Grinding track solving method for grinding front and rear cutter faces of ball-end milling blade by adopting standard grinding wheel

Abstract

The invention discloses a grinding track solving method for grinding a front cutter face and a rear cutter face of a ball-end milling blade by adopting a standard grinding wheel, which specifically comprises the following steps of: defining a corresponding coordinate system based on different structural characteristics of the ball-end milling blade, and constructing a blade line model by combining an equal-helix-angle helix model and a non-orthogonal S-shaped curve model with tooth deviation. Designing a corresponding grinding process scheme according to the machining types of the front and rear tool faces, selecting a corresponding grinding wheel, and adjusting a grinding area of the grinding wheel by introducing a swing angle and a lift angle; finally, a grinding wheel grinding track calculation method is deduced by analyzing the contact relation between the grinding wheel and the front and rear tool faces. Finally, simulation and actual machining experiments are carried out, by comparing a simulation design value with an actual machining result, it is proved that the grinding wheel interference phenomenon in the ball-end milling blade grinding process is effectively avoided, a smooth continuous model between different structures is achieved, and the grinding machining efficiency, the surface quality and the precision are improved.

Description

Technical Field

[0001] The invention belongs to the technical field of ball end milling insert structure design, and specifically designs a grinding trajectory solving method for grinding the front and rear cutting surfaces of a ball end milling insert using a standard grinding wheel. Background Art

[0002] As an important carbide tool for processing high-performance materials, the ball-end milling insert system consists of a toolholder clamping module and a ball-end milling insert. The toolholder clamping module is responsible for the radial positioning and axial clamping of the tool system, while the ball-end milling insert is responsible for completing the processing of the workpiece material. Compared with integral tools, the ball-end milling insert system has a wide range of uses and high processing efficiency. It has good adaptability and flexible and adjustable posture [Dong Yongheng, Li Shujuan, Li Yan, et al. Modeling and simulation of surface topography processed by ball-end milling cutter [J]. Journal of Mechanical Engineering, 2018, 54(19): 212-223.], [Xu Youqian. Research on cutting characteristics of indexable plane milling inserts with complex three-dimensional grooves [D]. Shanghai: East China University of Science and Technology, 2015.].

[0003] The front and rear cutting edges of a ball-end milling insert are external extensions of the tool's edge line performance. Based on the edge line distribution characteristics, they can be divided into the front and rear cutting edges of the cylindrical circumferential cutting edge and the front and rear cutting edges of the ball-end end cutting edge. In the study of the front and rear cutting edge grinding process of the circumferential cutting edge of a ball-end milling cutter, Yang et al., starting from the contact relationship between the grinding wheel and the tool, established a criterion for the contact conditions of the grinding points of each axial section of the circumferential cutting edge of a tapered end mill, and proposed a method for calculating the grinding posture of the grinding wheel on the front cutting edge of a rotating tool [Yang J, Wang L, Fang Y, et al. A novel approach to wheel path generation for 4-axis CNC flank grinding of conical end-mills [J]. The International Journal of Advanced Manufacturing Technology, 2020, 109: 565-578.]. Based on the geometric model of ball-nosed end mills proposed by previous researchers, Ji et al. obtained dispersed grinding point data by discretizing the grinding wheel grinding path to evaluate the manufacturing performance of ball-nosed end mills with chamfered cutting edges. They then proposed a grinding method for the front and rear cutting edges of ball-nosed end mills [Ji W, Liu X, Wang L, et al. Research on modelling of ball-nosed end mill with chamfered cutting edge for 5-axis grinding [J]. The International Journal of Advanced Manufacturing Technology, 2016, 87: 2731-2744.]. Nguyen et al. proposed a mathematical model for ball-nosed end mills with constant lead and constant normal rake angle. By constraining the grinding wheel posture, they ensured the consistency between the ball end rake angle and the rake face width [Nguyen H, Ko S L. Amathematical model for simulating and manufacturing ballend mill [J]. Computer-Aided Design, 2014, 50: 16-26.].Chen et al. constructed a mathematical model for ball-end cutting edges with equal rake and clearance angles and realized ball-end milling of complex surfaces based on the conical grinding wheel envelope principle [Chen F, Hu S, Yin SA novel mathematical model for grinding ball-end milling cutter with equal rake and clearance angle [J]. The International Journal of Advanced Manufacturing Technology, 2012, 63: 109-116.]. Lai et al. combined the principles of radial equidistant lines and oblique equidistant lines to constrain the ball-end cutting edge line and used the grinding wheel envelope principle to solve the grinding wheel posture during rake face grinding [Lai H Y. A high-precision surface grinding model for general ball-end milling cutters [J]. The International Journal of Advanced Manufacturing Technology, 2002, 19: 393-402.]. Xia Wensheng et al., based on the orthogonal spiral blade curve of a tapered ball-end milling cutter, introduced normal equidistant lines and constructed a mathematical model of the front and rear cutting edges of a tapered ball-end milling cutter with equal normal rake angles and equal clearance angles [Xia Wensheng, Zhao Xianfeng, Gao Fei, et al. Research on the mathematical model of grinding of tapered ball-end milling cutters [J]. Combined Machine Tools and Automated Machining Technology, 2016, (01): 122-126.]. In summary, although certain progress has been made in the connection and transition of the front and rear cutting edges of the tool in the research on the grinding process of ball-end milling inserts, its adaptability is still insufficient and there are certain difficulties in practical application. Summary of the Invention

[0004] In response to the above problems, the present invention designs a corresponding grinding process solution according to the processing type of the front and rear cutting edges, and provides a method for solving the grinding trajectory of the front and rear cutting edges of a ball-end milling insert using a standard grinding wheel.

[0005] A method for solving a grinding trajectory when grinding the front and rear cutting surfaces of a ball-end milling insert using a standard grinding wheel of the present invention comprises the following steps:

[0006] Step 1: Create a ball-end milling insert peripheral edge line model.

[0007] Establish workpiece coordinate system O W -X W Y W Z W, take the center of the cross section corresponding to the starting point of the peripheral edge as the origin O W , coordinate axis Z W is the tool axis, coordinate axis Y W From the origin O W and the starting point of the peripheral blade, the coordinate axis Y W Determined by the right-hand rule; the definition point P is any axial displacement z p Corresponding to the grinding point on the blade, the parameter expression of the peripheral edge line in the workpiece coordinate system is:

[0008]

[0009] Where z p The edge line point P is at Z W The change component on the axis, R W is the tool rotation radius, L W is the circumferential blade length, Axis X d In X W O W Z W Plane projection and axis Y W The included angle is k, the taper angle of the milling cutter, and β is the helix angle of the milling cutter.

[0010] Step 2: Establish the end edge curve model of the ball end milling insert.

[0011] Create a tool rotation axis with Z d Shaft, with the bottom surface of the ball end edge as X d O d Y d A plane with its center as origin O d End edge coordinate system O d -X d Y d Z d , which is converted to the workpiece coordinate system by the transformation matrix T d-W for:

[0012]

[0013] The end edge curve modeling is described in the end edge coordinate system:

[0014] Non-orthogonal "S"-shaped blade curve model.

[0015] The coordinates of any point P0 on the curve in the end blade coordinate system are expressed as:

[0016]

[0017] Where R d Indicates the end blade ball head radius, represents the rotation angle of the position where P0 is located; the independent variable θ represents the latitude angle, θ d Indicates the latitude angle of the end of the non-orthogonal "S" shaped edge line, and its value is affected by the tooth center amount l h The calculation method is as follows:

[0018]

[0019] Modeling of tooth center curve.

[0020] The tooth passes through the center edge line from the end point P of the non-orthogonal "S" edge line 2d The derived tangent segment and the tool axis form a tangent plane that intersects with the rotating sphere; According to formula (4), the end point P of the "S" curve is obtained 2d The coordinate expression and tangent vector F p , introduce the independent variable t to represent the point on the tangent segment and the end point P of the non-orthogonal "S" edge line 2d distance, and t d is the latitude variable on the tooth passing through the center edge line corresponding to the variable value t on the tangent segment, then the coordinates of the blade point P0 of this segment of the curve are expressed as:

[0021]

[0022] Step 3: Define the front and rear cutting edge coordinate systems and transformation matrix.

[0023] Coordinate system of the main section of the peripheral blade:

[0024] Define the main section coordinate system O of the peripheral blade m -X m Y m Z m To describe the shape of the front and rear blades of the peripheral edge and the posture of the grinding wheel; it takes any edge line point P0 on the peripheral edge as the origin O m The straight line from the center of the circle at the latitude of the edge line point P0 to the edge line point P0 is X m Axis, with the tangent of the latitude circle where the edge line point P0 on the circumferential edge is located as Y m axis; then the transformation matrix from the peripheral blade coordinate system to the workpiece coordinate system is:

[0025]

[0026] Where R m-W represents the rotation matrix from the peripheral tool coordinate system to the workpiece coordinate system, T m-W represents the corresponding translation matrix.

[0027] Coordinate system of main section of end blade:

[0028] Define the end edge main section coordinate system O md -X md Ymd Z md Describe the shape of the front and rear blades of the end edge and the posture of the grinding wheel; the end edge line point P0 is taken as the origin O md , the tangent of the tool rotation body where P0 is located is Z md Axis, with the tangent of the circle at the latitude of P0 as Y m axis; then the transformation matrix from the end blade main section coordinate system to the end blade coordinate system is:

[0029]

[0030] Where R md-d represents the rotation matrix from the end edge main section coordinate system to the end edge coordinate system, T md-d represents the corresponding translation matrix.

[0031] Step 4: Define the initial grinding posture and process parameters of the grinding wheel.

[0032] Grinding wheel type selection:

[0033] The 11V9 cup grinding wheel should be used for flank grinding, and the 1V1 conical grinding wheel should be used for rake grinding.

[0034] Initial grinding posture of the rake face:

[0035] According to the rake face forming principle, the center of the conical grinding wheel O g In plane X md Y md Define the grinding wheel end face in plane X md Y md Projection inside and X md The angle between the axes is the rake angle γ.

[0036] Grinding wheel center coordinate O g The expression in the end edge coordinate system is as follows:

[0037]

[0038] Where, O Og_md Indicates O g The coordinate vector at the initial pose, R g is the large end radius of the conical grinding wheel, and l0 is the width of the rake face.

[0039] Initial grinding posture of the flank face:

[0040] To describe the grinding process of the flank, let the center of the large end of the bowl grinding wheel O g1 Located on axis Z md On the X plane, define the large end face of the grinding wheel md Z md The projection inside and Ymd The angle between the axes is the back angle λ1.

[0041] Definition of process parameters:

[0042] Define the normal vector F of the rake face g , the conical grinding wheel can move around vector F g Rotate the swing angle μ to avoid interference and define the tangent vector F of the flank g1 , the cup grinding wheel can move around vector F g1 Rotate the lift angle μ to avoid interference.

[0043] Step 5: Grinding posture after introducing posture adjustment parameters.

[0044] The attitude adjustment parameters of the swing angle and lift angle are introduced under the initial attitude of the grinding wheel to control the attitude of the grinding wheel in order to avoid interference and sudden attitude changes during the grinding process.

[0045] Grinding wheel swing angle:

[0046] In order to avoid interference between the grinding wheel and the front and rear cutting edge surfaces, the instantaneous normal vector drawn from the grinding point P0 to the direction perpendicular to the end face of the grinding wheel is defined as the parallel grinding wheel axis vector F g The grinding wheel swing angle is defined as the angle of the grinding wheel around F g The angle of the grinding wheel center O is the angle of the clockwise rotation. g After the swing angle μ is transformed, it finally reaches O' g Place.

[0047] Assume that the transformation matrix of the rotation angle ω around any unit vector N(u,v,w) in space is Rot(N,ω), and its expression is as follows:

[0048]

[0049] Where, versω=1-cosω; after introducing the grinding swing angle μ, the radial vector F parallel to the grinding wheel b and the tangent vector F t Transformed into F′ b and F′ t , the transformation process is as follows:

[0050]

[0051] Grinding wheel lift angle:

[0052] When grinding the back face of a ball-end milling insert, it is necessary to avoid surface contact interference between the edge of the bowl-shaped grinding wheel and the workpiece surface to be machined. The vector F1 along the width direction of the back face of the cutting edge point P0 is defined as the rotation vector of the grinding wheel swing angle. The lift angle δ is the angle of the grinding wheel rotating counterclockwise around F1. The radial vector F b1 After the swing angle transformation, the final vector F' b1 Place.

[0053] After the grinding lift angle δ is introduced, the radial vector F of the cup grinding wheel is g1 Transformed into F′ g1 , the transformation process is as follows:

[0054] F′ g1_md =Rot(F 1_md ,δ)F g1_md (15)

[0055] Transition parameter settings at the connection between the front and rear cutting edges:

[0056] A short continuous grinding wheel posture change process is set at the connection between the peripheral edge and the end edge. Since the peripheral edge line is connected to the end edge line, the four grinding reference points of the ball end milling insert are defined according to the structural characteristics of the peripheral edge and the end edge: the peripheral edge starting point P1, the peripheral edge end point, that is, the end edge "S" edge starting point P2, the end edge "S" edge end point, that is, the end edge tooth passing edge starting point P3, and the end edge tooth passing edge end point P4; further, the transition expression of the process parameters between adjacent grinding reference points of the ball end milling insert is obtained as follows:

[0057]

[0058] Step 6: Grinding trajectory calculation.

[0059] In order to facilitate the calculation of the grinding trajectory of the end edge of the grinding wheel, the grinding wheel model posture of each edge line point of the end edge of the ball-end milling insert is calculated based on the determined end edge line model and the grinding wheel reference posture. Then, the spatial position relationship between the grinding wheel and the workpiece rotating body is obtained through the coordinate transformation matrix (3), (8), (9), (10), and (11), which is the grinding wheel model posture in the workpiece coordinate system.

[0060] Calculation of rake face grinding trajectory:

[0061] When grinding the rake face of a ball-end milling insert, its radial cross-sectional profile is determined by the contact area between the large end face of the grinding wheel and the workpiece. The grinding process of the circumferential rake face can be described as a composite motion process in which the grinding wheel shifts the rake face width along the radial vector direction at the grinding point P and then moves continuously tangentially along the edge line. The displacement range of the grinding wheel grinding point P is 0≤z p ≤L W .

[0062] Under the constraints of the grinding wheel process parameters, the large end face of the conical grinding wheel is always in contact with the peripheral edge line; according to equations (8) and (9), the coordinates of the grinding wheel center of the peripheral edge part O g It is expressed in the workpiece coordinate system as:

[0063] O g_W =T m-W R m-W Rot(Fg_m ,μ)O g_m (19)

[0064] F g_W =R m-W Rot(F g_m ,μ)F g_m (20)

[0065] The principle of the rake face grinding of the circumferential edge is consistent. When grinding the rake face of the end edge, the posture of the grinding wheel is constrained by the rake face structural parameters and the blade edge line model. When the grinding wheel moves from the starting point of the end edge "S" to the end point of the tooth passing edge, the rake face width is offset along the radial vector direction of the grinding wheel. The latitude angular displacement range of the grinding point P0 is k≤θ≤90°. According to equations (10) and (11), the center point O of the grinding wheel at the end edge is g It is expressed in the workpiece coordinate system as:

[0066] O g_W =M d-W T md-d R md-d Rot(F g_m ,μ)O g_md (twenty one)

[0067] F g_W =M d-W T md-d R md-d Rot(F g_m ,μ)F g_md (twenty two)

[0068] Flank grinding trajectory calculation:

[0069] The edge of the bowl-shaped grinding wheel is used for flank grinding. According to the contact relationship when the grinding wheel is grinding the flank, the following constraints need to be met: the radial vector F of the grinding wheel b1 is parallel to the edge line tangent vector at point P0; the grinding wheel large end circle tangent vector F1 is parallel to the direction vector of the back cutting edge under the edge line main section; Combining equations (19) and (20), the grinding wheel posture during grinding of the peripheral edge is converted from the peripheral edge main section coordinate system to the workpiece coordinate system, as shown below:

[0070] O g1_W =T m-W R m-W Rot(F t1_md ,δ)O g1_m (twenty three)

[0071] F g1_W =T m-W R m-W Rot(F t1_md ,δ)F g1_m (twenty four)

[0072] Similarly, the grinding wheel position when grinding the ball end edge is converted from EMCS to WCS as shown below:

[0073] O g1_W =T m-W R m-W Rot(F t1_md ,δ)O g1_m (25)

[0074] F g1_W =T m-W R m-W Rot(F t1_md ,δ)F g1_m (26)

[0075] The beneficial technical effects of the present invention compared with the prior art are:

[0076] This paper studies the CNC modeling process for the front and rear cutting edges of ball-end milling inserts. By combining a helical line model with a constant helix angle and a non-orthogonal "S"-shaped curve model with tooth offset to construct an edge line model, a grinding wheel grinding process design method for the front and rear cutting edges of ball-end milling inserts is proposed to ensure a smooth transition between different structures. Through grinding simulation and actual machining, a ball-end milling insert with an 8mm radius was successfully manufactured. The overall error between the measured and theoretical values remained within 3%, meeting the design requirements and verifying the correctness and effectiveness of the grinding return algorithm.

[0077] The present invention effectively avoids the interference phenomenon of the grinding wheel during the grinding process of the ball-end milling blade, realizes a smooth continuous model between different structures, and improves the grinding efficiency, surface quality and precision. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 Schematic diagram of modeling the cutting edge curve of the circumferential edge of a ball-end milling insert.

[0079] Figure 2 Schematic diagram of modeling the edge line of the end edge of the ball end milling insert.

[0080] Figure 3 Schematic diagram of the latitude angle range corresponding to different gear offsets.

[0081] Figure 4 Schematic diagram of the workpiece coordinate system and the peripheral blade main section coordinate system.

[0082] Figure 5 Schematic diagram of the end edge coordinate system and the end edge main section coordinate system.

[0083] Figure 6 Definition of the geometric parameters of the 1V1 / 1A1 standard grinding wheel.

[0084] Figure 7 Schematic diagram of the initial posture of the grinding wheel corresponding to the rake face.

[0085] Figure 8 Schematic diagram of the initial posture of the grinding wheel corresponding to the back cutting surface.

[0086] Figure 9 This is a schematic diagram of the grinding wheel swing angle adjustment.

[0087] Figure 10 This is a schematic diagram of the grinding wheel lifting angle adjustment.

[0088] Figure 11 Schematic diagram of the grinding reference point position of the ball end milling insert.

[0089] Figure 12 Schematic diagram of the contact relationship between the grinding wheel and the rotating body contour during circumferential cutting edge rake face grinding.

[0090] Figure 13 Schematic diagram of the contact relationship between the grinding wheel and the rotating body contour during end edge rake face grinding.

[0091] Figure 14 Schematic diagram of the contact relationship between the grinding wheel and the blank during flank grinding.

[0092] Figure 15 Schematic diagram of the simulation results of the front and rear cutting edges of the ball-end milling insert.

[0093] Figure 16 This is a physical picture of the ball end milling insert on the tool tester. DETAILED DESCRIPTION

[0094] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0095] A method for solving a grinding trajectory when grinding the front and rear cutting surfaces of a ball-end milling insert using a standard grinding wheel of the present invention comprises the following steps:

[0096] Step 1: Create a ball-end milling insert peripheral edge line model.

[0097] The modeling method of the milling cutter edge line is relatively mature. The present invention uses a spiral line model with equal helical angle to describe the geometric characteristics of the edge line of the milling cutter and establishes the workpiece coordinate system O W -X W Y W Z W ,like Figure 1 As shown, the center of the cross section corresponding to the starting point of the peripheral edge is the origin O W , coordinate axis Z W is the tool axis, coordinate axis Y W From the origin O W and the starting point of the peripheral blade, the coordinate axis Y WDetermined by the right-hand rule; the definition point P is any axial displacement z p Corresponding to the grinding point on the blade, the parameter expression of the peripheral edge line in the workpiece coordinate system is:

[0098]

[0099]

[0100] Where z p The edge line point P is at Z W The change component on the axis, R W is the tool rotation radius, L W is the circumferential blade length, Axis X d In X W O W Z W Plane projection and axis Y W The included angle is k, the taper angle of the milling cutter, and β is the helix angle of the milling cutter.

[0101] Step 2: Establish the end edge curve model of the ball end milling insert.

[0102] Create a tool rotation axis with Z d Shaft, with the bottom surface of the ball end edge as X d O d Y d A plane with its center as origin O d End edge coordinate system O d -X d Y d Z d , which is converted to the workpiece coordinate system by the transformation matrix T d-W for:

[0103]

[0104] The end edge curve modeling is described in the end edge coordinate system:

[0105] Non-orthogonal "S"-shaped blade curve model.

[0106] The present invention refers to a non-orthogonal "S"-shaped ball-end cutter blade curve with a tooth offset h constructed by CHENG et al. to model the blade. Figure 2 As shown. The coordinates of any point P0 on the curve in the end blade coordinate system are expressed as:

[0107]

[0108] Where R d Indicates the end blade ball head radius, represents the rotation angle of the position where P0 is located; the independent variable θ represents the latitude angle, θd Indicates the latitude angle of the end of the non-orthogonal "S" shaped edge line, and its value is affected by the tooth center amount l h The calculation method is as follows:

[0109]

[0110] Modeling of tooth center curve.

[0111] The tooth passes through the center edge line from the end point P of the non-orthogonal "S" edge line 2d The derived tangent segment and the tool axis form a tangent plane that intersects with the rotating sphere, such as Figure 3 As shown; According to formula (4), the end point P of the "S" curve is obtained 2d The coordinate expression and tangent vector F p , introduce the independent variable t to represent the point on the tangent segment and the end point P of the non-orthogonal "S" edge line 2d distance, and t d is the latitude variable on the tooth passing through the center edge line corresponding to the variable value t on the tangent segment, then the coordinates of the blade point P0 of this segment of the curve are expressed as:

[0112]

[0113] Step 3: Define the front and rear cutting edge coordinate systems and transformation matrix.

[0114] Coordinate system of the main section of the peripheral blade:

[0115] Define the main section coordinate system O of the peripheral blade m -X m Y m Z m To describe the shape of the front and rear blades of the peripheral edge and the posture of the grinding wheel, such as Figure 4 As shown. It takes any edge line point P0 on the peripheral edge as the origin O m The straight line from the center of the circle at the latitude of the edge line point P0 to the edge line point P0 is X m Axis, with the tangent of the latitude circle where the edge line point P0 on the circumferential edge is located as Y m axis; then the transformation matrix from the peripheral blade coordinate system to the workpiece coordinate system is:

[0116]

[0117] Where R m-W represents the rotation matrix from the peripheral tool coordinate system to the workpiece coordinate system, T m-W represents the corresponding translation matrix.

[0118] Coordinate system of main section of end blade:

[0119] Define the end edge main section coordinate system O md -Xmd Y md Z md Describe the shape of the front and rear blades of the end edge and the posture of the grinding wheel, such as Figure 5 As shown. The edge line point P0 of the end edge is taken as the origin O md , the tangent of the tool rotation body where P0 is located is Z md Axis, with the tangent of the circle at the latitude of P0 as Y m axis; then the transformation matrix from the end blade main section coordinate system to the end blade coordinate system is:

[0120]

[0121] Where R md-d represents the rotation matrix from the end edge main section coordinate system to the end edge coordinate system, T md-d represents the corresponding translation matrix.

[0122] Step 4: Define the initial grinding posture and process parameters of the grinding wheel.

[0123] Grinding wheel type selection:

[0124] At present, the most commonly used grinding wheel in grinding is the 1V1 / 1A1 grinding wheel specified in the GB / T 6409-2009 standard. Figure 6 To achieve flexible adjustment of the grinding wheel's posture during front and rear face grinding, an 11V9 cup grinding wheel should be used for flank grinding. However, when grinding the rake face, the grinding wheel axis must be tilted at a certain angle to the tool plane, and the side of the grinding wheel must be involved in the grinding. Therefore, a 1V1 conical grinding wheel should be selected.

[0125] Initial grinding posture of the rake face:

[0126] According to the rake face forming principle, the center of the conical grinding wheel O g In plane X md Y md Define the grinding wheel end face in plane X md Y md Projection inside and X md The angle between the axes is the rake angle γ, such as Figure 7 shown.

[0127] Grinding wheel center coordinate O g The expression in the end edge coordinate system is as follows:

[0128]

[0129] Where, O Og_md Indicates O g The coordinate vector at the initial pose, R g is the large end radius of the conical grinding wheel, and l0 is the width of the rake face.

[0130] Initial grinding posture of the flank face:

[0131] To describe the grinding process of the flank, let the center of the large end of the bowl grinding wheel O g1 Located on axis Z md On the X plane, define the large end face of the grinding wheel md Z md The projection inside and Y md The angle between the axes is the back angle λ1, as Figure 8 shown.

[0132] Definition of process parameters:

[0133] Considering the actual grinding process, in order to control the posture of the grinding wheel and avoid sudden changes in posture and interference, the swing angle and lift angle are introduced to adjust the initial posture of the grinding wheel. The present invention defines the normal vector F of the rake face. g , the conical grinding wheel can move around vector F g Rotate the swing angle μ to avoid interference and define the tangent vector F of the flank g1 , the cup grinding wheel can move around vector F g1 Rotate the lift angle μ to avoid interference.

[0134] Step 5: Grinding posture after introducing posture adjustment parameters.

[0135] According to the actual machining conditions of the front and rear cutting edges, if the grinding wheel is continuously ground from the peripheral edge to the end edge in the initial posture during the entire grinding process, it is easy to interfere with the machined surface, thereby causing machining errors on the front and rear cutting edges. Therefore, the posture adjustment parameters of the swing angle and lift angle are introduced at the initial posture of the grinding wheel to control the grinding wheel posture to avoid interference and sudden posture changes during the grinding process.

[0136] Grinding wheel swing angle:

[0137] In order to avoid interference between the grinding wheel and the front and rear cutting edge surfaces, the instantaneous normal vector drawn from the grinding point P0 to the direction perpendicular to the end face of the grinding wheel is defined as the parallel grinding wheel axis vector F g The grinding wheel swing angle is defined as the angle of the grinding wheel around F g The angle of the grinding wheel center O is the angle of the clockwise rotation. g After the swing angle μ is transformed, it finally reaches O' g Place, such as Figure 9 shown.

[0138] Assume that the transformation matrix of the rotation angle ω around any unit vector N(u,v,w) in space is Rot(N,ω), and its expression is as follows:

[0139]

[0140] Where, versω=1-cosω; after introducing the grinding swing angle μ, the radial vector F parallel to the grinding wheel b and the tangent vector F t Transformed into F′ b and F′ t , the transformation process is as follows:

[0141]

[0142] Grinding wheel lift angle:

[0143] When grinding the back face of a ball-end milling insert, it is necessary to avoid surface contact interference between the edge of the bowl-shaped grinding wheel and the workpiece surface to be machined. The vector F1 along the width direction of the back face of the cutting edge point P0 is defined as the rotation vector of the grinding wheel swing angle. The lift angle δ is the angle of the grinding wheel rotating counterclockwise around F1. The radial vector F b1 After the swing angle transformation, the final vector F' b1 Place, such as Figure 10 shown.

[0144] After the grinding lift angle δ is introduced, the radial vector F of the cup grinding wheel is g1 Transformed into F′ g1 , the transformation process is as follows:

[0145] F′ g1_md =Rot(F 1_md ,δ)F g1_md (15)

[0146] Transition parameter settings at the connection between the front and rear cutting edges:

[0147] In the actual production of the back face of the ball-end milling insert, in order to avoid the sudden change of the grinding wheel posture at the connection between the peripheral edge and the end edge due to different process parameters and to ensure the safety of the grinding process during actual processing, the present invention sets a short and continuous grinding wheel posture change process at the connection between the peripheral edge and the end edge. Since the peripheral edge line is connected to the end edge line, the four grinding reference points of the ball-end milling insert are defined according to the structural characteristics of the peripheral edge and the end edge, namely, the peripheral edge starting point P1, the peripheral edge end point, that is, the end edge "S" edge starting point P2, the end edge "S" edge end point, that is, the end edge tooth passing edge starting point P3, and the end edge tooth passing edge end point P4, as shown in FIG. Figure 11 As shown. The transition expression of the process parameters between adjacent grinding reference points of the ball-end milling insert is further obtained as follows:

[0148]

[0149]

[0150] Step 6: Grinding trajectory calculation.

[0151] In order to facilitate the calculation of the grinding trajectory of the end edge of the grinding wheel, the grinding wheel model posture of each edge line point of the end edge of the ball-end milling insert is calculated based on the determined end edge line model and the grinding wheel reference posture. Then, the spatial position relationship between the grinding wheel and the workpiece rotating body is obtained through the coordinate transformation matrix (3), (8), (9), (10), and (11), which is the grinding wheel model posture in the workpiece coordinate system.

[0152] Calculation of rake face grinding trajectory:

[0153] When grinding the rake face of a ball-end milling insert, its radial cross-sectional profile is determined by the contact area between the large end face of the grinding wheel and the workpiece, such as Figure 12 The grinding process of the circumferential rake face can be described as a composite motion process in which the grinding wheel shifts the rake face width along the radial vector direction at the grinding point P and then moves continuously along the tangential direction of the edge line. The displacement range of the grinding wheel grinding point P is 0≤z p ≤L W .

[0154] Under the constraints of the grinding wheel process parameters, the large end face of the conical grinding wheel is always in contact with the peripheral edge line; according to equations (8) and (9), the coordinates of the grinding wheel center of the peripheral edge part O g It is expressed in the workpiece coordinate system as:

[0155] O g_W =T m-W R m-W Rot(F g_m ,μ)O g_m (19)

[0156] F g_W =R m-W Rot(F g_m ,μ)F g_m (20)

[0157] The same principle as the peripheral edge rake face grinding, the grinding wheel posture during the end edge rake face grinding is constrained by the rake face structural parameters and the blade edge line model, such as Figure 13 As shown in the figure, when the grinding wheel moves from the starting point of the end edge "S" to the end point of the tooth passing edge, a given rake face width is offset along the radial vector direction of the grinding wheel, where the latitude angular displacement range of the grinding point P0 is k≤θ≤90°; according to equations (10) and (11), the center point O of the grinding wheel at the end edge is g It is expressed in the workpiece coordinate system as:

[0158] O g_W =M d-W T md-d R md-d Rot(F g_m ,μ)O g_md (twenty one)

[0159] F g_W =M d-W T md-d R md-d Rot(F g_m ,μ)F g_md (twenty two)

[0160] Flank grinding trajectory calculation:

[0161] The edge of the bowl-shaped grinding wheel is used for flank grinding. According to the contact relationship when the grinding wheel is grinding the flank, the following constraints need to be met: the radial vector F of the grinding wheel b1 It is parallel to the cutting edge tangent vector at point P0; the grinding wheel large end circle tangent vector F1 is parallel to the direction vector of the back cutting edge under the main section of the cutting edge, such as Figure 14 Combining equations (19) and (20), the grinding wheel position during grinding of the peripheral edge is converted from the peripheral edge main section coordinate system to the workpiece coordinate system, as shown below:

[0162] O g1_W =T m-W R m-W Rot(F t1_md ,δ)O g1_m (twenty three)

[0163] F g1_W =T m-W R m-W Rot(F t1_md ,δ)F g1_m (twenty four)

[0164] Similarly, the grinding wheel position when grinding the ball end edge is converted from EMCS to WCS as shown below:

[0165] O g1_W =T m-W R m-W Rot(F t1_md ,δ)O g1_m (25)

[0166] F g1_W =T m-W R m-W Rot(F t1_md ,δ)F g1_m (26)

[0167] Simulation verification:

[0168] Based on VC++ environment, the present invention develops a set of algorithm modules, which realizes the (O g ,F g) format tool location file. Import the tool location file generated by the algorithm into VERICUT 8.0, and you can get the following Figure 15 The simulation results of grinding the front and rear cutting edges of the ball-end milling insert are shown in Table 1.

[0169] Table 2 Simulation parameter measurement of the front and rear cutting edges of ball-end milling inserts

[0170]

[0171] Simulation results show that, during the simulated grinding of the front and rear cutting edges of a ball-end milling insert, adjusting the grinding posture by setting the lift and swing angle transition equations effectively prevents interference between the grinding wheel and the workpiece. Specifically, there is no interference between the grinding wheel and the workpiece, good process synergy between the front and rear cutting edges, and a continuous and smooth transition is achieved in the edge line connection area between different structures. Comparing the designed values with the simulated measured values shows that the relative error between the tool geometric parameters and the theoretical design values does not exceed 1%, verifying the effectiveness of the algorithm in terms of tool geometric parameter accuracy and grinding wheel motion trajectory planning.

[0172] The NC program obtained through post-processing can be used to grind the ball-end milling inserts on the carbide tool blank on a five-axis CNC grinder. The tool geometry parameters and process parameters are consistent with the parameters in the grinding simulation. In order to facilitate measurement, this paper uses the PG1000 tool measuring instrument to shoot and measure the processing results of the ball-end milling insert after clamping the tool holder clamping module. The actual processing shooting results are as follows: Figure 16 The comparative analysis of the measured values and theoretical design values of the front and rear cutting edge geometric parameters is shown in Table 2.

[0173] Table 3 Ball end milling insert machining measurement parameters

[0174]

[0175] Experimental verification demonstrates that during the actual grinding process, the grinding wheel does not interfere with the workpiece, and the front and rear cutting edges achieve a continuous and smooth transition between different structures. Comparative analysis of measured parameters reveals that while the error between the measured and theoretical values is larger than that of the simulation, it remains within 3% overall. This error is attributed to errors in the machine tool itself, grinding wheel wear during grinding, and manual inspection errors. The machining results meet the design specifications.

Claims

1. A method for solving the grinding trajectory of a ball-end milling insert using a standard grinding wheel, characterized in that: The following steps are involved: Step 1: Establish the circumferential edge line model of the ball end milling insert; Establish workpiece coordinate system O W -X W Y W Z W , take the center of the cross section corresponding to the starting point of the peripheral edge as the origin O W , coordinate axis Z W is the tool axis, coordinate axis Y W From the origin O W and the starting point of the peripheral blade, the coordinate axis Y W Determined by the right-hand rule; the definition point P is any axial displacement z p Corresponding to the grinding point on the blade, the parameter expression of the peripheral edge line in the workpiece coordinate system is: Where z p The edge line point P is at Z W The change component on the axis, R W is the tool rotation radius, L W is the circumferential blade length, Axis X d In X W O W Z W Plane projection and axis Y W The included angle is k, the taper angle of the milling cutter, and β is the helix angle of the milling cutter; Step 2: Establish the end edge curve model of the ball end milling insert; Create a tool rotation axis with Z d Shaft, with the bottom surface of the ball end edge as X d O d Y d A plane with its center as origin O d End edge coordinate system O d -X d Y d Z d , which is converted to the workpiece coordinate system by the transformation matrix T d-W for: The end edge curve is modeled and described in the end edge coordinate system: Non-orthogonal "S" shaped blade curve model: The coordinates of any point P0 on the curve in the end blade coordinate system are expressed as: Where R d Indicates the end blade ball head radius, represents the rotation angle of the position where P0 is located; the independent variable θ represents the latitude angle, θ d Indicates the latitude angle of the end of the non-orthogonal "S" shaped blade line, and its value is affected by the tooth center amount l h The calculation method is as follows: Modeling of tooth center curve: The tooth passes through the center edge line from the end point P of the non-orthogonal "S" edge line 2d The derived tangent segment and the tool axis form a tangent plane that intersects with the rotating sphere; According to formula (4), the end point P of the "S" curve is obtained. 2d The coordinate expression and tangent vector F p , introduce the independent variable t to represent the point on the tangent segment and the end point P of the non-orthogonal "S" shaped edge line 2d distance, and t d is the latitude variable on the tooth passing through the center edge line corresponding to the variable value t on the tangent segment, then the coordinates of the blade point P0 of this segment of the curve are expressed as: Step 3: Define the front and rear cutting edge coordinate system and transformation matrix; Coordinate system of the main section of the peripheral blade: Define the main section coordinate system O of the peripheral blade m -X m Y m Z m To describe the shape of the front and rear blades of the peripheral edge and the posture of the grinding wheel; It takes any edge line point P0 on the peripheral edge as the origin O m The straight line from the center of the circle at the latitude of the edge line point P0 to the edge line point P0 is X m Axis, with the tangent of the latitude circle where the edge line point P0 on the circumferential edge is located as Y m axis; then the transformation matrix from the peripheral blade coordinate system to the workpiece coordinate system is: Where R m-W represents the rotation matrix from the peripheral tool coordinate system to the workpiece coordinate system, T m-W represents the corresponding translation matrix; Coordinate system of main section of end blade: Define the end edge main section coordinate system O md -X md Y md Z md Describe the shapes of the front and rear blades of the end edge and the posture of the grinding wheel; The origin O is the edge line point P0 of the end edge. md , the tangent of the tool rotation body where P0 is located is Z md Axis, with the tangent of the circle at the latitude of P0 as Y m axis; then the transformation matrix from the end blade main section coordinate system to the end blade coordinate system is: Where R md-d represents the rotation matrix from the end edge main section coordinate system to the end edge coordinate system, T md-d represents the corresponding translation matrix; Step 4: Define the initial grinding posture and process parameters of the grinding wheel; Grinding wheel type selection: When grinding the back face of the cutting tool, the 11V9 cup grinding wheel should be used, and when grinding the front face of the cutting tool, the 1V1 conical grinding wheel should be used. Initial grinding posture of the rake face: According to the rake face forming principle, the center of the conical grinding wheel O g In plane X md Y md Define the grinding wheel end face in plane X md Y md Projection inside and X md The angle between the axes is the rake angle γ; Grinding wheel center coordinate O g The expression in the end edge coordinate system is as follows: Where, O Og_md Indicates O g The coordinate vector at the initial pose, R g is the radius of the large end face of the conical grinding wheel, l0 is the width of the rake face; Initial grinding posture of the flank face: To describe the grinding process of the flank, let the center of the large end of the bowl grinding wheel O g1 Located on axis Z md On the X plane, define the large end face of the grinding wheel md Z md The projection inside and Y md The angle between the axes is the back angle λ1; Definition of process parameters: Define the normal vector F of the rake face g , the conical grinding wheel can move around vector F g Rotate the swing angle μ to avoid interference and define the tangent vector F of the flank g1 , the cup grinding wheel can move around vector F g1 Rotate the lift angle μ to avoid interference; Step 5: Grinding posture after introducing posture adjustment parameters; The attitude adjustment parameters of the swing angle and lift angle are introduced under the initial attitude of the grinding wheel to control the attitude of the grinding wheel to avoid interference and sudden attitude changes during the grinding process. Grinding wheel swing angle: In order to avoid interference between the grinding wheel and the front and rear cutting edge surfaces, the instantaneous normal vector drawn from the grinding point P0 to the direction perpendicular to the end face of the grinding wheel is defined as the parallel grinding wheel axis vector F g The grinding wheel swing angle is defined as the angle of the grinding wheel around F g The angle of the grinding wheel center O is the angle of the clockwise rotation. g After the swing angle μ is transformed, it finally reaches O' g Department; Assume that the transformation matrix of the rotation angle ω around any unit vector N(u,v,w) in space is Rot(N,ω), and its expression is as follows: Where, versω=1-cosω; after introducing the grinding swing angle μ, the radial vector F parallel to the grinding wheel b and the tangent vector F t Transformed into F′ b and F′ t , the transformation process is as follows: Grinding wheel lift angle: When grinding the back face of a ball-end milling insert, it is necessary to avoid surface contact interference between the edge of the bowl-shaped grinding wheel and the workpiece surface to be machined. The vector F1 along the width direction of the back face of the cutting edge point P0 is defined as the rotation vector of the grinding wheel swing angle. The lift angle δ is the angle of the grinding wheel rotating counterclockwise around F1. The radial vector F b1 After the swing angle transformation, the final vector F' b1 Department; After the grinding lift angle δ is introduced, the radial vector F of the cup grinding wheel is g1 Transformed into F′ g1 , the transformation process is as follows: F′ g1_md =Rot(F 1_md ,δ)F g1_md (15) Transition parameter settings at the connection between the front and rear cutting edges: A short continuous grinding wheel posture change process is set at the connection between the peripheral edge and the end edge. Since the peripheral edge line is connected to the end edge line, the four grinding reference points of the ball end milling insert are defined according to the structural characteristics of the peripheral edge and the end edge: the peripheral edge starting point P1, the peripheral edge end point, that is, the end edge "S" edge starting point P2, the end edge "S" edge end point, that is, the end edge tooth passing edge starting point P3, and the end edge tooth passing edge end point P4; further, the transition expression of the process parameters between adjacent grinding reference points of the ball end milling insert is obtained as follows: Step 6: Grinding trajectory calculation; In order to facilitate the calculation of the grinding trajectory of the end edge of the grinding wheel, the grinding wheel model posture of each edge line point of the end edge of the ball-end milling insert is calculated based on the determined end edge line model and the grinding wheel reference posture. Then, the spatial position relationship between the grinding wheel and the workpiece rotating body is obtained through the coordinate transformation matrix (3), (8), (9), (10), (11), which is the grinding wheel model posture in the workpiece coordinate system; Calculation of rake face grinding trajectory: When grinding the rake face of a ball-end milling insert, its radial cross-sectional profile is determined by the contact area between the large end face of the grinding wheel and the workpiece. The grinding process of the circumferential rake face can be described as a composite motion process in which the grinding wheel shifts the rake face width along the radial vector direction at the grinding point P and then moves continuously tangentially along the edge line. The displacement range of the grinding wheel grinding point P is 0≤z p ≤L W ; Under the constraints of the grinding wheel process parameters, the large end face of the conical grinding wheel is always in contact with the peripheral edge line; according to equations (8) and (9), the coordinates of the grinding wheel center of the peripheral edge part O g It is expressed in the workpiece coordinate system as: THE g_W =T m-W R m-W Rot(F g_m ,μ)The g_m (19) F g_W =R m-W Rot(F g_m ,μ)F g_m (20) The principle of the rake face grinding of the circumferential edge is consistent. When grinding the rake face of the end edge, the posture of the grinding wheel is constrained by the rake face structural parameters and the blade edge line model. When the grinding wheel moves from the starting point of the end edge "S" edge to the end point of the tooth passing edge, the rake face width is offset along the radial vector direction of the grinding wheel. The latitude angular displacement range of the grinding point P0 is k≤θ≤90°. According to equations (10) and (11), the center point O of the grinding wheel at the end edge is g It is expressed in the workpiece coordinate system as: THE g_W =M d-W T md-d R md-d Rot(F g_m ,μ)The g_md (21) F g_W =M d-W T md-d R md-d Rot(F g_m ,μ)F g_md (22) Flank grinding trajectory calculation: The edge of the bowl-shaped grinding wheel is used for flank grinding. According to the contact relationship when the grinding wheel is grinding the flank, the following constraints need to be met: the radial vector F of the grinding wheel b1 is parallel to the edge line tangent vector at point P0; the grinding wheel large end circle tangent vector F1 is parallel to the direction vector of the back cutting edge under the edge line main section; Combining equations (19) and (20), the grinding wheel posture during grinding of the peripheral edge is converted from the peripheral edge main section coordinate system to the workpiece coordinate system, as shown below: THE g1_W =T m-W R m-W Rot(F t1_md ,δ)O g1_m (23) F g1_W =T m-W R m-W Rot(F t1_md ,δ)F g1_m (24) Similarly, the grinding wheel position when grinding the ball end edge is converted from EMCS to WCS as shown below: THE g1_W =T m-W R m-W Rot(F t1_md ,δ)O g1_m (25) F g1_W =T m-W R m-W Rot(F t1_md ,δ)F g1_m (26)。

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