Grinding method for convex edge shovel back of integral end mill

Abstract

The invention relates to the technical field of end mill machining, in particular to a grinding method for a convex edge shovel back of an integral end mill. In the grinding method, the relief shape is regulated and controlled by giving the margin width, the convex edge inclination angle, the convex edge depth and the relief depth of the integral end mill, the edge strength can be improved by reducing the convex edge depth, and the chip containing space can be improved by increasing the relief depth; the purpose of considering the blade strength and the chip containing space of the end mill is achieved by coordinating the convex blade depth and the relief depth. And determining a grinding wheel path required for grinding the relief back by taking conjugation of a grinding wheel revolution surface and a blade width curve, tangent of a grinding wheel arc boundary circle and a convex blade depth revolution surface and tangent of the grinding wheel revolution surface and a relief back depth curve as constraint conditions, so that four given geometric parameters of the convex blade relief back can be accurately processed, and accurate processing of the convex blade relief back is realized. And the cutting edge strength and the chip containing space of the end mill can be simultaneously considered.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of end mill machining, and particularly relates to a grinding method for convex blade back of a whole end mill. BACKGROUND

[0002] In the manufacturing of a whole end mill, the width of the blade of some models of the end mill cannot meet the design requirements due to a small number of grooves or a special groove design. At this time, the width of the blade can be reduced and the strength of the blade can be improved by adding a convex blade back process.

[0003] However, the existing grinding process for the convex blade back of the whole end mill cannot simultaneously consider the strength of the blade and the chip space. If higher strength of the blade is pursued, the depth of the back is reduced, and thus the chip space is insufficient. If a larger chip space is pursued, the depth of the back is increased, and thus the strength of the blade is weakened.

[0004] Therefore, it is necessary to provide an improved technical solution for the above-mentioned problems of the prior art. SUMMARY

[0005] The purpose of the present application is to provide a grinding method for the convex blade back of a whole end mill to solve or alleviate the above-mentioned problems in the prior art.

[0006] In order to achieve the above-mentioned purpose, the present application provides the following technical solution: A grinding method for the convex blade back of a whole end mill, characterized in that the grinding method comprises the following steps: Step 1, giving each parameter function in the whole end mill, each parameter function comprising a blade width function, a convex blade inclination angle function, a convex blade depth function and a back depth function; obtaining a blade width curve, a blade width curve unit normal vector, a convex blade depth surface and a back depth curve according to each parameter function; Then discretize the blade width curve to obtain a series of blade width points; Step 2, setting the following constraint condition at a blade width point position in the series of blade width points: first, making the grinding wheel rotation surface tangent to the blade width curve at the blade width point, and making the normal vector of the grinding wheel rotation surface and the blade width curve at the blade width point collinear; Step 3, under the constraint condition of step 2, adjusting the grinding wheel pose to make the grinding wheel circular arc division circle tangent to the convex blade depth surface and the grinding wheel rotation surface tangent to the back depth curve, thereby determining the grinding wheel pose at the blade width point position; Step 4, repeating steps 2-3 to determine the grinding wheel pose at each blade width point position on the blade width curve, and obtaining the grinding wheel path required for grinding the convex blade back of the end mill by collecting the grinding wheel poses at each blade width point position.

[0007] The method for grinding the convex edge and the chip breaker of the solid end mill as described above, preferably, in step 1, the coordinate system S of the end mill is established t (O t - x t , y t , z t ), which is fixed with the end mill, the origin O t is coincided with the center of the end face of the end mill, the z t axis is coincided with the axis of the end mill. Given the functions of the outer circle radius , the width of the edge , the inclination angle of the convex edge , the depth of the convex edge , and the depth of the chip breaker . represents the vertical distance between the cross section of the end mill and the end face of the end mill.

[0008] The method for grinding the convex edge and the chip breaker of the solid end mill as described above, preferably, in step 1, the position vector of a point on the edge curve is rotated by an angle around the axis of the end mill to obtain an edge width curve, the position vector of a point on the edge width curve is represented by , and the edge width curve is discretized into n edge width points by setting . The unit tangent vector of a point on the edge width curve is: . In a cross section of the end mill, the unit vector of the tangent line of the convex edge and the chip breaker profile at the edge width point is represented by , and the unit normal vector of the edge width point is defined as: .

[0009] The method for grinding the convex edge and the chip breaker of the solid end mill as described above, preferably, in step 1, in a cross section of the end mill, a convex edge depth circle is drawn with the center point of the cross section as the center and the radius of , and the convex edge depth circles in different cross sections form a convex edge depth revolving surface.

[0010] The method for grinding the convex edge and the chip breaker of the solid end mill as described above, preferably, in step 1, in a cross section of the end mill, a chip breaker depth circle is drawn with the center point of the cross section as the center and the radius of , and the intersection point D of the chip breaker depth circle and the flute profile forms a chip breaker depth curve.

[0011] The method for grinding the convex edge and the chip breaker of the solid end mill as described above, preferably, in step 2, the coordinate system S w (O w - xw , y w , z w ), origin O w is coincident with the center of the side surface of the grinding wheel, z w axis is coincident with the axis of the grinding wheel; The position vector of a point on the grinding wheel rotation surface in the grinding wheel coordinate system S w is: ; In the formula, represents the radius of the grinding wheel gradually changing along the axis of the grinding wheel; The unit normal vector of a point on the grinding wheel rotation surface is: ; In the formula, , .

[0012] The grinding method of the convex edge of the solid end mill as described above, preferably, in step 2, the conversion matrix of the grinding wheel coordinate system S w to the tool coordinate system S t is established, and the point and the normal vector on the grinding wheel rotation surface are converted to the tool coordinate system through coordinate transformation, and are represented by symbols and respectively; A reference coordinate system S r (O r – x r , y r , z r ) is established, the z r axis is coincident with the z t axis, and the origin O w of the grinding wheel coordinate system is located in the x r -y r plane; Wherein, the coordinates of the origin O w of the grinding wheel coordinate system in the x r -y r plane are a x , a y , the distance from the origin O t of the end mill coordinate system to the origin O r of the reference coordinate system is a z , the included angle between the axis of the grinding wheel and the axis of the end mill is λ, and the rotation angle of the end mill around its own axis is δ.

[0013] The grinding method of the convex edge of the solid end mill as described above, preferably, in step 2, the grinding wheel rotation surface is tangent to the edge width curve at the i-th edge width point, and the normal vector of the grinding wheel rotation surface and the edge width curve at the tangent point is collinear, that is, it satisfies: (1) (2) wherein, represents the position vector of the i-th land point, represents the unit normal vector of the land curve at the i-th land point, represents the position vector of the tangent point of the grinding wheel rotary surface, represents the unit normal vector of the grinding wheel rotary surface at the tangent point; The pose of the grinding wheel relative to the tool satisfies the following formula from formula (1) and formula (2): (3) wherein, ; ; ; ; wherein, , , represents the coordinate of the i-th land point in the tool coordinate system S t , , represents the coordinate of the unit normal vector of the land curve at the i-th land point in the tool coordinate system S t .

[0014] The grinding method of the convex land and the relief of the solid end mill as described above, preferably, in step 3, the point on the convex land depth rotary surface is circularly projected around the grinding wheel axis to the x w -z w plane, and the upper envelope line of the circular projection of the convex land depth rotary surface is obtained according to the envelope principle, when the line connecting a point on the grinding wheel circular arc boundary circle and a point on the envelope line is parallel to the x w axis, and the point on the grinding wheel circular arc boundary circle and the same point on the envelope line coincide with each other, the grinding wheel circular arc boundary circle and the convex land depth rotary surface satisfy the tangential relationship.

[0015] The grinding method of the convex land and the relief of the solid end mill as described above, preferably, in step 3, the point on the convex land depth rotary surface is circularly projected around the grinding wheel axis to the x w -z w plane; In the x w -z w plane, when the circular projection of the relief depth curve is tangent to the grinding wheel axis cross-sectional profile, the grinding wheel rotary surface and the relief depth curve satisfy the tangential relationship.

[0016] ​Compared with the closest prior art, the technical scheme of the embodiment of the present application has the following beneficial effects: In the grinding method, the shape of the shoveling back is regulated by giving the land width, the land angle, the land depth and the shoveling back depth of the whole end mill, the land depth is reduced to improve the strength of the cutting edge, the shoveling back depth is increased to improve the chip space, and the land depth and the shoveling back depth are coordinated to achieve the purpose of considering the strength of the cutting edge and the chip space of the end mill.

[0017] Then, the grinding wheel rotation surface and the land width curve are conjugated, the grinding wheel circular arc boundary circle and the land depth rotation surface are tangent, and the grinding wheel rotation surface and the shoveling back depth curve are tangent as the constraint conditions, the grinding wheel path required for grinding the shoveling back is determined, the four given geometric parameters of the land shoveling back can be accurately machined, and the accurate machining of the land shoveling back is realized, so that the strength of the cutting edge and the chip space of the end mill can be considered at the same time. BRIEF DESCRIPTION OF DRAWINGS

[0018] The drawings accompanying the specification of the present application serve to provide further understanding of the present application, and the illustrative embodiments of the present application and the description thereof serve to explain the present application, and do not constitute improper limitations on the present application. Among them: Figure 1 The land shoveling back of the whole end mill provided according to some embodiments of the present application; Figure 2 The cross-sectional profile of the whole end mill provided according to some embodiments of the present application; Figure 3 The grinding wheel rotation surface and the axial cross-sectional profile provided according to some embodiments of the present application; Figure 4 The movement relationship and the coordinate system of the grinding wheel and the end mill provided according to some embodiments of the present application; Figure 5 The circular arc projection of the grinding wheel axial cross-sectional profile and the land depth rotation surface provided according to some embodiments of the present application; Figure 6 The circular arc projection of the grinding wheel axial cross-sectional profile and the shoveling back depth curve provided according to some embodiments of the present application.

[0019] Explanation of reference signs: 1, cutting edge curve; 2, land width curve; 3, land shoveling back surface; 4, shoveling back depth curve; 5, chip space; 6, end mill cross-sectional outer circle; 7, land depth circle; 8, shoveling back depth circle; 9, grinding wheel circular arc boundary circle; 10, grinding wheel rotation surface; 11, grinding wheel axial cross-sectional profile; 12, grinding wheel; 13, end mill; 14, circular arc projection of the land depth rotation surface; 15, upper envelope line of the circular arc projection of the land depth rotation surface; 16, circular arc projection of the shoveling back depth curve. DETAILED DESCRIPTION

[0020] The present application will be described in detail below with reference to the attached drawings and embodiments. Various examples are provided by way of explanation of the present application but are not intended to limit the present application. It will be obvious to a person skilled in the art that modifications and variations of the present application can be made without departing from the scope or spirit of the present application. For example, features shown or described as part of one embodiment can be used in another embodiment to create yet another embodiment. It is, therefore, desired that what is claimed be determined by the scope of the appended claims and equivalents thereof.

[0021] In the following description, the terms "first / second / third" are merely to distinguish similar objects, and do not represent a specific order of the objects. Understandably, the "first / second / third" can be interchanged in a specific order or sequence as allowed, so that the embodiments of the present application described herein can be implemented in an order other than that illustrated or described herein.

[0022] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. The terminology used in the description herein is for describing the embodiments of the present disclosure only and is not intended to be limiting of the present disclosure.

[0023] In the description of the present application, the terms "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", and the like indicate the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and do not require the present application to be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation of the present application. The terms "connected", "connected", "provided" used in the present application should be understood broadly, for example, it can be fixedly connected or detachably connected; it can be directly connected or indirectly connected through intermediate components; it can be wired electrical connection, wireless electrical connection or wireless communication signal connection, and the specific meaning of the above terms can be understood by a person of ordinary skill in the art according to the specific circumstances.

[0024] The present application will be described in detail below with reference to the attached drawings and embodiments. It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0025] According to a specific embodiment of the present application, as shown in Figures 1-6 The present application provides a grinding method for the convex blade and the land of a solid end mill, the grinding method comprising the following steps: Step 1, given the parameter functions in the solid end mill, the parameter functions include the blade width function, the convex blade angle function, the convex blade depth function and the land depth function.

[0026] Based on the functions of each parameter, the cutting width curve 2, the unit normal vector of the cutting width curve 2, the convex cutting depth rotation surface, and the back cutting depth curve 4 are obtained.

[0027] Then, the cutting width curve 2 is discretized to obtain a series of cutting width points.

[0028] Step 2: At one of the cutting width points in a series of cutting width points, set the following constraints: First, make the grinding wheel rotating surface 10 tangent to the cutting width curve 2 at the cutting width point, and make the normal vectors of the grinding wheel rotating surface 10 and the cutting width curve 2 collinear at the cutting width point.

[0029] Step 3: Under the constraints of Step 2, by adjusting the grinding wheel position, the grinding wheel arc dividing circle 9 is made tangent to the convex edge depth rotation surface, while the grinding wheel rotation surface 10 is made tangent to the back edge depth curve 4, thereby determining the grinding wheel position at the edge width point.

[0030] Step 4: Repeat steps 2-3 to determine the grinding wheel pose at each cutting edge point on the cutting edge curve 2. Combine the grinding wheel poses at each cutting edge point to obtain the grinding wheel path required for grinding the convex back edge of the end mill.

[0031] In this grinding method, the shape of the chip back is controlled by giving the cutting edge width, rake angle, rake depth and chip back depth of the integral end mill. Decreasing the rake depth can improve the cutting edge strength, while increasing the chip back depth can improve the chip space. By coordinating these two parameters, the cutting edge strength and chip space of the end mill are balanced.

[0032] Then, using the conjugate of the grinding wheel rotation surface 10 and the cutting width curve 2, the tangency of the grinding wheel arc dividing circle 9 and the convex cutting depth rotation surface, and the tangency of the grinding wheel rotation surface 10 and the back cutting depth curve 4 as constraints, the grinding wheel path required for grinding the back cutting is determined. This allows for the precise machining of the four geometric parameters given for the convex cutting back cutting, thereby achieving precise machining of the convex cutting back cutting and ensuring that the cutting edge strength and chip space of the end mill can be taken into account simultaneously.

[0033] In this embodiment, the back surface 3 of the convex blade is the machining surface of the grinding wheel 12 on the end mill 13; in the attached Figure 2 In the end mill, the back of the convex blade shovel 3 is represented by curve BCD in the cross-section of the end mill, that is, the profile of the convex blade shovel back in the cross-section.

[0034] In step 1, the end mill coordinate system S is established. t (O t - x t , y t , z t ), fixed to the end mill, origin O t Coinciding with the center of the end mill face, z t The axis coincides with the axis of the end mill; Given outside radius function , land width function , convex edge inclination function , convex edge depth function , clearance depth function ; represents the perpendicular distance between the end face of the end mill and the cross section of the end mill.

[0035] In this embodiment, the designed end mill profile is obtained by giving the functions of the plurality of geometric parameters in the end mill. The given outside radius function represents the outside radius of the end mill; when the main structure of the end mill is cylindrical, the outside radius function is a constant value at different cross sections of the end mill; when the main structure of the end mill is conical, the outside radius function is a gradually changing value at different cross sections of the end mill.

[0036] Land width function represents the gradual change of the land width along the axial direction of the end mill.

[0037] Convex edge inclination function represents the gradual change of the convex edge inclination along the axial direction of the end mill.

[0038] Convex edge depth function represents the gradual change of the convex edge depth along the axial direction of the end mill.

[0039] Clearance depth function represents the gradual change of the clearance depth along the axial direction of the end mill.

[0040] In one cross section of the end mill, as shown in FIG. 1, Figure 2 is a point on the edge curve 1, is a point on the land width curve 2, is the center of the cross section outside circle 6 of the end mill, the curve BCD is the convex edge clearance profile, which is composed of a concave circular arc BC and a convex circular arc CD, the curve EDG is the flute 5 profile, the point D is the intersection point of the flute 5 profile and the convex edge clearance profile, the point H is the intersection point of the ray OC and the cross section outside circle 6 of the end mill, the point F is the intersection point of the ray OD and the cross section outside circle 6 of the end mill, the ray BI is the tangent of the convex edge clearance profile at the point B, is the land width of the end mill , is the convex edge inclination of the end mill , the length of the line segment is the convex edge depth , and the length of the line segment is the clearance depth ​, the outer circle radius of the end mill cross section is .

[0041] In the embodiment, the convex edge depth revolving surface is a revolving surface formed by the convex edge depth circles 7 of different cross sections of the end mill; and the gullet depth curve 4 is a set line of the points D of different cross sections of the end mill.

[0042] In step 1, each point on the tool edge curve 1 is rotated by an angle to obtain the edge width curve 2, and the position vector of a point on the edge width curve 2 is represented by , and to discretize the edge width curve 2 into n edge width points; The unit tangent vector of a point on the edge width curve 2 is: ; In a cross section of the end mill, the unit vector of the tangent line of the convex edge gullet profile at the edge width point is represented by , and the unit normal vector of the edge width point is defined as: .

[0043] In the embodiment, as shown in Figure 2 , given the edge band width function , each point A on the tool edge curve 1 is rotated by an angle to obtain each edge width point B, and each edge width point B constitutes the edge width curve 2; then the edge width curve 2 is discretized into a plurality of edge width points, and the unit tangent vector at an edge width point is crossed with the unit vector of the tangent line of the convex edge gullet profile at the edge width point to obtain the unit normal vector of the edge width point.

[0044] In step 1, in a cross section of the end mill, a convex edge depth circle 7 is made with the center point of the cross section as the center and as the radius, and the convex edge depth circles 7 in different cross sections constitute the convex edge depth revolving surface.

[0045] In the embodiment, in the attached Figure 2 , the radius of the convex edge depth circle 7 in a cross section of the tool is obtained by subtracting the value of the convex edge depth function at the cross section from the value of the outer circle radius function at the cross section, and then the convex edge depth circle 7 is made with O as the center, and different convex edge depth circles 7 in different cross sections are fitted to form the convex edge depth revolving surface.

[0046] In step 1, in a cross section of the end mill, a gullet depth circle 8 is made with the center point of the cross section as the center and as the radius, and the gullet depth circle 8 intersects with the groove profile at the point D, and the intersection points D in different cross sections constitute the gullet depth curve 4.

[0047] In this embodiment, in the appendix Figure 2 In the process, the radius of the back depth circle 8 in the cross section is obtained by subtracting the value of the back depth function in the cross section from the value of the outer circle radius function in the cross section. Then, the back depth circle 8 is drawn with O as the center. The back depth circle 8 intersects the profile of the chip groove 5 at point D. The radius of the back depth circle 8 is also the distance from point D to point O. The back depth curve 4 is formed by fitting point D in different cross sections.

[0048] In step 2, the grinding wheel coordinate system S is established. w (O w – x w , y w , z w ), origin O w Coinciding with the center of the grinding wheel's side, z w The shaft coincides with the axis of the grinding wheel; A point on the rotating surface 10 of the grinding wheel in the grinding wheel coordinate system S w The position vector in is: ; In the formula, This indicates the radius of the grinding wheel, which gradually changes along the axis of the grinding wheel. The unit normal vector of a point on the rotating surface 10 of the grinding wheel is: ; In the formula, , .

[0049] In this embodiment, as Figure 3 As shown, the profile 11 of the grinding wheel shaft section includes circular arc KL, straight line LM, and circular arc MN, with point M circling around z. w The rotation of the shaft forms the arc dividing circle 9 of the grinding wheel. In the grinding wheel coordinate system, the unit normal vector of a point on the grinding wheel rotation surface 10 is obtained based on the position vector of that point.

[0050] In step 2, the grinding wheel coordinate system S is established. w To tool coordinate system S t The transformation matrix, through coordinate transformation, transforms the points and normal vectors on the grinding wheel's rotating surface 10 to the tool coordinate system, respectively using symbols... and express.

[0051] In this embodiment, the motion relationship between the grinding wheel and the end mill during grinding the convex edge back is as follows: Figure 4 As shown, coordinate system S r (O r – x r , y r , z r) is the reference coordinate system, z r axis coincides with z t axis, the origin O of the grinding wheel coordinate system is located at x w , r -y r plane, a x , a y , a z represents the position of the grinding wheel relative to the end mill, λ represents the angle between the grinding wheel axis and the end mill axis, and the angle λ is also the angle between the z r axis and the z w axis; δ represents the rotation angle of the end mill around its own axis, wherein the own axis of the end mill is the z r axis (i.e. the z t axis).

[0052] a x , a y , a z , λ, δ together determine the pose of the grinding wheel relative to the end mill. The conversion matrix of the grinding wheel coordinate system S w to the tool coordinate system S t is: ; thus, according to the above conversion matrix, the point and normal vector on the grinding wheel rotation surface 10 are converted to the tool coordinate system.

[0053] In step 2, the grinding wheel rotation surface 10 is tangent to the blade width curve 2 at the i-th blade width point, and the normal vector of the grinding wheel rotation surface 10 at the tangent point is collinear with the blade width curve 2, that is, it satisfies: (1) (2) In the formula, r represents the position vector of the i-th blade width point, represents the unit normal vector of the blade width curve 2 at the i-th blade width point, represents the position vector of the tangent point of the grinding wheel rotation surface 10, represents the unit normal vector of the grinding wheel rotation surface 10 at the tangent point. From formula (1) and formula (2), it can be obtained that the pose of the grinding wheel relative to the tool satisfies the following formula: (3) In the formula, ; ; ; ; wherein, , , This indicates that the i-th cutting edge width point is located in the tool coordinate system S. t The coordinates below, , , This represents the unit normal vector of the cutting width curve 2 at the i-th cutting width point in the tool coordinate system S. t The coordinates below.

[0054] In this embodiment, equation (3) expresses the grinding wheel pose as a function of the pose control parameters. and The function, by adjusting and The value is used to adjust the position of the grinding wheel so that the arc dividing circle 9 of the grinding wheel is tangent to the depth rotation surface of the convex edge, while the rotation surface 10 of the grinding wheel is also tangent to the back depth curve 4 of the shovel.

[0055] In step 3, the point on the depth-of-rotation surface of the convex cutting edge is projected onto the x-axis via an arc around the grinding wheel axis. w -z w The upper envelope line 15 of the circular arc projection of the depth of the convex cutting edge, obtained by the principle of envelope, is when the line connecting a point on the arc dividing circle 9 of the grinding wheel and a point on the envelope line is parallel to x. w When the axis is such that a point on the arc dividing circle 9 of the grinding wheel coincides with the same point on the envelope, the arc dividing circle 9 of the grinding wheel and the depth rotation surface of the convex cutting edge satisfy the tangent relationship.

[0056] In this embodiment, in order to determine the positional relationship between the grinding wheel arc dividing circle 9 and the convex cutting edge depth rotation surface, the points on the convex cutting edge depth rotation surface are projected onto the x-axis of the grinding wheel via an arc. w -z w The plane, the grinding wheel coordinate system x, is obtained from the following formula. w -z w 14. Circular projection of the depth-revolving surface of the convex cutting edge in the plane: ; In the formula, , , The point on the rotating surface representing the depth of the convex cutting edge in the grinding wheel coordinate system S w The coordinates below.

[0057] x w -z w The arc projection of the depth of the convex cutting edge in the plane as shown in Figure 14 Figure 5 As shown, the upper envelope line 15 of the circular arc projection of the depth of the convex cutting edge is obtained by the envelope principle. A line parallel to x is drawn through point M on the profile of the grinding wheel shaft section 11. w A straight line along the axis intersects at point P the upper envelope of the circular arc projection of the convex cutting edge depth revolution surface. The length of line segment PM is defined as the convex cutting edge depth error. When , the point M and the point P coincide, at this time, the grinding wheel circular arc boundary circle 9 and the convex blade depth rotary surface satisfy the tangential relationship. The value of depends on the grinding wheel pose, therefore can be regarded as a function of the pose control parameters , i.e. .

[0058] In step 3, the point on the shovel back depth curve 4 is projected to the x w -z w plane around the grinding wheel axis circular arc; in the x w -z w plane, when the circular arc projection 16 of the shovel back depth curve and the grinding wheel axis cross section profile 11 are tangent, the grinding wheel rotary surface 10 and the shovel back depth curve 4 satisfy the tangential relationship.

[0059] In this embodiment, in order to judge the positional relationship of the grinding wheel rotary surface 10 and the shovel back depth curve 4, the point on the shovel back depth curve 4 is projected to the x w -z w plane around the grinding wheel axis circular arc, the circular arc projection 16 of the shovel back depth curve in the x w -z w plane of the grinding wheel coordinate system is obtained by the following formula: ; In the formula, , , the coordinates of the point on the shovel back depth curve 4 in the grinding wheel coordinate system S w are represented. The circular arc projection 16 of the shovel back depth curve in the x w -z w plane is shown in FIG. 6, a straight line parallel to the x w axis is drawn through a point Q on the shovel back depth curve 4, compared with the point R, the length of the line segment QR changes with the position of the point Q, when the point Q is inside the grinding wheel axis cross section profile 11, the length of the line segment QR is negative, as shown in FIG. 6a; when the point Q is outside the grinding wheel axis cross section profile 11, the length of the line segment QR is positive, as shown in FIG. 6b. The minimum value of the length of the line segment QR is defined as the shovel back depth error , when the circular arc projection 16 of the shovel back depth curve and the grinding wheel axis cross section profile 11 intersect, , as Figure 6 c; when the circular arc projection 16 of the shovel back depth curve and the grinding wheel axis cross section profile 11 are apart, , as Figure 6 d; when At this time, the circular arc projection 16 of the gullet depth curve is tangent to the grinding wheel axis cross section profile 11, as shown in Fig. 3. Figure 6 e. When the grinding wheel rotary surface 10 is tangent to the gullet depth curve 4. The value of depends on the grinding wheel pose, thus can be regarded as a function of the pose control parameters and , i.e. In order to make the grinding wheel circular arc boundary circle 9 tangent to the convex edge depth rotary surface while the grinding wheel rotary surface 10 is tangent to the gullet depth curve 4, the grinding wheel pose parameters should be adjusted so that and are both 0.

[0060] The grinding wheel pose parameters satisfying the requirements can be obtained by solving the following equations.

[0061] ; The above process is repeated to determine the grinding wheel pose of each edge width point, and the grinding wheel path required for grinding the gullet of the convex edge is obtained from the grinding wheel pose of each edge width point.

[0062] The above only describes the preferred embodiments of the present application and is not used to limit the present application. Various modifications and changes can be made by those skilled in the art based on the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A grinding method of a convex land chip back of a solid end mill, characterized by, The grinding method comprises the following steps: Step 1, given the parameter functions in the whole end mill, the parameter functions include the blade width function, the convex blade inclination angle function, the convex blade depth function and the shoveling back depth function; According to the parameter functions, the blade width curve, the blade width curve unit normal vector, the convex blade depth rotary surface and the shoveling back depth curve are obtained; Then the blade width curve is discretized to obtain a series of blade width points; Step 2, at a blade width point position in the series of blade width points, the constraint conditions are set as follows: firstly, the grinding wheel rotary surface is tangent to the blade width curve at the blade width point, and the normal vector of the grinding wheel rotary surface and the blade width curve at the blade width point is collinear; Step 3, under the constraint condition of step 2, by adjusting the grinding wheel pose, the grinding wheel circular arc boundary circle is tangent to the convex blade depth rotary surface at the same time, and the grinding wheel rotary surface is tangent to the shoveling back depth curve, so as to determine the grinding wheel pose at the blade width point position; Step 4, repeat steps 2-3 to determine the grinding wheel pose at each blade width point position on the blade width curve, and the grinding wheel path required for grinding the convex blade shoveling back of the end mill is obtained by collecting the grinding wheel poses at each blade width point position.

2. The grinding method of a convex land chip back of a solid end mill according to claim 1, characterized by, In step 1, establish the end mill coordinate system S t (O t - x t , y t , z t ), which is fixed with the end mill, the origin O t coincides with the center of the end mill end face, and the z t axis coincides with the end mill axis; Given outside radius function , land width function , convex land inclination function , convex land depth function , land back depth function ; represents the perpendicular distance between the end face of the end mill and the cross section of the end mill.

3. The grinding method of a convex land chip back of a solid end mill according to claim 2, characterized by, In step 1, each point on the blade curve is rotated by an angle around the axis of the end mill to obtain a blade width curve, the position vector of a point on the blade width curve is represented by , and let discretize the blade width curve into n blade width points; The unit tangent vector of a point on the blade width curve is: ； In one cross-section of the end mill, the unit vector of the tangent of the convex flank chip-breaker profile at the said land point is denoted by and the unit normal vector of the said land point is defined as: 。 4. The grinding method of a convex land chip back of a solid end mill according to claim 3, characterized by, In step 1, in one cross section of the end mill, a convex edge depth circle is made with the center point of the cross section as the center and with a radius of In different cross sections, the convex edge depth circles form a convex edge depth rotary surface.

5. The method of grinding a convex land chip back of a solid end mill according to claim 4, wherein, In step 1, in one cross section of the end mill, a gash depth circle is made with the center point of the cross section as the center and with a radius of In step 1, in one cross section of the end mill, a gash depth circle is made with the center point of the cross section as the center and with a radius of 6. The grinding method of a convex land chip back of a solid end mill according to claim 5, wherein In step 2, the grinding wheel coordinate system S is established w (O w – x w , y w , z w ), the origin O w is coincident with the grinding wheel side surface center, and the z w axis is coincident with the grinding wheel axis; The position vector of a point on the rotary surface of the grinding wheel in the grinding wheel coordinate system S is: w ​ ； wherein represents the radius of the grinding wheel which varies gradually along the grinding wheel axis; The unit normal vector of a point on the grinding wheel rotary surface is: ； In the formulae, , .

7. The method of grinding a convex land chip back of a solid end mill according to claim 6, wherein, In step 2, the grinding wheel coordinate system S is established. w To tool coordinate system S t The transformation matrix, through coordinate transformation, transforms the points and normal vectors on the grinding wheel's rotating surface to the tool coordinate system, respectively using the symbols... and express; Establishing the reference coordinate system S r (O r – x r , y r , z r ), z r axis coincides with the z t axis, and the grinding wheel coordinate system origin O w is located in the x r -y r plane; Wherein, the origin O of the grinding wheel coordinate system w In x r -y r The coordinates in the plane are a x a y O, the origin of the end mill coordinate system t To the origin O of the reference coordinate system r The distance is a z The angle between the grinding wheel axis and the end mill axis is λ, and the rotation angle of the end mill around its own axis is δ.

8. The grinding method of a convex land chip back of a solid end mill according to claim 7, characterized by, In step 2, the grinding wheel rotary surface is tangent to the i-th blade width point on the blade width curve, and the normal vector of the grinding wheel rotary surface and the blade width curve at the tangent point is collinear, that is, it satisfies: （1） （2） wherein represents a position vector of the i-th land point, represents a unit normal vector of the land curve at the i-th land point, represents a position vector of the tangent point of the grinding wheel's rotational surface, represents a unit normal vector of the grinding wheel's rotational surface at the tangent point; From formula (1) and formula (2), the grinding wheel pose relative to the cutter satisfies the following formula: （3） In the formula, ； ； ； ； wherein , , denotes the coordinates of the i-th blade width point in the tool coordinate system S t , , , denotes the coordinates of the unit normal vector of the blade width curve at the i-th blade width point in the tool coordinate system S t .

9. The grinding method of a convex land chip back of a solid end mill according to claim 8, wherein, In step 3, the point on the convex edge depth rotary surface is projected to x w -z w plane, the envelope principle obtains the upper envelope line of the circular arc projection of the convex edge depth rotary surface, when the line connecting a point on the circular arc demarcation circle of the grinding wheel and a point on the envelope line is parallel to x w axis, and the point on the circular arc demarcation circle of the grinding wheel and the same point on the envelope line coincide with each other, the circular arc demarcation circle of the grinding wheel and the convex edge depth rotary surface satisfy the tangential relationship.

10. The method of grinding a convex land chip back of a solid end mill according to claim 9, wherein, In step 3, the point on the shovel back depth curve is projected to x w - z w plane; In x w -z w In the plane, when the circular arc projection of the back depth curve is tangent to the cross section profile of the grinding wheel shaft, the grinding wheel rotation surface and the back depth curve satisfy the tangent relationship.

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