Corner smoothing method of Airthoid curve based on strain energy optimization

Abstract

The invention relates to the technical field of motion planning, and discloses an Airthoid curve corner smoothing method based on strain energy optimization, which is used to smooth a corner composed of straight line segments in a tool path, and uses the smoothing curve as an actual processing path of the tool; the method comprises: obtaining an approximate error constraint and a segment length constraint according to a given corner size, a corner side length and an approximate error; determining a feasible domain of a transition length and a deflection angle according to the approximate error constraint and the segment length constraint; selecting a parameter combination that minimizes the strain energy of the smoothing curve in the feasible domain according to the strain energy of the smoothing curve; calculating the arc length and curvature extreme value of three pairs of Airthoid curves constituting the smoothing curve according to the parameter combination; and the generated tool path has the advantages of being expressed based on arc length parameters, controllable contour error, and having curvature extreme value and arc length analytical expression.

Description

Technical Field

[0001] The invention relates to the technical field of motion planning, and in particular to an Airthoid curve corner smoothing method based on strain energy optimization. Background Art

[0002] Computer-aided design software usually uses NURBS curves to generate three-dimensional design files for complex spatial surfaces. However, it is difficult for most CNC systems to process parametric curves directly, and G01 codes are widely used to describe tool trajectories in actual production. However, the geometric discontinuity of adjacent straight line segments will inevitably lead to discontinuity in the feed speed and acceleration of the tool at the connection point, which will cause machine tool vibration and reduce processing quality. Existing smoothing methods often use the method of connecting a parametric curve in the corner to achieve path smoothing connection, but the effect is not as significant as the method of externally connecting smooth curves. Existing external connection methods are mostly spline curves generated by geometric iteration, which cannot express smooth curves and have a large computational load.

[0003] Reference 1: "He S, Yan C, Deng Y, et al. A tolerance constrained G2continuous path smoothing and interpolation method for industrial SCARArobots [J]. Robotics and Computer-Integrated Manufacturing, 2020, 63101907-101907." discloses a G2 continuous local smoothing method. This method uses cubic B-spline curves to smooth the corners composed of straight line segments based on a geometric iteration method. Although it is an external smoothing path, it cannot analytically express the smoothing curve.

[0004] Reference 2: "Xu F, Sun Y. A circumscribed corner rounding method based on double cubic B-splines for a five-axis linear tool path [J]. The International Journal of Advanced Manufacturing Technology, 2018, 94 (1-4): 451-462." discloses a G2-continuous local smoothing method, which uses a circumscribed cubic B-spline curve to smooth the corners formed by straight line segments, but cannot analytically express the approximate error.

[0005] Reference 3: "Fan W, Lee C, Chen J. A realtime curvature-smooth interpolationscheme and motion planning for CNC machining of short line segments [J] .International Journal of Machine Tools and Manufacture , 2015 , 96: 27-46." discloses a local smoothing method that uses an iterative method to generate an external quartic Bézier spline smoothing path.

[0006] The typical characteristics of the above literature are: although the external smoothing curve method is used to achieve the smooth transition of the processing path composed of continuous small line segments, and a larger transition speed is achieved through a smaller curvature distribution, the smoothing method in the literature cannot simultaneously have the properties of controllable approximate error and analytical calculation of curvature and arc length. Iterative calculation prolongs the time of the look-ahead process and limits the online application of the smoothing algorithm. Summary of the invention

[0007] In order to solve the above technical problems, the present invention provides an Airthoid curve corner smoothing method based on strain energy optimization.

[0008] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0009] A method for smoothing the corners of Airthoid curves based on strain energy optimization is proposed by constructing an external smoothing curve , the original tool path consists of straight line segments and The corner formed To smooth, , is the total number of corners in the tool path; smooth curve It is composed of three pairs of symmetrical Airthoid curves, namely and , and as well as and ; and is the connection point between the straight line segment and the smooth curve, and All in straight line superior, Outside the corner, The length mapped to the tool path is recorded as the transition length , the tool is The direction of motion and the straight line The angle between ;

[0010] Calculate the transition length based on the corner size, corner edge length and approximation error and deflection angle The feasible domain of

[0011] According to the transition length and deflection angle Establish the strain energy expression of the smoothing curve;

[0012] The section where the minimum strain energy point is located is calculated according to the boundary of the feasible region, and the parameter combination of transition length and deflection angle that minimizes the strain energy of the smooth curve is calculated in the section through the strain energy expression;

[0013] The arc lengths and curvature extremes of three pairs of Airthoid curves constituting the smoothing curve with the best strain energy are calculated according to the parameter combination, and the smoothing curve circumscribed by the tool path is obtained.

[0014] Further, in Construct a local coordinate system , the unit vector With straight line Collinear, unit vectors Pointing to the outside of the corner; Construct a local coordinate system and , the unit vector With straight line Collinear, unit vectors Pointing outside the corner, unit vector , Respectively , Opposite direction; based on the coordinate system The Airthoid curve on the coordinate system The Airthoid curve on the , based on the coordinate system The Airthoid curve on , and in Tangents and corners at The angle bisector of a is perpendicular; corner The angle bisector and the straight line The intersection point is recorded as point ; Coordinate system , , Respectively , , Symmetric about the angle bisector of the corner;

[0015] The transition length is calculated based on the corner size, corner side length and approximate error. and deflection angle The feasible domain includes:

[0016] The maximum contour error of the smooth curve circumscribed to the corner occurs at the tangent point between the parallel line of the corner edge and the transition curve. The maximum contour error is recorded as the approximate error. , approximate error Indicates the maximum distance between the smoothing curve and the tool path; for a given approximate error upper limit , transition length and deflection angle The approximation error constraints that should be satisfied are:

[0017] ;

[0018] in For the tool The direction of movement at The angle between the moving directions at ; For the tool Chuhe The position line at The angle between the moving directions at ; is the deflection angle The maximum value of , Indicates corner Angle Respectively indicate the tool movement to When the unit vector The displacement components on the unit vector The displacement component on ; They represent the unit vector when the tool moves to the position with the maximum approximate error. The displacement components on the unit vector The displacement component on ; ; ; , ;

[0019] Straight line segment Curve Replacement, straight line segment The length of the transition section To avoid and The smooth curve of the straight line Overlap interference occurs on the transition section. The segment length constraint must be satisfied; Line segments continuous corners, transition length and deflection angle The segment length constraints that should be satisfied are:

[0020] ;

[0021] ;

[0022] in It is the upper limit of the transition segment length, which is related to the length of the two straight line segments that form the corner; , Straight line segments , Length;

[0023] Transition length determined by approximation error constraint and segment length constraint and deflection angle The feasible domain is:

[0024] ;

[0025] in is the deflection angle when the smooth curve satisfies both the approximate error constraint and the segment length constraint. The value of is obtained by solving the following equation:

[0026] ;

[0027] equation ,equation The closed area enclosed by the image and the X-axis and Y-axis is the transition length and deflection angle feasible domain.

[0028] Further, the transition length and deflection angle The strain energy expression of the smoothing curve is established, including:

[0029] Strain energy of a single corner smoothing curve It is expressed as:

[0030] ;

[0031] in Airthoid curve exist Tangent and Line Segments at Points The angle of ; Respectively indicate the tool movement to When the unit vector is at the point The displacement components on the unit vector The displacement component on ; ; .

[0032] Furthermore, the section where the minimum strain energy point is located is calculated according to the boundary of the feasible region, and the parameter combination of the transition length and the deflection angle that minimizes the strain energy of the smoothing curve is calculated in the section through the strain energy expression, specifically including:

[0033] By transition length and deflection angle The boundary of the feasible region of , and the section where the minimum strain energy point is located is determined as:

[0034] ;

[0035] Calculate the strain energy on the cut surface The minimum point , as the strain energy Minimum transition length and deflection angle The combination of parameters.

[0036] Furthermore, the arc lengths and curvature extremes of three pairs of Airthoid curves constituting the smoothing curve with the best strain energy are calculated according to the parameter combination to obtain the smoothing curve circumscribed to the tool path, specifically including:

[0037] Represents the Airthoid curve Characteristic parameter of the rapidity of the curvature change , represents the Airthoid curve Characteristic parameter of the rapidity of the curvature change , represents the Airthoid curve Characteristic parameter of the rapidity of the curvature change , represents the Airthoid curve Characteristic parameter of the rapidity of the curvature change Respectively expressed as:

[0038] ;

[0039] It is used to measure the local distortion of the smooth curve. The larger the value, the smoother the curve deviates from the tool path.

[0040] Airthoid Curve Characteristic parameters , Airthoid curve Characteristic parameters Respectively expressed as:

[0041] ;

[0042] It is used to measure the local distortion of the smooth curve. The larger the value, the smoother the process of smooth curve returning to the tool path is.

[0043] Airthoid Curve Arc length , Airthoid curve Arc length , Airthoid curve Arc length and Airthoid curve Arc length Respectively expressed as:

[0044] ;

[0045] Airthoid Curve Arc length , Airthoid curve Arc length It is expressed as:

[0046] ;

[0047] The curvature extreme value of the smooth curve Occurs at point Department:

[0048] ;

[0049] Get the Airthoid curve Arc length , Airthoid curve Arc length , Airthoid curve Arc length , Airthoid curve Arc length , Airthoid curve Arc length , Airthoid curve Arc length and the curvature extreme value of the smooth curve After that, the smoothing curve circumscribed to the tool path is obtained, and the original tool path is replaced by the smoothing curve as the actual processing path of the tool.

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

[0051] In order to achieve the smooth transition of continuous corners composed of straight segments of continuous tool path, the present invention proposes an improved smoothing curve based on Airthoid curve, which is expressed based on arc length parameters and A local corner smoothing method is proposed based on the improved smoothing curve. The tool path generated by this method has the advantages of arc length parameter expression, Advantages of continuity, controllable contour error, curvature extremes and analytical expression of arc length. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solutions in the specific implementation modes of the present invention, the drawings required for use in the description of the specific implementation modes will be briefly introduced below. Obviously, the drawings described below are some implementation modes of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0053] Figure 1 It is a schematic flow chart of the smoothing method of the present invention.

[0054] Figure 2 It is a schematic diagram of smoothing an embodiment using the smoothing method of the present invention.

[0055] Figure 3 It is a schematic diagram of part of the corner edges and part of the smoothing curves when the smoothing method of the present invention is used to smooth the embodiment.

[0056] Figure 4 The graphs are respectively obtained by smoothing the original contour of the corner in the embodiment using the method of inscribed Airthoid curve and the smoothing method of the present invention.

[0057] Figure 5 It is a curve curvature distribution diagram obtained by smoothing the original contour of the corner in the embodiment using the method of inscribed Airthoid curve and the smoothing method of the present invention respectively. DETAILED DESCRIPTION

[0058] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0059] The purpose of the present invention is to generate a smooth curve for a tool path which is originally a plurality of straight line segments, so as to improve the processing quality.

[0060] The present invention designs a method based on the arc length of the Airthoid curve as a parameter and having Continuous smooth curves, specifically, constructing three pairs of symmetrical Airthoid curves , and , and is the connection point of the straight line segment and the smooth curve that form the corner, and All in straight line superior, Outside the corner, the straight line , are equal in length, The length mapped to the tool path is recorded as the transition length , the tool is The direction of motion and the straight line The angle between .exist Construct a local coordinate system ,exist Construct a local coordinate system and , the unit vector With straight line Collinear, unit vectors , Respectively , The direction is opposite. Established in the coordinate system, established in the coordinate system The Airthoid curve on , and in The tangent at is perpendicular to the angle bisector of the corner. Local Coordinate System , , Respectively , , Symmetric about the angle bisector of the corner.

[0061] As a specific implementation of the present invention, when designing a smooth curve, a smooth curve consisting of three pairs of symmetrical Airthoid curves is introduced to perform a smooth transition on the corner. Specifically, the following steps are included:

[0062] S1, calculate the transition length based on the corner size, corner edge length and approximate error and deflection angle The feasible domain is:

[0063] Two adjacent straight line segments and The corner formed is connected to a smooth curve composed of three pairs of Airthoid curves. The maximum contour error of the transition curve occurs at the tangent point between the parallel line of the corner edge and the transition curve. This maximum contour error is recorded as the approximation error. , approximate error Indicates the maximum distance between the smooth curve and the tool path. For a given approximate error upper limit , with transition length and deflection angle The approximation error constraints that should be satisfied are:

[0064] ;

[0065] in For the tool The direction of movement at The angle between the moving directions at ; For the tool Chuhe The position line at The angle between the moving directions at ; For parameters The maximum value of ; ; ; Respectively indicate the tool movement to When the unit vector The displacement components on the unit vector The displacement component on .

[0066] Straight line segment Replaced by a smoothing curve, whose length is recorded as the segment length To avoid overlapping interference between two smooth curves on the same straight line segment, the segment length The segment length constraint must be satisfied. Line segments continuous corners, transition length and deflection angle The segment length constraints that should be satisfied are:

[0067] ;

[0068] ;

[0069] in is the upper limit of the segment length, and its length is related to the length of the two straight line segments that form the corner; , Straight line segments , Length.

[0070] The transition length is calculated by approximate error constraints and segment length constraints and deflection angle The feasible domain is:

[0071] ;

[0072] in The deflection angle when the smooth curve satisfies both the approximate error constraint and the segment length constraint can be obtained by solving the equation We get the equation and The image and the closed area enclosed by the X-axis and Y-axis are parameters feasible domain.

[0073] S2, according to the transition length and deflection angle Establish the strain energy expression of the smoothing curve.

[0074] The strain energy of the smoothing curve of a single corner is expressed as:

[0075] ;

[0076] in Airthoid curve exist Tangent line and straight line at a point The angle of ; ; ; ; Respectively indicate the tool movement to When the unit vector is at the point The displacement components on the unit vector The displacement component on .

[0077] S3, calculating the section where the strain energy minimum point is located according to the boundary of the feasible domain, and calculating the parameter combination of transition length and deflection angle that minimizes the strain energy of the smoothing curve in the section through the strain energy expression.

[0078] The parameters determined in step S1 and Find the strain energy in the feasible domain Minimum parameter combination Thus, the three pairs of Airthoid curves constituting the smoothing curve can be determined.

[0079] By transition length and deflection angle The boundary of the feasible region of , and the section where the minimum strain energy point is located is determined as:

[0080] ;

[0081] Calculate the strain energy on the cut surface The minimum point , as the strain energy Minimum transition length and deflection angle The combination of parameters.

[0082] S4, the arc lengths and curvature extremes of three pairs of Airthoid curves constituting the smoothing curve with the best strain energy are calculated according to the parameter combination, and the smoothing curve circumscribed to the tool path is obtained.

[0083] Represents the Airthoid curve Characteristic parameter of the rapidity of the curvature change , represents the Airthoid curve Characteristic parameter of the rapidity of the curvature change , represents the Airthoid curve Characteristic parameter of the rapidity of the curvature change , represents the Airthoid curve Characteristic parameter of the rapidity of the curvature change Respectively expressed as:

[0084] ;

[0085] Airthoid Curve Characteristic parameters , Airthoid curve Characteristic parameters Respectively expressed as:

[0086] ;

[0087] It is used to measure the local distortion of the smooth curve. The larger the value, the smoother the curve deviates from the tool path. It is used to measure the local distortion of the smooth curve. The larger the value, the smoother the process of smooth curve returning to the tool path.

[0088] Airthoid Curve Arc length , Airthoid curve Arc length , Airthoid curve Arc length and Airthoid curve Arc length Respectively expressed as:

[0089] ;

[0090] Airthoid Curve Arc length , Airthoid curve Arc length It is expressed as:

[0091] ;

[0092] The curvature extreme value of the smooth curve Occurs at point Department:

[0093] .

[0094] The analytical expression of curvature extreme value and arc length of the smooth curve improves the calculation efficiency of speed preview and reduces the pressure of computing resources of the CNC system.

[0095] In the above steps S1 to S4, the value range of i is 1 to n. Repeating the above process can smooth the tool path with n consecutive corners. When i=1, the principle of the smoothing method of the present invention is as follows Figure 2 In addition, the connection problem of the smooth curves corresponding to the two corners is explained as follows: and hour, Smoothing curve point and Smoothing curve point coincide; or hour, and The smooth curve passes through the straight line segment Connected and straight line segments In the straight line In order to more clearly express the connection problem of the smooth curves corresponding to the two corners, and Added a superscript, , Indicates the i-th corner corresponding to Point and point.

[0096] Example

[0097] This embodiment takes a tool path with a corner as an example, and the tool position coordinates are , , , set the approximate error for .

[0098] The curve diagram of smoothing the original contour of the corner formed in the embodiment by using the method of inscribing the Airthoid curve and the smoothing method of the present invention is as follows: Figure 4 shown.

[0099] The curvature distribution diagram of the curve obtained by smoothing the original corner contour formed in the embodiment using the method of inscribing the Airthoid curve and the smoothing method of the present invention is as follows: Figure 5 shown.

[0100] According to the extreme curvature and arc length of the smooth curve, prepare for the subsequent speed planning.

[0101] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them. The protection scope of the present invention is not limited thereto. Although the present invention is described in detail with reference to the above embodiments, those skilled in the art should understand that any person skilled in the art can still modify the technical solutions recorded in the above embodiments within the technical scope disclosed by the present invention, or can easily think of changes, or make equivalent replacements for some of the technical features therein; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A method for smoothing the corners of Airthoid curves based on strain energy optimization, by constructing an external smoothing curve , the original tool path consists of straight line segments and The corner formed To smooth, , is the total number of corners in the tool path; smooth curve It is composed of three pairs of symmetrical Airthoid curves, namely and , and as well as and ; and is the connection point between the straight line segment and the smooth curve, and All in straight line superior, Outside the corner, The length mapped to the tool path is recorded as the transition length , the tool is The direction of motion and the straight line The angle between ; Calculate the transition length based on the corner size, corner edge length and approximation error and deflection angle The feasible domain of According to the transition length and deflection angle Establish the strain energy expression of the smoothing curve; The section where the minimum strain energy point is located is calculated according to the boundary of the feasible region, and the parameter combination of transition length and deflection angle that minimizes the strain energy of the smooth curve is calculated in the section through the strain energy expression; The arc lengths and curvature extremes of three pairs of Airthoid curves constituting the smooth curve with the best strain energy are calculated according to the parameter combination, and the smooth curve circumscribed to the tool path is obtained; exist Construct a local coordinate system , the unit vector With straight line Collinear, unit vectors Pointing to the outside of the corner; Construct a local coordinate system and , the unit vector With straight line Collinear, unit vectors Pointing outside the corner, unit vector , Respectively , Opposite direction; based on the coordinate system The Airthoid curve on the coordinate system The Airthoid curve on the , based on the coordinate system The Airthoid curve on , and in Tangents and corners at The angle bisector of a is perpendicular; corner The angle bisector and the straight line The intersection point is recorded as point ; Coordinate system , , Respectively , , Symmetric about the angle bisector of the corner; The transition length is calculated based on the corner size, corner side length and approximate error. and deflection angle The feasible domain includes: The maximum contour error of the smooth curve circumscribed to the corner occurs at the tangent point between the parallel line of the corner edge and the transition curve. The maximum contour error is recorded as the approximate error. , approximate error Indicates the maximum distance between the smoothing curve and the tool path; for a given approximate error upper limit , transition length and deflection angle The approximation error constraints that should be satisfied are: ； in For the tool The direction of movement at The angle between the moving directions at ; For the tool Chuhe The position line at The angle between the moving directions at ; is the deflection angle The maximum value of , Indicates corner Angle Respectively indicate the tool movement to When the unit vector The displacement components on the unit vector The displacement component on ; They represent the unit vector when the tool moves to the position with the maximum approximate error. The displacement components on the unit vector The displacement component on ; ; ; , ; Straight line segment Curve Replacement, straight line segment The length of the transition section To avoid and The smooth curve of the straight line Overlap interference occurs on the transition section. The segment length constraint must be satisfied; Line segments continuous corners, transition length and deflection angle The segment length constraints that should be satisfied are: ； ； in It is the upper limit of the transition segment length, which is related to the length of the two straight line segments that form the corner; , Straight line segments , Length; Transition length determined by approximation error constraint and segment length constraint and deflection angle The feasible domain is: ； in is the deflection angle when the smooth curve satisfies both the approximate error constraint and the segment length constraint. The value of is obtained by solving the following equation: ； equation ,equation The closed area enclosed by the image and the X-axis and Y-axis is the transition length and deflection angle feasible domain.

2. The Airthoid curve corner smoothing method based on strain energy optimization according to claim 1, characterized in that: According to the transition length and deflection angle The strain energy expression of the smoothing curve is established, including: Strain energy of a single corner smoothing curve It is expressed as: ； in Airthoid curve exist Tangent and Line Segments at Points The angle of ; Respectively indicate the tool movement to When the unit vector is at the point The displacement components on the unit vector The displacement component on ; ; .

3. The Airthoid curve corner smoothing method based on strain energy optimization according to claim 2, characterized in that: The section where the minimum strain energy point is calculated according to the boundary of the feasible region, and the parameter combination of the transition length and the deflection angle that minimizes the strain energy of the smoothing curve is calculated in the section through the strain energy expression, specifically including: By transition length and deflection angle The boundary of the feasible region of , and the section where the minimum strain energy point is located is determined as: ； Calculate the strain energy on the cut surface The minimum point , as the strain energy Minimum transition length and deflection angle The combination of parameters.

4. The Airthoid curve corner smoothing method based on strain energy optimization according to claim 3 is characterized in that: The method of calculating the arc lengths and curvature extremes of three pairs of Airthoid curves constituting the smoothing curve with the best strain energy according to the parameter combination, and obtaining the smoothing curve circumscribed to the tool path, specifically includes: Represents the Airthoid curve Characteristic parameter of the rapidity of the curvature change , represents the Airthoid curve Characteristic parameter of the rapidity of the curvature change , represents the Airthoid curve Characteristic parameter of the rapidity of the curvature change , represents the Airthoid curve Characteristic parameter of the rapidity of the curvature change Respectively expressed as: ； It is used to measure the local distortion of the smooth curve. The larger the value, the smoother the process of the smooth curve deviating from the tool path is. Airthoid Curve Characteristic parameters , Airthoid curve Characteristic parameters Respectively expressed as: ； It is used to measure the local distortion of the smooth curve. The larger the value, the smoother the process of smooth curve returning to the tool path. Airthoid Curve Arc length , Airthoid curve Arc length , Airthoid curve Arc length and Airthoid curve Arc length Respectively expressed as: ； Airthoid Curve Arc length , Airthoid curve Arc length It is expressed as: ； The curvature extreme value of the smooth curve Occurs at point Department: ； Get the Airthoid curve Arc length , Airthoid curve Arc length , Airthoid curve Arc length , Airthoid curve Arc length , Airthoid curve Arc length , Airthoid curve Arc length and the curvature extreme value of the smooth curve After that, the smoothing curve circumscribed to the tool path is obtained, and the original tool path is replaced by the smoothing curve as the actual processing path of the tool.

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