1 + tan 2 (k G ));n G_Gr The subscript Gr indicates that the representation under GCSR is considered; Based on equation (19), the normal vector N at any point on the surface of the grinding wheel during the movement of the grinding wheel's tool face after grinding can be further calculated. W In WCS, this is represented as: （20） Since the standard grinding wheel grinds the flank face along the cutting edge to ensure the integrity of the cutting edge, any point on the cutting edge is a grinding point in contact with the grinding wheel. According to the conjugate surface theory, during the flank face grinding process, the grinding wheel surface and the cutting edge curve should have a common normal at the contact point, i.e., n r =N W (λ1, δ, h, ψ) and G W (dx, dy, dz,λ1, δ, h, ψ)=P e (u), based on the conditions, the following expression is listed: （21） （22） For ease of calculation, equation (22) is further expressed as: （23） By matrix transformation, the right-hand side of equation (23) is rotated. , , Moving the equation to the left side, we obtain the following equation: （24） Right now: （25） The expression for parameter ψ obtained from equation (25) is as follows: （26） Based on equation (25), the following relationship can be derived: （27） （28） In the formula, V1 and V2 are respectively: （29） The results are obtained from equations (27) and (28): （30） According to equation (21), the position parameters dx, dy, and dz of the grinding wheel trajectory are expressed as: （31） In the formula: （32） Given the parameters λ1, h, and u, substitute them into equation (26) to obtain the parameter ψ, then substitute the parameter ψ into equation (30) to obtain the parameter δ, substitute the obtained ψ and δ into equation (31), and combine with equation (32) to solve for the grinding wheel position parameters dx, dy, and dz; complete the calculation and solution of the grinding wheel grinding posture of the screw tip tap rake face based on constant back angle and cutting edge line constraint.

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