Cantilever type workpiece milling chatter self-sensing sliding mode control method and system

Abstract

The present application belongs to the technical field of cutting processing control, and provides a milling chatter self-sensing sliding mode control method and system for cantilever type workpieces, aiming at the defects and improvement needs of the prior art, proposes a milling chatter self-sensing sliding mode control method and control system for cantilever type workpieces, the control method mainly includes the following steps: collecting limited measuring point vibration response, and based on the obtained vibration data, the vibration response of the machining position is predicted in real time according to the mode superposition method and the beam function combination method; the milling system is simplified as a single degree of freedom system, and the workpiece modal dominant machining system dynamics model is established; the controller is designed based on the sliding mode control algorithm. The displacement of the limited measuring point is expanded to the machining position, the real-time self-sensing prediction of the machining point vibration response is realized, the uncertainty of the system and the displacement self-sensing prediction error are taken as disturbance errors, and the system has strong robustness to interference and unmodeled dynamics.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field related to milling processing, and particularly relates to a milling chatter self-sensing sliding mode control method and system for cantilever type workpieces. BACKGROUND

[0002] The statements in this section merely provide background information related to the application and do not necessarily constitute prior art.

[0003] At present, in engineering, cantilever type workpieces are widely used in engine blades, frames and aircraft structural parts in the field of aerospace as a classic structure. Such parts usually have characteristics such as thin wall, thin bottom and weak stiffness, and the main processing method adopted is milling processing, with a large material removal rate in the processing process. Influenced by moving load and material removal, the dynamic characteristics of the workpiece are time-varying, and the processing position is time-varying, and the chatter is prone to occur, thereby causing poor workpiece surface quality, low tool life and low production efficiency. The active control method can adapt to the time-varying dynamic characteristics in the processing process, and has gradually become an effective milling chatter control strategy.

[0004] In the currently disclosed technology and data, the active control scheme of milling chatter of cantilever type workpieces is not perfect, and the following two key problems exist:

[0005] (1) Most control systems regard the workpiece as rigid, and consider that the flexibility of the spindle system is the main factor causing chatter, and the control object is mainly the spindle or tool holder. This is very suitable for rough machining process. In the initial stage of material removal, the stiffness of the workpiece is much greater than that of the tool. However, as the processing proceeds, the material is continuously removed, especially in the finishing process, the thin-wall characteristics and weak stiffness characteristics of the workpiece gradually increase, so that its flexibility is close to or even weaker than that of the spindle system. At this time, the flexibility of the workpiece becomes the main source of the flexibility of the processing system, and the workpiece mode becomes the dominant factor of chatter.

[0006] (2) In the milling process, the processing position changes all the time, and the displacement sensor can only be arranged at a limited fixed position, so it is difficult to obtain the real-time vibration displacement at the processing point, and it is impossible to provide accurate control feedback for the controller. Limited by this problem, some active control algorithms are proposed, in which the target damping position and the vibration monitoring position do not coincide, but the control effect and precision need to be further improved. Designing some auxiliary devices to make the sensor move synchronously with the processing point is a kind of optional solution, but this scheme is limited by the space limitation in the processing system, and the synchronous motion precision of the sensor and the processing point is also difficult to guarantee. SUMMARY

[0007] To solve at least one technical problem in the background art, the present application provides a milling chatter self-sensing sliding mode control method and system for cantilever type workpieces, which takes the chatter caused by workpiece flexibility in the milling process as the control object and actively controls the device with a piezoelectric actuator as the core. When the workpiece mode dominates the chatter caused by the milling force of the milling system, the beam function combination method and the mode superposition method are used to extend the displacement measurement results at the limited measuring points to the machining position, realize real-time self-sensing prediction of the vibration response at the machining point, and transmit the predicted vibration state to the upper computer control software. The control software further calculates the control input at the current time according to the designed sliding mode control algorithm and the received real-time vibration state at the machining position, and then drives the piezoelectric actuator to generate an actuating force on the machining system to realize chatter control. In order to effectively suppress the machining chatter of the cantilever type workpiece, a cantilever plate displacement prediction method based on the vibration response of the limited measuring points is proposed to realize real-time prediction of the vibration response at the machining point and provide feedback information for the controller.

[0008] To achieve the above-mentioned purpose, the present application adopts the following technical solutions:

[0009] The first aspect of the present application provides a milling chatter self-sensing sliding mode control method for cantilever type workpieces, which includes the following steps:

[0010] The displacement measurement results at the limited measuring points are extended to the machining position to self-sensing predict the vibration response at the machining position;

[0011] The milling system is simplified as a single degree of freedom system, and a milling dynamics model of the workpiece mode dominant machining system is established;

[0012] The vibration response at the machining position is taken as the control feedback, the sliding mode control algorithm is used in combination with the milling dynamics model of the machining system to design the controller, and the control input at the current time is calculated;

[0013] Based on the control input at the current time, the piezoelectric actuator is driven to output the control force acting on the workpiece to realize chatter control.

[0014] The second aspect of the present application provides a milling chatter self-sensing sliding mode control system for cantilever type workpieces, which includes a plurality of displacement sensors and a control device, and the control device includes a controller and a piezoelectric actuator;

[0015] The plurality of displacement sensors are used to obtain displacement measurement results at limited measuring points;

[0016] The controller is configured to extend the displacement measurement results at the limited measuring points to the machining position to self-sensing predict the vibration response at the machining position;

[0017] The milling system is simplified as a single degree of freedom system, a workpiece modal dominant milling dynamics model of the machining system is established, the vibration response of the machining position is taken as the control feedback, the current time control input is calculated by adopting the sliding mode control algorithm combined with the milling dynamics model of the machining system;

[0018] Based on the control input at the current time, the piezoelectric actuator is driven to output the control force acting on the workpiece to realize the chatter control.

[0019] The beneficial effects of the present application are:

[0020] 1. The displacement measurement results of the limited measuring points are extended to the machining position, the vibration response of the machining position is predicted by self-sensing, the milling system is simplified as a single degree of freedom system, a workpiece modal dominant milling dynamics model of the machining system is established, the vibration response of the machining position is taken as the control feedback, the current time control input is calculated by adopting the sliding mode control algorithm combined with the milling dynamics model of the machining system, the piezoelectric actuator is driven to output the control force acting on the workpiece, the chatter active control for the workpiece is realized, the milling of the weak stiffness thin-walled workpiece can be adapted, especially the chatter generation characteristics and control requirements in the finishing process.

[0021] 2. The target damping position and the vibration measurement position in the control scheme are consistent by the real-time self-sensing prediction of the vibration response of the workpiece machining position, and the control accuracy is higher.

[0022] 3. By simplifying the additional structure of the control target, compared with the active spindle system, the machining system does not need to be obviously changed in structure, and the application of the displacement self-sensing prediction method avoids the space limitation problem faced by the sensor following monitoring.

[0023] 4. From the control algorithm point of view, the sliding mode control can overcome the uncertainty of the system and the error of the displacement self-sensing prediction link, and has strong robustness to interference and unmodeled dynamics.

[0024] The advantages of the additional aspects of the present application will be partially given in the following description, partially will become obvious from the following description, or will be understood by the practice of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0025] The drawings accompanying the specification of the present application form a part thereof, serve to provide further understanding of the present application, and together with the description of the exemplary embodiments of the present application and the explanation thereof serve to explain the present application, and do not constitute improper limitations on the present application.

[0026] Figure 1 The flowchart of the milling chatter self-sensing sliding mode control method for the cantilever type workpiece of the embodiment one of the present application.

[0027] Figure 2Fig. 4(c) is a block diagram of the milling chatter self-sensing sliding mode control for the corresponding cantilever plate of Example Two of the present application.

[0028] Figures 3(a)-3(b) Fig. 3(b) is a milling dynamics model for the corresponding machining system of Example Three of the present application.

[0029] Figure 4 Fig. 3(a) is a schematic diagram of the cantilever plate of Example Three of the present application.

[0030] Figures 5(a)-5(c) Fig. 4(c) is a block diagram of the milling chatter self-sensing sliding mode control for the corresponding cantilever plate of Example Two of the present application. Figure 5(a) 、 5(b) Fig. 5(c) corresponds to verification point V3.

[0031] Figure 6 Fig. 4(c) is a block diagram of the milling chatter self-sensing sliding mode control for the corresponding cantilever plate of Example Two of the present application.

[0032] Figure 7 Fig. 4(c) is a block diagram of the milling chatter self-sensing sliding mode control for the corresponding cantilever plate of Example Two of the present application.

[0033] Figure 8 Fig. 4(c) is a block diagram of the milling chatter self-sensing sliding mode control for the corresponding cantilever plate of Example Two of the present application. DETAILED DESCRIPTION

[0034] The present application will be further described with reference to the drawings and examples.

[0035] It should be noted that the following detailed description is merely exemplary in nature and is intended to provide further description of the present application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0036] It is to be understood that the singular forms "a," "an," and "the" include plural referents unless the context clearly dictates otherwise. It should also be noted that, as used herein, the term "and / or" includes any and all combinations of one or more of the associated listed items. In addition, it should be noted that, as used herein, the terms "the" and / or "a," and "one" or "an" when used in the context of a patent claim, are to be construed to cover a singular as well as the plural, unless otherwise indicated by context.

[0037] In view of the defects and improvement needs of the prior art, the present application proposes a milling chatter self-sensing sliding mode control method and system for cantilever type workpieces. Based on a mechanical model and a control model, in the actual implementation process, first, the layout of the chatter active control device is completed; the active control device includes a displacement sensor, a piezoelectric actuator, an upper computer and a control device. After the control device is laid out, the system processing parameters and control parameters required for the execution of the control scheme are identified / optimized, the number of measurement points is selected and the measurement point positions are optimized. In the processing process, the processing position coordinates are calculated in real time, and based on the beam function combination method and the mode superposition method, the displacement measurement results at the limited measurement points are extended to the processing position, realizing real-time self-sensing prediction of the vibration response of the processing point. Then, the predicted vibration state is transmitted to the upper computer control software, and the control software further calculates the control input at the current time according to the designed mechanical and control models and the obtained real-time vibration state, and applies a control voltage to the piezoelectric actuator. Under the action of the control voltage, the piezoelectric actuator outputs a control force acting on the workpiece, achieving the purpose of suppressing the vibration state of the workpiece, and finally realizing chatter control.

[0038] Embodiment one

[0039] With reference to Figure 1 The present embodiment provides a milling chatter self-sensing sliding mode control method for cantilever type workpieces, comprising the following steps:

[0040] Step 1: obtaining displacement measurement results at limited measurement points;

[0041] Step 2: extending the displacement measurement results at the limited measurement points to the processing position to self-sensing predict the vibration response of the processing position;

[0042] Step 3: simplifying the milling system into a single degree of freedom system, and establishing a milling dynamics model of the processing system dominated by the workpiece mode;

[0043] Step 4: taking the vibration response of the processing position as the control feedback, and using the sliding mode control algorithm to design a controller combined with the milling dynamics model of the processing system to calculate the control input at the current time;

[0044] Step 5: based on the control input at the current time, driving the piezoelectric actuator to output a control force acting on the workpiece to realize chatter control.

[0045] In step 2, the vibration response of the processing position is predicted by extending the displacement measurement results at the limited measurement points to the processing position using the mode superposition method and the beam function combination method, which specifically includes the following steps:

[0046] Step 201: defining the workpiece coordinate system and setting the boundary conditions;

[0047] A cantilever plate xyz coordinate system is established, and the x axis and the y axis are respectively distributed along the free boundary and the fixed boundary perpendicular to each other, and the z axis is along the plate thickness direction, and the coordinate system is set to satisfy the right-hand rule of the space coordinate system.

[0048] The boundary conditions of the workpiece along the x axis direction are set as fixed-free, and the boundary conditions along the y axis direction are set as free-free; the sizes of the workpiece along the x, y and z directions are denoted as a, b and δ respectively.

[0049] Step 202: based on the workpiece coordinate system and the boundary conditions, the mode function of the workpiece is solved;

[0050] The (p, q) order mode function at the coordinate (x, y) of the cantilever plate is expressed as:

[0051] W pq (x, y) = W p (x)W q (y)

[0052] In the formula, W p (x) and W q (y) are the pth and qth order mode functions corresponding to the boundary conditions at the two ends of the x and y directions respectively, and the calculation formulas are respectively:

[0053] W p (x) = (chα p x-cosα p x)-α p (shα p x-sinα p x)

[0054]

[0055] In the formula, α p and α q are the mode coefficients along the x and y directions respectively, and the calculation formulas are respectively:

[0056]

[0057] In the formula, (αa) p and (αb) q are the frequency coefficients along the x and y directions respectively, and the calculation formulas are respectively:

[0058]

[0059] Since N displacement sensors are arranged on the non-machining side of the workpiece surface, the vibration responses of N measuring points are collected, and the collected displacement data are expanded to the machining position, and the following formula is used to predict the vibration response of the machining point in the workpiece milling process in real time:

[0060]

[0061] where N1 and N2 are the order of x and y direction vibration mode, respectively, and N = N1N2; T pq (t) is the pq-th superposition coefficient at time t.

[0062] In particular, the self-sensing here refers to displacement self-sensing of the control system, i.e., the system realizes self-sensing of vibration displacement of the machining position in the cutting process according to vibration response measurement results at limited measurement points and makes a prediction.

[0063] Step 203: Based on the displacement data of each measurement point obtained at time t, a vibration mode superposition equation set is obtained, and a superposition coefficient matrix is solved.

[0064] Solving the superposition coefficient T pq (t) in the vibration response expression, based on the displacement data of each measurement point obtained by the displacement sensor at time t, a vibration mode superposition equation set containing N equations and N1N2 unknowns is obtained:

[0065] W N×pq ·T pq×1 =w N×1 ,p=1,2,…,N1,q=1,2,…,N2

[0066] where W is a non-time-varying vibration mode matrix determined by the vibration mode function expression and the measurement position, T is a time-dependent superposition coefficient matrix, and w is the displacement measured by the sensor at N positions at time t, and the calculation formulas are respectively:

[0067]

[0068]

[0069] w=[w1(t) … w N (t)] T

[0070] In the case where the number of sensors N, the measurement point position and the vibration mode order pq are all selected, W N×pq and w N×1 are determined, and thus the solving formula of the superposition coefficient matrix T is:

[0071] T=(W T W) -1 W T w

[0072] Step 204: Substitute the superposition coefficient matrix and the machining position vibration mode function into the vibration response expression to obtain the real-time vibration response of the machining position (x, y) as:

[0073]

[0074] Further, since there is measurement error in the data acquisition process of the sensor, the influence of the measurement error on the prediction accuracy is reduced by optimizing the measurement position of the displacement sensor.

[0075] In the mode superposition equation system W·T=w, W is a non-time-varying mode matrix, the value of which only depends on the mode function and the measurement position coordinates, so W is accurate, and under this premise, the displacement sensor measurement error calculation formula is:

[0076] Δw=WΔT

[0077] The calculation error of the superposition coefficient matrix T is expressed as follows:

[0078] ΔT=W -1 Δw

[0079] Taking the two norms of both sides of W·T=w, we get

[0080] ||WT||2=||w||2

[0081] From the two norm properties, the following relationship is obtained:

[0082]

[0083] According to the above derivation process, we further obtain

[0084]

[0085] In the formula, is the error coefficient, the smaller the value, the smaller the influence of the displacement sensor measurement error on the prediction accuracy.

[0086] Based on the established coordinate system, the x and y of each measurement point on the workpiece surface are searched in a loop, and when the combination of all measurement point coordinates makes the error coefficient The value is the smallest, the measurement point is taken as the best sensor measurement position.

[0087] In step 3, the milling system is simplified as a single degree of freedom system, and a milling dynamics model of the workpiece modal dominant machining system is established, which specifically includes:

[0088] The vibration direction of the workpiece is set as the X direction, and the motion differential equation of the machine tool-workpiece system without control input is established as follows:

[0089]

[0090] In the formula, X(t) respectively represents the acceleration, velocity and displacement of the machining position along the vibration direction at time t, m, c and k respectively represent the modal mass, modal damping and modal stiffness, and F j(t) is the cutting force of the jth tooth, λ is the number of cutter teeth, F(t) is the cutting force acting in the system, and the related parameter solving formula is:

[0091]

[0092] where ω n represents the natural frequency in radians per second, ξ is the damping ratio of the system, a p is the axial cutting width, K tc is the tangential cutting force coefficient, a XX (t) is the direction coefficient, ΔX(t, τ) represents the difference in workpiece vibration displacement between the current tooth and the previous tooth in the milling process, τ is the rotation period of each tooth, and the solving formula of the related parameters is:

[0093] ω n = 2πf

[0094]

[0095] ΔX(t, τ) = X(t) - X(t - τ)

[0096]

[0097] where f represents the natural frequency in Hz, is the instantaneous contact angle of tooth j, K r is the ratio of the radial cutting force coefficient K rc and the tangential cutting force coefficient K tc , is the phase angle between two teeth, a XX is the average direction coefficient, X(t) and X(t - τ) represent the workpiece vibration displacements corresponding to the current tooth and the previous tooth in the milling process, respectively, and Ω is the spindle speed in radians per second, and are the entry and exit angles, respectively, and the solving formulas of Ω and a XX are as follows:

[0098]

[0099]

[0100] where n is the spindle speed in revolutions per minute.

[0101] For down milling, and are calculated using the following formulas, respectively:

[0102]

[0103] For up milling, and The following formulas are used to calculate, respectively:

[0104]

[0105] In the formula, a e / R is the cutting ratio, a e and R are the radial cutting depth and the radius of the milling cutter, respectively.

[0106] In step 4, the vibration response of the machining position is used as the control feedback, and a sliding mode control algorithm is used to design the controller combined with the milling dynamics model of the machining system, which specifically includes:

[0107] Step 401: Based on the vibration response of the machining position in step 2, the motion differential equation of the machine-tool-workpiece system without control input solved in step 3 is considered, and the following perturbation system is established:

[0108]

[0109] In the formula, I(t) is the control input in the system, and d(t) is the disturbance existing in the system, and the calculation formula is as follows:

[0110]

[0111] In the formula, Δm, Δc, Δk and ΔF represent the uncertainty of the coefficients, and Δd(X(t)) is the error term caused by the displacement prediction error in step 1, and Δd(t) is the external disturbance, and the calculation formula of the related disturbance term is as follows:

[0112]

[0113]

[0114] In the formula, ΔX(t) and ΔX(t-τ) are the errors of the current and previous displacement prediction values relative to the true values, respectively.

[0115] Step 402: A sliding mode control algorithm is used to design the controller, and the following dynamic output feedback sliding surface is defined:

[0116]

[0117] s(t) = ξ + VX(t)

[0118] In the formula, Z and V are normal numbers.

[0119] The following reaching law is designed:

[0120]

[0121] Step 403: in combination with the designed sliding mode surface and the approaching law, the control input of the system is determined in the following form:

[0122]

[0123] In the formula, the correlation coefficient and the function are calculated by the following formula:

[0124] μ = g(t),

[0125] In the formula, A1, A2 and A3 are all constants greater than 0.

[0126] Further, in order to avoid the chattering of the sliding mode control caused by the discontinuity of the sign function s(t) / |s(t)|, the following boundary layer method is introduced:

[0127]

[0128] In the formula, ε is a positive real number.

[0129] The advantages of the above scheme are that the active control of chatter for the workpiece is realized, which can adapt to the milling of the weak stiffness thin-walled workpiece, especially the characteristics and control requirements of the chatter in the finishing process. In addition, the real-time self-sensing prediction of the vibration response of the workpiece machining position is realized, so that the target damping position and the vibration measurement position in the control scheme are consistent, and the control precision is higher. The additional structure for realizing the control target is simple, compared with the active spindle system, and no obvious structural change is needed for the machining system; the application of the displacement self-sensing prediction method avoids the space limitation problem faced by the sensor follow-up monitoring. From the perspective of control algorithm, the sliding mode control can overcome the uncertainty of the system and the error of the displacement self-sensing prediction link, and has strong robustness to disturbance and unmodeled dynamics.

[0130] Embodiment Two

[0131] With reference to Figure 2 The embodiment provides a milling chatter self-sensing sliding mode control system for a cantilever type workpiece, which comprises a plurality of displacement sensors and a control device, wherein the control device comprises a controller and a piezoelectric actuator.

[0132] The plurality of displacement sensors are used to obtain displacement measurement results at limited measurement points.

[0133] The controller is configured to extend the displacement measurement results at the limited measurement points to the machining position, and predict the vibration response of the machining position.

[0134] The milling system is simplified as a single degree of freedom system, and a milling dynamics model of the workpiece modal dominant machining system is established; the vibration response of the machining position is taken as the control feedback, and the sliding mode control algorithm is combined with the milling dynamics model of the machining system to calculate the control input at the current time;

[0135] Based on the control input at the current time, the piezoelectric actuator is driven to output a control force acting on the workpiece to realize chatter control.

[0136] The extension of the displacement measurement results obtained at the limited measuring points to the machining position to predict the vibration response of the machining position includes:

[0137] The workpiece coordinate system is defined, and the boundary conditions are set;

[0138] The vibration mode function of the workpiece is solved based on the workpiece coordinate system and the boundary conditions;

[0139] Based on the displacement data of each measuring point obtained at time t, the vibration mode superposition equation set is obtained, and the superposition coefficient matrix is solved.

[0140] The vibration mode function of the workpiece and the superposition coefficient matrix are substituted into the vibration response expression of the machining point in the workpiece milling process to obtain the real-time vibration response of the machining position.

[0141] When obtaining the displacement data of each measuring point, based on the set workpiece coordinate system, the coordinate values of each measuring point on the workpiece surface are searched in a loop, and when the combination of all measuring point coordinates makes the error coefficient value minimum, the measuring points are taken as the best measuring position.

[0142] It can be understood that in other embodiments, the displacement sensor can be an eddy current displacement sensor or a laser displacement sensor, which measures the vibration signal in a non-contact manner to avoid mass effect. Those skilled in the art can set it according to the specific working conditions, which will not be described in detail here.

[0143] It should be noted that in the present embodiment, the piezoelectric actuator acts on the workpiece, and acts on the non-machining side surface.

[0144] The scheme has the advantages that the active chatter control for the workpiece is realized, and the milling machining of the workpiece with weak stiffness and thin wall can be adapted, especially the chatter occurrence characteristics and control requirements in the finishing process. In addition, the real-time self-sensing prediction of the vibration response of the workpiece machining position is realized, so that the target damping position and the vibration measurement position in the control scheme are consistent, and the control precision is higher. The additional structure for realizing the control target is simple, compared with the active spindle system, and the machining system does not need to be obviously changed in structure; the application of the displacement self-sensing prediction method avoids the space limitation problem of the sensor follow-up monitoring. From the control algorithm point of view, the sliding mode control can overcome the uncertainty of the system and the error of the displacement self-sensing prediction link, and has strong robustness to interference and unmodeled dynamics.

[0145] Embodiment three

[0146] Based on the same inventive concept, that is, in the actual implementation process, first, the arrangement of the active chatter control device is completed; the active control device includes a displacement sensor, a piezoelectric actuator, an upper computer and a control device. After the control device is arranged, the system machining parameters and control parameters required for the control scheme are identified / optimized, the number of measurement points is selected and the measurement point positions are optimized. In the machining process, the machining position coordinates are calculated in real time, and based on the beam function combination method and the mode superposition method, the displacement measurement results at the limited measurement points are extended to the machining position, to realize the real-time self-sensing prediction of the vibration response of the machining point. Then, the predicted vibration state is transmitted to the upper computer control software, and the control software further calculates the control input at the current time according to the designed mechanical and control models and based on the obtained real-time vibration state, and applies a control voltage to the piezoelectric actuator. Under the action of the control voltage, the piezoelectric actuator outputs a control force acting on the workpiece, so as to suppress the vibration state of the workpiece, and finally realize the chatter control.

[0147] In order to further illustrate the effectiveness of the displacement self-sensing prediction algorithm, the simulation analysis of the displacement self-sensing prediction algorithm is carried out based on the milling chatter self-sensing sliding mode control method for the cantilever workpiece in this embodiment.

[0148] This embodiment takes a specific cantilever plate workpiece system as an example for illustration, as shown in FIGS. 3(a) and 3(b), the system includes a cantilever plate 1, a first eddy current displacement sensor 2, a second eddy current displacement sensor 3, a piezoelectric actuator 4, a third eddy current displacement sensor 5, a fourth eddy current displacement sensor 6 and a milling cutter 7.

[0149] Under this milling dynamics model, the simulation analysis of the cantilever plate under the action of the moving load is studied by means of ABAQUS software. Figure 4

[0150] The size parameters, material properties, load conditions and measurement points and verification points of the cantilever plate are set as follows: ​

[0151] Dimensional parameters: a = b = 80 mm, δ = 4 mm;

[0152] Material properties: Density is 2.81 g / cm³ 3 The Young's modulus is 71 GPa and the Poisson's ratio is 0.33.

[0153] Load conditions: The moving load F(t) = 50sin(2πt) moves along a straight line x = 0.06m at a speed of 25mm / s;

[0154] Measurement points: 4, namely M1(0.04,0.01,0), M2(0.07,0.01,0), M3(0.07 0.07,0), and M4(0.04,0.07,0);

[0155] Verification points: 3, namely V1(0.06,0.01,0), V2(0.06,0.04,0), and V3(0.06 0.07,0).

[0156] Since chatter in a machining system is generally caused by the excitation of the first two to three modes, the first four modes are superimposed according to the method in Example 1 to obtain... Figures 5(a)-5(c) The comparison results of simulated and predicted displacements of the cantilever plate are shown in Figures 5(a), 5(b), and 5(c), which correspond to verification points V1, V2, and V3, respectively. Figures 5(a)-5(c) It can be seen that the displacement self-sensing prediction method proposed in this invention can achieve better prediction of the vibration response at the processing position of the cantilever plate, thereby providing real-time control feedback for the designed sliding mode control algorithm and realizing flutter control. The error between the predicted displacement and the actual displacement has been taken into account as interference and unmodeled dynamics in the control algorithm. The use of sliding mode control can overcome the uncertainty of the system and the error of the displacement self-sensing prediction link.

[0157] To more clearly describe the effectiveness of the control method, some simulation analyses are presented. In the simulation analysis, the system's modal parameters, processing parameters, and control parameters are set as follows:

[0158] Modal parameters: k = 2.22 × 10 6 N / m, f=598.1Hz, ξ=0.0199;

[0159] Processing parameters: K tc =796MPa, K rc =169MPa, λ=3, a e =4mm, a p =1.1mm, R=5mm, n=7407r / min, machining method is reverse milling;

[0160] Control parameter: A1 = 5.2s-1 , A2=25N / (m·s), A3=800N / s, V=1000, ρ=0.1s -1 , s0=100m, Z=1N / m, ε=5×10 -3 m.

[0161] Simulation results are as follows Figure 6 , Figure 7 and Figure 8 As shown, by Figure 6 It is known that the open-loop milling process is unstable without active control. Therefore, the active control algorithm proposed in this invention is applied to the milling process to form a closed-loop system, which rapidly and effectively suppresses chatter, achieving the goal of chatter control. Furthermore, the control input required to achieve system stability is very small.

[0162] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method of milling chatter self-sensing sliding mode control for cantilever-like workpieces, characterized by, The method comprises the following steps: The displacement measurement results obtained at the limited measuring points are extended to the machining position, and the vibration response of the machining position is predicted by self-sensing, comprising: Defining a workpiece coordinate system and setting boundary conditions; Solving the vibration mode function of the workpiece based on the workpiece coordinate system and the boundary conditions; Based on The displacement data of each measuring point obtained at the moment is used to obtain a mode superposition equation group, and a superposition coefficient matrix is solved. Substituting the vibration mode function of the workpiece and the superposition coefficient matrix into the vibration response expression of the machining point in the workpiece milling process to obtain the real-time vibration response of the machining position; Simplifying the milling system into a single degree of freedom system, and establishing a workpiece modal dominant machining system milling dynamics model; Taking the vibration response of the machining position as the control feedback, using the sliding mode control algorithm combined with the machining system milling dynamics model to design the controller, and calculating the control input at the current time; Based on the control input at the current time, the piezoelectric actuator is driven to output the control force acting on the workpiece to realize chatter control.

2. The method of milling chatter self-sensing sliding mode control for cantilever type workpieces of claim 1, wherein, The displacement measurement results obtained at the limited measuring points are extended to the machining position by using the mode superposition method and the beam function combination method to predict the vibration response of the machining position.

3. The method of chisel flutter self-sensing sliding mode control for cantilever type workpiece as claimed in claim 1, wherein, When obtaining the displacement data of each measuring point, based on the set workpiece coordinate system, the coordinate values of each measuring point on the workpiece surface are searched in a loop. When the combination of all measuring point coordinates makes the error coefficient value minimum, the corresponding measuring point is taken as the best measuring position.

4. The method for milling chatter self-sensing sliding mode control for cantilever type workpiece as claimed in claim 1, wherein, The workpiece modal dominant machining system milling dynamics model is: wherein, , , respectively represent the acceleration, velocity and displacement of the machining position along the vibration direction at time t, t m , c , k respectively represent the modal mass, modal damping and modal stiffness, F j t is the cutting force of the jth tooth, j is the number of teeth of the milling cutter, λ F t is the cutting force acting in the system;​​​​ , , ω n Represents the natural frequency in radians per second. ξ The damping ratio of the system, a p The axial cutting width. K tc The tangential cutting force coefficient is... a XX ( t ) represents the direction coefficient, Δ X ( t , τ This represents the difference in workpiece vibration displacement between the current tooth and the preceding tooth during the milling process. τ The number of rotation cycles per tooth.

5. The method for milling chatter self-sensing sliding mode control for cantilever type workpieces as claimed in claim 1, wherein, Taking the vibration response of the machining position as the control feedback, using the sliding mode control algorithm combined with the machining system milling dynamics model to design the controller, and calculating the control input at the current time, specifically comprising: Taking the vibration response of the machining position as the control feedback, based on the motion differential equation of the machine tool-workpiece system without control input, considering the control input of the system, and establishing a perturbed system; Using the sliding mode control algorithm to design the controller, and defining the dynamic output feedback sliding surface; Combined with the designed sliding surface and the approaching law, the control input of the system is determined.

6. The method for milling chatter self-sensing sliding mode control for cantilever type workpieces of claim 1, wherein, When the sliding mode control algorithm is combined with the machining system dynamics model to design the controller, the uncertainty of the system and the displacement self-sensing prediction error are taken as disturbance errors.

7. A milling chatter self-sensing sliding mode control system for cantilever type workpieces, characterized by, Comprise: A plurality of displacement sensors and a control device, the control device comprising a controller and a piezoelectric actuator; The plurality of displacement sensors are used to obtain displacement measurement results at limited measuring points; The controller is configured to: extend the displacement measurement results obtained at the limited measuring points to the machining position, and predict the vibration response of the machining position by self-sensing, comprising: Defining a workpiece coordinate system and setting boundary conditions; Solving the vibration mode function of the workpiece based on the workpiece coordinate system and the boundary conditions; Based on The displacement data of each measuring point obtained at the moment is used to obtain a mode superposition equation group, and a superposition coefficient matrix is solved. Substituting the vibration mode function of the workpiece and the superposition coefficient matrix into the vibration response expression of the machining point in the workpiece milling process to obtain the real-time vibration response of the machining position; Simplifying the milling system into a single degree of freedom system, and establishing a workpiece modal dominant machining system milling dynamics model; taking the vibration response of the machining position as the control feedback, using the sliding mode control algorithm combined with the machining system milling dynamics model, and calculating the control input at the current time; Based on the control input at the current time, the piezoelectric actuator is driven to output the control force acting on the workpiece to realize chatter control.

8. The milling chatter self-sensing sliding mode control system for cantilever-like workpieces of claim 7, wherein, In the acquisition of each measuring point displacement data, based on the set workpiece coordinate system, the coordinate value of each measuring point on the workpiece surface is searched circularly, when the combination of all measuring point coordinates makes the error coefficient value minimum, the corresponding combination of measuring points is taken as the best measuring position.

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