Five-axis lathe tool path generation method based on cutting force prediction and optimization

Abstract

The invention relates to the technical field of machine tool cutter path control, in particular to a five-axis lathe cutter path generation method based on cutting force prediction and optimization, which comprises the following steps of: carrying out discrete sampling on a curved surface to be processed in a parameter domain to obtain a cutter center path point sequence; calculating the instantaneous main cutting force of the cutter at each cutter center track point based on the instantaneous cutting thickness; taking the maximum instantaneous main cutting force minimization, the cutting force fluctuation minimization, the residual height minimization, the track geometric fairness and the machining time as optimization objectives, and constructing a comprehensive objective function; solving the comprehensive objective function by adopting an improved non-dominated sorting genetic algorithm, and outputting an optimized tool path point sequence; and performing NURBS curve fitting on the verified tool path point sequence to generate a final tool center path. According to the method, the maximum cutting force and the cutting force fluctuation variance can be reduced, the surface residual height is reduced, the posture switching of the machine tool is stable, and the machining precision, stability and efficiency of complex curved surface five-axis turning are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of machine tool tool path control, in particular to a five-axis lathe tool path generation method based on cutting force prediction and optimization. BACKGROUND

[0002] Currently, the generation of five-axis machine tool tool path is mainly based on geometric feature constraints, such as residual height control, tool interference elimination, posture continuity and fairness optimization. The existing geometric constraint type trajectory planning method usually realizes surface precision control by calculating the distribution of tool contact points (CC points) or tool center points (CL points), including tool position generation methods based on fixed step or constant scallop height (Scallop Height), smooth orientation control based on normal optimization, and NURBS, B-spline curve fitting trajectory to improve smoothness. Such methods ignore the mechanical behavior (cutting force, torque, vibration, etc.) in the cutting process; the tool posture change and machine tool axis motion characteristics are not coupled with the cutting load, which is prone to local force peaks or vibrations; the fairness index only considers geometric curvature and does not consider dynamic smoothness.

[0003] Cutting force modeling and monitoring methods, some research and patents try to predict cutting force through experience or semi-analytical models (such as Kienzle model, mechanical energy model), or use force sensors, spindle power, vibration signals, etc. to monitor cutting force during processing. It is mostly feedback control or real-time compensation, rather than active optimization in the trajectory generation stage. Force prediction is only used for processing state judgment and cannot participate in trajectory optimization decision-making. The system relies on external sensors, which is high in cost and poor in stability. The existing five-axis machining trajectory planning technology method lacks systematic consideration of cutting force distribution and machine kinematics characteristics, making it difficult to achieve uniform machining force and machining stability. SUMMARY

[0004] To solve the technical problems existing in the prior art, the present application provides a five-axis lathe tool path generation method based on cutting force prediction and optimization, which realizes the transformation of trajectory generation mode from geometry to mechanics by embedding cutting force prediction and multi-objective optimization in the trajectory generation stage. It can reduce the maximum cutting force and cutting force fluctuation variance, reduce the surface residual height, make the machine tool posture switching smooth, and improve the machining precision, stability and efficiency of complex surface five-axis turning.

[0005] The object of the present application can be achieved by adopting the following technical solutions:

[0006] A five-axis lathe tool path generation method based on cutting force prediction and optimization, comprising the following steps:

[0007] S1, discretely sampling the machining surface in the parameter domain to obtain a tool center trajectory point sequence;

[0008] S2, calculating the instantaneous cutting thickness according to the distance between the tool and the workpiece surface, and calculating the instantaneous main cutting force of the tool at each tool center trajectory point based on the instantaneous cutting thickness;

[0009] S3, calculating the maximum instantaneous main cutting force and the cutting force fluctuation based on the instantaneous main cutting force at each tool center trajectory point, taking the minimum maximum instantaneous main cutting force, the minimum cutting force fluctuation, the minimum residual height, the trajectory geometric smoothness and the machining time as the optimization objectives, and obtaining a comprehensive objective function based on the normalized weighting of each optimization objective;

[0010] S4, solving the comprehensive objective function based on the tool center trajectory point sequence and the preset constraint condition by using an improved non-dominated sorting genetic algorithm, outputting an optimized tool trajectory point sequence and verifying the same;

[0011] S5, fitting the verified tool trajectory point sequence into a NURBS curve to generate a final tool center trajectory.

[0012] Specifically, the tool center trajectory point sequence includes spatial coordinates of N tool center trajectory points and spatial attitude angles of the tool at each spatial coordinate, and the spatial attitude angles of the tool at each spatial coordinate include an inclination angle of the tool relative to a normal direction of the workpiece surface and a deflection angle of the tool around the normal direction.

[0013] Specifically, the calculation of the instantaneous cutting thickness according to the distance between the tool and the workpiece surface and the calculation of the instantaneous main cutting force of the tool at each tool center trajectory point based on the instantaneous cutting thickness include:

[0014] S21, calculating the instantaneous cutting thickness according to the distance between the tool size and the workpiece surface;

[0015] S22, calculating the uncut chip cross-sectional area according to the instantaneous cutting thickness and the effective cutting width, and calculating the instantaneous main cutting force at each tool center trajectory point according to the uncut chip cross-sectional area and the material cutting coefficient.

[0016] Specifically, the calculation formula of the instantaneous main cutting force is:

[0017] ;

[0018] wherein F c (t k ) represents the instantaneous main cutting force of the tool at time t k , h k represents the instantaneous cutting thickness, b k is the effective cutting width, and m represents the cutting thickness index.

[0019] Specifically, the step of solving the comprehensive objective function using an improved non-dominated sorting genetic algorithm based on the tool center trajectory point sequence and preset constraints, outputting an optimized tool trajectory point sequence, and verifying it includes:

[0020] S41. Set preset constraints, which include: cutting force constraints, machine tool axis travel constraints, machine tool axis speed and acceleration constraints, tool interference and collision constraints, and residual height constraints after smoothing.

[0021] S42. Based on the tool center trajectory point sequence and preset constraints, an improved non-dominated sorting genetic algorithm is used to solve the comprehensive objective function. For tool center trajectory points that do not meet the constraints, a local repair operation is performed to adjust the feed rate, step distance, and tool attitude angle, and an optimized tool center trajectory point sequence is output.

[0022] S43. Perform digital twin verification on the optimized trajectory point sequence to obtain the verified trajectory point sequence.

[0023] Specifically, the cutting force constraint includes: the instantaneous main cutting force of the tool at all trajectory points in the trajectory is less than or equal to the maximum cutting force threshold allowed by the machine tool, tool, and workpiece system;

[0024] The machine tool axis travel constraint includes: the position variable of the machine tool motion axis is greater than or equal to the minimum allowable travel limit of the machine tool motion axis, and less than or equal to the maximum allowable travel limit of the machine tool axis;

[0025] The machine tool axis speed and acceleration constraints include: the machine tool axis speed is less than or equal to the maximum allowable speed limit of the machine tool axis, and the acceleration is less than or equal to the maximum allowable speed limit of the machine tool axis.

[0026] The tool interference and collision constraints include: at all tool center trajectory points in the trajectory, the tool, tool holder, and machine tool components shall not collide or interfere with the workpiece or machine tool structure;

[0027] The residual height constraint after smoothing includes: given a sequence of tool center trajectory points X, selecting the maximum residual height among all surface sampling points that is less than or equal to the maximum allowable residual height threshold.

[0028] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0029] This invention provides a five-axis lathe tool trajectory generation method based on cutting force prediction and optimization. The method optimizes the maximum instantaneous main cutting force, cutting force fluctuation, residual height, trajectory geometrical smoothness, and machining time. A comprehensive objective function is obtained by normalizing and weighting each objective. Based on the tool center trajectory point sequence and preset constraints, an improved non-dominated sorting genetic algorithm is used to solve the comprehensive objective function. This enables active control of the cutting force during the trajectory generation stage, avoiding machine tool vibration and tool wear caused by force peak fluctuations. By embedding cutting force prediction and multi-objective optimization in the trajectory generation stage, a shift from a geometry-driven to a mechanics-driven trajectory generation mode is achieved. Compared with traditional geometric trajectory planning, this method reduces the maximum cutting force and the variance of cutting force fluctuation, decreases the residual height on the surface, ensures smooth machine tool posture switching without sudden acceleration changes, and improves the machining accuracy, stability, and efficiency of five-axis turning of complex curved surfaces. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0031] Figure 1 This is a flowchart of a five-axis lathe tool trajectory generation method based on cutting force prediction and optimization in an embodiment of the present invention. Detailed Implementation

[0032] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments, and the implementation of the present invention is not limited thereto. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0033] Example 1:

[0034] This embodiment takes the machining of complex curved surfaces on a five-axis lathe as an example and proposes a tool trajectory generation method based on cutting force prediction and adaptive optimization. By introducing cutting force prediction, compliance control and machine tool kinematic constraints in the trajectory generation stage, a multi-objective optimization model is established to achieve force uniformity and machining efficiency improvement while meeting surface accuracy requirements.

[0035] like Figure 1The diagram shown is a flowchart of a five-axis lathe tool trajectory generation method based on cutting force prediction and optimization according to an embodiment of the present invention. The tool trajectory generation method based on cutting force prediction and adaptive optimization of the present invention includes the following steps:

[0036] S1. Discretize the surface to be machined (target freeform surface) in the parameter domain, calculate several tool center trajectory points, and obtain the tool center trajectory point sequence.

[0037] Specifically, the tool center trajectory point sequence includes the spatial coordinates of N tool center trajectory points and the spatial attitude angle of the tool at each spatial coordinate. The spatial attitude angle of the tool at each spatial coordinate includes the tilt angle of the tool relative to the normal direction of the workpiece surface and the deflection angle of the tool around the normal direction. The tool center trajectory point sequence X can be represented as:

[0038] ;

[0039] Among them, X k Let X represent the spatial coordinates and spatial attitude angle of the k-th tool center trajectory point, and N represent the total number of points after discretizing the tool center trajectory in the parameter domain or path direction. Each trajectory point X... k Represented as:

[0040] ;

[0041] in, Represents the (x, y, z) spatial coordinates of the k-th tool center trajectory point, (α) k , β k ) represents the spatial attitude angle of the tool at the k-th tool center trajectory point, where α k β is the inclination angle of the tool relative to the normal of the workpiece surface. k Let α be the deflection angle of the tool around the normal direction. k , β k Both of these factors uniquely determine the orientation of the tool axis in space, corresponding to the actual motion angles of the two rotary axes of the machine tool (such as the A / C axis or the B / C axis).

[0042] S2. Calculate the instantaneous cutting thickness based on the distance between the tool and the workpiece surface, and calculate the instantaneous main cutting force based on the instantaneous cutting thickness.

[0043] S21. Calculate the instantaneous cutting thickness based on the distance between the tool size and the workpiece surface.

[0044] Taking a ball end mill as an example, let the tool radius be R and the radial projection distance from the tool center to the workpiece surface be d. kAssuming the workpiece surface is planar and the contact area between the tool and the workpiece satisfies spherical geometry, the geometric relationship between the radial projection distance from the tool center to the workpiece surface can be derived using the Pythagorean theorem. Therefore, the instantaneous cutting thickness h... k It can be represented as:

[0045]

[0046] Where R is the tool radius, d k The radial projection distance from the tool center to the workpiece surface is represented by the formula, which reflects the fundamental relationship between the depth of cut and the radial projection distance.

[0047] S22. Calculate the uncut cross-sectional area based on the instantaneous cutting thickness and effective cutting width, and calculate the instantaneous main cutting force based on the uncut cross-sectional area and the material cutting coefficient.

[0048] The area of ​​the uncut cross-section is calculated based on the instantaneous cutting thickness and effective cutting width. The formula for calculating the area of ​​the uncut cross-section is as follows:

[0049] ;

[0050] Among them, h k Indicates the instantaneous cutting thickness, b k For the effective cutting width, b k It can be obtained from the local contact arc length between the tool and the workpiece, representing the contact width of the tool participating in cutting at that position. Its size is related to the tool shape, tool attitude angle, and local surface geometry of the workpiece.

[0051] The instantaneous principal cutting force at each tool center trajectory point is calculated based on the uncut cross-sectional area and the material cutting coefficient. The formula for calculating the instantaneous principal cutting force is as follows:

[0052] ;

[0053] Among them, F c (t) k () indicates the tool at time t k (or tool center trajectory point X) k The instantaneous main cutting force at point K c The material cutting coefficient, K, is used to characterize the cutting characteristics of the workpiece material and tool combination. It is usually obtained through trial cutting experiments or empirical calibration. c A comprehensive reflection of factors such as material hardness, tool material, and tool geometry parameters, b k Represents the tool center trajectory point X k The effective cutting width at that location.

[0054] When higher precision is required, an empirical power model can be used. The formula for calculating the instantaneous main cutting force is:

[0055] ;

[0056] Here, m represents the cutting thickness exponent, used to describe the nonlinear relationship between cutting force and cutting thickness. The cutting thickness exponent m is usually obtained through experimental fitting and reflects the nonlinear characteristics of material cutting behavior. Under given material conditions, the cutting force is proportional to the effective cutting width and has a power function relationship with the cutting thickness. This model can quickly estimate the cutting force at each trajectory point during the tool path generation stage, providing a mechanical basis for subsequent tool posture optimization, feed adjustment, and multi-objective trajectory optimization.

[0057] S3. The maximum instantaneous main cutting force and cutting force fluctuation are calculated based on the instantaneous main cutting force at each tool center trajectory point. The optimization objectives are to minimize the maximum instantaneous main cutting force, minimize the cutting force fluctuation, minimize the residual height, improve trajectory smoothness, and reduce machining time. The comprehensive objective function is obtained by normalizing and weighting each optimization objective.

[0058] Specifically, the maximum instantaneous main cutting force is calculated based on the instantaneous main cutting force at each tool center trajectory point, and the minimization of the maximum instantaneous main cutting force can be expressed as:

[0059] ;

[0060] Where X represents the sequence of tool center trajectory points, F c (t) k The instantaneous main cutting force of the tool at time point Tk.

[0061] Specifically, the cutting force fluctuation is calculated based on the instantaneous main cutting force at each tool center trajectory point. The minimization of the cutting force fluctuation can be expressed in the form of the fluctuation variance between the instantaneous main cutting force and the average cutting force:

[0062] ;

[0063] Among them, F c (t) k () indicates that the tool is at time point T k Or the instantaneous principal cutting force at trajectory point k, This represents the average instantaneous main cutting force over the entire trajectory. This represents the deviation (squared difference) between the instantaneous main cutting force and the average value, reflecting the degree of cutting force fluctuation. It can be used to assess the stability of the cutting force throughout the entire tool path: If the force value changes significantly, the variance is large, indicating that the tool load is unstable and prone to vibration. If the force value changes slightly, the variance is small, indicating that the tool load is uniform and the machining is more stable.

[0064] Specifically, minimizing the residual surface height means ensuring that the residual height at all surface points does not exceed the allowable range, thereby guaranteeing that the machined surface meets the accuracy and surface quality requirements. Minimizing the residual surface height can be expressed as:

[0065] ;

[0066] in, This represents the set of discrete sampling points on the machined surface of a workpiece, used to evaluate the surface morphology after machining. This can be obtained by uniform sampling on the parametric domain or a surface mesh. Represents a set Any surface sampling point in the sample, This represents the sampling points under a given tool center trajectory sequence X. The residual height at the point represents the maximum normal distance between the actual machined surface and the theoretical target surface. This value reflects the approximation accuracy of the tool path to the target surface. This represents the maximum residual height among all surface sampling points.

[0067] Specifically, trajectory smoothness is measured by a second-order difference smoothing index. express:

[0068] ;

[0069] Where X represents the sequence of tool center trajectory points (CL point set), X k Let X represent the spatial coordinates and spatial attitude angle of the k-th tool center trajectory point. k-1、 X k、 X k+1 The spatial coordinates and spatial attitude angles of three adjacent consecutive tool center trajectory points in the trajectory represent the tool position and attitude state at the previous, current, and next time moments, respectively. The discrete second derivative of the trajectory is approximated by a second-order difference term with a center trajectory sequence, reflecting the curvature or trend of the trajectory at that position. The squared L2 norm of the vector is used to measure the magnitude of the second-order difference term. All internal points in the trajectory are summed to avoid endpoint effects.

[0070] In this example, the second-order difference smoothing index, acting as a geometric compliance constraint or optimization objective, works in conjunction with the cutting force objective function to achieve synergistic optimization of the trajectory's mechanics and geometry. By minimizing the second-order difference between adjacent trajectory points, sharp bends and abrupt changes in the trajectory are suppressed, resulting in smoother and more continuous tool movement. In five-axis machining, this index not only improves the geometric continuity of the trajectory but also reduces abrupt changes in machine tool axis speed and acceleration, thereby reducing vibration risk and improving machining stability and surface quality.

[0071] Specifically, the processing time is obtained by summing the time steps between all adjacent trajectory points in the entire trajectory. The processing time can be expressed as:

[0072] ;

[0073] in, This represents the time step between adjacent trajectory points.

[0074] Specifically, by normalizing and weighting the minimization of maximum instantaneous main cutting force, minimization of cutting force fluctuation, minimization of residual height, path smoothness, and machining time, a comprehensive objective function is obtained. This function can be used to evaluate the overall performance of a given tool path under various performance indicators. The comprehensive objective function J... total (X) is represented as:

[0075] ;

[0076] in, It is a normalized residual height minimization index used to characterize machining geometric accuracy. This is a normalized maximum cutting force index used to constrain the peak cutting force. It is a normalized cutting force fluctuation index used to evaluate the stability of cutting forces. It is a normalized trajectory geometric smoothness index used to suppress trajectory abrupt changes. This is a normalized processing time indicator used to improve processing efficiency. These are the weight coefficients corresponding to each optimization objective, used to adjust the relative importance of different objectives in the overall optimization, and typically satisfy the following:

[0077] ;

[0078] In this example, The values ​​can be 0.25, 0.25, 0.2, 0.2, or 0.1. This ratio can be adjusted according to the workpiece surface accuracy and processing efficiency requirements.

[0079] By constructing a comprehensive objective function and normalizing and weighting multiple performance indicators such as geometric accuracy, cutting force level, cutting force stability, trajectory smoothness, and machining time, collaborative optimization of five-axis tool trajectories can be achieved. The constructed comprehensive objective function can improve machine tool motion smoothness and machining efficiency while ensuring machining accuracy and cutting stability, providing a systematic and adjustable trajectory optimization method for asymmetric complex surface machining on five-axis lathes.

[0080] S4. Set preset constraints, and use an improved non-dominated sorting genetic algorithm to solve the comprehensive objective function based on the preset constraints. Output the optimized tool trajectory point sequence and verify it.

[0081] S41. Set preset constraints, which include: cutting force constraints, machine tool axis travel constraints, machine tool axis speed and acceleration constraints, tool interference and collision constraints, and residual height constraints after smoothing.

[0082] Specifically, the cutting force constraint includes: the instantaneous main cutting force at all trajectory points of the tool is less than or equal to the maximum allowable cutting force threshold of the machine tool, tool, and workpiece system. This constraint is used to limit the peak cutting force of the tool throughout the machining process from exceeding a safe upper limit, in order to prevent accelerated tool wear, workpiece deformation, or machine tool structural overload caused by excessive cutting force. The cutting force constraint can be expressed as:

[0083] ;

[0084] This represents the instantaneous main cutting force of the tool at the k-th trajectory point; This indicates the maximum permissible cutting force threshold of the machine tool-cutting tool-workpiece system. This means that the constraint holds true for all discrete points in the trajectory.

[0085] During trajectory optimization, when the predicted cutting force at a certain trajectory point exceeds the threshold, the tool posture, feed rate, or trajectory distribution are adjusted to meet the constraint condition, thereby ensuring the safety and stability of the machining process.

[0086] Machine tool axis travel constraint: The positional variable of a machine tool axis is greater than or equal to the minimum allowable travel limit of the machine tool axis, and less than or equal to the maximum allowable travel limit of the machine tool axis. The machine tool axis travel constraint can be expressed as:

[0087] ;

[0088] in, Indicates time t k Or, at the k-th trajectory point, the position variable of the i-th machine tool motion axis. q i It can correspond to linear axes (X, Y, Z) or rotary axes (A, B, C), where i represents the i-th machine tool motion axis, used to distinguish between different linear and rotary axes. The minimum allowable travel limit of the i-th machine tool motion axis is determined by the machine tool structural parameters. The maximum allowable travel limit of the i-th machine tool axis. This means that the constraint condition holds true for all machine tool motion axes and all discrete points of the trajectory.

[0089] Specifically, machine tool axis speed and acceleration constraints include: the machine tool axis speed is less than or equal to the maximum allowable speed limit of the machine tool axis, and the acceleration is less than or equal to the maximum allowable speed limit of the machine tool axis. Machine tool axis speed and acceleration constraints can be expressed as:

[0090] ;

[0091] in Indicates time t k Or, at the k-th trajectory point, the variable of the i-th machine tool motion axis, wherein the motion axis includes a linear axis and a rotary axis. The time step between two adjacent trajectory points. The maximum permissible speed limit for the i-th machine tool axis The maximum allowable acceleration limit for the i-th machine tool axis is determined by the machine tool performance parameters.

[0092] Specifically, This represents a discrete velocity approximation term between trajectory points, used to estimate the instantaneous velocity of the machine tool axis at trajectory point k.

[0093] Specifically, This is represented as a discrete acceleration approximation term between trajectory points, used to estimate the instantaneous acceleration of the machine tool axis at trajectory point k. Taking the absolute value of the discrete acceleration approximation term is used to constrain the forward and reverse velocities and accelerations of the axis motion.

[0094] By introducing constraints on machine tool axis speed and acceleration, it can be ensured that the speed and acceleration of each machine tool axis do not exceed the machine tool's permissible physical limits during tool path generation and optimization. This effectively avoids servo following errors, structural vibrations, or resonance risks caused by excessive axis movement or sudden acceleration changes, thereby improving the stability, machining accuracy, and machine tool safety of the five-axis machining process.

[0095] Specifically, tool interference and collision constraints include ensuring that at all tool center trajectory points in the trajectory, the tool, tool holder, and machine tool components do not collide or interfere with the workpiece or machine tool structure.

[0096] In this example, one or more methods, such as minimum distance calculation, bounding box intersection detection, sampling point intrusion detection, or digital twin simulation, can be used to determine whether the tool, tool holder, and machine tool components interfere with the workpiece or machine tool structure at a given trajectory point. This ensures that the tool, tool holder, and machine tool components do not collide or interfere with the workpiece or machine tool structure throughout the entire tool movement. During trajectory generation and optimization, collision detection is performed on each discrete trajectory point, and only trajectory schemes that satisfy this constraint are retained. That is, the sequence of tool center trajectories in which the tool, tool holder, and machine tool components do not collide or interfere with the workpiece or machine tool structure at all tool center trajectory points in the trajectory, thereby ensuring the executability and machining safety of the generated tool trajectory on an actual five-axis lathe.

[0097] Specifically, the residual height constraint after smoothing includes: given a sequence of tool center trajectory points X, selecting the maximum residual height among all surface sampling points that is less than or equal to the maximum allowable residual height threshold. The residual height constraint after smoothing can be expressed as:

[0098] ;

[0099] Where X^ is the smoothed trajectory after NURBS fitting, This represents the set of discrete sampling points on the machined surface of a workpiece, used to evaluate the surface morphology after machining. The set of discrete sampling points can be obtained by uniform sampling on a parametric domain or a surface mesh. It represents any surface sampling point in the set of discrete sampling points. The value represents the residual height at the surface sampling point under the condition of the tool center trajectory point sequence X, and the value represents the normal distance between the actual machined surface and the theoretical target surface. This indicates that the maximum residual height is selected from all surface sampling points. The maximum allowable residual height threshold is preset according to processing accuracy requirements or process specifications.

[0100] S42. Based on the tool center trajectory point sequence and preset constraints, an improved non-dominated sorting genetic algorithm is used to solve the comprehensive objective function. For tool center trajectory points that do not meet the constraints, a local repair operation is performed to adjust the feed rate, step distance, and tool attitude angle, and an optimized tool center trajectory point sequence is output.

[0101] Specifically, an improved non-dominated sorting genetic algorithm, NSGA-II, is employed. NSGA-II is a classic multi-objective optimization algorithm. The population size can be set to 80, with 200 iterations. In each generation, local repair operations are performed on individuals that do not meet the constraints, i.e., the tool center trajectory. When the predicted cutting force exceeds a threshold F... maxWhen the feed rate is less than 1, the feed rate is reduced or the step distance is shortened. When the machine tool axis acceleration exceeds the limit, the tool attitude angle (α, β) is adjusted. Each individual in the genetic algorithm corresponds to a complete tool center trajectory. When any discrete trajectory point in the trajectory violates the cutting force constraint, machine tool kinematic constraint, or collision-free constraint, the individual is determined to be unsatisfactory. For such individuals, a repair operation is performed on the local trajectory points that violate the constraints to bring them back to the feasible solution space, rather than regenerating the entire trajectory.

[0102] S43. Perform digital twin verification on the output optimized trajectory point sequence to obtain the verified trajectory point sequence.

[0103] Specifically, the optimized trajectory point sequence can be imported into a five-axis machine tool digital twin model to simulate and verify the cutting force curve, spindle torque spectrum, and residual height distribution. Resonance and overload risks are assessed by analyzing the spindle torque spectrum and cutting force curve. If resonance risk or torque exceedance exists, the trajectory point sequence is further corrected. The trajectory undergoes compliance verification in the digital twin virtual machine tool environment; if a dynamic or mechanical abrupt change is detected, trajectory correction is performed.

[0104] S5. Perform NURBS curve fitting on the verified trajectory point sequence to generate the final tool center trajectory and export the corresponding NC machining program.

[0105] The verified trajectory point sequence is read and stored in a file. NURBS curve fitting is then performed to obtain a smooth curve. The fitted curve is discretized to generate the tool center trajectory, i.e., a series of dense points, for subsequent NC code generation. Based on the tool center trajectory, the corresponding NC machining program (e.g., G-code) is generated. NURBS fitting transforms discrete trajectory points into a continuous, smooth toolpath, significantly improving machining quality and efficiency. NURBS (Non-Uniform Rational B-Spline) curve fitting uses a mathematical model of curve fitting to adjust control points, weights, and node vectors to generate a smooth trajectory. The fitting process is typically optimized based on a discrete point set to reduce noise or discretization errors and obtain a smooth path with continuous derivatives.

[0106] This embodiment provides a five-axis lathe tool trajectory generation method based on cutting force prediction and optimization. This method is applicable to five-axis turning of complex curved surfaces, including rotating bodies, non-axisymmetric swept bodies, and blade-like surfaces. It enables active control of the cutting force during the trajectory generation stage, avoiding machine tool vibration and tool wear caused by force peak fluctuations. Compared with traditional geometric trajectory planning, this invention can reduce the maximum cutting force by 20%–35%, reduce the cutting force fluctuation variance by approximately 40%, reduce the surface residual height by approximately 25%, and ensure smooth machine tool posture switching without sudden acceleration changes. Therefore, this method can significantly improve the machining quality and stability of five-axis turning of complex curved surfaces.

[0107] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for generating tool path of five-axis lathe based on cutting force prediction and optimization, characterized in that, The method comprises the following steps: S1, discretely sampling a machining surface in a parameter domain to obtain a tool center locus point sequence; S2, calculating an instantaneous cutting thickness according to the distance between the tool and the workpiece surface, and calculating the instantaneous main cutting force of the tool at each tool center locus point based on the instantaneous cutting thickness; S3, calculating the maximum instantaneous main cutting force and the cutting force fluctuation based on the instantaneous main cutting force at each tool center locus point, taking the minimum maximum instantaneous main cutting force, the minimum cutting force fluctuation, the minimum residual height, the trajectory geometric smoothness and the machining time as the optimization objectives, and obtaining a comprehensive objective function based on the normalized weighting of each optimization objective; S4, solving the comprehensive objective function by using an improved non-dominated sorting genetic algorithm based on the tool center locus point sequence and the preset constraint condition, outputting the optimized tool locus point sequence and verifying it; S5, fitting the verified tool locus point sequence into a NURBS curve to generate a final tool center locus.

2. A method for generating tool path of five-axis lathe based on cutting force prediction and optimization according to claim 1, characterized in that, The tool center locus point sequence comprises the spatial coordinates of N tool center locus points and the spatial attitude angles of the tool at each spatial coordinate, and the spatial attitude angles of the tool at each spatial coordinate include the inclination angle of the tool relative to the normal of the workpiece surface and the deflection angle of the tool around the normal direction.

3. The method of claim 1, wherein, The calculation of the instantaneous cutting thickness according to the distance between the tool and the workpiece surface and the calculation of the instantaneous main cutting force of the tool at each tool center locus point based on the instantaneous cutting thickness comprise: S21, calculating the instantaneous cutting thickness according to the distance between the tool size and the workpiece surface; S22, calculating the uncut chip section area according to the instantaneous cutting thickness and the effective cutting width, and calculating the instantaneous main cutting force at each tool center locus point according to the uncut chip section area and the material cutting coefficient.

4. The method of claim 1, wherein, The calculation formula of the instantaneous main cutting force is: ； where F c (t k ) represents the instantaneous main cutting force of the tool at time t k , h k represents the instantaneous cutting thickness, b k is the effective cutting width, and m represents the cutting thickness exponent.

5. The method of claim 1, wherein, The trajectory smoothness is by a second order difference smoothness index denotes: ； wherein X denotes a sequence of tool center trajectory points, X k denotes the spatial coordinates and spatial orientation angles of the kth tool center trajectory point, X k-1、 X k、 X k+1 denotes the spatial coordinates and spatial orientation angles of the three consecutive tool center trajectory points adjacent in the trajectory.

6. The method of claim 1, wherein, The solving of the comprehensive objective function by using the improved non-dominated sorting genetic algorithm based on the tool center locus point sequence and the preset constraint condition, the output of the optimized tool locus point sequence and the verification thereof comprise: S41, setting the preset constraint condition, which comprises the cutting force constraint, the machine tool axis stroke constraint, the machine tool axis speed and acceleration constraint, the tool interference and collision constraint and the residual height constraint after smoothing; S42, solving the comprehensive objective function by using the improved non-dominated sorting genetic algorithm based on the tool center locus point sequence and the preset constraint condition, performing a local repair operation on the tool center locus points that do not meet the constraint, adjusting the feed speed, the step distance and the tool attitude angle, and outputting the optimized tool center locus point sequence; S43, verifying the optimized locus point sequence by digital twinning to obtain the verified locus point sequence.

7. The method of claim 6, wherein, The cutting force constraint comprises that the instantaneous main cutting force of the tool at all locus points in the trajectory is less than or equal to the maximum cutting force threshold allowed by the machine tool, tool and workpiece system; The machine tool axis stroke constraint comprises that the position variable of the machine tool motion axis is greater than or equal to the minimum stroke limit allowed by the machine tool motion axis, and less than or equal to the maximum stroke limit allowed by the machine tool axis; The machine tool axis speed and acceleration constraint comprises that the machine tool axis speed is less than or equal to the maximum speed limit allowed by the machine tool axis, and the acceleration is less than or equal to the maximum speed limit allowed by the machine tool axis. The tool interference and collision constraints include that at all tool center locus points in the locus, the tool, the tool holder and the machine components do not collide or interfere with the workpiece or the machine structure; The post-smoothing residual height constraints include that under the condition of a given tool center locus point sequence X, the maximum value of the residual height selected from all surface sampling points is less than or equal to the allowed maximum residual height threshold.

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