Time optimal feeding speed planning method for multi-axis numerical control machine tool

Abstract

The invention discloses a time optimal feeding speed planning method of a multi-axis numerical control machine tool, which relates to the technical field of numerical control machining, and comprises the following steps of: acquiring an NURBS cutter path curve of the multi-axis numerical control machine tool, uniformly segmenting the NURBS cutter path curve, and describing by using a B spline curve to obtain a plurality of cutter speed curves; control point arrangement of the tool speed curves is used as an optimization variable, and feeding speed optimization is conducted on the multiple tool speed curves to obtain multiple optimized tool speed curves; the multiple optimized cutter speed curves are connected in sequence, then feeding speed optimization is conducted on a connection area, and a time optimal feeding speed curve of the multi-axis numerical control machine tool is obtained; the optimization of the feeding speed is achieved through a simulated annealing optimization algorithm and a mode search optimization algorithm in a multi-round alternating mode. According to the method, the time optimal feeding speed planning is realized by adopting an optimization algorithm in which simulated annealing and mode search are alternated, and the calculation efficiency is improved while the efficiency and the precision of numerical control machining are ensured.

Description

Technical Field

[0001] The present invention relates to a time-optimal feed rate planning method for a multi-axis numerically controlled machine tool, belonging to the technical field of numerical control machining. Background Art

[0002] In high-speed and high-precision numerical control machining, the feed rate planning method considering geometric constraints and high-order drive constraints is of great significance for improving machining efficiency and shortening machining time. Compared with developing new machining methods and technologies, optimizing the feed rate control method of the machine tool cutter on the existing machine tool machining method to achieve a time-optimal feed rate planning method can significantly improve production efficiency without increasing costs, and is often considered a more competitive choice.

[0003] Currently, the popular feed rate planning methods include the look-ahead-based algorithm and the optimization-based algorithm. The former preprocesses a small segment of the tool path to detect sudden changes in the feed motion, so that there is enough distance for the feed rate to decelerate without violating the constraints. However, it requires frequent backtracking processes, reducing the computational efficiency, and the planned feed rate is not time-optimal. The latter optimizes the speed curve by using optimization methods such as heuristic algorithms and non-heuristic algorithms. However, the optimization ability of the algorithm is often a challenge, and the convergence is even a problem when solving the feed rate planning problem with high-order constraints. In addition, the computational efficiency of the algorithm is also a key issue worthy of attention. For algorithms based on swarm intelligence, such as particle swarm optimization, genetic algorithms and their variants, due to their characteristics of evolving relying on the population, redundant calculations widely exist, greatly reducing the computational efficiency.

[0004] Therefore, a time-optimal feed rate planning method for a multi-axis numerically controlled machine tool is urgently needed. Summary of the Invention

[0005] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a time-optimal feed rate planning method for a multi-axis numerically controlled machine tool, which realizes the time-optimal feed rate planning by using an optimization algorithm that alternates simulated annealing and pattern search, and improves the computational efficiency while ensuring the efficiency and accuracy of numerical control machining.

[0006] To achieve the above purpose, the present invention is implemented by the following technical solutions:

[0007] On the one hand, the present invention provides a time-optimal feed rate planning method for a multi-axis numerically controlled machine tool, including:

[0008] Obtain the NURBS tool path curve of the multi-axis numerically controlled machine tool;

[0009] Uniformly segment the NURBS tool path curve to obtain multiple NURBS tool path segments;

[0010] Describe the feed rate of each NURBS tool path segment using B-spline curves to obtain multiple tool speed curves;

[0011] Taking the arrangement of the control points of the tool speed curve as the optimization variable, perform feed rate optimization on multiple tool speed curves respectively to obtain multiple optimized tool speed curves;

[0012] Connect multiple optimized tool speed curves in sequence, and perform feed rate optimization on the connection area of two adjacent optimized tool speed curves to obtain the time-optimal feed rate curve of the multi-axis CNC machine tool;

[0013] Among them, the feed rate optimization is realized by alternately performing multiple rounds of the simulated annealing optimization algorithm and the pattern search optimization algorithm.

[0014] Furthermore, the NURBS tool path segment is obtained by evenly dividing based on the number of knots of the NURBS tool path curve.

[0015] Furthermore, the expression of the tool speed curve is:

[0016] ;

[0017] Among them, represents the tool speed curve, m represents the number of control points of the tool speed curve, V i represents the i-th control point, represents the k-th B-spline basis function defined on the knot vector , k represents the degree of the NURBS tool path segment, represents the parametric variable of the tool speed curve.

[0018] Furthermore, the feed rate optimization method specifically includes: S1. Initialize the tool speed curve;

[0019] S2. Taking the arrangement of the control points of the tool speed curve as the optimization variable, use the simulated annealing optimization algorithm to perform feed rate optimization on the tool speed curve to obtain a once-optimized tool speed curve;

[0020] S3. Taking the arrangement of the control points of the once-optimized tool speed curve as the optimization variable, use the pattern search optimization algorithm to perform feed rate optimization to obtain a twice-optimized tool speed curve;

[0021] S4. Take the arrangement of control points of the secondary optimized tool speed curve as the optimization variable, and repeat S2 - S4 to alternately perform multiple rounds of simulated annealing optimization algorithm and pattern search optimization algorithm until the difference between the objective function value of the arrangement of control points of the secondary optimized tool speed curve obtained in the current round and the objective function value of the arrangement of control points of the secondary optimized tool speed curve obtained in the previous round is less than the preset threshold, and obtain the preliminary optimized speed curve; S5. Refine the knot vector of the preliminary optimized speed curve, and repeat S2 - S5 to optimize the arrangement of control points until the difference between the objective function value of the arrangement of control points of the preliminary optimized speed curve after the current knot vector refinement and the objective function value of the arrangement of control points of the preliminary optimized speed curve before the current knot vector refinement is less than the preset threshold, and obtain the optimized speed curve.

[0022] Further, taking the arrangement of control points of the tool speed curve as the optimization variable, and using the simulated annealing optimization algorithm to optimize the feed speed of the tool speed curve to obtain the primary optimized tool speed curve, including:

[0023] A. Randomly perturb the arrangement of control points of the tool speed curve to obtain a new arrangement of control points;

[0024] B. Calculate the probability of taking the new arrangement of control points as the current arrangement of control points, and the expression is as follows:

[0025] ;

[0026] ;

[0027] Wherein, represents the probability of taking the (j + 1)-th arrangement of control points as the current arrangement of control points, represents the objective function value of the j-th arrangement of control points, represents the objective function value of the (j + 1)-th arrangement of control points, represents the temperature at the current iteration, represents the initial temperature, represents the control decay rate constant, represents the current iteration number;

[0028] The initial temperature in each iteration process gradually decreases according to the decay rate;

[0029] C. Obtain the current arrangement of control points according to the probability, and repeat A - C until the maximum number of iterations is reached to obtain the primary optimized tool speed curve.

[0030] Further, using the control point arrangement of the primary optimized tool speed curve as the optimization variable, the feed speed is optimized by using the pattern search optimization algorithm to obtain the secondary optimized tool speed curve, including:

[0031] a. Obtain the preset initial search grid size and the positive definite expansion set, and the expression of the positive definite expansion set is , where d represents the direction vector of the control point arrangement, and n represents the direction dimension;

[0032] b. Use the control point arrangement of the primary optimized tool speed curve as the current control point arrangement, and calculate the objective function value of the current control point arrangement;

[0033] c. Search in randomly selected directions in the positive definite expansion set for the current control point arrangement, and calculate the objective function value of the control point arrangement after the search;

[0034] If the objective function value of the control point arrangement after the search is greater than the objective function value of the current control point arrangement, then traverse all the remaining directions in the positive definite expansion set. If a control point arrangement with a smaller objective function value still cannot be found, then shrink the step size, and repeat step c until the grid threshold or the maximum number of iterations is reached, and use the current control point arrangement as the secondary optimized tool speed curve;

[0035] If the objective function value of the changed control point arrangement is less than the objective function value of the current control point arrangement, then use the control point arrangement after the search as the current control point arrangement, and repeat step c until the grid threshold or the maximum number of iterations is reached to obtain the secondary optimized tool speed curve.

[0036] Further, in each round, the maximum number of iterations of the simulated annealing optimization algorithm and the pattern search optimization algorithm is determined by the progressive iteration number reduction strategy, and the expression of the progressive iteration number reduction strategy is:

[0037] ;

[0038] where represents the maximum number of iterations of the simulated annealing optimization algorithm or the pattern search optimization algorithm in the i-th round, represents the attenuation factor, represents the maximum number of iterations of the simulated annealing optimization algorithm or the pattern search optimization algorithm in the (i + 1)-th round.

[0039] Further, the expression of the objective function is:

[0040] ;

[0041] ;

[0042] ;

[0043] Among them, represents the objective function, represents the total tool running time, represents the weight of the total tool running time, represents the sum of the tolerance amounts of the tool speed curve, represents the current tool running time, represents the arc length of the tool speed curve, represents the parameterized variable of the tool speed curve, represents the arc length of the tool speed curve with respect to the parameterized variable differential, represents the tool speed curve, represents the number of constraint conditions of the objective function, represents the number of monitoring points of the tool speed curve, represents the tolerance amount of the NURBS tool path segment at the j-th monitoring point under the i-th constraint condition, represents the maximum allowable tolerance amount under the i-th constraint condition. The tolerance amount is the amount exceeding the allowable value, and its calculation method is the prior art and will not be elaborated here.

[0044] Furthermore, the objective function has constraint conditions, and the constraint conditions are divided into linear constraint conditions and non-linear constraint conditions. Among them, the linear constraint conditions include chord error constraint, speed constraint, and speed constraints of each axis in a multi-axis CNC machine tool. The expression of the linear constraint conditions is:

[0045] ;

[0046] Among them, represents the speed, represents the maximum speed, represents the interpolation period, represents the interpolation period the maximum value of the chord error, represents the axis in a multi-axis CNC machine tool speed, represents the maximum speed of the axis

[0047] The non-linear constraint conditions include acceleration constraint, jerk constraint, acceleration constraints of each axis in a multi-axis CNC machine tool, and jerk constraints of each axis in a multi-axis CNC machine tool. The expression of the non-linear constraint conditions is:

[0048] ;

[0049] ;

[0050] ;

[0051] ;

[0052] ;

[0053] ;

[0054] ;

[0055] ;

[0056] wherein, represents acceleration, represents velocity, represents the first-order differential of velocity, represents the first-order differential of the arc length of the tool velocity curve, represents the second-order differential of the arc length of the tool velocity curve, represents the maximum acceleration, represents jerk, represents the second-order differential of velocity, represents the maximum jerk, represents axis in a multi-axis CNC machine tool, represents axis in a multi-axis CNC machine tool, represents axis in a multi-axis CNC machine tool, represents axis in a multi-axis CNC machine tool, ~ represents a constant parameter, represents axis in a multi-axis CNC machine tool, represents axis in a multi-axis CNC machine tool, represents axis in a multi-axis CNC machine tool,

[0057] Furthermore, the left and right endpoints of the connection region between two adjacent optimized tool velocity curves are obtained by calculation, and the calculation expressions are as follows:

[0058] ;

[0059] wherein, represents the left endpoint of the connection region, Represents the right endpoint of the connection area, Represents the connection point of two adjacent optimized tool path speed curves, Represents the connection point of the previous two adjacent optimized tool path speed curves, Represents the connection point of the next two adjacent optimized tool path speed curves.

[0060] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0061] The present invention first evenly segments the nodes of the NURBS tool path and then uses B-spline curves to represent the speed curves of each segment. The optimization method is to first perform parallel optimization on each segment and then perform parallel optimization on the connection areas of adjacent segments, which improves the calculation efficiency. Moreover, the simulated annealing optimization algorithm and the pattern search optimization algorithm are alternately used multiple times to achieve feed speed optimization. The pattern search optimization algorithm stably converges to the regional optimal value. And due to this interleaved structure, the algorithm is given better global search ability, so that it can jump out of the local optimal trap and prevent the algorithm from prematurely converging to the local optimum, and finally achieve the global optimum of the machining time. Compared with the population-based swarm intelligence algorithm, the optimization time is significantly shortened while the machining efficiency is improved, and the smoothness and saturation of the generated time-optimal feed speed curve are also improved;

[0062] When the present invention optimizes the connection areas of adjacent segments, an overlapping part is set between adjacent optimized connection areas, so as to enable the algorithm to have the ability to consider the neighborhood, and make the finally obtained feed speed curve have better time optimality.

[0063] The present invention extracts common factors from the expressions of the constraint conditions, which greatly reduces the number of multiplications for evaluating each constraint and further improves the calculation efficiency.

[0064] The proposed interleaved simulated annealing-pattern search algorithm of the present invention has great advantages in calculation time compared with the population-based swarm intelligence algorithms, such as particle swarm algorithm, genetic algorithm and their variants. The calculation time in the following embodiments does not exceed 60% of the population-based algorithms. This algorithm is optimized based on individuals and can obtain the time-optimal feed speed curve with fewer evaluations of the objective function. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 It is a schematic flow chart of the time-optimal feed speed planning method for a multi-axis numerical control machine tool in an embodiment of the present invention;

[0066] Figure 2 It is a schematic flow chart of the speed optimization method of the time-optimal feed speed planning method for a multi-axis numerical control machine tool in an embodiment of the present invention;

[0067] Figure 3 Schematic diagram of the three-dimensional tool path curve in the shape of a leaf in Embodiment 1 of the present invention;

[0068] Figure 4 Schematic diagram of the time-optimal feed rate curve generated in Embodiment 1 of the present invention;

[0069] Figure 5 Schematic diagram of the chord error constraint comparison of the time-optimal feed rate curve generated in Embodiment 1 of the present invention;

[0070] Figure 6 Schematic diagram of the acceleration constraint comparison of the time-optimal feed rate curve generated in Embodiment 1 of the present invention;

[0071] Figure 7 Schematic diagram of the jerk constraint comparison of the time-optimal feed rate curve generated in Embodiment 1 of the present invention;

[0072] Figure 8 Schematic diagram of the speed constraint comparison of each axis of the machine tool corresponding to the time-optimal feed rate curve generated in Embodiment 1 of the present invention;

[0073] Figure 9 Schematic diagram of the acceleration constraint comparison of each axis of the machine tool corresponding to the time-optimal feed rate curve generated in Embodiment 1 of the present invention;

[0074] Figure 10 Schematic diagram of the jerk constraint comparison of each axis of the machine tool corresponding to the time-optimal feed rate curve generated in Embodiment 1 of the present invention;

[0075] Figure 11 Schematic diagram of the three-dimensional tool path curve in the shape of a thousand paper cranes in Embodiment 2 of the present invention;

[0076] Figure 12 Schematic diagram of the time-optimal feed rate curve generated in Embodiment 2 of the present invention;

[0077] Figure 13 Schematic diagram of the chord error constraint comparison of the time-optimal feed rate curve generated in Embodiment 2 of the present invention;

[0078] Figure 14 Schematic diagram of the acceleration constraint comparison of the time-optimal feed rate curve generated in Embodiment 2 of the present invention;

[0079] Figure 15 Schematic diagram of the jerk constraint comparison of the time-optimal feed rate curve generated in Embodiment 2 of the present invention. Detailed implementation manners

[0080] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0081] Embodiment 1:

[0082] As Figure 1 shown, the embodiment of the present invention provides a time-optimal feed speed planning method for a multi-axis numerical control machine tool, which specifically includes the following steps:

[0083] Obtain the NURBS (Non-Uniform Rational B-Spline) tool path curve of the multi-axis numerical control machine tool. In this embodiment, the NURBS tool path curve of the multi-axis numerical control machine tool is a three-dimensional tool path curve in the shape of a leaf as Figure 3 shown.

[0084] The control point vector of this curve includes: [(73.1210, -4.0764, 7.0783), (61.5924, 15.7962, -7.2203), (52.4841,44.3312, -14.0482), (52.4841, 52.9936, -10.5441), (49.3631, 37.1975, -15.0000), (40.1911, 23.9490, -11.8411), (31.5287, 13.5032, -5.6688),(28.7261, 9.4268, -2.7404), (29.4904, 19.8726, -9.7321), (22.1019, 32.1019, -14.5213), (11.1465, 31.5924, -14.4208), (7.5796, 29.0446, -13.7796),(11.9108, 38.4713, -14.9682), (-3.1210, 41.7834, -14.6024), (-10.2548,42.5478, -14.4606), (-6.1783, 47.3885, -13.0837), (-21.7197, 48.4076, -12.6931), (-30.1274, 47.6433, -12.9892), (-17.3885, 52.4841, -10.8125),(6.3057, 60.8917, -5.6281), (0.1911, 62.6752, -4.3675), (-12.9936, 74.9045,4.6618), (-36.2420, 75.9236, 5.3819), (-23.1847, 77.1975, 6.2622), (-15.3503,88.9172, 12.7553), (-23.5032, 99.6178, 14.9973), (-20.7006, 111.3376,12.6537), (-30.8280, 123.3121, 5.9129), (-19.3631, 119.2357, 8.5809),(1.0191, 112.8662, 12.0017), (10.9554, 117.1975, 9.7880), (23.1210, 104.4586,14.6288), (17.3248, 117.1975, 9.7880), (33.1210, 153.8854, -13.5241),(39.7452, 168.6624, -14.3671), (40.5096, 163.0573, -14.9990), (57.5159,143.4395, -8.4842), (60.3822, 149.5541, -11.8141), (67.7707, 122.5478,6.4353), (68.2166, 108.5350, 13.6547), (75.4140, 125.6051, 4.2971), (86.8790,134.7771, -2.5090), (88.0892, 129.4268, 1.4894), (94.7134, 135.5414, -3.0722), (101.9108, 148.0255, -11.0738), (107.5159, 153.3758, -13.3544),(109.2357, 135.0318, -2.6972), (112.0382, 124.5860, 5.0235), (108.5350,97.8344, 14.9122), (129.6178, 103.6943, 14.7448), (135.7325, 105.4777,14.4409), (125.5414, 98.0892, 14.9316), (129.9363, 93.7580, 14.2754),(104.4586, 78.9809, 7.4511), (94.7771, 74.1401, 4.1136), (117.4522, 74.6497,4.4798), (116.1783, 67.0064, -1.1821), (126.8790, 67.7707, -0.6099),(133.5032, 61.1465, -5.4505), (142.4204, 59.1083, -6.8439), (127.8981,57.3248, -8.0054), (104.2038, 45.8599, -13.6057), (111.3376, 38.2166, -14.9794), (98.5987, 42.8025, -14.4087), (84.3312, 46.1146, -13.5241),(84.5860, 30.3185, -14.1289), (93.5032, 22.6752, -11.2310), (56.(8153, 43.0573, -14.3544), (50.7006, 56.0510, -8.7966), (59.6178, 28.7898, -13.7030), (75.6688, 5.3503, 0.3014), (78.7261, 4.3312, 1.0649), (73.1210, -4.0764, 7.0783).

[0085] The weight factor vector includes: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

[0086] The knot vector includes: [0, 0, 0, 0, 0.0143, 0.0286, 0.0429, 0.0571, 0.0714, 0.0857, 0.1000, 0.1143, 0.1286, 0.1429, 0.1571, 0.1714, 0.1857, 0.2000, 0.2143, 0.2286, 0.2429, 0.2571, 0.2714, 0.2857, 0.3000, 0.3143, 0.3286, 0.3429, 0.3571, 0.3714, 0.3857, 0.4000, 0.4143, 0.4286, 0.4429, 0.4571, 0.4714, 0.4857, 0.5000, 0.5143, 0.5286, 0.5429, 0.5571, 0.5714, 0.5857, 0.6000, 0.6143, 0.6286, 0.6429, 0.6571, 0.6714, 0.6857, 0.7000, 0.7143, 0.7286, 0.7429, 0.7571, 0.7714, 0.7857, 0.8000, 0.8143, 0.8286, 0.8429, 0.8571, 0.8714, 0.8857, 0.9000, 0.9143, 0.9286, 0.9429, 0.9571, 0.9714, 0.9857, 1.0000, 1.0000, 1.0000, 1.0000]

[0087] The NURBS tool path curve is evenly segmented based on the number of knots of the NURBS tool path curve to obtain multiple NURBS tool path segments.

[0088] The feed rate of each NURBS tool path segment is described by a B-spline curve to obtain multiple tool speed curves. The expression of the B-spline curve representing the tool speed curve is:

[0089] ;

[0090] where represents the tool speed curve, m represents the number of control points of the tool speed curve, V i represents the i-th control point, represents the k-th B-spline basis function defined on the knot vector , k represents the degree of the NURBS tool path segment, represents the parametric variable of the tool speed curve.

[0091] Taking the arrangement of the control points of the tool speed curve as the optimization variable, after separately optimizing the feed rate of multiple tool speed curves, multiple optimized tool speed curves are obtained. The feed rate optimization uses the simulated annealing optimization algorithm and the pattern search optimization algorithm in multiple rounds of alternation. As Figure 2 shown, the specific process is as follows: S1. Initialize the tool speed curve with a sparse knot vector and control point vector;

[0092] S2. Taking the arrangement of the control points of the tool speed curve as the optimization variable, use the simulated annealing optimization algorithm to optimize the feed rate of the tool speed curve to obtain a once-optimized tool speed curve. Specifically:

[0093] A. Randomly perturb the arrangement of the control points of the tool speed curve to obtain a new arrangement of control points;

[0094] B. Calculate the probability of taking the new arrangement of control points as the current arrangement of control points. The expression is as follows: ; ;

[0095] where represents the probability of taking the (j + 1)-th arrangement of control points as the current arrangement of control points, represents the objective function value of the j-th arrangement of control points, represents the objective function value of the (j + 1)-th arrangement of control points, represents the temperature at the current iteration, represents the initial temperature, represents the control attenuation rate constant, Represents the current iteration number;

[0096] It should be noted that the initial temperature in each iteration process gradually decreases according to the decay rate, and the decay rate is 0.9 in this embodiment.

[0097] C. Obtain the current control point arrangement according to the probability, and repeat A - C until the maximum number of iterations is reached to obtain an optimized tool speed curve once.

[0098] S3. Take the control point arrangement of the optimized tool speed curve once as the optimization variable, and use the pattern search optimization algorithm to optimize the feed speed to obtain the second - optimized tool speed curve. Specifically:

[0099] a. Preset the initial grid size and the positive definite expansion set. The expression of the positive definite expansion set is , where d represents the direction vector of the control point arrangement, such as , the elements of the direction vector correspond to the control points one by one, and n represents the direction dimension;

[0100] b. Take the control point arrangement of the optimized tool speed curve once as the current control point arrangement, and calculate the objective function value of the current control point arrangement;

[0101] c. Search in randomly selected directions in the positive definite expansion set for the current control point arrangement, and calculate the objective function value of the control point arrangement after the search;

[0102] If the objective function value of the changed control point arrangement is greater than the objective function value of the current control point arrangement, then traverse all the remaining directions in the positive definite expansion set. If a control point arrangement with a smaller objective function value is still not found, then shrink the step size, and repeat c until the grid size threshold or the maximum number of iterations is reached, and take the current control point arrangement as the second - optimized tool speed curve.

[0103] If the objective function value of the changed control point arrangement is less than the objective function value of the current control point arrangement, then take the control point arrangement after the search as the current control point arrangement, and repeat c to obtain the second - optimized tool speed curve.

[0104] S4. Take the control point arrangement of the second - optimized tool speed curve as the optimization variable, and repeat S2 - S4 alternately for multiple rounds of the simulated annealing optimization algorithm and the pattern search optimization algorithm until the difference between the objective function values of the control point arrangements of the second - optimized tool speed curve obtained in the current round and the second - optimized tool speed curve obtained in the previous round is less than the preset threshold, and obtain the preliminary optimized speed curve; S5. Refine the knot vector of the preliminarily optimized speed curve, and repeat S2 - S5 to optimize the arrangement of control points until the difference between the objective function value of the arrangement of control points of the preliminarily optimized speed curve after the current knot vector refinement and the objective function value of the arrangement of control points of the preliminarily optimized speed curve before the current knot vector refinement is less than the preset threshold , and obtain the optimized speed curve.

[0105] The knot vector refinement is achieved by inserting knots into the knot vector. For the -th B-spline curve defined on the knot vector and the control point vector k , if a new knot v ( u ) is inserted into the knot vector of the B-spline curve, the new obtained knot vector U and control point vector are as follows: where ; and is an arbitrary natural number. To keep the shape of the B-spline curve unchanged, the method for determining the new control point vector is: ; where the coefficient is calculated by the following formula: ;

[0106] The expression of the objective function used in the above optimization algorithm is: ; ; ;

[0107] where represents the objective function, represents the total tool running time, represents the weight of the total tool running time, represents the sum of the over-tolerance amounts of the tool speed curve, represents the current tool running time, represents the arc length of the tool speed curve, represents the parametric variable of the tool speed curve, represents the differential of the arc length of the tool speed curve with respect to the parametric variable , represents the tool speed curve, and here the value of the tool speed curve at the parametric variable is substituted. represents the number of constraint conditions of the objective function, represents the number of monitoring points of the tool speed curve, represents the overlimit amount of the NURBS tool path segment at the j-th monitoring point under the i-th constraint condition, represents the maximum allowable overlimit amount under the i-th constraint condition.

[0108] The objective function has constraint conditions, which are divided into linear constraint conditions and non-linear constraint conditions. Among them, the linear constraint conditions include chord error constraint, speed constraint, and speed constraints of each axis in a multi-axis CNC machine tool. The expression of the linear constraint condition is: ;

[0109] Among them, represents the speed, represents the maximum speed, represents the interpolation period, represents the interpolation period the maximum value of the chord error, represents the axis in a multi-axis CNC machine tool represents the axis in a multi-axis CNC machine tool

[0110] The non-linear constraint conditions include acceleration constraint, jerk constraint, acceleration constraints of each axis in a multi-axis CNC machine tool, and jerk constraints of each axis in a multi-axis CNC machine tool. The expression of the non-linear constraint condition is: ; ; ; ; ; ; ; ;

[0111] Among them, represents the acceleration, represents the speed, represents the first derivative of the speed, represents the first derivative of the arc length of the tool speed curve, represents the second derivative of the arc length of the tool speed curve, represents the maximum acceleration, represents the jerk, Represents the second derivative of velocity, Represents the maximum jerk, Represents the axis in a multi-axis CNC machine tool Acceleration, Represents the axis in a multi-axis CNC machine tool Maximum acceleration, Represents the axis in a multi-axis CNC machine tool Jerk, Represents the axis in a multi-axis CNC machine tool Maximum jerk, ~ Represents a constant parameter, Represents the axis in a multi-axis CNC machine tool The first derivative of the arc length of the tool velocity curve, Represents the axis in a multi-axis CNC machine tool The second derivative of the arc length of the tool velocity curve, Represents the axis in a multi-axis CNC machine tool The third derivative of the arc length of the tool velocity curve.

[0112] As shown in the above formula transformation, in this implementation, common factors are extracted from the expressions, reducing the number of multiplications required for each constraint from 16 times to 7 times, further improving the operation efficiency.

[0113] In this embodiment, the dynamic constraint values (upper limit values) of each axis of the machine tool are shown in Table 1:

[0114] Table 1: Dynamic constraint values of each axis of the machine tool

[0115] Connect multiple tool velocity curves in sequence, and perform the feed speed optimization on the connection area of two adjacent optimized tool velocity curves as described above. The left and right endpoints of the connection area are obtained through calculation, and their calculation expressions are as follows: ;

[0116] Wherein, Represents the left endpoint of the connection area, Represents the right endpoint of the connection area, Represents the connection point of the current two adjacent optimized tool velocity curves, Represents the connection point of the previous two adjacent optimized tool velocity curves, Represents the connection point of the next two adjacent optimized tool velocity curves.

[0117] Finally, the time-optimal feed speed curve of the multi-axis CNC machine tool is obtained, as shown in Figure 4As shown in the figure, it can be seen that the time-optimal feed rate curve obtained by the method of the present invention has high smoothness and saturation.

[0118] The chord error, acceleration, and jerk overshoot results of the time-optimal feed rate curve of the multi-axis CNC machine tool are respectively as Figure 5 , Figure 6 , Figure 7 shown. The overshoot results of the speed, acceleration, and jerk of each axis of the multi-axis CNC machine tool are respectively as Figure 8 , Figure 9 , Figure 10 shown. The red dashed line in the figure is the constraint upper and lower limits. It can be seen from the figure that this embodiment can plan a time-optimal feed rate curve without exceeding the constraint limits, and the CNC machining time using the time-optimal feed rate curve of this embodiment on the multi-axis CNC machine tool is only 10.85 s, which has great advantages in the optimality of machining time. The optimal machining time of the currently reported algorithm in this case is 10.96 s, and its calculation time is 1638.1 s, which is about 7 times that of this method.

[0119] Embodiment 2:

[0120] Based on the time-optimal feed rate planning method of the multi-axis CNC machine tool in Embodiment 1, the NURBS tool path curve of the multi-axis CNC machine tool is a three-dimensional tool path curve in the shape of a thousand paper cranes as Figure 11 shown.

[0121] The control point vector of the three-dimensional tool path curve in the shape of a thousand paper cranes includes: [(67.977,-0.005,36.659),(63.682,4.079,80.255),(61.468,4.339,74.019),(11.983,11.125,-39.238),( 38.757,21.631,38.549),( 12.423,23.172,30.127 ),( -0.220,146.508,24.772 ),( -2.673,70.259,17.139),( -36.818,18.851,60.084),( -23.458,18.454,-18.584),( -20.809,1.6012,11.298),(-85.977,0.0102,115.51),(-20.809,-1.5967,11.302),(-23.457,-18.454,-18.586),(-36.819,-18.85,60.081),(-2.6744,-70.251,17.139),(-0.22019,-146.51,24.773),(12.421,-23.175,30.124),(38.758,-21.63,38.553),(11.985,-11.127,-39.237),(61.461,-4.336,74.018 ),(63.677,-4.076,80.257 ),( 67.978, -0.005,36.66)]

[0122] The weight factor vector includes: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

[0123] The knot vector includes: [0, 0, 0, 0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, 1, 1, 1, 1]

[0124] In this embodiment, the dynamic constraint values (upper limit values) of each axis of the machine tool are shown in Table 2:

[0125] Table 2 Dynamic Constraint Values of Each Axis of the Machine Tool

[0126] Combined with the dynamic constraints of each axis of the machine tool and the time-optimal feed speed planning method of the multi-axis CNC machine tool described in Embodiment 1, the time-optimal feed speed curve of the multi-axis CNC machine tool is as follows Figure 12 shown. It can be seen from the figure that the time-optimal feed speed curve obtained by using the method of the present invention has high smoothness and saturation

[0127] The chord error, acceleration, and jerk overshoot results of the time-optimal feed speed curve of the multi-axis CNC machine tool are respectively as follows Figure 13 , Figure 14 , Figure 15 shown, indicating that the method of the present invention can plan a time-optimal feed speed curve without exceeding the constraint limit. Moreover, when the multi-axis CNC machine tool uses the time-optimal feed speed curve of this embodiment for numerical control machining, the time required is only 13.63 s, which has great advantages in terms of time optimality. The optimal machining time obtained after applying the currently reported optimal algorithm to this case is 14.06 s. And due to the inherent limitations of its swarm intelligence algorithm, in this case, its calculation time is close to 3 times that of the method of the present invention

[0128] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the technical principle of the present invention, several improvements and deformations can be made, and these improvements and deformations should also be regarded as the protection scope of the present invention

Claims

1. A time-optimal feed rate planning method for a multi-axis CNC machine tool, characterized in that, Including: Obtain the NURBS tool path curve of a multi-axis numerical control machine tool; Uniformly segment the NURBS tool path curve to obtain multiple NURBS tool path segments; Use B-spline curves to describe the feed speed of each NURBS tool path segment to obtain multiple tool speed curves; Taking the arrangement of the control points of the tool speed curve as the optimization variable, perform feed speed optimization on multiple tool speed curves respectively to obtain multiple optimized tool speed curves; Connect multiple optimized tool speed curves in sequence, and perform feed speed optimization on the connection area of two adjacent optimized tool speed curves to obtain the time-optimal feed speed curve of the multi-axis numerical control machine tool; Wherein, the feed speed optimization is realized by alternately performing multiple rounds of simulated annealing optimization algorithm and pattern search optimization algorithm.

2. The time-optimal feed rate planning method for a multi-axis CNC machine tool according to claim 1, characterized in that, The NURBS tool path segment is obtained by uniformly dividing based on the number of knots of the NURBS tool path curve.

3. The time-optimal feed rate planning method for a multi-axis CNC machine tool according to claim 1, characterized in that, The expression of the tool speed curve is: ； Among them, represents the tool speed curve, m represents the number of control points of the tool speed curve, and V i represents the i-th control point, represents the k-th B-spline basis function defined on the knot vector , k represents the degree of the NURBS tool path segment, represents the parameterization variable of the tool speed curve.

4. The time-optimal feed rate planning method for a multi-axis CNC machine tool according to claim 1, wherein The specific steps of the feed speed optimization method include: S1. Initialize the tool speed curve; S2. Taking the arrangement of the control points of the tool speed curve as the optimization variable, use the simulated annealing optimization algorithm to perform feed speed optimization on the tool speed curve to obtain a once-optimized tool speed curve; S3. Taking the arrangement of the control points of the once-optimized tool speed curve as the optimization variable, use the pattern search optimization algorithm to perform feed speed optimization to obtain a twice-optimized tool speed curve; S4. Taking the arrangement of the control points of the twice-optimized tool speed curve as the optimization variable, repeat S2~S4 to alternately perform multiple rounds of simulated annealing optimization algorithm and pattern search optimization algorithm until the difference between the objective function value of the arrangement of the control points of the twice-optimized tool speed curve obtained in the current round and the objective function value of the arrangement of the control points of the twice-optimized tool speed curve obtained in the previous round is less than a preset threshold, to obtain a preliminary optimized speed curve; S5. Refine the knot vector of the preliminary optimized speed curve, and repeat S2~S5 to optimize the arrangement of the control points until the difference between the objective function value of the arrangement of the control points of the preliminary optimized speed curve after the current knot vector refinement and the objective function value of the arrangement of the control points of the preliminary optimized speed curve before the current knot vector refinement is less than a preset threshold, to obtain an optimized speed curve.

5. The time-optimal feed rate planning method for a multi-axis CNC machine tool according to claim 4, characterized in that, The step of taking the arrangement of the control points of the tool speed curve as the optimization variable and using the simulated annealing optimization algorithm to perform feed speed optimization on the tool speed curve to obtain a once-optimized tool speed curve includes: A. Randomly perturb the arrangement of the control points of the tool speed curve to obtain a new arrangement of the control points; B. Calculate the probability of taking the new arrangement of the control points as the current arrangement of the control points, and the expression is as follows: ； ； Among them, represents the probability of arranging the (j + 1)-th control point arrangement as the current control point arrangement, represents the objective function value of the j-th control point arrangement, represents the objective function value of the (j + 1)-th control point arrangement, represents the temperature at the current iteration number, represents the initial temperature, represents the control attenuation rate constant, represents the current iteration number; The initial temperature in each iteration process gradually decreases according to the decay rate; C. Obtain the current arrangement of the control points according to the probability, and repeat A~C until the maximum number of iterations is reached to obtain a once-optimized tool speed curve.

6. The time-optimal feed rate planning method for a multi-axis CNC machine tool according to claim 4, characterized in that, The step of taking the arrangement of the control points of the once-optimized tool speed curve as the optimization variable and using the pattern search optimization algorithm to perform feed speed optimization to obtain a twice-optimized tool speed curve includes: a. Obtain a preset initial search grid size and a positive definite expansion set, and the expression of the positive definite expansion set is , where d represents the direction vector of the control point arrangement, and n represents the direction dimension; b. Take the arrangement of control points for optimizing the tool speed curve for the first time as the current arrangement of control points, and calculate the objective function value of the current arrangement of control points; c. Conduct a search in a randomly selected partial direction of the positive definite expansion set for the current arrangement of control points, and calculate the objective function value of the arrangement of control points after the search; If the objective function value of the arrangement of control points after the search is greater than the objective function value of the current arrangement of control points, then traverse all the remaining directions in the positive definite expansion set. If an arrangement of control points with a smaller objective function value still cannot be found, then shrink the step size, and repeat step c until the grid threshold or the maximum number of iterations is reached, and take the current arrangement of control points as the tool speed curve optimized for the second time; If the objective function value of the changed arrangement of control points is less than the objective function value of the current arrangement of control points, then take the arrangement of control points after the search as the current arrangement of control points, and repeat step c until the grid threshold or the maximum number of iterations is reached to obtain the tool speed curve optimized for the second time.

7. The time-optimal feed rate planning method for a multi-axis CNC machine tool according to claim 4, characterized in that In each round, the maximum number of iterations of the simulated annealing optimization algorithm and the pattern search optimization algorithm is determined by the progressive iteration number reduction strategy. The expression of the progressive iteration number reduction strategy is: ； Among them, represents the maximum number of iterations of the simulated annealing optimization algorithm or the pattern search optimization algorithm in the i-th round, represents the attenuation factor, represents the maximum number of iterations of the simulated annealing optimization algorithm or the pattern search optimization algorithm in the (i + 1)-th round.

8. The time-optimal feed rate planning method for a multi-axis CNC machine tool according to claim 4, characterized in that, The expression of the objective function is: ； ； ； Among them, represents the objective function, represents the total tool running time, represents the weight of the total tool running time, represents the sum of the tolerance exceedances of the tool speed curve, represents the current tool running time, represents the arc length of the tool speed curve, represents the parametric variable of the tool speed curve, represents the arc length of the tool speed curve with respect to the parametric variable the differential of, represents the tool speed curve, represents the number of constraint conditions of the objective function, represents the number of monitoring points of the tool speed curve, represents the excess amount of the NURBS tool path segment at the j-th monitoring point under the i-th constraint condition, represents the maximum allowable excess amount under the i-th constraint condition.

9. The time-optimal feed rate planning method for a multi-axis CNC machine tool according to claim 8, characterized in that The objective function has constraint conditions, which are divided into linear constraint conditions and non-linear constraint conditions. Among them, the linear constraint conditions include chord error constraint, speed constraint, and speed constraints of each axis in a multi-axis numerical control machine tool. The expression of the linear constraint conditions is: ； Among them, represents speed, represents the maximum speed, represents the interpolation period, represents the interpolation period the maximum value of the under chord error, represents the axis in a multi-axis numerical control machine tool speed, represents the axis in a multi-axis numerical control machine tool the maximum speed; The non-linear constraint conditions include acceleration constraint, jerk constraint, acceleration constraints of each axis in a multi-axis numerical control machine tool, and jerk constraints of each axis in a multi-axis numerical control machine tool. The expression of the non-linear constraint conditions is: ； ； ； ； ； ； ； ； Among them, represents acceleration, represents velocity, represents the first derivative of velocity, represents the first derivative of the arc length of the tool velocity curve, represents the second derivative of the arc length of the tool velocity curve, represents the maximum acceleration, represents jerk, represents the second derivative of velocity, represents the maximum jerk, represents the axis acceleration in a multi-axis CNC machine tool, represents the axis maximum acceleration in a multi-axis CNC machine tool, represents the axis jerk in a multi-axis CNC machine tool, represents the axis maximum jerk in a multi-axis CNC machine tool, ~ represents a constant parameter, represents the axis first derivative of the arc length of the tool velocity curve in a multi-axis CNC machine tool, represents the axis second derivative of the arc length of the tool velocity curve in a multi-axis CNC machine tool, represents the axis third derivative of the arc length of the tool velocity curve in a multi-axis CNC machine tool.

10. The time-optimal feed rate planning method for a multi-axis CNC machine tool according to claim 1, characterized in that, The left and right endpoints of the connection area between two adjacent optimized tool speed curves are obtained through calculation, and the calculation expression is as follows: ； Among them, represents the left endpoint of the connection area, represents the right endpoint of the connection area, represents the connection point of two adjacent optimized tool speed curves, represents the connection point of the previous two adjacent optimized tool speed curves, represents the connection point of the next two adjacent optimized tool speed curves.

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