Screw tap screw tip groove precision forming and grinding method based on unified parameter geometric model

Abstract

The invention discloses a screw tap screw tip groove precision forming and grinding method based on a unified parameterized geometric model, and the method specifically comprises the steps: firstly, building an accurate UPGM of an SPF by considering specific design parameters of the SPF and overdetermined structural constraints generated by a straight groove; geometric information such as the end face contour, the cutting edge inclination angle lambda, the front angle gamma and the cutting edge length L of the SPF is comprehensively described, and a solid foundation is provided for follow-up grinding machining; secondly, the mapping relation between the UPGM and the SPF bus is revealed, and calculation of the geometric drive grinding track of the spiral groove is achieved; then, on the basis of the line contact conjugate theory, a formed grinding wheel contour calculation method considering the flexible grinding posture is provided; different forming grinding wheel contours determined by initial postures are adopted, and precise groove shape control and precise forming grinding of the SPF are achieved. The SPF grinding quality of the screw tip tap is guaranteed, and the method has certain accuracy and effectiveness and has high engineering application potential.

Description

Technical Field

[0001] The present invention belongs to the field of precision grinding of numerical control tools, and particularly relates to a precision forming grinding method for the spiral tip groove of a tap based on a unified parametric geometric model. Background Art

[0002] The spiral tip tap (as shown in Figure 1 ) has the advantages of high structural strength, small tapping friction and torque, high machining accuracy, high efficiency, etc., and is a special tool for internal threads in fields such as aerospace, automotive, and equipment manufacturing. It is an improved type of straight flute tap, formed by machining a spiral tip groove (SPF) with a core thickness increment at one cutting edge of the straight flute, ensuring that the chip evacuation direction is consistent with the feed direction, avoiding chip jamming and chip scratching of the machined thread. The spiral tip tap usually consists of SPF, straight flute, cutting cone, etc. Among them, SPF is the most important structural feature, which can form tightly curled chips, expand the chip space, control the chip evacuation direction, and has a significant impact on tapping torque and accuracy.

[0003] Compared with end mills, hole machining tools such as taps work in a narrower cutting space and require a more precise cutting state to manufacture threads with good profile accuracy and surface quality. Therefore, high-performance tap profiles require strict precision to achieve reliable chip breaking, chip curling, and chip evacuation within the limited SPF range of the tap. However, due to the complexity and conflict of the SPF design parameters and the straight flute structure constraints, the lack of a unified parametric geometric model (UPGM) hinders the accurate description of the SPF spatial structure. This complicates the design of the form grinding process and results in poor manufacturability due to the differences between the design and process models. In addition, the grinding wheel profile, grinding trajectory, and attitude have a great impact on the final grinding accuracy of SPF, and should be flexibly adjusted to avoid grinding interference. Therefore, considering the overdetermined structural constraints generated by the specified design parameters of SPF and the straight flute, establishing an accurate UPGM of SPF, and designing and calculating the grinding wheel profile, trajectory, and attitude during form grinding on this basis are the keys to realizing the precision grinding of SPF.

[0004] Currently, considering the complex and conflicting structural constraints brought by specific design parameters, there is little research on the unified geometric modeling of the SPF of spiral tip taps, and little research on the grinding process design (including tapered oblique grooves and spiral grooves) of SPF. For tools such as end mills, the grinding of spiral grooves has been widely studied, providing valuable insights for the grinding of SPF spiral grooves. For ordinary straight flutes with a spiral angle of zero, the existing methods are effective. However, the grinding of SPF tapered oblique grooves has high complexity, and the process design and optimization methods using standard grinding wheels or form grinding wheels studied by previous scholars cannot be directly applied to the grinding of the oblique cone straight grooves of SPF, but can provide important insights.

[0005] The research on standard grinding wheels mainly focuses on the optimization of grinding wheel trajectories, geometric parameters, and postures. In the grinding of the spiral groove of a tapered end mill, Li Yong et al. proposed a new method for optimizing the grinding wheel posture and geometric parameters by analyzing the sensitivity of cross-section parameters and the formation mechanism of the core thickness radius, considering the overall cross-section curve matching error. Zheng Gaojun et al. proposed a grinding wheel positioning method during the grinding of the spiral groove of a tapered end mill 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 a tapered end mill on a four-axis CNC grinding machine, which discretizes the tapered end mill into several cylindrical end mills and determines the position of the grinding wheel in sequence. In the grinding of cylindrical spiral grooves, relevant research shows that it is difficult to determine and optimize the position and orientation of the grinding wheel based on given spiral groove parameters. Zhao Xianfeng et al. used an accurate spiral groove model to analyze in detail the influence of the grinding wheel radius, fillet radius, and taper angle on the helix angle and opening angle of the spiral 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 spiral groove and the grinding wheel trajectory based on the envelope theory. Rababah et al. proposed a method for determining the position and orientation of the grinding wheel according to the designed helix angle and core radius. Ren Lei et al. and Habibi et al. established complex nonlinear equations to mathematically relate the grinding wheel position to the spiral groove parameters. Generally speaking, it is very time-consuming to obtain the position and orientation of the grinding wheel by numerically solving the above mathematical relationships. Therefore, some researchers adopt intelligent algorithms to improve the calculation accuracy and efficiency. Karpuschewsk et al. proposed an algorithm that can automatically search for the grinding wheel trajectory when using a standard grinding wheel to approximate the required operating profile during the grinding of spiral grooves. Li Guochao et al. optimized the grinding wheel posture using an artificial intelligence algorithm and established a general model for calculating the grinding wheel trajectory of spiral grooves. Fang Yang et al. proposed combining the particle swarm optimization algorithm with genetic algorithm technology to optimize the position and orientation of the grinding wheel, thereby improving the grinding accuracy and efficiency.

[0006] However, the above research on standard grinding wheels mainly focuses on grinding cylindrical spiral grooves to ensure spiral groove geometric parameters such as rake angle and core radius, but it may not fully achieve the ideal spiral groove profile and accuracy. To achieve high-precision grinding of SPF, it is usually necessary to use a form grinding wheel for meticulous grinding. During the spiral groove form grinding process, it is crucial to calculate the grinding wheel profile based on the spiral groove profile and grinding trajectory of the specified cross-section. Chen Zhan et al. proposed a calculation method for determining the grinding wheel profile by analyzing the contact line during the spiral groove grinding process using the analytical envelope and form geometry theory. In their research, they derived the spiral-shaped spiral groove profile using the envelope theory, while other researchers adopted the conjugate contact theory, which states that the normal contact point between the grinding wheel and the spiral groove surface must intersect with the grinding wheel axis to determine its profile. Kang et al. established a spiral groove grinding model based on the contact theory, combining 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. adopted a special continuous equation to represent the uncertain normal direction at the singular points. Shi Zhongde et al. explored the allowable 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 spiral grooves and determined the grinding wheel profile based on the conjugate contact theory. Wasif et al. proposed a grinding wheel profile optimization method based on the differential evolution algorithm. Mohan et al. simulated the contact curve during the spiral groove form grinding process using CAD software.

[0007] In summary, although significant progress has been made in the research on spiral groove grinding in terms of grinding wheel profile, trajectory, and attitude calculation, there is relatively little literature on the grinding process of conical helical grooves. In addition, the overconstrained determined structure and the lack of an accurate geometric model to characterize SPF pose challenges to the precise surface control of conical helical groove grinding. The above research is a valuable attempt and exploration of spiral groove grinding for SPF, but the SPF of conical helical groove spiral-point taps is the main form of SPF grinding due to its controllability and reliable groove parameters. Summary of the Invention

[0008] Aiming at the problems existing in the prior art, the present invention provides a precise form grinding method for the spiral-point groove of a tap based on a unified parametric geometric model.

[0009] The precise form grinding method for the spiral-point groove of a tap based on a unified parametric geometric model of the present invention includes the following steps:

[0010] Step 1: Establish a unified parametric geometric model of the spiral-point groove.

[0011] (1) Define the unified geometric parameters of the spiral-point groove.

[0012] First, establish a workpiece coordinate system WCS with the end face as the reference plane, denoted as O W -X W Y W Z W , whose origin O W is located at the center of the end face, and the positive direction of the coordinate axis Z W coincides with the center of the tap rotation and points to the clamping part; the end face contour parameter of the straight groove is denoted as v, and the point P s on the end face is denoted as P s (v)=[x s (v),y s (v),z s (v)] T , and its bus unit vector is denoted as V st =[i st ,j st ,k st T ; the angle ε is defined as the inclination angle of the plane formed by V st and the axis Z W relative to the Y W O W Z W coordinate plane; the core thickness increment angle α1 is defined as the included angle between V st and the Z W axis; then V st in WCS is expressed as:

[0013]

[0014] The straight groove surface H(x,y,z) is generated by sweeping P s (v) along V st , and is expressed as:

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

[0016] where t1 is the length ratio of V st .

[0017] Then, define the end face contour, edge inclination angle, rake angle, and edge length of the spiral tip groove respectively.

[0018] The end face contour P t (u): The opening direction angle η represents the included angle formed by the line connecting P t1 and the O W point relative to the Y W axis. Any point on the SPF end face contour is represented by P t (u)=[x t (u),y t (u),z​t (u)] T It is represented, where u is the SPF end face profile parameter.

[0019] Helix angle γ: The section C at a distance L1 from the SPF end face is defined as the specified measurement section, and C(x, y, z) = [x, y, L1] T , where x, y ∈ R; within the section C, a point on the SPF section profile is marked as P W1 -X W1 Y W1 in the section profile coordinate system; the intersection point of the section and the conical outer surface is denoted as P cs1 ; the intersection point of the section profile and the helix angle measurement circle with a diameter μ times that of the section circle is denoted as P cs1 ; cs2 The included angle between and is γ, and is expressed as:

[0020]

[0021] Edge inclination angle λ: The edge inclination angle λ is defined as the included angle between the tangent vector V e1 of the edge point P at a distance L2 from the end face e1 relative to the tap axis vector V Zw = [0, 0, 1], and is expressed as:

[0022]

[0023] Edge length L: The P at the end of the cutting edge e2 = [x e2 , y e2 , z e2 T is the intersection point of the SPF and the straight flute on the calibration cylinder surface; therefore, the edge length L of the SPF is defined as the distance from the point P e2 to the end face, so L = z e2 .

[0024] (2) Establish a unified geometric model for the spiral point flute.

[0025] Define the unit vector of the spiral point flute bus as V tp = [i tp , j tp , k tp T , and its lift angle and swing angle are represented by α and β respectively; where, α represents the angle of V tp relative to the X W O W Z W plane, and β represents the angle of V tp in the X W O​​W Z W Projection on the plane with respect to the coordinate axis Z W Angle; V tp Expressed as:

[0026]

[0027] The geometric model of the SPF is expressed as T(x, y, z):

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

[0029] Where t is the length variable of the SPF along V tp Direction.

[0030] α and β are undetermined in equations (5) - (6) and are determined according to the mapping relationship between the geometric design parameters of the SPF and V tp Between.

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

[0032] Considering that the cutting cone surface G(x, y, z) is a rotational surface of the working part, it is expressed in the WCS as:

[0033]

[0034] Where d and κ are the diameter of the cylindrical surface and the taper angle of the conical surface of the working part respectively; L3 is the length of the conical surface along the Z W Axis.

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

[0036]

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

[0038]

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

[0040]

[0041]

[0042] The correlation between γ of SPF and V tp with respect to α and β:

[0043] The profile point P of SPF on the cross-section C in WCS cs is expressed as:

[0044]

[0045] Based on γ and P cs , the point P cs1 = [x cs1 , y cs1 , z cs1 T and P cs2 = [x cs2 , y cs2 , z cs2 T are respectively expressed as:

[0046]

[0047] In Equation (13), x t (u1), y t (u1) and x t (u2), y t (u2) are the point coordinates on the SPF end face profile corresponding to P in WCS cs1 and P cs2 , and they are constrained by the following conditions:

[0048]

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

[0050]

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

[0052] The point P e2 , as the intersection point of the three surfaces of SPF, straight groove, and cylinder, is expressed in WCS as:

[0053]

[0054]

[0055] where x s (v1), y s (v1), and z s (v1) are the point coordinates on the end face contour of the straight groove corresponding to P in the WCS. e2

[0056] Then the side length L is calculated as:

[0057]

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

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

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

[0061] Establish the grinding wheel coordinate system GCS, that is, O G -X G Y G Z G , O w1 -X W1 Y W1 Z W1 The coordinate system is obtained by first rotating the WCS 90° around the Z W axis, then rotating 90° around the Y W axis, and then translating the origin O w along X W and Y W by a x and a y respectively; the grinding wheel coordinate system GCS is obtained by rotating the O w1 -X W1 Y W1 Z W1 coordinate system by an angle β around the X W1 axis; the coordinate plane X G O G Y G is located in the end face of the grinding wheel, and Z G represents the grinding wheel axis; the origin O G in the WCS = [a x , a y , 0] T is located on the grinding wheel axis, where a x and a y are the position parameters of the grinding wheel, representing the offset distance and the center distance respectively; the initial included angle between the Y G axis and the Y W1 axis is β, and the X G axis is parallel to YW Axis, with an offset distance of a x ; Coordinate transformation matrix M from GCS to WCS G_W_1 It is expressed as:

[0062]

[0063] The minimum distance from point O W to the SPF end face contour is denoted as r min , Considering the geometric constraints between the SPF and the grinding wheel, the range of the position parameters for the grinding wheel to avoid interference during grinding is expressed as:

[0064]

[0065] The initial attitude of the grinding wheel is determined by a y and V tp , and a x is determined according to the radius of the formed grinding wheel and the internal space of the grinding machine. For the convenience of installation, it is set to zero; The initial coordinates of O G in WCS are expressed as O G = [0, a y , 0] T .

[0066] In the initial state, the axis of the grinding wheel is parallel to the XwOwZw plane and perpendicular to V tp , then the initial axis vector F G_ini of the grinding wheel in WCS is expressed as:

[0067]

[0068] The value range of η of the SPF is determined by the position of the grinding wheel in WCS; P t1 and P t2 are the intersection points of the SPF end face contour and the conical surface of the working part; θ1 and θ2 respectively represent the angles between the tangents of P t1 , P t2 and the Y W axis; The tangent slopes of P t1 and P t2 are obtained by differentiating their respective coordinates, and θ1 and θ2 are expressed as:

[0069]

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

[0071] In addition, to avoid interference, it is necessary to use the adjustment angle ξ to adjust the attitude of the grinding wheel; This angle represents the rotation of the initial grinding wheel attitude around the X GRotation of the axis, and it must satisfy ξ ≤ 90 - |β|; thus, the actual grinding wheel axis vector F in the WCS G is expressed as:

[0072]

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

[0074] Point O in the feed trajectory G0 is expressed as:

[0075]

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

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

[0078]

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

[0080] O in the retraction trajectory G2 point is expressed as:

[0081]

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

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

[0084] The parametric surface expression of the SPF is:

[0085]

[0086] n MG is expressed as:

[0087]

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

[0089]

[0090] Therefore, due to n M , n MG and F G_WCoplanar, so 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 into equation (27) together with u to calculate the point P on the contact line m_W = [x m_W , y m_W , z m_W T ; Establish the transformation matrix M between the WCS and the GCS G_W , indicating the actual grinding attitude of the grinding wheel as follows:

[0094]

[0095] On this basis, transform P in the WCS m_W into the GCS:

[0096]

[0097] By calculating the distance from point M on the meshing line to the axis Z of the grinding wheel G , the profile of the grinding wheel is obtained; Any point P on the grinding wheel profile in the GCS g_G is expressed as:

[0098]

[0099] After completing the above two steps, combine the specified design parameters and process parameters based on the unified parametric geometric model of the spiral tip groove to form a process parameter design calculation driven by the design parameters. The precision profile grinding of the spiral tip groove can be realized through the calculated profile of the formed grinding wheel and the grinding position and attitude of the grinding wheel.

[0100] The beneficial technical effects of the present invention compared with the prior art are:

[0101] In order to realize the SPF precision grinding of the spiral tip tap, considering the specific design parameters of the SPF and the over-determined structural constraints brought by the straight groove, the UPGM of the SPF is constructed. It solves the structural conflict problem between the geometric parameters of the SPF and the straight groove in the modeling process, reveals the mapping relationship between the UPGM and the SPF generatrix, and improves the modeling accuracy of the SPF.

[0102] ​The present invention establishes a full integration of the forming grinding process model and the SPF design parameter model, realizing more reliable and accurate calculation of grinding trajectories and wheel postures, and improving the practicality of this method.

[0103] Based on the line contact conjugate theory, the present invention proposes a method for calculating the profile of a formed grinding wheel considering a flexible grinding posture. It can obtain different grinding wheel profiles according to different initial wheel postures, enhancing the adaptability of form grinding and thus improving the grinding accuracy of SPF.

[0104] The method is verified through simulation and actual grinding experiments. The results show that the relatively small errors can be ignored, ensuring good grinding quality of SPF and proving the accuracy and effectiveness of the proposed precision form grinding method. Description of the Drawings

[0105] Figure 1 It is a schematic structural diagram of a spiral point tap.

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

[0107] Figure 3 It is the end face profile of the spiral point groove.

[0108] Figure 4 It is a schematic diagram of the rake angle of the spiral point groove in section C.

[0109] Figure 5 It is the cutting edge and edge length of the spiral point tap.

[0110] Figure 6 It is the spiral point groove bus and related parameters.

[0111] Figure 7 It is a schematic diagram of the initial grinding posture of the spiral point groove grinding wheel.

[0112] Figure 8 It is a schematic diagram of the range of the opening direction angle of the spiral point groove.

[0113] Figure 9 It is a schematic diagram of the actual grinding posture of the spiral point groove.

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

[0115] Figure 11 It is the SPF forming profile and the grinding trajectory calculation process.

[0116] Figure 12 It is the NC code and the simulation grinding environment.

[0117] Among them, (a) is the NC code and (b) is the simulation grinding environment.

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

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

[0120] Figure 14 For the simulation grinding result.

[0121] Figure 15 For the actual grinding device and measuring device of the spiral point tap.

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

[0123] Figure 16 For the actual grinding result of the spiral point groove.

[0124] Among them, (a) is the cutting edge length result, (b) is the cutting edge inclination angle result, and (c) is the end face profile and rake angle result. Specific implementation mode

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

[0126] A precision forming grinding method for the spiral point groove of a tap based on a unified parametric geometric model of the present invention includes the following steps:

[0127] Step 1: Establish a unified parametric geometric model of the spiral point groove.

[0128] (1) Define the unified geometric parameters of the spiral point groove.

[0129] First, establish a workpiece coordinate system (WCS) with the end face as the reference plane as shown in Figure 2 and denote it as O W -X W Y W Z W , the origin O W is located at the center of the end face, and the positive direction of the coordinate axis Z W coincides with the tap rotation center and points to the clamping part.

[0130] As shown in Figure 2 , the end face profile parameter of the straight groove is denoted as v, and the point P s on the end face is denoted as P s (v) = [x s (v), y s (v), z s (v)] T , and its bus unit vector is denoted as V st = [i st , j st, k st T ; The angle ε is defined as the angle between V st and the axis Z W in the plane formed with respect to the Y W O W Z W coordinate plane; The core thickness increment angle α1 is defined as the angle between V st and the Z W axis; Then V in the WCS st is expressed as:

[0131]

[0132] The straight groove surface H(x, y, z) is generated by sweeping P s (v) along V st and is expressed as:

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

[0134] Then, the end face profile, edge inclination angle, rake angle, and edge length of the screw tip groove are defined respectively.

[0135] The end face profile P t (u):

[0136] As Figure 3 shown, the end face profile is the projection curve of the SPF on the X W O W Y W plane. The opening direction angle η represents the angle formed by the line connecting P t1 and the O W point with respect to the Y W axis. Any point on the SPF end face profile is represented by P t (u) = [x t (u), y t (u), z t (u)] T where u is the SPF end face profile parameter.

[0137] The rake angle γ:

[0138] The rake angle γ is usually defined and measured on a certain cross-section of the SPF perpendicular to the Z W axis. The cross-section C at a distance L1 from the SPF end face is used as the specified measurement cross-section, and is expressed as C(x, y, z) = [x, y, L1] T , where x, y ∈ R. As Figure 4 ​As shown, within cross-section C, a point on the SPF cross-section profile is at O W1 -X W1 Y W1 and is marked as P in the cross-section profile coordinate system cs1 ; denote the intersection point of the cross-section and the outer surface of the cone as P cs1 , and denote the intersection point of the cross-section profile and the rake angle measurement circle with a diameter μ times that of the cross-section circle as P cs2 .

[0139] The included angle between and

[0140]

[0141] is γ, expressed as:

[0142] The rake angle λ: e1 The rake angle λ is defined as the included angle between the tangent vector V e1 of the cutting edge point P at a distance L2 from the end face Zw and the tap axis vector V Figure 5 = [0, 0, 1], as

[0143]

[0144] shown, and it is expressed as:

[0145] As Figure 5 shown, P e2 = [x e2 , y e2 , z e2 T is the intersection point of SPF and the straight groove on the calibration cylinder surface; thus, the cutting edge length L of SPF is defined as the distance from point P e2 to the end face, so L = z e2 .

[0146] (2) Establish a unified geometric model for the spiral point groove.

[0147] As Figure 6 shown, define the unit vector of the spiral point groove generatrix as V tp = [i tp , j tp , k tp T , and its lift angle and swing angle are represented by α and β respectively; among them, α represents the angle of V tp relative to the X W O W Z W plane, and β represents the angle of V tp in the X W O W Z​​W The projection on the plane with respect to the coordinate axis Z W angle.

[0148] In the WCS, V tp is expressed as:

[0149]

[0150] The geometric model of the SPF is expressed as T(x, y, z):

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

[0152] where t is the length variable of the SPF along V tp direction.

[0153] α and β are not determined in Eqs. (5) - (6) and are determined according to the mapping relationship between the geometric design parameters of the SPF and V tp .

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

[0155] Considering that the cutting cone surface G(x, y, z) is a rotational surface of the working part and is expressed in the WCS as:

[0156]

[0157] where d and κ are the diameter of the cylindrical surface and the taper angle of the conical surface of the working part respectively; L3 is the length of the conical surface along the Z W axis.

[0158] Any cutting edge point P in the WCS e is expressed as:

[0159]

[0160] By calculating the partial derivatives of x, y, z respectively from Eq. (8), the tangent vector V of the cutting edge point P e1 = [x e1 , y e1 , z e1 T is expressed as: e1 = [i e1 , j e1 , k e1 T is expressed as:

[0161]

[0162] ​​Subsequently, by combining Equation (4) and Equation (9), the relationship between λ of SPF and α and β of V tp is expressed as:

[0163]

[0164] The correlation between γ of SPF and α, β of V tp is:

[0165] The profile point P of SPF on the cross-section C in WCS cs is expressed as:

[0166]

[0167] Based on γ and P cs , the point P cs1 = [x cs1 , y cs1 , z cs1 T and P cs2 = [x cs2 , y cs2 , z cs2 T are respectively expressed as:

[0168]

[0169] In Equation (13), x t (u1), y t (u1) and x t (u2), y t (u2) are the point coordinates corresponding to P cs1 and P cs2 on the end face profile of SPF in WCS, and they are constrained by the following conditions:

[0170]

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

[0172]

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

[0174] The point P e2 as the intersection point of the three surfaces of SPF, straight groove, and cylinder is expressed in WCS as:

[0175]

[0176] where x​​s (v1), y s (v1) and z s (v1) is the point coordinate on the straight groove end face contour corresponding to P in the WCS. e2 The corresponding point coordinates on the straight groove end face contour.

[0177] Then the side length L is calculated as:

[0178]

[0179] Step 2: Form grinding calculation of the screw tip groove.

[0180] It includes the definition of the grinding pose of the form grinding wheel, the solution of the grinding trajectory of the grinding wheel, and the solution part of the form grinding wheel contour.

[0181] (1) Definition of the grinding pose of the form grinding wheel.

[0182] To describe the contour and pose of the grinding wheel, a grinding wheel coordinate system GCS is established, that is, O G -X G Y G Z G , as Figure 7 shown. O w1 -X W1 Y W1 Z W1 The coordinate system is obtained by first rotating the WCS 90° around the Z W axis, then rotating 90° around the Y W axis, and then translating the origin O w along the X W and Y W by a x and a y respectively; the grinding wheel coordinate system GCS is obtained by rotating the O w1 -X W1 Y W1 Z W1 coordinate system by an angle β around the X W1 axis; the coordinate plane X G O G Y G is located in the grinding wheel end face, and Z G represents the grinding wheel axis; the origin O G in the WCS = [a x , a y , 0] T is located on the grinding wheel axis, where a x and a y are the position parameters of the grinding wheel, representing the offset distance and the center distance respectively; the initial included angle between the Y G axis and the Y W1 axis is β, and the X G axis is parallel to the Y WAxis, with an offset distance of a x ; Coordinate transformation matrix M from GCS to WCS G_W_1 Expressed as:

[0183]

[0184] Let the minimum distance from point O W to the end face contour of the SPF be denoted as r min , considering the geometric constraints between the SPF and the grinding wheel, the range of the position parameters for the grinding wheel to avoid interference during grinding is expressed as:

[0185]

[0186] The initial attitude of the grinding wheel is determined by a y and V tp , and a x is determined according to the radius of the forming wheel and the internal space of the grinding machine. For the convenience of installation, it is set to zero; The initial coordinates of O G in WCS are expressed as O G = [0, a y , 0] T .

[0187] In the initial state, the axis of the grinding wheel is parallel to the XwOwZw plane and perpendicular to V tp , then the initial axis vector F G_ini of the grinding wheel in WCS is expressed as:

[0188]

[0189] The range of the η value of the SPF is determined by the position of the grinding wheel in WCS; As Figure 8 shown, P t1 and P t2 are the intersection points of the end face contour of the SPF and the conical surface of the working part; θ1 and θ2 respectively represent the angles between the tangents of P t1 , P t2 and the Y W axis; The tangent slopes of P t1 and P t2 are obtained by differentiating their respective coordinates, and θ1 and θ2 are expressed as:

[0190]

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

[0192] In addition, in order to reduce grinding interference and enhance the adaptability of the grinding wheel attitude, it is necessary to use the adjustment angle ξ to adjust the attitude of the grinding wheel; As Figure 9As shown, this angle represents the rotation of the initial grinding wheel attitude about the X G axis, and it must satisfy ξ ≤ 90 - |β|; therefore, the actual grinding wheel axis vector F in the WCS G is expressed as:

[0193]

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

[0195] The point O in the feed trajectory G0 is expressed as:

[0196]

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

[0198] The point O in the grinding trajectory G1 is expressed as:

[0199]

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

[0201] The O in the retraction trajectory G2 point is expressed as:

[0202]

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

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

[0205] As Figure 10 shown, the parametric surface expression of the SPF is:

[0206]

[0207] n MG is expressed as:

[0208]

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

[0210]

[0211] Therefore, since nM , n MG and F G_W are coplanar. Therefore, 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, it will cause the parameter t to change, thus causing the obtained engagement line to change, resulting in 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 the point P m_W = [x m_W , y m_W , z m_W T ; Establish the transformation matrix M G_W between the WCS and the GCS, representing the actual grinding posture of the grinding wheel as follows:

[0216]

[0217] On this basis, transform P m_W in the WCS into the GCS:

[0218]

[0219] By calculating the distance from point M on the engagement line to the grinding wheel axis Z G , the profile of the grinding wheel is obtained; Any point P g_G on the grinding wheel profile in the GCS is expressed as:

[0220]

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

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

[0223] (1) Simulation 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 according to the specified SPF design parameters and the grinding wheel posture. Then, the corresponding NC code is generated according to the coordinate transformation relationship and the execution file is output. The calculation process is as Figure 11 shown, and the NC code and simulation environment are as Figure 12 shown.

[0225] The specified design parameters of SPF are shown in Table 1. Through these parameters, the lift angle α, swing angle β, and opening direction angle η during the simulated grinding process can be calculated. The detailed grinding parameters are shown in Table 2.

[0226] Table 1 SPF design parameters

[0227]

[0228] Table 2 Grinding parameters for simulating SPF

[0229]

[0230] The simulated grinding experiment was carried out in VERICUT 9.0 to verify the method. The calculation environment includes a Dell Vostro 5890 computer, equipped 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 can be determined by the process parameters specified in Table 2. The designed end face profile of SPF and the calculated grinding wheel profile are as Figure 13 shown.

[0231] Combining Table 2 with equations (21) and (23), the angle between F G and the X W axis is calculated as β + ξ = 5.60°, and the center O G of the grinding wheel is located on the Y W axis 102.50 mm away from the origin. According to the calculated grinding wheel grinding posture, the grinding wheel profile can be deduced according to equations (30) and (34), as Figure 13 (b) shown. The maximum radius of the grinding wheel profile is 100.521 mm, and the width of the grinding wheel is 4.520 mm. Then, the calculated profile and trajectory are output to the execution file and put into the software for simulated grinding analysis. The results are as Figure 14 shown.

[0232] To calculate λ, 6 sets of points near L2 = 4.00 mm were selected from the simulation model, as shown in Table 3. Specifically, the tangent of each selected point set was used to measure λ, and the average angle value λ between the tangent and the Z W axis was calculated as 12.881° according to equation (5).

[0233] Table 3 Calculation of λ from the point set of the simulation model

[0234]

[0235] The measured edge length L is 10.810 mm, and the rake angle γ is 28.469°. As can be seen from Table 4, the relative errors and the maximum profile error of λ, γ, and L during the simulated grinding process are 0.923%, 0.867%, 0.028%, and 0.000 mm of the design values, respectively. The results show that the simulated grinding results are in good agreement with the geometric design parameters of the SPF, and the errors are all less than 1.000%, proving the effectiveness and feasibility of the proposed precision forming method.

[0236] Table 4 Comparison of the design values and simulation values of the SPF geometric parameters

[0237]

[0238] (2) Actual grinding experiment:

[0239] To further verify the proposed grinding method, the SPF grinding of the spiral point tap was carried out using a five-axis CNC grinding machine as shown in Figure 15 (a), and the parameters used in the actual grinding experiment were the same as those used in the simulated grinding. The grinding wheel used was a formed 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 shown in Figure 15 (b).

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

[0241] Table 5 Comparison of the design values and actual grinding values of the SPF geometric parameters

[0242]

[0243]

[0244] As can be seen from Table 5, 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 within the allowable tolerance range, further verifying the accuracy and effectiveness of the proposed precision forming grinding method.

Claims

1. A precision forming grinding method for the spiral tip groove of a tap based on a unified parametric geometric model, characterized in that It includes the following steps: Step 1: Establish a unified parametric geometric model of the spiral point flute: (1) Define the unified geometric parameters of the spiral point flute: First, establish a workpiece coordinate system WCS with the end face as the reference plane, denoted as O W -X W Y W Z W , whose origin O W is located at the center of the end face, and the positive direction of the coordinate axis Z W coincides with the center of the tap rotation and points to the clamping part; the straight groove end face profile parameter is denoted as v, and the point P s is denoted as P s (v) = [x s (v), y s (v), z s (v)] T , and its bus unit vector is denoted as V st = [i st , j st , k st T ; the angle ε is defined as the inclination angle of the plane formed by V st and the axis Z W relative to the Y W O W Z W coordinate plane; the core thickness increment angle α1 is defined as the included angle between V st and the Z W axis; then V st in the WCS is expressed as:​ The straight groove curved surface H(x, y, z) passes through P s (v) Along V st Swept generation, expressed as: H(x,y,z) = P s (v) + t1V st (2) where t1 is the length ratio of V st ; Then, define the end face profile, edge inclination angle, rake angle, and edge length of the spiral point flute respectively: End face contour P t (u): The opening direction angle η represents P t1 and O W The included angle formed by the line connecting the points with respect to the Y W axis, and any point on the SPF end face contour is represented by P t (u) = [x t (u), y t (u), z t (u)] T where u is the SPF end face contour parameter; Rake angle γ: The cross-section C at a distance L1 from the end face of the SPF is defined as the specified measurement cross-section, with C(x,y,z) = [x,y,L1] T , where x,y ∈ R; within the cross-section C, a point on the SPF cross-section profile is marked as P W1 -X W1 Y W1 in the cross-section profile coordinate system cs1 ; the intersection point of the cross-section and the outer surface of the cone is denoted as P cs1 , and the intersection point of the cross-section profile and the rake angle measurement circle with a diameter μ times that of the cross-section circle is denoted as P cs2 ; The angle between is γ, expressed as: Rake angle λ: The rake angle λ is defined as the angle between the cutting vector V e1 of the cutting edge point P at a distance L2 from the end face e1 and the tap axis vector V Zw = [0, 0, 1], expressed as: Cutting edge length L: P at the end of the cutting edge e2 = [x e2 , y e2 , z e2 T is the intersection point of the SPF and the straight flute on the calibrated cylindrical surface;​ Therefore, the blade length L of the SPF is defined as the distance from point P e2 to the end face, so L = z e2 ; (2) Define the unified geometric model of the spiral point flute: Define the unit vector of the spiral tip groove busbar as V tp = [i tp , j tp , k tp T , where the lift angle and swing angle are represented by α and β respectively; among them, α represents the angle of V tp relative to the X W O W Z W plane, and β represents the angle of the projection of V tp on the X W O W Z W plane relative to the coordinate axis Z W ; V tp is expressed as:​ The geometric model of the SPF is expressed as T(x, y, z): T(x, y, z) = P t (u) + tV tp , t ≥ 0 (6) where t is the length variable of SPF along the V tp direction; α and β are undetermined in Formulas (5) to (6) and are determined according to the mapping relationship between the geometric design parameters of the SPF and V tp ; the correlation between λ of the SPF and α and β of V tp : Considering that the cutting cone surface G(x, y, z) is the rotating surface of the working part, it is expressed in the WCS as: where d and κ are the diameter of the cylindrical surface and the taper angle of the conical surface of the working part respectively; L3 is the length of the conical surface along the Z W axis; Any cutting edge point P in the WCS e Is expressed as: By calculating the partial derivatives of \(x\), \(y\), and \(z\) in Equation (8) respectively, the edge point \(P\) is obtained e1 =[[x e1 ,[[y e1 ,[[z e1 T The tangent vector \(V\) of e1 =[[i e1 ,[[j e1 ,[[k e1 T is expressed as:​​ Subsequently, by combining Equation (4) and Equation (9), the relationship between λ of SPF and α and β of V tp is expressed as: γ and V of SPF tp Correlation between α and β of Profile point P of SPF on cross-section C in the WCS cs Expressed as: Based on γ and P cs , the point P cs1 = [x cs1 , y cs1 , z cs1 T and P cs2 = [x cs2 , y cs2 , z cs2 T are respectively expressed as:​​ In Equation (13), x t (u1), y t (u1) and x t (u2), y t (u2) are the point coordinates corresponding to P cs1 and P cs2 in the WCS on the SPF end face contour, and they are subject to the following conditions: According to equations (3), (13), and (14), the relationship between γ of the SPF and α, β of Vtp is expressed as: L and V of SPF tp Correlation between α and β: Point P e2 As the intersection point of the three surfaces of SPF, straight groove, and cylinder, it is represented in the WCS as: where x s (v1), y s (v1), and z s (v1) are the point coordinates on the end face contour of the straight groove corresponding to P e2 in the WCS; Then the side length L is calculated as: Step 2: Calculation of the spiral point flute form grinding: It includes the definition of the grinding pose of the form grinding wheel, the solution of the grinding trajectory of the grinding wheel, and the solution part of the form grinding wheel profile; (1) Definition of the grinding attitude of the form grinding wheel: Establish the grinding wheel coordinate system GCS, that is, O G -X G Y G Z G , O w1 -X W1 Y W1 Z W1 The coordinate system is obtained by first rotating the WCS by 90° around the Z W axis, then rotating by 90° around the Y W axis, and then translating the origin O w along X W and Y W by a x and a y respectively; the grinding wheel coordinate system GCS is obtained by rotating the O w1 -X W1 Y W1 Z W1 coordinate system by an angle β around the X W1 axis; the coordinate plane X G O G Y G is located in the end face of the grinding wheel, and Z G represents the grinding wheel axis; the origin O G in the WCS = [a x , a y , 0] T is located on the grinding wheel axis, where a x and a y are the position parameters of the grinding wheel, representing the offset distance and the center distance respectively; the initial angle between the Y G axis and the Y W1 axis is β, the X G axis is parallel to the Y W axis, and the offset distance is a x ; the coordinate transformation matrix M G_W_1 from GCS to WCS is expressed as: The minimum distance from point O W to the end face profile of the SPF is denoted as r min , considering the geometric constraints between the SPF and the grinding wheel, the range of the position parameters for the grinding wheel to avoid interference during grinding is expressed as: The initial attitude of the grinding wheel is determined by a y and V tp where a x is determined according to the radius of the form grinding wheel and the internal space of the grinding machine. For the convenience of installation, it is set to zero; The initial coordinates of O G in the WCS are represented as O G = [0, a y , 0] T ; In the initial state, the axis of the grinding wheel is parallel to the XwOwZw plane and perpendicular to V tp , then the initial axis vector F of the grinding wheel in the WCS G_ini is expressed as: The η value range of the SPF is determined by the position of the grinding wheel in the WCS; P t1 and P t2 are the intersection points of the SPF end face profile and the conical surface of the working part; θ1 and θ2 respectively represent the angles between the tangents of P t1 and P t2 and the Y W axis; the tangent slopes of P t1 and P t2 are obtained by differentiating their respective coordinates, and θ1 and θ2 are expressed as: Therefore, η should be in the range of η0 - θ1 ≤ η ≤ η0 - θ2, where η0 is the initial opening direction angle of the SPF end face profile; In addition, to avoid interference, it is necessary to adjust the attitude of the grinding wheel using the adjustment angle ξ; this angle represents the rotation of the initial grinding wheel attitude about the X G axis and must satisfy ξ ≤ 90 - |β|; therefore, the actual grinding wheel axis vector F in the WCS G is expressed as: (2) Calculation of the grinding trajectory of the form grinding wheel: Point O in the feed path G0 It is expressed as: where L F is the axial feed distance of the SPF, and t2 is the length of V tp . Point O in the grinding trajectory G1 It is expressed as: where L G is the grinding length of SPF, and t3 is the grinding length of V tp ; O in the retraction path G2 The point is represented as: where t4 is the length of V tp ; (3) Calculation of the form grinding wheel profile: The parametric surface expression of the SPF is: n MG Expressed as: Cross-multiply the partial derivatives of \(T(u, t)\) with respect to \(u\) and \(t\) to obtain \(n\) of the SPF surface M as follows: Therefore, since n M , n MG and F G_W 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 the point P on the contact line m_W =[x m_W ,y m_W ,z m_W T ; Establish the transformation matrix M between the WCS and the GCS G_W , indicating the actual grinding attitude of the grinding wheel as follows:​ On this basis, convert P in the WCS m_W to the GCS: By calculating the distance from point M on the engagement line to the axis Z of the grinding wheel, the profile of the grinding wheel is obtained; any point P on the grinding wheel profile in the GCS G is expressed as: g_G All are expressed as:

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