A cycloid-like machining trajectory generation method with high cutting stability

Abstract

The present invention provides a method for generating a cycloidal machining trajectory with high cutting stability. The method first divides the complex surface cycloidal milling into regions, and establishes a mapping relationship between three-dimensional space and plane isoparametric domains; then, based on the cycloidal milling dynamic stability prediction model, by controlling the constant engagement angle between the tool and the workpiece during tool machining, the tool cutting load is kept stable, and a variable radius cycloidal milling tool path is planned in the isoparametric domain, and the cycloidal trajectory in the parameter domain is inversely mapped to the three-dimensional machining surface; finally, with the goal of minimizing the frequency / time of use of the machine tool's rotating axis, the tool posture in the cycloidal cutting stroke is optimized to obtain a cycloidal milling trajectory suitable for complex surfaces. The cycloidal milling trajectory generation method proposed in the present invention can effectively control the tool-workpiece engagement angle and the air cutting stroke during machining, and improve the trajectory planning accuracy and efficiency.

Description

Technical Field

[0001] The invention belongs to the field of mechanical processing and manufacturing, and in particular relates to a method for generating a cycloid-like processing trajectory with high cutting stability. Background Art

[0002] Complex curved parts such as aircraft casings have various surface morphological features, irregular allowance distribution, high machining accuracy requirements, and high material removal rates. When machining such parts, traditional machining tool paths such as circular cutting and line cutting contain a large number of concave and convex corners, which can easily aggravate the fluctuation of the meshing angle between the tool and the workpiece, leading to sudden changes in cutting load, increased cutting temperature, severe tool wear, poor surface quality, and other problems. Cycloidal milling is an effective means to solve the above problems. Cycloidal machining uses a smooth transition curve trajectory to gradually remove materials in multiple times. The cutting force changes more smoothly, which can better reduce the tool load and effectively avoid severe impact on the machine tool.

[0003] After consulting the prior art and literature, it was found that the document "M, Otkur, and, et al. Trochoidal milling [J]. International Journal of Machine Tools and Manufacture, 2007." proposed a cycloidal milling modeling method and disclosed a double cycloidal milling trajectory planning method, which effectively improved the processing efficiency of cycloidal milling; the document "Wang C, Li B, Wu S, et al. Trochoidal machining for the high-speed milling of pockets [J]. Journal of Materials Processing Technology, 2016." proposed a control strategy suitable for trochoidal milling of cavities, pointing out that by increasing the axial cutting depth, the milling efficiency and tool wear of the trochoidal milling method are better than the feed rate adjustment method; the invention patent CN108845541A discloses a cycloidal milling trajectory planning method for rough machining of free curve boundary cavities, so that the tool-workpiece meshing angle is always small during the cycloidal machining process, thereby ensuring the stability of the tool load and reducing tool wear. However, the above research and technology mainly focus on the optimization of tool feed speed and the setting of cutting force threshold, but rarely pay attention to the stability of cycloidal milling. Unreasonable trajectory parameters such as cycloidal step distance and radius will induce or even cause problems such as chatter. In a single cutting cycle of the existing cycloidal model, the tool-workpiece engagement angle changes continuously with the processing process. The engagement angle only reaches the maximum value at one point, while the engagement angle at most cutting positions is lower than the maximum value. Since there is a certain correspondence between the radial cutting depth of the tool and the engagement angle, the radial cutting depth of the tool also changes periodically, affecting the cutting stability. In addition, the traditional cycloidal path not only has poor adaptability to complex processing areas, but also has a large amount of empty cutting stroke in each cycloidal cycle, which increases the processing trajectory and is prone to overlap and redundancy of tool trajectories, affecting the processing efficiency. Therefore, how to effectively control the tool-workpiece engagement angle and empty cutting stroke during the processing process is an urgent problem to be solved in generating tool paths with high cutting stability. Summary of the invention

[0004] In order to solve the problems existing in the prior art, the purpose of the present invention is to provide a cycloidal machining trajectory generation method with high cutting stability in view of the shortcomings of the prior art. In combination with the cycloidal milling dynamics model, an iterative extension trajectory optimization method is adopted to control the tool-workpiece engagement angle to be constant during tool machining, and the cycloidal milling trajectory is segmentedly planned within a single tool trajectory cycle to maintain a stable material removal rate while ensuring machining stability.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for generating a cycloid-like machining trajectory with high cutting stability comprises the following steps:

[0007] Step 1: Obtain the complex surface morphology feature information and divide the cycloid processing area.

[0008] Step 2: Establish a spatial mapping relationship between the three-dimensional space and the plane isoparametric domain, obtain the boundary of the processing area in the isoparametric domain, and use the offset curve of the processing boundary П as the trajectory guide line I.

[0009] Step 3: Establish a cycloidal milling dynamics model, obtain a three-dimensional stable boundary, and preset the spindle speed n and axial cutting depth a. p and radial depth of cut a e The cycloid step threshold Str[Str min ,Str max ]. Then the single-cycle variable radius cycloidal milling trajectory is planned in the isoparametric domain, as follows:

[0010] (1) Select the desired step length Str0 from the required cycloid step length threshold Str to obtain the tool position angle Cycloidal radius R and tool-workpiece engagement angle Considering factors such as tool life and machining accuracy, with the goal of reducing machining time, the dynamic cutting parameters are optimized and the critical tool-workpiece engagement angle θ0 is determined.

[0011] (2) From the cutting path L r , middle section cutting trajectory L z , cut out the cutting trajectory L c Three-segment planning of cycloid milling segment trajectory:

[0012] ① Cutting track L r

[0013] Cutting track L r The trochoidal model cutting trajectory is used. Let S be the starting point of the cutting trajectory of the cut-in segment, O be the center of the tool circle, the tool contour intersects with the cutting trajectory of the previous cycle at point D, and the tangent point with the cutting trajectory of the current cycle is C. n , and The angle between the tool and the workpiece is the tool-workpiece meshing angle θ. d is the intersection of the direction curve passing through point D and parallel to the trajectory guide line Ι and the cutting trajectory in the current cycle. d is taken as the end point of the cutting trajectory E in the cutting segment. n According to the critical tool-workpiece engagement angle described in (1), Solve the tool position angle when the tool-workpiece meshing angle is θ0 in the current cycle Indicates the tool position angle range in which the tool-workpiece meshing angle in the cutting trajectory L is not less than θ0. At this time, the cutting trajectory L of the cutting segment r It cannot be determined uniquely, so the maximum inscribed circle radius R of the current processing area max The initial radius of the cycloid trajectory is preset to R1, and the cutting trajectory L is in the middle section. z R1 needs to be further optimized;

[0014] ② Middle section cutting trajectory L z

[0015] Assume the cutting trajectory L SEn is the process cutting trajectory L i (i is the number of iterations). To ensure that the tool is in the middle of the cutting path L z The engagement angle during cutting is as close to the critical value θ0 as possible, based on the process cutting trajectory L i , the intermediate cutting path L is obtained by iterative extension trajectory optimization method z The steps of iterative extension trajectory optimization method are as follows:

[0016] A. Discrete cutting trajectory L i , get the tool contact point set U = {u1,u2,...,u i-1 ,u i}, point E n Introduce U to generate a new point set U = {u1,u2,...,u i-1 ,u i ,E n};

[0017] B. Get the coordinates of the first and last points in U U(first) = [S xi ,S yi ]、U(end)=[E xi ,E yi ] and find the tangent vector at two points: starting point and the end point tangent vector Using the above four groups of parameters in S, E n The cutting trajectory L is obtained by spline interpolation between two points g ;

[0018] C. Establish cutting trajectory L g The cubic parameter spline function H is optimized with the goodness of fit and mean square error of U and H as the optimization target, and the conjugate direction method is used to determine U(first), U(end), The optimal value combination parameters are substituted into the cubic parametric spline function to construct a new process cutting trajectory L i+1 ;

[0019] D. Determine the cutting trajectory L i+1 Whether it exceeds the processing boundary П: If it exceeds the cutting boundary, the process cutting trajectory L i As the middle cutting trajectory L z , continue to step E, otherwise return to step A;

[0020] E. Solve the angular displacement in the cutting trajectory where the tool-workpiece meshing angle is constant at θ0 set up is the expected angle range, and the cutting trajectory L in the middle section is determined z Is it satisfied If the expectation is not met, return to step ①, optimize the cycloid radius R1 in the cut-in segment trajectory, and obtain a new cut-in segment trajectory L r ; If the expectation is met, output the middle cutting trajectory L z ;

[0021] ③ Cut out the cutting trajectory L c

[0022] Middle cutting path L z The common inscribed arc with the machining boundary П Transition connection, the intersection points are J1 and J2, set is the tangent vector at point J1, is the tangent vector of point J2, and the arc Set as the initial cutting segment cutting trajectory L z0 ; To ensure the stability of the cycloid machining process, the cycloid curvature radius R tro Need to meet R tro ≥KR tool , where R tool is the tool radius; K is the empirical coefficient, and the J1 type value point and the corresponding tangent vector are obtained by optimization, and the cutting trajectory L of the cut-out segment is further obtained. c To ensure the curvature continuity of the cutting trajectory, similar to step C in the iterative extension trajectory optimization method, the complete cutting trajectory L is optimized and constructed between S and J2. tro ≥KR tool , optimize R1 and return to step ①;

[0023] (3) Non-cutting segment trajectory planning: The non-cutting segment trajectory does not need to consider the tool cutting stability, so the non-cutting segment trajectory is mainly a straight line. In order to ensure a smooth transition between the non-cutting segment trajectory and the cutting segment trajectory, a tangent arc is made at the starting point S (entry point) and the end point J2 (exit point) to obtain the entry segment transition trajectory L e1 and the cut-out transition trajectory L e2 , the two transition trajectories are connected by a common tangent, thereby obtaining the cycloidal milling trajectory L within a complete single cutting cycle.

[0024] Step 4: Offset the cycloid milling trajectory toward the tool axis to obtain a cycloid-like tool cutting trajectory C i ; C i For the unit tool path, the isoparametric cycloid trajectory X is generated by multiple iterations along the trajectory guide line Ι to cover the isoparametric machining area.

[0025] Step 5: Inversely map the isoparametric cycloid trajectory X to the three-dimensional machining surface M, and consider the motion characteristics of the machine tool to minimize the use frequency of the rotating axis during the cutting process, while taking into account constraints such as cutting vibration, optimize the tool axis posture change in the cycloid tool path, adjust the local tool path, and finally obtain the three-dimensional cycloid machining tool path Z.

[0026] Beneficial effects of the present invention:

[0027] (1) The stability boundary of cycloidal milling is obtained through the milling dynamics model. The trajectory parameters such as cycloidal step size and curvature radius are selected within the stability threshold to ensure the stability of the milling process and effectively improve the efficiency and accuracy of tool path planning.

[0028] (2) Based on the cycloidal tool path, a quasi-cycloidal milling trajectory is obtained through multi-segment spline interpolation, which combines the smoothness of the cycloidal trajectory with the flexibility of the free curve, overcoming the problem of unstable material removal rate caused by the change of radial cutting depth under the existing cycloidal machining strategy. In addition, in the air cutting stroke, a straight line trajectory is used instead of the curved trajectory in the cycloidal strategy to reduce the tool path length and improve the machining efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a flow chart of the method for generating a cycloid-like machining trajectory with high cutting stability according to the present invention;

[0030] Figure 2 The three-dimensional stability lobe diagram of the cycloidal milling process of the present invention;

[0031] Figure 3 is a relationship diagram between the tool position angle and the tool-workpiece meshing angle under different cycloid radii of the present invention;

[0032] Figure 4 It is a schematic diagram of the cutting trajectory of the cycloid-like cutting segment of the present invention;

[0033] Figure 5 An example of a cutting boundary is given for the cutting trajectory of the process of the present invention;

[0034] Figure 6 This is a trajectory diagram of the iterative extension trajectory optimization method of the present invention;

[0035] Figure 7 This is a flow chart of the iterative extension trajectory optimization method of the present invention;

[0036] Figure 8 It is a schematic diagram of the cutting trajectory of the cycloid-like cutting segment of the present invention;

[0037] Fig. 9 It is a schematic diagram of the single-cycle cycloid milling trajectory of the present invention;

[0038] Fig.10 A diagram showing the relationship between the position angle of the cycloid-like tool and the tool-workpiece engagement angle of the present invention;

[0039] Fig.11 A schematic diagram of a cycloid-like tool trajectory generated along a trajectory guide line according to the present invention;

[0040] Fig.12 Schematic diagram of the inverse mapping of the isoparametric cycloid trajectory to the three-dimensional machining surface in the present invention DETAILED DESCRIPTION

[0041] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0042] See also Figure 1 , a cycloid-like machining trajectory generation method with high cutting stability, which comprises the following steps:

[0043] Step 1: Obtain the complex surface morphology feature information and divide the cycloid processing area.

[0044] Step 2: Establish a spatial mapping relationship between the three-dimensional space and the plane isoparametric domain, obtain the boundary of the processing area in the isoparametric domain, and use the offset curve of the processing boundary П as the trajectory guide line I.

[0045] Step 3: Establish the cycloidal milling dynamics model, such as Figure 2 The three-dimensional stable boundary diagram of trochoidal milling is shown, based on which the spindle speed n, axial cutting depth a are preset. p and radial depth of cut a e The cycloid step threshold Str[Str min ,Str max ], planning the single-cycle variable-radius cycloidal milling trajectory in the isoparametric domain.

[0046] Select the desired step length Str0 from the required step length threshold Str, see Figure 3 , get the tool position angle Cycloidal radius R and tool-workpiece engagement angle relationship;

[0047] (1) Considering factors such as tool life and machining accuracy, with the goal of reducing machining time, the dynamic cutting parameters are optimized and the critical tool-workpiece engagement angle θ0 is determined.

[0048] (2) From the cutting path L r , middle section cutting trajectory L z , cut out the cutting trajectory L c Three-segment planning of cycloid milling segment trajectory:

[0049] ① Cutting track L r

[0050] Cutting track L r Follow the trochoidal model cutting path. Figure 4 , let S be the starting point of the cutting trajectory of the cut-in segment, point O be the center of the tool circle, the tool contour intersects with the cutting trajectory of the previous cycle at point D, and the tangent point with the cutting trajectory of the current cycle is C n , and The angle between the tool and the workpiece is the tool-workpiece meshing angle θ. d is the intersection of the direction curve passing through D and parallel to the trajectory guide line Ι and the cutting trajectory in the current cycle. d is taken as the end point of the cutting trajectory E in the cutting segment. n According to the tool-workpiece engagement angle described in (1) Solve the tool position angle when the tool-workpiece meshing angle is θ0 in the current cycle Indicates the tool position angle range in which the tool-workpiece meshing angle in the cutting trajectory L is not less than θ0. At this time, the cutting trajectory L of the cutting segment r It cannot be determined uniquely, so the maximum inscribed circle radius R of the current processing area max The initial radius of the cycloid trajectory is preset to R1, and the cutting trajectory L is in the middle section. z R1 needs to be further optimized;

[0051] ② Middle section cutting trajectory L z

[0052] See also Figure 5 , set cutting trajectory is the process cutting trajectory L i (i is the number of iterations). To ensure that the tool is in the middle of the cutting path L z The engagement angle during cutting is as close to the critical value θ0 as possible, based on the process cutting trajectory L i , the intermediate cutting path L is obtained by iterative extension trajectory optimization method z .

[0053] See also Figure 6 ,The steps of iterative extension trajectory optimization method are as follows:

[0054] A. Discrete cutting trajectory L i , get the tool contact point set U = {u1,u2,...,u i-1 ,u i}, point En Introduce U to generate a new point set U = {u1,u2,...,u i-1 ,u i ,E n};

[0055] B. Get the coordinates of the first and last points in U U(first) = [S xi ,S yi ]、U(end)=[E xi ,E yi ] and find the tangent vector at two points: starting point and the end point tangent vector Using the above four sets of parameters in two S, E n The cutting trajectory L is obtained by spline interpolation between points g ;

[0056] C. Establish cutting trajectory L g The cubic parameter spline function H is optimized with the goodness of fit and mean square error of U and H as the optimization target, and the conjugate direction method is used to determine U(first), U(end), The optimal value combination parameters are substituted into the cubic parametric spline function to construct a new process cutting trajectory L i+1 ;

[0057] D.See Figure 7 , judging the cutting trajectory L i+1 Whether it exceeds the cutting boundary П: If it exceeds the cutting boundary, directly change the process cutting trajectory L i As the middle cutting trajectory L z , continue to step E, otherwise return to step A;

[0058] E. Solve the angular displacement in the cutting trajectory where the tool-workpiece meshing angle is constant at θ0 set up is the expected angle range, and the cutting trajectory L in the middle section is determined z Is it satisfied If the expectation is not met, return to step ①, optimize the cycloid radius R1 in the cut-in segment trajectory, and obtain a new cut-in segment trajectory L r ; If the expectation is met, output the middle cutting trajectory L z ;

[0059] ③ Cut out the cutting trajectory L c

[0060] See also Figure 8 , middle cutting trajectory L z The common inscribed arc with the machining boundary П Transition connection, the intersection points are J1 and J2, set is the tangent vector of point J1, is the tangent vector of point J2, and the arc Set as the initial cutting segment cutting trajectory L z0 ; To ensure the stability of the cycloid machining process, the cycloid curvature radius needs to satisfy R tro ≥KR tool (R tool is the tool radius; K is the empirical coefficient, generally 0.4), and the J1 type value point and the corresponding tangent vector are optimized to further obtain the cutting trajectory L of the cut-out segment. c To ensure the curvature continuity of the cutting trajectory, similar to step C in the iterative extension trajectory optimization method, the complete cutting trajectory L is optimized and constructed between S and J2. tro ≥KR tool , optimize R1 and return to step ①;

[0061] (3) The non-cutting segment trajectory does not need to consider the tool cutting stability, so the non-cutting segment trajectory is mainly a straight line. Fig. 9 To ensure a smooth transition between the non-cutting segment trajectory and the cutting segment trajectory, a tangent arc is made at the starting point S (entry point) and the end point J2 (exit point) to obtain the entry segment transition trajectory L e1 and the cut-out transition trajectory L e2 , the two transition trajectories are connected by a common tangent, thereby obtaining a trochoidal milling trajectory L within a complete single cutting cycle; see Fig.10 , the tool-workpiece engagement angle θ of the cycloidal milling trajectory L in a single cutting cycle can remain constant for a long time, effectively improving the cutting efficiency.

[0062] Step 4: See Fig.11 , offset the cycloid milling trajectory toward the tool axis to obtain the cycloid tool cutting trajectory C i ; C i For the unit tool path, the isoparametric cycloidal tool path X is generated by multiple iterations along the trajectory guide line Ι, covering the isoparametric machining area.

[0063] Step 5: See Fig.12 , the isoparametric cycloid trajectory X is inversely mapped to the three-dimensional machining surface M, and the motion characteristics of the machine tool are considered to minimize the frequency of use of the rotating axis during the cutting process, while taking into account constraints such as cutting vibration, optimizing the tool axis posture change in the cycloid tool path, adjusting the local tool path, and finally obtaining the three-dimensional cycloid machining tool path Z.

Claims

1. A method for generating a cycloid-like machining trajectory with high cutting stability, characterized in that: The following steps are involved: Step 1, obtaining the complex surface morphology feature information and dividing the cycloid processing area; Step 2: Establish a spatial mapping relationship between the three-dimensional space and the plane isoparametric domain, obtain the processing area boundary in the isoparametric domain, and use the offset curve of the processing boundary П as the trajectory guide line I; Step 3: Establish a cycloidal milling dynamics model, obtain a three-dimensional stable boundary, and preset the spindle speed n and axial cutting depth a. p and radial depth of cut a e Dynamic parameters, solve the cycloid step threshold Str[Str min ,Str max ]; then plan the single-cycle variable radius cycloidal milling trajectory in the isoparametric domain; Step 4: Offset the cycloid milling trajectory toward the tool axis to obtain a cycloid-like tool cutting trajectory C i ; C i For the unit tool path, the isoparametric cycloid trajectory X is generated by multiple iterations along the trajectory guide line Ι, covering the isoparametric machining area; Step 5: Inversely map the isoparametric cycloid trajectory X to the three-dimensional machining surface M, and consider the motion characteristics of the machine tool to reduce the frequency of use of the rotating axis during the cutting process, while taking into account the constraints including cutting vibration, optimize the tool axis posture change in the cycloid tool path, adjust the local tool path, and finally obtain the three-dimensional cycloid machining tool path Z.

2. A cycloid-like machining trajectory generation method with high cutting stability according to claim 1, characterized in that: The single-cycle variable radius cycloidal milling trajectory is planned in the isoparametric domain as follows: (1) Select the desired step length Str0 from the required cycloid step length threshold Str to obtain the tool position angle Cycloidal radius R and tool-workpiece engagement angle With the goal of reducing machining time, the dynamic cutting parameters are optimized and the critical tool-workpiece engagement angle θ0 is determined; (2) From the cutting path L r , middle section cutting trajectory L z , cut out the cutting trajectory L c Three-segment planning of cycloid milling segment trajectory: ① Cutting track L r Cutting track L r The trochoidal model cutting trajectory is used; let S be the starting point of the cutting trajectory of the cut-in segment, point O be the center of the tool circle, the tool contour intersects with the cutting trajectory of the previous cycle at point D, and the tangent point with the cutting trajectory of the current cycle is C n , and The angle between the tool and the workpiece is the tool-workpiece meshing angle θ; d is the intersection of the direction curve passing through point D and parallel to the trajectory guide line Ι and the cutting trajectory in the current cycle, and d is taken as the end point of the cutting trajectory E in the cutting segment. n ; According to the critical tool-workpiece engagement angle described in (1) Solve the tool position angle when the tool-workpiece meshing angle is θ0 in the current cycle Indicates the tool position angle range in which the tool-workpiece meshing angle in the cutting trajectory L is not less than θ0. At this time, the cutting trajectory L of the cutting segment r It cannot be determined uniquely, so the maximum inscribed circle radius R of the current processing area max The initial radius of the cycloid trajectory is preset to R1, and the cutting trajectory L is in the middle section. z R1 needs to be further optimized; ② Middle section cutting trajectory L z Set cutting trajectory is the process cutting trajectory L i , i is the number of iterations; to ensure that the tool is in the middle cutting path L z The engagement angle during cutting is as close to the critical value θ0 as possible, based on the process cutting trajectory L i , the intermediate cutting path L is obtained by iterative extension trajectory optimization method z ; ③ Cut out the cutting trajectory L c Middle cutting path L z The common inscribed arc with the machining boundary П Transition connection, the intersection points are J1 and J2, set is the tangent vector at point J1, is the tangent vector of point J2, and the arc Set as the initial cutting segment cutting trajectory L z0 ; To ensure the stability of the cycloid machining process, the cycloid curvature radius needs to satisfy R tro ≥KR tool , where R tool is the tool radius; K is the empirical coefficient, and the J1 type value point and the corresponding tangent vector are obtained by optimization, and the cutting trajectory L of the cut-out segment is further obtained. c ; To ensure the curvature continuity of the cutting trajectory, similar to step C in the iterative extension trajectory optimization method, optimize and construct the complete cutting trajectory L between S and J2; if the cutting trajectory of the cut-out segment cannot meet R tro ≥KR tool , optimize R1 and return to step ①; (3) Non-cutting segment trajectory planning: The non-cutting segment trajectory does not need to consider the cutting stability of the tool, so the non-cutting segment trajectory is mainly a straight line. To ensure a smooth transition between the non-cutting segment trajectory and the cutting segment trajectory, a tangent arc is made at the starting point S and the end point J2 to obtain the cutting segment transition trajectory L. e1 and the cut-out transition trajectory L e2 , the two transition trajectories are connected by a common tangent, thereby obtaining the cycloidal milling trajectory L within a complete single cutting cycle.

3. A cycloid-like machining trajectory generation method with high cutting stability according to claim 2, characterized in that: The iterative extension trajectory optimization method comprises the following steps: A. Discrete cutting trajectory L i , get the tool contact point set U = {u1,u2,...,u i-1 ,u i }, point E n Introduce U to generate a new point set U = {u1,u2,...,u i-1 ,u i ,E n }; B. Get the coordinates of the first and last points in U U(first) = [S xi ,S yi ]、U(end)=[E xi ,E yi ] and find the tangent vector at two points: starting point and the end point tangent vector Using the above four groups of parameters in S, E n The cutting trajectory L is obtained by spline interpolation between two points g ; C. Establish cutting trajectory L g The cubic parameter spline function H is optimized with the goodness of fit and mean square error of U and H as the optimization target, and the conjugate direction method is used to determine U(first), U(end), The optimal value combination parameters are substituted into the cubic parametric spline function to construct a new process cutting trajectory L i+1 ; D. Determine the cutting trajectory L i+1 Whether it exceeds the processing boundary П: If it exceeds the cutting boundary, the process cutting trajectory L i As the middle cutting trajectory L z , continue to step E, otherwise return to step A; E. Solve the angular displacement in the cutting trajectory where the tool-workpiece meshing angle is constant at θ0 set up is the expected angle range, and the cutting trajectory L in the middle section is determined z Is it satisfied If the expectation is not met, return to step ①, optimize the cycloid radius R1 in the cut-in segment trajectory, and obtain a new cut-in segment trajectory L r ; If the expectation is met, output the middle cutting trajectory L z .

Images