Five-axis ball milling free-form surface texture morphology digital model building method

Abstract

The invention discloses a five-axis ball-end milling free-form surface texture morphology digital model building method. The method comprises the following steps that S1, a ball-end milling cutter universal cutting edge mathematical model facing discretization and a five-axis ball-end milling free-form surface cutting edge point kinematics expression are built; s2, obtaining an effective cutting edge range of the cutter contact by adopting an approximate solution solving method; s3, establishing parameter mean discretization of a workpiece curved surface on a parameter domain and parameter non-mean discretization of a constant grid length; s4, establishing cutting path discretization on the parameter domain; s5, effective cutting edge discretization at the cutter contact is established; and S6, establishing a five-axis ball milling free-form surface texture morphology digital model. According to the method, the five-axis ball milling free-form surface workpiece machining result can be predicted in advance, machining errors are reduced, the cost is reduced, and the production efficiency is improved.

Description

Technical Field

[0001] The invention relates to the technical field of five-axis milling surface morphology, and in particular to a method for establishing a digital model of free-form surface texture morphology by five-axis ball head milling. Background Art

[0002] In recent years, with the rapid development of industries such as aerospace, automobiles, and ships, free-form surfaces have been increasingly used in ship propellers, engine blades, automobile and aircraft shell parts due to their excellent aerodynamic and fluid dynamic properties, such as aircraft engine blades, large turbine blades, etc. Five-axis CNC machine tools are widely used in the processing of complex parts surfaces due to their advantages such as high degrees of freedom. Surface texture morphology refers to the microscopic peaks and valleys of various shapes and sizes on the surface of the workpiece, which is an important indicator reflecting the quality of the workpiece surface morphology. The overall trend of the surface texture morphology has an unignorable influence on the accuracy and performance of the workpiece, and is crucial to high-precision parts. It directly affects the physical properties, mechanical properties and service life of the workpiece. A digital model of the surface texture morphology is often established to predict the processing results in advance.

[0003] Most of the existing research on milling surface morphology modeling is only focused on planes or surfaces with elementary analytical expressions, and there is little research on free-form surface workpieces. It is difficult to meet the increasing practical needs of complex surfaces in industrial products that cannot be expressed by elementary analytical expressions. Existing modeling methods are often based on the discretization of workpiece surfaces based on two-dimensional projection surfaces and path discretization methods based on time domain. There are certain limitations for free-form surface workpieces. The entire cutting edge is discretized, calculations are redundant, and simulation efficiency is low, resulting in large processing errors, high costs, and low production efficiency. Summary of the invention

[0004] In order to solve the problem that the existing modeling method of surface texture morphology digital model results in large processing errors, high costs and low production efficiency, the present invention proposes a method for establishing a digital model of free-form surface texture morphology by five-axis ball head milling to solve the above problems.

[0005] A method for establishing a digital model of free-form surface texture morphology by five-axis ball head milling, comprising the following steps:

[0006] S1. Establish a discretization-oriented mathematical model of the universal cutting edge of a ball-end milling cutter and a kinematic expression of the cutting edge point of a free-form surface in five-axis ball-end milling;

[0007] S2, using the approximate solution method to obtain the effective cutting edge range of the tool contact point;

[0008] S3, establishing parameter mean discretization of the workpiece surface in the parameter domain and parameter non-mean discretization with a constant grid length;

[0009] S4, establishing cutting path discretization in parameter domain;

[0010] S5, establishing discretization of effective cutting edge at the tool contact point;

[0011] S6. Establish a digital model of free-form surface texture morphology by five-axis ball head milling.

[0012] Preferably, the S1 comprises the following steps:

[0013] S11. For the subsequent discretization of the cutting edge, mathematical models of the cutting edge of the ball head surface and the cylindrical surface are established based on the axial angle α, and the first cutting edge coordinate system O is established with the origin along the positive direction of the Z axis and at a distance of R from the tool tip. B -X B Y B Z B , R is the tool radius;

[0014] S12, when the cutting edge point q B When located on the ball head surface, q B ′ is the cutting edge point q B In X B Y B Z B The projection on the surface, let β be q B 'OB and X B The angle between them satisfies the formula:

[0015]

[0016] Where, δ is the cutting edge helix angle;

[0017] In the first cutting edge coordinate system O B -X B Y B Z B The cutting edge point q on the ball nose surface B The expression is:

[0018]

[0019] Among them, (x qB ,y qB , z qB ) is the cutting edge point q on the ball head surface in the first cutting edge coordinate system B The coordinate value of

[0020] S13, when the cutting edge point q C When the cutting edge point q is located on the cylindrical surface C The height value h can be expressed as:

[0021]

[0022] but:

[0023] β = -cotα·tanδ;

[0024] In the first cutting edge coordinate system O B -X B Y B Z B In the figure, the cutting edge point q on the cylindrical surface C The expression is:

[0025]

[0026] Among them, (x qC ,y qC , Z qC ) is the cutting edge point q on the cylindrical surface in the first cutting edge coordinate system C The coordinate value of

[0027] S14, based on homogeneous coordinate transformation Combined with the cutting edge point expression in the first cutting edge coordinate system, the workpiece coordinate system O is established. W -X W Y W Z W Kinematic expression of the cutting edge point of free-form surface in five-axis ball head milling:

[0028]

[0029] Among them, x W ,y W 、z W They are workpiece coordinate system O W -X W Y W Z W The expression of the lower cutting point corresponding to x, y, z, x, y, z are the coordinate values ​​of the cutting edge point in the first cutting edge coordinate system, and T represents matrix transpose.

[0030] Preferably, S2 comprises the following steps:

[0031] S21, obtain ball end milling cutter O b The upper limit of the maximum thickness of the effective cutting edge at different geometric feature surfaces;

[0032] When the surface is a plane, thic = a p , a p is the cutting depth;

[0033] When the surface is convex, thic<a p ;

[0034] When the surface is concave, first obtain the minimum curvature radius r of the concave surface on the workpiece surface min , approximate the local surface at the contact point of the concave knife to be a radius of r min The concave sphere O a According to the geometric relationship between the cutting edge and the concave spherical surface, the maximum thickness upper limit a of the intersection between the cutting edge and the curved surface is obtained. p1 , that is, thic<a p1 , the maximum thickness limit a where the cutting edge intersects the curved surface p1 The calculation formula is:

[0035] d c =r-(Ra p );

[0036]

[0037] a p1 =R-Rcos(π-a);

[0038] S22, obtain the minimum axial phase angle λ of the effective cutting edge when the inclination angle φ = 0° min and the maximum axis phase angle λ max ;

[0039] S23, obtain the minimum axial phase angle λ of the effective cutting edge when the inclination angle φ≠0° min ′ and maximum axis phase angle λ max ′;

[0040] Preferably, the S22 comprises the following steps:

[0041] The lowest point of the effective cutting edge is always at the bottom of the cutting edge, that is, λ = 0°, λ is the cutting edge axis phase angle, then λ min =0°;

[0042] In order to make the calculation result include all effective cutting edges, thic takes the upper limit value, and the maximum axial angle λ of the effective cutting edge is obtained according to the cutting edge mathematical model. max :

[0043] RR cosλ max =thic;

[0044]

[0045] Where R is the tool radius.

[0046] Preferably, the S23 comprises the following steps:

[0047] According to the coordinate value of the contact point C [x C ,y C , z C], the maximum effective cutting edge thickness thic and the normal vector n at that point C =[n C1 , n C2 , n C3 ], we can get the plane f p Up one point C p =[x Cp ,y Cp , z Cp ], and its calculation formula is as follows:

[0048] C p =C+n C ·thic;

[0049] Distance from knife contact point c The equation of the plane at and parallel to the contact point is:

[0050] f p =n C1 ·(x Cp -x C )+n C2 ·(y Cp -y C )+n C3 ·(z Cp -z C );

[0051] The cutting edge is discretized by using approximate solution, and the coordinates of the discrete points of the cutting edge are obtained according to the mathematical model of the cutting edge.

[0052] Traverse the discrete points of the cutting edge and determine the discrete points of the cutting edge and the plane f p The geometric relationship between the cutting edge and the plane f p The axial angle range corresponding to the intersection point is [λ1, λ2] or [λ1', λ2'];

[0053] According to the cutting edge and plane f p The geometric interaction determines the minimum axis phase angle λ min ' and maximum axis phase angle λ max ', including the following three situations:

[0054] Cutting edge and plane f p There are two intersection points, then λ max '=λ2',λ min ' = λ1;

[0055] Cutting edge and plane f p There is only one intersection point. If the upper boundary point of the range where the intersection point is located is in the plane, then the intersection point is the minimum axial angle point, λ max ′=90°,λ min′=λ1. If the upper boundary point of the intersection is outside the plane, the intersection is the maximum axial angle point, λ max ′=λ2,λ min ′=0°;

[0056] Cutting edge and plane f p If there is no intersection, then λ max ′=90°,λ min ′=0°.

[0057] Preferably, S3 comprises the following steps:

[0058] The parameter domain discrete grid point matrix UV is obtained by discretizing the parameter mean of the workpiece surface or the parameter non-mean discretization of a constant grid length in the parameter domain. The corresponding coordinate values ​​x, y, z are calculated according to the uv parameter value of each grid point, and x is stored in the matrix X, y is stored in the matrix Y, and z is stored in the matrix H.

[0059] Preferably, the parameter mean discretization comprises the following steps:

[0060] In the parameter domain, the workpiece surface is discretized with the accuracy du along the u direction and the accuracy dv along the v direction, where the maximum discretization grid length d max Satisfy the following formula:

[0061]

[0062] Among them, f z is the feed per tooth, a e is the cutting row distance;

[0063] The parameter non-mean discretization of the constant grid length comprises the following steps:

[0064] Limit the discrete grid length d on the workpiece surface to d max ±ε, where ε is the error value;

[0065] In the u direction, set the initial value du of the discrete length of the grid point p(u, v) in the parameter domain, and the grid point p(u, v) corresponds to the initial grid discrete point p′(u+du, v); use the bisection method to reduce the du value until the distance between the grid point p(u, v) and the point on the workpiece surface corresponding to p′(u+du, v) satisfies d max ±ε;

[0066] In the v direction, set the initial value dv of the discrete length of the grid point p(u, v) on the parameter domain, and the grid point p(u, v) corresponds to the initial grid discrete point p′(u, v+dv); use the bisection method to reduce the dv value until the distance between the grid point p(u, v) and p′(u, v+dv) corresponding to the point on the workpiece surface satisfies dmax ±ε.

[0067] Preferably, S4 comprises the following steps:

[0068] S41, according to the condition that the longest sweep trajectory projection curve of the discrete points of the blade within the unit time Δt is less than or equal to the minimum grid projection length, Δt is obtained, according to the spindle speed N, the feed per tooth f z And the number of cutting teeth Z n Get the feed speed v f , the movement length dc of the knife contact per unit time Δt is obtained as: dc = v f ×Δt;

[0069] S42, approximate the curve between the two discrete tool contact points as a line segment, discretize the cutting path in the parameter domain, obtain the parameter domain discrete line segment with the maximum length on the workpiece surface, and obtain the corresponding point P of the line segment skm (skm), we get point P on the parameter domain skm (skm) Distance from point p on the path skm (skm) The approximate solution point p′ whose length is equal to dc skm (skm′), the discrete precision of cutting path Δs is: Δs=s′ ukm -s ukm , where s′ ukm is the approximate solution point p′ skm Corresponding parameter value, s ukm For point p skm Corresponding parameter value;

[0070] S43, the cutting path is discretized in the parameter domain according to the discrete precision Δs, and the uv value at each discrete tool contact point is obtained. The distance between the discrete tool contacts is accumulated to obtain the tool contact movement length l on the cutting path. C , the cutting time t at the knife contact point is: t = l C / v f .

[0071] Preferably, S5 comprises the following steps:

[0072] The cutting edge is approximated as an arc, and two adjacent discrete cutting edge points are cutting edge microelements. Let X W O W Y W The maximum projection length of the cutting edge microelement in the plane is l Δλ , in Discrete the mesh for the workpiece in X W O W Y W The calculation formula of the minimum projection length of the surface and the discrete axial angle Δλ is:

[0073]

[0074] The effective cutting edge is discretized into several cutting edge points by Δλ.

[0075] Preferably, S6 comprises the following steps:

[0076] S61, establish a mathematical model of the workpiece surface, initialize simulation parameters, the simulation parameters include cutting parameters and tool geometric parameters, the cutting parameters include spindle speed N, feed per tooth f z , cutting depth a p , tool inclination angle φ and rotation angle θ. The tool geometric parameters include: tool tooth number Z n , cutting edge helix angle δ and cutting edge radius R;

[0077] S62. Establish a cutting edge element instantaneous sweep quadrilateral according to the cutting edge element in the unit path segment, update the workpiece grid point height value by judging the interaction relationship between the sweep quadrilateral and the workpiece grid point, make multiple judgments until the cutting of the entire workpiece surface is completed, and obtain the final five-axis ball head milling surface texture morphology digital model.

[0078] Beneficial effects of the present invention:

[0079] The present invention establishes a digital model of surface texture morphology for five-axis ball head milling of free-form surface workpieces on the basis of improving calculation efficiency. It can predict the processing results in advance, reduce processing errors, reduce costs, and improve production efficiency. At the same time, it provides a theoretical basis for related research on five-axis milling of free-form surfaces. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 A flow chart of a method for establishing a digital model of free-form surface texture morphology by five-axis ball head milling according to an embodiment of the present invention;

[0081] Figure 2 A schematic diagram of the geometric features of a tool and a first cutting edge coordinate system according to an embodiment of the present invention;

[0082] Figure 3 A schematic diagram for determining the maximum thickness of a concave effective cutting edge according to an embodiment of the present invention;

[0083] Figure 4 This is a schematic diagram of solving the lowest and highest points of the effective cutting edge when φ=0° in an embodiment of the present invention;

[0084] Figure 5 This is a schematic diagram of solving the lowest and highest points of the convex effective cutting edge when φ≠0° according to an embodiment of the present invention;

[0085] Figure 6It is a schematic diagram of solving the lowest and highest points of the concave effective cutting edge when φ≠0° in an embodiment of the present invention;

[0086] Figure 7 This is a schematic diagram of UV averaging discrete workpieces according to an embodiment of the present invention;

[0087] Figure 8 A schematic diagram of a UV non-mean discrete workpiece with a constant grid length according to an embodiment of the present invention;

[0088] Fig. 9 A schematic diagram of the discrete cutting edge of an embodiment of the present invention;

[0089] Fig.10 A flow chart for establishing a digital model of free-form surface texture morphology by five-axis ball head milling according to an embodiment of the present invention;

[0090] Fig.11 Schematic diagram of a digital model of texture morphology when θ=-45° and φ=30° according to an embodiment of the present invention;

[0091] Fig.12 Schematic diagram of the residual height texture morphology of the Z value when θ=-45° and φ=30° in an embodiment of the present invention. DETAILED DESCRIPTION

[0092] In order to make the objectives, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below with reference to the accompanying drawings and examples.

[0093] The present application embodiment discloses a method for establishing a digital model of free-form surface texture morphology by five-axis ball head milling, such as Figure 1 As shown, the following steps are included:

[0094] S1. Establish a discretization-oriented mathematical model of the universal cutting edge of a ball-end milling cutter and a kinematic expression of the cutting edge point for five-axis ball-end milling of free-form surfaces.

[0095] S11, such as Figure 2 As shown in the figure, for the subsequent discretization of the cutting edge, the mathematical models of the spherical head surface and the cylindrical surface are established based on the axial angle α, and the first cutting edge coordinate system O is established with the origin along the positive direction of the Z axis and at a distance from the tool tip point R. B -X B Y B Z B , R is the tool radius. Among them, Figure 2 (a) is the cutting edge point of the ball end mill. Figure 2 (b) is the cutting edge point on the cylindrical surface at X B O B Z B Projection on a plane, Figure 2 (c) is the cutting edge point on the ball head surface at XB O B Z B Projection on a plane.

[0096] S12, when the cutting edge point q B When located on the ball head surface, q B ′ is the cutting edge point q B In X B Y B Z B The projection on the surface, let β be q B 'OB and X B The angle between them satisfies the formula:

[0097]

[0098] Where, δ is the cutting edge helix angle;

[0099] In the first cutting edge coordinate system O B -X B Y B Z B The cutting edge point q on the ball nose surface B The expression is:

[0100]

[0101] Among them, (xqB, yqB, zqB) are the coordinate values ​​of the cutting edge point qB on the ball head surface in the first cutting edge coordinate system.

[0102] S13, when the cutting edge point q C When the cutting edge point q is located on the cylindrical surface C The height h can be represented by β and δ or angle α, respectively, as:

[0103]

[0104] The two equations can be solved together to obtain β, then:

[0105] β = -cotα·tanδ;

[0106] In the first cutting edge coordinate system O B -X B Y B Z B In the figure, the cutting edge point q on the cylindrical surface C The expression is:

[0107]

[0108] Among them, (x qC ,y qC , z qC) is the cutting edge point q on the cylindrical surface in the first cutting edge coordinate system C The coordinate value of .

[0109] S14, based on homogeneous coordinate transformation Combined with the cutting edge point expression in the first cutting edge coordinate system, the workpiece coordinate system O is established. W -X W Y W Z W Kinematic expression of the cutting edge point of free-form surface in five-axis ball head milling:

[0110]

[0111] Among them, x W ,y W , Z W They are workpiece coordinate system O W -X W Y W Z W The expression of the lower cutting point corresponding to x, y, and z, where x, y, and z are the coordinate values ​​of the cutting edge point in the first cutting edge coordinate system (i.e. x qB ,y qB 、z qB or x qC ,y qC 、z qC ), T represents matrix transpose.

[0112] S2. In order to improve the calculation efficiency, the approximate solution method is used to quickly obtain the effective cutting edge range of the tool contact point.

[0113] S21, obtain ball end milling cutter O b The upper limit of the maximum thickness of the effective cutting edge at different geometric feature surfaces.

[0114] When the surface is a plane, thic = a p , a p is the cutting depth;

[0115] When the surface is convex, thic<a p ;

[0116] like Figure 3 As shown in the figure, when the surface is concave, the minimum curvature radius r of the concave surface on the workpiece surface is first obtained. min , approximate the local surface at the contact point of the concave knife to be a radius of r min The concave sphere O a According to the geometric relationship between the cutting edge and the concave spherical surface, the maximum thickness upper limit a of the intersection between the cutting edge and the curved surface is obtained. p1 , that is, thic<a p1, the maximum thickness limit a where the cutting edge intersects the curved surface p1 The calculation formula is:

[0117] d cc =r min -(Ra p1 );

[0118]

[0119] a p1 =RR cos(π-a);

[0120] Among them, d cc It is the distance from the center of the concave spherical surface to the center of the ball end surface of the ball end milling cutter.

[0121] S22, obtain the minimum axial phase angle λ of the effective cutting edge when the inclination angle φ = 0° min and the maximum axis phase angle λ max .

[0122] like Figure 4 As shown, Figure 4 (a) is a schematic diagram for solving the lowest and highest points of the effective cutting edge on a convex surface. Figure 4 (b) is a schematic diagram for solving the lowest and highest points of the effective cutting edge on a concave surface. The lowest point of the effective cutting edge is always located at the bottom of the cutting edge, that is, λ = 0°, λ is the phase angle of the cutting edge axis, then λ min =0°;

[0123] In order to make the calculation result include all effective cutting edges, thic takes the upper limit value, and the maximum axial angle λ of the effective cutting edge is obtained according to the cutting edge mathematical model. max :

[0124] RR cosλ max =thic;

[0125]

[0126] S23, obtain the minimum axial phase angle λ of the effective cutting edge when the inclination angle φ≠0° min ′ and maximum axis phase angle λ max ′.

[0127] like Figure 5 and Figure 6 As shown, Figure 5 is convex, Figure 6 is concave, Figure 5 and Figure 6 (a) shows the tool and plane f p Schematic diagram of the interaction. According to the coordinate value of the contact point C [x C ,y C , zC ], the maximum effective cutting edge thickness thic and the normal vector n at that point C =[n C1 , n C2 , n C3 ], we can get the plane f p Up one point C p =[x C x,y Cp , z Cp ], and its calculation formula is as follows:

[0128] C p =C+n C ·thic;

[0129] Further obtain the distance from the knife contact point thic and parallel to the contact plane f p The equation is:

[0130] f p =n C1 ·(x Cp -x C )+n C2 ·(y Cp -y C )+n C3 ·(z Cp -z C );

[0131] Using approximate solution, the cutting edge is discretized, and the coordinates of the discrete points of the cutting edge are obtained according to the mathematical model of the cutting edge. Traverse the discrete points of the cutting edge to determine the relationship between the discrete points of the cutting edge and the plane f p The geometric relationship between the cutting edge and the plane f p The axial angle range corresponding to the intersection point is [λ1, λ2] or [λ1′, λ2′]. p The geometric interaction determines the minimum axis phase angle λ min ′ and maximum axis phase angle λ max ', including the following three situations:

[0132] like Figure 5 and Figure 6 As shown in (b), the cutting edge and the plane f p There are two intersection points, then λ max ′=λ2′,λ min ′=λ1.

[0133] like Figure 5 and Figure 6 As shown in (c) and (d), the cutting edge and the plane f p There is only one intersection point. If the upper boundary point of the range where the intersection point is located is in the plane, then the intersection point is the minimum axial angle point, λ max′=90°,λ min ′=λ1; if the upper boundary point of the intersection is outside the plane, then the intersection is the maximum axial angle point, λ max ′=λ2,λ min ′=0°.

[0134] Cutting edge and plane f p If there is no intersection, then λ max ′=90°,λ min ′=0°.

[0135] S3. Establish the parameter mean discretization of the workpiece surface in the parameter domain and the parameter non-mean discretization with constant grid length.

[0136] The parameter domain discrete grid point matrix UV is obtained by discretizing the parameter mean of the workpiece surface or the parameter non-mean discretization of a constant grid length in the parameter domain. The corresponding coordinate values ​​x, y, z are calculated according to the uv parameter value of each grid point, and x is stored in the matrix X, y is stored in the matrix Y, and z is stored in the matrix H.

[0137] like Figure 7 As shown, the parameter mean discretization includes the following steps:

[0138] In the parameter domain, the workpiece surface is discretized with the accuracy du along the u direction and the accuracy dv along the v direction, where the maximum discretization grid length d max Satisfy the following formula:

[0139]

[0140] Among them, f z is the feed per tooth, a e is the cutting row distance.

[0141] like Figure 8 As shown in Figure 2, the parameter non-mean discretization with constant grid length includes the following steps:

[0142] Limit the discrete grid length d on the workpiece surface to d max ±ε, where ε is the error value.

[0143] In the u direction, set the initial value du of the discrete length of the grid point p(u, v) in the parameter domain, and the grid point p(u, v) corresponds to the initial grid discrete point p′(u+du, v); use the bisection method to reduce the du value until the distance between the grid point p(u, v) and the point on the workpiece surface corresponding to p′(u+du, v) satisfies d max ±ε.

[0144] The same is true for the discretization in the v direction. Discrete points are searched row by row until the mesh discretization of the entire workpiece surface is completed. In the v direction, the initial value dv of the discrete length of the grid point p(u, v) in the parameter domain is set. The initial grid discretization point corresponding to the grid point p(u, v) is p′(u, v+dv); the dv value is reduced by the bisection method until the distance between the grid points p(u, v) and p′(u, v+dv) corresponding to the points on the workpiece surface satisfies d max ±ε.

[0145] S4. Establish cutting path discretization in parameter domain.

[0146] S41, according to the condition that the longest sweep trajectory projection curve of the discrete points of the blade within the unit time Δt is less than or equal to the minimum grid projection length, Δt is obtained, according to the spindle speed N, the feed per tooth f z And the number of cutting teeth Z n Get the feed speed v f , the movement length dc of the knife contact per unit time Δt is obtained as: dc = v f ×Δt.

[0147] S42, approximate the curve between the two discrete tool contact points as a line segment, discretize the cutting path in the parameter domain, obtain the parameter domain discrete line segment with the maximum length on the workpiece surface, and obtain the corresponding point p of the line segment skm (skm), we get point p on the parameter domain skm (skm) Distance from point p on the path skm (skm) length equal to d C The approximate solution point p′ skm (skm′), the discrete precision of cutting path Δs is: Δs=s′ ukm -s ukm , where s′ ukm is the approximate solution point p′ skm Corresponding parameter value, s ukm For point p skm Corresponding parameter value.

[0148] S43, the cutting path is discretized in the parameter domain according to the discrete precision Δs, and the uv value at each discrete tool contact point is obtained. The distance between the discrete tool contacts is accumulated to obtain the tool contact movement length l on the cutting path. C , the cutting time t at the knife contact point is: t = l C / v f .

[0149] S5. Establish discretization of the effective cutting edge at the tool contact point.

[0150] like Fig. 9 As shown in the figure, the cutting edge is approximated as an arc, and two adjacent discrete cutting edge points are cutting edge microelements. Let X W OW Y W The maximum projection length of the cutting edge microelement in the plane is l Δλ , in Discrete the mesh for the workpiece in X W O W Y W The calculation formula of the minimum projection length of the surface and the discrete axial angle Δλ is:

[0151]

[0152] The effective cutting edge is discretized into several cutting edge points by Δλ.

[0153] S6. Establish a digital model of free-form surface texture morphology by five-axis ball head milling.

[0154] S61, such as Fig.10 As shown, in a specific embodiment, taking a bowl-shaped free-form surface as an example, a NURBS mathematical model of a workpiece surface is established, and its node vector is as follows:

[0155]

[0156] The control point matrix looks like this:

[0157]

[0158] Initialize the simulation parameters, including cutting parameters and tool geometry parameters. Set the cutting parameters: spindle speed N = 6000r / min, feed per tooth f z =0.5mm / r, cutting depth a p =0.2mm, tool inclination angle φ = 30°, rotation angle θ = -450°. Use the equal parameter method to plan the milling path and set the maximum residual height h = 0.1mm. Set the tool geometry parameters: tool teeth number Z n =2, cutting edge helix angle δ = 30°, cutting edge radius R = 5mm.

[0159] S62, according to S3, the workpiece surface mesh discrete matrix H is obtained, and according to S4, the cutting path discrete accuracy Δs=9.6×10 -6 To obtain the discrete unit path segment, the effective cutting edge range at the tool contact point [λ min ,λ max], according to S5, the discrete axial angle of the cutting edge is obtained by Δλ=0.567° to obtain the discrete effective cutting edge element, and then the discretization result is obtained based on the above steps. In the unit path segment, the instantaneous sweep quadrilateral of the cutting edge element is established according to the cutting edge element, and it is judged whether the sweep quadrilateral interacts with the workpiece grid point. If so, the height value of the workpiece grid point is updated. Then it is judged whether the cutting simulation of the entire workpiece is completed. If so, the final digital model of the ball head milling surface texture morphology is obtained; if not, the next instantaneous sweep quadrilateral and the workpiece grid point interaction judgment is performed. Multiple judgments are made until the cutting of the entire workpiece surface is completed, and the following is obtained. Fig.11 The final five-axis ball head milling surface texture morphology digital model is shown. Fig.12 As shown in the figure, in order to observe the surface milling texture morphology more clearly, the surface texture morphology digital model is transformed into an X-ray machine. W O W Y W The surface projection obtains the Z value residual height texture morphology.

[0160] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for establishing a digital model of free-form surface texture morphology by five-axis ball head milling, characterized in that: The following steps are involved: S1. Establish a discretization-oriented mathematical model of the universal cutting edge of a ball-end milling cutter and a kinematic expression of the cutting edge point of a free-form surface in five-axis ball-end milling; S2, using the approximate solution method to obtain the effective cutting edge range of the tool contact point; S3, establishing parameter mean discretization of the workpiece surface in the parameter domain and parameter non-mean discretization with a constant grid length; S4, establishing cutting path discretization in parameter domain; S5, establishing discretization of effective cutting edge at the tool contact point; S6. Establish a digital model of free-form surface texture morphology by five-axis ball head milling.

2. The method for establishing a digital model of free-form surface texture morphology by five-axis ball head milling according to claim 1, characterized in that: The S1 comprises the following steps: S11, based on the axial angle α, mathematical models of the cutting edge of the ball head surface and the cylindrical surface are established respectively, and the first cutting edge coordinate system O is established with the origin along the positive direction of the Z axis and at a distance R from the tool tip. B -X B Y B Z B , R is the tool radius; S12, when the cutting edge point q B When located on the ball head surface, q B ′ is the cutting edge point q B In X B Y B Z B The projection on the surface, let β be q B 'OB and X B The angle between them satisfies the formula: Where, δ is the cutting edge helix angle; In the first cutting edge coordinate system O B -X B Y B Z B The cutting edge point q on the ball nose surface B The expression is: Among them, (x qB ,y qB ,z qB ) is the cutting edge point q on the ball head surface in the first cutting edge coordinate system B The coordinate value of S13, when the cutting edge point q C When the cutting edge point q is located on the cylindrical surface C The height value h can be expressed as: but: β=-cosα·tanδ; In the first cutting edge coordinate system O B -X B Y B Z B In the figure, the cutting edge point q on the cylindrical surface C The expression is: Among them, (x qC ,y qC ,z qC ) is the cutting edge point q on the cylindrical surface in the first cutting edge coordinate system C The coordinate value of S14, based on homogeneous coordinate transformation Combined with the cutting edge point expression in the first cutting edge coordinate system, the workpiece coordinate system O is established. W -X W Y W Z W Kinematic expression of the cutting edge point of free-form surface in five-axis ball head milling: Among them, x W ,y W 、z W They are workpiece coordinate system O W -X W Y W Z W The expression of the lower cutting point corresponding to x, y, z, x, y, z are the coordinate values ​​of the cutting edge point in the first cutting edge coordinate system, and T represents matrix transpose.

3. The method for establishing a digital model of free-form surface texture morphology by five-axis ball head milling according to claim 2, characterized in that: The S2 comprises the following steps: S21, obtain ball end milling cutter O b The upper limit of the maximum thickness of the effective cutting edge at different geometric feature surfaces; When the surface is a plane, thic = a p , a p is the cutting depth; When the surface is convex, thickness p ;​ When the surface is concave, first obtain the minimum curvature radius r of the concave surface on the workpiece surface min , approximate the local surface at the contact point of the concave knife to be a radius of r min The concave sphere O a According to the geometric relationship between the cutting edge and the concave spherical surface, the maximum thickness upper limit a of the intersection between the cutting edge and the curved surface is obtained. p1 , that is, thic p1 , the maximum thickness limit a where the cutting edge intersects the curved surface p1 The calculation formula is:​ a p1 =R-Rcos(π-a); S22, obtain the minimum axial phase angle λ of the effective cutting edge when the inclination angle φ = 0° min and the maximum axis phase angle λ max ; S23, obtain the minimum axial phase angle λ of the effective cutting edge when the inclination angle φ≠0° min ′ and maximum axis phase angle λ max ′.

4. The method for establishing a digital model of free-form surface texture morphology by five-axis ball head milling according to claim 3, characterized in that: The S22 comprises the following steps: The lowest point of the effective cutting edge is always at the bottom of the cutting edge, that is, λ = 0°, λ is the cutting edge axis phase angle, then λ min =0°; In order to make the calculation result include all effective cutting edges, thic takes the upper limit value, and the maximum axial angle λ of the effective cutting edge is obtained according to the cutting edge mathematical model. max : Where R is the tool radius.

5. The method for establishing a digital model of free-form surface texture morphology by five-axis ball head milling according to claim 4, characterized in that: The S23 comprises the following steps: According to the coordinate value of the contact point C [x C ,y C ,z C ], the maximum effective cutting edge thickness thic and the normal vector n at that point C =[n C1 ,n C2 ,n C3 ], we can get the plane f p Up one point C p =[x Cp ,y Cp ,z Cp ], and its calculation formula is as follows: C p =C+n C ·thic; The equation of the plane at the thic distance from the knife contact point and parallel to the contact point is: f p =n C1 ·(x cp -x c )+n c2 ·(y cp -y C )+n C3 ·(z Cp -z C ): The cutting edge is discretized by using approximate solution, and the coordinates of the discrete points of the cutting edge are obtained according to the mathematical model of the cutting edge. Traverse the discrete points of the cutting edge and determine the discrete points of the cutting edge and the plane f p The geometric relationship between the cutting edge and the plane f p The axial angle range corresponding to the intersection point is [λ1,λ2] or [λ1′,λ2′]; According to the cutting edge and plane f p The geometric interaction determines the minimum axis phase angle λ min ′ and maximum axis phase angle λ max ', including the following three situations: Cutting edge and plane f p There are two intersection points, then λ max ′=λ2′,λ min ′=λ1; Cutting edge and plane f p There is only one intersection point. If the upper boundary point of the range where the intersection point is located is in the plane, then the intersection point is the minimum axial angle point, λ max ′=90°,λ min ′=λ1. If the upper boundary point of the intersection is outside the plane, the intersection is the maximum axial angle point, λ max ′=λ2,λ min ′=0°; Cutting edge and plane f p If there is no intersection, then λ max ′=90°,λ min ′=0°.

6. The method for establishing a digital model of free-form surface texture morphology by five-axis ball head milling according to claim 5, characterized in that: The S3 comprises the following steps: The parameter domain discrete grid point matrix UV is obtained by discretizing the parameter mean of the workpiece surface or the parameter non-mean discretization of a constant grid length in the parameter domain. The corresponding coordinate values ​​x, y, z are calculated according to the uv parameter value of each grid point, and x is stored in the matrix X, y is stored in the matrix Y, and z is stored in the matrix H.

7. The method for establishing a digital model of free-form surface texture morphology by five-axis ball head milling according to claim 6, characterized in that: The parameter mean discretization comprises the following steps: In the parameter domain, the workpiece surface is discretized with the accuracy du along the u direction and the accuracy dv along the v direction, where the maximum discretization grid length d max Satisfy the following formula: Among them, f z is the feed per tooth, a e is the cutting row distance; The parameter non-mean discretization of the constant grid length comprises the following steps: Limit the discrete grid length d on the workpiece surface to d max ±ε, where ε is the error value; In the u direction, set the initial value du of the discrete length of the grid point p(u,v) in the parameter domain, and the grid point p(u,v) corresponds to the initial grid discrete point p′(u+du,v); use the bisection method to reduce the du value until the distance between the grid point p(u,v) and the point on the workpiece surface corresponding to p′(u+du,v) satisfies d max ±ε; In the v direction, set the initial value dv of the discrete length of the grid point p(u,v) in the parameter domain, and the grid point p(u,v) corresponds to the initial grid discrete point p′(u,v+dv); use the bisection method to reduce the dv value until the distance between the grid point p(u,v) and the point on the workpiece surface corresponding to p′(u,v+dv) satisfies d max ±ε.

8. The method for establishing a digital model of free-form surface texture morphology by five-axis ball head milling according to claim 7, characterized in that: The S4 comprises the following steps: S41, according to the condition that the longest sweep trajectory projection curve of the discrete points of the blade within the unit time Δt is less than or equal to the minimum grid projection length, Δt is obtained, according to the spindle speed N, the feed per tooth f z And the number of cutting teeth Z n Get the feed speed v f , the movement length dc of the knife contact per unit time Δt is obtained as: dc = v f ×Δt; S42, approximate the curve between the two discrete tool contact points as a line segment, discretize the cutting path in the parameter domain, obtain the parameter domain discrete line segment with the maximum length on the workpiece surface, and obtain the corresponding point p of the line segment skm (skm), we get point p on the parameter domain skm (skm) Distance from point p on the path skm (skm) The approximate solution point p′ whose length is equal to dc skm (skm′), the discrete precision of cutting path Δs is: Δs=s′ ukm -s ukm , where s′ ukm is the approximate solution point p′ skm Corresponding parameter value, s ukm For point p skm Corresponding parameter value; S43, the cutting path is discretized in the parameter domain according to the discrete precision Δs, and the uv value at each discrete tool contact point is obtained. The distance between the discrete tool contacts is accumulated to obtain the tool contact movement length l on the cutting path. C , the cutting time t at the knife contact point is: t = l C / v f .

9. The method for establishing a digital model of free-form surface texture morphology by five-axis ball head milling according to claim 8, characterized in that: The S5 comprises the following steps: The cutting edge is approximated as an arc, and two adjacent discrete cutting edge points are cutting edge microelements. Let X W O W Y W The maximum projection length of the cutting edge microelement in the plane is l Δλ , in Discrete the mesh for the workpiece in X W O W Y W The calculation formula of the minimum projection length of the surface and the discrete axial angle Δλ is: The effective cutting edge is discretized into several cutting edge points by Δλ.

10. The method for establishing a digital model of free-form surface texture morphology by five-axis ball head milling according to claim 9, characterized in that: The S6 comprises the following steps: S61, establish a mathematical model of the workpiece surface, initialize simulation parameters, the simulation parameters include cutting parameters and tool geometric parameters, the cutting parameters include spindle speed N, feed per tooth f z , cutting depth a p , tool inclination angle φ and rotation angle θ. The tool geometric parameters include: tool tooth number Z n , cutting edge helix angle δ and cutting edge radius R; S62. Establish a cutting edge element instantaneous sweep quadrilateral according to the cutting edge element in the unit path segment, update the workpiece grid point height value by judging the interaction relationship between the sweep quadrilateral and the workpiece grid point, make multiple judgments until the cutting of the entire workpiece surface is completed, and obtain the final five-axis ball head milling surface texture morphology digital model.

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