Milling force simulation and feed rate optimization considering robot pose-dependent dynamic effects

Abstract

The application belongs to the technical field of robots, and discloses a milling force simulation and feed rate optimization method considering the pose-dependent dynamic effect of a robot. The application firstly performs modal testing at different poses in the milling area of the robot. Then, a dynamic model is established in the cutting area of the robot. At the same time, the workpiece surface is dynamically updated based on the dynamic sweeping track of the cutting edge and the workpiece model, so as to ensure the calculation accuracy of the instantaneous cutting thickness and the cutting force. Finally, based on the simulated accurate cutting force, the feed rate is segmented and adaptively planned under the constraint of the cutting force peak value, and the robot milling of the curved surface part and the machining error measurement experiment are carried out. The application realizes the effective improvement of the milling machining efficiency and accuracy of the curved surface part, and the cutting force in the machining process is more stable. The application has important significance for the improvement of the stability and machining performance in the robot machining process.

Description

Technical Field

[0001] This invention belongs to the field of robotics technology, and in particular relates to a method for milling force simulation and feed rate optimization that considers the pose-dependent dynamic effects of robots. Background Technology

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

[0003] By accurately simulating milling forces, we can gain a deeper understanding of the variation patterns of milling forces under different process parameters before machining, predict potential machining defects such as excessive cutting forces and tool breakage, and thus optimize machining plans in advance, effectively avoiding abnormal situations during machining and significantly improving product quality. Simultaneously, optimizing process parameters through milling force simulation can significantly improve machining efficiency and reduce machining costs while ensuring machining quality, achieving efficient resource utilization. This not only helps enhance a company's competitiveness in the market but is also a key link in promoting the intelligent and high-end development of the manufacturing industry.

[0004] Current research on simulation of cutting forces in robotic milling largely remains at the numerical simulation stage, lacking actual milling experiments to verify the accuracy of the simulation models. A few studies have conducted experimental verification, but these did not consider the impact of robot pose-dependent dynamics on the instantaneous undeformed chip thickness, nor the dynamic updates of the workpiece surface. Furthermore, all studies only conducted linear milling of planar workpieces, neglecting robotic milling experiments on complex curved surfaces. In addition, the dynamic characteristics of robotic milling systems are heavily dependent on pose, exhibiting significant variations in their distribution across the workspace. This leads to low stability in robotic milling, with marked changes in milling performance across different machining zones and a narrow window of available process parameters. Therefore, process parameter optimization is crucial for improving machining accuracy. Existing research primarily focuses on machining error compensation and stability prediction based on simulated or predicted cutting forces, lacking research on process parameter optimization based on simulated robotic milling forces. Therefore, a method for optimizing process parameters based on simulated robotic milling forces is urgently needed.

[0005] Based on the above analysis, the problems and shortcomings of the existing technology are as follows:

[0006] (1) At present, most of the simulation studies on cutting forces in robot milling are still in the numerical simulation stage, and no actual milling experiments have been conducted to verify the accuracy of the simulation model. A few studies have conducted milling experiments to verify the model, but they have not considered the influence of robot pose-dependent dynamic effects on the instantaneous undeformed chip thickness, as well as the dynamic updates of the workpiece surface. Furthermore, all of these studies have only carried out linear milling of planar workpieces and have not conducted robot milling experiments on complex curved parts.

[0007] (2) The dynamic characteristics of the robot milling system are heavily dependent on the pose, 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 machining areas, and a narrow window of available process parameter options. Therefore, process parameter optimization is of great significance for improving machining accuracy.

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

[0009] To address the problems existing in the prior art, this invention provides a method for milling force simulation and feed rate optimization that considers the dynamic effects dependent on robot pose.

[0010] This invention is implemented as follows: a milling force simulation and feed rate optimization method considering robot pose-dependent dynamic effects includes:

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

[0012] S2, establish mechanical force and dynamic models in the robot cutting area; dynamically update the workpiece surface based on the dynamic sweep trajectory of the cutting edge and the workpiece model to ensure the accuracy of instantaneous cutting thickness and cutting force calculation;

[0013] S3, based on the predicted modal parameters and mechanical force model, the initial cutting force is calculated to solve the steady-state dynamic displacement caused by the robot dynamics effect, and superimposed 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 workpiece surface dynamic update mechanism.

[0014] S4. Based on the accurate cutting force obtained from simulation, piecewise adaptive planning of feed rate under peak cutting force constraint is carried out, and robot milling and machining error measurement experiments on curved parts are conducted to verify the performance of the model.

[0015] Furthermore, in step S1, multiple measurement points for modal parameters are uniformly set in the area above the robot's worktable. Modal testing is performed with the tool axis vector perpendicular to the worktable plane. Modal parameters are obtained using modal analysis software, and the robot joint angles at each pose are recorded. Since it is necessary to predict multiple modal parameters and consider the correlation between modal parameters, this paper establishes a modal parameter prediction model based on a common-region intrinsic model and using Multi-Task Gaussian Process Regression (MTGPR).

[0016] Indicates by Different inputs The set that constitutes the joint angles of all measured points; for There are 3 modes to be predicted, and their label space is represented as follows:

[0017]

[0018] in This represents the j-th tag value of the i-th input; for each line That is, all modal parameters, have ;

[0019] latent function To obtain the relationship between different modal parameters, a Gaussian prior is set up. Assuming the mean of GPs is 0, let:

[0020]

[0021] In the formula A positive semi-definite (PSD) matrix describing the similarity between modal parameters. Let be the covariance function of the input vector, which captures the correlation between different poses of the same modal parameter. Let be the variance of the l-th modal parameter;

[0022] This model is derived using the standard GP formula for the mean and variance of the prediction distribution, as well as the covariance function given in the above formula; for new data points in the l-th mode... The mean prediction is calculated as follows:

[0023]

[0024] In the formula Represents the Kronecker product. for The lth column, For training points and test points The covariance vector between them The covariance matrix between all training point pairs; It is A diagonal matrix, where the (l, l)th element is , It is matrix;

[0025] In the training set, given labels A gradient-based method is used to learn the matrix. and parameters Make the edges seem similar Maximize; ensured by using the Cholesky decoupling method. Positive semi-determinism; lower triangular matrix It can be parameterized as:

[0026]

[0027] In the formula for The number of hyperparameters is determined by optimizing the hyperparameters of the MTGPR model by minimizing the negative log marginal likelihood; given an input... According to conditional probability The predicted values ​​are calculated; MTGPR combines multiple pose-related modal parameters into a regression model and learns the correlation between modal parameters, thereby improving prediction performance.

[0028] Furthermore, the modal parameters are measured when the tool axis vector is perpendicular to the robot's worktable plane; however, during robotic milling of complex surfaces, the tool direction is time-varying; this is determined by the tilt angle. and roll angle The calculated transformation matrix transforms the frequency response function (FRF) fitted to the modal parameters 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 follows:

[0029]

[0030] in and Represented 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] in, and These represent the reference and instantaneous FRF matrices, respectively.

[0037] Furthermore, in step S2, firstly, a mechanical force model is established, and a workpiece coordinate system (WCS) is defined in robot multi-axis milling. Tool Coordinate System (TCS) Feed coordinate system (FCS) The WCS is fixed to the workpiece, and the origin of the TCS is at the center of the tool. Direction along the tool axis The axial direction is from the center of the tool to the first cutting edge. The origin of the FCS is at the tool contact point. Along the tool path direction, Following the normal direction of the workpiece surface; the idea behind the mechanical cutting force model is to discretize the milling cutter along its axial direction into several equal micro-units, given a rotation angle. The instantaneous cutting force under TCS is the sum of the cutting forces of all micro-elements 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] In the formula The cutting force under TCS, and These are the number of cutting edges and the number of discrete units, respectively. Indicates the radial, tangential, and axial shear force coefficients; Indicates the radial, tangential, and axial cutting force coefficients; The width of the discrete cutting unit is determined by... The calculation yields the following result: The height of the discrete element. Indicates height Axial immersion angle at the location; The upper and lower limits of axial engagement of the cutting edge are determined by the tool radius, the tool's rake angle and side rake angle, and the instantaneous curvature of the workpiece surface. The rotational transformation matrix from the micro-cutting force to the tool coordinate system is expressed as:

[0040]

[0041] Indicates the axial height of the j-th cutting edge. The radial penetration angle at point is expressed as

[0042]

[0043] In the formula Main spindle speed and These represent the pitch angle between two consecutive cutting edges and the helix angle of the tool, respectively. The length of the infinitesimal element of the cutting edge is calculated using the following formula:

[0044]

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

[0046]

[0047] In the formula The feed per tooth can be calculated and expressed as: , For feed rate;

[0048] In the above formula It is a function characterizing the entry or exit of the cutting edge, defined as:

[0049]

[0050] in, and The axial height of the tool The angle of entry and the angle of exit at the point;

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

[0052]

[0053] In the formula The transformation matrix from TCS to WCS is related to the tool's rake angle and tilt angle.

[0054] Due to the influence of robot dynamics, the cutting tool will undergo dynamic displacement under the action of cutting force. The dynamic displacement has a significant impact on the current cutting edge position and the machined surface formed by the sweeping surface of the previous cutting edge, resulting in dynamic undeformed chip thickness and time-varying tool-workpiece engagement (CWE) region. After obtaining the initial cutting force, the robot milling dynamics model of the cutting region is established as follows:

[0055]

[0056] In the formula , and Let the mass matrix, damping matrix, and stiffness matrix of the robotic milling system be represented as follows:

[0057]

[0058] In the tool coordinate system, the stiffness in the Z direction is much higher than that 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 Runge-Kutta. First, the state vector is defined and transformed into a system of first-order differential equations to improve the computational efficiency of the solution, expressed as:

[0059]

[0060]

[0061] The actual position of the cutting edge is further determined by using the dynamic displacement calculated at each time step.

[0062] To obtain the cutting morphology of the workpiece surface, it is first necessary to establish a dynamic cutting edge sweep trajectory based on the tool parameters, tool position information, and the generated dynamic displacement. As the tool rotates along the tool position, considering the influence of the tool movement trajectory and the tool dynamic displacement, the actual position and sweep trajectory of all height points on each tool edge at each time step are obtained.

[0063] In robot machining, the toolpath under WCS is represented as follows:

[0064]

[0065] in It is the planned toolpath. , , It refers to the position in three directions; It is the tool axis vector. , and These are Euler angles describing the attitude;

[0066] This is the dynamic displacement under the TCS of the robot milling area, which is converted to WCS and represented as:

[0067]

[0068] Typically, the planned toolpath Represented in the form of the tool contact point; It is the normal vector of the tool contact point on the machined surface. It is the center point of the tool; in order to calculate the sweeping surface of the cutting edge, In WCS, this is represented as:

[0069]

[0070] In TCS, the height of the j-th blade The position of the blade tip The calculation is as follows:

[0071]

[0072] In the formula Let the helix angle be denoted as , and then the tool position curve and the corresponding tool axial vector are considered to calculate the tool sweep surface, as shown in WCS:

[0073]

[0074] In the formula Angular velocity, Let be the rotation matrix about the tool axis;

[0075] 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 morphology of the machined surface. Considering the differences in cutting with different cutting edges and the timeliness of cutting load calculation, a dynamic update mechanism for the machined surface within the cutting edge cycle is proposed. In the first revolution range of the tool entering the workpiece, assuming the robot is rigid, the initial machined surface is generated according to the theoretical trajectory of the tool motion. In each subsequent discrete time step, the instantaneous dynamic displacement is calculated according to the method proposed above. The dynamic displacement is superimposed on the theoretical tool center point position, and combined with the position of the cutting edge point to obtain the new actual cutting edge sweep trajectory point, which is stored. After one cutting edge is completed, the machined surface of the workpiece is updated, and the workpiece surface is updated along the entire path according to this update mechanism and the tool feed.

[0076] Furthermore, in step S3, the initial cutting force calculated based on the predicted modal parameters and mechanical force model is used to solve for the steady-state dynamic displacement caused by the robot dynamics effect, 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 workpiece surface dynamic update mechanism.

[0077] Based on the aforementioned tool sweep trajectory model and machining surface dynamic update mechanism, the coupled robot dynamics model and mechanical force model can accurately calculate the instantaneous undeformed chip thickness and micro-element load under the influence of dynamic displacement, thereby calculating 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 force of all micro-elements on the helical end mill is calculated. Within the initial tool rotation cycle of the simulation, the initial cutting force is calculated using the rigid body cutting force model. The initial workpiece machining surface is generated; subsequently, combined with the robot joint angles, the modal parameters under continuous machining pose are predicted using the aforementioned modal parameter prediction model; the calculated initial cutting forces in the X and Y directions are then incorporated into the dynamic model of the cutting region to perform dynamic displacement in the X and Y directions. and The solution is obtained by superimposing it onto the theoretical trajectory points to obtain the actual blade position points. , is represented as:

[0078]

[0079] To simplify the calculation process, improve computational efficiency, and consider the influence of the theoretical subcycloidal motion trajectory of the cutting edge and the dynamic displacement of the robot, the instantaneous undeformed chip thickness is calculated in the tool coordinate system; the current center point of the tool is... ,straight line The intersection point with the previous cutting edge's tool path is It can be determined using a linear equation and an interpolation curve model. The length is the actual instantaneous undeformed chip thickness, and then the instantaneous cutting force is calculated, expressed as:

[0080]

[0081] in, and These represent the actual cutting edge positions on the cutting trajectories generated by the current and previous cutting edge cycles, respectively. It is the tooth passage cycle;

[0082] Using the cutting force as the excitation source, the new dynamic displacement and actual position are calculated. When the difference between the prediction results of adjacent actual positions is less than a set threshold, convergence is considered and the actual position is stored. Then, the simulation prediction for the next time step begins. After the cutting edge completes cutting, the actual position points at each time step are interpolated using an interpolation algorithm to update the machined surface. Subsequent cutting edges are used to calculate the dynamic displacement, instantaneous undeformed chip thickness, and cutting force based on this surface, and iterative updates are performed until the simulation ends.

[0083] Furthermore, in step S4, due to the influence of the robot's pose-dependent dynamic characteristics, the robot end effector has relatively weak stiffness in certain poses. Under the action of milling force, it will produce more significant dynamic stiffness deformation, reducing the machining performance of the end effector and generating machining errors. In addition, the machining path generated by the CAM software maintains a fixed feed rate during the cutting process, without considering the feed rate optimization between different tool positions, and the feed rate of the empty cutting path also has a large optimization space. The feed rate at different tool positions can be optimized based on the above simulated cutting force results, making the cutting force more stable and improving the overall machining efficiency and accuracy. Under the condition of satisfying the given cutting resultant force threshold, considering the influence of pose-dependent dynamic characteristics on the cutting force simulation, the feed rate is segmented and optimized according to the path length.

[0084] First, each machining path is divided into multiple segments, and the initial feed rate in the toolpath file is... Based on the dynamic milling force model and changing modal parameters established in the preceding chapters, the maximum resultant milling force for each small path segment is calculated. The specific optimization objective is to maximize the cutting force along the cutting path, but not exceed an upper limit, i.e., minimize the allowable cutting force. With maximum cutting force The difference between them; The pre-set allowable milling force is taken as the average of the peak milling forces in each machining path; according to right Set a certain constraint range ( , ), To constrain the variation of milling force amplitude and ensure that the maximum milling force remains relatively stable throughout the entire machining process; for the first Segment feed rate Also set the range of constraints ( , The process must meet the robot's performance requirements while ensuring that the feed rate changes are not too drastic. The optimal feed rate is obtained using a feed rate optimization model, and the feed rate for each milling path is obtained and stored. These feed rates are then assigned to intermediate feed rate data through spline interpolation to ensure the smoothness of the feed rate during tool movement. The optimized feed rate is output, and an executable file is generated for robot milling experiments to further verify machining accuracy, efficiency, and cutting force.

[0085] Another objective of this invention is to provide a milling force simulation and feed rate optimization system that considers robot pose-dependent dynamic effects, comprising:

[0086] The modal testing module is used to perform modal testing in different poses of the robot milling area. Based on the acquired robot joint angles and modal parameters, a predictive model of reference modal parameters under the vertical tool axis vector is established, and the modal parameters in the instantaneous tool direction are obtained through the transformation matrix.

[0087] The model building module is used to build mechanical force and dynamic models in the robot cutting area; based on the dynamic sweeping trajectory of the cutting edge and the workpiece model, the workpiece surface is dynamically updated to ensure the calculation accuracy of instantaneous cutting thickness and cutting force.

[0088] The solver module is used to calculate the initial cutting force based on the predicted modal parameters and mechanical force model, solve for the steady-state dynamic displacement caused by the robot dynamics effect, and superimpose it onto the nominal instantaneous undeformed chip thickness, calculate the instantaneous cutting force at each time step, and perform iterative calculation by coupling the workpiece surface dynamic update mechanism.

[0089] The adaptive planning module is used to perform piecewise adaptive planning of the feed rate under the peak cutting force constraint based on the accurate cutting force in simulation, and to conduct machining error measurement experiments on robot milling and curved parts to verify the performance of the model.

[0090] Another object of the present invention is to provide a computer device including a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the milling force simulation and feed rate optimization method considering robot pose-dependent dynamic effects.

[0091] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the milling force simulation and feed rate optimization method that considers robot pose-dependent dynamic effects.

[0092] Another objective of this invention is to provide an information data processing terminal for implementing the milling force simulation and feed rate optimization system that considers the robot pose-dependent dynamic effects.

[0093] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0094] Firstly, the purpose of this invention is to provide a milling force simulation and feed rate optimization method that considers the robot pose-dependent dynamic effects. It takes into account the influence of robot pose-dependent dynamic effects on instantaneous cutting thickness and establishes an accurate cutting force simulation model based on the dynamic update mechanism of the workpiece surface. Segmented adaptive feed rate optimization is carried out under the constraint of peak cutting force to improve machining accuracy and efficiency, stabilize the cutting force, and significantly enhance machining stability and performance.

[0095] This invention establishes a force-position coupling iterative algorithm that considers the dynamic update mechanism of the workpiece surface and the dynamic characteristics of pose dependence. It realizes accurate simulation of cutting force in the robot surface milling process under variable workpiece placement position, and has potential application value for process parameter optimization, tool wear prediction, and improvement of machining accuracy and surface quality.

[0096] This invention considers pose-dependent dynamic characteristics, establishes an MTGPR model for predicting robot modal parameters under the vertical tool axis vector, and transforms the reference FRF to the instantaneous tool direction. The instantaneous robot modal parameters are used for cutting force simulation to ensure the accuracy of cutting force iteration. This significantly reduces the number of experiments required for modal testing and analysis, thereby reducing equipment usage and time costs.

[0097] This invention enables adaptive planning of the feed rate during milling based on the precise cutting force obtained through simulation, thereby improving machining accuracy and efficiency and making the cutting force more stable. It has the potential to be applied in practical industrial settings.

[0098] Secondly, traditional methods obtain the robot's pose-related dynamic characteristics, i.e., modal parameters, through numerous modal testing experiments. This patent, however, employs a multi-task Gaussian process regression (MTGPR) model to simultaneously predict multiple modal parameters, effectively reducing the number of modal testing experiments and testing costs. Furthermore, in existing industrial scenarios, machining parameter optimization often relies on empirical trial cutting or offline simulation software, which is time-consuming and cannot dynamically adapt to changing cutting conditions. This patent considers the dynamic effects dependent on robot pose and the dynamic update mechanism of the workpiece surface. It pre-simulates the cutting force using 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 this invention is transformed, milling experiments using the optimized feed rate can improve machining accuracy and efficiency, replacing expensive simulation tools and reducing software procurement costs. Adaptive feed rate planning under cutting force peak constraints makes the cutting force more stable, improving machining stability, avoiding tool overload, reducing tool wear and replacement frequency, reducing downtime and machining costs, and increasing profitability.

[0099] This invention relates to the field of milling force simulation and feed rate optimization. Current research on robot milling force simulation rarely considers the dynamic updating of the workpiece surface and neglects the impact of robot pose-dependent dynamic characteristics on the cutting force simulation model. Furthermore, it is currently believed that robot dynamic characteristics (such as modal parameters) need to be obtained through frequent experiments. In addition, existing research on robot feed rate optimization only analyzes the correlation between process parameters and machining errors, requiring extensive process experiments to optimize and obtain better process parameters. Moreover, these studies lack mechanistic modeling for process parameter optimization, resulting in poor experimental results and generalization ability. This invention comprehensively considers the influence of the workpiece surface dynamic updating mechanism and the robot pose-related dynamic characteristics, and establishes a force-position coupling iterative model by coupling modal parameters predicted by a multi-task Gaussian process regression model, achieving accurate simulation of robot milling forces. Furthermore, offline feed rate pre-planning under peak force constraints stabilizes the cutting force, improving milling accuracy and efficiency. Overcoming technical biases includes reducing the number of modal parameter experiments, simplifying complex processes, reducing the number of trial cuts and process parameter optimizations, reducing processing and measurement costs, and improving processing operation stability, safety, and reliability. Attached Figure Description

[0100] Figure 1 This is a flowchart of a milling force simulation and feed rate optimization method that considers robot pose-dependent dynamic effects, provided in an embodiment of the present invention.

[0101] Figure 2 This is a block diagram of a milling force simulation and feed rate optimization system that considers robot pose-dependent dynamic effects, provided in an embodiment of the present invention.

[0102] Figure 3 This is a schematic diagram of the basic method flow provided in the embodiments of the present invention.

[0103] Figure 4 This is a schematic diagram of the instantaneous RFR conversion provided in an embodiment of the present invention.

[0104] Figure 5 This is a schematic diagram of the ball end mill and surface milling principle provided in the embodiment of the present invention.

[0105] Figure 6 This is a schematic diagram illustrating the calculation of the instantaneous uncut chip thickness in the cutting region, provided by an embodiment of the present invention.

[0106] Figure 7 This is a flowchart of force-position coupling iterative milling force simulation provided in an embodiment of the present invention.

[0107] Figure 8 This is a flowchart of feed rate planning provided in an embodiment of the present invention.

[0108] Figure 9This is a curved workpiece drawing based on the design of the engine casing, provided in an embodiment of the present invention.

[0109] Figure 10 This is a diagram of a robot milling and data acquisition system provided in an embodiment of the present invention.

[0110] Figure 11 This is an experimental diagram of workpiece machining error measurement provided in an embodiment of the present invention.

[0111] Figure 12 This is a diagram of a robot modal testing experiment provided in an embodiment of the present invention.

[0112] Figure 13 This is a comparison chart of the X-direction modal parameter prediction and measurement results provided in this embodiment of the invention.

[0113] Figure 14 This is a comparison chart of the Y-direction modal parameter prediction and measurement results provided in this embodiment of the invention.

[0114] Figure 15 This is a comparison chart of the calculated values ​​and measured values ​​of the mechanical force model provided in this embodiment of the invention.

[0115] Figure 16 This is a comparison chart of the simulated and measured values ​​of the cutting force for Task A provided in this embodiment of the invention.

[0116] Figure 17 This is a comparison chart of the simulated and measured values ​​of the cutting force for Task B provided in this embodiment of the invention.

[0117] Figure 18 This is a comparison chart of the simulated and measured values ​​of the cutting force for Task C provided in this embodiment of the invention.

[0118] Figure 19 This is a comparison chart of the fixed and planned feed rates provided in the embodiments of the present invention.

[0119] Figure 20 This is a comparison chart of cutting force and machining efficiency under fixed and planned feed rates provided in the embodiments of the present invention.

[0120] Figure 21 This is a comparison chart of the contour errors processed under fixed and planned feed rates provided in the embodiments of the present invention. Detailed Implementation

[0121] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0122] One of the most pressing and challenging problems in robotic milling is that the cutting force distortion caused by joint compliance and tool-workpiece coupling vibrations drifts sharply along the pose. Traditional rigid body mechanics models or fixed modal assumptions cannot capture this change in "dynamic compliance," which in turn induces feed overload, chatter, and surface shape errors. The proposed method obtains the joint angle-modal parameter mapping through multi-pose modal testing, treats the pose-related natural frequencies and damping as random fields, and reconstructs the "reference frequency response cloud" in the function space through multi-task Gaussian process regression, laying a differentiable and interpolable dynamic reference surface for servo simulation.

[0123] To avoid anisotropic misjudgment caused by tool axis direction deflection, the algorithm first calibrates the modal parameters in the tool axis vertical coordinate system, and then uses a double rotation matrix composed of the tilt angle and the yaw angle to perform frequency response function transformation. This is equivalent to reprojecting the compliance ellipsoid in the instantaneous tool coordinate system, so that the principal mode shape under any posture is coaxial with the actual cutting depth direction, thereby ensuring that the compliance tensor does not have coordinate mismatch when participating in subsequent coupling.

[0124] The cutting force prediction process does not simply treat the milling cutter as a rigid body. Instead, it discretizes the cutter axis along the generation line into several micro-elements and assigns radial, tangential, and axial force coefficients. Then, the helix angle, feed vector, and axial engagement limit are written into the cutting integral kernel to generate a three-dimensional micro-cutting load flow in real time. The mechanical force field constructed in this way and the predicted compliance matrix are convolved to give the displacement response, implicitly considering the modulation of steady-state amplitude by robot structural damping and equivalent stiffness.

[0125] The dynamic equations are solved using fourth-order Runge-Kutta iterations after state-space expansion. The inner loop of the iteration feeds back the displacement of each infinitesimal element to the undeformed chip thickness at the next moment, forming a "displacement-thickness-force" closed loop. Since the workpiece surface mesh is refreshed with each gear pass cycle, the sweep trajectory and dynamic machining residuals are superimposed to generate the real-time machining morphology, which in turn drives the mechanical equations to the next quasi-static equilibrium. This weakly coupled multiphysics solution chain effectively suppresses numerical divergence and precisely locks the peaks and valleys of the cutting force as the attitude drifts.

[0126] During the feed rate planning phase, the algorithm divides the entire toolpath into several arc segments and constructs a penalty function based on the difference between the maximum resultant cutting force and the allowable force threshold for each segment. By constraining the gradient of the cutting force amplitude and the feed jump variable, a smooth piecewise feed curve is obtained using quadratic programming. Spline interpolation makes the velocity-time curve coherent and differentiable in joint space, avoiding acceleration saturation or vibration re-excitation of the robot at high curvature inflection points.

[0127] In the experiment, the optimized NC program was deployed to a six-axis robot. Real-time force sensing and laser coordinate measuring machine (CMM) results showed that the peak value of the cutting force was consistently suppressed below the allowable threshold, and the surface machining error was significantly reduced. This demonstrates that the proposed method, through a three-layer mechanism of "attitude mapping-dynamic coupling-adaptive feed," linearizes the originally nonlinear, coupled, and uncertain robot milling process into an observable, predictable, and controllable closed-loop system, achieving a systematic solution to the problems of inaccurate mechanical models and machining quality fluctuations in existing technologies.

[0128] like Figure 1 As shown, the milling force simulation and feed rate optimization method considering robot pose-dependent dynamic effects provided by this embodiment of the invention includes the following steps:

[0129] S1. Modal tests are performed in different poses of the robot milling area. Based on the obtained robot joint angles and modal parameters, a prediction model of the reference modal parameters under the vertical tool axis vector is established, and the modal parameters in the instantaneous tool direction are obtained through the transformation matrix.

[0130] S2, establish mechanical force and dynamic models in the robot cutting area; dynamically update the workpiece surface based on the dynamic sweep trajectory of the cutting edge and the workpiece model to ensure the accuracy of instantaneous cutting thickness and cutting force calculation;

[0131] S3, based on the predicted modal parameters and mechanical force model, the initial cutting force is calculated to solve the steady-state dynamic displacement caused by the robot dynamics effect, and superimposed 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 workpiece surface dynamic update mechanism.

[0132] S4. Based on the accurate cutting force obtained from simulation, piecewise adaptive planning of feed rate under peak cutting force constraint is carried out, and robot milling and machining error measurement experiments on curved parts are conducted to verify the performance of the model.

[0133] like Figure 2 As shown, an embodiment of the present invention provides a milling force simulation and feed rate optimization system that considers robot pose-dependent dynamic effects, comprising:

[0134] The modal testing module is used to perform modal testing in different poses of the robot milling area. Based on the acquired robot joint angles and modal parameters, a predictive model of reference modal parameters under the vertical tool axis vector is established, and the modal parameters in the instantaneous tool direction are obtained through the transformation matrix.

[0135] The model building module is used to build mechanical force and dynamic models in the robot cutting area; based on the dynamic sweeping trajectory of the cutting edge and the workpiece model, the workpiece surface is dynamically updated to ensure the calculation accuracy of instantaneous cutting thickness and cutting force.

[0136] The solver module is used to calculate the initial cutting force based on the predicted modal parameters and mechanical force model, solve for the steady-state dynamic displacement caused by the robot dynamics effect, and superimpose it onto the nominal instantaneous undeformed chip thickness, calculate the instantaneous cutting force at each time step, and perform iterative calculation by coupling the workpiece surface dynamic update mechanism.

[0137] The adaptive planning module is used to perform piecewise adaptive planning of the feed rate under the peak cutting force constraint based on the accurate cutting force in simulation, and to conduct machining error measurement experiments on robot milling and curved parts to verify the performance of the model.

[0138] Another object of the present invention is to provide a computer device including a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the milling force simulation and feed rate optimization method considering robot pose-dependent dynamic effects.

[0139] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the milling force simulation and feed rate optimization method that considers robot pose-dependent dynamic effects.

[0140] Another objective of this invention is to provide an information data processing terminal for implementing the milling force simulation and feed rate optimization system that considers the robot pose-dependent dynamic effects.

[0141] Specific implementation of the present invention:

[0142] like Figure 3 A milling force simulation and feed rate optimization method considering robot pose-dependent dynamics effects is proposed. Multiple modal parameter measurement points are uniformly set in the area above the robot's worktable. Modal testing is performed with the tool axis vector perpendicular to the worktable plane. Modal parameters are obtained using modal analysis software, and robot joint angles are recorded under various poses. Due to the need to predict multiple modal parameters and consider the correlation between them, this paper is based on a common-region intrinsic model. A modal parameter prediction model is established using Multi-Task Gaussian Process Regression (MTGPR).

[0143] Indicates by Different inputs The set that comprises the joint angles of all measured points. For There are 3 modes to be predicted, and their label space is represented as follows:

[0144]

[0145] in This represents the j-th tag value of the i-th input. For each line That is, all modal parameters, have .

[0146] latent function To obtain the relationship between different modal parameters, a Gaussian prior is set up. Assuming the mean of GPs is 0, let:

[0147]

[0148] In the formula This is the positive semi-definite (PSD) matrix representing the similarity between modal parameters. Let be the covariance function of the input vector, which captures the correlation between different poses of the same modal parameter. Let be the variance of the l-th modal parameter.

[0149] This model is derived using the standard GP formula for the mean and variance of the prediction distribution, as well as the covariance function given in the above formula. For new data points in the l-th mode... The mean prediction is calculated as follows:

[0150]

[0151] In the formula Represents the Kronecker product. for The lth column, For training points and test points The covariance vector between them Let be the covariance matrix between all training point pairs. It is A diagonal matrix, where the (l, l)th element is , It is matrix.

[0152] In the training set, given labels A gradient-based method is used to learn the matrix. and parameters Make the edges seem similar Maximize. This is ensured using the Cholesky decoupling method. The positive semi-determinism of the lower triangular matrix. It can be parameterized as:

[0153]

[0154] In the formula for The number of hyperparameters is reduced, and the hyperparameters of the MTGPR model are optimized by minimizing the negative log marginal likelihood. Given an input... According to conditional probability The predicted values ​​are calculated. MTGPR combines multiple pose-related modal parameters into a single regression model and learns the correlations between the modal parameters, thereby improving prediction performance.

[0155] The modal parameters mentioned above were measured when the tool axis vector was perpendicular to the robot's table plane. However, during robotic milling of complex surfaces, the tool direction is time-varying. This is determined by the tilt angle... and roll angle The calculated transformation matrix transforms the frequency response function (FRF) fitted to the modal parameters 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), as shown below. Figure 4 As shown. The transformation matrix from MCS to IMCS is defined as:

[0156]

[0157] in and Represented as:

[0158]

[0159] The inverse transformation matrix is ​​defined as:

[0160]

[0161] The force excitation and response signals are decomposed and synthesized to obtain the instantaneous FRF matrix:

[0162]

[0163] in, and These represent the reference and instantaneous FRF matrices, respectively.

[0164] Then, a mechanical force model is established, and the workpiece coordinate system (WCS) is defined in robot multi-axis milling. Tool Coordinate System (TCS) Feed coordinate system (FCS) ,like Figure 5 As shown. The WCS is fixed to the workpiece, and the origin of the TCS is at the center of the tool. Direction along the tool axis The axial direction is from the center of the tool to the first cutting edge. The origin of the FCS is at the tool contact point. Along the tool path direction, Following the normal direction of the workpiece surface. The idea behind the mechanical cutting force model is to discretize the milling cutter along its axis into several equal micro-elements, given a rotation angle. The instantaneous cutting force under TCS is the sum of the cutting forces of all micro-elements on all cutting edges. Combining the calibrated radial, tangential, and axial cutting force coefficients, the cutting force is converted under TCS and expressed as:

[0165]

[0166] In the formula The cutting force under TCS, and These represent the number of cutting edges and the number of discrete units, respectively. Indicates the radial, tangential, and axial shear force coefficients. Indicates the radial, tangential, and axial cutting force coefficients. The width of the cutting unit is determined by... The calculation yields the following result: The height of the discrete element. Indicates height The axial immersion angle at that location. The upper and lower limits of axial engagement of the cutting edge are determined by the tool's rake angle and side rake angle, as well as the instantaneous curvature of the workpiece surface, which is the tool radius. The rotational transformation matrix from the micro-cutting force to the tool coordinate system is expressed as:

[0167]

[0168] Indicates the axial height of the j-th cutting edge. The radial penetration angle at point is expressed as

[0169]

[0170] In the formula Main spindle speed and These represent the pitch angle between the two continuous cutting edges and the helix angle of the tool, respectively. The length of the infinitesimal element of the cutting edge is calculated using the following formula:

[0171]

[0172] In the above formula The theoretical instantaneous undeformed chip thickness of the cutting edge element can be expressed as:

[0173]

[0174] In the formula The feed per tooth can be calculated and expressed as: , This is the feed rate.

[0175] In the above formula It is a function characterizing the entry or exit of the cutting edge, defined as:

[0176]

[0177] in, and The axial height of the tool The angle of entry and the angle of exit at the point.

[0178] Finally, the cutting force is converted to WCS and expressed as:

[0179]

[0180] In the formula This is the transformation matrix from TCS to WCS, which is related to the tool's rake angle and tilt angle.

[0181] Due to the influence of robot dynamics, the cutting tool undergoes dynamic displacement under the action of cutting force. This dynamic displacement significantly affects both the current cutting edge position and the machined surface formed by the sweeping surface of the previous cutting edge, resulting in dynamic undeformed chip thickness and a time-varying tool-workpiece engagement (CWE) region. After obtaining the initial cutting force, the robot milling dynamics model of the cutting region is established as follows:

[0182]

[0183] In the formula , and Let the mass matrix, damping matrix, and stiffness matrix of the robotic milling system be represented as follows:

[0184]

[0185] In the tool coordinate system, the stiffness in the Z direction is much higher than that 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 Runge-Kutta. First, the state vector is defined and transformed into a system of first-order differential equations to improve the computational efficiency of the solution, expressed as:

[0186]

[0187]

[0188] The actual position of the cutting edge is further determined by using the dynamic displacement calculated at each time step.

[0189] To obtain the cutting morphology of the workpiece surface, a dynamic cutting edge sweep trajectory must first be established based on tool parameters, tool position information, and the resulting dynamic displacement. As the tool rotates along the tool position, considering the influence of the tool's motion trajectory and dynamic displacement, the actual positions and sweep trajectories of all height points on each tool edge at each time step are obtained.

[0190] In robot machining, the toolpath under WCS is represented as follows:

[0191]

[0192] in It is the planned toolpath. , , It refers to the position in three directions. It is the tool axis vector. , and These are Euler angles that describe the attitude.

[0193] This is the dynamic displacement under the TCS of the robot milling area, which is converted to WCS and represented as:

[0194]

[0195] Typically, the planned toolpath It is represented in the form of the tool contact point. It is the normal vector of the tool contact point on the machined surface. It is the center point of the cutting tool. This is used to calculate the sweeping surface of the cutting edge. In WCS, this is represented as:

[0196]

[0197] In TCS, the height of the j-th blade The position of the blade tip The calculation is as follows:

[0198]

[0199] In the formula Let the helix angle be denoted as , and then the tool position curve and the corresponding tool axial vector are considered to calculate the tool sweep surface, as shown in WCS:

[0200]

[0201] In the formula Angular velocity, Let be the rotation matrix about the tool axis.

[0202] 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 morphology of the machined surface. Considering the differences in cutting performance between different cutting edges and the time-sensitivity of cutting load calculation, a dynamic surface update mechanism within the cutting edge cycle is proposed. In the first revolution of the tool into the workpiece, assuming the robot is rigid, an initial machined surface is generated according to the theoretical tool motion trajectory. At each subsequent discrete time step, the instantaneous dynamic displacement is calculated using the proposed method. This dynamic displacement is superimposed on the theoretical tool center point position, and combined with the cutting edge position to obtain the new actual cutting edge sweep trajectory point, which is then stored. After one cutting edge completes its cut, the workpiece surface is updated, and this update mechanism, along with the tool feed, completes the workpiece surface update along the entire path.

[0203] Based on the aforementioned tool sweep trajectory model and machining surface dynamic update mechanism, the coupled robot dynamics model and mechanical force model can accurately calculate the instantaneous undeformed chip thickness and micro-element load under the influence of dynamic displacement, thereby calculating the instantaneous dynamic cutting force. The simulation process is discretized into a series of instantaneous time steps, at which the micro-cutting force of all micro-elements on the helical end mill is calculated. Within the initial tool rotation cycle of the simulation, the initial cutting force is calculated using a rigid body cutting force model. The initial workpiece machining surface is generated. Then, combining the robot joint angles, the modal parameters under continuous machining poses are predicted using the aforementioned modal parameter prediction model. The calculated initial cutting forces in the X and Y directions are then input into the dynamic model of the cutting region to perform dynamic displacement in the X and Y directions. and The solution is obtained by superimposing it onto the theoretical trajectory points to obtain the actual blade position points. , is represented as:

[0204]

[0205] To simplify the calculation process, improve computational efficiency, and consider the influence of the theoretical subcycloidal 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, such as... Figure 6 As shown. The current center point of the tool is... ,straight line The intersection point with the previous cutting edge's tool path is It can be determined using a linear equation and an interpolation curve model. The length is the actual instantaneous undeformed chip thickness, and then the instantaneous cutting force is calculated, expressed as:

[0206]

[0207] in, and These represent the actual cutting edge positions on the cutting trajectories generated by the current cutting edge and the previous cutting edge's tooth pass cycle, respectively. It is the tooth passage cycle.

[0208] Using the cutting force as the excitation source, new dynamic displacement and actual position are calculated. Convergence is considered achieved when the difference between adjacent predicted actual positions is less than a set threshold, and this actual position is stored. The simulation then begins for the next time step. After the cutting edge completes its cut, an interpolation algorithm is used to interpolate the actual position points at each time step to update the machined surface. Subsequent cutting edges calculate dynamic displacement, instantaneous undeformed chip thickness, and cutting force based on this surface, and iteratively update until the simulation ends. Detailed iterative simulation procedures can be found in [link to detailed simulation process]. Figure 7 .

[0209] Due to the influence of robot pose-dependent dynamic characteristics, the robot end effector exhibits relatively weak stiffness in certain poses. Under milling forces, this leads to more significant dynamic stiffness deformation, reducing the end effector's machining performance and causing machining errors. Furthermore, the machining path generated by the CAM software maintains a fixed feed rate during cutting, failing to consider feed rate optimization between different tool positions, and the feed rate of the empty cutting path also has considerable optimization potential. Based on the simulated cutting force results, the feed rate at different tool positions can be optimized to achieve more stable cutting forces and improve overall machining efficiency and accuracy. Under the given cutting force threshold, considering the impact of pose-dependent dynamic characteristics on cutting force simulation, the feed rate is optimized in segments based on the path length.

[0210] First, each machining path is divided into multiple segments, and the initial feed rate in the toolpath file is... Using the dynamic milling force model established in the preceding chapters, the maximum resultant milling force for each small path segment is calculated. The specific optimization objective is to maximize the cutting force along the cutting path, but not exceed an upper limit, i.e., minimize the difference between the allowable cutting force and the maximum cutting force, defined as:

[0211]

[0212] in The pre-set allowable milling force is taken as the average of the peak milling forces in each machining toolpath. The constraint conditions are:

[0213]

[0214] in To constrain the variation of milling force amplitude, ensuring that the maximum milling force remains relatively stable throughout the entire machining process. and To constrain the feed rate, it is necessary to meet the robot's performance requirements while ensuring that feed changes are not too drastic. For the first Feed rate for short path segments.

[0215] The allowable milling force is calculated according to the following formula. Calculate the feed rate The iteration method is as follows:

[0216]

[0217] Simulated new feed rate Maximum milling force .if If the optimization objective is not met, the optimal feed rate is determined through further iterative calculation using the following formula. And recalculate the maximum milling force until the preset constraints are met.

[0218]

[0219] and The range must meet the constraints.

[0220] Finally, the feed rate for each milling path is obtained and stored. These feed rates are then assigned to intermediate feed rate data through spline interpolation to ensure smooth feed rate during tool movement. The optimized feed rate is output, and an executable file is generated for robotic milling experiments to further verify machining accuracy, efficiency, and cutting force. The overall optimization process is as follows: Figure 8 As shown.

[0221] The curved surface parts designed for milling experiments are derived from the inner and outer air passage surfaces of a scaled-down engine casing, such as... Figure 9 As shown in (a), based on the extracted feature surfaces, three workpieces of 6061 aluminum alloy were designed, as follows: Figure 9 As shown in (b). To verify the universality 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 ability is reflected in three aspects: the variability of the workpiece surface shape and size, and the variability of the workpiece placement position. This enriches the diversity of process information expressed by cutting force, machining error and process parameters, machined surface features, and workpiece placement position.

[0222] Table 1 Designed processing tasks

[0223]

[0224] The overall scheme of the robotic milling system is as follows: Figure 10 As shown in Table 2, the milling experiment was conducted using a six-DOF industrial robot (COMAU Smart5 NJ 220-2.7). The robot's maximum load was 220 kg, and its repeatability was 0.06 mm. The milling spindle (Jager Z100-H540.08 S3W2) had a maximum speed of 30,000 rpm and a maximum torque of 5 Nm. A force gauge (Kistler 9129AA) was mounted on the worktable, with the workpiece fixed on it. The cutting force sampling frequency was 25 kHz. A 10 mm diameter, 40° helix end mill (SANDVIK 2B330-1000-NC H10F) was used for rough milling. A planned path was used to remove the entire surface of the curved part; the machining parameters are shown in Table 2.

[0225] Table 2 Milling parameters

[0226]

[0227] The machining error was obtained by measuring the milled workpiece using a coordinate measuring machine (HEXAGON GLOBAL Classic SR 07.10.07), such as... Figure 11 As shown. The measurement accuracy of this device is approximately 1 μm, which meets the measurement requirements. The contour error is calculated based on the measurement results and used to evaluate the machining error of the part.

[0228] The workpiece is mounted on a worktable at a certain height. The workpiece height is relatively small, therefore the tool tip's position range in the XY plane is greater than its range in the Z direction. To cover the workpiece mounting area and to ensure the acquired positions cover the milling task on the worktable as much as possible, the workspace above the worktable is meshed, resulting in 24 tool tip measurement points, including two planes at Z=900mm and 1000mm. At each measurement point, the tool axis remains perpendicular to the XY plane. Considering the feasible range of the redundancy angle and its impact on pose, a redundancy angle with a large variation range at each position (…) ),like Figure 12 As shown in (a). Therefore, the total number of measured postures is 168. Force excitation was generated using an impact hammer (PCB086C01), and the response was detected using a miniature accelerometer (PCB352C23) fixed to the blade tip. Three repeated impact tests were performed on the measurement points for each posture, and the average of the three results was taken as the blade tip frequency response for that posture to ensure the validity of the experimental data. Figure 12 As shown in (b), the signal was processed and analyzed using the modal testing and analysis module of CutPro software, while the joint angles of the robot in each pose were collected.

[0229] Modal parameters obtained from modal analysis include modal frequencies. Damping ratio and modal stiffness Although the robot system has multiple vibration modes, the dominant mode contributes the most to the calculation of cutting forces during robot milling. The modal mass is then obtained using the following formula. and modal damping :

[0230]

[0231] Select 30% of the training data, i.e., 50 measured poses, as the test set for the model. The predictive performance of a model is evaluated using a value, defined as:

[0232]

[0233] In the formula, and These are the predicted value and the measured value, respectively. This is the average value of the measured results. The sample size is shown in the scatter plot of the predicted and measured values ​​in the X and Y directions of the test set. Figure 13 and 14 As shown, the predicted values ​​and the measured values The values ​​are all above 0.9. The results show that the predicted values ​​agree well with the measured values, indicating that the method can capture data trends effectively. For some locations, the prediction accuracy is slightly lower, but still within the limits allowed by dynamic modeling.

[0234] 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 accuracy are shown in Table 3. Table 3 shows that the prediction accuracy for modal parameters in all directions is greater than 90%, demonstrating good prediction performance. The robot's joint angles were obtained through inverse kinematics calculation of the machining pose in the milling task, and then used to predict changes in modal parameters. The predicted reference modal parameters were fitted to obtain the frequency response function matrix. Then, the frequency response function under the tool posture changing over time was calculated based on the tilt 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 was divided into 10 segments. The modal parameters for each segment were obtained through curve fitting and used for cutting force simulation and feed rate optimization.

[0235] Table 3 Comparison of predicted and measured modal parameters for specific poses

[0236]

[0237] A milling experiment using the same tool-workpiece material combination as the robotic milling experiment was conducted on a CNC machine tool to calibrate the cutting force coefficient. A total of 6 sets of slot milling experiments with different feed rates were carried out, and the machining parameters are shown in Table 4.

[0238] Table 4. Process parameters used for calibrating cutting force coefficients

[0239]

[0240] The cutting force coefficient was fitted and calibrated using the average cutting force and the least squares method, and the results are as follows:

[0241]

[0242] In the formula, , and These are the shear cutting force coefficients in the radial, tangential, and axial directions, respectively. , and These are the radial, tangential, and axial cutting force coefficients, respectively.

[0243] The cutting force under the machining parameters in group 6 of Table 4 was calculated using a rigid body mechanical force model combined with the calibrated cutting force coefficients, and compared with the measured values ​​from machine tool and robot milling experiments under the same machining parameters. Figure 15As shown, 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 also been verified. However, since the dynamic deformation and instantaneous cutting thickness changes under the influence of robot dynamics are not considered, there is a significant difference from the measured values ​​of robot milling.

[0244] A low-pass filter with a cutoff frequency of 1000Hz was used to eliminate noise fluctuations in the original measured cutting force data. The predicted modal parameters and calibrated cutting force coefficients were used for further cutting force simulation. The cutting force simulation method proposed above was used to calculate the cutting force under different machining tasks. Each machining task involved a workpiece with multiple milling trajectories; segments of two trajectories were selected for cutting force simulation to verify the model's simulation accuracy. The selected trajectories were named: AT1, AT2, BT1, BT2, CT1, and CT2. The model's adaptability is reflected in two aspects. First, during single-trajectory machining, pose-dependent robot modal parameters lead to changes in the calculated dynamic displacement and instantaneous undeformed chip thickness, resulting in variations in the peak cutting force. Second, applying different process parameters under different machining tasks also produces different cutting force distribution profiles. Comparison results are shown below. Figure 16-18 The figures show the simulated and measured cutting force distributions for machining tasks A, B, and C, respectively. The results demonstrate that the proposed model achieves good simulation accuracy in both cases. The contour matching between the calculated and measured values ​​is good, although some deviations exist in local areas, they are within acceptable limits.

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

[0246]

[0247]

[0248] In the formula, and These are the simulated value and the measured value, respectively. The sample size is given. Performance evaluation metrics are listed in Table 5. The results show that the deviation between the extracted simulated and measured peak cutting forces is small, and the RMSE is less than 15% of the peak cutting force, demonstrating good prediction accuracy.

[0249] Table 5 Results of Simulation Model Performance Evaluation Indicators

[0250]

[0251] Based on the accurate cutting force obtained from simulation, the feed rate is optimized using the feed rate planning method proposed above. Constraints are placed on the variation of the milling force amplitude. The allowable force is set to 5%. The minimum feed rate is set to 100 mm / min, and the maximum feed rate is set to 800 mm / min. To improve machining efficiency, the feed rate for idle cutting is set to 1200 mm / min. The results of segmented feed rate optimization are interpolated, and the feed rates before and after optimization are compared as follows: Figure 19 As shown, the feed rate is optimized while maintaining a constant value, under the constraint of the peak cutting force during the cutting stage. Results show that, under the constraint of the peak cutting force, the designed method can achieve adaptive feed rate planning for the milling path.

[0252] The proposed feed rate planning method considers pose-dependent robot modal parameters during machining, achieving accurate cutting force simulation and performing segmented adaptive feed rate planning under cutting force peak constraints. Compared to the fixed feed rate maintained before optimization, larger cutting forces are easily generated at the infeed and poses with poor robot rigidity. The feed rate is reduced to smooth out the cutting force and lower the peak cutting force. Cutting forces are collected during milling, and the machining error of the workpiece before and after feed rate 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 peak cutting force under each machining task is calculated. A comparison of machining time and cutting force before and after feed rate optimization is provided. Figure 20 As shown in the figure, the peak value of the cutting force is effectively reduced and the machining efficiency is improved after feed rate optimization. Specific machining performance indicators are compared in Table 6, where the overall task indicators are the average values ​​of each task. The peak cutting forces of tasks A, B, and C decreased by 53.94%, 46.02%, and 52.82%, respectively; the average peak cutting forces decreased by 23.56%, 24.04%, and 20.73%, respectively; and the machining times decreased by 29.69%, 36.31%, and 28.56%, respectively. The machining errors of the workpiece before and after feed rate optimization are shown in the figure. Figure 21 As shown, the machining error of the parts is significantly reduced after parameter optimization. After feed rate planning, the maximum contour errors of tasks A, B, and C are reduced by 34.98%, 43.96%, and 33.13%, respectively, and the average contour errors are reduced by 34.17%, 31.41%, and 29.46%, respectively.

[0253] Table 6 Comparison of machining performance indicators under fixed feed rate and planned feed rate

[0254]

[0255] The specific application areas or related products of this invention.

[0256] Data-Driven Intelligent Manufacturing: This invention utilizes data such as tool and workpiece information, cutting force coefficients, process parameters, pose-dependent robot dynamics parameters, and machining path information to simulate cutting forces and optimize feed rates in robotic milling. In an intelligent manufacturing environment, this data can be integrated into the enterprise's big data platform, allowing for the discovery of potential patterns and optimization points in the machining process through data analysis. For example, based on the characteristics of different product parts, milling forces can be intelligently simulated, and the robot's machining path planning and cutting parameter settings can be adjusted to achieve personalized and precise production solutions. This not only improves production efficiency but also enhances the stability and reliability of the entire automated production process, ensuring consistent product quality and enabling robotic milling to be better integrated into intelligent manufacturing and industrial automation production lines.

[0257] Ensuring precision machining accuracy: In precision machining fields, such as the manufacturing of aerospace components and high-end medical devices, high precision is required. Feed rate optimization technology based on robotic milling cutting force simulation utilizes optimized feed rates in milling experiments, effectively reducing machining errors and improving machining efficiency. Before part production, pre-optimization of machining parameters can effectively reduce the number of trial cuts and parameter tuning, as well as the associated time costs. This achieves the synergistic development of precision machining and efficient production, meeting the dual demands of modern manufacturing for high-quality and high-efficiency production.

[0258] Extending tool life: Cutting force is one of the key factors affecting tool life, and 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, when it is found that excessive cutting force may lead to excessive tool wear, cutting parameters can be adjusted in time, such as reducing the feed rate, thereby reducing tool load, effectively extending tool life, reducing tool replacement frequency and cost, and improving tool resource utilization efficiency.

[0259] Reducing Energy Consumption: In robotic milling, unreasonable machining parameter settings (such as excessively high cutting speeds and cutting forces) often lead to excessive energy consumption. Milling force simulation and feed rate optimization techniques allow for the optimization of the feed rate before actual production. For example, if a large machining error is found to be due to excessively high feed speeds and cutting forces, reducing the feed rate will reduce the cutting force. This not only improves machining accuracy but also reduces the additional energy consumption required to overcome excessive cutting forces, thus achieving energy conservation and emission reduction goals.

[0260] In conclusion, the simulation of milling force and optimization of feed rate in robotic milling have wide and important applications in many important fields, and are of great significance for improving the performance of robotic machining, the overall level of the manufacturing industry, and achieving sustainable development.

[0261] Evidence related to the technical effects obtained by the embodiments of the present invention.

[0262] Modal parameter prediction model: The proposed MTGPR model is used to predict modal parameters. Scatter plots of predicted and measured values ​​in the X and Y directions of the test set are shown below. Figure 13 and 14 As shown, the difference between predicted and measured values The values ​​are all above 0.9. The results show that the predicted values ​​agree well with the measured values, indicating that the method can capture data trends effectively. For some positions, the prediction accuracy is slightly lower, but still 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 accuracy are shown in Table 3. As can be seen from Table 3, the prediction accuracy of modal parameters in all directions is greater than 90%, demonstrating good prediction performance.

[0263] Milling Force Simulation Accuracy: The proposed cutting force simulation method is used to calculate the cutting force under different machining tasks. Each machining task involves multiple milling trajectories; partial segments of two trajectories are selected for cutting force simulation to verify the model's accuracy. The model's adaptability is reflected in two aspects. First, during single-trajectory machining, pose-dependent robot modal parameters lead to changes in the calculated dynamic displacement and instantaneous undeformed chip thickness, resulting in variations in the peak cutting force. Second, applying different process parameters under different machining tasks will also produce different cutting force distribution profiles. Comparison results are shown below. Figure 16-18 As shown, the simulated and measured cutting force distribution diagrams for machining tasks A, B, and C are presented respectively. The results show that the proposed model achieves good simulation accuracy in both cases. The contour matching between the calculated and measured values ​​is good, although some deviations exist in local areas, they are within acceptable limits. Peak cutting force is particularly important for monitoring the robot's milling state. Therefore, the peak values ​​of the simulated and measured cutting forces in each rotation cycle are extracted and compared statistically. Mean absolute error (MAE) and root mean square error (RMSE) are used as evaluation indicators for the model's predictive performance, and the performance evaluation indicators are listed in Table 5. The results show that the deviation between the extracted simulated and measured peak cutting forces is small, and the RMSE is less than 15% of the maximum cutting force, demonstrating good prediction accuracy.

[0264] Feed rate optimization effect: Based on the accurate cutting force simulated, the feed rate is optimized using the proposed feed rate planning method. A comparison of the feed rates before and after planning is shown below. Figure 19As shown. The feed rate is optimized while maintaining a constant value, under the constraint of peak cutting force during the cutting stage. Results show that the proposed method can achieve adaptive feed rate planning for the milling path under the constraint of peak cutting force. The proposed feed rate planning method considers the pose-dependent robot modal parameters during machining, achieves accurate cutting force simulation, and performs segmented adaptive feed rate planning under the constraint of peak cutting force. Compared to the fixed feed rate maintained before optimization, a large cutting force is generated at the infeed and at poses with poor robot rigidity. Reducing the feed rate smooths out the cutting force and reduces the peak cutting force. Cutting forces are collected during milling, 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 peak cutting force for each machining task is calculated. A comparison of machining time and cutting force before and after feed rate optimization is shown. Figure 20 As shown in the figure, the peak value of the cutting force is effectively reduced and the machining efficiency is improved after feed rate optimization. Specific machining performance indicators are compared in Table 6, where the overall task indicators are the average values ​​of each task. The peak cutting forces of tasks A, B, and C decreased by 53.94%, 46.02%, and 52.82%, respectively; the average peak cutting forces decreased by 23.56%, 24.04%, and 20.73%, respectively; and the machining times decreased by 29.69%, 36.31%, and 28.56%, respectively. The machining errors of the workpiece before and after feed rate optimization are shown in the figure. Figure 21 As shown, the machining error of the parts is significantly reduced after parameter optimization. After feed rate planning, the maximum contour errors of tasks A, B, and C are reduced by 34.98%, 43.96%, and 33.13%, respectively, and the average contour errors are reduced by 34.17%, 31.41%, and 29.46%, respectively.

[0265] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as 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 circuitry 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., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0266] The above description is merely 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 those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for milling force simulation and feed rate optimization considering robot pose-dependent dynamic effects, characterized in that, Includes the following steps: a. Modal testing is performed in multiple poses of the robot milling area. Based on the obtained joint angles and modal parameters, a reference modal parameter prediction model is established when the tool axis is perpendicular to the working plane using Gaussian process regression. The modal parameters in the instantaneous tool direction are obtained through the transformation matrix. b. Establish mechanical force and dynamic models in the robot's cutting area; The workpiece surface is dynamically updated based on the dynamic sweeping trajectory of the cutting edge and the workpiece model. Dynamic updates include: representing the workpiece surface as a Z-map vector aligned with the Z-axis, passing through grid points on the XY plane; calculating the intersection of the Z-map vector and the tool sweep surface based on the simulated dynamic sweep trajectory and cutting parameters, updating the vector, and thus dynamically updating the morphology of the machined surface; updating the machined surface of the workpiece after one cutting edge is completed, and updating the workpiece surface along the entire path according to this update mechanism and the tool feed. Among them, the center point of the tool In the workpiece coordinate system WCS, it is represented as: ； Let R be the planned toolpath, R be the tool radius, and n(t) be the normal vector of the tool contact point on the machined surface. For dynamic displacement under WCS; In the tool coordinate system TCS, the height of the j-th cutting edge The position of the blade tip for: ； N e The number of cutting edges, Given the helix angle, the tool sweep surface under WCS is calculated considering the tool position curve and the corresponding tool axial vector: ； Angular velocity, Let be the rotation matrix about the tool axis; c. Based on the predicted modal parameters and the mechanical force model, the cutting force is calculated to solve for the dynamic displacement, which is then superimposed 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. This includes: using predicted modal parameters, substituting the calculated initial cutting forces in the X and Y directions into the dynamic model of the cutting region to solve for the dynamic displacements in the X and Y directions under TCS. and The actual blade position is obtained by superimposing the theoretical trajectory point onto it. , is represented as: ； The feed per tooth. For the j-th cutting edge at the axial height Radial immersion angle at point, k(z) i (height) Axial immersion angle at the location; calculate And calculate the instantaneous cutting force; and These represent the actual cutting edge positions generated by the current cutting edge and the previous cutting edge, respectively. For the tooth-passing cycle; n s Main spindle speed; d. Based on the cutting force obtained in step c, the feed rate is segmented adaptively planned under the constraint of the peak cutting force, and the optimized feed rate is output for robot milling.

2. The method as described in claim 1, characterized in that, The mechanical cutting force model in step b discretizes the milling cutter into several equal-length micro-elements along the axial direction, calculates the radial and tangential axial components of each micro-element, and sums them in the tool coordinate system to obtain the instantaneous cutting force.

3. The method as described in claim 1, characterized in that, The robot dynamics model in step b only considers the vibration in the X and Y directions within the tool plane. Second-order differential equations for mass, damping, and stiffness are established, and the dynamic displacement is solved using Runge-Kutta.

4. The method as described in claim 1, characterized in that, Step d divides each machining path into several segments, and obtains the optimal feed rate by minimizing the difference between the preset allowable cutting force and the maximum cutting force of each segment, and by applying cutting force amplitude constraints and feed variation constraints.

5. A milling force simulation and feed rate optimization system considering robot pose-dependent dynamic effects, used to implement the method of claim 1, characterized in that, The system includes: The modal testing module is used to perform modal testing in different poses of the robot milling area. Based on the acquired robot joint angles and modal parameters, a predictive model of reference modal parameters under the vertical tool axis vector is established, and the modal parameters in the instantaneous tool direction are obtained through the transformation matrix. The model building module is used to build mechanical force and dynamic models in the robot cutting area; based on the dynamic sweeping trajectory of the cutting edge and the workpiece model, the workpiece surface is dynamically updated to ensure the calculation accuracy of instantaneous cutting thickness and cutting force. The solver module is used to calculate the initial cutting force based on the predicted modal parameters and mechanical force model, solve for the steady-state dynamic displacement caused by the robot dynamics effect, and superimpose it onto the nominal instantaneous undeformed chip thickness, calculate the instantaneous cutting force at each time step, and perform iterative calculation by coupling the workpiece surface dynamic update mechanism. The adaptive planning module is used to perform piecewise adaptive planning of the feed rate under the peak cutting force constraint based on the accurate cutting force in simulation, and to conduct machining error measurement experiments on robot milling and curved parts to verify the performance of the model.

6. A computer-readable storage medium having instructions stored thereon, which, when executed by a processor, cause the processor to perform the method of any one of claims 1 to 4.

7. A control device comprising a processor and a memory, the memory storing instructions that, when executed by the processor, cause the processor to: perform the method according to any one of claims 1 to 4, generate an optimized feed rate, and send the feed rate to a robot control system via a communication interface.

8. A robotic milling machine, comprising an industrial robot, a milling spindle, and the control device as described in claim 7, characterized in that, When the equipment executes the optimized feed rate output by the control device, the instantaneous peak value of the cutting force along the entire machining path does not exceed the preset allowable cutting force, thereby ensuring that the machining error of the curved part is lower than the predetermined tolerance.

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