High-speed corner trajectory planning method based on jerk constraint in numerical control machining

Abstract

The invention relates to the technical field of numerical control machining, and discloses a high-speed corner trajectory planning method based on jerk constraint in numerical control machining, and the method comprises the steps: carrying out the smooth acceleration / deceleration transition of a tool path corner based on an asymmetric corner smooth model of a two-stage jerk curve; based on a seven-stage S-type acceleration / deceleration algorithm, reachability analysis and time distribution are carried out on the motion of the remaining straight line segment of the tool path, and the accelerations of the two ends of the remaining straight line segment are not zero; a bidirectional look-ahead planning algorithm is adopted, a low-speed corner point is recognized, look-ahead segmentation is conducted, the feeding rate of the corner point and remaining straight line segments are planned from the front direction and the back direction, tracks in the two directions are combined, and a feeding rate curve of the whole tool path is obtained. According to the method, sustainable acceleration / deceleration can be realized at multiple corners, and the method has excellent performance and robustness in the aspects of real-time characteristic, processing efficiency and geometric accuracy.

Description

Technical Field

[0001] The invention relates to the technical field of numerical control machining, and in particular to a high-speed corner trajectory planning method based on jerk constraint in numerical control machining. Background Art

[0002] With the improvement of computer-aided design (CAD) modeling capabilities, industrial parts are increasingly using complex free-form surfaces, such as NURBS. Computer-aided manufacturing (CAM) software usually generates a series of linear motion instructions (G01) tool paths for complex free-form surfaces instead of analytical parametric curves. However, there are only G01s at the junction of adjacent linear segments. 0 Continuity. Discontinuities in curvature and feed rate at joints can cause machine tool vibrations, which can reduce surface quality and machining efficiency.

[0003] To address this problem, various corner smoothing methods have been proposed to generate continuous motion without full stops. In general, the existing methods can be divided into two categories. One is the global corner smoothing method, which uses a curve to fit all discrete tool path positions. The global corner smoothing method usually adjusts the curve iteratively to meet the kinematic and error constraints. This method has the potential to improve machining efficiency, but it is difficult to ensure the smoothness of the solution during the iteration process, and the computational complexity makes real-time calculation challenging. The other is the local corner smoothing method, which introduces specific local micro-curves to smooth adjacent linear segments and locally adjusts the error between the smoothed curve and the original path at each corner. In addition, some studies have also considered other local transition curves, such as Pythagorean Hodograph (PH) curves, Akima curves, and cycloid curves. After smoothing the sharp corners using these typical curves, the next step is to plan the feed rate along the smooth trajectory to meet the kinematic constraints. This two-step smoothing method, also known as the geometric method, is widely used in three-axis and five-axis machine tools.

[0004] In recent years, corner trajectory planning has evolved from simply removing corners to focusing on performance improvement. Planning the feed rate along a specific geometric trajectory limits further improvements in machining efficiency. Therefore, developments in recent years have focused on one-step trajectory planning methods that directly plan the motion of each drive axis, taking into account kinematic and error constraints. In kinematic models, corner trajectories are usually parameterized by machining time, and the difficulty lies in ensuring kinematic continuity at both ends of the corner. Most local corner smoothing models first decelerate and then accelerate, limiting the improvement of feed rates. Wang et al. proposed a two-stage asymmetric corner smoothing model to achieve acceleration / deceleration transition at corners. These methods comprehensively consider the motion performance of each drive axis within the specified corner tolerance range. They used a three-segment or seven-segment jerk-limited profile (JLAP) to convert the motion state of the remaining straight segments between adjacent corners.

[0005] However, current JLAP planning methods perform poorly in handling arbitrary initial and final acceleration states and arbitrary displacement increments. Although the three-stage JLAP can be applied to any initial and final acceleration states, it cannot adjust the stage duration according to arbitrary displacements. This approach only provides suboptimal solutions to avoid complex iterative calculations. This bottleneck prevents the simultaneous application of asymmetric smoothing models on adjacent corners, resulting in incompatible acceleration / deceleration patterns between the corner point and the remaining linear segments, thus limiting the sustainable increase in feed rate on consecutive corner segments. Summary of the invention

[0006] The purpose of the present invention is to provide a high-speed corner trajectory planning method based on jerk constraint in CNC machining, which combines the generalized jerk bounded curve (JLAP) planning method of the two-stage asymmetric corner smoothing strategy, and proposes a two-way planning adjustment strategy to realize real-time forward planning, thereby achieving continuous acceleration of multiple corner segments and significantly improving machine tool efficiency.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] A high-speed corner trajectory planning method based on jerk constraint in numerical control machining, the method comprising the following steps:

[0009] S1, an asymmetric corner smoothing model based on a two-stage jerk curve, performs smooth acceleration / deceleration transition at the tool path corner;

[0010] S2, based on the seven-stage S-shaped acceleration / deceleration algorithm, the reachability analysis and time allocation of the motion of the remaining straight line segments of the tool path are performed, where the acceleration at both ends of the remaining straight line segments is non-zero;

[0011] S3 adopts a bidirectional forward planning algorithm to identify low-speed corner points, perform forward segmentation, plan the feed rate of the corner points and the remaining straight line segments from both the forward and backward directions, merge the trajectories in the two directions, and obtain the feed rate curve of the entire tool path.

[0012] In addition, the method also includes: when a trajectory accessibility problem occurs, adjusting the errors of adjacent corners and correcting the feed rate curve accordingly.

[0013] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects: the high-speed corner trajectory planning method based on jerk constraint in CNC machining provided by the present invention, (1) at the corner, a two-stage asymmetric model is adopted to achieve a smooth acceleration / deceleration transition; (2) for the straight line segment of the remaining part of s, a new seven-segment JLAP planning method is proposed, which can quickly perform accessibility analysis and time allocation based on arbitrary initial and final acceleration and displacement increments; (3) a bidirectional forward planning algorithm is used to identify low-speed corner points, forward segment them, and bidirectionally plan the acceleration trajectory from each low-speed point. When the trajectory accessibility problem occurs, the error of the adjacent corners is adjusted, and the feed rate planning is corrected accordingly.

[0014] In summary, the present invention adopts a generalized jerk bounded curve (JLAP) planning method combined with a two-stage asymmetric corner smoothing strategy, and proposes a two-way planning adjustment strategy to achieve real-time forward planning, thereby achieving continuous acceleration of multiple corner segments and significantly improving machine tool efficiency. The method described in the present invention can generate a jerk bounded corner trajectory that meets user-specified tolerances and kinematic constraints in real time, and embodies excellent performance and robustness in terms of real-time characteristics, processing efficiency and geometric accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0016] Figure 1 It is a flow chart of a high-speed corner trajectory planning method based on jerk constraint in numerical control machining of the present invention;

[0017] Figure 2 It is a schematic diagram of the two-stage acceleration (TPACC) corner model of the present invention;

[0018] Figure 3 It is a schematic diagram of the two-stage deceleration (TPDEC) corner model of the present invention;

[0019] Figure 4 It is a schematic diagram of the motion on the remaining line segments of the present invention;

[0020] Figure 5 This is a schematic diagram of the 7-segment S-shaped acceleration and deceleration curve of the present invention;

[0021] Figure 6 A schematic diagram of a clover-shaped tool path and its interpolation result according to an embodiment of the present invention;

[0022] Figure 7 Schematic diagram for comparing feed rate curves of different algorithms along the clover-shaped tool path;

[0023] Figure 8 Schematic diagram for comparing the axial kinematic curves of different algorithms along the clover-shaped tool path, where (a)-(f) represent the X-axis velocity curve, Y-axis velocity curve, X-axis acceleration curve, Y-axis acceleration curve, X-axis jerk curve, and Y-axis jerk curve, respectively;

[0024] Fig. 9 A schematic diagram of a butterfly tool path and its interpolation result according to an embodiment of the present invention;

[0025] Fig.10 Schematic diagram for comparing the kinematic curves of different algorithms along the butterfly tool path, where (a)-(g) represent the tangential velocity curve, X-axis velocity curve, Y-axis velocity curve, X-axis acceleration curve, Y-axis acceleration curve, X-axis jerk curve, and Y-axis jerk curve, respectively;

[0026] Fig.11 Schematic diagrams of the three-dimensional tool path and its interpolation results according to an embodiment of the present invention, wherein (a) is a schematic diagram of the three-dimensional tool path according to the present invention, and (b)-(e) are kinematic curve schematic diagrams of the three-dimensional tool path of different algorithms. DETAILED DESCRIPTION

[0027] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only 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.

[0028] In CNC machining, most tool paths consist of a large number of linear motion instructions (G01). High-speed corner trajectory planning at the junction of adjacent segments is of great research value for machining efficiency. However, current research has incompatible acceleration / deceleration modes between corner points and the remaining linear segments, which limits the sustainable improvement of speed. To address this problem, this paper proposes a novel real-time trajectory planning method to achieve global acceleration along the G01 path. Specifically, we adopt the generalized jerk-bounded curve (JLAP) planning method combined with a two-stage asymmetric corner smoothing strategy. Subsequently, a bidirectional planning adjustment strategy is proposed to achieve real-time look-ahead planning, thereby achieving continuous acceleration of multiple corner segments and significantly improving machine tool efficiency. The final example and comparison with the current state-of-the-art technology demonstrate the superior performance and robustness of our method in terms of real-time characteristics, machining efficiency and geometric accuracy.

[0029] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0030] like Figure 1 As shown, the high-speed corner trajectory planning method based on acceleration constraint in numerical control machining provided by the present invention comprises the following steps:

[0031] S1, an asymmetric corner smoothing model based on a two-stage jerk curve, performs smooth acceleration / deceleration transition at the tool path corner;

[0032] S2, based on the seven-stage S-shaped acceleration / deceleration algorithm, the reachability analysis and time allocation of the motion of the remaining straight line segments of the tool path are performed, where the acceleration at both ends of the remaining straight line segments is non-zero;

[0033] S3 adopts a bidirectional forward planning algorithm to identify low-speed corner points, perform forward segmentation, plan the feed rate of the corner points and the remaining straight line segments from both the forward and backward directions, merge the trajectories in the two directions, and obtain the feed rate curve of the entire tool path.

[0034] The specific technical solution of the high-speed corner trajectory planning method based on jerk constraint is introduced as follows:

[0035] 1. Two-stage asymmetric corner smoothing model

[0036] The S1, based on the asymmetric corner smoothing model of the two-stage acceleration curve, performs smooth acceleration / deceleration transition at the corner of the tool path, specifically including:

[0037] In order to achieve the acceleration / deceleration transition at the corners, the asymmetric corner smoothing model with two-stage acceleration curve (DJ-ACS) proposed by Wang et al. (Wang W, Hu C, Zhou K, et al. Local asymmetrical corner trajectory smoothing with bidirectional planning and a adjusting algorithm for CNC machining [J]. Robotics and Computer-Integrated Manufacturing, 2021, 68: 102058.) was introduced.

[0038] First, define the two-stage asymmetric acceleration (TPACC) model as Figure 2 shown.

[0039] At the corner point P i , the starting and ending points of the transition are S i and E i .like Figure 2 As shown, the kinematic relationship is as follows:

[0040]

[0041] in, and is the corner point P i The processing direction of two adjacent line segments A s ,A e ,V s ,V e ,D s ,D e Respectively represent point S i and E i The acceleration, velocity and the turning point P i Assume that the corner point P i The acceleration curve at The constant acceleration of the two stages and These two accelerations are in the direction of the angle bisector. collinear in opposite directions. Therefore, the jerk curve at the corner can be expressed as:

[0042]

[0043] in, T1 and T2 represent the duration of each stage. Assume that the angle bisector of the corner is reached at time T1, and denote this position as M i, which serves as the segmentation point between the two stages. i At , the following kinematic equations are satisfied:

[0044]

[0045] Assumption A s =A e And define λ:=(J2 / J1) 1 / 3 Substitute the above assumptions and formula (1) into formula (3) and compare and The amount of

[0046]

[0047] Among them, λ is the asymmetry factor, which reflects the degree of asymmetry at both ends of the corner; ε represents the error at the corner, J1 and J2 are the magnitudes of the jerk in the two stages, and J represents the acceleration along J1. The magnitude of the directional component, J Xmax , J Ymax , J Zmax They represent the jerk constraints of each axis of the machine tool, They respectively represent the directions of each coordinate axis in the machine tool coordinate system.

[0048] Since all terms in the above equations are non-negative, we can infer that λ∈[0.5,1] and λ reflects the acceleration capability around corners.

[0049] Now consider the kinematic constraints that need to be satisfied at the corner. First, Where λ≤1, so we only need to ensure Within the jerk constraint range, that is:

[0050]

[0051] Then there are:

[0052]

[0053] Pick therefore

[0054] Next, consider acceleration and Within the constraints:

[0055]

[0056] in, Indicates M iThe acceleration at the corner is assumed to be reached at time T1, and this position is represented by M i point, which serves as the segmentation point between the two stages; Xmax , A Ymax , A Zmax Respectively represent the acceleration constraints of each axis of the machine tool;

[0057] Consider speed and Within the constraints:

[0058]

[0059] in, Indicates M i The speed at

[0060]

[0061] It should be noted that when This means that λ ≥ λ0, where λ0∈[0.5,1] is the equation The only root in the interval [0.5,1]. Therefore, λ should belong to [λ0,1].

[0062] In order to avoid overlapping of adjacent corner joints, the length of the joint D s and D e The following conditions should also be met.

[0063]

[0064] The initial setting is If equations (7) to (9) are not satisfied, reduce T1 until all constraints are satisfied. max Indicates the maximum allowable error in processing.

[0065] If T'1=αT1, where α∈[0,1], then

[0066]

[0067] Therefore, given λ, the two-stage asymmetric corner smooth acceleration trajectory can be fully determined. However, λ, which reflects the acceleration capability, cannot be determined based on a single corner alone. Multiple adjacent sections need to be checked to evaluate whether acceleration can be achieved and to what extent. The detailed lookahead and backtracking strategies will be discussed below.

[0068] Similarly, if Figure 3 As shown, a two-stage corner smooth deceleration (TPDEC) trajectory can also be determined.

[0069]

[0070] The kinematic parameters of the deceleration model are as follows:

[0071]

[0072] They satisfy the following kinematic and error constraints:

[0073]

[0074] 2. About the motion on the remaining straight line segments

[0075] like Figure 4 As shown, except for each line segment P i P i+1 The remaining linear motion on the line segment, except for the transition parts at both ends, is planned by a seven-stage S-type acceleration / deceleration algorithm. The curve has limited jerk, which ensures the stability of machine tool motion and high computational efficiency, and is therefore widely used in real-time interpolation of CNC systems. However, most S-type acceleration / deceleration algorithms are only applicable to situations where the acceleration at both ends is zero, or can only be used for planning long straight line segments. In order to better achieve the goal of continuous acceleration at multiple corners, the present invention proposes a novel seven-stage S-type acceleration / deceleration algorithm, which can be applied to line segments of arbitrary lengths, where the acceleration at both ends is non-zero.

[0076] S2, based on the seven-stage S-type acceleration / deceleration algorithm, performs reachability analysis and time allocation on the motion of the remaining straight line segments of the tool path, specifically including:

[0077] like Figure 5 As shown, the S-shaped feed rate curve has seven stages I, II, III, IV, V, VI, and VII, and the corresponding time nodes are t1-t7;

[0078] J m , A m and V m Respectively represent the line segments P i P i+1 The upper bounds of jerk, acceleration, and velocity are:

[0079]

[0080] The jerk for each phase is as follows:

[0081]

[0082] According to E i S i+1 The acceleration at both ends, the reachability analysis can be divided into the following four cases:

[0083] · Case A: a s ≥0, a e ≤0;

[0084] · Case B: a s ≥0, a e >0;

[0085] · Case C: a s <0, a e ≤0;

[0086] · Case D: a s <0, a e >0;

[0087] where a s and a e represent the accelerations at the starting and ending points of the straight-line segment, respectively;

[0088] Let S0 be the minimum distance that satisfies motion reachability. When the distance ΔL between the starting and ending points of each stage is < S0, the motion is unreachable and the corner points at both ends need to be adjusted; A0 represents the extreme value of the acceleration curve; when the velocity increment is, A0 is the minimum value; when is, A0 is the maximum value.

[0089] The time and look-ahead adjustment strategy for each stage are determined based on the distance between the starting and ending points.

[0090] · Let S0 be the minimum distance that satisfies motion reachability. When ΔL ≥ S0, the motion is reachable, i.e., the corner points at both ends do not need to be adjusted.

[0091] · Let S1 be the minimum distance required for the acceleration a(t) to reach the maximum value A m . When ΔL ≥ S1, T2 ≥ 0. There is a uniformly accelerated stage (II).

[0092] · Let S2 be the minimum distance required for a(t) to reach the minimum value -A m . When ΔL ≥ S2, T6 ≥ 0, and there is a uniformly decelerated stage (VI).

[0093] · Let S3 be the minimum distance required for the velocity v(t) to reach the maximum value V m . When ΔL ≥ S3, there is a uniformly velocity stage (IV).

[0094] 2.1 Reachability Analysis and Time Allocation for Case A

[0095] The velocity increment is defined as ΔV = v e - v s. Based on the change of ΔV, the relationship between S0, S1, S2, and S3 is different, resulting in different reachability and time allocation in each stage.

[0096] CaseA1:

[0097] In this case, The S-shaped curve that ensures reachability must include the constant deceleration stage (VI), so S2 is excluded as a segmentation point.

[0098] When ΔL < S0, the motion is unreachable. K s =(v s , a s ) should be reduced, and the corner of P i needs to be adjusted by a factor of . Then enter CaseA2 and re-plan the S-shaped curve on E i-1 S' i .

[0099] When ΔL ≥ S0, the motion is reachable. The value of V m also affects the time allocation scheme. The specific situation is as follows:

[0100] (1) If then 0 < S0 < S1 < S3.

[0101] When S0 < ΔL ≤ S1, the curve includes stages (I, III, V, VI, VII), and the following equation should be solved. This equation is a quartic equation for T1.

[0102]

[0103] When S1 < ΔL ≤ S3, the curve includes stages (I, II, III, V, VI, VII), and the following equation needs to be solved.

[0104] This equation is a quadratic equation for T2.

[0105]

[0106] When S3 < ΔL < +∞, the curve includes stages (I, II, II, IV, V, VI, VII), and the time for each stage is

[0107]

[0108] (2) If then 0 < S0 < S3. When reaching the maximum acceleration Am Previously, the speed has been accelerated to V m , so there is no uniformly accelerated phase (II), and the corner point S1 does not need to be considered.

[0109] When S0 < ΔL ≤ S3, the curve has phases (I, III, V, VI, VII), and the duration of each phase can be obtained by solving formula (17).

[0110] When S3 < ΔL < +∞, the curve has phases (I, II, IV, V, VI, VII), and the duration of each phase is as follows:

[0111]

[0112] CaseA2:

[0113] In this case, the curve that satisfies reachability must include phases (3, 5, 7),

[0114] When ΔL < S0, the motion is unreachable. K s =(v s , a s ) should be reduced, and the corner of P i should be adjusted by a factor of . Then enter Case A3 and re-plan the S-curve at E i-1 S' i .

[0115] When ΔL ≥ S0, the motion is reachable. Specifically:

[0116] (1) If then 0 ≤ S0 ≤ S3.

[0117] When S0 < ΔL ≤ S3, the curve includes phases (1, 3, 5, 7), and the duration of each phase can be obtained by solving the following equations. These equations are cubic with respect to T1 and T7.

[0118]

[0119] When S3 < ΔL < +∞, the curve includes phases (I, III, IV, V, VII), and the following equations need to be solved:

[0120]

[0121] (2) If then 0 < S0 < S1 < S3.

[0122] When S0 < ΔL ≤ S1, the S-shaped curve includes stages (I, III, V, VII), and the duration of each stage can be obtained by solving the equation formula (21). When S1 < ΔL ≤ S3, the curve includes stages (I, II, III, V, VII), and the following equation needs to be solved. This equation is a quartic equation about T7.

[0123]

[0124] When S3 < ΔL < +∞, the curve includes stages (I, II, III, IV, V, VII), and

[0125]

[0126] CaseA3:

[0127] In this case, the minimum reachability curve only includes stages (III, V), and its threshold distance is:

[0128]

[0129] When ΔL < S0, the movement is unreachable. K s =(v s , a s ) and K e =(v e , a e ) should be reduced, and the adjacent corner points of P i and P i+1 should be adjusted by a factor . Then K' s =(α 2 v s , αa s ), K' e =(α 2 v e , αa e ), and

[0130]

[0131] E' i S' i+1 is just reachable. Then, re-plan the S-shaped curve on E i-1 S' i .

[0132] When ΔL ≥ S0, the movement is reachable. The time planning is similar to the discussion in CaseA2.

[0133] Theorem 1: Symmetry of the S-shaped curve with respect to the initial and final motion states. Under the same kinematic constraints J m , A m , V m and the same displacement ΔL, if the initial and final states of two motions are opposite, i.e., and then the duration of each stage in the S-shaped curve has symmetry, i.e.:

[0134]

[0135] Proof:

[0136] Let Substitute it into Algorithm 1, and simplifying the equation will yield:

[0137]

[0138] Case A4:

[0139] In this case, the curve satisfying reachability must include stages (I, III, V), and its threshold distances are:

[0140]

[0141] When ΔL < S0, the motion is unreachable. K e =(v e , a e ) should be reduced, and the corner points of P i+1 should be adjusted by a factor . Then And:

[0142]

[0143] Then continue with Case A3.

[0144] When ΔL ≥ S0, the motion is reachable. According to Theorem 8, the situation of Case A4 is the same as that of Case A2. Just swap the initial and final states and to determine the reachability and the duration of each stage.

[0145] Case A5:

[0146] In this case, the curve satisfying reachability must include stages (I, II, III, V), and its threshold distances are:

[0147]

[0148] When ΔL < S0, the movement is unreachable. K e =(v e , a e ) should be reduced, and the corner points of P i+1 should be adjusted by a factor of . Then and:

[0149]

[0150] Then continue with CaseA4.

[0151] When ΔL ≥ S0, the movement is reachable. According to Theorem8, the situation of CaseA5 is the same as that of CaseA1. Just swap the initial and final states and to determine the reachability and the duration of each stage.

[0152] 2.2 Reachability analysis and time planning for CaseB

[0153] The reachability of this case is more complex. Under specific conditions, is reachable, while is unreachable. Let the endpoints of these intervals be denoted as For the feasible conditions in various cases, please refer to Table 9, (where Another similar situation of

[0154] CaseB4:

[0155] First, the fastest mode to achieve ΔV is (I,III).

[0156]

[0157] When or , the movement is unreachable. K e =(v e , a e ) should be reduced, and the corner points of P or should be adjusted by a factor of i+1 . Then set and go to CaseB3.

[0158] when In order to maintain the speed increment ΔV, it is necessary to reduce the acceleration time of phase (I), reduce the acceleration capacity, and re-accelerate in phase (VII). In this case, the curve that satisfies the reachability includes phases (I, II, VII).

[0159]

[0160] As the distance increment ΔL increases, the time of phase (I) decreases to 0, and only phases (III, VII) exist.

[0161]

[0162] If ΔL continues to increase at this time, the velocity increment ΔL cannot be maintained under the S-type acceleration-deceleration model, making the motion unreachable until At this time, the mode is (III, V, VII), and the minimum acceleration is

[0163]

[0164] when When K is reached, the motion is achievable and the time planning can be similar to Case A. s =(v s ,a s ) to K e =(v e ,a e ) is regarded as K s =(v s ,a s ) to K' e =(v' e ,0), and K' e =(v' e ,0) to K e =(v e ,a e ). The first segment can be regarded as Case A, while the second segment is a natural extension of phase (VII), that is, T i =T' i (i=1,…,6).

[0165]

[0166] 2.3Case C reachability analysis and time planning

[0167] According to theorem: the symmetry of the S-curve to the initial and final motion states, Case C can also be handled by Case B. Just change the initial state and the final state Exchange to determine reachability and the duration of each stage.

[0168] 2.4 Reachability analysis and time planning for Case D

[0169] In this case, the time planning can also be simplified by Case A. The process from K s =(v s , a s ) to K e =(v e , a e ) is regarded as three paragraphs: K s =(v s , a s ) to K' s =(v' s , 0), K' s =(v' s , 0) to K' e =(v' e , 0), and K' e =(v' e , 0) to K e =(v e , a e ). The second paragraph belongs to Case A, while the first paragraph is an extension of stage (1), and the third paragraph is an extension of stage (7), that is

[0170] 3. Regarding the bidirectional look-ahead planning algorithm

[0171] For the aforementioned S3, the bidirectional look-ahead planning algorithm is adopted to identify low-speed corner points, perform look-ahead segmentation, plan the feed rate of the corner points and the remaining straight line segments from both the forward and backward directions, merge the trajectories in both directions, and obtain the feed rate curve of the entire tool path, specifically including:

[0172] S301, Determine the segmentation points at the corners with the local minimum inscribed circle radius, given N points P1,...,P N , initialize k f =1, where the meaning of k f is the subscript of the current forward corner point;

[0173] S302, When k f =N, the algorithm ends; when k f <N, find the next corner with the local minimum inscribed circle radius If there is no such k R ∈(k f , N), then take kR =N, set k b =k R >k f , considering k b At the corner, set And call TPACC(k b ), where k b Indicates the corner mark of the current reverse corner point, k R The meaning of is the corner mark of the segmented corner point;

[0174] S303, when k f <k b When -1, compare the speed of forward and backward planning. If Perform forward planning and go to step S304. Otherwise, go to step S305 and perform backward planning. f =k b When -1, go to step S306;

[0175] S304, from k f +1 corner to perform forward planning, through ForwardTPACC(k f +1) Get the right To determine the shape and acceleration capability of the corner, call Get k f +1, and then call LineSPlan(k f ) Planning from arrive The trajectory of f =k f +1;

[0176] S305, from k b -1 corner for backward planning, through BackwardTPDEC(k b -1) Get the right lambda kb-1 , by calling Get k b -1 corner track, and then call LineSPlan(k b -1) Planning from arrive The trajectory of b =k b -1;

[0177] S306, when k f =k b When -1, merge the trajectories in the two directions and call LineSPlan(k f ) Planning from arrive Then, set k f =k R , proceed to step S302.

[0178] In order to improve the efficiency of the bidirectional programming algorithm and meet the real-time processing requirements in industrial applications, the look-ahead algorithm first needs to segment the G01 instruction. In the absence of user-defined segmentation points, the algorithm determines the segmentation points at the corners of the local minimum inscribed circle radius. In S301, the segmentation points are determined at the corners of the local minimum inscribed circle radius, specifically including:

[0179] The radius of the inscribed circle of the i-th corner is

[0180]

[0181] Among them, θ i =∠P i-1 P i P i+1 It is the corner P i If R i ≤R i-1 And R i ≤R i+1 , then the i-th corner is considered to be a segmentation point. i At i =1 and call TPACC(i,1).

[0182] Furthermore, in S304, the appropriate λ of the kth corner point is pre-determined by ForwardTPACC(k). k Value, thereby determining the motion state of the corner point, including:

[0183] S3041, set λ k =1 and λ k+1 = 1, to preliminarily plan the trajectory and obtain the reference speed;

[0184] S3042, call TryFPlan(k-1) to try to k-1 To S k Get a feasible S-shaped feed rate curve. Different from LineSPlan(k-1), only the parameters of the kth corner point are adjusted without changing the planned result. Based on this, call TryFPlan(k) to try to get the feed rate curve from E k To S k+1 Obtain a feasible S-shaped curve, obtain feasible parameters of two corner points, and reference accelerations on the straight line segments on both sides of the corner point k;

[0185] If one of them fails, reachflag = 0, then set λ k= 1 and return. In the subsequent steps, the feasible solution for moving along the straight line segment is obtained by adjusting the (k-1)th corner point;

[0186] S3043, will and ε=ε max Substitute into formula (4) to obtain the kinematic values ​​of other corner points;

[0187] S3044, if It means that from E k To S k+1 Need to slow down, which means V e The size is not appropriate, so Use V s and V e Update the kinematic parameters of the corner point, A ref :=A s =A e ;

[0188] S3045, check whether If the velocity constraint is violated, reduce V e , and in [V s ,V e ] Find the optimal V that satisfies the bounded condition in the interval e ;

[0189] S3046, needs to be satisfied therefore The acceleration of the kth corner point that meets the above conditions is

[0190] S3047, according to formula (4), substitute and A to obtain the λ of the corner point k ;

[0191] S3048, assign k in ForwardTPACC(k) to f +1 Repeat steps S3041-S3047 to obtain a suitable λ kf+1 To determine the shape and acceleration capability of the corner.

[0192] Note that ForwardTPACC(k) only outputs the expected factor λ k The k+1th corner point in the planning process is only used as a reference and therefore will not be stored in the result of the planning trajectory.

[0193] In addition, BackwardTPDEC(k) is similar to ForwardTPACC(k).

[0194] Specifically, in S3, BackwardTPDEC(k) and ForwardTPACC(k) use the same algorithm, namely steps S3041-S3047, except that in S3042, TryDPlan(k) only adjusts the (k-1)th corner point. If TryDPlan(k) fails, BackwardTPDEC(k) returns

[0195] λ k =1;

[0196] The value of k in BackwardTPDEC(k) is k b -1 Repeat steps S3041-S3047 to obtain the appropriate

[0197] 4. Simulation and experimental verification

[0198] The effectiveness and performance of the proposed algorithm are demonstrated through multiple examples. Compared with the previous kinematic corner smoothing method, the proposed method has advantages in processing efficiency and tool path quality. In addition, the computational efficiency is analyzed to prove the feasibility of its real-time calculation.

[0199] For clarity, the local asymmetric corner trajectory smoothing method proposed by Wang et al. is referred to as LACS. Tajima et al. planned jerk trajectories at corner points with constrained acceleration and unconstrained acceleration, which are called AI-KCS and AU-KCS, respectively. In addition, P2P refers to a simple point-to-point motion with a complete stop at each corner point.

[0200] 4.1 Simulation

[0201] First, a two-dimensional “cloverleaf” shaped tool path is shown, e.g. Figure 6 As shown, its parameter equation is:

[0202]

[0203] Where i = 0,...,54. The path contains 55 G01 codes. The user-specified tolerance is 10μm. The maximum feed rate is 60mm / s, and the X / Y axis speed limit is [V Xmax ,V Ymax ]=[100,100]mm / s. The acceleration limit of X / Y axis is [A Xmax ,A Ymax ]=[1000,2000]mm / s 2 , the acceleration limit of X / Y axis is [J Xmax ,J Ymax ]=[30000,60000]mm / s3 Our method can effectively utilize corner tolerance for transition. This is mainly because the proposed generalized JLAP planning method can sometimes achieve reachability without adjusting the errors of adjacent corners.

[0204] Figure 7 The feed rate curves planned by the four methods are shown. Figure 7 A partial zoom of the feed rate curve for a section of the tool path is provided (from the 20th to the 27th corner point). It can be observed that the AU-KCS and AI-KCS methods decelerate and then accelerate before each corner point, limiting the increase in feed rate at the corners. The LACS method can accelerate at certain corners, but cannot continuously use the acceleration / deceleration corner model. Based on the generalized JLAP planning method and the bidirectional planning adjustment strategy, the method of the present invention can achieve sustainable acceleration on continuous corner sections, thereby reducing the processing time.

[0205] The kinematic curves of the X / Y axis of the clover-shaped tool path for different algorithms are shown in Figure 2. Figure 8 shown.

[0206] like Figure 8 As shown, all four methods are able to generate jerk-bounded trajectories that comply with the given kinematic constraints. Finally, the results and computational performance comparison of each method are summarized in Table 1.

[0207] Table 1

[0208]

[0209] All four methods are implemented using MATLAB R2020b software on a PC equipped with an Intel i9 2.60 GHz CPU. Since AI-KCS does not require bidirectional lookahead, the algorithm has the shortest running time. Our algorithm has a very short computation time and can meet the real-time processing requirements in industry. In the LACS method, each corner point must be calculated using the SJ-ACS and DJ-ACS models. Finally, the model with a higher average turning speed is selected. Therefore, the computation time of this algorithm is relatively long.

[0210] Next, a complex butterfly toolpath is shown as another example. Fig. 9 The path contains 401 G01 codes, with line segment lengths ranging from 0.103mm to 1.943mm and corner angles from 76.86° to 179.97°. The corner tolerance for all four methods is set to 0.03mm. The maximum feed rate and X / Y axis speed limit are 4000mm / min. The X / Y axis acceleration and jerk limits are 1500mm / s respectively. 2 and 15000mm / s 3 .

[0211] Fig.10 The kinematic curves of different methods are shown. Fig.10 As shown, the method of the present invention can accelerate the feed rate to a higher level when passing through consecutive obtuse corners. The LACS method exhibits a lower corner speed at sharp corners, which limits the improvement of the overall feed rate. The AI-KCS method plans a lower feed rate due to the limitation of the segment length. Similarly, AU-KCS is also limited by the segment length, resulting in reduced processing efficiency. Although the acceleration capabilities vary, they all meet the specified kinematic constraints.

[0212] Table 2

[0213]

[0214] The performance comparison of the butterfly toolpath is summarized in Table 2. The test environment is the same. Our algorithm shows significant improvement in cycle time with a shorter computation time. The processing time of the LACS algorithm and the AI-KCS algorithm is comparable; however, due to the complexity of the AI-KCS algorithm, its computation time exceeds the processing time and fails to meet the real-time requirement.

[0215] Finally, we show a 3D toolpath as a test case, e.g. Fig.11 As shown in (a).

[0216] This case contains 3,215 G01 codes with line lengths ranging from 0.015mm to 44.81mm. The tolerance for all four methods is set to 0.01mm. The maximum feed rate is set to 50mm / s. The speed, acceleration, and jerk limits for the X / Y / Z axes are 100mm / s, 1000mm / s, respectively. 2 and 30000mm / s 3 .like Fig.11 As shown in (b)-(e), all four methods can reach the maximum feed rate on the long straight segments. It is worth noting that our method can quickly reach and maintain the maximum feed rate on a series of short smooth segments. The LACS method compares the average of the starting and ending velocities of SJ-ACS and DJ-ACS at each corner. Therefore, although the starting and ending velocities of the SJ-ACS corner are relatively high, the speed in the middle of the corner is lower, resulting in frequent acceleration and deceleration and a lower overall feed rate.

[0217] The performance comparison of the 3D tool paths is summarized in Table 3.

[0218] Table 3

[0219]

[0220] 4.2 Experiments

[0221] In this section, the machining experiment of the butterfly tool path described previously was conducted. The experiment used a JDHGT400-A10SH three-axis CNC machining tool with a sampling frequency of 1kHz. The cutting parameters of the tool path were the same as those in the simulation. The trajectories obtained by the four corner smoothing methods were interpolated at 1ms intervals, and then the interpolated points were transferred to the machine tool for machining. Finally, the machined workpiece was scanned and measured using a 3D optical profiler. According to the scanning results, the experimental results show that our method can improve machining efficiency and machining quality.

[0222] A novel high-speed corner smoothing method is proposed, which can generate jerk-bounded corner trajectories that meet user-specified tolerances and kinematic constraints in real time. At the corners, a two-stage asymmetric model is adopted to achieve smooth acceleration / deceleration transitions. For the straight segments of the remaining part of s, a novel seven-segment JLAP planning method is proposed. The method can quickly perform reachability analysis and time allocation based on arbitrary initial and final acceleration and displacement increments. The bidirectional look-ahead planning algorithm identifies low-speed corner points, looks-ahead segments them, and bidirectionally plans the jerk trajectory from each low-speed point. When trajectory reachability issues occur, the errors of adjacent corners are adjusted and the feed rate planning is corrected accordingly. Simulation results show that the method can achieve sustainable acceleration / deceleration on multiple corners, especially on gentle and dense short segments, thereby significantly improving the machining efficiency. Compared with other local kinematic corner smoothing methods, the total cycle time can be reduced by 8.55% to 64.51%. Experimental verification confirms the effectiveness of the method in implementing high-speed and high-precision real-time interpolation G01 instructions in CNC systems.

[0223] The present invention also provides an electronic device, comprising one or more processors; a memory; and one or more applications, wherein the one or more applications are stored in the memory and configured to be executed by the one or more processors, and the one or more programs are configured to execute the high-speed corner trajectory planning method based on acceleration constraints in CNC machining as described above.

[0224] Of course, those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing related hardware (such as a processor, a controller, etc.) through a computer program, and the program can be stored in a computer-readable storage medium, and the program can include the processes of the above-mentioned method embodiments when executed. The storage medium can be a memory, a disk, an optical disk, etc.

[0225] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A high-speed corner trajectory planning method based on jerk constraint in CNC machining, characterized in that: The following steps are involved: S1, an asymmetric corner smoothing model based on a two-stage jerk curve, performs smooth acceleration / deceleration transition at the tool path corner; S2, based on the seven-stage S-shaped acceleration / deceleration algorithm, the reachability analysis and time allocation of the motion of the remaining straight line segments of the tool path are performed, where the acceleration at both ends of the remaining straight line segments is non-zero; S3 adopts a bidirectional forward planning algorithm to identify low-speed corner points, perform forward segmentation, plan the feed rate of the corner points and the remaining straight line segments from both the forward and backward directions, merge the trajectories in the two directions, and obtain the feed rate curve of the entire tool path.

2. The high-speed corner trajectory planning method based on jerk constraint in CNC machining according to claim 1, characterized in that: The S1, based on the asymmetric corner smoothing model of the two-stage acceleration curve, performs smooth acceleration / deceleration transition at the corner of the tool path, specifically including: S101, define a two-stage asymmetric acceleration TPACC model to perform a smooth acceleration transition at the corner of the tool path, wherein the kinematic parameters of the two-stage asymmetric acceleration TPACC model are as follows: In the formula, T1 and T2 represent the duration of each stage respectively; and is the corner point P i The processing directions of two adjacent line segments, and A s ,A e ,V s ,V e ,D s ,D e Respectively represent point S i and E i The acceleration, velocity and the turning point P i The distance between point S i and E i They are the corner points P i The starting and ending points of the transition; represents the direction of the angle bisector; λ is the asymmetry factor, reflecting the degree of asymmetry at both ends of the corner; ε represents the error at the corner, J1 and J2 are the magnitudes of the jerk in the two stages, and J represents the acceleration along J1. The magnitude of the directional component, J Xmax , J Ymax , J Zmax They represent the jerk constraints of each axis of the machine tool, Respectively represent the directions of each coordinate axis in the machine tool coordinate system; The kinematic constraints of the two-stage asymmetric acceleration TPACC model are as follows: make sure Within the jerk constraint: Among them, take therefore Consider acceleration and Within the constraints: in, Indicates M i The acceleration at the corner is assumed to be reached at time T1, and this position is represented by M i point, which serves as the segmentation point between the two stages; Xmax , A Ymax , A Zmax Respectively represent the acceleration constraints of each axis of the machine tool; Consider speed and Within the constraints: in, Indicates M i The speed at when This means that λ ≥ λ0, where λ0∈[0.5,1] is the equation The only root in the interval [0.5,1], therefore, λ should belong to [λ0,1]; The length D of the connection between adjacent corners s and D e The following conditions are met: The initial setting is If equations (7) to (9) are not satisfied, reduce T1 until all constraints are satisfied; where ε max Indicates the maximum allowable error in processing; S102, defining a two-stage deceleration TPDEC corner model to perform a smooth deceleration transition at the corner of the tool path, wherein the kinematic parameters of the two-stage deceleration TPDEC corner model are as follows: The following kinematic constraints and error constraints are satisfied:

3. The high-speed corner trajectory planning method based on jerk constraint in CNC machining according to claim 2, characterized in that: S2, based on the seven-stage S-type acceleration / deceleration algorithm, performs reachability analysis and time allocation on the motion of the remaining straight line segments of the tool path, specifically including: The S-shaped feed rate curve has seven stages I, II, III, IV, V, VI, and VII, and the corresponding time nodes are t1-t7; J m , A m and V m Respectively represent the line segments P i P i+1 The upper bounds of jerk, acceleration, and velocity are: The jerk for each phase is as follows: According to E i S i+1 The acceleration at both ends, the reachability analysis is divided into the following four cases: a s ≥0,a e ≤0; a s ≥0,a e >0; a s <0,a e ≤0; a s <0,a e >0; Among them, a s 、a e They represent the acceleration at the starting point and the end point of the straight line segment respectively; Let \(S_0\) be the minimum distance that satisfies motion reachability. When the distance \(\Delta L\) between the starting point and the ending point at each stage is less than \(S_0\), the motion is unreachable and the corner points at both ends need to be adjusted; \(A_0\) represents the extreme value of the acceleration curve; when the velocity increment is less than 0, \(A_0\) is the minimum value; when is greater than 0, \(A_0\) is the maximum value.

4. The high-speed corner trajectory planning method based on jerk constraint in CNC machining according to claim 3, characterized in that: Said S2 further comprises: The timing and forward adjustment strategy for each stage is determined based on the distance between the start and end points: Let S0 be the minimum distance that satisfies the reachability of the motion. When ΔL ≥ S0, the motion is reachable, that is, the corner points at both ends do not need to be adjusted; Let S1 be the acceleration a(t) reaching its maximum value A m The minimum distance required, when ΔL ≥ S1, T2 ≥ 0, there is a uniform acceleration phase II; Let S2 be a(t) to reach the minimum value -A m The minimum distance required, when ΔL ≥ S2, T6 ≥ 0, there is a uniform deceleration stage VI; Let S3 be the velocity v(t) reaching its maximum value V m The minimum distance required, when ΔL ≥ S3, There is a uniform velocity phase IV.

5. The high-speed corner trajectory planning method based on jerk constraint in CNC machining according to claim 4, characterized in that: S3 adopts a bidirectional forward planning algorithm to identify low-speed corner points, perform forward segmentation, plan the feed rate of the corner points and the remaining straight line segments from the forward and backward directions, merge the trajectories in the two directions, and obtain the feed rate curve of the entire tool path, which specifically includes: S301, by determining the segmentation points at the corners of the local minimum inscribed circle radius, given N points P1,...,P N , initialize k f =1, where k f It is the corner mark of the current positive corner point; S302, when k f = N, the algorithm ends; when k f < N, find the next corner with the local minimum inscribed circle radius If there is no such k R ∈(k f , N), then take k R = N, set k b = k R > k f , consider the corner at k b , set and call TPACC(k b ); where k b represents the subscript of the current reverse corner point, and the meaning of k R is the subscript of the segmented corner point; S303, when k f <k b When -1, compare the speed of forward and backward planning. If Perform forward planning and go to step S304. Otherwise, go to step S305 and perform backward planning. f =k b When -1, go to step S306; S304, from k f +1 corner to perform forward planning, through ForwardTPACC(k f +1) Get the right To determine the shape and acceleration capability of the corner, call Get k f +1, and then call LineSPlan(k f ) Planning from arrive The trajectory of f =k f +1; S305, from k b -1 corner for backward planning, through BackwardTPDEC(k b -1) Get the right By calling Get k b -1 corner track, and then call LineSPlan(k b -1) Planning from arrive The trajectory of b =k b -1; S306, when k f =k b When -1, merge the trajectories in the two directions and call LineSPlan(k f ) Planning from arrive Then, set k f =k R , proceed to step S302.

6. The high-speed corner trajectory planning method based on jerk constraint in CNC machining according to claim 5, characterized in that: In S301, determining the segmentation point at the corner of the local minimum inscribed circle radius specifically includes: The radius of the inscribed circle of the i-th corner is Among them, θ i =∠P i-1 P i P i+1 It is the corner P i If R i ≤R i-1 And R i ≤R i+1 , then the i-th corner is considered to be a segmentation point. i At i =1 and call TPACC(i,1).

7. The high-speed corner trajectory planning method based on jerk constraint in CNC machining according to claim 5, characterized in that: In S304, the appropriate λ of the kth corner point is pre-determined by ForwardTPACC(k). k Value, thereby determining the motion state of the corner point, including: S3041, set λ k =1 and λ k+1 = 1, to preliminarily plan the trajectory and obtain the reference speed; S3042, call TryFPlan(k-1) to try to k-1 To S k Get a feasible S-shaped feed rate curve. Different from LineSPlan(k-1), only the parameters of the kth corner point are adjusted without changing the planned result. Based on this, call TryFPlan(k) to try to get the feed rate curve from E k To S k+1 Obtain a feasible S-shaped curve, obtain feasible parameters of two corner points, and reference accelerations on the straight line segments on both sides of the corner point k; If one of them fails, reachflag = 0, then set λ k = 1 and return. In the subsequent steps, the feasible solution for moving along the straight line segment is obtained by adjusting the (k-1)th corner point; S3043, will and ε=ε max Substitute into formula (4) to obtain the kinematic values ​​of other corner points; S3044, if It means that from E k To S k+1 Need to slow down, which means V e The size is not appropriate, so Use V s and V e Update the kinematic parameters of the corner point, A ref :=A s =A e ; S3045, check whether If the velocity constraint is violated, reduce V e , and in [V s ,V e ] Find the optimal V that satisfies the bounded condition in the interval e ; S3046, needs to be satisfied therefore The acceleration of the kth corner point that meets the above conditions is S3047, according to formula (4), substitute and A to obtain the λ of the corner point k ; S3048, assign k in ForwardTPACC(k) to f +1 Repeat steps S3041-S3047 to obtain the appropriate To determine the shape and acceleration capability of the corner.

8. The high-speed corner trajectory planning method based on jerk constraint in CNC machining according to claim 7, characterized in that: In S3, BackwardTPDEC(k) and ForwardTPACC(k) use the same algorithm, namely steps S3041-S3047, except that in S3042, TryDPlan(k) only adjusts the (k-1)th corner point. If TryDPlan(k) fails, BackwardTPDEC(k) returns λ k =1; The value of k in BackwardTPDEC(k) is k b -1 Repeat steps S3041-S3047 to obtain the appropriate 9. The high-speed corner trajectory planning method based on jerk constraint in CNC machining according to claim 1, characterized in that: The method also includes: when a trajectory accessibility problem occurs, adjusting the errors of adjacent corners and correcting the feed rate curve accordingly.

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