A method applied to five-axis short straight line trajectory smoothing and foresight

Abstract

The application relates to the technical field of five-axis machining, in particular to a five-axis short straight line trajectory smoothing foresight method, which takes the position trajectory of a tool tip point and a position point on a tool shaft as an attitude trajectory, takes the midpoint of two adjacent original data points in machining as an inflection point division, adopts double PH curves to realize G2 trajectory smoothing at the inflection point, adopts a cubic B spline to keep the G2 continuity of the remaining straight line segment after PH smoothing, and keeps the G2 continuity of the joint point of the PH spline and the B spline; efficient calculation of PH curve spline interpolation and B spline interpolation is realized. The method can be applied to the case where the joint angle does not change, keeps G2 continuity for the whole machining trajectory, keeps machining precision, has high machining efficiency, can be applied to short straight line machining, simplifies arc length calculation, improves operation efficiency, and keeps real-time performance.

Description

Technical Field

[0001] This invention relates to the field of five-axis machining technology, and in particular to a smooth look-ahead method for five-axis short straight-line trajectories. Background Technology

[0002] Complex curved surface parts have wide applications in many fields, such as aerospace, defense, and energy. A five-axis machine tool has three translational axes and two rotary axes, and can synchronously control the movement of all five axes. Therefore, the main method in machining complex curved surfaces is five-axis linkage machining.

[0003] In five-axis CNC machining, trajectory smoothing synchronization technology is the most critical. Existing trajectory smoothing synchronization is mainly divided into local smoothing synchronization and global smoothing synchronization. Local smoothing synchronization technology is more widely used because it has more controllable errors and higher precision compared to global smoothing.

[0004] Reference 1, "Q.Hu, Y.Chen, X.Jin, et al., A Real-Time C3 Continuous Tool Path Smoothing and Interpolation Algorithm for Five-Axis Machine Tools, Journal of Manufacturing Science and Engineering, 2020, 142(4): 1-43," discloses a method using a double eleven-degree PH curve. Reference 1 performs trajectory smoothing on the tool tip position in workpiece coordinates and the corners of the two rotational axes in joint coordinates. The remaining straight segments after smoothing are represented using cubic B-splines. After smoothing, the entire trajectory can maintain C3 continuity. However, in actual machining, the rotational axis angle often does not change, and the rotational axis PH curve cannot be smoothed, making it impossible to guarantee that its speed is continuous with the subsequent speed when it is not zero. Furthermore, this reference has a large curvature at the corners generated by smoothing small line segments, which reduces machining efficiency to ensure machining accuracy.

[0005] Reference 2, "J. Shi, Q. Bi, et al., Corner rounding of linear five-axis tool path by dual PH curves blending[J]. International Journal of Machine Tools & Manufacture: Design, research and application, 2015, 88: 223-236," discloses a method using dual pentagonal PH curves. Reference 2 performs trajectory smoothing on the tool tip and tool axis positions in the workpiece coordinate system, respectively. For the remaining straight segments, a linear processing method is used. Since the tool axis position changes accordingly with the tool tip position, trajectory smoothing can be performed while the joint angle remains constant. However, when smoothing multiple trajectory segments simultaneously, the linear processing of the remaining straight segments cannot guarantee simultaneous velocity continuity with the two preceding and following PH curves at the junction. Summary of the Invention

[0006] The purpose of this invention is to overcome the problems of the prior art and provide a smoothing look-ahead method for five-axis short straight-line trajectories. In five-axis machining, the machining speed at the junctions before and after the rotation axis angle remains unchanged is not zero, while the trajectory maintains G2 continuity throughout the entire machining process. This trajectory smoothing look-ahead algorithm has excellent applications in short-segment trajectories. It solves the problems of traditional techniques, such as the inability to guarantee the continuity of speed with the subsequent segment when it is not zero, the large curvature at corners generated by smoothing in short-segment trajectories leading to reduced machining efficiency to ensure machining accuracy, and the inability to guarantee simultaneous speed continuity with the two preceding and following PH curves at the junctions when smoothing multiple trajectory segments simultaneously using linear processing.

[0007] The above objectives are achieved through the following technical solutions:

[0008] A smooth look-ahead method for five-axis short straight-line trajectories includes the following steps:

[0009] Step (1) Task module division, the task modules include raw data distribution task module, smoothing task module, speed planning task module and interpolation task module;

[0010] Step (2) Obtain the tool tip position trajectory in the workpiece coordinate system and the two rotation angle trajectories of the tool axis posture in the joint coordinate system according to the required free curve trajectory. Then, according to the kinematic relationship, convert the two rotation axis angle trajectories into the trajectory of a point on the tool axis to represent the posture trajectory.

[0011] Step (3) Ensure that the smoothed corner contains a B-spline segment. The starting point of the initial corner is the starting point of the original trajectory, and the ending point of the final corner is the ending point of the original trajectory. The starting point and ending point of the other corners are the midpoints of two adjacent line segments in the original trajectory.

[0012] Step (4) uses the double quintic pH curve method to perform asymmetrical corner smoothing on the starting point, ending point and corner point in step (3);

[0013] Step (5) Use cubic B-spline curve fitting for the remaining straight line segment to ensure G2 continuity at the junction of the B-spline and the PH curve spline;

[0014] Step (6) Calculate the actual speed at the end of each segment based on the PH curve parameters obtained from the smoothing module;

[0015] Step (7) Based on the distance in the real-time planned motion, select the corresponding PH curve or B-spline interpolation function to calculate and obtain the synchronization parameters, and calculate the actual interpolation point based on the synchronization parameters.

[0016] Further, the workflow of each module in step (1) is as follows: the raw data distribution task module distributes raw data information, which includes system parameters, user input parameters and position and angle data blocks; the optical smoothing synchronization task module distributes the data to the speed planning task module after optical smoothing synchronization; the speed planning task module performs speed planning and distributes the planned partial data; and the interpolation task module performs real-time interpolation.

[0017] Further, step (4) specifically involves: using the double quintic pH curve method to perform asymmetric corner smoothing, where the pH curve of the i-th corner of the position trajectory is represented as D. Pi (u), the PH curve at the i-th corner of the attitude trajectory is represented as D. Qi (u), where u is a synchronization parameter, and its value range is [0, 1].

[0018] Further, step (5) specifically involves: using a cubic B-spline for the remaining straight line segment, where the B-spline representation of the remaining segment of the i-th straight line position trajectory is B... Pi (u), the B-spline representation of the remaining segment of the i-th attitude trajectory is B Qi (u);

[0019] Let E PHi (u)=(D Qi (u)-D Pi (u)) / ||D Qi (u)-D Pi (u)||,E Bi (u)=(B Qi(u)-B Pi (u)) / ||B Qi (u)-B Pi (u)||,s PHi (u), s Bi (u) represents the arc length of the i-th PH curve position and the arc length of the B-spline position, respectively;

[0020] To ensure G2 continuity at the junction of the B-spline and the PH curve spline, it is necessary to satisfy the following at the junction point:

[0021]

[0022] Among them, dE PHi (0) / ds PHi (0) indicates that at parameter u = 0, the curve E PHi For s PHi The first derivative;

[0023] dE Bi (1) / ds Bi (1) indicates that at the point where parameter u = 1, the curve E Bi For s Bi The first derivative, that is, the first derivative of the curve at the intersection point of the PH curve and the B-spline curve is equal;

[0024] This indicates that at parameter u = 0, E PHi For s PHi The second derivative;

[0025] This indicates that at parameter u = 1, curve E Bi For s Bi The second derivative, that is, the second derivative of the curve at the intersection point of the PH curve and the B-spline curve is equal.

[0026] Further, step (6) specifically involves: the speed planning module first using the maximum point of the PH smooth curve, i.e., when the synchronization parameter is 0.5, as the segment point, and calculating the maximum limit value of the final speed of each segment as V. ie =min(V iJ V iA V iε V f V iO );

[0027] Among them, the maximum jerk J max Speed ​​limit Maximum centripetal acceleration A max Speed ​​limit V iA =(A max / k i ) 1 / 2Positional height error ε max Speed ​​limit

[0028] Where T s For the interpolation period, the user-defined position speed limit speed V f The user gives the instruction to rotate the axis at a speed V. O Speed ​​limit V iO =V O L iP / L iO The actual final velocity is determined by the forward and reverse sweeps of each segment.

[0029] Further, step (7) specifically involves: the interpolation module calculating the curve parameter v based on the PH curve construction method. i2 u i0 and u i2 For a B-spline segment, the arc length of the B-spline can be directly calculated by the distance between the starting point and the intermediate interpolation point. During real-time interpolation, the synchronization parameters can be calculated from the displacement of the position using the simplified PH curve, the arc length formula of the B-spline, and Newton's iteration. Then, the actual interpolation point can be calculated based on the synchronization parameters.

[0030] Beneficial effects

[0031] The present invention provides a smooth look-ahead method for five-axis short straight-line trajectories, applicable to situations where joint angles remain unchanged. It maintains G2 continuity throughout the entire machining trajectory, preserving machining accuracy while achieving high machining efficiency. It can be applied to short straight-line machining, simplifies arc length calculation, improves operational efficiency, and maintains real-time performance. This method also has the following advantages:

[0032] 1. This smoothing algorithm can also be used when the joint angle does not change.

[0033] 2. G2 continuity is not limited to corners, but is maintained throughout the entire machining trajectory.

[0034] 3. While maintaining machining accuracy, it improves machining efficiency and can be applied to the machining of short straight lines.

[0035] 4. Simplify arc length calculation, improve computational efficiency, and ensure real-time performance. Attached Figure Description

[0036] Figure 1 This is a flowchart of a smooth look-ahead method for five-axis short straight-line trajectories as described in this invention;

[0037] Figure 2 This is a diagram illustrating the interaction between various task modules in a five-axis short straight-line trajectory smoothing look-ahead method as described in this invention.

[0038] Figure 3 The tool tip position and tool axis position are the data generated in the five-axis short straight line trajectory smoothing look-ahead method described in this invention.

[0039] Figure 4 This is the tool tip position interpolation trajectory velocity map generated in Reference 1 in the five-axis short straight line trajectory smoothing look-ahead method described in this invention;

[0040] Figure 5 This is a tool tip position interpolation trajectory velocity map applied to a five-axis short straight line trajectory smoothing look-ahead method as described in this invention;

[0041] Figure 6 This is an acceleration map of the tool tip position interpolation trajectory in a five-axis short straight line trajectory smoothing look-ahead method as described in this invention;

[0042] Figure 7 This is a velocity map of the X-joint, Y-joint, and Z-joint interpolation trajectory generated in a five-axis short straight-line trajectory smoothing look-ahead method as described in this invention.

[0043] Figure 8 This is an X-joint, Y-joint, and Z-joint interpolation trajectory acceleration map generated in a five-axis short straight-line trajectory smoothing look-ahead method as described in this invention;

[0044] Figure 9 This is a magnified view of the X-joint, Y-joint, and Z-joint interpolation trajectory acceleration generated in a five-axis short straight-line trajectory smoothing look-ahead method as described in this invention.

[0045] Figure 10 This is a velocity map of C-joint and B-joint interpolation trajectory generated in a five-axis short straight-line trajectory smoothing look-ahead method as described in this invention;

[0046] Figure 11 This is an acceleration map of the C-joint and B-joint interpolation trajectory generated in a five-axis short straight-line trajectory smoothing look-ahead method as described in this invention;

[0047] Figure 12 This is a magnified view of the acceleration of the C-joint and B-joint interpolation trajectory generated in the smooth look-ahead method for five-axis short straight-line trajectories described in this invention.

[0048] Figure 13 The curvature generated by the present invention and the smooth look-ahead method for five-axis short straight-line trajectories, as described in this invention, is the same as that generated in Reference 1.

[0049] Figure 14 This refers to the error between the smoothed tool tip trajectory and the original trajectory in the smoothing look-ahead method for five-axis short straight-line trajectories described in this invention. Detailed Implementation

[0050] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. The described embodiments are merely some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] like Figure 1 As shown, a smooth look-ahead method for five-axis short straight-line trajectories includes the following steps:

[0052] Step (1) Task module division, the task modules include raw data distribution task module, smoothing task module, speed planning task module and interpolation task module;

[0053] Step (2) Obtain the tool tip position trajectory in the workpiece coordinate system and the two rotation angle trajectories of the tool axis posture in the joint coordinate system according to the required free curve trajectory. Then, according to the kinematic relationship, convert the two rotation axis angle trajectories into the trajectory of a point on the tool axis to represent the posture trajectory.

[0054] Step (3) Ensure that the smoothed corner contains a B-spline segment. The starting point of the initial corner is the starting point of the original trajectory, and the ending point of the final corner is the ending point of the original trajectory. The starting point and ending point of the other corners are the midpoints of two adjacent line segments in the original trajectory.

[0055] Step (4) uses the double quintic pH curve method to perform asymmetrical corner smoothing on the starting point, ending point and corner point in step (3);

[0056] Step (5) Use cubic B-spline curve fitting for the remaining straight line segment to ensure G2 continuity at the junction of the B-spline and the PH curve spline;

[0057] Step (6) Calculate the actual speed at the end of each segment based on the PH curve parameters obtained from the smoothing module;

[0058] Step (7) Based on the distance in the real-time planned motion, select the corresponding PH curve or B-spline interpolation function to calculate and obtain the synchronization parameters, and calculate the actual interpolation point based on the synchronization parameters.

[0059] In this embodiment, the workflow of each module in step (1) is as follows: the raw data distribution task module distributes raw data information, which includes system parameters, user input parameters, and position and angle data blocks; the optical smoothing synchronization task module distributes the data to the speed planning task module after optical smoothing synchronization; the speed planning task module performs speed planning and distributes the planned partial data; and the interpolation task module performs real-time interpolation.

[0060] In this embodiment, step (2) specifically involves: first, obtaining the tool tip position trajectory in the workpiece coordinate system and the two rotation angle trajectories of the tool axis posture in the joint coordinate system according to the required free curve trajectory; then, converting the two rotation axis angle trajectories into the trajectory of a point on the tool axis according to the kinematic relationship, thereby representing the posture trajectory.

[0061] In this embodiment, step (3) is specifically as follows: In order to ensure that the corner is smoothed, it must contain a B-spline segment. Except for the starting point of the starting corner and the ending point of the ending corner, which are the starting points of the original trajectory and the ending points of the ending corner, the starting points and ending points of the other corners are the midpoints of two adjacent line segments in the original trajectory.

[0062] In this embodiment, step (4) specifically involves: using the double quintic pH curve method to perform asymmetric corner smoothing, where the pH curve of the i-th corner of the position trajectory is represented as D. Pi (u), the PH curve at the i-th corner of the attitude trajectory is represented as D. Qi (u), where u is a synchronization parameter, and its value range is [0, 1].

[0063] In this embodiment, step (5) specifically means: G2 continuity at the corner, but the entire trajectory is not yet G2 continuous at the junction of the remaining straight segment and the corner spline. Therefore, a cubic B-spline is used for the remaining straight segment, and the B-spline representation of the remaining segment of the trajectory at the i-th straight position is B. Pi (u), the B-spline representation of the remaining segment of the i-th attitude trajectory is B Qi (u);

[0064] Let E PHi (u)=(D Qi (u)-D Pi (u)) / ||D Qi (u)-D Pi (u)||,E Bi (u)=(B Qi (u)-B Pi (u)) / ||B Qi (u)-B Pi (u)||,s PHi (u), s Bi (u) represents the arc length of the i-th PH curve position and the arc length of the B-spline position, respectively;

[0065] To ensure G2 continuity at the junction of the B-spline and the PH curve spline, it is necessary to satisfy the following at the junction point:

[0066]

[0067] Among them, dEPHi (0) / ds PHi (0) indicates that at parameter u = 0, the curve E PHi For s PHi The first derivative;

[0068] dE Bi (1) / ds Bi (1) indicates that at the point where parameter u = 1, the curve E Bi For s Bi The first derivative, that is, the first derivative of the curve at the intersection point of the PH curve and the B-spline curve is equal;

[0069] This indicates that at parameter u = 0, E PHi For s PHi The second derivative;

[0070] This indicates that at parameter u = 1, curve E Bi For s Bi The second derivative, that is, the second derivative of the curve at the intersection point of the PH curve and the B-spline curve is equal;

[0071] For dE PHi (1) / ds PHi (1) dE Bi+1 (0) / ds Bi+1 (0) The meaning can be found above.

[0072] In this embodiment, step (6) specifically involves the speed planning module first using the maximum point of the PH smooth curve, i.e., when the synchronization parameter is 0.5, as the segment point, and calculating the maximum limit value of the final speed of each segment as V. ie =min(V iJ V iA V iε V f V iO );

[0073] Among them, the maximum jerk J max Speed ​​limit Maximum centripetal acceleration A max Speed ​​limit V iA =(A max / k i ) 1 / 2 Positional height error ε max Speed ​​limit Where T s For the interpolation period, the user-defined position speed limit speed V f The user gives the instruction to rotate the axis at a speed V. O Speed ​​limit V iO=V O L iP / L iO The actual final velocity is determined by the forward and reverse sweeps of each segment.

[0074] In this embodiment, step (7) specifically involves: for the interpolation module, calculating the curve parameter v according to the PH curve construction method in Reference 2. i2 u i0 and u i2 This simplifies the calculation of the pH curve arc length by the parameter v. i2 u i0 and u i2 For B-spline segments, since they represent straight line segments, the arc length can be directly calculated from the distance between the starting point and the intermediate interpolation points. Therefore, the arc length can be analytically calculated by simplifying the curve representation after the basis functions are applied. During real-time interpolation, the synchronization parameters can be calculated from the displacement of the position using the simplified PH curve, the arc length formula of the B-spline, and Newton's iteration. The actual interpolation points can then be calculated based on these synchronization parameters.

[0075] As a specific embodiment of this solution, such as Figure 2 As shown, the task is divided into four modules: raw data distribution module, smoothing module, speed planning module, and interpolation module.

[0076] In this example, the raw data delivery task module delivers raw data information, including system parameters, user input parameters, and position and angle data blocks. The real-time interpolation period is set to 1ms. In this example, the bow height error is 0.01mm, the position smoothing and attitude smoothing errors are both set to 0.1mm, the position limit velocity is 50mm / s, the normal acceleration is 1000mm / s², the jerk is 10000mm / s³, and the acceleration and deceleration are 1000mm / s².

[0077] 1. Process the original data's position and angle information, and based on kinematic relationships, convert it into the position information of the tool tip and a point on the tool axis, such as... Figure 3 The data shown is the data generated in this example;

[0078] 2. The smoothing module receives the generated data and performs PH smoothing on the corners. For the remaining straight sections after corner smoothing, cubic B-splines are used for smoothing.

[0079] 3. Calculate the maximum curvature point k of the position axis after smooth synchronization. i =8v i2 / (u i0 +u i2 ), where the subscript containing i indicates the i-th segment, v i2 u i0 and ui2 These represent the position and pH curve parameters of segment i, respectively.

[0080] 4. Divide the data into segments based on the two curvature maxima, and calculate the actual velocity at the end of each segment according to the PH curve parameters obtained from the smoothing module;

[0081] 5. Based on the distance traveled during real-time planning, select the appropriate PH or B-spline interpolation function for calculation;

[0082] Figure 4 and Figure 5 The images show the tool tip linear velocity diagrams generated by Reference 1 and this patent, respectively, based on the data in this example. The horizontal axis represents the machining cycle, and the unit is ms. The comparison shows that this patent has higher machining efficiency.

[0083] Figure 6 The point-to-line acceleration diagram of the blade tip generated for this patent shows that it is continuous.

[0084] Figures 7-12 The velocity and acceleration diagrams are shown in the coordinate system of each joint. The acceleration remains continuous throughout the entire interpolation trajectory motion, i.e., G2 continuity.

[0085] Figure 13 The maximum curvature values ​​generated at the corners are those of Reference 1 and this patent. Reference 1 has large curvature at some corners, which limits the speed of some segments, while the method of this patent is relatively stable and smaller.

[0086] Figure 14 The error value between the interpolation trajectory and the original curve in this patent does not exceed the limit of 0.1, thus meeting the accuracy requirements.

[0087] The above description is merely illustrative of the embodiments of the present invention and is not intended to limit the present invention. For those skilled in the art, any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for smoothing look-ahead trajectories applied to five-axis short straight-line trajectories, characterized in that, include: Step (1) Task module division, the task modules include raw data distribution task module, smoothing task module, speed planning task module and interpolation task module; Step (2) Obtain the tool tip position trajectory in the workpiece coordinate system and the two rotation angle trajectories of the tool axis posture in the joint coordinate system according to the required free curve trajectory. Then, according to the kinematic relationship, convert the two rotation angle trajectories into the trajectory of a point on the tool axis to represent the posture trajectory. Step (3) Ensure that the smoothed corner contains a B-spline segment. The starting point of the initial corner is the starting point of the original trajectory, and the ending point of the final corner is the ending point of the original trajectory. The starting point and ending point of the other corners are the midpoints of two adjacent line segments in the original trajectory. Step (4) uses the double quintic pH curve method to perform asymmetrical corner smoothing on the starting point, ending point and corner point in step (3); Step (5) Use cubic B-spline curve fitting for the remaining straight line segment to ensure G2 continuity at the junction of the B-spline and the PH curve spline; Step (6) Calculate the actual speed at the end of each segment based on the PH curve parameters obtained from the smoothing module; Step (7) Based on the distance in the real-time planned motion, select the corresponding PH curve or B-spline interpolation function to calculate and obtain the synchronization parameters, and calculate the actual interpolation point based on the synchronization parameters; Step (4) specifically involves: using the double quintic pH curve method for asymmetric corner smoothing, where the pH curve of the i-th corner of the position trajectory is represented as follows: The PH curve at the i-th corner of the attitude trajectory is represented as ,in This is a synchronization parameter, and its value range is: ; Step (5) specifically involves: using cubic B-splines for the remaining straight line segments, where the B-spline representation of the remaining segment of the trajectory of the i-th straight line position is as follows: The B-spline representation of the remaining segment of the i-th attitude trajectory is as follows: ; make ， , Let represent the arc length of the i-th PH curve position and the arc length of the B-spline position, respectively; To ensure G2 continuity at the junction of the B-spline and the PH curve spline, it is necessary to satisfy the following at the junction point: ， in, Indicates parameters At that point, the curve right The first derivative; Indicates parameters At that point, the curve right The first derivative; Then it represents the parameter place, right The second derivative; Indicates parameters At that point, the curve right The second derivative.

2. The method for smoothing look-ahead trajectory application to five-axis short straight-line trajectories according to claim 1, characterized in that, The workflow of each module in step (1) is as follows: the raw data distribution task module distributes raw data information, which includes system parameters, user input parameters and position and angle data blocks; After performing optical smoothing synchronization, the optical smoothing synchronization task module sends the data to the speed planning task module. The speed planning task module performs speed planning and sends out the planned partial data. The interpolation task module then performs real-time interpolation.

3. The method for smoothing look-ahead trajectory application to five-axis short straight-line trajectories according to claim 1, characterized in that, The specific steps (6) are as follows: The speed planning module first uses the maximum point of the PH smooth curve, i.e., when the synchronization parameter is 0.5, as the segment point, and calculates the maximum limit value of the final speed of each segment. , Among them, maximum jerk Speed ​​limit Maximum centripetal acceleration Speed ​​limit Position and height error Speed ​​limit ; in For the interpolation period, the user-defined position speed limit is set. User-defined rotation axis speed Speed ​​limit The actual final velocity is determined by the forward and reverse sweeps of each segment.

4. The method for smoothing look-ahead trajectory application to five-axis short straight-line trajectories according to claim 3, characterized in that, The specific step (7) is as follows: the interpolation module calculates the curve parameters according to the PH curve construction method. , and For a B-spline segment, the arc length of the B-spline is directly calculated from the distance between the starting point and the intermediate interpolation points. During real-time interpolation, the synchronization parameters can be calculated from the displacement, using the simplified PH curve, the arc length formula of the B-spline, and Newton's iteration. The actual interpolation points can then be calculated based on these synchronization parameters. , and These represent the position and pH curve parameters of segment i.

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