Robust sliding mode control method and system for milling chatter of frame beam type aviation thin-walled workpiece

Abstract

The invention belongs to the technical field of vibration control, and provides a robust sliding mode control method and system for milling chatter of a frame beam type aviation thin-walled workpiece, and the technical scheme is as follows: determining cutter chatter active control application conditions; modeling is conducted on all corner milling technological processes through kinematics and dynamics, the corner milling process chip thicknesses in all the technological processes are established respectively, and the instantaneous milling force of a cutter is calculated in combination with the chip thicknesses; the flexibility of the cutter is considered, and a milling system flutter motion equation is established; based on a flutter motion equation of the milling system, considering cutting-in working condition change, unmodeled dynamics and external interference existing in the system, and designing a robust sliding mode controller of the system; the electromagnetic force in the milling system is calculated based on the designed electromagnetic force actuator control scheme, the control current of the electromagnetic actuator is calculated according to the input of the robust sliding mode controller of the system and the electromagnetic force, and non-contact control over the rotary cutter handle is achieved. The problem that milling chatter active control is poor in robustness and reliability is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of vibration control, and particularly relates to a milling chatter robust sliding mode control method and system for frame beam type thin-walled aviation parts. Background Art

[0002] The statements in this part merely provide background technical information related to the present invention and do not necessarily constitute prior art.

[0003] Thin-walled parts are widely used in the high-end equipment manufacturing in the aviation field. Most of these parts are integral structural parts, and the material removal rate during the machining process is extremely high. From the perspective of structural characteristics, thin-walled parts have typical weak rigidity characteristics, and chatter frequently occurs during the cutting process. Traditional passive control technologies cannot sense the machining state of parts and have insufficient adaptability to the changes in the dynamic characteristics of thin-walled parts. Active control technologies can measure the machining vibration data in real time, and based on this, apply active control forces to the spindle system based on control algorithms and appropriate actuators. However, the existing active control schemes have the following problems:

[0004] (1) Most of the control algorithms are based on traditional control theories, which are not robust to the changes in machining parameters caused by the change of cutting conditions. At the same time, the control process pays insufficient attention to the changes in the geometric characteristics of the workpiece, and the reliability of the control system is poor.

[0005] (2) To determine the applicable process range of the active control scheme for tool chatter, it is necessary to identify the stiffness of the workpiece in different machining stages. The existing modal identification methods rely heavily on manual work, especially for the results of batch tests, and the processing process is time-consuming.

[0006] (3) Most of the reported active control schemes are based on piezoelectric actuators, and actively control the rotor structure by means of conventional ball bearings. The radial force applied is likely to cause overheating of the bearings, and it is difficult to adjust the installation distance of the actuator. Summary of the Invention

[0007] In order to solve at least one of the above technical problems in the background art, the present invention provides a milling chatter robust sliding mode control method and system for frame beam type thin-walled aviation parts. Based on the high-quality and high-efficiency machining requirements of aviation parts, it is necessary to combine the actual machining characteristics such as multi-working conditions of the side walls and corners of thin-walled parts and the changes in cutting parameters, and propose a milling chatter robust sliding mode control method for frame beam type thin-walled aviation parts.

[0008] In order to achieve the above object, the present invention adopts the following technical solutions:

[0009] The first aspect of the present invention provides a milling chatter robust sliding mode control method for frame beam type thin-walled aviation parts, including the following steps:

[0010] Identify the stiffness of the to-be-machined thin-walled aircraft frame and beam parts, and determine the applicable conditions for active control of tool chatter based on the stiffness of the to-be-machined thin-walled aircraft frame and beam parts;

[0011] Model each process of corner milling through kinematics and dynamics, establish the chip thickness in the corner milling process for each process respectively, and calculate the instantaneous milling force of the tool in combination with the chip thickness;

[0012] Establish a chatter dynamics model of the milling system considering tool flexibility;

[0013] Based on the chatter motion equation of the milling system, considering the changes in cutting depth conditions, unmodeled dynamics, and external disturbances existing in the system, design a robust sliding mode controller for the system;

[0014] Calculate the electromagnetic force in the milling system based on the designed electromagnetic force actuator control scheme, calculate the control current of the electromagnetic actuator according to the input of the system robust sliding mode controller and the electromagnetic force, and apply the control current to the electromagnetic force actuator to generate electromagnetic force to achieve non-contact control of the rotating tool shank.

[0015] Furthermore, the identification process of the stiffness of the to-be-machined thin-walled aircraft frame and beam parts includes:

[0016] Obtain a dataset of frequency response curve pictures of the side wall milling of frame and beam parts with different thicknesses;

[0017] Construct a training dataset based on the dataset of frequency response curve pictures of the side wall milling of frame and beam parts with different thicknesses, train the frequency response curve quality classification model to obtain the trained frequency response curve quality classification model, and classify the to-be-identified frame and beam parts using the trained frequency response curve quality classification model to obtain the classification result;

[0018] Based on the trained frequency response curve quality classification model, identify the to-be-identified frame and beam parts to obtain the classification result, and conduct stiffness identification of the thin-walled parts for the frequency response curve data that meets the modal identification requirements to obtain the stiffness identification result of the thin-walled parts.

[0019] Furthermore, when obtaining the dataset of frequency response curve pictures of the side wall milling of frame and beam parts with different thicknesses, conduct impact tests at different positions on the side wall thin plate, strike multiple times at each measuring point, obtain the time-domain signals of the impact force and displacement, segment the time-domain signals of the impact force and displacement, each segment of data only includes the result of a single strike, conduct frequency-domain analysis on the segmented time-domain data, and draw the frequency response diagram corresponding to each segment of test data.

[0020] Furthermore, the modeling of each process of corner milling through kinematics and dynamics includes:

[0021] For the straight-line entry and straight-line exit stages, by analyzing the geometric characteristics of the straight-line entry stage, calculate the contact arc length:

[0022] L arc = rα, α = arccos[(r - a e ) / r];

[0023] In the arc stage, calculate the intersection coordinates (x P , y P ) of the cutting edge and the pre - machining contour:

[0024] (x P - x O ) 2 +(y P - y O ) 2 = r 2 ,

[0025]

[0026] In the arc exit stage, the intersection coordinates (x P , y P ) of the cutting edge and the pre - machining contour are:

[0027] (x P - x O ) 2 +(y P - y O ) 2 = r 2 , y P = a e ,

[0028] For the contour of the machined workpiece, the intersection coordinates (x C , y C ) of the cutting edge and the workpiece surface are:

[0029] x C = x O - r, y C = y O ,

[0030] Using the coordinates (x P , y P ) and (x C , y C ), calculate the chord length L cho formed by the intersection coordinates of the cutting edge and the pre - machining and post - machining contours:

[0031]

[0032] x C = x O - r, y C = y O

[0033] The arc lengths swept by the cutting edge during the arc stage and the arc exit stage are as follows:

[0034] L arc = rα, α = 2arcsin[L cho / (2r)],

[0035] where L arc is the contact arc length, the tool diameters and radial depths of cut at the corner position are r and a e , R1 is the radius of the corner arc before machining, (x O , y O ) are the coordinates of the tool center point; α is the contact angle.

[0036] Furthermore, considering the flexibility of the tool, the milling system chatter motion equation is established as:

[0037]

[0038] where

[0039]

[0040] In the formula, and q(t) are the acceleration, velocity and displacement vectors respectively, q x (t) and q y (t) represent the vibrations of the tool in the x and y directions respectively. M, C, and K are the modal mass matrix, stiffness matrix and damping matrix respectively, which are composed of the nominal values and the sums of the perturbation terms m(t), c(t) and k(t). k x (t) and k y (t) are the stiffness change amounts in the x and y directions respectively, c x (t) and c y (t) are the damping coefficient change amounts in the x and y directions respectively, m x (t) and m y (t) are the modal mass change amounts in the x and y directions respectively, is the nominal stiffness in the x and y directions, and are the nominal damping coefficients in the x and y directions respectively, is the nominal modal mass in the x and y directions, F d (t) is the dynamic cutting force, F s (t) is the static cutting force.

[0041] Furthermore, the control law of the robust sliding mode controller is:

[0042] u = -ω + K vs - ψ,

[0043]

[0044] where u is the control law of the robust sliding mode controller, ω is the intermediate expression term of the control input, K v is the diagonal matrix of the sliding mode function, s is the sliding mode function, ψ is the robust compensation term, Λ is a positive matrix, Λ is the tracking error coefficient, q d (t) is the ideal position, e is the system tracking error, the derivative of the system tracking error, M and C are the modal mass matrix and stiffness matrix respectively, Δ is the boundary layer thickness, δ and χ correspond to the unmodeled dynamics and external disturbances respectively, sat(s) is the saturation function, δ N and T D are the compensation reference values of the unmodeled dynamics and external disturbances respectively, γ is the sliding mode function coefficient, k v is the diagonal value of the diagonal matrix of the sliding mode function.

[0045] Furthermore, based on the designed electromagnetic force actuator control scheme, the electromagnetic force calculation formula in the milling system is obtained as follows:

[0046]

[0047] where F a is the resultant force applied to the rotor or spindle, k i and k s represent the current stiffness and displacement stiffness respectively, i c is the control current, i0 is the bias current, c0 is the nominal air gap, α0 is the included angle of the control forces generated by the two magnetic poles, and s is the change in the air gap.

[0048] The second aspect of the present invention provides a robust sliding mode control system for milling chatter of aviation thin-walled parts of frame beams, including:

[0049] A stiffness identification module, which is used to identify the stiffness of the aviation thin-walled parts of frame beams to be machined, and determine the applicable conditions for active control of tool chatter based on the stiffness of the aviation thin-walled parts of frame beams to be machined;

[0050] A process optimization module, which is used to model each process of corner milling through kinematics and dynamics, establish the chip thickness in the corner milling process of each process respectively, and calculate the instantaneous milling force of the tool in combination with the chip thickness;

[0051] A dynamics modeling module, which is used to establish the chatter motion equation of the milling system considering the flexibility of the tool;

[0052] A controller design module, which is used to design a robust sliding mode controller for the system based on the milling system chatter motion equation, considering the cutting depth condition change, unmodeled dynamics, and external disturbances existing in the system;

[0053] An active control module, which is used to calculate the electromagnetic force in the milling system based on the designed electromagnetic force actuator control scheme, calculate the control current of the electromagnetic actuator according to the input of the system robust sliding mode controller and the electromagnetic force, and apply the control current to the electromagnetic actuator to generate electromagnetic force, so as to achieve non-contact control of the rotating tool shank.

[0054] Furthermore, the stator of the electromagnetic actuator and the eddy current displacement sensor are installed coaxially with the tool shank, and the installation position of the eddy current displacement sensor is close to the electromagnetic actuator.

[0055] The third aspect of the present invention provides a program product.

[0056] A program product, which is a computer program product and includes a computer program. When the computer program is executed by a processor, the steps in the above-mentioned milling chatter robust sliding mode control method for frame beam type aviation thin-walled parts are realized.

[0057] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0058] 1. Based on the high-quality and high-efficiency processing requirements of aviation parts, combined with the actual processing characteristics such as multi-working conditions of the side walls and corners of thin-walled parts and changes in cutting parameters, the present invention constructs a robust sliding mode controller for milling chatter of frame beam type aviation thin-walled parts, improving the robustness and reliability of active control of milling chatter.

[0059] 2. The present invention uses a neural network model to quickly identify the quality of the amplitude-frequency curve of the hammering test, greatly improving the modal parameter identification efficiency, and defining the effective working conditions applicable to active control of tool chatter by identifying the relative flexibility between the tool and the workpiece.

[0060] 3. The present invention adopts a robust sliding mode control law. Compared with traditional active control methods, it is robust to the working condition changes caused by cutting parameter changes and the unknown disturbances existing in the system, and the controller performance is better.

[0061] 4. By solving the kinematic and dynamic models of the corner, the present invention proposes a corner deceleration scheme, which combines corner deceleration and active control to effectively alleviate the sudden change of cutting vibration at the corner position.

[0062] The advantages of the additional aspects of the present invention will be partially given in the following description, partially become obvious from the following description, or be understood through the practice of the present invention. Description of the Drawings

[0063] The accompanying drawings forming a part of this invention are used to provide a further understanding of the invention. The schematic embodiments and descriptions thereof of the invention are used to explain the invention and do not unduly limit the invention.

[0064] Figure 1 It is a flowchart of a milling chatter robust sliding mode control method for a frame beam type aerospace thin-walled part provided by an embodiment of the invention;

[0065] Figure 2 It is the tool feed process during corner milling provided by an embodiment of the invention; (a) is the continuous tool feed process, and (b) is the classification of the main machining stages;

[0066] Figure 3 It is the tool dynamics model provided by an embodiment of the invention;

[0067] Figure 4 It is an active control scheme based on an electromagnetic actuator provided by an embodiment of the invention: (a) is the actuator scheme; (b) is the sensing scheme; In the figure, 1. housing and connection mechanism; 2. tool shank; 3. electromagnetic actuator; 4. eddy current displacement sensor; 5. milling cutter; 6. ball bearing; 7. bearing sleeve; 8. acceleration sensor;

[0068] Figure 5 It is the results of different neural network models on the validation set: (a) is the accuracy; (b) is the loss value.

[0069] Figure 6 It is the confusion matrix of different neural network models on the test set: (a) AlexNet; (b) BiLSTM; (c) CNN; (d) ResNet.

[0070] Figure 7 It is a schematic diagram of the machining path of a frame part. In the figure, ①③⑤ represent the straight machining areas, ②④ represent the corner areas, A is the machining starting point, and B is the machining ending point.

[0071] Figure 8 It is the active control test results of a frame part: (a) stage ①; (b) stage ②; (c) stage ③ - x direction; (d) stage ③ - y direction; (e) stage ④; (f) stage ⑤. Detailed implementation manners

[0072] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0073] It should be noted that the following detailed descriptions are all illustrative and are intended to provide a further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs.

[0074] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular forms are also intended to include the plural forms. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they specify the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0075] Embodiment 1

[0076] As Figure 1 shown, this embodiment provides a milling chatter robust sliding mode control method for frame beam type aviation thin-walled parts, including the following steps:

[0077] Step 1: Identify the stiffness of the to-be-machined frame beam type aviation thin-walled part, and determine the applicable conditions for active control of tool chatter based on the stiffness of the to-be-machined frame beam type aviation thin-walled part;

[0078] Specifically, it includes the following steps:

[0079] Step 101: Obtain a dataset of milling amplitude-frequency curve pictures of the side walls of frame beam type parts with different thicknesses;

[0080] In this embodiment, for frame beam type parts with different thicknesses, modal identification is carried out using an eddy current displacement sensor and a force hammer; impact tests are carried out at different positions on the side wall thin plate, and each measuring point is hammered multiple times to obtain the time-domain signals of the hammering force and displacement; the time-domain signals of the hammering force and displacement are segmented, and each segment of data only includes the results of a single hammering. The segmented time-domain data is subjected to frequency-domain analysis, and the amplitude-frequency response diagram corresponding to each segment of test data is drawn. A dataset of milling amplitude-frequency curve pictures of the side walls of frame beam type parts is established based on multiple groups of test results.

[0081] Step 102: Construct a training dataset based on the dataset of milling amplitude-frequency curve pictures of the side walls of frame beam type parts with different thicknesses, train the amplitude-frequency curve quality classification model to obtain a trained amplitude-frequency curve quality classification model, and use the trained amplitude-frequency curve quality classification model to classify the to-be-identified frame beam type parts to obtain a classification result;

[0082] Specifically, it includes the following steps:

[0083] Step 1021: Construct a training dataset based on the dataset of milling amplitude-frequency curve pictures of the side walls of frame beam type parts with different thicknesses;

[0084] In this embodiment, the quality of the amplitude-frequency curve of each picture is manually classified. The label that meets the modal identification requirements is 1, and the one with many burrs in the curve is marked as 0. To avoid the neural network model being biased due to sample imbalance, the number of samples marked as 1 and 0 in the dataset is 1:1. The dataset is divided into a training set, a validation set, and a test set according to the ratio of 6:2:2, and there is no data leakage between each data sample.

[0085] Step 1022: Construct an amplitude-frequency curve quality classification model and train the amplitude-frequency curve quality classification model.

[0086] First, select the model training parameters, including the regularization type, weight decay coefficient, batch size, number of epochs, loss function type, optimizer type, learning rate, learning rate optimizer, learning rate adjustment strategy and learning rate adjustment step size, adjustment coefficient gamma, and activation function, etc.; Second, use the training set to train four deep learning models, namely AlexNet, BiLSTM, CNN, and ResNet, respectively; Finally, use the test set to test the recognition effects of these four models respectively, and select the neural network model with high accuracy and fast convergence speed from them.

[0087] Step 1023: Based on the trained amplitude-frequency curve quality classification model, obtain the classification result for the frame beam parts to be recognized, and carry out the stiffness identification of thin-walled parts for the amplitude-frequency curve data that meets the modal identification requirements.

[0088] For frame beam parts, analyze the modal test results at different processing stages and convert them into gray spectrograms, and input them into the trained neural network model to achieve rapid classification of the amplitude-frequency curve quality.

[0089] Use the amplitude-frequency curve data that meets the modal identification requirements to carry out the stiffness identification of thin-walled parts, compare the workpiece stiffness and the tool stiffness to determine the applicable conditions for tool active control, and select the tool active damping scheme when the workpiece stiffness is significantly greater than the tool.

[0090] Based on the stiffness identification process of the frame beam type aviation thin-walled parts described in Step 1, the workpiece stiffness identification efficiency is greatly improved, and time is saved. At the same time, the applicable conditions for the active control of tool chatter can be accurately defined to ensure the effectiveness of the control scheme.

[0091] Step 2: Model each process of corner milling through kinematics and dynamics, establish the chip thickness in the corner milling process in each process respectively, calculate the instantaneous milling force of the tool in combination with the chip thickness, and optimize the corner milling process.

[0092] Specifically, it includes the following steps:

[0093] Step 201, modeling each process of corner milling through kinematics and dynamics, and establishing the chip thickness of the corner milling process in each process;

[0094] Figure 2 is the tool feeding process of corner milling, r, R1 and R2 are the tool radius at the corner position, the corner radius before machining and the corner radius after machining, respectively, and a e is the radial cutting depth at the corner position, A~E are the intersection points of the tool cutting edge and the contour before processing, A', C', D', E' are the intersection points of the tool cutting edge and the contour after processing, o1, o 1m 、o2、o 2n , o3, o4 are the positions of the tool center points during the machining process, and α is the contact angle.

[0095] Four stages are used to describe the corner milling process, which are defined as straight line cutting in, arc stage, arc exit stage and straight line cutting out stage.

[0096] First, the geometric characteristics of the linear cutting stage are analyzed. The milling cutter gradually approaches point A from a farther processing position. The radial cutting depth remains unchanged during the feeding process, and the contact angle α = arccos[(ra e ) / r] is a constant value, and the arc length obtained by the cutting edge sweep is L arc = rα. For the linear cutting stage, a model similar to the cutting process is adopted, assuming that the tool contact characteristics remain unchanged.

[0097] Then, in the arc stage, the cutting edge enters the corner contour left on the workpiece surface after the previous machining. O ,y O ) is the coordinate of the tool center point. The intersection coordinates (x) of the cutting edge and the contour before machining are solved by combining equations (1) and (2): P ,y P ):

[0098] (x P -x O ) 2 +(y P -y O ) 2 =r 2 (1)

[0099]

[0100] Finally, for the arc exit stage, the tool still feeds in the y direction, but the cutting edge has exited the corner contour left after the previous processing. In addition, the final contour of the current corner has not yet been formed. P ,y P ) is described as:

[0101] (x P -x O ) 2 +(y P -y O ) 2 =r 2 (3),

[0102] y P =a e (4),

[0103] For the contour of the workpiece after machining, the coordinates of the intersection points between the cutting edge and the workpiece surface are solved as

[0104] x C =x O -r, y C =y O (5),

[0105] Using the coordinates (x P , y P ) and (x C , y C ), the chord length formed by the intersection points between the cutting edge and the pre-machining and post-machining contours is further solved to obtain formula (6):

[0106]

[0107] Furthermore, the arc lengths swept by the cutting edge in the arc stage and the arc exit stage are:

[0108] L arc =rα, α=2arcsin[L cho / (2r)] (7),

[0109] Step 202: Calculate the instantaneous milling force of the tool in combination with the chip thickness;

[0110] The tool is discretized axially. For the cutting microelement with a height of dz, the cutting forces in the x, y, and z directions are respectively solved as

[0111]

[0112] In the formula, represents the chip thickness, and K tc , K rc , K ac are defined as the shear force coefficients, and K te , K re , K ae correspond to the plowing force coefficients.

[0113] The microelement cutting force is decomposed in the x, y, and z directions to obtain

[0114]

[0115] Integrate Equation (11) and solve for the resultant force of all the cutting edges to obtain the instantaneous milling force of the tool:

[0116]

[0117] where,

[0118]

[0119] In the formula, σ is the number of cutting edges, are the engagement and disengagement angles respectively, v f is the feed rate, β is the helix angle, is the general form of the tool contact angle.

[0120] Taking up milling as an example, obtain

[0121]

[0122] Solve for the resultant force acting on the tool:

[0123]

[0124] The contribution of the plowing force to the resultant force is usually considered relatively small, and the terms related to K te , K re and K ae are ignored when solving the milling force. According to the above analysis process, the chip thickness L arc in the corner milling process increases significantly, and the milling force will increase rapidly. The sudden change of the milling force is likely to trigger severe chatter. In addition, the cutting force is proportional to the feed rate v f , and it is advisable to appropriately decelerate in the corner area to alleviate the sudden change of the cutting force caused by the increase of the chip thickness.

[0125] Step 3: Establish a chatter dynamics model of the milling system considering tool flexibility;

[0126] Specifically, it includes the following steps:

[0127] Step 301: Calculate the instantaneous cutting thickness of the cutting edge;

[0128] Figure 3 is the tool dynamics model. Establish a coordinate system xoy, with point o located at the center of the tool. The tool system is approximated as a two-degree-of-freedom model along the x and y directions. is the instantaneous contact angle, q j (t) and q j (t - τ) are the dynamic vibrations of two adjacent teeth. is the instantaneous cutting thickness of the j-th cutting edge, F tjand F rj are the tangential and radial milling forces acting on the tooth j, n is the spindle speed, k x and k y are stiffness coefficients, c x and c y are damping coefficients.

[0129] Based on the regenerative chatter mechanism, the instantaneous cutting thickness of the j-th tooth is solved as

[0130]

[0131] where f z is the feed per tooth; q j (t) and q j (t - τ) represent the vibrations of two adjacent teeth respectively; τ = 60 / (σn) is defined as the tooth passing period, and σ and n are the number of teeth and the speed respectively; represents the instantaneous contact angle, and the expression is:

[0132]

[0133] Step 302: Calculate the tangential and radial cutting forces acting on each tooth according to the calculated instantaneous cutting thickness of the tooth, and further calculate the resultant force of all teeth;

[0134] The tangential and radial cutting forces acting on the tooth j are:

[0135]

[0136] where a p corresponds to the axial depth of cut, K r = K rc / K tc , K rc and K tc are the radial and tangential shear force coefficients respectively.

[0137] Decompose the cutting force along the x and y directions, and solve the resultant force of all teeth:

[0138]

[0139] Substitute equations (19) - (21) into equation (22) to obtain the dynamic cutting force F d (t) = [F x F y T .

[0140] Step 303: Construct the chatter dynamics model of the milling system;

[0141] ​In addition, combining with the static cutting force expression, the cutting force of the milling system is solved as follows:

[0142]

[0143] In Equation (23), F d (t) = [F x F y T is the dynamic cutting force, F s (t) is the static cutting force, q(t) = [q x (t) q y (t)] T is the vibration displacement vector of the current tooth, q(t - τ) = [q x (t - τ) q y (t - τ)] T is the vibration displacement vector of the previous tooth, τ is the time delay, f z is the feed speed of the tooth, q x (t) and q y (t) respectively represent the vibration of the tool in the x and y directions.

[0144] H(t) is called the dynamic milling force coefficient matrix. Using the average value approximated by the Fourier series expansion for H(t), the coefficient matrix is obtained:

[0145]

[0146] Among them,

[0147]

[0148] Considering the possible changes in cutting parameters, using a p (t) and a e (t) to replace the axial and radial depths of cut a p and a e , finally, the motion equation of the milling system is obtained as:

[0149]

[0150] Among them

[0151]

[0152]

[0153] In the formula, and q(t) are the acceleration, velocity, and displacement vectors respectively, M, C, and K are the modal mass matrix, stiffness matrix, and damping matrix respectively. Since the nominal value is composed of the sum of the perturbation terms m(t), c(t), and k(t), k x ​(t) and k y (t) are the stiffness variation amounts in the x and y directions respectively, and c x (t) and c y (t) are the damping coefficient variation amounts in the x and y directions respectively, and m x (t) and m y (t) are the modal mass variation amounts in the x and y directions respectively, are the nominal stiffnesses in the x and y directions, are the nominal damping coefficients in the x and y directions, are the nominal modal masses in the x and y directions.

[0154] Step 4: Based on the milling system chatter motion equation, considering the cutting depth condition change, unmodeled dynamics and external disturbances existing in the system, design a robust sliding mode controller for the system;

[0155] In the milling dynamics model, since the static cutting thickness has nothing to do with the regeneration mechanism, the influence of the static milling force is ignored. Considering the cutting depth condition change, unmodeled dynamics and external disturbances existing in the system, the motion equation is rewritten as:

[0156]

[0157] Among them,

[0158]

[0159] In the formula, T(t) is the control input, δ(t) and χ(t) correspond to the unmodeled dynamics and external disturbances respectively, and a p (t) is the axial cutting depth, and according to different working conditions, a p (t) can take different values.

[0160] Set the ideal position as q d (t), and the system tracking error is:

[0161]

[0162] The final control objective under ideal conditions is

[0163] Adopt the following control input:

[0164]

[0165] Substitute equations (27) and (28) into (26), and at the same time combine the time-delay terms into the unmodeled dynamics and disturbances, to obtain

[0166]

[0167] In the formula,

[0168] The sliding mode function satisfies the following form:

[0169]

[0170] where Λ is a positive matrix.

[0171] Based on Eqs. (29) and (30), the control system expression is obtained:

[0172]

[0173] The control system (31) is rewritten as:

[0174]

[0175] where

[0176]

[0177] Select the sliding mode function (30) as the system evaluation signal, and then the evaluation index is defined as follows:

[0178]

[0179] where Eq. (33) represents the L2 norm of d(t), and J is the L2 gain of the system, which measures the anti-interference ability of the system.

[0180] The robust sliding mode control law of the system is designed as

[0181] u = -ω + K v s - ψ (35)

[0182] where

[0183]

[0184] in the formula, u is the control law of the robust sliding mode controller, ω is the intermediate expression term of the control input, K v is the diagonal matrix of the sliding mode function, s is the sliding mode function, ψ is the robust compensation term, Λ is a positive matrix, Λ is the tracking error coefficient, q d (t) is the ideal position, e is the system tracking error, the derivative of the system tracking error, Δ is the boundary layer thickness, δ and χ correspond to the unmodeled dynamics and external disturbances respectively, sat(s) is the saturation function, δ N and T D are the compensation reference values of the unmodeled dynamics and external disturbances respectively, γ is the sliding mode function coefficient, k v is the diagonal value of the diagonal matrix of the sliding mode function.

[0185] Based on the Hamilton-Jacobi inequality and Lyapunov stability theory, the control system based on the control input (35) satisfies the robustness condition J ≤ γ.

[0186] To mitigate the chattering phenomenon that may occur during the control process, the saturation function is optimized in the following form:

[0187]

[0188] where Δ is the boundary layer thickness.

[0189] Step 5: Calculate the electromagnetic force in the milling system based on the designed electromagnetic force actuator control scheme. Calculate the control current of the electromagnetic actuator according to the input of the system robust sliding mode controller and the electromagnetic force. Apply the control current to the electromagnetic force actuator to generate electromagnetic force, and achieve non-contact control of the rotating tool shank.

[0190] As Figure 4 shown in (a) of the figure, an active control structure based on an electromagnetic actuator is adopted to apply the active control force. The stator of the electromagnetic actuator 3 and the eddy current displacement sensor 4 are installed coaxially with the tool shank 2 by means of the housing and the connecting mechanism 1. The eddy current displacement sensor 4 is installed close to the electromagnetic actuator 3, and can measure the vibration displacement in the mutually perpendicular directions. Apply the control current to the electromagnetic actuator 3, and the coil winding around the stator core of the electromagnetic actuator 3 generates electromagnetic force, realizing non-contact control of the rotating tool shank 2.

[0191] Optionally, to improve the vibration signal measurement ability of the active control system, as Figure 4 shown in (b) of the figure, a ball bearing 6 and a bearing sleeve 7 are installed at the end of the tool shank 2, and the bearing sleeve 7 does not rotate with the tool shank 2. An acceleration sensor 8 is attached to the surface of the bearing sleeve 7 for measuring acceleration signals.

[0192] In the described sensing scheme, the number of both the eddy current displacement sensor 4 and the acceleration sensor 8 is two, and they are arranged in the mutually perpendicular directions to measure the tool vibration signals.

[0193] Active control is achieved using an 8-pole radial magnetic bearing. According to the designed control scheme based on the electromagnetic actuator, first only consider a single magnetic pole pair. The included angle between the control forces generated by the two magnetic poles is α0, and the control force F is calculated using the following formula:

[0194]

[0195] where

[0196]

[0197] where c0 is the air gap, μ0 represents the vacuum permeability, A corresponds to the magnetic flux area, and N is the number of coil turns.

[0198] Adopt differential excitation, where one magnet is driven by the sum of the bias current i0 and the control current i c and the other is excited by the difference between i0 and i c The two sets of magnets respectively generate positive forces F + and negative forces F - . Denote the nominal air gap as c0 and s as the air gap change. Then the air gaps of the two symmetric magnetic pole pairs in the actual working process are c0 - s and c0 + s respectively, and the resultant force applied to the rotor or the main shaft is solved as

[0199]

[0200] In the milling processing system, since s << c0 is satisfied, simplify and linearize Equation (38) to obtain

[0201] F a = k i i c + k s s (39),

[0202] where

[0203]

[0204] In the formula, k i and k s respectively represent the current stiffness and the displacement stiffness.

[0205] Calculate the control current based on the control input (35) and the electromagnetic force (39).

[0206] To analyze the performance of different neural network models in the identification of the amplitude-frequency curve quality of modal tests, a hammering test was carried out on a thin plate with three sides fixed and one side free with dimensions of 120 mm × 30 mm × 1 mm for length, width and thickness respectively, where the free side is the 120 mm long side. Hammering was carried out at multiple points on the surface of the thin plate to obtain the time-domain data of the hammering force and the vibration displacement. Perform frequency-domain analysis on the time-domain data to obtain the amplitude-frequency curve and draw pictures. Establish an amplitude-frequency curve picture database, which includes a total of two hundred pictures, and divide the pictures into two categories of 1 (normal) and 0 (abnormal) according to the curve noise and burr states. To avoid the neural network model being biased due to unbalanced sample distribution, the number of samples with labels 1 and 0 in the data set is 100 groups each, and the data set is divided into a training set, a validation set and a test set according to the ratio of 6:2:2.

[0207] The main parameter settings of the training process are as follows: the regularization type is Mean-Std, the weight decay coefficient is 1e-5, the batch size is 16, the number of epochs is 150, the loss function is the cross-entropy loss function, the optimizer type is SGD, the learning rate is 1e-5, the learning rate optimizer is Adam, the learning rate adjustment strategy is MultiStepLR, the learning rate adjustment step is 10, the adjustment coefficient gamma is 0.1, and the activation function is ReLU. The training set is input into four models, namely AlexNet, BiLSTM, CNN, and ResNet, for training respectively.

[0208] According to Figure 5 As shown in (a) and (b) of , all four neural networks have relatively strong recognition capabilities for the amplitude-frequency curve quality. Comparing the loss value curves and accuracy curves of these four neural network models, the accuracy of the AlexNet model and the CNN model on the validation set is higher than that of the BiLSTM and ResNet models, reaching the inflection point before the 20th epoch with an accuracy of 100%. After reaching the inflection point, the model accuracy and loss value tend to be stable without oscillation. Compared with the AlexNet and CNN models, the ResNet model has a faster convergence speed and reaches the inflection point before the 10th epoch, but its accuracy is lower than that of the AlexNet and CNN models. Among the four models, the BiLSTM model has the relatively lowest accuracy and the slowest convergence speed, and there is an obvious oscillation process.

[0209] Furthermore, according to Figure 6 the confusion matrix shown in , all four models show precise recognition capabilities for amplitude-frequency curve samples of different qualities. Except for the BiLSTM model, the accuracy of the other three models for normal and inferior samples is 100%, meeting the requirements for precise sample identification.

[0210] To test the vibration suppression effect of the control method, an active control experiment is carried out on a thin-walled part with a rectangular box. The tool feed path during the machining process and the workpiece dimensions after machining are as Figure 7 shown in . The machining process starts from point A and ends at point B, including five stages ① - ⑤. Among them, ①③⑤ correspond to the straight machining areas, where the tool feed speed is set to 400 mm / min in this area, and ② and ④ represent the corner areas, where the feed speed is 100 mm / min in this area. The tool used is a 3-flute solid end mill with a diameter of 8 mm. According to Figure 7 , stage ① corresponds to stage ⑤, both are straight paths; stage ② corresponds to stage ④, both are corner areas. The controller is turned on around 18.6 s, and the displacements before and after the controller is turned on are compared. The control parameters are set as follows: k i = 24.7 N / A, k s = 1.23×10 5N / m, Λ = diag(2.5, 2.5), γ = 0.03, δ N = 2.0 N, T D = 0.5 N, Δ = 0.005 m.

[0211] According to Figure 8 the results in: A1x = 87.2 μm, A1y = 167.0 μm, A5x = 67.9 μm, A5y = 110.6 μm. After applying the control, the displacement amplitudes in the x and y directions are reduced by 22.1% and 33.8% respectively. A2x = 174.5 μm, A2y = 203.6 μm, A4x = 136.8 μm, A4y = 191.6 μm. After applying the control, the displacement amplitudes in the x and y directions are reduced by 21.6% and 5.9% respectively. Before the control, A3x1 = 156.6 μm, A3y1 = 129.4 μm; after the control, A3x2 = 113.8 μm, A3y2 = 90.8 μm; after applying the control, the displacement amplitudes in the x and y directions are reduced by 27.3% and 29.8% respectively.

[0212] Therefore, based on the proposed robust sliding mode control method for milling chatter of frame beam type aerospace thin-walled parts, the cutting vibration of the workpiece is effectively controlled.

[0213] Embodiment 2

[0214] This embodiment provides a robust sliding mode control system for milling chatter of frame beam type aerospace thin-walled parts, including:

[0215] A stiffness identification module, which is used to identify the stiffness of the to-be-machined frame beam type aerospace thin-walled part, and determine the applicable conditions for active control of tool chatter based on the stiffness of the to-be-machined frame beam type aerospace thin-walled part;

[0216] A process optimization module, which is used to model each process of corner milling through kinematics and dynamics, establish the chip thickness in the corner milling process of each process respectively, calculate the instantaneous milling force of the tool in combination with the chip thickness, and optimize the corner milling process;

[0217] A dynamics modeling module, which is used to establish the chatter motion equation of the milling system considering the flexibility of the tool;

[0218] A controller design module, which is used to design a robust sliding mode controller for the system based on the chatter motion equation of the milling system, considering the changes in cutting depth conditions, unmodeled dynamics, and external disturbances existing in the system;

[0219] An active control module, which is used to calculate the electromagnetic force in the milling processing system based on the designed electromagnetic force actuator control scheme, calculate the control current of the electromagnetic actuator according to the input of the system robust sliding mode controller and the electromagnetic force, apply the control current to the electromagnetic force actuator to generate electromagnetic force, and realize the non-contact control of the rotating tool holder.

[0220] It should be noted that the specific implementation of the milling chatter robust sliding mode control system for the frame beam type of aerospace thin-walled parts in the embodiments of the present invention is similar to that of the milling chatter robust sliding mode control method for the frame beam type of aerospace thin-walled parts in the embodiments of the present invention. For details, please refer to the description in the method section. To avoid redundancy, it will not be elaborated here.

[0221] Embodiment III

[0222] This embodiment provides a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, it implements the steps in a milling chatter robust sliding mode control method for a frame beam type of aerospace thin-walled part as described above.

[0223] Embodiment IV

[0224] This embodiment provides a computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the steps in a milling chatter robust sliding mode control method for a frame beam type of aerospace thin-walled part as described above.

[0225] Embodiment V

[0226] This embodiment provides a program product, which is a computer program product, including a computer program. When the computer program is executed by a processor, it implements the steps in a milling chatter robust sliding mode control method for a frame beam type of aerospace thin-walled part as described above.

[0227] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a hardware embodiment, a software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories and optical memories, etc.) containing computer-usable program code.

[0228] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to the embodiments of the present invention. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, as well as the combination of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate for implementing in the process Figure 1 one process or multiple processes and / or blocks Figure 1means for the functions specified in one or more boxes.

[0229] These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory produce a manufacture including an instruction means that implements the functions specified in one Figure 1 one or more processes and / or boxes Figure 1 means for the functions specified in one or more boxes.

[0230] These computer program instructions may also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are performed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one Figure 1 one or more processes and / or boxes Figure 1 means for the functions specified in one or more boxes.

[0231] Those of ordinary skill in the art can understand that all or part of the processes of implementing the methods in the above embodiments can be completed by instructing relevant hardware through a computer program. The program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above methods. Among them, the storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM), etc.

[0232] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A milling chatter robust sliding mode control method for aircraft thin-walled parts of frame beams, characterized in that, It includes the following steps: Identify the stiffness of the to-be-machined thin-walled aircraft frame and beam parts, and determine the applicable conditions for active control of tool chatter based on the stiffness of the to-be-machined thin-walled aircraft frame and beam parts; Model each process of corner milling through kinematics and dynamics, respectively establish the chip thickness in the corner milling process of each process, and calculate the instantaneous milling force of the tool in combination with the chip thickness; Establish a chatter dynamics model of the milling system considering the flexibility of the tool; Based on the chatter motion equation of the milling system, considering the changes in cutting depth conditions, unmodeled dynamics, and external disturbances existing in the system, design a robust sliding mode controller for the system; Calculate the electromagnetic force in the milling processing system based on the designed control scheme of the electromagnetic force actuator, calculate the control current of the electromagnetic actuator according to the input of the system robust sliding mode controller and the electromagnetic force, and apply the control current to the electromagnetic force actuator to generate electromagnetic force to achieve non-contact control of the rotating tool shank.

2. A milling chatter robust sliding mode control method for a frame beam type aerospace thin-walled part as described in claim 1, characterized in that, The identification process of the stiffness of the to-be-machined thin-walled aircraft frame and beam parts includes: Obtain a dataset of amplitude-frequency curve pictures of the side wall milling of frame and beam parts with different thicknesses; Construct a training dataset based on the dataset of amplitude-frequency curve pictures of the side wall milling of frame and beam parts with different thicknesses, train the amplitude-frequency curve quality classification model to obtain the trained amplitude-frequency curve quality classification model, and use the trained amplitude-frequency curve quality classification model to classify the to-be-identified frame and beam parts to obtain a classification result; Based on the trained amplitude-frequency curve quality classification model, identify the to-be-identified frame and beam parts to obtain a classification result, and carry out stiffness identification of the thin-walled parts for the amplitude-frequency curve data that meet the modal identification requirements to obtain the stiffness identification result of the thin-walled parts.

3. A milling chatter robust sliding mode control method for a frame beam type thin-walled aircraft part as described in claim 2, characterized in that, When obtaining the dataset of amplitude-frequency curve pictures of the side wall milling of frame and beam parts with different thicknesses, conduct impact tests at different positions on the side wall thin plate, hammer each measurement point multiple times, obtain the time-domain signals of the impact force and displacement, segment the time-domain signals of the impact force and displacement, each segment of data only includes the result of a single hammering, and conduct frequency-domain analysis on the segmented time-domain data to draw the amplitude-frequency response diagram corresponding to each segment of test data.

4. A milling chatter robust sliding mode control method for a frame beam type thin-walled aviation part as described in claim 1, characterized in that, The modeling of each process of corner milling through kinematics and dynamics includes: For the straight-line cutting-in and straight-line cutting-out stages, by analyzing the geometric characteristics of the straight-line cutting-in stage, calculate the contact arc length: L arc = rα, α = arccos[(r - a e ) / r]; At the arc stage, calculate the intersection coordinates (x P , y P ) of the cutting edge and the pre-machining contour: (x P -x O ) 2 +(y P -y O ) 2 = r 2 , At the arc exit stage, the intersection coordinates (x P , y P ) of the cutting edge and the pre-machined contour are as follows: (x P - x O ) 2 +(y P - y O ) 2 = r 2 , y P = a e , For the machined workpiece contour, the coordinates (x C , y C ) of the intersection point between the cutting edge and the workpiece surface are as follows: x C = x O - r, y C = y O , Using the coordinates (x P , y P ) and (x C , y C ), calculate the chord length L cho formed by the intersection coordinates of the cutting edge with the pre - machining and post - machining contours: x C = x O - r, y C = y O The arc lengths swept by the cutting edge in the arc stage and the arc exit stage are: L arc = rα, α = 2 arcsin[L cho / (2r)], Among them, L arc is the contact arc length, the tool diameter and the radial depth of cut at the corner position are r and a respectively e , R1 is the radius of the corner arc before machining, (x O , y O ) is the coordinate of the tool center point; α is the contact angle.

5. A milling chatter robust sliding mode control method for a frame beam type thin-walled aircraft part as described in claim 1, characterized in that Considering the flexibility of the tool, the chatter motion equation of the milling system is established as: where q(t) = [q x (t) q y (t)] T , Wherein, and q(t) are the acceleration, velocity and displacement vectors respectively, and q x (t) and q y (t) respectively represent the vibrations of the cutting tool in the x and y directions. M, C, and K are the modal mass matrix, stiffness matrix, and damping matrix respectively, which are composed of the nominal values and the sums of the perturbation terms m(t), c(t), and k(t). k x (t) and k y (t) are the stiffness variations in the x and y directions respectively. c x (t) and c y (t) are the damping coefficient variations in the x and y directions respectively. m x (t) and m y (t) are the modal mass variations in the x and y directions respectively, and are the nominal stiffnesses in the x and y directions, and are the nominal damping coefficients in the x and y directions, and are the nominal modal masses in the x and y directions. F d (t) is the dynamic cutting force, and F s (t) is the static cutting force.

6. A milling chatter robust sliding mode control method for a frame beam type thin-walled aircraft part as described in claim 1, characterized in that, The control law of the robust sliding mode controller is: u = -ω + K v s - ψ, Λ = diag(Λ, Λ), K v = diag(k v , k v ), where \(u\) is the control law of the robust sliding mode controller, \(\omega\) is the intermediate expression term of the control input, \(K\) v is the diagonal matrix of the sliding mode function, \(s\) is the sliding mode function, \(\psi\) is the robust compensation term, \(\varLambda\) is a positive matrix, \(\varLambda\) is the tracking error coefficient, \(q\) d (t) is the ideal position, \(e\) is the system tracking error, the derivative of the system tracking error, \(M\) and \(C\) are the modal mass matrix and the stiffness matrix respectively, \(\Delta\) is the boundary layer thickness, \(\delta\) and \(\chi\) correspond to the unmodeled dynamics and the external disturbance respectively, \(\text{sat}(s)\) is the saturation function, \(\delta\) N and \(T\) D are the compensation reference values of the unmodeled dynamics and the external disturbance respectively, \(\gamma\) is the sliding mode function coefficient, \(k\) v is the diagonal value of the diagonal matrix of the sliding mode function.

7. A milling chatter robust sliding mode control method for a frame beam type thin-walled aircraft part as described in claim 1, characterized in that The calculation formula for the electromagnetic force in the milling processing system calculated based on the designed control scheme of the electromagnetic force actuator is: F a = k i i c + k s s, Among them, F a is the resultant force applied to the rotor or the main shaft, k i and k s represent the current stiffness and the displacement stiffness respectively, i c is the control current, i0 is the bias current, c0 is the nominal air gap, α0 is the included angle of the control forces generated by the two magnetic poles, and s is the change in the air gap.

8. A milling chatter robust sliding mode control system for aerospace thin-walled parts of frame beams, characterized in that, It includes: A stiffness identification module, which is used to identify the stiffness of the to-be-machined thin-walled aircraft frame and beam parts, and determine the applicable conditions for active control of tool chatter based on the stiffness of the to-be-machined thin-walled aircraft frame and beam parts; A process optimization module, which is used to model each process of corner milling through kinematics and dynamics, respectively establish the chip thickness in the corner milling process of each process, and calculate the instantaneous milling force of the tool in combination with the chip thickness; A dynamics modeling module, which is used to establish a chatter motion equation of the milling system considering the flexibility of the tool; A controller design module, which is used to design a robust sliding mode controller for the system based on the milling system chatter motion equation, considering the changes in cutting depth conditions, unmodeled dynamics, and external disturbances existing in the system; An active control module, which is used to calculate the electromagnetic force in the milling system based on the designed electromagnetic force actuator control scheme, calculate the control current of the electromagnetic actuator according to the input of the system robust sliding mode controller and the electromagnetic force, apply the control current to the electromagnetic force actuator to generate electromagnetic force, and realize non-contact control of the rotating tool holder.

9. A milling chatter robust sliding mode control system for a frame beam type thin-walled aircraft part as described in claim 8, characterized in that, Install the stator of the electromagnetic actuator and the eddy current displacement sensor coaxially with the tool holder, and the installation position of the eddy current displacement sensor is close to the electromagnetic actuator.

10. A program product, which is a computer program product and includes a computer program, characterized in that, When the computer program is executed by a processor, the steps in a milling chatter robust sliding mode control method for a box beam type aviation thin-walled part as described in any one of claims 1-7 are implemented.

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