A precise forming and grinding method for the tip slot of a tap based on a unified parameter geometric model

Abstract

The application discloses a precision forming grinding method for a tap screw point slot based on a unified parameterized geometric model, and particularly relates to the following steps: firstly, considering specific design parameters of an SPF and over-determined structure constraints generated by a straight slot, an accurate UPGM of the SPF is established; geometric information such as an end face profile, a blade rake angle λ, a rake angle γ and a blade length L of the SPF is comprehensively described, thereby providing a solid foundation for subsequent grinding processing; secondly, a mapping relationship between the UPGM and a SPF generatrix is disclosed, thereby realizing calculation of a spiral slot geometric driving grinding track; then, based on a linear contact conjugate theory, a forming grinding wheel profile calculation method considering a flexible grinding posture is provided; different forming grinding wheel profiles determined by initial postures are adopted, thereby realizing accurate slot shape control and precision forming grinding of the SPF. The application guarantees the SPF grinding quality of the screw point tap, has certain accuracy and effectiveness, and has strong engineering application potential.

Description

Technical Field

[0001] This invention belongs to the field of precision grinding of CNC cutting tools, and particularly relates to a precision forming grinding method for tap and screw tip grooves based on a unified parametric geometric model. Background Technology

[0002] Screw taps (such as...) Figure 1 The screw tap (as shown) boasts advantages such as high structural strength, low tapping friction and torque, high machining accuracy, and high efficiency, making it a specialized tool for internal threads in aerospace, automotive, and equipment manufacturing industries. It is an improved version of the straight flute tap, formed by machining a screw tip (SPF) with increased core thickness on one side of the straight flute's cutting edge. This ensures that the chip removal direction is consistent with the feed direction, preventing chip clogging and scratching of the machined thread. A screw tip tap typically consists of an SPF, a straight flute, and a cutting cone. Among these, the SPF is the most important structural feature, creating tightly coiled chips, expanding the chip space, and controlling the chip removal direction, significantly impacting tapping torque and accuracy.

[0003] Compared to end mills, hole-machining tools such as taps operate within a narrower cutting space, requiring more precise cutting conditions to produce threads with good profile accuracy and surface quality. Therefore, high-performance tap profiles need stringent precision to achieve reliable chip breaking, chip curling, and chip removal within the tap's limited SPF (Surface Mount Factor). However, the lack of a Unified Parametric Geometry (UPGM) model hinders the accurate description of the SPF spatial structure due to the complexity and conflict between SPF design parameters and flute structural constraints. This complicates the design of the form grinding process and leads to poor manufacturability due to differences between the design and process models. Furthermore, the wheel profile, grinding trajectory, and attitude significantly affect the final grinding accuracy of the SPF and should be flexibly adjusted to avoid grinding interference. Therefore, considering the overdetermined structural constraints generated by the specified design parameters of the SPF and flute, establishing an accurate UPGM for the SPF, and designing and calculating the wheel profile, trajectory, and attitude during form grinding based on this, is crucial for achieving precision grinding of the SPF.

[0004] Currently, considering the complex and conflicting structural constraints imposed by specific design parameters, there is limited research on unified geometric modeling of SPF (Surface Mount Factoring) for screw-tip taps, and even less research on grinding process design for SPF (including tapered sloping grooves and helical grooves). For tools such as end mills, the grinding of helical grooves has been extensively studied, providing valuable insights into grinding SPF helical grooves. For ordinary straight grooves with a zero helix angle, existing methods are effective. However, grinding tapered sloping grooves in SPF is highly complex, and previous research on process design and optimization methods using standard or shaped grinding wheels cannot be directly applied to grinding tapered straight grooves in SPF, although they can provide important insights.

[0005] Research on standard grinding wheels mainly focuses on optimizing the grinding wheel trajectory, geometric parameters, and attitude. In the grinding of helical grooves with tapered end mills, Li Yong et al. proposed a new method for optimizing grinding wheel attitude and geometric parameters, considering the overall cross-sectional curve matching error, by analyzing the sensitivity of cross-sectional parameters and the formation mechanism of the core thickness radius. Zheng Gaojun et al. proposed a grinding wheel positioning method during the grinding of helical grooves with tapered end mills, based on establishing the conjugate relationship between the grinding wheel surface and the cutting edge curve. Yang Jianping et al. proposed a method for calculating the grinding trajectory of tapered end mills on a four-axis CNC grinding machine, which discretizes the tapered end mill into several external cylindrical end mills and sequentially determines the position of the grinding wheel. In the grinding of cylindrical helical grooves, related research shows that it is difficult to determine and optimize the position and orientation of the grinding wheel given the helical groove parameters. Zhao Xianfeng et al. used a precise helical groove model to analyze in detail the influence of the grinding wheel radius, fillet radius, and taper angle on the rake angle and opening angle of the helical groove. Wang Liming et al. transformed the grinding wheel trajectory of a five-axis CNC grinding machine into a kinematic optimization model and determined the relationship between the geometric parameters of the helical groove and the grinding wheel trajectory based on envelope theory. Rababah et al. proposed a method to determine the grinding wheel position and orientation based on the designed rake angle and core radius. Ren Lei et al. and Habibi et al. established complex nonlinear equations to mathematically link the grinding wheel position with the helical groove parameters. In general, obtaining the grinding wheel position and orientation by numerically solving the above mathematical relationships is very time-consuming. Therefore, some researchers have adopted intelligent algorithms to improve the accuracy and efficiency of the calculation. Karpuschewsk et al. proposed an algorithm that can automatically search for the grinding wheel trajectory during helical groove grinding when using a standard grinding wheel to approximate the required operating profile. Li Guochao et al. used artificial intelligence algorithms to optimize the grinding wheel attitude and established a general model for calculating the grinding wheel trajectory in helical groove grinding. Fang Yang et al. proposed combining particle swarm optimization algorithm with genetic algorithm technology to optimize the grinding wheel position and orientation, thereby improving grinding accuracy and efficiency.

[0006] However, the aforementioned studies on standard grinding wheels mainly focus on grinding cylindrical helical grooves to ensure the geometric parameters of the helical groove, such as the rake angle and core radius, but may not be able to completely achieve the ideal helical groove profile and accuracy. To achieve high-precision grinding with SPF (Special Power Forecasting), fine grinding with a shaped grinding wheel is usually required. In the process of helical groove shaped grinding, calculating the grinding wheel profile based on the helical groove profile of a specified cross-section and the grinding trajectory is crucial. Chen Zhan et al. used analytical envelope and shaped geometry theory to propose a calculation method for determining the grinding wheel profile by analyzing the contact line in the helical groove grinding process. In their study, they derived the helical groove profile using envelope theory, while other researchers used conjugate contact theory, which holds that the normal contact point between the grinding wheel and the surface of the helical groove must intersect with the grinding wheel axis to determine its profile. Kang et al. established a helical groove grinding model based on contact theory, combined with differential geometry and kinematic principles. However, the establishment of the envelope equation is hindered by singular points on the grinding wheel. To solve this problem, Nguyen et al. used a special continuity equation to represent the uncertain normal direction at the singular point. Shi Zhongde et al. explored the permissible setting conditions for smooth workpiece profiles and workpiece profiles with one or more singular points. Hsieh et al. combined coordinate transformation with conjugate surface theory to characterize the grinding kinematics of helical grooves and determined the grinding wheel profile based on conjugate contact theory. Wasif et al. proposed a grinding wheel profile optimization method based on differential evolution algorithm. Mohan et al. used CAD software to simulate the contact curves during the helical groove forming grinding process.

[0007] In summary, although significant progress has been made in the calculation of wheel profile, trajectory, and attitude in helical groove grinding, there is relatively little literature on the process of conical slant groove grinding. Furthermore, the over-constrained structure and the lack of precise geometric models to characterize surface finish (SPF) pose challenges to accurate surface control in conical slant groove grinding. The aforementioned research represents a valuable attempt and exploration of SPF in helical groove grinding; however, the SPF of conical slant groove screw-tip grinding remains the primary form of SPF grinding due to its controllable and reliable groove parameters. Summary of the Invention

[0008] To address the problems existing in the prior art, this invention provides a precision forming grinding method for tap and screw tip grooves based on a unified parametric geometric model.

[0009] The present invention provides a precision forming grinding method for tap tip flutes based on a unified parametric geometric model, comprising the following steps:

[0010] Step 1: Establish a unified parametric geometric model for the screw tip groove.

[0011] (1) Define the uniform geometric parameters of the screw tip groove.

[0012] First, establish the workpiece coordinate system WCS with the end face as the reference plane, denoted as O. W -X W Y W Z W Its origin O W Located at the center of the end face, coordinate axis Z W The positive direction coincides with the tap rotation center and points towards the clamping part; the straight groove end face profile parameter is denoted as v, and point P on the end face... s Let it be P s (v)=[x s (v),y s (v),z s (v)] T Its generatrix unit vector is denoted as V. st =[i st ,j st ,k st ] T Angle ε is defined as V st With axis Z W The formed plane relative to Y W O W Z W The tilt angle of the coordinate plane; the core thickness increment angle α1 is defined as V. st With Z W The included angle of the axis; then V in WCS st Represented as:

[0013]

[0014] The straight groove surface H(x,y,z) passes through P s (v) along V st Sweep generation, represented as:

[0015] H(x,y,z)=P s (v)+t1V st (2)

[0016] In the formula, t1 is V st The length ratio.

[0017] The end face profile, cutting inclination angle, rake angle, and cutting length of the screw tip groove are then defined separately.

[0018] End face profile P t (u): Opening direction angle η represents P t1 With O W The line connecting the points relative to Y W The angle formed by the axes, any point on the SPF end face profile is represented by P. t (u)=[x t (u),y t (u),zt (u)] T This indicates that u is the SPF end face profile parameter.

[0019] Rake angle γ: The section C at a distance L1 from the SPF end face is used as the specified measurement section, denoted as C(x,y,z)=[x,y,L1]. T Where x, y ∈ R; within section C, a point on the SPF section profile lies at O. W1 -X W1 Y W1 Marked as P in the cross-sectional profile coordinate system cs1 The intersection of the cross section and the outer surface of the cone is denoted as P. cs1 The intersection point of the cross-sectional profile and the front angle measurement circle with a diameter μ times the diameter of the cross-sectional circle is denoted as P. cs2 ; and The included angle between them is γ, which is expressed as:

[0020]

[0021] Cutting edge angle λ: The cutting edge angle λ is defined as the cutting edge point P at a distance L2 from the end face. e1 tangent vector V e1 Relative to the tap axis vector V Zw The angle between [0,0,1] is represented as:

[0022]

[0023] Cutting edge length L: P at the tip of the cutting edge e2 =[x e2 ,y e2 ,z e2 ] T Let P be the intersection of the SPF and the straight groove on the calibration cylindrical surface; therefore, the cutting length L of the SPF is defined as the distance from point P. e2 The distance to the end face, therefore L = z e2 .

[0024] (2) Establish a unified geometric model for the screw tip groove.

[0025] The unit vector of the spiral tip groove generatrix is ​​defined as V. tp =[i tp ,j tp ,k tp ] T Its lift angle and swing angle are represented by α and β, respectively; where α represents V tp Relative to X W O W Z W Angle in a plane, β represents V tp In X W OW Z W The projection on the plane relative to the coordinate axis Z W Angle; V tp Represented as:

[0026]

[0027] The geometric model of SPF is represented by T(x,y,z) as follows:

[0028] T(x,y,z)=P t (u)+tV tp ,t≥0 (6)

[0029] In the formula, t is the SPF along V tp The length variable of the direction.

[0030] α and β are uncertain in equations (5) to (6), depending on the geometric design parameters of SPF and V. tp The mapping relationship between them is determined.

[0031] λ and V of SPF tp The correlation between α and β:

[0032] Considering the cutting cone surface G(x,y,z) as the plane of revolution of the working part, it is represented in WCS as:

[0033]

[0034] In the formula, d and κ are the diameter of the cylindrical surface and the taper angle of the working part's conical surface, respectively; L3 is the diameter along Z... W The length of the conical surface of the shaft.

[0035] Any cutting edge point P in WCS e Represented as:

[0036]

[0037] By calculating the partial derivatives of x, y, and z with respect to equation (8), the cutting edge point P is obtained. e1 =[x e1 ,y e1 ,z e1 ] T tangent vector V e1 =[i e1 ,j e1 ,k e1 ] T Represented as:

[0038]

[0039] Subsequently, by combining equations (4) and (9), the λ of SPF is related to V.tp The relationship between α and β is expressed as:

[0040]

[0041]

[0042] SPF's γ and V tp The correlation between α and β:

[0043] Section point P of SPF on section C in WCS cs Represented as:

[0044]

[0045] Based on γ and P cs Point P cs1 =[x cs1 ,y cs1 ,z cs1 ] T and P cs2 =[x cs2 ,y cs2 ,z cs2 ] T They are represented as follows:

[0046]

[0047] In equation (13), x t (u1),y t (u1) and x t (u2),y t (u2) represents the P in WCS on the SPF end face profile. cs1 and P cs2 The coordinates of the points are subject to the following conditions:

[0048]

[0049] According to equations (3), (13), and (14), the relationship between γ of SPF and α and β of Vtp is expressed as follows:

[0050]

[0051] L and V of SPF tp The correlation between α and β:

[0052] Point P e2 As the intersection of the three curved surfaces—SPF, straight groove, and cylinder—it is represented in WCS as:

[0053]

[0054]

[0055] In the formula x s (v1),y s (v1) and z s (v1) is P in WCS e2 The coordinates of the point on the corresponding straight groove end face profile.

[0056] The side length L is then calculated as follows:

[0057]

[0058] Step 2: Calculation of the screw tip groove forming grinding process.

[0059] It includes the definition of the grinding posture of the forming grinding wheel, the solution of the grinding wheel trajectory, and the solution of the profile of the forming grinding wheel.

[0060] (1) Definition of grinding posture of the forming grinding wheel.

[0061] Establish the grinding wheel coordinate system GCS, i.e., O G -X G Y G Z G O w1 -X W1 Y W1 Z W1 The coordinate system is first adjusted by rotating the WCS around the Z-axis. W Rotate the axis 90°, and then around the Y-axis. W Rotate the axis 90°, then return the origin O to its original position. w Along X respectively W and Y W Translate a respectively x and a y The grinding wheel coordinate system GCS is the coordinate system of O. w1 -X W1 Y W1 Z W1 Coordinate system around X W1 The coordinate plane X is obtained by rotating the axis by an angle β. G O G Y G Located inside the end face of the grinding wheel, Z G Represents the grinding wheel axis; O is the origin in WCS. G =[a x ,a y ,0] T Located on the grinding wheel shaft, where a x and a y Here are the position parameters of the grinding wheel, representing the offset distance and center distance, respectively; Y G axis and Y W1 The initial included angle between the axes is β, X G The axis is parallel to Y.W Axis, offset distance a x The coordinate transformation matrix M from GCS to WCS G_W_1 Represented as:

[0062]

[0063] From O W The minimum distance from a point to the SPF end face profile is denoted as r. min Considering the geometric constraints between the SPF and the grinding wheel, the range of positional parameters for avoiding interference during grinding is expressed as follows:

[0064]

[0065] The initial orientation of the grinding wheel is determined by a. y and V tp Definitely, and a x It is determined based on the radius of the forming grinding wheel and the internal space of the grinding machine; for ease of installation, it is set to zero; O in WCS G The initial coordinates are represented as O G =[0,a y ,0] T .

[0066] Initially, the grinding wheel axis is parallel to the XwOwZw plane and perpendicular to the V plane. tp Then the initial axis vector F of the grinding wheel in WCS G_ini Represented as:

[0067]

[0068] The range of η values ​​for SPF is determined by the position of the grinding wheel in the WCS; P t1 and P t2 The intersection of the SPF end face profile and the conical surface of the working part; θ1 and θ2 represent P t1 P t2 tangent to Y W The included angle of the axis; P t1 and P t2 The slopes of the tangents are obtained by differentiating their respective coordinates, and θ1 and θ2 are expressed as:

[0069]

[0070] Therefore, η should be within the range of η0-θ1≤η≤η0-θ2, where η0 is the initial opening direction angle of the SPF end face profile.

[0071] Furthermore, to avoid interference, the grinding wheel's orientation needs to be adjusted using an adjustment angle ξ; this angle represents the initial grinding wheel orientation around X. GThe rotation of the axis must satisfy ξ≤90-|β|; therefore, the actual grinding wheel axis vector F in WCS is... G Represented as:

[0072]

[0073] (2) Calculation of grinding trajectory of profiled grinding wheel:

[0074] Point O in the tool path G0 Represented as:

[0075]

[0076] In the formula, L F t1 is the axial feed distance of SPF, and t2 is the V. tp The length.

[0077] Point O in the grinding trajectory G1 Represented as:

[0078]

[0079] In the formula L G t3 is the grinding length of SPF, and t3 is V. tp The grinding length.

[0080] O in the retraction trajectory G2 Points are represented as:

[0081]

[0082] In the formula, t4 is V tp The length.

[0083] (3) Calculation of the profile of the forming grinding wheel:

[0084] The parameterized SPF surface expression is:

[0085]

[0086] n MG Represented as:

[0087]

[0088] Cross-multiplying the partial derivatives of u and t in T(u,t) yields the n of the SPF surface. M for:

[0089]

[0090] Therefore, due to n M n MG and F G_WSince they are coplanar, the equation of the contact line with respect to t is:

[0091] n M (u,t)·(n MG ×F G )=B1t+B2=0 (30)

[0092]

[0093] After determining u, calculate t according to equation (30), and substitute it together with u into equation (27) to calculate point P on the contact line. m_W =[x m_W ,y m_W ,z m_W ] T Establish the transformation matrix M between WCS and GCS. G_W The actual grinding posture of the grinding wheel is as follows:

[0094]

[0095] Based on this, P in WCS m_W Transform into GCS:

[0096]

[0097] By calculating the distance from point M on the meshing line to the grinding wheel axis Z... G The distance is used to obtain the profile of the grinding wheel; any point P on the grinding wheel profile in GCS... g_G All are represented as:

[0098]

[0099] After completing the above two steps, the specified design parameters and process parameters are combined based on the unified parametric geometric model of the screw tip groove to form a process parameter design calculation driven by the design parameters. The precision forming grinding of the screw tip groove can be achieved by calculating the forming grinding wheel profile and grinding wheel grinding posture.

[0100] The beneficial technical effects of this invention compared to the prior art are as follows:

[0101] This invention aims to achieve precision grinding of SPF (Surface Mount Factor) taps. Considering the specific design parameters of SPF and the overdeterministic structural constraints brought about by the straight flute, a UPGM (Upright Dimensioning General Mesh) for SPF is constructed. This solves the structural conflict between SPF geometric parameters and the straight flute during modeling, reveals the mapping relationship between the UPGM and the SPF generatrix, and improves the modeling accuracy of SPF.

[0102] This invention establishes a full integration of the form grinding process model and the SPF design parameter model. This enables more reliable and accurate calculation of the grinding trajectory and grinding wheel attitude, improving the practicality of the method.

[0103] This invention proposes a method for calculating the profile of a forming grinding wheel that considers flexible grinding posture, based on the line contact conjugate theory. It can obtain different grinding wheel profiles according to different initial grinding wheel postures, enhancing the adaptability of profile grinding and thus improving the grinding accuracy of SPF (Surface Mount Factor).

[0104] The method was validated through simulation and actual grinding experiments. The results show that the relatively small error is negligible, ensuring good grinding quality of SPF, and proving the accuracy and effectiveness of the proposed precision profile grinding method. Attached Figure Description

[0105] Figure 1 This is a schematic diagram of a screw-tip tap.

[0106] Figure 2 This is a schematic diagram of the straight groove structure parameters.

[0107] Figure 3 This is the profile of the screw tip groove end face.

[0108] Figure 4 This is a schematic diagram of the rake angle of the screw tip groove on section C.

[0109] Figure 5 The cutting edge and blade length of the screw-tip tap.

[0110] Figure 6 This refers to the screw tip and groove busbar and related parameters.

[0111] Figure 7 This is a schematic diagram of the initial grinding posture of the grinding wheel for the screw tip groove.

[0112] Figure 8 This is a schematic diagram showing the range of the opening direction angle of the screw tip groove.

[0113] Figure 9 This is a schematic diagram of the actual grinding posture of the screw tip groove.

[0114] Figure 10 This is a schematic diagram of the meshing line between the SPF surface and the grinding wheel surface.

[0115] Figure 11 The calculation process for SPF forming profile and grinding trajectory.

[0116] Figure 12 For NC code and simulated grinding environment.

[0117] (a) represents the NC code, and (b) represents the simulated grinding environment.

[0118] Figure 13 The end face profile of the SPF and the calculated grinding wheel profile.

[0119] Wherein, (a) is the SPF end face profile and some coordinate points, and (b) is the calculated grinding wheel profile and profile coordinate points.

[0120] Figure 14 This is for simulating grinding results.

[0121] Figure 15 This is the actual grinding and measuring device for screw-tip taps.

[0122] (a) is the actual grinding device, and (b) is the measuring device.

[0123] Figure 16 This is the actual grinding result of the screw tip groove.

[0124] Among them, (a) is the result of the blade length, (b) is the result of the blade inclination angle, and (c) is the result of the end face profile and rake angle. Detailed Implementation

[0125] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0126] The present invention provides a precision forming grinding method for tap tip flutes based on a unified parametric geometric model, comprising the following steps:

[0127] Step 1: Establish a unified parametric geometric model for the screw tip groove.

[0128] (1) Define the uniform geometric parameters of the screw tip groove.

[0129] First, establish such as Figure 2 The workpiece coordinate system (WCS) shown is defined with the end face as the reference plane, denoted as O. W -X W Y W Z W Its origin O W Located at the center of the end face, coordinate axis Z W The positive direction coincides with the center of rotation of the tap and points towards the clamping part.

[0130] like Figure 2 As shown, the profile parameter of the straight groove end face is denoted as v, and point P on the end face... s Let it be P s (v)=[x s (v),y s (v),z s (v)] T Its generatrix unit vector is denoted as V. st =[i st ,j st,k st ] T Angle ε is defined as V st With axis Z W The formed plane relative to Y W O W Z W The tilt angle of the coordinate plane; the core thickness increment angle α1 is defined as V. st With Z W The included angle of the axis; then V in WCS st Represented as:

[0131]

[0132] The straight groove surface H(x,y,z) passes through P s (v) along V st Sweep generation, represented as:

[0133] H(x,y,z)=P s (v)+t1V st (2) In the formula, t1 is V st The length ratio.

[0134] The end face profile, cutting inclination angle, rake angle, and cutting length of the screw tip groove are then defined separately.

[0135] End face profile P t (u):

[0136] like Figure 3 As shown, the end face profile is SPF in X W O W Y W The projection curve on the plane. The opening direction angle η represents P. t1 With O W The line connecting the points relative to Y W The angle formed by the axes, any point on the SPF end face profile is represented by P. t (u)=[x t (u),y t (u),z t (u)] T This indicates that u is the SPF end face profile parameter.

[0137] Anterior angle γ:

[0138] The rake angle γ is usually perpendicular to Z. W The measurement is performed on a specific section of the SPF (Specified Particulate Filter) of the shaft. The section C, located at a distance L1 from the SPF end face, is used as the specified measurement section, denoted as C(x,y,z) = [x,y,L1]. T , where x, y ∈ R. For example... Figure 4 As shown, within section C, a point on the SPF section profile is at point O.W1 -X W1 Y W1 Marked as P in the cross-sectional profile coordinate system cs1 The intersection of the cross section and the outer surface of the cone is denoted as P. cs1 The intersection point of the cross-sectional profile and the front angle measurement circle with a diameter μ times the diameter of the cross-sectional circle is denoted as P. cs2 .

[0139] and The included angle between them is γ, which is expressed as:

[0140]

[0141] Cutting edge angle λ:

[0142] The cutting edge inclination angle λ is defined as the cutting edge point P located at a distance L2 from the end face. e1 tangent vector V e1 Relative to the tap axis vector V Zw The angle between [0,0,1], such as Figure 5 As shown, it is represented as:

[0143]

[0144] Blade length L:

[0145] like Figure 5 As shown, P at the tip of the cutting edge e2 =[x e2 ,y e2 ,z e2 ] T Let P be the intersection of the SPF and the straight groove on the calibration cylindrical surface; therefore, the cutting length L of the SPF is defined as the distance from point P. e2 The distance to the end face, therefore L = z e2 .

[0146] (2) Establish a unified geometric model for the screw tip groove.

[0147] like Figure 6 As shown, the unit vector of the screw tip groove generatrix is ​​defined as V. tp =[i tp ,j tp ,k tp ] T Its lift angle and swing angle are represented by α and β, respectively; where α represents V tp Relative to X W O W Z W Angle in a plane, β represents V tp In X W O W Z WThe projection on the plane relative to the coordinate axis Z W The angle.

[0148] In WCS, V tp Represented as:

[0149]

[0150] The geometric model of SPF is represented by T(x,y,z) as follows:

[0151] T(x,y,z)=P t (u)+tV tp ,t≥0 (6)

[0152] In the formula, t is the SPF along V tp The length variable of the direction.

[0153] α and β are uncertain in equations (5) to (6), depending on the geometric design parameters of SPF and V. tp The mapping relationship between them is determined.

[0154] λ and V of SPF tp The correlation between α and β:

[0155] Considering the cutting cone surface G(x,y,z) as the plane of revolution of the working part, it is represented in WCS as:

[0156]

[0157] In the formula, d and κ are the diameter of the cylindrical surface and the taper angle of the working part's conical surface, respectively; L3 is the diameter along Z... W The length of the conical surface of the shaft.

[0158] Any cutting edge point P in WCS e Represented as:

[0159]

[0160] By calculating the partial derivatives of x, y, and z with respect to equation (8), the cutting edge point P is obtained. e1 =[x e1 ,y e1 ,z e1 ] T tangent vector V e1 =[i e1 ,j e1 ,k e1 ] T Represented as:

[0161]

[0162] Subsequently, by combining equations (4) and (9), the λ of SPF is related to V.tp The relationship between α and β is expressed as:

[0163]

[0164] SPF's γ and V tp The correlation between α and β:

[0165] Section point P of SPF on section C in WCS cs Represented as:

[0166]

[0167] Based on γ and P cs Point P cs1 =[x cs1 ,y cs1 ,z cs1 ] T and P cs2 =[x cs2 ,y cs2 ,z cs2 ] T They are represented as follows:

[0168]

[0169] In equation (13), x t (u1),y t (u1) and x t (u2),y t (u2) represents the P in WCS on the SPF end face profile. cs1 and P cs2 The coordinates of the points are subject to the following conditions:

[0170]

[0171] According to equations (3), (13), and (14), the γ and V of SPF tp The relationship between α and β is expressed as:

[0172]

[0173] L and V of SPF tp The correlation between α and β:

[0174] Point P e2 As the intersection of the three curved surfaces—SPF, straight groove, and cylinder—it is represented in WCS as:

[0175]

[0176] In the formula x s (v1),y s(v1) and z s (v1) is P in WCS e2 The coordinates of the point on the corresponding straight groove end face profile.

[0177] The side length L is then calculated as follows:

[0178]

[0179] Step 2: Calculation of screw tip groove forming grinding.

[0180] It includes the definition of the grinding posture of the forming grinding wheel, the solution of the grinding wheel trajectory, and the solution of the profile of the forming grinding wheel.

[0181] (1) Definition of grinding posture of the forming grinding wheel.

[0182] To describe the profile and orientation of the grinding wheel, a grinding wheel coordinate system GCS, i.e., O, is established. G -X G Y G Z G ,like Figure 7 As shown. O w1 -X W1 Y W1 Z W1 The coordinate system is first adjusted by rotating the WCS around the Z-axis. W Rotate the axis 90°, and then around the Y-axis. W Rotate the axis 90°, then return the origin O to its original position. w Along X respectively W and Y W Translate a respectively x and a y The grinding wheel coordinate system GCS is the coordinate system of O. w1 -X W1 Y W1 Z W1 Coordinate system around X W1 The coordinate plane X is obtained by rotating the axis by an angle β. G O G Y G Located inside the end face of the grinding wheel, Z G Represents the grinding wheel axis; O is the origin in WCS. G =[a x ,a y ,0] T Located on the grinding wheel shaft, where a x and a y Here are the position parameters of the grinding wheel, representing the offset distance and center distance, respectively; Y G axis and Y W1 The initial included angle between the axes is β, X G The axis is parallel to Y. W Axis, offset distance a xThe coordinate transformation matrix M from GCS to WCS G_W_1 Represented as:

[0183]

[0184] From O W The minimum distance from a point to the SPF end face profile is denoted as r. min Considering the geometric constraints between the SPF and the grinding wheel, the range of positional parameters for avoiding interference during grinding is expressed as follows:

[0185]

[0186] The initial orientation of the grinding wheel is determined by a. y and V tp Definitely, and a x It is determined based on the radius of the forming wheel and the internal space of the grinding machine; for ease of installation, it is set to zero; O in WCS G The initial coordinates are represented as O G =[0,a y ,0] T .

[0187] Initially, the grinding wheel axis is parallel to the XwOwZw plane and perpendicular to the V plane. tp Then the initial axis vector F of the grinding wheel in WCS G_ini Represented as:

[0188]

[0189] The range of η values ​​for SPF is determined by the position of the grinding wheel in the WCS; for example Figure 8 As shown, P t1 and P t2 The intersection of the SPF end face profile and the conical surface of the working part; θ1 and θ2 represent P t1 P t2 tangent to Y W The included angle of the axis; P t1 and P t2 The slopes of the tangents are obtained by differentiating their respective coordinates, and θ1 and θ2 are expressed as:

[0190]

[0191] Therefore, η should be within the range of η0-θ1≤η≤η0-θ2, where η0 is the initial opening direction angle of the SPF end face profile.

[0192] Furthermore, to reduce grinding interference and enhance the adaptability of the grinding wheel posture, it is necessary to adjust the grinding wheel posture using the adjustment angle ξ; such as Figure 9 As shown, this angle represents the initial grinding wheel orientation around X.G The rotation of the axis must satisfy ξ≤90-|β|; therefore, the actual grinding wheel axis vector F in WCS is... G Represented as:

[0193]

[0194] (2) Solving the grinding trajectory of the forming grinding wheel:

[0195] Point O in the tool path G0 Represented as:

[0196]

[0197] In the formula, L F t1 is the axial feed distance of SPF, and t2 is the V. tp The length.

[0198] Point O in the grinding trajectory G1 Represented as:

[0199]

[0200] In the formula L G t3 is the grinding length of SPF, and t3 is V. tp The grinding length.

[0201] O in the retraction trajectory G2 Points are represented as:

[0202]

[0203] In the formula, t4 is V tp The length.

[0204] (3) Solving the profile of the forming grinding wheel:

[0205] like Figure 10 As shown, the parameterized SPF surface expression is:

[0206]

[0207] n MG Represented as:

[0208]

[0209] Cross-multiplying the partial derivatives of u and t in T(u,t) yields the n of the SPF surface. M for:

[0210]

[0211] Therefore, due to n M n MGand F G_W Since they are coplanar, the equation of the contact line with respect to t is:

[0212] n M (u,t)·(n MG ×F G )=B1t+B2=0 (30)

[0213]

[0214] When ξ≠0, the actual grinding wheel axis does not coincide with the initial grinding wheel axis during grinding. As can be seen from equation (31), when the value of ξ is non-zero, the parameter t will change, which will lead to a change in the obtained meshing line, thereby producing a deformable grinding wheel profile determined by the flexible grinding posture.

[0215] After determining u, calculate t according to equation (30), and substitute it together with u into equation (27) to calculate point P on the contact line. m_W =[x m_W ,y m_W ,z m_W ] T Establish the transformation matrix M between WCS and GCS. G_W The actual grinding posture of the grinding wheel is as follows:

[0216]

[0217] Based on this, P in WCS m_W Transform into GCS:

[0218]

[0219] By calculating the distance from point M on the meshing line to the grinding wheel axis Z... G The distance is used to obtain the profile of the grinding wheel; any point P on the grinding wheel profile in GCS... g_G All are represented as:

[0220]

[0221] At this point, the precision forming grinding method of UPGM based on SPF has been completed, which enables the SPF profile and geometric parameters to be precision ground.

[0222] Step 3: Simulation and actual grinding experiments.

[0223] (1) Simulated grinding experiment:

[0224] To verify the accuracy and practicality of the proposed method, a set of method modules was developed on the VC++ platform. These modules can calculate the grinding wheel profile and grinding trajectory based on specified SPF design parameters and grinding wheel posture. Then, based on the coordinate transformation relationship, the corresponding NC code is generated and an executable file is output. The calculation process is as follows: Figure 11 As shown, the NC code and simulation environment are as follows: Figure 12 As shown.

[0225] The specified design parameters for SPF are shown in Table 1. These parameters can be used to calculate the lift angle α, swing angle β, and opening direction angle η during the simulated grinding process. Detailed grinding parameters are shown in Table 2.

[0226] Table 1 SPF Design Parameters

[0227]

[0228] Table 2. Grinding parameters for simulated SPF.

[0229]

[0230] Simulated grinding experiments were conducted in VERICUT 9.0 to validate the method. The computing environment included a Dell Vostro 5890 computer with a 64-bit Windows 10 operating system, a CPU frequency of 2.60 GHz, 16 GB of RAM, and 2 GB of video memory. The profile and trajectory of the grinding wheel could be determined using the process parameters specified in Table 2. The design end face profile of the SPF and the calculated grinding wheel profile are shown below. Figure 13 As shown.

[0231] Combining Table 2 with equations (21) and (23), F G With coordinate axis X W The included angle is calculated as β + ξ = 5.60°, and the center of the grinding wheel is O. G Y is located 102.50 mm from the origin. W On the shaft. Based on the calculated grinding posture of the grinding wheel, the grinding wheel profile can be derived according to equations (30) and (34), such as Figure 13 As shown in (b), the maximum radius of the grinding wheel profile is 100.521 mm, and the wheel width is 4.520 mm. Then, the calculated profile and trajectory output executable file is entered into the software for simulated grinding analysis. The results are as follows... Figure 14 As shown.

[0232] To calculate λ, six sets of points near L2 = 4.00 mm were selected from the simulation model, as shown in Table 3. Specifically, λ was measured using the tangent of each selected set of points, and the tangent and Z were calculated according to equation (5). W The average angle λ between the axes is 12.881°.

[0233] Table 3 shows the calculation of λ from the point set of the simulation model.

[0234]

[0235] The measured cutting length L was 10.810 mm, and the rake angle γ was 28.469°. Table 4 shows that the relative errors and maximum profile errors of λ, γ, and L during the simulated grinding process were 0.923%, 0.867%, 0.028%, and 0.000 mm, respectively, of the design values. The results indicate that the simulated grinding results agree well with the geometric design parameters of the SPF, with errors all less than 1.000%, demonstrating the effectiveness and feasibility of the proposed precision forming method.

[0236] Table 4 Comparison of Design and Simulation Values ​​of SPF Geometric Parameters

[0237]

[0238] (2) Actual grinding experiment:

[0239] To further validate the proposed grinding method, the following method was used: Figure 15 (a) shows a five-axis CNC grinder performing SPF grinding on a screw tip tap. The parameters used in the actual grinding experiment were consistent with those used in the simulated grinding. The grinding wheel used was a shaped grinding wheel with a large end face radius of 100.521 mm. A PG1000 tool measuring instrument was used to measure the structural parameters after SPF grinding. The measuring device is as follows: Figure 15 As shown in (b).

[0240] The measurement results of SPF end face profile, rake angle, cutting edge length, and cutting edge inclination angle are as follows: Figure 16 As shown in Table 5, the comparison between the design values ​​and actual grinding values ​​of the SPF geometric parameters is presented.

[0241] Table 5 Comparison of Design Values ​​and Actual Grinding Values ​​of SPF Geometric Parameters

[0242]

[0243]

[0244] Table 5 shows that the maximum relative errors between the actual grinding values ​​and the design values ​​of λ, γ, and L are 1.492%, 2.557%, 2.000%, and 0.029 mm, respectively, and the absolute errors are 0.194°, 0.716°, 0.220°, and 0.029 mm, respectively. It can be seen that all relative errors do not exceed 2.600%, and the absolute errors are all within the allowable tolerance range, further verifying the accuracy and effectiveness of the proposed precision forming grinding method.

Claims

1. A method for precision forming grinding of tap tip grooves based on a unified parametric geometric model, characterized in that, Includes the following steps: Step 1: Establish a unified parametric geometric model for the screw tip groove: (1) Define the uniform geometric parameters of the screw tip groove: First, establish the workpiece coordinate system WCS with the end face as the reference plane, denoted as O. W -X W Y W Z W Its origin O W Located at the center of the end face, coordinate axis Z W The positive direction coincides with the tap rotation center and points towards the clamping part; the straight groove end face profile parameter is denoted as v, and point P on the end face... s Let it be P s (v)=[x s (v),y s (v),z s (v)] T Its generatrix unit vector is denoted as V. st =[i st ,j st ,k st ] T Angle ε is defined as V st With axis Z W The formed plane relative to Y W O W Z W The tilt angle of the coordinate plane; the core thickness increment angle α1 is defined as V. st With Z W The included angle of the axis; then V in WCS st Represented as: The straight flute curved surface H(x, y, z) passes through P s (v) along V st swept, expressed as: H(x, y, z) = P s (v) + t1V st (2) wherein t1 is V st the length ratio of t1 to t2; The end face profile, cutting inclination angle, rake angle, and cutting length of the screw tip groove are then defined separately: End face profile P t (u): Opening direction angle η represents P t1 With O W The line connecting the points relative to Y W The angle formed by the axes, any point on the SPF end face profile is represented by P. t (u)=[x t (u),y t (u),z t (u)] T This indicates that u represents the SPF end face profile parameter; Rake angle γ: The section C at a distance L1 from the SPF end face is used as the specified measurement section, denoted as C(x,y,z)=[x,y,L1]. T Where x, y ∈ R; within section C, a point on the SPF section profile lies at O. W1 -X W1 Y W1 Marked as P in the cross-sectional profile coordinate system cs1 The intersection of the cross section and the outer surface of the cone is denoted as P. cs1 The intersection point of the cross-sectional profile and the front angle measurement circle with a diameter μ times the diameter of the cross-sectional circle is denoted as P. cs2 ; and The included angle between them is γ, which is expressed as: The blade inclination angle λ is defined as the angle between the tangent vector V e1 at the blade point P e1 at the distance L2 from the end face relative to the tap axial vector V Zw = [0, 0, 1] and is expressed as: Blade length L: P of the end of the cutting blade e2 = [x e2 , y e2 , z e2 ] T is the intersection point of the SPF and the straight slot on the calibrated cylindrical surface; Therefore, the blade length L of the SPF is defined as the length from point P. e2 The distance to the end face, therefore L = z e2 ; (2) Define a unified geometric model for the screw tip groove: The unit vector of the spiral tip groove generatrix is ​​defined as V. tp =[i tp ,j tp ,k tp ] T Its lift angle and swing angle are represented by α and β, respectively; where α represents V tp Relative to X W O W Z W Angles in a plane, β represents V tp In X W O W Z W The projection on the plane relative to the coordinate axis Z W Angle; V tp Represented as: The geometric model of SPF is represented by T(x,y,z) as follows: T(x, y, z) = P t (u) + tV tp t > 0 (6) where t is the length variable of the SPF along the V tp direction. α and β are undetermined in the formula (5)~(6), determined according to the mapping relationship between the geometric design parameters of the SPF and V tp ; the correlation of the SPF's λ and V tp 's α, β: Considering the cutting cone surface G(x,y,z) as the plane of revolution of the working part, it is represented in WCS as: In the formula, d and κ are the diameter of the cylindrical surface and the taper angle of the working part's conical surface, respectively; L3 is the diameter along Z... W The length of the conical surface of the shaft; Any cutting edge point P in the WCS e is represented as: By calculating the partial derivatives of x, y, and z with respect to equation (8), the cutting edge point P is obtained. e1 =[x e1 ,y e1 ,z e1 ] T tangent vector V e1 =[i e1 ,j e1 ,k e1 ] T Represented as: Subsequently, the relationship of λ of the SPF with α and β of the SPF is expressed by simultaneous equations (4) and (9) tp is expressed as: SPF's gamma versus V tp Correlation of alpha, beta of A profile point P of the SPF on the section C in the WCS cs is represented as: Based on γ and P cs , point P cs1 = [x cs1 , y cs1 , z cs1 ] T and P cs2 = [x cs2 , y cs2 , z cs2 ] T are represented as: In formula (13), x t (u1), y t (u1), and x t (u2), y t (u2) are the coordinates of points P cs1 and P cs2 in the corresponding WCS on the SPF end face profile, which are subject to the following conditions: According to equations (3), (13), and (14), the relationship between γ of SPF and α and β of Vtp is expressed as follows: SPF of L with V tp Correlation of a, b: Point P e2 As the intersection of the three curved surfaces of the SPF, straight slot, and cylinder, it is represented in the WCS as: where x s (v1),y s (v1) and z s (v1) is P e2 corresponding point coordinates on the straight-sided end face profile; The side length L is then calculated as follows: Step 2: Grinding calculation for screw tip groove forming: It includes the definition of the grinding posture of the forming grinding wheel, the solution of the grinding wheel trajectory, and the solution of the profile of the forming grinding wheel; (1) Definition of grinding posture of profile grinding wheel: Establish the grinding wheel coordinate system GCS, i.e., O G -X G Y G Z G O w1 -X W1 Y W1 Z W1 The coordinate system is first adjusted by rotating the WCS around the Z-axis. W Rotate the axis 90°, and then around the Y-axis. W Rotate the axis 90°, then return the origin O to its original position. w Along X respectively W and Y W Translate a respectively x and a y The grinding wheel coordinate system GCS is the coordinate system of O. w1 -X W1 Y W1 Z W1 Coordinate system around X W1 The coordinate plane X is obtained by rotating the axis by an angle β. G O G Y G Located inside the end face of the grinding wheel, Z G Represents the grinding wheel axis; O is the origin in WCS. G =[a x ,a y ,0] T Located on the grinding wheel shaft, where a x and a y Here are the position parameters of the grinding wheel, representing the offset distance and center distance, respectively; Y G axis and Y W1 The initial included angle between the axes is β, X G The axis is parallel to Y. W Axis, offset distance a x The coordinate transformation matrix M from GCS to WCS G_W_1 Represented as: From O W The minimum distance from a point to the SPF end face profile is denoted as r. min Considering the geometric constraints between the SPF and the grinding wheel, the range of positional parameters for avoiding interference during grinding is expressed as follows: The initial orientation of the grinding wheel is determined by a. y and V tp Definitely, and a x It is determined based on the radius of the forming wheel and the internal space of the grinding machine; for ease of installation, it is set to zero; O in WCS G The initial coordinates are represented as O G =[0,a y ,0] T ; Initially, the grinding wheel axis is parallel to the XwOwZw plane and perpendicular to the V plane. tp Then the initial axis vector F of the grinding wheel in WCS G_ini Represented as: The range of η values ​​for SPF is determined by the position of the grinding wheel in the WCS; P t1 and P t2 The point where the SPF end face profile intersects with the conical surface of the working part; θ1 and θ2 represent P respectively t1 P t2 tangent to Y W The included angle of the axis; P t1 and P t2 The slopes of the tangents are obtained by differentiating them using their respective coordinates, and θ1 and θ2 are expressed as: Therefore, η should be within the range of η0-θ1≤η≤η0-θ2, where η0 is the initial opening direction angle of the SPF end face profile; Furthermore, to avoid interference, the grinding wheel's orientation needs to be adjusted using an adjustment angle ξ; this angle represents the initial grinding wheel orientation around X. G The rotation of the axis must satisfy ξ≤90-|β|; therefore, the actual grinding wheel axis vector F in WCS is... G Represented as: (2) Calculation of grinding trajectory of profiled grinding wheel: Point O in the tool path G0 Represented as: wherein L F is the axial feed distance of the SPF, t2is the length of the V tp . Point O in the grinding trajectory G1 Represented as: In the formula L G t3 is the grinding length of SPF, and t3 is V. tp Grinding length; O in the retraction trajectory G2 Points are represented as: In the formula, t4 is V tp Length; (3) Calculation of the profile of the forming grinding wheel: The parameterized SPF surface expression is: n MG is represented by: Cross-multiplying the partial derivatives of T(u, t) with respect to u and t gives n M is: Therefore, due to n M n MG and F G_W Since they are coplanar, the equation of the contact line with respect to t is: n M (u,t)·(n MG ×F G )=B1t+B2=0 (30) After determining u, calculate t according to equation (30), and substitute it together with u into equation (27) to calculate point P on the contact line. m_W =[x m_W ,y m_W ,z m_W ] T Establish the transformation matrix M between WCS and GCS. G_W The actual grinding posture of the grinding wheel is as follows: Based on this, P in WCS m_W Transform into GCS: By calculating the distance from point M on the meshing line to the grinding wheel axis Z... G The distance is used to obtain the profile of the grinding wheel; any point P on the grinding wheel profile in GCS... g_G All are represented as:

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