A Tool Profile Optimization Method for End Milling of Curved Surface Parts

Abstract

The present invention belongs to the technical field of numerical control machining, and discloses a method for optimizing the tool profile of end milling machining of curved surface parts. By performing grid sampling on the curved surface, a sampling point array is formed; the feed direction of the sampling points is specified to construct a feed vector field for curved surface machining; the tool profile is defined by a straight line and a quadratic polynomial curve, and the quadratic polynomial curve is changed to obtain different tool shapes; according to the selected tool, the cutting row width of the five-axis tool path driven by the vector field at different sampling positions is calculated; the position where the minimum cutting row width is located is determined, and the tool profile is optimized to increase the cutting row width; the row width calculation of the sampling points and the tool profile optimization are repeated until the tool profile reaches the optimum. By optimizing the tool profile to increase the machining row width, the present invention can, on the one hand, provide a reference for the selection of tools for machining curved surface parts, and on the other hand, reduce the programming difficulty of high-efficiency five-axis machining, having significant engineering significance.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical control machining, and particularly relates to a method for optimizing the tool profile of end milling of curved surface parts. Background Art

[0002] Complex curved surface parts are widely used in important fields such as aerospace and national defense. To ensure the machining accuracy of these parts, five-axis end milling has become an important or even the only machining method. Currently, process engineers generally use mature CAM software to generate five-axis machining paths. During this process, the tool geometric information is determined by process engineers based on experience. The tool type is directly related to the machining result. For example, the cutting width of a ball-end mill is limited, which will restrict the improvement of machining efficiency; non-ball-end mills such as flat-end mills and torus mills have high machining efficiency, but their tool axis control algorithms are complex and prone to machining undercuts.

[0003] Starting from the existing process, designing a special tool that matches the geometric characteristics of the part is expected to increase the cutting width, improve efficiency, and reduce production costs on the basis of unchanged programming process. The literature "Synchronous Optimization Method of Tool Profile and Trajectory for Side Milling of Free-Form Surfaces [J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(11): 423720" improved the surface quality and efficiency of side milling by establishing a synchronous optimization model of tool profile and machining trajectory based on machining error and tool axis smoothness. The patent "Tool Optimization and Machining Trajectory Generation Method for Side Milling of Complex Curved Surfaces" (CN112486094B) can be used to determine the optimal tool shape for side milling of flat surfaces. However, the end milling condition is quite different from the side milling condition, and the tool profile optimization method applicable to side milling cannot be directly used for end milling. The doctoral thesis "Design and Manufacture of the Blade Shape of Non-Spherical End Milling Cutters and Its Tool Path Generation Algorithm, Harbin University of Science and Technology, 2016" studied the application of three shapes, namely ellipse, parabola, and "8"-shaped curve, in the design of the tool profile of end milling cutters. The simulation results show that compared with ball-end mills, the new tool shape is beneficial to increasing the cutting width and speed. However, this method does not deeply explore the influence of the shape evolution of the profile curve on the tool design result, and its working condition is only limited to three-axis inclined plane milling.

[0004] From the above analysis, it can be seen that tool profile optimization provides a low-threshold and low-cost method to give full play to the machining potential of multi-axis machine tools. However, for the common five-axis end milling of complex curved surfaces in production, researchers have not developed customized tools suitable for it. Therefore, relevant research needs to be carried out urgently. Summary of the Invention

[0005] The present invention aims to provide a method for optimizing the tool profile of end milling of curved surface parts, which can automatically calculate the optimal profile of the tool surface in the five-axis end milling of complex curved surfaces, is beneficial to reducing the difficulty of path programming, and at the same time realizes the improvement of five-axis machining efficiency.

[0006] The technical solution of the present invention is as follows: A tool profile optimization method for end milling of curved surface parts, comprising:

[0007] Step 1: Form a sampling point array by grid sampling the surface part;

[0008] Step 2: Specify the tool direction of the sampling point array and construct the tool vector field for surface machining;

[0009] Step 3: Define the tool profile by a straight line and a quadratic polynomial curve, and change the parameters of the quadratic polynomial curve to obtain different tool profile shapes;

[0010] Step 4: According to the selected tool, calculate the cutting line width of the five-axis tool position driven by the tool vector field at different sampling points;

[0011] Step 5: Determine the sampling point where the minimum cutting line width is located, and optimize the tool profile to increase the cutting line width;

[0012] Step 6: Repeat steps 4-5 until the tool profile is optimal.

[0013] The process of step 1 is as follows:

[0014] Assume S(u,v) represents the surface to be processed, the value range of u and v is [0,1], and the parameters u and v are uniformly sampled, the number of samples is m and n respectively, and the m×n sampling point array S(u i ,v j ).

[0015] The process of step 2 is as follows:

[0016] The process personnel specify the sampling point array S(u i ,v j ) of the tool path direction f i,j , calculate f i,j Unit projection vector d in the uv parameter domain i,j , fitting {d i,j |i∈[1,m],j∈[1,n]}, and obtain the mathematical equation of the tool vector field for surface machining.

[0017] Assume that the expression of the continuous tool vector field E(u,v) is as follows:

[0018]

[0019] Among them, N i,3 (u), N j,3 (v) is the cubic B-spline basis function, n1 and n2 are the number of control points along the u and v directions, γ i,jRepresents the control point, which is the unknown in E(u, v); according to the incompressible plane potential flow theory, at any sampling position, E(u, v) and d i,j Satisfy:

[0020]

[0021] Wherein, E u (u i , v j ) and E v (u i , v j ) represent the first-order partial derivatives of E(u, v) in the u i , v j ) direction along u and v, And Represent the components of d i,j Along u and v. By establishing the above equations at all sampling positions and organizing, a hyperpositive definite linear equation system about γ i,j Can be obtained, and the least squares method is used to solve γ i,j .

[0022] The process of step 3 is as follows:

[0023] Establish a plane coordinate system O-XY, where O is the origin, X is the horizontal axis, and Y is the vertical axis; set the tool radius as R, make a straight line segment OD1 with a length of r1 along the X axis, and the quadratic polynomial curve is denoted as C(s), where s is the curve parameter, and C(s) satisfies the following conditions:

[0024]

[0025] Wherein, C′(0) represents the first-order tangent vector of the quadratic polynomial curve when s = 0, And Φ are the shape control parameters of C(s);

[0026] Determine the point on C(s) with the abscissa of R, denoted as D2, and draw a line segment D2D3 along the Y axis through D2. The length of D2D3 is L; insert a smooth transition arc with a radius of r3 between C(s) and D2D3, and the connection position of the transition arc and C(s) is s end , s end Satisfy:

[0027] R - C x (s end ) + r3(C′ y (s end ) / ||C′(s end )|| - 1) = 0

[0028] Wherein, C x (s end ) represents C(send )'s abscissa, C y (s end ) represents the ordinate of C(s end );

[0029] For any determined C(s), when C y (s end ) ≥ τ, where τ is a set threshold, then the straight-line segment OD1 and the part of C(s) on [0, s end jointly form the cutting profile of the tool; otherwise, adjust to calculate the new tool profile shape.

[0030] The process of step 4 is as follows:

[0031] When initially executing step 4, the tool used is a toroidal cutter. When subsequently executing step 4, the tool used is the tool obtained by rotating the optimized tool profile in step 5 around the Y-axis;

[0032] According to the feed vector field in step 2, establish the local coordinate system FBN of the tool attitude at S(u i , v j ):

[0033]

[0034] Among them, S u (u i , v j ) and S v (u i , v j ) represent the first-order partial derivative vectors of the surface in the u and v directions at (u i , v j ). F, B, and N respectively represent the unit vectors in the feed direction, the row width direction, and the normal vector direction.

[0035] Set the side cutting angle β of the tool to 0, and the rake angle α is determined by the following formula:

[0036] α = α min + c(α max - α min )

[0037] Among them, c is a given coefficient, α min is the minimum rake angle without local undercut of the tool at S(u i , v j ), α max is the angle between the normal vector of the tool surface at C(s end ) and the Y-axis. For a toroidal cutter, α max = π / 4;

[0038] Calculate the cutting width of the cutting tool:

[0039]

[0040] Among them, R b is the radius of curvature of the surface to be machined at S(u i , v j ) along the cutting width direction, r e is the effective cutting radius of the cutting tool, and h is the set residual height; when the local concavity and convexity of the surface to be machined along the cutting width direction is concave, the denominator part in the formula is '-'; when the local concavity and convexity of the surface along the width direction is convex, the denominator part in the formula is '+'.

[0041] The process of step 5 is as follows:

[0042] Search for the minimum value of the cutting width among all sampling points and its location;

[0043] Set and the change range of Φ, and uniformly discretize and Φ respectively. The obtained discrete values are and m1 and m2 are respectively and the discrete numbers of Φ;

[0044] Combine with arbitrarily and calculate the tool profile according to step 3, determine the cutting width corresponding to different tool shapes under the drive of the feed vector field, and select the corresponding to the maximum cutting width as the current optimal tool shape parameter.

[0045] The determination criterion for the tool profile to reach the optimum in step 6 is:

[0046]

[0047] Among them, w a is the minimum cutting width after tool optimization, w b is the minimum cutting width before tool optimization, and ρ is the set threshold.

[0048] The connection position s end is solved by the bisection method.

[0049] The value range of c is [0.3, 0.7], and the set threshold ρ ≤ 2%.

[0050] Compared with the prior art, the beneficial effects of the present invention are:

[0051] (1) The present invention provides an optimization framework for the profile of an end milling cutter, which can automatically calculate the cutter shape matching the surface to be machined, reducing the dependence on the experience of process personnel during cutter selection;

[0052] (2) The present invention improves the machining efficiency by optimizing the cutter profile and reduces the path programming difficulty of high-efficiency five-axis machining;

[0053] (3) The execution process of the present invention is clear and concise, and is easy to be realized by programming. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a flowchart of a method for optimizing the profile of an end milling cutter for machining a surface part.

[0055] Figure 2 is a schematic diagram of the surface to be machined.

[0056] FIG. 3(a) is a schematic diagram of a quadratic polynomial curve varying with ;

[0057] FIG. 3(b) is a schematic diagram of a quadratic polynomial curve varying with Φ.

[0058] Figure 4 is the optimized cutter surface.

[0059] Figure 5 is the surface machining path generated based on the optimized cutter. DETAILED DESCRIPTION OF THE INVENTION

[0060] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This process helps those skilled in the art to further understand the present invention, but does not limit the present invention in any form. It should be noted that any modification or equivalent replacement of the present invention made without creative efforts, but without departing from the spirit and scope of the technical solution of the present invention, falls within the protection scope of the present invention.

[0061] The present invention designs a profile of an end milling cutter for machining a surface part by using a quadratic polynomial curve, providing a new solution for improving the efficiency of five-axis end milling of complex surfaces. The process is as Figure 1 shown in the flowchart and specifically includes:

[0062] Step 1: As Figure 2 shown, S(u, v) is the surface to be machined. The maximum dimensions of the surface in the length, width, and height directions are 600 mm × 280 mm × 130 mm. Uniform sampling is performed along the parameter u and parameter v directions, and the number of sampling points is 200 and 100 respectively, obtaining a 200 × 100 sampling array of points S(u i , v j ).

[0063] Step 2: Specify the tool path direction as the isoparametric curve along the u - direction of the surface. Then, the unit projection vector of the tool path direction in the parameter domain is d i,j = [1, 0], which is used to fit the control points γ i,j of the vector field i,j The number of control points is 20×20. At each sampling point, the relationship between E(u, v) and d i,j satisfies:

[0064]

[0065] Establish the above equations at all sampling positions. After rearrangement, a hyper - positive definite linear equation system about γ i,j can be obtained. Solve γ i,j using the least - squares method, and then obtain the analytical expression of the vector field:

[0066]

[0067] Step 3: (1) The coordinate system for describing the tool profile is the plane coordinate system O - XY;

[0068] (2) The tool radius for surface machining is R = 15 mm. Draw a line segment OD1 with a length of r1 = 10 mm along the X - axis. The quadratic polynomial curve is denoted as C(s), and C(s) satisfies the following conditions:

[0069]

[0070] Among them, C′(0) represents the first - order tangent vector of the curve when u = 0, and Φ are the shape control parameters of C(s). Different will form different curves. The schematic diagram of the curve variation is shown in Figure 3;

[0071] (3) Determine the point on C(s) with an abscissa of R, denoted as D2. Draw a line segment D2D3 along the Y - axis through D2. The length of D2D3 is L. Insert an arc with a radius of r3 = 0.5 mm between C(s) and D2D3 to form a smooth transition. The connection position of the transition arc and C(s) is denoted as s end , s end satisfies:

[0072] R - C x (s end ) + r3(C′ y (s end ) / ||C′(s end )|| - 1) = 0

[0073] Among them, C x (s end ) represents the abscissa of C(s end ), C′y (s end ) represents the ordinate of C′(s end ), and s end can be solved by the bisection method;

[0074] (4) For any determined C(s), let τ = 1. If C y (s end ) ≥ τ, where C y (s end ) represents the ordinate of C(s end ), then the line segment OD1 and the part of C(s) on [0, s end together form the cutting profile of the tool; otherwise, adjust and recalculate the tool shape.

[0075] Step 4: (1) The tool used for the first execution of this step is a toroidal cutter with a toroidal cutter radius of 15 mm and a radius of the toroidal part of 5 mm. The tool used for subsequent executions of this step should be the tool obtained by rotating the optimized tool profile in Step 5 around the Y-axis;

[0076] (2) According to the feed vector field in Step 2, establish a local coordinate system FBN for characterizing the tool attitude at S(u i , v j ):

[0077]

[0078] Set the side rake angle β of the tool to 0, and the front rake angle α is determined by the following formula:

[0079] α = α min + c(α max - α min )

[0080] where c = 0.5 is set, α min is the minimum non-local undercut front rake angle of the tool at the surface point S(u i , v j ), and α max is the angle between the normal vector of the tool surface at C(s end ) and the Y-axis. When the tool is a toroidal cutter, α max = π / 4;

[0081] (3) Calculate the cutting width of the tool:

[0082]

[0083] where R b is the surface at S(u i , v j) Along the radius of curvature of B, r e is the effective cutting radius of the tool, h = 0.05 is the set residual height. When the local concavity-convexity of the surface along B is concave, the denominator part in the formula is '-'; when the local concavity-convexity along B is convex, the denominator part in the formula is '+'.

[0084] Step 5: (1) Search for the minimum value of the cutting row width among all sampling points and its location;

[0085] (2) Set The variation range of is [5, 50], and the variation range of Φ is (15, 30]. Discretize and Φ uniformly respectively, and the obtained discrete values are and Φ respectively, where j (1 ≤ j ≤ m2), m1 and m2 are respectively the discretization numbers of and Φ. Given m1 = 50, m2 = 20;

[0086] (3) Combine and Φ arbitrarily and calculate the tool profile according to Step 3. Determine the cutting row width corresponding to different tool shapes under the vector field drive, and select the corresponding j with the maximum row width as the current optimal tool shape parameter. as the current optimal tool shape parameter.

[0087] Step 6: Repeat Steps 4 - 5 until the tool profile reaches the optimum. The determination criterion for the tool profile to reach the optimum is:

[0088]

[0089] where w a is the machining row width after tool optimization, w b is the machining row width before tool optimization, and ρ = 0.02.

[0090] After optimization, the optimal shape control parameters of the tool profile are Φ2 = 26.874, Figure 4 shows the optimized profile of the surface of revolution. To verify the optimization effect of the tool, for the surface to be machined, a ball-end cutter with a radius of 15 mm, the initial annular cutter used in Step 4, and the optimized tool are used for machining respectively. The positioning methods of the three tools are the same, and the tool path is the same. Generate all the paths required for surface machining according to the residual height of 0.05 mm. Among them, the surface machining path generated by using the optimal tool is as shown in Figure 5As shown. Table 1 lists the comparison of the minimum, maximum, and average values of the row widths obtained by machining with different tools. Table 2 lists the comparison of the total length and total number of paths required for surface machining generated by different tools. It can be seen that compared with the initial toroidal cutter, the optimized tool has an improvement of 23.58%, 187.19%, and 50.54% in the minimum, maximum, and average values respectively, the number of paths is reduced by 26, and the total length is shortened by 12643 mm; compared with the ball-end cutter, the optimized tool has an improvement of 107.11%, 474.38%, and 168.87% in the minimum, maximum, and average values respectively, the number of paths is reduced by 91, and the total length is shortened by 44019 mm. This shows that compared with the ball-end cutter and the toroidal cutter, the optimized tool has achieved a positive improvement in the machining row width, which is beneficial to reducing the tool path length, thus proving the advantage of the new tool in terms of machining efficiency.

[0091] Table 1 Comprehensive Comparison of Row Widths Machined by Different Tools

[0092]

[0093] Table 2 Comparison of Path Lengths and Quantities Generated by Different Tools

[0094]

Claims

1. A tool profile optimization method for end milling of curved surface parts, characterized in that, Including: Step 1: Form an array of sampling points by performing grid sampling on the surface part; Step 2: Specify the feed direction of the sampling point array to construct the feed vector field for surface machining; Step 3: Define the tool profile by a straight line and a quadratic polynomial curve, and change the quadratic polynomial curve parameters to obtain different tool profile shapes; Step 4: According to the selected tool, calculate the cutting width of the five-axis tool positions driven by the feed vector field at different sampling points; Step 5: Determine the sampling point where the minimum cutting width is located, and optimize the tool profile to increase the cutting width; Step 6: Repeat steps 4 - 5 until the tool profile reaches the optimum.

2. The tool profile optimization method for end milling of curved surface parts according to claim 1, characterized in that The process of step 1 is as follows: Let \(S(u, v)\) represent the surface to be machined, where the value ranges of \(u\) and \(v\) are both \([0, 1]\). Uniform sampling is performed on the parameter \(u\) and the parameter \(v\), and the number of sampling points is \(m\) and \(n\) respectively, obtaining a sampling point array \(S(u i , v j ).

3. The tool profile optimization method for end milling of curved surface parts according to claim 2, characterized in that, The process of step 2 is as follows: Specify the sampling point array S(u i , v j ) of the tool path direction f i，j , calculate f i，j Unit projection vector d in the uv parameter domain i，j , fitting {d i，j |i∈[1,m],j∈[1,n]}, and obtain the mathematical equation of the tool vector field for surface machining.

4. The tool profile optimization method for end milling of curved surface parts according to claim 3, characterized in that The process of step 3 is as follows: Establish a plane coordinate system O-XY, where O is the origin, X is the horizontal axis, and Y is the vertical axis; set the tool radius as R, make a straight line segment OD1 with a length of r1 along the X-axis, and the quadratic polynomial curve is denoted as C(s), where s is the curve parameter, and C(s) satisfies the following conditions: where C′(0) represents the first-order tangent vector of the quadratic polynomial curve at s = 0, and Φ are respectively the shape control parameters of C(s); Determine the point on C(s) with abscissa R, denoted as D2. Draw a line segment D2D3 along the Y-axis through D2, and the length of D2D3 is L. Insert a smooth transition arc with radius r3 between C(s) and D2D3, and the connection position of the transition arc and C(s) is s end , s end Satisfy: R-C x (s end )+r3(C′ y (s end ) / ||C′(s end )||-1)=0 Among them, C x (s end ) represents the abscissa of C(s end ), and C y (s end ) represents the ordinate of C(s end ); For any determined C(s), when C y (s end ) ≥ τ, where τ is a set threshold, the straight-line segment OD1 and the part of C(s) on [0, s end together form the cutting profile of the tool; otherwise, adjust to calculate the shape of a new tool profile.

5. The tool profile optimization method for end milling of surface parts according to claim 4, characterized in that The process of step 4 is as follows: The tool used for the first execution of step 4 is a torus cutter, and the tool used for subsequent executions of step 4 is the tool obtained by rotating the optimized tool profile in step 5 around the Y-axis; According to the feed vector field in step 2, establish a local coordinate system for the tool attitude at S(u i , v j ), set the side cutting edge inclination angle β of the tool to 0, and determine the rake angle α of the tool using the following formula: α＝α min +c(α max -α min ) where c is a given coefficient, α min is the minimum local undercut-free rake angle of the cutting tool at S(u i , v j ), and α max is the angle between the normal vector of the cutting tool surface at C(s end ) and the Y-axis; Calculate the cutting width of the tool: Among them, R b is the radius of curvature of the surface to be machined along the cutting pass width direction at S(u i , v j ), r e is the effective cutting radius of the cutting tool, and h is the set residual height; when the local concavity-convexity of the surface to be machined along the cutting pass width direction is concave, the denominator part in the formula is '-'; when the local concavity-convexity of the surface along the pass width direction is convex, the denominator part in the formula is '+'.

6. The tool profile optimization method for end milling of curved surface parts according to claim 5, characterized in that, The process of step 5 is as follows: Search for the minimum value of the cutting widths of all sampling points and its location; Settings and the variation range of Φ, discretize and Φ uniformly respectively, and the obtained discrete values are and m1 and m2 are respectively the discrete numbers of Combine with in any combination and calculate the tool profile according to Step 3 to determine the cutting row width corresponding to different tool shapes under the drive of the feed vector field, and select the as the current optimal tool shape parameter.

7. The tool profile optimization method for end milling of curved surface parts according to claim 6, characterized in that The determination criterion for the tool profile to reach the optimum in step 6 is: where w a is the minimum cutting pass width after tool optimization, w b is the minimum cutting pass width before tool optimization, and ρ is the set threshold value.

8. The tool profile optimization method for end milling of curved surface parts according to any one of claims 4-7, characterized in that, The connection position s end is solved by the bisection method.

9. The tool profile optimization method for end milling of curved surface parts according to claim 7, characterized in that The value range of c is [0.3, 0.7], and the set threshold ρ ≤ 2%; for the annular knife, α max = π / 4.

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