Milling force simulation and feed rate optimization method considering robot pose dependent dynamics effect

Abstract

The invention belongs to the technical field of robots, and discloses a milling force simulation and feed rate optimization method considering a robot pose dependence dynamics effect, and the method comprises the steps: firstly carrying out modal testing under different poses of a robot milling area; then, a kinetic model is established in a robot cutting area; and meanwhile, the surface of the workpiece is dynamically updated based on the dynamic sweeping track of the blade and the workpiece model, so that the calculation precision of the instantaneous cutting thickness and the cutting force is guaranteed. And finally, based on the simulated accurate cutting force, feed rate segmented self-adaptive planning under the cutting force peak value constraint is carried out, and robot curved surface part milling and machining error measurement experiments are carried out. The milling efficiency and precision of the curved surface part robot are effectively improved, and the cutting force in the machining process is more stable. And the method is of great significance to improvement of the stability and the machining performance in the robot machining process.

Description

Technical Field

[0001] The present invention belongs to the technical field of robots, and in particular relates to a milling force simulation and feed rate optimization method considering the posture-dependent dynamic effects of the robot. Background Art

[0002] The rapid development of modern manufacturing has driven the pursuit of product processing quality, efficiency, and economy to new heights, making precise control of the processing process crucial. Industrial robots have been widely used in key processing fields such as aerospace and automotive manufacturing due to their good accessibility, high flexibility, scalability, and economy. Milling force, as the core physical quantity in the robotic milling process, is generated by the complex interaction between the milling cutter and the workpiece. It is closely related to the stability of the processing, the service life of the tool, and the processing accuracy. Compared with other monitoring indicators, milling force can more directly and accurately reflect subtle changes in the processing process. Therefore, the simulation analysis of milling force and the optimization of process parameters based on this are of great significance to improving the accuracy and performance of robotic milling.

[0003] By accurately simulating milling forces, we can gain a deeper understanding of how milling forces vary under different process parameters before machining, predicting potential machining defects such as excessive cutting forces and tool breakage. This allows us to optimize machining plans in advance, effectively avoid abnormalities during machining, and significantly improve product quality. Furthermore, optimizing process parameters with milling force simulation can significantly improve machining efficiency, reduce machining costs, and achieve efficient resource utilization while ensuring machining quality. This not only helps enhance a company's competitiveness in the market but also plays a key role in driving the intelligent and high-end development of the manufacturing industry.

[0004] Currently, most simulation studies of cutting forces in robotic milling remain at the numerical simulation stage, without conducting actual milling experiments to verify the accuracy of the simulation models. A small number of studies have conducted milling experiments, but these have not considered the impact of the robot's posture-dependent dynamic effects on the instantaneous undeformed chip thickness or the dynamic updating of the workpiece surface. Furthermore, these studies have only conducted linear milling of planar workpieces, with no robotic milling experiments conducted on complex curved parts. Furthermore, the dynamic characteristics of robotic milling systems are heavily dependent on their posture, with significant differences in their distribution across the workspace. This results in low robotic milling stability, significant variations in milling performance across different machining areas, and a narrow window of available process parameter options. Therefore, process parameter optimization is crucial for improving machining accuracy. However, most existing research focuses on machining error compensation and stability prediction based on simulated or predicted cutting forces. No research has yet been conducted on process parameter optimization based on robotic simulated milling forces. Therefore, a process parameter optimization method based on robotic simulated milling forces is urgently needed.

[0005] Through the above analysis, the problems and defects of the existing technology are as follows:

[0006] (1) Currently, most of the simulation research on cutting forces in robotic milling remains at the numerical simulation stage, without conducting actual milling experiments to verify the accuracy of the simulation model. A small number of studies have conducted milling experiments, but they have not considered the influence of the robot's posture-dependent dynamic effects on the instantaneous undeformed chip thickness and the dynamic update of the workpiece surface. In addition, they have only conducted linear milling of planar workpieces, and have not conducted robotic milling experiments on complex curved surface parts.

[0007] (2) The dynamic characteristics of the robot milling system are heavily dependent on the posture, and there are significant differences in the distribution of the workspace. This results in low robot milling stability, significant changes in milling performance in different processing areas, and a narrow window of available process parameter options. Therefore, process parameter optimization is of great significance for improving processing accuracy.

[0008] (3) Most of the existing research work is based on simulated or predicted cutting forces to carry out research on machining error compensation, stability prediction, etc., and no relevant research has been carried out on process parameter optimization based on robot simulation milling force. Summary of the Invention

[0009] In response to the problems existing in the prior art, the present invention provides a milling force simulation and feed rate optimization method taking into account the robot posture-dependent dynamic effects.

[0010] The present invention is implemented as follows: a method for milling force simulation and feed rate optimization considering the robot posture-dependent dynamic effects includes:

[0011] S1, modal tests are performed at different positions in the robot milling area. Based on the obtained robot joint angles and modal parameters, a prediction model of the reference modal parameters under the perpendicular tool axis vector is established, and the modal parameters in the instantaneous tool direction are obtained through the transformation matrix;

[0012] S2, establishes a mechanical force model and a dynamic model in the robot cutting area; dynamically updates the workpiece surface based on the dynamic sweep trajectory of the blade and the workpiece model to ensure the calculation accuracy of the instantaneous cutting thickness and cutting force;

[0013] S3, based on the predicted modal parameters and the initial cutting force calculated by the mechanical force model, solves the steady-state dynamic displacement caused by the robot dynamics effect, and superimposes it on the nominal instantaneous undeformed chip thickness. The instantaneous cutting force at each time step is calculated and iterative calculation is performed by coupling the dynamic update mechanism of the workpiece surface;

[0014] S4, based on the accurate cutting force of the simulation, the feed rate segmented adaptive planning under the cutting force peak constraint is carried out, and the robot milling and surface part processing error measurement experiments are carried out to verify the performance of the model.

[0015] Furthermore, in step S1, multiple modal parameter measurement points are evenly set in the area above the robot workbench, and modal testing is performed when the tool axis vector is perpendicular to the workbench plane. Modal parameters are obtained using modal analysis software, and the robot joint angles in various postures are recorded at the same time. Since multiple modal parameters need to be predicted and the correlation between modal parameters is considered, this paper establishes a modal parameter prediction model based on a co-regionalized intrinsic model using multi-task Gaussian process regression (MTGPR).

[0016] X represents the M different inputs X=(x1,x2,...,x M ) T The set of components is the joint angles of all measurement points. For N modes to be predicted, the label space is expressed as:

[0017]

[0018] where y il represents the jth label value of the i-th input; for each row y of Y i , that is, all modal parameters, there are y i ={f d ,ξ d ,M d ,C d ,K d},i=1,...,M,d=x,y;

[0019] The latent function {q l} is set as a Gaussian prior to obtain the relationship between different modal parameters. Assuming that the mean of GPs is 0, let:

[0020]

[0021] Where K q is the positive semidefinite (PSD) matrix describing the similarity between modal parameters, k x is the covariance function of the input vector, which captures the correlation between different poses of the same modal parameter. is the variance of the lth modal parameter;

[0022] The model is derived using the standard GP formula for the mean and variance of the predictive distribution and the covariance function given above; for a new data point x in the lth mode * (l=(l j,j=1,...,N)), the mean prediction is calculated as follows:

[0023]

[0024] In the formula represents the Kronecker product, K q The first column of For training points and test points x * The covariance vector between x is the covariance matrix between all training point pairs; A is an M×M diagonal matrix, where the (l, l)th element is H is a MN×MN matrix;

[0025] In the training set, given a label y t , using a gradient-based method to learn the matrix K q and k x The parameter θ x , so that the marginal likelihood p(y t |X,θ x ,K q ) is maximized; Cholesky decoupling method is used to ensure K q The positive semi-determinism of ; the lower triangular matrix L can be parameterized as:

[0026]

[0027] In the formula K q The number of hyperparameters is used to optimize the hyperparameters of the MTGPR model by minimizing the negative log-marginal likelihood; given an input (x * ,l * ), according to the conditional probability P(y * |X,l,y,x * ,l * ) calculates its predicted value; MTGPR combines multiple pose-related modal parameters in a regression model and learns the correlation between the modal parameters to improve the prediction performance.

[0028] Furthermore, the modal parameters are measured when the tool axis vector is perpendicular to the robot table plane; however, during the robot milling process of complex surfaces, the direction of the tool is time-varying; by the rake angle θ L and the roll angle θ TThe calculated transformation matrix transforms the frequency response function (FRF) of the modal parameter fitting to the instantaneous tool direction, and then the modal parameters are obtained through curve fitting. The reference FRF is measured in the measurement coordinate system (MCS) when the tool axis vector is perpendicular, and the instantaneous direction FRF is measured in the instantaneous coordinate system (IMCS). The transformation matrix from MCS to IMCS is defined as:

[0029] R t (θ T ,θ L )=R y (θ L )R x (θ T )

[0030] where R y (θ L ) and R x (θ T ) is expressed as:

[0031]

[0032] The inverse transformation matrix is ​​defined as:

[0033]

[0034] The force excitation and response signals are decomposed and synthesized to obtain the instantaneous FRF matrix:

[0035]

[0036] Among them, H O (ω) and H T (ω) denote the reference and instantaneous FRF matrices, respectively.

[0037] Furthermore, in step S2, first, a mechanical force model is established to define a workpiece coordinate system (WCS) in robot multi-axis milling. WCS ,x WCS y WCS z WCS}、Tool Coordinate System (TCS) {O TCS ,x TCS y TCS z TCS} and feed coordinate system (FCS) {O FCS ,x FCS y FCS z FCS}; WCS is fixed on the workpiece, the origin of TCS is at the tool center, z TCS Direction along the tool axis, y TCS The axis direction is from the tool center to the point z=0 on the first edge; the origin of FCS is at the tool contact point, x FCSAlong the tool path direction, z FCS Follow the normal direction of the workpiece surface; the idea of ​​the mechanical cutting force model is to discretize the milling cutter into several equal micro units along its axis, and give a rotation angle The instantaneous cutting force under TCS is the sum of the cutting forces of all micro-units on all cutting edges. Combining the calibrated radial, tangential and axial cutting force coefficients, the cutting force is converted under TCS and expressed as:

[0038]

[0039] Where F cq (q=x,y,z) is the cutting force under TCS, N e and N z are the number of cutting edges and the number of discrete units respectively; K dc (d=r,t,a) represents radial, tangential and axial shear force coefficients; K de (d=r,t,a) represents the radial, tangential and axial cutting force coefficients; Δb is the width of the discrete cutting unit, which is given by Δb=Δz / sink(z i ) is calculated, where Δz is the height of the discrete unit, k(z i )=cos -1 ((Rz i ) / R) represents the height z i R is the tool radius. The upper and lower limits of the axial engagement of the cutting edge are determined by the rake angle and side rake angle of the tool and the instantaneous curvature of the workpiece surface. M is the rotation transformation matrix from the micro-cutting force to the tool coordinate system, which is expressed as:

[0040]

[0041] Indicates the jth cutting edge at the axial height z i The radial immersion angle at

[0042]

[0043] Where n s is the spindle speed, ψ picth =2π / N and β represent the pitch angle between two consecutive edges and the helix angle of the tool respectively; ds is the length of the cutting edge element, and the calculation formula is:

[0044]

[0045] In the above formula is the theoretical instantaneous undeformed chip thickness of the cutting edge element, which can be expressed as:

[0046]

[0047] Where f pt is the feed per tooth, which can be calculated as f pt =f / (N e ·n s ), f is the feed rate;

[0048] In the above formula is a function that characterizes the cutting edge's penetration or extrusion, and is defined as:

[0049]

[0050] in, and The tool axial height z is i The entry and exit angles at

[0051] Finally, the cutting force is converted to WCS and expressed as:

[0052] [F w 1] T =B[F cx F cy F cz 1] T

[0053] Where B is the transformation matrix from TCS to WCS, which is related to the rake angle and side rake angle of the tool;

[0054] Influenced by the robot's dynamic effects, the tool will experience dynamic displacement under the action of the cutting force. This dynamic displacement has a significant impact on both the current cutting edge position and the machined surface formed by the previous cutting edge's sweep, resulting in a dynamic undeformed chip thickness and a time-varying tool-workpiece engagement (CWE) area. After obtaining the initial cutting force, the robot milling dynamics model of the cutting area is established as follows:

[0055]

[0056] Where M c , C c and K c are the mass matrix, damping matrix and stiffness matrix of the robot milling system, respectively, expressed as:

[0057] M c =diag(m x ,m y ,m z ),C c =diag(c x ,c y ,c z ),K c =diag(k x ,ky ,k z )

[0058] In the tool coordinate system, the stiffness in the Z direction is much higher than in the X and Y directions, and the cutting force in the Z direction is generally smaller. Therefore, only the dynamic vibration and modal parameters in the X and Y directions are considered. The dynamic model is a second-order ordinary differential equation, which can be solved using algorithms such as the Runge-Kutta algorithm. First, the state vector is defined and converted into a system of first-order differential equations to improve the computational efficiency of the solution. It is expressed as:

[0059]

[0060] The actual position of the cutting edge is further determined using the dynamic displacement solved at each time step;

[0061] To obtain the cutting topography of the workpiece surface, a dynamic cutting edge sweep trajectory must first be established based on the tool parameters, tool location information, and the resulting dynamic displacement. As the tool rotates along the tool location, the actual position and sweep trajectory of all height points on the tool edge at each time step are determined, taking into account the influence of the tool's motion trajectory and dynamic displacement.

[0062] During robot machining, the tool path under the WCS is represented as:

[0063]

[0064] where tp plan (t) is the planned tool path, x plan (t), y plan (t), z plan (t) is the position in three directions; v(t) is the tool axis vector, a(t), b(t) and c(t) are the Euler angles describing the posture;

[0065] disp dy (t){px vib (t)y vib (t)z vib (t)] T} is the dynamic displacement of the robot milling area under TCS, which is converted to WCS and expressed as:

[0066]

[0067] Typically, the planned tool path tp plan (t) is expressed in the form of the tool contact point; n(t) is the normal vector of the tool contact point on the machining surface, and O(t) is the tool center point; in order to calculate the swept area of ​​the tool edge, O(t) is expressed in WCS as:

[0068]

[0069] In TCS, the height z of the jth edge is i The blade point position C(j,z i ) is calculated as:

[0070]

[0071] Where β is the helix angle. The tool position curve and the corresponding tool axial vector are then considered to calculate the tool edge sweep surface. The calculation in WCS is as follows:

[0072] S p (t,j,z i )=O(t)+BR(ωt)C(j,z i )

[0073] Where ω = 2πn s / 60 is the angular velocity, R(ωt) is the rotation matrix about the tool axis;

[0074] The workpiece surface is represented as a Z-map vector aligned with the Z axis passing through the grid points on the XY plane; then, the intersection of the Z-map vector and the tool sweep surface is calculated in combination with the simulated dynamic sweep trajectory and cutting parameters, the vector is updated, and the morphology of the machined surface is dynamically updated; considering the differences in cutting of different blades and the timeliness of cutting load calculation, a dynamic update mechanism for the machined surface within the blade cycle is proposed; within the first rotation range of the tool cutting into the workpiece, the robot is assumed to be rigid, and the initial machined surface is generated according to the theoretical trajectory of the tool motion; at each subsequent discrete time step, the instantaneous dynamic displacement is calculated according to the above-mentioned method; the dynamic displacement is superimposed on the theoretical tool center point position, and then combined with the position of the blade point to obtain a new actual blade sweep trajectory point, which is stored; the machined surface of the workpiece is updated after one blade cutting is completed, and the workpiece surface update along the entire path is completed according to this update mechanism and the tool feed.

[0075] Furthermore, in step S3, the steady-state dynamic displacement caused by the robot dynamics effect is solved based on the predicted modal parameters and the initial cutting force calculated by the mechanical force model, and is superimposed on the nominal instantaneous undeformed chip thickness. The instantaneous cutting force at each time step is calculated, and iterative calculation is performed based on the dynamic update mechanism of the workpiece surface.

[0076] Based on the above-mentioned blade sweep trajectory model and the dynamic update mechanism of the machined surface, the coupling robot dynamics model and the mechanical force model can realize the accurate calculation of the instantaneous undeformed chip thickness and micro-element load under the influence of dynamic displacement, and then calculate the instantaneous dynamic cutting force; the simulation process is discretized into a series of instantaneous time steps, and at each time step, the micro-cutting forces of all micro-elements on the spiral milling cutter are calculated; during the initial tool rotation period of the simulation, the rigid body cutting force model is used to calculate the initial cutting force F ini , and generate the initial workpiece processing surface; then, combined with the robot joint angle, the modal parameter prediction model is used to predict the modal parameters under continuous processing posture; the calculated initial cutting forces in the X and Y directions are brought into the dynamic model of the cutting area to perform dynamic displacement in the X and Y directions and The actual blade position point S is obtained by superimposing it on the theoretical trajectory point P , expressed as:

[0077]

[0078] In order to simplify the calculation process and improve the calculation efficiency, and considering the influence of the theoretical trochoid motion trajectory of the cutting edge point and the dynamic displacement of the robot, the instantaneous undeformed chip thickness is calculated in the tool coordinate system; the center point of the current tool is O, and the straight line OS P The intersection point with the previous cutting tool path is S T , which can be determined by the straight line equation and interpolation curve model, S P S T The length of is the actual instantaneous undeformed chip thickness, and then the instantaneous cutting force is calculated, which is expressed as:

[0079]

[0080] in, and Represents the actual cutting edge point position on the cutting path generated by the current cutting edge and the previous cutting edge tooth pass cycle respectively; τ=60 / N e n s is the tooth-through period;

[0081] The new dynamic displacement and actual position are calculated using the cutting force as the excitation source. When the difference between adjacent actual position prediction results is less than the set threshold, it is considered converged and the actual position is stored. Then the simulation prediction of the next time step begins. After the cutting edge completes the cutting, the actual position points at each time step are interpolated using the interpolation algorithm to update the machined surface. The subsequent blades calculate the dynamic displacement, instantaneous undeformed chip thickness and cutting force based on this surface, and perform iterative updates until the end of the simulation.

[0082] Furthermore, in step S4, due to the influence of the robot's posture-dependent dynamic characteristics, the robot end has weak stiffness in certain postures, and under the action of the milling force, it will produce more significant dynamic stiffness deformation, reducing the machining performance of the end and causing machining errors. In addition, the machining path generated by the CAM software maintains a fixed feed speed during the cutting process, and does not consider the feed speed optimization between different tool positions, and the feed speed of the empty cutting path also has a large optimization space. The feed speed at different tool positions can be optimized based on the above-mentioned simulated cutting force results, so that the cutting force is more stable and the overall machining efficiency and accuracy are improved. Under the condition of meeting a given cutting force threshold, the influence of the posture-dependent dynamic characteristics on the cutting force simulation is considered, and the feed speed is optimized in sections according to the path length.

[0083] First, each machining path is divided into multiple small segments. For the initial feed rate f0 in the tool location file, the maximum milling force F of each small segment is calculated through the dynamic milling force model established in the previous chapter and the changing modal parameters. maxi The specific optimization goal is to make the cutting force along the cutting path as large as possible, but not exceeding an upper limit, that is, to minimize the allowable cutting force F per and maximum cutting force F maxi The difference between per is the preset allowable milling force, which is taken as the average value of the peak milling force in each machining path; according to F per F maxi Set a certain constraint range (F per -dF,F per +dF), dF is the change constraint of the milling force amplitude, ensuring that the maximum milling force remains relatively stable during the entire processing process; for the i-th segment feed speed f i Also set the constraint range (f min , f max ), which must not only meet the performance requirements of the robot, but also ensure that the feed changes are not too drastic; use the feed rate optimization model to obtain the optimal feed rate, and finally obtain and store the feed speed of each path milling, and assign these feed speeds to intermediate feed rate data through spline interpolation to ensure the smoothness of the feed speed of the tool during movement; output the optimized feed speed, and generate an executable file for robot milling processing experiments, and further verify the processing accuracy, efficiency and cutting force.

[0084] Another object of the present invention is to provide a milling force simulation and feed rate optimization system considering the robot posture-dependent dynamic effects, comprising:

[0085] The modal testing module is used to perform modal testing at different positions in the robot milling area. Based on the obtained robot joint angles and modal parameters, a prediction model for the reference modal parameters under the perpendicular tool axis vector is established, and the modal parameters in the instantaneous tool direction are obtained through the transformation matrix.

[0086] The model building module is used to establish the mechanical force model and dynamic model in the robot cutting area; based on the dynamic sweep trajectory of the blade and the workpiece model, the workpiece surface is dynamically updated to ensure the calculation accuracy of the instantaneous cutting thickness and cutting force;

[0087] The solution module is used to solve the steady-state dynamic displacement caused by the robot dynamics effect based on the predicted modal parameters and the initial cutting force calculated by the mechanical force model, and superimpose it on the nominal instantaneous undeformed chip thickness to calculate the instantaneous cutting force at each time step. It is then coupled with the dynamic update mechanism of the workpiece surface for iterative calculation;

[0088] The adaptive planning module is used to perform segmented adaptive planning of feed rates under cutting force peak constraints based on the simulated accurate cutting forces, and to conduct robotic milling and machining error measurement experiments on curved parts to verify the performance of the model.

[0089] Another object of the present invention is to provide a computer device, which includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the milling force simulation and feed rate optimization method considering the robot posture-dependent dynamic effects.

[0090] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the processor to perform the steps of the milling force simulation and feed rate optimization method considering the robot posture-dependent dynamic effects.

[0091] Another object of the present invention is to provide an information data processing terminal, which is used to implement the milling force simulation and feed rate optimization system that takes into account the robot posture-dependent dynamic effects.

[0092] In combination with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are as follows:

[0093] First, the present invention aims to provide a milling force simulation and feed rate optimization method that considers the dynamic effects of robot posture dependence. This method considers the impact of robot posture dependence on instantaneous cutting thickness and establishes an accurate cutting force simulation model based on the dynamic update mechanism of the workpiece surface. This method performs segmented feed rate adaptive optimization under the constraints of peak cutting force to improve machining accuracy and efficiency, stabilize cutting forces, and significantly enhance machining stability and performance.

[0094] The present invention establishes a force-position coupling iterative algorithm that takes into account the dynamic update mechanism of the workpiece surface and the posture-dependent dynamic characteristics, and realizes the accurate simulation of the cutting force during the robot surface milling process under variable workpiece placement. It has potential application value for process parameter optimization, tool wear prediction, and improvement of machining accuracy and surface quality.

[0095] This method considers pose-dependent dynamic characteristics and establishes a MTGPR model for predicting robot modal parameters with the tool axis vector perpendicular. The reference FRF is then converted to the instantaneous tool orientation. These instantaneous robot modal parameters are used in cutting force simulation to ensure the accuracy of cutting force iteration. This significantly reduces the number of experimental runs required for modal testing and analysis, thereby reducing equipment usage and time costs.

[0096] The present invention realizes adaptive planning of feed rate during milling based on simulated precise cutting force, improves machining accuracy and efficiency, makes cutting force more stable, and has the potential to be promoted to actual industrial applications.

[0097] Second, the traditional method obtains the dynamic characteristics related to the robot posture, that is, the modal parameters, through a large number of modal test experiments, while this patent uses a multi-task Gaussian process regression (MTGPR) model to simultaneously predict multiple modal parameters, effectively reducing the number of modal test experiments and testing costs. In addition, in existing industrial scenarios, the optimization of processing parameters mostly relies on empirical trial cutting or offline simulation software, which is time-consuming and cannot dynamically adapt to changing cutting conditions. This patent takes into account the dynamic effects of the robot posture and the dynamic update mechanism of the workpiece surface, pre-simulates the cutting force through a force-position coupling iterative algorithm, and optimizes the dynamic feed rate in advance based on the simulated cutting force. After the technical solution of the present invention is converted, the optimized feed rate is used to carry out milling processing experiments, which can achieve improvements in processing accuracy and efficiency, replace high-priced simulation tools, and reduce software procurement costs. The adaptive feed rate planning under the cutting force peak constraint makes the cutting force more stable, improves processing stability, avoids tool overload, reduces tool wear and replacement frequency, reduces downtime and processing costs, and increases profits.

[0098] The present invention relates to the technical field of milling force simulation and feed rate optimization. For robot milling force simulation, current research has rarely considered the dynamic update of the workpiece surface, and has ignored the influence of the dynamic characteristics of the robot posture dependence on the cutting force simulation model. It is currently believed that the dynamic characteristics of the robot (such as modal parameters) need to be obtained through frequent experiments. In addition, existing research on robot feed rate optimization has only analyzed the correlation between process parameters and processing errors, and a large number of process experiments are needed to optimize in order to obtain better process parameters. Moreover, these studies have not carried out mechanism modeling for process parameter optimization, and the experimental effect and generalization ability are poor. The present invention comprehensively considers the influence of the dynamic update mechanism of the workpiece surface and the dynamic characteristics related to the robot posture, and couples the modal parameters predicted by the multi-task Gaussian process regression model to establish a force-position coupling iterative model, thereby realizing the accurate simulation of the robot milling force. Further, offline feed rate pre-planning under peak force constraint is carried out to stabilize the cutting force and improve milling accuracy and efficiency. The technical biases overcome include a reduction in the number of modal parameter experiments, simplification of complex process flows, a reduction in the number of trial cuts and process parameter optimizations, a reduction in processing and measurement costs, and improvements in processing operation stability, safety, and reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] Figure 1 This is a flow chart of a method for milling force simulation and feed rate optimization that takes into account the robot posture-dependent dynamic effects, provided by an embodiment of the present invention.

[0100] Figure 2 This is a structural block diagram of a milling force simulation and feed rate optimization system that takes into account the robot posture-dependent dynamic effects, provided by an embodiment of the present invention.

[0101] Figure 3 It is a schematic flow chart of the basic method provided by an embodiment of the present invention.

[0102] Figure 4 This is a schematic diagram of the instantaneous RFR conversion principle provided by an embodiment of the present invention.

[0103] Figure 5 This is a schematic diagram of the ball end milling cutter and curved surface milling principle provided by an embodiment of the present invention.

[0104] Figure 6 It is a schematic diagram of calculating the instantaneous uncut chip thickness in the cutting area provided by an embodiment of the present invention.

[0105] Figure 7 It is a flow chart of force-position coupling iterative milling force simulation provided by an embodiment of the present invention.

[0106] Figure 8 This is a flow chart of feed rate planning provided by an embodiment of the present invention.

[0107] Figure 9This is a curved workpiece drawing designed according to an engine casing provided by an embodiment of the present invention.

[0108] Figure 10 2 is a diagram of a robot milling and data acquisition system provided by an embodiment of the present invention.

[0109] Figure 11 This is a diagram of a machining error measurement experiment of a workpiece provided by an embodiment of the present invention.

[0110] Figure 12 This is a diagram of a robot modal test experiment provided by an embodiment of the present invention.

[0111] Figure 13 3 is a comparison result diagram of the XX direction modal parameter prediction and measurement results provided by an embodiment of the present invention.

[0112] Figure 14 3 is a comparison result diagram of the YY direction modal parameter prediction and measurement results provided by an embodiment of the present invention.

[0113] Figure 15 3 is a graph comparing the calculated values ​​and the measured values ​​of the mechanical force model provided by an embodiment of the present invention.

[0114] Figure 16 3 is a comparison result diagram between the cutting force simulation value and the measured value of Task A provided by an embodiment of the present invention.

[0115] Figure 17 3 is a comparison result diagram between the cutting force simulation value and the measured value of Task B provided by an embodiment of the present invention.

[0116] Figure 18 3 is a comparison result diagram between the simulation value and the measured value of the cutting force of task C provided by an embodiment of the present invention.

[0117] Figure 19 3 is a graph comparing fixed and planned feed rates according to an embodiment of the present invention.

[0118] Figure 20 3 is a graph comparing cutting force and machining efficiency under fixed and planned feed rates provided by an embodiment of the present invention.

[0119] Figure 21 3 is a graph comparing contour errors produced at fixed and planned feed rates according to an embodiment of the present invention. DETAILED DESCRIPTION

[0120] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0121] The most pressing challenge in robotic milling scenarios is that the distortion of cutting forces caused by joint compliance and tool-workpiece coupled vibration can drift significantly along the pose. Traditional rigid-body mechanics models or fixed modal assumptions cannot capture this "dynamic compliance" variation, which can lead to feed overload, chatter, and surface errors. The proposed method uses multi-pose modal testing to obtain a mapping between joint angles and modal parameters. It treats the pose-related natural frequencies and damping as random fields and reconstructs a "reference frequency response cloud" in function space through multi-task Gaussian process regression, establishing a differentiable and interpolable dynamic reference surface for follow-up simulation.

[0122] To avoid anisotropy misjudgment caused by tool axis direction deflection, the algorithm first calibrates the modal parameters in the tool axis perpendicular coordinate system, and then uses a double rotation matrix consisting of the rake angle and the roll angle to implement the frequency response function transformation; this is equivalent to reprojecting the flexibility ellipsoid in the instantaneous tool coordinate system, so that the main vibration mode in any posture is coaxial with the actual cutting depth direction, thereby ensuring that there is no coordinate mismatch when the flexibility tensor participates in subsequent coupling.

[0123] The cutting force prediction process does not simply treat the milling cutter as a rigid body. Instead, the cutter axis is discretized into several microelements along the generating line and assigned radial, tangential, and axial force coefficients. The helix angle, feed vector, and axial engagement limit are then incorporated into the cutting integral kernel to generate a three-dimensional micro-cutting load flow in real time. The mechanical force field thus constructed is convolved with the predicted compliance matrix to produce a displacement response, implicitly accounting for the modulation of the steady-state amplitude by the robot's structural damping and equivalent stiffness.

[0124] After state-space expansion, the dynamic equations are solved using a fourth-order Runge-Kutta iteration. The inner loop of the iteration feeds back the displacement of each microelement to the undeformed chip thickness at the next instant, forming a closed "displacement-thickness-force" loop. Since the workpiece surface mesh is refreshed with each tooth pass cycle, the sweep trajectory is superimposed on the dynamic machining residual to generate the real-time machining topography, which in turn drives the mechanical equations to the next quasi-static equilibrium. This weakly coupled multi-physics solution chain effectively suppresses numerical divergence while precisely tracking cutting force peaks and valleys as they drift along the cutting surface.

[0125] During the feedrate planning phase, the algorithm divides the entire tool path into several arc segments and constructs a penalty function based on the difference between the maximum cutting force and the allowable force threshold in each segment. By constraining the cutting force amplitude gradient and feed jump, a smooth segmented feedrate curve is derived using quadratic programming. Spline interpolation ensures that the velocity-time curve is coherent and differentiable in the joint space, preventing acceleration saturation or vibration re-excitation at high-curvature inflection points.

[0126] In the experiment, the optimized NC program was sent to a six-axis robot. Real-time force sensing and laser three-dimensional coordinate measurement results showed that the peak cutting force was firmly suppressed below the allowable threshold, significantly reducing surface machining errors. This demonstrates that the proposed method, through the three-layer mechanism of "posture mapping-dynamic coupling-adaptive feed," linearizes the originally nonlinear, coupled, and uncertain robotic milling process into an observable, predictable, and controllable closed-loop system, achieving a systematic solution to the existing problems of mechanical model inaccuracy and machining quality fluctuations.

[0127] like Figure 1 As shown, a method for milling force simulation and feed rate optimization considering the robot posture-dependent dynamic effects provided by an embodiment of the present invention includes the following steps:

[0128] S1, modal tests are performed at different positions in the robot milling area. Based on the obtained robot joint angles and modal parameters, a prediction model of the reference modal parameters under the perpendicular tool axis vector is established, and the modal parameters in the instantaneous tool direction are obtained through the transformation matrix;

[0129] S2, establishes a mechanical force model and a dynamic model in the robot cutting area; dynamically updates the workpiece surface based on the dynamic sweep trajectory of the blade and the workpiece model to ensure the calculation accuracy of the instantaneous cutting thickness and cutting force;

[0130] S3, based on the predicted modal parameters and the initial cutting force calculated by the mechanical force model, solves the steady-state dynamic displacement caused by the robot dynamics effect, and superimposes it on the nominal instantaneous undeformed chip thickness. The instantaneous cutting force at each time step is calculated and iterative calculation is performed by coupling the dynamic update mechanism of the workpiece surface;

[0131] S4, based on the accurate cutting force of the simulation, the feed rate segmented adaptive planning under the cutting force peak constraint is carried out, and the robot milling and surface part processing error measurement experiments are carried out to verify the performance of the model.

[0132] like Figure 2 As shown, an embodiment of the present invention provides a milling force simulation and feed rate optimization system considering the robot posture-dependent dynamic effects, including:

[0133] The modal testing module is used to perform modal testing at different positions in the robot milling area. Based on the obtained robot joint angles and modal parameters, a prediction model for the reference modal parameters under the perpendicular tool axis vector is established, and the modal parameters in the instantaneous tool direction are obtained through the transformation matrix.

[0134] The model building module is used to establish the mechanical force model and dynamic model in the robot cutting area; based on the dynamic sweep trajectory of the blade and the workpiece model, the workpiece surface is dynamically updated to ensure the calculation accuracy of the instantaneous cutting thickness and cutting force;

[0135] The solution module is used to solve the steady-state dynamic displacement caused by the robot dynamics effect based on the predicted modal parameters and the initial cutting force calculated by the mechanical force model, and superimpose it on the nominal instantaneous undeformed chip thickness to calculate the instantaneous cutting force at each time step. It is then coupled with the dynamic update mechanism of the workpiece surface for iterative calculation;

[0136] The adaptive planning module is used to perform segmented adaptive planning of feed rates under cutting force peak constraints based on the simulated accurate cutting forces, and to conduct robotic milling and machining error measurement experiments on curved parts to verify the performance of the model.

[0137] Another object of the present invention is to provide a computer device, which includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the milling force simulation and feed rate optimization method considering the robot posture-dependent dynamic effects.

[0138] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the processor to perform the steps of the milling force simulation and feed rate optimization method considering the robot posture-dependent dynamic effects.

[0139] Another object of the present invention is to provide an information data processing terminal, which is used to implement the milling force simulation and feed rate optimization system that takes into account the robot posture-dependent dynamic effects.

[0140] The present invention is specifically implemented:

[0141] like Figure 3 A milling force simulation and feed rate optimization method that considers the dynamic effects of robot posture dependence is proposed. Multiple modal parameter measurement points are evenly spaced above the robot worktable. Modal testing is performed with the tool axis vector perpendicular to the worktable plane. Modal parameters are obtained using modal analysis software, while the robot joint angles are recorded at each posture. Because multiple modal parameters need to be predicted and their correlations considered, this paper employs a co-regionalized intrinsic model. A modal parameter prediction model is established using Multi-Task Gaussian Process Regression (MTGPR).

[0142] X represents the M different inputs X=(x1,x2,...,x M ) T The set of is the joint angles of all measurement points. For N modes to be predicted, the label space is expressed as:

[0143]

[0144] where y il represents the jth label value of the i-th input. For each row y of Y i , that is, all modal parameters, there are y i ={f d ,ξ d ,M d ,C d ,K d},i=1,...,M,d=x,y.

[0145] The latent function {q l} is set as a Gaussian prior to obtain the relationship between different modal parameters. Assuming that the mean of GPs is 0, let:

[0146]

[0147] Where K q is the positive semidefinite (PSD) matrix of the similarity between modal parameters, k x is the covariance function of the input vector, which captures the correlation between different poses of the same modal parameter. is the variance of the lth modal parameter.

[0148] The model is derived using the standard GP formula for the mean and variance of the predictive distribution and the covariance function given above. For a new data point x in the lth mode * (l=(l j ,j=1,...,N)), the mean prediction is calculated as follows:

[0149]

[0150] In the formula represents the Kronecker product, K q The first column of For training points and test points x * The covariance vector between x is the covariance matrix between all training point pairs. A is an M×M diagonal matrix, where the (l, l)th element is H is a MN×MN matrix.

[0151] In the training set, given a label y t , using a gradient-based method to learn the matrix K q and k x The parameter θ x , so that the marginal likelihood p(y t |X,θ x ,K q) is maximized. The Cholesky decoupling method is used to ensure K q The lower triangular matrix L can be parameterized as:

[0152]

[0153] In the formula K q The number of hyperparameters is used to optimize the hyperparameters of the MTGPR model by minimizing the negative log marginal likelihood. Given an input (x * ,l * ), according to the conditional probability P(y * |X,l,y,x * ,l * ) to calculate its predicted value. MTGPR combines multiple pose-related modal parameters in a regression model and learns the correlation between the modal parameters to improve the prediction performance.

[0154] The above modal parameters are measured when the tool axis vector is perpendicular to the robot table plane. However, in the process of performing robotic milling of complex surfaces, the direction of the tool is time-varying. L and the roll angle θ T The calculated transformation matrix transforms the frequency response function (FRF) of the modal parameter fitting to the instantaneous tool direction, and then the modal parameters are obtained by curve fitting. The reference FRF is measured in the measurement coordinate system (MCS) when the tool axis vector is perpendicular, and the instantaneous direction FRF is measured in the instantaneous coordinate system (IMCS), such as Figure 4 As shown. The transformation matrix from MCS to IMCS is defined as:

[0155] R t (θ T ,θ L )=R y (θ L )R x (θ T )

[0156] where R y (θ L ) and R x (θ T ) is expressed as:

[0157]

[0158] The inverse transformation matrix is ​​defined as:

[0159]

[0160] The force excitation and response signals are decomposed and synthesized to obtain the instantaneous FRF matrix:

[0161]

[0162] Among them, H O (ω) and H T (ω) denote the reference and instantaneous FRF matrices, respectively.

[0163] Then, the mechanical force model is established and the workpiece coordinate system (WCS) is defined in the robot multi-axis milling. WCS ,x WCS y WCS z WCS}、Tool Coordinate System (TCS) {O TCS ,x TCS y TCS z TCS} and feed coordinate system (FCS) {O FCS ,x FCS y FCS z FCS},like Figure 5 As shown. The WCS is fixed on the workpiece, the origin of the TCS is at the tool center, and z TCS Direction along the tool axis, y TCS The axis direction is from the tool center to the point z = 0 on the first edge. The origin of FCS is at the tool contact point, x FCS Along the tool path direction, z FCS Follow the normal direction of the workpiece surface. The idea of ​​the mechanical cutting force model is to discretize the milling cutter into several equal micro units along its axis. The instantaneous cutting force under TCS is the sum of the cutting forces of all micro-units on all cutting edges. Combining the calibrated radial, tangential, and axial cutting force coefficients, the cutting force is converted under TCS and expressed as:

[0164]

[0165] Where F cq (q=x,y,z) is the cutting force under TCS, N e and N z are the number of cutting edges and the number of discrete units respectively. dc (d=r,t,a) represents radial, tangential and axial shear force coefficients. K de (d=r,t,a) represents the radial, tangential and axial blade force coefficients. Δb is the width of the cutting unit, which is given by Δb=Δz / sink(z i ) is calculated, where Δz is the height of the discrete unit, k(z i )=cos -1 ((Rz i ) / R) represents the height z iThe axial immersion angle at the cutting edge is 0.001mm. R is the tool radius. The upper and lower limits of the axial engagement of the cutting edge are determined by the rake angle and side rake angle of the tool and the instantaneous curvature of the workpiece surface. M is the rotation transformation matrix from the micro-cutting force to the tool coordinate system, which is expressed as:

[0166]

[0167] Indicates the jth cutting edge at the axial height z i The radial immersion angle at

[0168]

[0169] Where n s is the spindle speed, ψ picth =2π / N and β represent the pitch angle between two consecutive edges and the helix angle of the tool respectively. ds is the length of the cutting edge element, calculated as:

[0170]

[0171] In the above formula is the theoretical instantaneous undeformed chip thickness of the cutting edge element, which can be expressed as:

[0172]

[0173] Where f pt is the feed per tooth, which can be calculated as f pt =f / (N e ·n s ), f is the feed rate.

[0174] In the above formula is a function that characterizes the cutting edge's penetration or extrusion, and is defined as:

[0175]

[0176] in, and The tool axial height z is i The entry and exit angles at the .

[0177] Finally, the cutting force is converted to WCS and expressed as:

[0178] [F w 1] T =B[F cx F cy F cz 1] T

[0179] Where B is the transformation matrix from TCS to WCS, which is related to the rake angle and side rake angle of the tool.

[0180] Influenced by the robot's dynamic effects, the tool undergoes dynamic displacement under the action of cutting forces. This dynamic displacement significantly affects both the current cutting edge position and the machined surface formed by the previous cutting edge's sweep, resulting in a dynamic undeformed chip thickness and a time-varying tool-workpiece engagement (CWE) area. After obtaining the initial cutting forces, the robot milling dynamics model for the cutting area is established as follows:

[0181]

[0182] Where M c , C c and K c are the mass matrix, damping matrix and stiffness matrix of the robot milling system, respectively, expressed as:

[0183] M c =diag(m x ,m y ,m z ),C c =diag(c x ,c y ,c z ),K c =diag(k x ,k y ,k z )

[0184] In the tool coordinate system, the Z-direction has much higher stiffness than the X- and Y-directions, and the cutting forces in the Z-direction are generally smaller. Therefore, only the dynamic vibrations and modal parameters in the X- and Y-directions are considered. The dynamic model is a second-order ordinary differential equation, which can be solved using algorithms such as the Runge-Kutta algorithm. First, the state vector is defined and converted into a system of first-order differential equations to improve computational efficiency. This is expressed as:

[0185]

[0186] The actual position of the cutting edge is further determined using the dynamic displacement calculated at each time step.

[0187] To obtain the cutting topography of the workpiece surface, a dynamic cutting edge sweep trajectory must first be established based on the tool parameters, tool location information, and the resulting dynamic displacement. As the tool rotates along the tool location, the actual position and sweep trajectory of all height points on the tool edge at each time step are determined, taking into account the influence of the tool's motion trajectory and dynamic displacement.

[0188] During robot machining, the tool path under the WCS is represented as:

[0189]

[0190] where tp plan (t) is the planned tool path, x plan (t), y plan (t), z plan (t) is the position in three directions. v(t) is the tool axis vector, and a(t), b(t), and c(t) are the Euler angles describing the posture.

[0191] disp dy (t){[x vib (t)y vib (t)z vib (t)] T} is the dynamic displacement of the robot milling area under TCS, which is converted to WCS and expressed as:

[0192]

[0193] Typically, the planned tool path tp plan (t) is expressed in terms of the tool contact point. n(t) is the normal vector of the tool contact point on the machined surface, and O(t) is the tool center point. To calculate the swept area of ​​the tool edge, O(t) is expressed in terms of the WCS as:

[0194]

[0195] In TCS, the height z of the jth edge is i The blade point position C(j,z i ) is calculated as:

[0196]

[0197] Where β is the helix angle. The tool position curve and the corresponding tool axial vector are then considered to calculate the tool edge sweep surface. The calculation in WCS is as follows:

[0198] S p (t,j,z i )=O(t)+BR(ωt)C(j,z i )

[0199] Where ω = 2πn s / 60 is the angular velocity, and R(ωt) is the rotation matrix about the tool axis.

[0200] The workpiece surface is represented as a Z-map vector aligned with the Z axis, passing through grid points on the XY plane. Then, combining the simulated dynamic sweep trajectory and cutting parameters, the intersection of the Z-map vector and the tool sweep surface is calculated, and the vector is updated, thereby dynamically updating the machined surface topography. Considering the differences in cutting between different blades and the timeliness of cutting load calculation, a dynamic update mechanism for the machined surface within the blade cycle is proposed. Within the first rotation range of the tool entering the workpiece, the robot is assumed to be rigid, and the initial machined surface is generated according to the theoretical trajectory of the tool motion. At each subsequent discrete time step, the instantaneous dynamic displacement is calculated according to the proposed method. The dynamic displacement is superimposed on the theoretical tool center point position, and then combined with the position of the blade point to obtain the new actual blade sweep trajectory point, which is then stored. The machined surface of the workpiece is updated after a blade cut is completed, and the workpiece surface update along the entire path is completed according to this update mechanism and the tool feed.

[0201] Based on the above-mentioned blade sweep trajectory model and the dynamic update mechanism of the machined surface, the coupled robot dynamics model and the mechanical force model can realize the accurate calculation of the instantaneous undeformed chip thickness and micro-element load under the influence of dynamic displacement, and then calculate the instantaneous dynamic cutting force. The simulation process is discretized into a series of instantaneous time steps. At each time step, the micro-cutting force of all micro-elements on the spiral milling cutter will be calculated. During the initial tool rotation cycle of the simulation, the initial cutting force F is calculated using the rigid body cutting force model. ini , and generate the initial workpiece machining surface. Then, combined with the robot joint angle, the modal parameter prediction model is used to predict the modal parameters under continuous machining postures. The calculated initial cutting forces in the X and Y directions are brought into the dynamic model of the cutting area to perform dynamic displacement in the X and Y directions. and The actual blade position point S is obtained by superimposing it on the theoretical trajectory point P , expressed as:

[0202]

[0203] In order to simplify the calculation process and improve the calculation efficiency, and considering the influence of the theoretical trochoid motion trajectory of the cutting edge point and the dynamic displacement of the robot, the instantaneous undeformed chip thickness is calculated in the tool coordinate system, as follows: Figure 6 As shown. The center point of the current tool is O, and the straight line OS P The intersection point with the previous cutting tool path is S T , which can be determined by the straight line equation and interpolation curve model, S P S T The length of is the actual instantaneous undeformed chip thickness, and then the instantaneous cutting force is calculated, which is expressed as:

[0204]

[0205] in, and Represents the actual cutting edge point position on the cutting path generated by the current cutting edge and the previous cutting edge tooth pass cycle. τ=60 / N e n s is the tooth-passing cycle.

[0206] The cutting force is used as the excitation source to calculate the new dynamic displacement and actual position. When the difference between adjacent actual position prediction results is less than the set threshold, it is considered to have converged, and the actual position is stored, and then the simulation prediction of the next time step begins. After the cutting of the cutting edge is completed, the interpolation algorithm is used to interpolate the actual position points at each time step to update the machined surface. The subsequent blades calculate the dynamic displacement, instantaneous undeformed chip thickness and cutting force based on this surface, and perform iterative updates until the end of the simulation. The subsequent blades calculate the dynamic displacement, instantaneous undeformed chip thickness and cutting force based on this surface, and perform iterative updates until the end of the simulation. The detailed iterative simulation process can be seen. Figure 7 .

[0207] Due to the influence of the robot's posture-dependent dynamic characteristics, the robot end has weak stiffness in certain postures, and under the action of the milling force, it will produce more significant dynamic stiffness deformation, reducing the end's processing performance and causing processing errors. In addition, the processing path generated by the CAM software maintains a fixed feed speed during the cutting process, and does not consider the feed speed optimization between different tool positions. The feed speed of the empty cutting path also has a large optimization space. The feed speed at different tool positions can be optimized based on the above-mentioned simulation cutting force results, making the cutting force more stable and improving the overall processing efficiency and accuracy. Under the condition of meeting a given cutting force threshold, the influence of the posture-dependent dynamic characteristics on the cutting force simulation is considered, and the feed speed is optimized in segments according to the path length.

[0208] First, each machining path is divided into multiple segments. For the initial feed rate f0 in the tool location file, the maximum milling force F of each small segment is calculated using the dynamic milling force model established in the previous chapter. maxi The specific optimization goal is to make the cutting force along the cutting path as large as possible, but not exceeding an upper limit, that is, to minimize the difference between the allowable cutting force and the maximum cutting force, which is defined as:

[0209] min(F per -F maxi )

[0210] Among them F per is the preset allowable milling force, which is the average of the peak milling forces in each machining path. The constraints are:

[0211]

[0212] Where dF is the change constraint of the milling force amplitude, ensuring that the maximum milling force remains relatively stable during the entire machining process. min With f max The feed speed constraint range must meet the robot's performance requirements and ensure that the feed change is not too drastic. i is the feed rate of the i-th small path.

[0213] Use the permissible milling force F according to the following formula per Calculate the feed rate f i , the iteration method is as follows:

[0214]

[0215] Simulate new feed rate f i Maximum milling force F′ under maxi If F′ maxi If the optimization goal is not met, the optimal feed rate f is determined by further iterative calculation using the following formula i ′, and recalculate the maximum milling force until the preset constraints are met.

[0216]

[0217] And f i The range of ′ must satisfy the constraints.

[0218] Finally, the feed rate of each path milling is obtained and stored, and these feed rates are assigned to the intermediate feed rate data through spline interpolation to ensure the smoothness of the feed rate during the tool movement. The optimized feed rate is output and an executable file is generated for robot milling processing experiments to further verify the processing accuracy, efficiency and cutting force. The overall optimization process is as follows Figure 8 shown.

[0219] The curved surface parts designed for milling experiments are derived from the inner and outer airway surfaces of the engine casing scale parts, such as Figure 9 (a) Based on the extracted feature surfaces, three workpieces of 6061 aluminum alloy were designed, as shown in Figure 9 (b) To verify the versatility and practicality of the cutting force simulation and process parameter optimization model, three machining tasks, A, B, and C, were designed, as shown in Table 1. The model's generalization capability is reflected in three aspects: the variability of the workpiece surface shape and size, and the variability of the workpiece placement. This enriches the diversity of process information expressed between cutting forces, machining errors and process parameters, machined surface features, and workpiece placement.

[0220] Table 1 Designed processing tasks

[0221]

[0222] The overall scheme of the robot milling system is as follows Figure 10 As shown. The milling experiment was carried out using a six-degree-of-freedom industrial robot (COMAU Smart5 NJ 220-2.7). The maximum load of the robot is 220 kg and the repeatability is 0.06 mm. The maximum speed of the milling spindle (Jager Z100-H540.08 S3W2) is 30,000 rpm and the maximum torque is 5 Nm. The dynamometer (Kistler 9129AA) is installed on the workbench, the workpiece is fixed on the dynamometer, and the cutting force sampling frequency is 25 kHz. A double-flute carbide ball end mill (SANDVIK 2B330-1000-NC H10F) with a diameter of 10 mm and a helix angle of 40° was used for rough milling experiments. The planned path was used to remove the entire surface of the curved part, and the processing parameter settings are shown in Table 2.

[0223] Table 2 Milling processing parameters

[0224]

[0225] The workpiece after milling was measured using a three-dimensional coordinate measuring machine (HEXAGON GLOBAL Classic SR 07.10.07) to obtain the machining error, such as Figure 11 The device's measurement accuracy is approximately 1 μm, which meets measurement requirements. The contour error is calculated based on the measurement results and used to evaluate part machining errors.

[0226] The workpiece is mounted on a workbench with a certain height. The height of the workpiece is small, so the position range of the tool tip in the XY plane is larger than the position range in the Z direction. In order to cover the installation area of ​​the workpiece and make the acquired position cover the milling task on the workbench as much as possible, the workspace above the workbench is gridded to obtain 24 tool tip measurement points, including two planes of Z = 900mm and 1000mm. At each measurement point, the tool axis is perpendicular to the XY plane. Considering the feasible range of the redundant angle and its influence on the posture, the redundant angle with a large range of changes in each position is used. like Figure 12 (a) is shown. Therefore, the total number of measured postures is 168. An impact hammer (PCB086C01) is used to generate force excitation, and a micro accelerometer (PCB352C23) is fixed on the tool tip to detect the response. The impact test is repeated three times for each measurement point, and the average of the three results is taken as the tool tip frequency response of the posture to ensure the validity of the experimental data. Figure 12(b) The modal test analysis module of CutPro software is used to process and analyze the signals and collect the joint angles of the robot at each position.

[0227] The modal parameters obtained from modal analysis include modal frequency f n , damping ratio ξ m and modal stiffness K c Although the robot system has multiple vibration modes, the main mode contributes the most to the cutting force calculation during robot milling. Then, the modal mass M is obtained by the following formula c and modal damping C c :

[0228]

[0229] 30% of the training data, i.e. 50 measured poses, were selected as the test set for the model. 2 The value is used to evaluate the prediction performance of the model, which is defined as:

[0230]

[0231] Where, and are the predicted and measured values, respectively. is the average value of the measured results, n t is the sample size. The scatter plot of the predicted and measured values ​​in the test set XX and YY directions is as follows: Figure 13 and 14 As shown, the R 2 The values ​​are all above 0.9. The results show that the predicted values ​​are in good agreement with the measured values, indicating that the method can well capture the data trends. For some locations, the prediction accuracy is slightly lower, but it is within the range allowed by the dynamic modeling.

[0232] To further validate the trained MTGPR model, two additional poses not included in the training set were selected for modal parameter prediction. The prediction results and prediction accuracy are shown in Table 3. As can be seen from Table 3, the prediction accuracy for modal parameters in all directions is greater than 90%, demonstrating good prediction performance. The robot's joint angles are calculated through inverse kinematics of the machining poses in the milling task, and then used to predict changes in modal parameters. The predicted reference modal parameters are fitted to obtain a frequency response function matrix. The frequency response function of the tool posture that changes over time is then calculated based on the rake and roll angles during machining. Assuming that changes in modal parameters are ignored within a small robot motion range, each machining trajectory on the workpiece is divided into 10 segments. The modal parameters of each segment are obtained through curve fitting and used for cutting force simulation and feed rate optimization.

[0233] Table 3 Comparison of predicted and measured modal parameters for specific poses

[0234]

[0235] Milling experiments using the same tool-workpiece material combination as in the robotic milling experiments were conducted on a CNC machine tool to calibrate the cutting force coefficient. A total of six slot milling experiments were conducted at different feed rates, with the machining parameters shown in Table 4.

[0236] Table 4 Process parameters used to calibrate cutting force coefficient

[0237]

[0238] The cutting force coefficient is fitted and calibrated using the average cutting force and least squares method. The results are as follows:

[0239] K rc =304.7167 K re =8.0255

[0240] K tc =-819.0586 K te =-6.7657

[0241] K ac =-148.44 K ae =-1.8494

[0242] Where K rc , K tc and K ac are the shear cutting force coefficients in radial, tangential and axial directions, K re , K te and K ae are the radial, tangential and axial edge force coefficients, respectively.

[0243] The cutting force under the sixth group of machining parameters in Table 4 was calculated using the rigid body mechanical force model combined with the calibrated cutting force coefficient, and compared with the measured values ​​of the machine tool and robot milling experiments under the same machining parameters. Figure 15 As shown in the figure, the established mechanical force model can accurately simulate the milling force of the machine tool, and the accuracy of the calibrated cutting force coefficient has been verified. However, since the dynamic deformation and instantaneous cutting thickness changes under the influence of robot dynamics are not considered, there are significant differences with the actual measured values ​​of robot milling.

[0244] A low-pass filter with a cutoff frequency of 1000Hz is used to eliminate the noise fluctuations contained in the original measured cutting force data. The predicted modal parameters and calibrated cutting force coefficients are used for further cutting force simulation. The cutting force simulation method proposed above is used to calculate the cutting force under different machining tasks. The workpiece under each machining task contains multiple milling trajectories, and partial segments of two trajectories are selected for cutting force simulation to verify the simulation accuracy of the model. The selected trajectories are named: AT1, AT2, BT1, BT2, CT1 and CT2. The adaptability of the model is reflected in two aspects. First, during the machining of a single trajectory, the posture-dependent modal parameters of the robot will cause changes in the calculated dynamic displacement and instantaneous undeformed chip thickness, thereby leading to changes in the cutting force peak. Secondly, the application of different process parameters under different machining tasks will also produce different cutting force distribution profiles. The comparison results are shown in Figure 2. Figure 16-18 Figure 2 shows the simulated and measured cutting force distributions for machining tasks A, B, and C, respectively. The results show that the proposed model achieves good simulation accuracy in both cases. The profiles between the calculated and measured values ​​match well, and although there are some deviations in local areas, they are within an acceptable range.

[0245] Peak cutting force is particularly important for robot milling condition monitoring. Therefore, the peak values ​​of the simulated and measured cutting forces at each rotation cycle were extracted and compared statistically. The mean absolute error (MAE) and root mean square error (RMSE) were used as evaluation indicators for model prediction performance, defined as follows:

[0246]

[0247] Where, and are the ith simulation value and measured value, n f is the sample size. The performance evaluation indicators are listed in Table 5. The results show that the deviation between the extracted simulation and measured cutting force peaks is small, and the RMSE is less than 15% of the cutting force peak, showing good prediction accuracy.

[0248] Table 5 Results of simulation model performance evaluation indicators

[0249]

[0250] Based on the precise cutting force obtained from the simulation, the feed rate planning method proposed above is used to optimize the feed rate. The milling force amplitude change constraint dF is set to 5% of the allowable force. The minimum feed rate is set to 100 mm / min and the maximum feed rate is set to 800 mm / min. In order to improve the processing efficiency, the feed rate of the air cutting is set to 1200 mm / min. The results of the segmented optimized feed rate are interpolated, and the feed rate before and after planning is compared. Figure 19The feed rate is kept constant during optimization, and the feed rate is optimized under the cutting force peak constraint during the cutting stage. The results show that the designed method can achieve adaptive feed rate planning for milling paths under the cutting force peak constraint.

[0251] The proposed feed rate planning method takes into account the robot modal parameters that are posture-dependent during the machining process, achieves accurate cutting force simulation, and performs segmented feed rate adaptive planning under the constraint of the cutting force peak. Compared with the fixed feed rate maintained before optimization, larger cutting forces are easily generated at positions where the feed and robot rigidity are poor. By reducing the feed rate to stabilize the cutting force, the cutting force peak is reduced. The cutting force is collected during the milling process, and the machining error of the workpiece before and after speed planning is measured. The cutting force of each trajectory is divided into ten segments, the peak value of each segment is taken, and the average value of the cutting force peak under each machining task is calculated. The comparison of machining time and cutting force before and after feed rate optimization is shown in Figure 2. Figure 20 As shown in the figure, after the feed rate is optimized, the peak value of the cutting force is effectively reduced and the processing efficiency is improved. The specific processing performance indicators are compared in Table 6, where the indicators of the overall task are the average values ​​of each task. The peak cutting forces of tasks A, B and C are reduced by 53.94%, 46.02% and 52.82% respectively, the average values ​​of the peak cutting forces are reduced by 23.56%, 24.04% and 20.73% respectively, and the processing time is reduced by 29.69%, 36.31% and 28.56% respectively. The processing errors of the workpiece before and after feed rate optimization are shown in Table 6. Figure 21 As shown in the figure, after parameter optimization, the part processing error is significantly reduced. After feed rate planning, the maximum value of the contour error of tasks A, B, and C is reduced by 34.98%, 43.96%, and 33.13%, respectively, and the mean value of the contour error is reduced by 34.17%, 31.41%, and 29.46%, respectively.

[0252] Table 6 Comparison of machining performance indicators under fixed feed rate and planned feed rate

[0253]

[0254] The specific application fields or related products of the present invention.

[0255] Data-driven intelligent production: The present invention realizes the simulation of cutting force and feed rate optimization of robot milling processing by utilizing data such as tool and workpiece information, cutting force coefficient, process parameters, posture-dependent robot dynamic characteristic parameters, and processing path information. In an intelligent manufacturing environment, these data can be integrated into the enterprise's big data platform, and potential rules and optimization points in the processing process can be mined through data analysis. For example, according to the characteristics of different product parts, the milling force can be intelligently simulated, and the robot's processing path planning, cutting parameter settings, etc. can be adjusted to achieve personalized and precise production plan customization. This not only improves production efficiency, but also enhances the stability and reliability of the entire automated production process, ensures the consistency of product quality, and enables robot milling processing to be better integrated into the production line of intelligent manufacturing and industrial automation.

[0256] Ensuring precision machining accuracy: Precision machining applications, such as aerospace components and high-end medical devices, place high demands on machining accuracy. Feed rate optimization technology based on robotic milling cutting force simulation utilizes optimized feed rates to conduct milling experiments, effectively reducing machining errors and improving machining efficiency. Pre-optimizing machining parameters before part production can effectively reduce the number and time costs of trial cutting and parameter tuning. This achieves the coordinated development of precision machining and efficient production, meeting the dual demands of modern manufacturing for high-quality and efficient production.

[0257] Extending tool life: Cutting force is one of the key factors affecting tool life. Robotic milling cutting force simulation technology can accurately predict cutting force before machining. By analyzing the relationship between cutting force, feed rate, and machining error, if excessive cutting force is found to cause excessive tool wear, cutting parameters can be adjusted promptly, such as reducing the feed rate. This reduces tool load, effectively extending tool life, reducing the frequency and cost of tool replacement, and improving tool resource utilization.

[0258] Reduce energy consumption: During robotic milling, improper machining parameter settings (such as excessive cutting speeds and cutting forces) often lead to excessive energy consumption. Milling force simulation and feed rate optimization technologies can optimize the feed rate before actual production. For example, if a location with large machining errors is found to be due to excessive feed speeds and cutting forces, reducing the feed rate, and thus the cutting forces, can not only improve machining accuracy but also reduce the additional energy consumption required to overcome the excessive cutting forces, thereby achieving the goal of energy conservation and emission reduction.

[0259] In summary, the milling force simulation and feed rate optimization technology of robotic milling has extensive and important applications in many important fields, and is of great significance for improving the robot processing performance and the overall level of the manufacturing industry and achieving sustainable development.

[0260] Relevant evidence of the technical effects achieved by the embodiments of the present invention.

[0261] Modal parameter prediction model: The proposed MTGPR model is used to predict the modal parameters. The scatter plots of the predicted values ​​and measured values ​​in the XX and YY directions of the test set are shown in Figure 2. Figure 13 and 14 As shown, the R between the predicted value and the measured value 2 The values ​​are all above 0.9. The results show that the predicted values ​​are in good agreement with the measured values, indicating that the method can effectively capture data trends. For some positions, the prediction accuracy is slightly lower, but within the range allowed by dynamic modeling. To further validate the trained MTGPR model, two additional poses not included in the training set were selected for modal parameter prediction. The prediction results and prediction accuracy are shown in Table 3. As can be seen from Table 3, the prediction accuracy of the modal parameters in all directions is greater than 90%, demonstrating good prediction performance.

[0262] Milling force simulation accuracy: The proposed cutting force simulation method is used to calculate the cutting force under different machining tasks. The workpiece under each machining task contains multiple milling trajectories. Partial segments of two of the trajectories are selected for cutting force simulation to verify the simulation accuracy of the model. The adaptability of the model is reflected in two aspects. First, during the machining of a single trajectory, the posture-dependent modal parameters of the robot will cause changes in the calculated dynamic displacement and instantaneous undeformed chip thickness, thereby causing changes in the peak cutting force. Secondly, the application of different process parameters under different machining tasks will also produce different cutting force distribution profiles. The comparison results are as follows. Figure 16-18 As shown in the figure, the simulated and measured cutting force distribution diagrams of machining tasks A, B and C are shown respectively. The results show that the proposed model can achieve good simulation accuracy in both cases. The contours between the calculated and measured values ​​match well, and although there are some deviations in local areas, they are within an acceptable range. Peak cutting force is particularly important for robot milling state monitoring. Therefore, the peak values ​​of the simulated and measured cutting forces in each rotation cycle are extracted and compared statistically. The mean absolute error (MAE) and root mean square error (RMSE) are used as evaluation indicators of the model prediction performance, and the performance evaluation indicators are listed in Table 5. The results show that the deviation between the extracted simulated and measured cutting force peaks is small, and the RMSE is less than 15% of the maximum cutting force value, showing good prediction accuracy.

[0263] Feed rate optimization effect: Based on the precise cutting force of the simulation, the feed rate planning method is used to optimize the feed rate. The feed rate before and after planning is compared. Figure 19As shown. The feed rate before optimization is kept constant, and the feed rate is optimized under the cutting force peak constraint during the cutting stage. The results show that under the cutting force peak constraint, the designed method can realize adaptive feed rate planning of the milling path. The proposed feed rate planning method takes into account the robot modal parameters that depend on the posture during the processing, realizes accurate cutting force simulation, and performs segmented feed rate adaptive planning under the cutting force peak constraint. Compared with the fixed feed rate maintained before optimization, a larger cutting force will be generated at the position where the feed and robot rigidity are poor. By reducing the feed rate to stabilize the cutting force, the cutting force peak is reduced. The cutting force is collected during the milling process, and the machining error of the workpiece before and after speed planning is measured. The cutting force of each trajectory is divided into ten segments, the peak value of each segment is taken, and the average value of the cutting force peak under each processing task is calculated. The comparison of processing time and cutting force before and after feed rate optimization is shown in Figure 2. Figure 20 As shown in the figure, after the feed rate is optimized, the peak value of the cutting force is effectively reduced and the processing efficiency is improved. The specific processing performance indicators are compared in Table 6, where the indicators of the overall task are the average values ​​of each task. The peak cutting forces of tasks A, B and C are reduced by 53.94%, 46.02% and 52.82% respectively, the average values ​​of the peak cutting forces are reduced by 23.56%, 24.04% and 20.73% respectively, and the processing time is reduced by 29.69%, 36.31% and 28.56% respectively. The processing errors of the workpiece before and after feed rate optimization are shown in Table 6. Figure 21 As shown in the figure, after parameter optimization, the part processing error is significantly reduced. After feed rate planning, the maximum value of the contour error of tasks A, B, and C is reduced by 34.98%, 43.96%, and 33.13%, respectively, and the mean value of the contour error is reduced by 34.17%, 31.41%, and 29.46%, respectively.

[0264] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware portion can be implemented using dedicated logic; the software portion can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. Those skilled in the art will appreciate that the above-mentioned devices and methods can be implemented using computer-executable instructions and / or contained in processor control code, for example, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, or can be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0265] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with this technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered by the scope of protection of the present invention.

Claims

1. A method for milling force simulation and feed rate optimization considering the robot posture-dependent dynamic effects, characterized in that: The following steps are involved: a. Perform modal testing at multiple positions within the robot's milling area. Based on the acquired joint angles and modal parameters, establish a reference modal parameter prediction model when the tool axis is perpendicular to the work plane. Then, obtain the modal parameters in the instantaneous tool direction through coordinate transformation. b. Establish a mechanical cutting force model and a robot dynamics model in the milling area. Based on the modal parameters predicted in step a and the initial cutting force calculated using the rigid-body mechanical cutting force model, solve for the steady-state dynamic displacement caused by the robot dynamics. This displacement is then superimposed on the nominal instantaneous undeformed chip thickness to obtain the actual blade sweep trajectory. c. Dynamically update the workpiece surface using the actual blade dynamic sweep trajectory and the workpiece model. Simultaneously, the instantaneous cutting thickness and cutting force at each time step are iteratively calculated based on this blade sweep trajectory calculation method and update mechanism. c. d. Based on the accurate cutting force obtained in step c, perform segmented adaptive planning of the feed rate under the cutting force peak constraint, and output the optimized feed rate for robotic milling processing.

2. The method according to claim 1, wherein In step a, a multi-task Gaussian process regression is used to construct a modal parameter prediction model, and the prediction accuracy is improved by jointly learning the correlation between the modal parameters.

3. The method according to claim 1, wherein The mechanical cutting force model of step b discretizes the milling cutter into several micro-units of equal length along the axial direction, calculates the radial tangential axial component of each micro-unit and sums them in the tool coordinate system to obtain the instantaneous cutting force.

4. The method according to claim 1, wherein The robot dynamics model in step b only considers the vibration of two degrees of freedom in the tool plane, establishes the second-order differential equations of mass, damping, and stiffness, and uses numerical integration to solve the dynamic displacement.

5. The method according to claim 1, wherein In step d, each machining path is divided into several segments, and the optimal feed rate is obtained by minimizing the difference between the preset allowable cutting force and the maximum cutting force of each segment and applying cutting force amplitude constraints and feed change constraints.

6. A milling force simulation and feed rate optimization system considering the robot posture-dependent dynamic effects, characterized in that: include: Modal testing module, used to collect joint angles and modal parameters in different postures and establish a modal parameter prediction model; The model building module is used to build a mechanical cutting force model and a robot dynamics model, solve the actual cutting thickness based on the predicted modal parameters and the initial cutting force, and calculate the actual blade trajectory; The solution module is used to dynamically update the workpiece surface according to the actual dynamic sweep trajectory of the blade and the workpiece model, and iteratively calculate the instantaneous cutting thickness and cutting force at each time step; The adaptive planning module is used to optimize the feed rate in sections under the cutting force peak constraint and output the optimization results.

7. The system according to claim 6, wherein: The modal test module includes an excitation device, a response sensor and a data processing unit. The data processing unit uses a multi-task Gaussian process regression algorithm to generate a modal parameter prediction model.

8. A computer-readable storage medium having instructions stored thereon, wherein when the instructions are executed by a processor, the processor is caused to perform the method according to any one of claims 1 to 5.

9. A control device, comprising a processor and a memory, wherein the memory stores instructions, and when the instructions are executed by the processor, the processor: executes the method described in any one of claims 1 to 5, generates an optimized feed speed, and sends the feed speed to the robot control system through a communication interface.

10. A robotic milling device comprising an industrial robot, a milling spindle and the control device according to claim 9, characterized in that: When the equipment executes the optimized feed speed output by the control device, the instantaneous cutting force peak of the entire processing path does not exceed the preset allowable cutting force, thereby ensuring that the processing error of the curved surface part is lower than the predetermined tolerance.

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