Cutter path corner asymmetric smoothing method suitable for five-axis numerical control machining

Abstract

The invention discloses a tool path corner asymmetric smoothing method suitable for five-axis numerical control machining. Aiming at a small-line-segment tool path in five-axis numerical control machining, the tool path corner asymmetric smoothing method suitable for five-axis numerical control machining is provided by taking the minimum curvature extreme value as an optimization target and the monotonous curvature as a constraint, and the problems of frequent fluctuation of the tool speed, low machining speed and the like in the numerical control machining process are solved. The method aims at improving the machining precision and the machining speed of a numerical control machine tool, and the five-axis tool path composed of small line segments is smoothed.

Description

Technical Field

[0001] The invention relates to a tool path smoothing technology in the field of five-axis numerical control machining, in particular to an asymmetric smoothing method for tool path corners suitable for five-axis numerical control machining. Background Art

[0002] Compared with three-axis CNC machine tools, five-axis CNC machine tools have more freedom of movement of the tool in three-dimensional space during processing due to the addition of two rotating axes. Therefore, when processing parts with complex geometric configurations, the geometric adaptability between the tool and the processing surface is better, which can reduce the number of clamping times during part processing and greatly improve processing efficiency. However, because the CNC program generated by the current computer-aided manufacturing system is composed of a series of small line segments, and the low continuity of the discrete small line segment tool path will cause discontinuity in tool movement, resulting in a decrease in the surface processing quality of the part. Therefore, it is necessary to smooth the five-axis tool path composed of small line segments to improve the processing accuracy and processing speed of CNC machine tools. Summary of the invention

[0003] In order to solve the above problems existing in the prior art, the present invention aims to improve the machining accuracy and machining speed of CNC machine tools and smooth the five-axis tool path composed of small line segments. Therefore, the present invention provides a method for asymmetric smoothing of tool path corners suitable for five-axis CNC machining.

[0004] Specifically, the present invention aims at the small line segment tool path in five-axis CNC machining, takes the minimum extreme curvature as the optimization goal, and takes the monotonicity of curvature as the constraint, and proposes an asymmetric smoothing method for the tool path corners suitable for five-axis CNC machining, which solves the problems of frequent fluctuations in tool speed and low machining speed during CNC machining.

[0005] The asymmetric smoothing method of tool path corners suitable for five-axis CNC machining is as follows:

[0006] Step 1: Use two Bezier curves to perform asymmetric smoothing on the i-th corner of the tool tip point path in the five-axis tool path, and generate two smooth curves with different process parameters for the i-th corner of the tool tip point small line segment tool path. Where i is a positive integer; u is the process parameter of the Bezier curve, and its value range is [0,1];

[0007] (1) By determining the Bezier curve Control points on Get the first Bezier smooth curve used to smooth the tool path of the small line segment of the tool tip point Among them, the control point and The coordinates are as follows,

[0008]

[0009] in, For the first Bezier smooth curve Process parameters, w is the process parameter of the smooth curve, is the transition length of the smooth curve;

[0010] By calculating the unknown process parameters Values ​​determine control points and Coordinates, and then obtain the first Bezier smooth curve The solution process is as follows:

[0011] (1.1), based on vector The modulus length is the constraint coefficient, let Solving by the Law of Sines

[0012]

[0013] in, θ i is a unit vector and the unit vector The size of the angle, Point the small line segment corner as the tool tip size;

[0014] (1.2) Based on the maximum smoothing error allowed under given system conditions Constraints and small segment tool path length versus transition length The limit of calculating the transition length

[0015] First, due to the smoothing error of the Bezier curve in the process of smoothing the tool path of the small line segment at the tool tip point, b Less than the maximum smoothing error given by the system The constraint, therefore, the transition length The value of satisfies the following relationship,

[0016]

[0017] Then, based on the first Bezier smooth curve The length of the small line segment tool path at the tool tip point Smaller than small line segment tool path Length And the second Bezier smooth curve The length of the small line segment tool path at the tool tip point Smaller than small line segment tool path Length Therefore, the transition length l of the smooth curve is determined i b The values ​​are:

[0018]

[0019] in, and For the second Bezier smooth curve Process parameters;

[0020] (1.3) Based on the constraints of second-order geometric continuity and monotonically changing curvature, calculate the first Bezier smooth curve Process parameters The specific steps are as follows:

[0021] (1.3.1), cubic Bezier curve C i (u) The curvature calculation formula κ at any parameter u i (u) is:

[0022]

[0023] Among them, C i '(u),C i "(u) respectively represents the curve C at the parameter u point i The first and second derivative values ​​of (u),

[0024]

[0025] (1.3.2) Let the first Bezier smooth curve The second derivative C at the point where parameter u = 0 i,pre (0) is zero, because the first Bezier smooth curve At the point The curvature is zero, so the process parameters equal,

[0026]

[0027] (1.3.3) To ensure the first Bezier smooth curve Curvature monotonicity within parameter u∈[0,1], based on process parameters Equal, according to the curvature calculation formula (5) to obtain the first Bezier smooth curve The curvature κ i,pre (u),

[0028]

[0029] Then, the curvature κ of the formula i,pre (u) Take the derivative and calculate the first Bezier smooth curve The first derivative of curvature κ i ' ,pre (u),

[0030]

[0031] Among them, q1, q2, and q3 are intermediate parameters.

[0032] (1.3.4), because when the first Bezier smooth curve The first derivative of curvature κ i ' ,pre When (u) is greater than zero, there is the first Bezier smooth curve The curvature of is monotonically increasing within the parameter u∈[0,1]. Therefore, the first-order derivative of curvature κ is obtained i ' ,pre When (u) is greater than zero, the process parameters Satisfies the following relationship,

[0033]

[0034] Moreover, since the first Bezier smooth curve The curvature of is monotonically increasing, then the first Bezier smooth curve The curvature κ i,pre (u) Maximum value κ i,pre,max as follows,

[0035]

[0036] (1.3.5), due to the curvature κ i,pre (u) Maximum value κ i,pre,max With process parameters is monotonically increasing, so by reducing the curvature κ i,pre (u) Maximum value κ i,pre,max Increase processing speed and take curvature κ i,pre (u) Maximum value κ i,pre,max Minimum process parameters The value of

[0037] at this time, The values ​​of have been determined, so we only need to determine After the value of and Determine the first Bezier smooth curve

[0038] (2) By determining the Bezier curve Control points on Get the second Bezier smooth curve used to smooth the tool path of the small line segment of the tool tip point Among them, the control point and The coordinates are as follows,

[0039]

[0040] By calculating the unknown process parameters Determine control points and The coordinates of the second Bezier smooth curve are obtained The solution process is as follows:

[0041] (2.1) Based on the second Bezier smooth curve When the parameters u=0 and u=1 satisfy the second-order geometric continuity, the second Bezier smooth curve The curvatures at parameters u=0 and u=1 are equal, so the second Bezier smooth curve is obtained. Process parameters The value of

[0042]

[0043] (2.2) Based on the second-order geometric continuity and curvature monotonicity constraints, calculate the second Bezier smooth curve Process parameters

[0044] (2.2.1) According to the curvature calculation formula (5), the second Bezier smooth curve is obtained The curvature κ i,next (u),

[0045]

[0046] Among them, n is the intermediate parameter,

[0047]

[0048] Then, for the second Bezier smooth curve The curvature κ i,next (u) Take the derivative and get the first-order derivative of curvature κ' i,next (u),

[0049]

[0050] Among them, q4, q5, q6 and q7 are intermediate parameters.

[0051]

[0052] (2.2.2) Define the intermediate function Intermediate Function The first-order derivative with respect to parameter u is make Then the first-order derivative The zero point corresponds to the intermediate function The extreme point of

[0053] Then, based on the intermediate function The intermediate function at the extreme point and at the parameters u=0 and u=1 The value of is greater than zero, so that the curvature κ i,next (u) is monotonically increasing, so the actual value of the process parameter u at the i-th corner is finally calculated and determined by the binary iterative algorithm. The specific value of

[0054] at this time, The values ​​of have been determined, and in step (1) Therefore, the transition length of the smooth curve is finally obtained by formula (4): The value of

[0055] (3) Avoid overlapping of smooth curves at the corners of adjacent small line segments by reducing the transition length of the smooth curves. The value of eliminates overlap and corrects the transition length of the smooth curve As shown below,

[0056]

[0057] (4) Substitute the value of into formula (1) to obtain the first Bezier smooth curve The control point coordinates of the first Bezier smooth curve are obtained Will Substitute the value of into formula (12) to obtain the second Bezier smooth curve The control point coordinates of the second Bezier smooth curve are obtained

[0058] Step 2: Using the same method as step 1, two Bezier curves are used to perform asymmetric smoothing on the i-th corner of the small line segment tool path in the tool axis direction of the five-axis tool path, and two smooth curves with different process parameters are generated for the i-th corner of the small line segment tool path in the tool axis direction.

[0059] Step 3: Using the same asymmetric smoothing method for tool path corners as in steps 1 and 2, perform asymmetric smoothing on all corners on the five-axis small line segment tool path in turn to generate a second-order geometrically continuous five-axis tool path.

[0060] Since the geometric continuity of the small line segment tool path is low, only the zero-order geometric continuity is achieved, which results in discontinuity in the speed and acceleration of the tool movement during CNC machining, affecting the machining quality of the part surface. Therefore, the idea of ​​the asymmetric smoothing method for the corner of the five-axis tool path with second-order geometric continuity proposed in the present invention is compared with the prior art in that, under the constraints of second-order geometric continuity and smoothing error, the curvature extreme value of the curve is reduced by asymmetric smoothing, so that the curvature of the smoothed curve becomes smaller, thereby effectively reducing the speed fluctuation during CNC machining and improving the machining speed.

[0061] Compared with the prior art, when the present invention performs five-axis tool path smoothing, the tool path generated can maintain the second-order geometric continuity of the tool tip point and the tool direction smooth curve, and the generated tool path maintains a monotonic curvature in the parameter interval u∈[0,1]. Since the curvature of the generated tool path is monotonic, the method proposed by the present invention effectively reduces speed fluctuations and improves processing efficiency. Moreover, by using an asymmetric smoothing method to smooth the tool path corners, since the method proposed by the present invention reduces the extreme curvature of the curve, thereby increasing the maximum processing speed allowed on the generated tool path, further reducing the processing time, it can further achieve high-precision and high-efficiency CNC processing compared to the prior art.

[0062] Other features and advantages of the present invention will be described in the following description, and partly become apparent from the description, or understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained by the structures particularly pointed out in the description, claims and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] The accompanying drawings are used to provide a further understanding of the technical solution of the present invention and constitute a part of the specification. Together with the specific embodiments of the present invention, they are used to explain the technical solution of the present invention and do not constitute a limitation on the technical solution of the present invention.

[0064] Figure 1 , small line segment tool path smoothing model;

[0065] Figure 2 , five-axis small segment tool path;

[0066] Figure 3 , tool path of small line segment at tool tip point;

[0067] Figure 4 , a model for eliminating overlap of smooth curves at corners of adjacent small line segments;

[0068] Fig. 5(a), curvature on the tool path generated by method I and method II;

[0069] Fig. 5(b), Comparison of curvature optimization on tool paths generated by method I and method II;

[0070] Figure 6 , velocity, acceleration, and jerk curves generated by Method I and Method II. DETAILED DESCRIPTION

[0071] The present invention will be described in more detail below with reference to the accompanying drawings, in which preferred embodiments of the present invention are shown, and it should be understood that those skilled in the art can modify the present invention described herein and still achieve the beneficial effects of the present invention. Therefore, the following description should be understood as being widely known to those skilled in the art, and not as a limitation of the present invention.

[0072] In order to verify the performance of the method proposed in the present invention, an example is given for Figure 2 The five-axis small line segment tool path shown is smoothed, and the second-order geometrically continuous asymmetric five-axis tool path corner smoothing method proposed in this patent is called Method I (i.e., asymmetric method), and the second-order geometrically continuous symmetric five-axis tool path corner smoothing method is called Method II (i.e., symmetric method, Shujie Sun, Peng Zhao, Tao Zhang, Beibei Li, Dong Yu. Smoothing interpolation of five-axis tool path with less feedrate fluctuation and higher computation efficiency [J]. Journal of Manufacturing Processes, 2024, 109: 669-693).

[0073] The asymmetric smoothing method of tool path corners suitable for five-axis CNC machining is as follows:

[0074] Step 1: Figure 1As shown in the figure, two Bezier curves are used to perform asymmetric smoothing on the i-th corner of the tool tip point small line segment tool path in the five-axis tool path, and two smooth curves with different process parameters are generated for the i-th corner of the tool tip point small line segment tool path. Where i is a positive integer; u is the process parameter of the Bezier curve, and its value range is [0,1];

[0075] (1) By determining the Bezier curve Control points on Get the first Bezier smooth curve used to smooth the tool path of the small line segment of the tool tip point Among them, the control point and The coordinates are as follows,

[0076]

[0077] in, For the first Bezier smooth curve Process parameters, w is the process parameter of the smooth curve, is the transition length of the smooth curve;

[0078] Since in formula (1), only is an unknown quantity, so by calculating The value of the control point and Coordinates, and then obtain the first smooth curve

[0079] right The specific process of solving is as follows:

[0080] (1.1), due to the control point exist On the angle bisector of The modulus length is equal to the transition length So based on the vector The modulus length is the constraint coefficient, let Solving by the Law of Sines

[0081]

[0082] in, θ i is a unit vector and the unit vector The size of the angle, Point the small line segment corner as the tool tip size;

[0083] (1.2) The first Bezier smooth curve generated during the corner smooth transition process Satisfy the smoothing error constraint, based on the maximum smoothing error allowed under given system conditions Constraints and small segment tool path length versus transition length The limit of calculating the transition length

[0084] (1.2.1) The smoothing error e of the Bezier curve in the process of tool path smoothing based on the small line segment of the tool tip point b Less than the maximum smoothing error given by the system The transition length The value of satisfies the following relationship,

[0085]

[0086] (1.2.2) Based on the first Bezier smooth curve The length of the small line segment tool path at the tool tip point Smaller than small line segment tool path Length And the second Bezier smooth curve The length of the small line segment tool path at the tool tip point Smaller than small line segment tool path Length The transition length of the smooth curve is The values ​​are:

[0087]

[0088] in, and For the second Bezier smooth curve Process parameters;

[0089] (1.3) Based on the constraints of second-order geometric continuity and monotonically changing curvature, calculate the first Bezier smooth curve Process parameters Calculating unknown process parameters In the process of obtaining the first Bezier smooth curve of the corner that satisfies the second-order geometric continuity and monotonically changes the curvature As a goal, by modifying the process parameters The value of adjusts the first Bezier smooth curve defined in formula (1) Control Points Then we can obtain the first Bezier smooth curve of the corner that satisfies the second-order geometric continuity and monotonically changes the curvature. At this point, the unknown process parameters in formula (1) can be determined The value of

[0090] calculate The specific steps are as follows:

[0091] (1.3.1), cubic Bezier curve C i (u) The curvature calculation formula κ at any process parameter u i (u) is:

[0092]

[0093] Among them, C i '(u),C i "(u) respectively represents the process parameter u point curve C i The first and second derivative values ​​of (u),

[0094]

[0095] (1.3.2) Based on the second-order geometric continuity, the corner The first Bezier smooth curve at With small line segment Connection point The curvatures at the points are equal, and the small line segments At the point The curvature at is zero, then the first Bezier smooth curve exist The curvature of a point is zero;

[0096] Then, let the first Bezier smooth curve The second derivative at the process parameter u = 0 is zero, because the first Bezier smooth curve At the point The curvature is zero, then the process parameter equal,

[0097]

[0098] (1.3.3) To ensure the first Bezier smooth curve The curvature monotonicity within the process parameter u∈[0,1] is calculated by substituting formula (7) into formula (1), then substituting formula (1) into formula (6), and then calculating the curvature formula (5) to obtain the first Bezier smooth curve: The curvature κi,pre (u),

[0099]

[0100] Then, the first Bezier smooth curve is obtained by taking the derivative of formula (8): The first derivative of curvature κ i ' ,pre (u) is:

[0101]

[0102] Among them, q1, q2, and q3 are intermediate parameters.

[0103] (1.3.4), because when the first Bezier smooth curve The first derivative of curvature κ i ' ,pre When (u) is greater than zero, there is the first Bezier smooth curve The curvature of is monotonically increasing within the process parameter u∈[0,1]. Therefore, the first-order derivative of curvature κ is obtained i ' ,pre (u) Process parameters when it is greater than zero Satisfies the following relationship,

[0104]

[0105] When the process parameter u=1, the first Bezier smooth curve The curvature of is monotonically increasing, and the first Bezier smooth curve is calculated. The curvature κ i,pre (u) Maximum value κ i,pre,max ,

[0106]

[0107] (1.3.5), according to the above maximum curvature κ i,pre,max The calculation results show that κ i,pre,max Is related to process parameters There is a monotonically increasing relationship between them. In order to reduce the curvature κ i,pre (u) Maximum value κ i,pre,max The curvature of increases the processing speed, so the curvature extreme value κ of the above curve i,pre,max Minimize process parameters Take the minimum value and combine it with formula (10) The value range is determined by Value, that is

[0108] at this time, The values ​​of have been obtained, and only further determination is needed After the value of and Generate the first Bezier smooth curve

[0109] (2) By determining the Bezier curve Control points on Get the second Bezier smooth curve used to smooth the tool path of the small line segment of the tool tip point Control Points and The coordinates are as follows,

[0110]

[0111] because The value of is unknown, through the process parameters Solve to determine the control points and The coordinates of the second Bezier smooth curve are obtained

[0112] calculate The specific steps are as follows:

[0113] (2.1) Solve the second Bezier smooth curve under the constraints of second-order geometric continuity and curvature monotone Process parameters

[0114] Combined with the curvature calculation formula (5), when reducing When the value is The first derivative at the process parameter u = 0 and the second derivative are collinear, so the second Bezier smooth curve With small line segment Connection point The curvature is zero, which is the second Bezier smooth curve The second-order geometric continuity constraint is always satisfied at the process parameter u=0.

[0115] To ensure the curve At the connection point The second-order geometric continuity of The constraint of second-order geometric continuity is satisfied at the point where parameter u=1, and the two curves are at the point The curvatures of must be equal. Combining formulas (1), (5), (6), and (12), we get the second Bezier smooth curve Process parameters The values ​​are:

[0116]

[0117] At this time, the second Bezier smooth curve The second-order geometric continuity is satisfied at the process parameters u=0 and u=1, that is, the new tool path generated Satisfy the constraints of second-order geometric continuity;

[0118] (2.2) Solve the second Bezier smooth curve under the constraints of second-order geometric continuity and curvature monotone Process parameters

[0119] (2.2.1) According to the curvature calculation formula (5), the second Bezier smooth curve is obtained The curvature κ i,next (u),

[0120]

[0121] Among them, n is the intermediate parameter,

[0122]

[0123] Then, for the second Bezier smooth curve The curvature κ i,next (u) Take the derivative and get the first-order derivative of curvature

[0124] κ i,next (u),

[0125]

[0126] Among them, q4, q5, q6 and q7 are intermediate parameters.

[0127]

[0128] (2.2.2) To make the second Bezier curve smooth The curvature κ i,next (u) When the process parameter u∈[0,1] increases monotonically, the first-order derivative of curvature κ i ' ,next (u) must be greater than zero. According to the first-order derivative formula of curvature (16), we know that when the algebraic expression in the denominator is When it is established, the first-order derivative of curvature κ i ',next (u)>0 holds. Let Then the function The first-order derivative of the process parameter u is Also because is a quintic continuously differentiable function of the process parameter u, so its first-order derivative is The zero point corresponding function The extreme point of

[0129] Since we only need to ensure that the function At the extreme point and the function value at the process parameters u=0 and u=1 is greater than zero, there is Established, which will make the generated curve The curvature κ i,next (u) is monotonically increasing. Therefore, it is necessary to Under the constraint that the function value at the extreme point and process parameters u=0 and u=1 is greater than zero, the process parameter is calculated based on the actual value of the process parameter u at the i-th corner in this example. The specific values ​​of are as follows in this example:

[0130] First, the smooth curve at the i-th corner of the tool path of the small line segment of the tool tip point is calculated according to formulas (2) and (13): of Substituting the value into formula (17), when the intermediate function When the function value at parameters u=0 and u=1 is greater than zero, the process parameters can be determined. The value range is

[0131] Then, in The binary iteration is used to solve the cubic equation root-finding formula based on the parameter u varying between [0,1] and the actual value of the parameter u in this example. The zero point of The extreme point of , and substitute it into formula (17) to calculate the function The function value of .

[0132] By function If the function value at the extreme point is greater than zero and satisfies the binary iteration error as a constraint, the intermediate function can be determined. Under the condition that the function values ​​at the extreme points and parameters u=0 and u=1 are all greater than zero, the process parameters are calculated based on the actual value of the parameter u in this example through binary iteration. The specific value of , that is, the curvature is monotonic, and the smooth curve is obtained Process parameters The specific value of

[0133] Figure 3 for Figure 2 The tool tip point of the five-axis small line segment tool path at the mark in the middle is the small line segment tool path. Figure 3 Taking the two groups of tool tip points a and b as an example, the process parameters of the smoothed curve are The values ​​of can be obtained, and the results are shown in Table 1.

[0134] Table 1 Smooth curve process parameters

[0135]

[0136] at this time, The values ​​of have been obtained, and in step (1) The value of as well as Substituting into formula (18) we can get the corrected transition length value.

[0137] (3) Figure 4 The model of the overlapping corners of the small line segment tool path is the i-th corner of the small line segment where the tool tip point has been determined by steps (1) and (2). and the i+1th corner The smooth curve at Process parameters Then, according to formula (4), we can solve The value of the smooth curve on the small line segment of the tool tip is and The sum of may be greater than the small line segment Length This phenomenon is called the overlap of smooth curves at the corners of adjacent small line segments; therefore, in order to avoid the overlap of smooth curves at the corners of adjacent small line segments, the transition length is reduced. The value is further modified to eliminate overlap and obtain a smooth curve transition length As shown below,

[0138]

[0139] (4) So far, The values ​​of have been determined; Substitute the value of into formula (1) to obtain the first Bezier smooth curve The control point coordinates of the first Bezier smooth curve are obtained Will Substitute the value of into formula (12) to obtain the second Bezier smooth curve The control point coordinates of the second Bezier smooth curve are obtained

[0140] Step 2: Since the five-axis small line segment tool path is composed of the tool tip point small line segment tool path and the tool axis direction small line segment tool path, and the tool axis direction small line segment tool path and the tool tip point small line segment tool path are both composed of discrete instruction points; therefore, for the i-th corner of the tool axis direction small line segment tool path The same method as step 1 is used to splice two Bezier curves to perform asymmetric smoothing on the i-th corner of the small line segment tool path in the tool axis direction of the five-axis tool path, and generate two smooth curves with different process parameters for the i-th corner of the small line segment tool path in the tool axis direction.

[0141] Step 3: Using the same asymmetric smoothing method for tool path corners as in steps 1 and 2, perform asymmetric smoothing on all corners on the five-axis small line segment tool path in turn to generate a second-order geometrically continuous five-axis tool path.

[0142] Method I and method II were used to Figure 2 The five-axis small segment tool path shown is smoothed.

[0143] The simulation results show that the curvature of the tool path after smoothing by method I and method II is shown in Figure 5(a), and the optimization comparison of the two tool path smoothing methods is shown in Figure 5(b). Figure 6 The speed, acceleration and jerk curves of the two smoothing methods during the machining process. It can be seen from the reduction percentage curve in Figure 5 that compared with method II, the curvature of the smooth curve of the tool path generated by method I at the corner is reduced as a whole, and the curvature satisfies the monotonic change condition. This is because the asymmetric smoothing method of the present invention reduces the curvature of the curve. Figure 6 It can be seen that method I has a higher processing speed than method II in the CNC machining process and can ensure more efficient machining.

[0144] In summary, the five-axis tool path generated by the present invention has second-order geometric continuity, and the curvature extreme value of the curve is reduced by asymmetric smoothing, so that the smooth curve at the corner of the small line segment satisfies the curvature monotonicity. Therefore, under the constraint of second-order geometric continuity, when the tool tip point and the tool axis direction small line segment tool path are smoothed, the curvature of the cubic Bezier curve changes monotonically in the process parameter u∈[0,1], and the curvature extreme value of the curve is reduced by asymmetric smoothing, which effectively improves the processing speed in the CNC machining process and reduces speed fluctuations.

[0145] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. Asymmetric smoothing method for tool path corners suitable for five-axis CNC machining, characterized by Here are the steps: Step 1: Use two Bezier curves to perform asymmetric smoothing on the i-th corner of the small line segment tool path in the tool tip direction of the five-axis tool path, and generate two smooth curves with different process parameters for the i-th corner of the tool tip point small line segment tool path. Where i is a positive integer; u is the process parameter of the Bezier curve, and its value range is [0,1]; (1) By determining the Bezier curve Control points on Get the first Bezier smooth curve used to smooth the tool path of the small line segment of the tool tip point Among them, the control point and The coordinates are as follows, in, For the first Bezier smooth curve Process parameters, is the process parameter for the smooth curve, is the transition length of the smooth curve; By calculating the unknown process parameters Values ​​determine control points and Coordinates, and then obtain the first Bezier smooth curve The solution process is as follows: (1.1), based on vector The modulus length is the constraint coefficient, let Solving by the Law of Sines in, θ i is a unit vector and the unit vector The size of the angle, Point the small line segment corner as the tool tip size; (1.2) Based on the maximum smoothing error allowed under given system conditions Constraints and small segment tool path length versus transition length The limit of calculating the transition length First, due to the smoothing error of the Bezier curve in the process of smoothing the tool path of the small line segment at the tool tip point, b Less than the maximum smoothing error given by the system The constraint, therefore, the transition length The value of satisfies the following relationship, Then, based on the first Bezier smooth curve The length of the small line segment tool path at the tool tip point Smaller than small line segment tool path Length And the second Bezier smooth curve The length of the small line segment tool path at the tool tip point Smaller than small line segment tool path Length Therefore, the transition length of the smooth curve is determined The values ​​are: in, and For the second Bezier smooth curve Process parameters; (1.3) Based on the constraints of second-order geometric continuity and monotonically changing curvature, calculate the first Bezier smooth curve Process parameters The specific steps are as follows: (1.3.1), cubic Bezier curve C i (u) The curvature calculation formula κ at any parameter u i (u) is: Among them, C i '(u),C i "(u) respectively represents the curve C at the parameter u point i The first and second derivative values ​​of (u), (1.3.2) Let the first Bezier smooth curve The second derivative C" at the point where parameter u = 0 i,pre (0) is zero, because the first Bezier smooth curve At the point The curvature is zero, so the process parameters equal, (1.3.3) To ensure the first Bezier smooth curve Curvature monotonicity within parameter u∈[0,1], based on process parameters Equal, according to the curvature calculation formula (5) to obtain the first Bezier smooth curve The curvature κ i,pre (u), Then, the curvature κ of the formula i,pre (u) Take the derivative and calculate the first Bezier smooth curve The first-order derivative of curvature κ′ i,pre (u), Among them, q1, q2, and q3 are intermediate parameters. (1.3.4), because when the first Bezier smooth curve The first-order derivative of curvature κ′ i,pre When (u) is greater than zero, there is the first Bezier smooth curve The curvature of is monotonically increasing in the parameter u∈[0,1], so the first-order derivative of curvature κ is obtained i ' ,pre (u) Process parameters when it is greater than zero Satisfies the following relationship, Moreover, since the first Bezier smooth curve The curvature of is monotonically increasing, then the first Bezier smooth curve The curvature κ i,pre (u) Maximum value κ i,pre,max as follows, (1.3.5), due to the curvature κ i,pre (u) Maximum value κ i,pre,max With process parameters is monotonically increasing, so by reducing the curvature κ i,pre (u) Maximum value κ i,pre,max Increase processing speed and take curvature κ i,pre (u) Maximum value κ i,pre,max Minimum process parameters The value of at this time, The values ​​of have been determined, so we only need to determine After the value of and Determine the first Bezier smooth curve (2) By determining the Bezier curve Control points on Get the second Bezier smooth curve used to smooth the tool path of the small line segment of the tool tip point Among them, the control point and The coordinates are as follows, By calculating the unknown process parameters Determine control points and The coordinates of the second Bezier smooth curve are obtained The solution process is as follows: (2.1) Based on the second Bezier smooth curve When the parameters u=0 and u=1 satisfy the second-order geometric continuity, the second Bezier smooth curve The curvatures at parameters u=0 and u=1 are equal, so the second Bezier smooth curve is obtained. Process parameters The value of (2.2) Based on the second-order geometric continuity and curvature monotonicity constraints, calculate the second Bezier smooth curve Process parameters (2.2.1) According to the curvature calculation formula (5), the second Bezier smooth curve is obtained The curvature κ i,next (u), Among them, n is the intermediate parameter, Then, for the second Bezier smooth curve The curvature κ i,next (u) Take the derivative and get the first-order derivative of curvature κ′ i,next (u), Among them, q4, q5, q6 and q7 are intermediate parameters. (2.2.2) Define the intermediate function Intermediate Function The first-order derivative with respect to parameter u is make Then the first-order derivative The zero point corresponds to the intermediate function The extreme point of Then, based on the intermediate function The intermediate function at the extreme point and at the parameters u=0 and u=1 The value of is greater than zero, so that the curvature κ i,next (u) is monotonically increasing, so the actual value of the process parameter u at the i-th corner is finally calculated and determined by the binary iterative algorithm. The specific value of at this time, The values ​​of have been determined, and in step (1) Therefore, the transition length of the smooth curve is finally obtained by formula (4): The value of (3) Avoid overlapping of smooth curves at the corners of adjacent small line segments by reducing the transition length of the smooth curves. The value of eliminates overlap correction to obtain a smooth curve transition length As shown below, (4) Substitute the value of into formula (1) to obtain the first Bezier smooth curve The control point coordinates of the first Bezier smooth curve are obtained Will Substitute the value of into formula (12) to obtain the second Bezier smooth curve The control point coordinates of the second Bezier smooth curve are obtained Step 2: Using the same method as step 1, two Bezier curves are used to perform asymmetric smoothing on the i-th corner of the small line segment tool path in the tool axis direction of the five-axis tool path, and two smooth curves with different process parameters are generated for the i-th corner of the small line segment tool path in the tool axis direction. Step 3: Using the same asymmetric smoothing method for tool path corners as in steps 1 and 2, perform asymmetric smoothing on all corners on the five-axis small line segment tool path in turn to generate a second-order geometrically continuous five-axis tool path.

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