Nonlinear vibration suppression method, device, equipment, storage medium and product

Abstract

The present application relates to the field of mechanical processing dynamics technology, and discloses a nonlinear vibration suppression method, device, equipment, storage medium and product, the method comprising: establishing an instantaneous milling force model at the joint, and establishing the milling dynamics equation of the rectangular joint under the action of thermal-mechanical coupling based on the instantaneous milling force model, judging the chaotic vibration condition by a chaotic analytical function, and solving the bifurcation diagram of the rectangular joint under the action of the milling force according to the milling dynamics equation and the chaotic vibration condition, analyzing the influence of the milling process parameters on the vibration behavior, and performing a stable prediction of the nonlinear dynamic system by combining the influence law and the bifurcation diagram, and performing vibration suppression based on the stable prediction. Since the present application effectively suppresses the milling vibration during the machining process by establishing an instantaneous milling force model and constructing the milling dynamics equation, and combining the chaotic vibration condition, the influence law and the bifurcation diagram to suppress vibration, the machining quality and machining accuracy are improved.

Description

Technical Field

[0001] The present application relates to the field of mechanical processing dynamics technology, and in particular to a nonlinear vibration suppression method, device, equipment, storage medium and product. Background Art

[0002] At present, hardened steel is widely used in the manufacture of large automobile cover molds. In order to meet the production needs of medium and large automobile covers and stamping parts, a special splicing process is usually used due to the large weight and size of large molds. When the tool processes to the splicing area, it has a great impact on the workpiece vibration system, seriously affecting its processing quality. Summary of the invention

[0003] The main purpose of this application is to provide a nonlinear vibration suppression method, device, equipment, storage medium and product, aiming to solve the technical problem of low processing quality and processing accuracy due to large milling vibration during mold processing.

[0004] To achieve the above objectives, the present application proposes a nonlinear vibration suppression method, the method comprising:

[0005] Establishing an instantaneous milling force model at the joint, and establishing a milling dynamics equation of the rectangular joint under the action of thermal-mechanical coupling based on the instantaneous milling force model;

[0006] The chaotic vibration condition is determined by a chaotic analytical function, and the bifurcation diagram of the rectangular splicing piece under the milling force is solved according to the milling dynamics equation and the chaotic vibration condition;

[0007] The influence of the milling process parameters on the vibration behavior is analyzed, and a stable prediction of the nonlinear dynamic system is performed by combining the influence law and the bifurcation diagram, and vibration suppression is performed based on the stable prediction.

[0008] In one embodiment, the step of establishing an instantaneous milling force model at the joint and establishing a milling dynamics equation of the rectangular joint under the action of thermal-mechanical coupling based on the instantaneous milling force model includes:

[0009] The contact collision process is simplified by assuming that the tool-workpiece contact model is a single-degree-of-freedom collision model, and the contact collision process is further simplified by adopting an equivalent spring-damper model to describe the collision force;

[0010] Based on the contact collision process, an instantaneous milling force model at the joint seam is established, and an instantaneous milling force model under secondary impact force is established by combining the instantaneous milling force model and the secondary cutting impact force;

[0011] Based on the instantaneous milling force model under the secondary impact force, the milling dynamics equation of the rectangular splicing part under the action of thermal-mechanical coupling is established.

[0012] In one embodiment, the step of establishing the milling dynamics equation of the rectangular splicing piece under the action of thermal-mechanical coupling based on the instantaneous milling force model under the secondary impact force includes:

[0013] Based on the instantaneous milling force model under the secondary impact force, the equilibrium equation of the rectangular splicing piece under the action of thermal-mechanical coupling and the dynamic displacement in the modal direction are established;

[0014] The milling dynamics equation of the rectangular splicing piece under the action of thermal-mechanical coupling is established according to the equilibrium equation and the dynamic displacement.

[0015] In one embodiment, the step of determining the chaotic vibration condition by a chaotic analytical function and solving the bifurcation diagram of the rectangular splicing piece under the milling force according to the milling dynamics equation and the chaotic vibration condition comprises:

[0016] By using the variational method, the milling dynamics equation is simplified into a nonlinear dynamic system for milling of a single-degree-of-freedom rectangular mold assembly.

[0017] Solve the equilibrium equations of the rectangular spliced ​​pieces to obtain approximate solutions of physical quantities;

[0018] Calculating a chaotic analytical function based on the approximate solution of the physical quantity, and judging a chaotic vibration condition by comparing the value of the chaotic analytical function with a preset critical value;

[0019] The vibration behavior under the milling force is calculated by high-precision numerical integration method;

[0020] Under the nonlinear dynamic system, the chaotic vibration condition and the vibration behavior are combined to obtain a bifurcation diagram and a maximum Lyapunov index diagram of a rectangular splicing piece under the milling force.

[0021] In one embodiment, the step of obtaining a bifurcation diagram and a maximum Lyapunov index diagram of a rectangular splicing piece under a milling force in combination with the chaotic vibration condition and the vibration behavior under the nonlinear dynamic system includes:

[0022] Under the nonlinear dynamic system, an integral tolerance error is set, which varies with the process parameters of the milling process according to the vibration behavior analysis;

[0023] Combining the variation of the process parameters during the milling process and the chaotic vibration conditions, a bifurcation diagram of the rectangular splicing piece under the milling force is obtained;

[0024] The degree of chaos is evaluated based on the vibration behavior and a maximum Lyapunov exponent diagram is obtained.

[0025] In one embodiment, the step of analyzing the influence of milling process parameters on vibration behavior, performing a stable prediction of the nonlinear dynamic system by combining the influence law and the bifurcation diagram, and performing vibration suppression based on the stable prediction includes:

[0026] Analyze the influence of milling process parameters on vibration behavior through experimental methods and / or simulation methods, wherein the milling process parameters include cutting depth and spindle speed;

[0027] Combining the influence law and the bifurcation diagram, a stable prediction is performed on the nonlinear dynamic system to obtain a stable prediction result;

[0028] Based on the stability prediction result, vibration suppression is performed by optimizing the cutting depth and / or the spindle speed.

[0029] In addition, to achieve the above-mentioned purpose, the present application also proposes a nonlinear vibration suppression device, the nonlinear vibration suppression device comprising:

[0030] A model building module, used to build an instantaneous milling force model at the joint, and to build a milling dynamics equation of the rectangular joint under the action of thermal-mechanical coupling based on the instantaneous milling force model;

[0031] A chaos judgment module is used to judge the chaotic vibration condition through a chaotic analytical function, and solve the bifurcation diagram of the rectangular splicing piece under the milling force according to the milling dynamics equation and the chaotic vibration condition;

[0032] The vibration suppression module is used to analyze the influence of the milling process parameters on the vibration behavior, and to make a stable prediction of the nonlinear dynamic system by combining the influence law and the bifurcation diagram, and to suppress the vibration based on the stable prediction.

[0033] In addition, to achieve the above-mentioned purpose, the present application also proposes a nonlinear vibration suppression device, which includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program is configured to implement the steps of the nonlinear vibration suppression method described above.

[0034] In addition, to achieve the above-mentioned purpose, the present application also proposes a storage medium, which is a computer-readable storage medium, and a computer program is stored on the storage medium. When the computer program is executed by a processor, the steps of the nonlinear vibration suppression method described above are implemented.

[0035] In addition, to achieve the above-mentioned purpose, the present application also provides a computer program product, which includes a computer program, and when the computer program is executed by a processor, the steps of the nonlinear vibration suppression method described above are implemented.

[0036] The technical solution proposed in this application establishes an instantaneous milling force model at the joint, and based on the instantaneous milling force model, establishes the milling dynamics equation of the rectangular joint under the action of thermal-mechanical coupling, judges the chaotic vibration condition through the chaotic analytical function, and solves the bifurcation diagram of the rectangular joint under the action of the milling force according to the milling dynamics equation and the chaotic vibration condition, analyzes the influence of the process parameters of the milling process on the vibration behavior, and makes a stable prediction of the nonlinear dynamic system by combining the influence law and the bifurcation diagram, and performs vibration suppression based on the stable prediction. Because this application effectively suppresses the milling vibration during the processing process by establishing an instantaneous milling force model and constructing the milling dynamics equation, and combines the chaotic vibration conditions, influence law and bifurcation diagram to suppress vibration, it improves the processing quality and processing accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and, together with the description, serve to explain the principles of the present application.

[0038] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0039] Figure 1 A schematic diagram of a flow chart provided for the first embodiment of the nonlinear vibration suppression method of the present application;

[0040] Figure 2 It is the milling temperature test system and the milling temperature relationship curve;

[0041] Figure 3 Establish the relationship diagram of spindle speed-cutting depth-vibration acceleration for the experiment;

[0042] Figure 4 A schematic diagram of a flow chart provided for Embodiment 2 of the nonlinear vibration suppression method of the present application;

[0043] Figure 5 It is a schematic diagram of the knife-worker contact in the stitching seam;

[0044] Figure 6 A schematic diagram of a flow chart provided for Embodiment 3 of the nonlinear vibration suppression method of the present application;

[0045] Figure 7 The bifurcation diagram and maximum Lyapunov index diagram of the system vibration changing with the spindle speed;

[0046] Figure 8The bifurcation diagram and maximum Lyapunov index diagram of the system vibration changing with milling depth;

[0047] Fig. 9 This is a schematic diagram of the module structure of the nonlinear vibration suppression device according to an embodiment of the present application;

[0048] Fig.10 Schematic diagram of the device structure of the hardware operating environment involved in the nonlinear vibration suppression method in the embodiment of the present application.

[0049] The purpose, features and advantages of this application will be further described in conjunction with the embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0050] It should be understood that the specific embodiments described herein are only used to explain the technical solutions of the present application and are not used to limit the present application.

[0051] In order to better understand the technical solution of the present application, a detailed description will be given below in conjunction with the accompanying drawings and specific implementation methods.

[0052] When the tool processes to the mold splicing area, due to the different hardness of the left and right splicing bodies of the splicing piece, the tool generates a certain impact load when cutting into and out of the splicing seam, resulting in large milling vibration and low processing quality and accuracy on the surface of the splicing piece.

[0053] Therefore, in order to overcome the above-mentioned defects, the present application provides a solution by establishing an instantaneous milling force model and constructing the milling dynamics equation, combining chaotic vibration conditions, influence laws and bifurcation diagrams for vibration suppression, thereby effectively suppressing the milling vibration during the processing and improving the processing quality and processing accuracy.

[0054] It should be noted that the execution subject of each embodiment of the present application may be a computing service system with data processing, network communication and program running functions, such as a tablet computer, a personal computer, a mobile phone, etc., or an electronic system capable of realizing the above functions, a nonlinear vibration suppression system, etc. The following embodiments are described below taking the nonlinear vibration suppression system as an example.

[0055] Based on this, the embodiment of the present application provides a nonlinear vibration suppression method, referring to Figure 1 , Figure 1 This is a flow chart of the first embodiment of the nonlinear vibration suppression method of the present application.

[0056] In this embodiment, the nonlinear vibration suppression method includes steps S10 to S30:

[0057] Step S10, establishing an instantaneous milling force model at the joint seam, and establishing a milling dynamics equation of the rectangular joint piece under the action of thermal-mechanical coupling based on the instantaneous milling force model.

[0058] It should be noted that milling refers to the process of cutting mold parts made of multiple pieces of hardened steel using a high-speed rotating milling cutter. Milling is designed to meet the different precision and surface quality requirements of mold splicing parts. Instantaneous milling force refers to the cutting force generated at the moment the tool contacts the workpiece during the milling process.

[0059] Thermal coupling refers to the phenomenon of mutual influence and interaction between thermal effect and mechanical effect, and is the physical behavior of an object under the simultaneous action of thermal and mechanical forces. Figure 2 As shown, Figure 2 The milling temperature test system and the milling temperature relationship curve are used to measure and record the cutting temperature changes during the milling process. The milling temperature test system includes constantan sheet, hot end, flat-bottom end mill, cold end, constantan wire, charge amplifier and other components, which can monitor and record the changes in cutting temperature in real time. Thermal coupling is closely related to the milling temperature test system, and this relationship can be intuitively displayed through the milling temperature relationship curve.

[0060] It can be understood that according to the characteristics of milling processing and the actual situation of the joint, combined with cutting parameters, tool geometry, workpiece material and other factors, a mathematical model describing the instantaneous milling force at the joint is established. On the basis of the established instantaneous milling force model, the influence of the thermal-mechanical coupling effect on the milling process is further considered, and a mathematical equation describing the dynamic characteristics of the rectangular joint during the milling process is established, which can reflect the interaction and mutual influence of multiple aspects such as cutting force, cutting heat, and deformation of the workpiece and tool.

[0061] Step S20, determining the chaotic vibration condition by means of a chaotic analytical function, and solving the bifurcation diagram of the rectangular splicing piece under the milling force according to the milling dynamics equation and the chaotic vibration condition.

[0062] It should be noted that the chaos analytical function is a mathematical tool used to analyze chaotic phenomena. It can describe the dynamic behavior of the system and is used to determine whether the system is in a chaotic state, such as the Melnikov function.

[0063] Chaotic vibration conditions refer to the vibration characteristics of a system when it is in a chaotic state, which may include the range of variation of parameters such as amplitude and frequency.

[0064] A bifurcation diagram is a graph used to describe the dynamic behavior of a system as its parameters change, identifying the stability of the system under different parameters and the conditions for the occurrence of chaotic vibrations.

[0065] It can be understood that the chaotic analytical function is used to analyze the vibration during the milling process, determine whether the system is in a chaotic state, and determine the chaotic vibration conditions. Using the known milling dynamics equations and chaotic vibration conditions, the bifurcation diagram of the rectangular splicing piece under the milling force is solved through mathematical calculation.

[0066] Step S30, analyzing the influence of the milling process parameters on the vibration behavior, and performing a stable prediction on the nonlinear dynamic system by combining the influence law and the bifurcation diagram, and performing vibration suppression based on the stable prediction.

[0067] It should be noted that the milling process parameters refer to various parameters that affect the processing effect and accuracy during milling, such as cutting speed, feed rate, cutting depth, etc. Vibration behavior refers to the periodic or non-periodic reciprocating motion of an object when it is subjected to external forces. Nonlinear dynamic systems refer to systems whose dynamic behavior cannot be described by simple linear equations and are usually complex and unpredictable.

[0068] The step S30 may further include:

[0069] Analyze the influence of milling process parameters on vibration behavior through experimental methods and / or simulation methods, wherein the milling process parameters include cutting depth and spindle speed;

[0070] Combining the influence law and the bifurcation diagram, a stable prediction is performed on the nonlinear dynamic system to obtain a stable prediction result;

[0071] Based on the stability prediction result, vibration suppression is performed by optimizing the cutting depth and / or the spindle speed.

[0072] It should be noted that the experimental method refers to the method of collecting data and analyzing problems through actual operation and measurement. The simulation method refers to the method of using computer models and algorithms to simulate actual physical processes or systems.

[0073] It is understandable that during the milling process, process parameters (such as cutting depth and spindle speed) have a significant impact on the vibration behavior. In order to optimize the milling process, it is necessary to analyze how these process parameters affect the vibration behavior. Then, the influence law and bifurcation diagram can be used to make a stable prediction of the nonlinear dynamic system, thereby suppressing vibration based on the stable prediction results.

[0074] It should be understood that the experimental method for analyzing the influencing law can be achieved by designing experiments and setting different combinations of cutting depth and spindle speed.

[0075] like Figure 3 As shown, Figure 3A relationship diagram of spindle speed, cutting depth and vibration acceleration was established for the experiment. Under each combination, milling was performed, and vibration signals (such as acceleration, displacement, etc.) were measured. The vibration signals were analyzed to find out the vibration characteristics (such as amplitude, frequency, etc.) related to the process parameters.

[0076] For example, the influence of spindle speed and cutting depth changes on the vibration nonlinear chaos of the milling process of rectangular splicing parts is analyzed: in the milling experiment of rectangular splicing parts, the cutting depth and spindle speed are changed, and the spindle speed interval is 500rpm and the cutting depth interval is 0.05mm, and the rectangular splicing parts are milled twice with the same processing parameters.

[0077] Table 1 is the data table of spindle speed-cutting depth-vibration acceleration in the first thin-walled workpiece milling process, and Table 2 is the data table of spindle speed-cutting depth-vibration acceleration in the second spindle speed experiment.

[0078] Table 1 The first spindle speed-cutting depth-vibration acceleration experiment

[0079]

[0080] Table 2 The second spindle speed-cutting depth-vibration acceleration experiment

[0081]

[0082] It should be noted that the simulation method can use finite element analysis (FEA) or dynamic simulation software to establish a mathematical model of the milling process, set different cutting depths and spindle speed parameters in the model, run the simulation, simulate the milling process, output the vibration signal, analyze the simulation results, and find out the influence of process parameters on vibration behavior.

[0083] This embodiment establishes an instantaneous milling force model at the joint, and based on the instantaneous milling force model, establishes the milling dynamics equation of the rectangular joint under the action of thermal-mechanical coupling, judges the chaotic vibration condition through the chaotic analytical function, and solves the bifurcation diagram of the rectangular joint under the action of the milling force according to the milling dynamics equation and the chaotic vibration condition, analyzes the influence of the process parameters of the milling process on the vibration behavior, and makes a stable prediction of the nonlinear dynamic system by combining the influence law and the bifurcation diagram, and performs vibration suppression based on the stable prediction. By establishing an instantaneous milling force model and constructing the milling dynamics equation, and combining the chaotic vibration condition, the influence law and the bifurcation diagram to suppress vibration, the milling vibration in the processing process is effectively suppressed, and the processing quality and processing accuracy are improved.

[0084] Based on the first embodiment of this application, in the second embodiment of this application, the same or similar contents as those in the above embodiment 1 can be referred to the above introduction, and will not be repeated in the following. Figure 4, the step S10 may include steps S101 to S103:

[0085] Step S101 , simplifying the contact collision process by assuming the tool-workpiece contact model to be a single-degree-of-freedom collision model, and further simplifying the contact collision process by adopting an equivalent spring damping model to describe the collision force.

[0086] It is understandable that in mechanical processing, especially in milling and turning, the contact collision between the tool and the workpiece is a complex and critical process. By simplifying this process into a single degree of freedom (such as vertical direction) collision model and using an equivalent spring damping model to describe the collision force, it is easier to analyze and calculate, ignoring the complex shape of the contact surface and the distribution of the contact force, but retaining the main dynamic characteristics of the collision process.

[0087] The equivalent spring-damper model simplifies the energy dissipation and recovery characteristics during a collision into a combination of a spring and a damper. The spring represents the elastic recovery force during a collision, while the damper represents the energy dissipation (such as friction, plastic deformation, etc.). The equivalent spring-damper model makes it easier to calculate the magnitude and direction of the collision force.

[0088] Step S102: establishing an instantaneous milling force model at the joint based on the contact collision process, and establishing an instantaneous milling force model under secondary impact force by combining the instantaneous milling force model and the secondary cutting impact force.

[0089] It should be noted that in some cases, the tool may cut into the already machined area again (for example, due to tool wear, workpiece deformation or programming errors). This secondary cutting will generate additional impact force and affect the instantaneous milling force.

[0090] In order to more accurately describe the mechanical phenomena during secondary cutting, it is necessary to combine the instantaneous milling force model with the secondary cutting impact force. On the basis of the original instantaneous milling force model, a component describing the secondary cutting impact force is added to reflect the additional cutting force and impact force generated during secondary cutting.

[0091] Step S103, establishing a milling dynamics equation of the rectangular splicing piece under the action of thermal-mechanical coupling based on the instantaneous milling force model under the secondary impact force.

[0092] The step S103 may further include:

[0093] Based on the instantaneous milling force model under the secondary impact force, the equilibrium equation of the rectangular splicing piece under the action of thermal-mechanical coupling and the dynamic displacement in the modal direction are established;

[0094] The milling dynamics equation of the rectangular splicing piece under the action of thermal-mechanical coupling is established according to the equilibrium equation and the dynamic displacement.

[0095] It should be noted that under the action of thermal-mechanical coupling, the rectangular splicing parts will be subjected to a variety of forces, including cutting force, impact force, thermal stress, etc. These forces will cause stress distribution and deformation inside the workpiece. In order to describe this mechanical behavior, it is necessary to establish an equilibrium equation that can reflect the mechanical equilibrium state of the workpiece under the action of thermal-mechanical coupling, that is, the sum of all forces acting on the workpiece is zero.

[0096] In addition, it should be noted that under the action of thermal-mechanical coupling, the rectangular spliced ​​parts may cause dynamic displacement due to vibration. Therefore, the dynamic displacement in the modal direction needs to be considered to more accurately describe the vibration behavior of the workpiece.

[0097] For ease of understanding, the following is a combined explanation, but it does not limit the present application. The specific steps of establishing the milling dynamics equation of the rectangular splicing piece under the action of thermal-mechanical coupling based on the instantaneous milling force model and determining the chaotic vibration conditions may be:

[0098] 1. Establish the instantaneous milling force model at the joint

[0099] The physical model of milling dynamics is established. When the tool contacts and collides with the joint, the normal contact force (F N ) and tangential contact force (F T )as follows:

[0100]

[0101] Where K represents the stiffness coefficient; δ represents the elastic deformation of the collision object; n represents the nonlinear exponential factor; c r represents the collision restitution coefficient, Indicates the contact velocity of the contact object; represents the initial contact velocity; represents the end contact velocity; μ represents the friction coefficient.

[0102] When milling a rectangular spliced ​​mold part, the secondary cutting impact force is expressed as:

[0103]

[0104] Based on the transient milling force model, Figure 5 The geometric relationship of the tool-work contact diagram of the joint seam shows that the tool is F at the joint seam x , F y , F z Instantaneous milling force:

[0105]

[0106] In the formula, θ up ,θ down Expressed as axial integral angle; K ke , K re , K ae are the tangential, radial, and axial shear force coefficients θ respectively ex ,θ st It is expressed as the cutting edge's cutting-in angle and cutting-out angle, and h1 and h2 are expressed as the instantaneous cutting thickness.

[0107] according to Figure 5 Schematic diagram of the contact between the cutter and the worker in the joint seam, and the instantaneous cutting thickness h1 and h2 at different positions are obtained:

[0108]

[0109] Where θ is the position angle of the cutting edge micro-point; κ is the axial position angle of the cutting edge micro-point; r is the tool radius; f z It is expressed as the feed per tooth; t(i) is expressed as the tool rotation time.

[0110] 2. Establish the milling process model of the spliced ​​parts

[0111] The equilibrium equation of the rectangular joint under the milling force and milling heat during the milling process is expressed as:

[0112]

[0113]

[0114] Where D 1,2 It is expressed as bending stiffness; w is expressed as longitudinal displacement; M T Expressed as thermal moment; c 1,2 Expressed as the damping coefficient of the splice; ρ 1,2 It is represented by the material density of the splicing parts; h is represented by the thickness of the workpiece;

[0115] It is expressed as instantaneous milling force; E is the elastic modulus of the material; N T Expressed as heat;

[0116]

[0117] μ is Poisson's ratio.

[0118] The expressions of thermal force and thermal moment are:

[0119]

[0120] Where α0 is the linear expansion coefficient of the material; T(x, y, z) is the temperature field function generated by the cutting force during the milling process.

[0121] Workpiece temperature field function during milling:

[0122]

[0123] Where k represents the thermal conductivity of the workpiece;

[0124]

[0125]

[0126]

[0127]

[0128]

[0129] τ1 is the cutting time; τ is the time required for the tool to rotate one circle; ω c is the difference between the cutting angle and the cutting angle; q(τ) is the ratio of the tool-chip contact length to the uncut chip thickness.

[0130] Since the heat flux generated by the tool in the third deformation zone accounts for about 3% of the total heat flux generated by the tool to the workpiece, the heat flux generated by the tool to the first deformation zone and the second deformation zone can be superimposed to approximately equal the heat flux generated by the tool to the workpiece. Therefore, the heat flux q (τ) generated by the tool during milling is:

[0131]

[0132] In the formula, τ s , v, α n ,φ n , β a Represents shear stress, cutting speed, normal rake angle, normal shear angle, and friction angle.

[0133] The internal force equation of the rectangular splicing mold under hot state is:

[0134]

[0135] The rectangular splicing mold part is fixed on two sides and free on the other two sides. a and b are the side lengths of the rectangular splicing mold part. The boundary conditions are:

[0136]

[0137] The displacement function expression of w is obtained by calculation:

[0138]

[0139] Where: w m,n (t) is the Fourier coefficient in the displacement allowable function of the rectangular plate; the values ​​M and N of the expanded series terms m and n in the calculation process are called cutoff values.

[0140] In engineering practice, the system is most affected by the first-order main vibration mode, so equation (12) can be expressed as:

[0141]

[0142] Since the first equation in equation (5) and equation (6) contains the stress function This unknown function, therefore, needs to substitute the first equation in equation (7), equation (8) and equation (13) into the second equation in equation (5) and equation (6) to solve the stress function This unknown function can be calculated as:

[0143]

[0144] In the formula,

[0145]

[0146] According to the undetermined coefficient method, the stress function in equation (14) is calculated as

[0147]

[0148] In the formula,

[0149]

[0150]

[0151] According to the Galerkin principle, the first equation in equation (5) is calculated as follows:

[0152]

[0153] Substituting equation (7) and equation (15) into equation (16) above, we can obtain:

[0154]

[0155] In the formula,

[0156]

[0157]

[0158]

[0159] In the formula,

[0160]

[0161]

[0162]

[0163] In order to facilitate the nonlinear analysis of equation (17), let Therefore, formula (17) can be expressed as:

[0164]

[0165] The system natural frequency can be calculated by formula (18):

[0166] Since M, C, K, N>0, the following dimensionless parameters can be introduced:

[0167] t = ω0τ;

[0168] Finally, formula (18) is rewritten as:

[0169]

[0170] make f = εf1, then the equivalent system of system equation (19) is:

[0171]

[0172] When ε=0 in equation (20), the system is an undisturbed Hamiltonian system, and its Hamiltonian is:

[0173]

[0174] Through the qualitative analysis of equation (21), we can know that (0,0) is the center point of system equation (20), and (±1,0) is the saddle point of system equation (20). When , the system has two heteroclinic orbits connected to (±1,0), and the parametric equation of the heteroclinic orbit is:

[0175]

[0176] The Melnikov function of system (20) along the heteroclinic orbit is obtained:

[0177]

[0178] In the formula,

[0179] From formula (23), we can see that when the parameter δ, f1 satisfies:

[0180]

[0181] The perturbation system (20) is chaotic in the sense of Smale's horseshoe transformation.

[0182] This embodiment simplifies the contact and collision process between the tool and the workpiece through a single degree of freedom collision model and an equivalent spring damping model, establishes an instantaneous milling force model based on the simplified contact and collision process, and considers the secondary cutting impact force. Finally, the milling dynamics equation of the rectangular splicing part under the action of thermal-mechanical coupling is established, which improves the efficiency and accuracy of the dynamics analysis of the splicing part during the milling process, helps to optimize the milling parameters, reduce processing errors, and improve processing quality and efficiency.

[0183] Based on the first embodiment of the present application, in the third embodiment of the present application, the same or similar contents as those in the above-mentioned embodiment 1 can be referred to the above introduction, and will not be repeated in the following. Figure 6 , the step S20 may include steps S201 to S205:

[0184] Step S201, simplifying the milling dynamics equation into a nonlinear dynamic system for milling a single-degree-of-freedom rectangular mold assembly by using a variational method.

[0185] It should be noted that the variational method is a mathematical tool used to solve optimization problems and differential equations. In dynamic analysis, the variational method can be used to simplify complex dynamic equations into a more manageable form.

[0186] It should be understood that when simplifying the milling dynamics equation to a single-degree-of-freedom nonlinear dynamic system, we are actually looking for a simplified model that can describe the main vibration characteristics of the workpiece. This model contains only one degree of freedom, which is the vibration of the workpiece in a specific direction. By ignoring other minor degrees of freedom and nonlinear terms, an equation that is easier to analyze and solve can be obtained. This equation is usually a nonlinear differential equation that is used to describe the vibration behavior of the workpiece during the milling process.

[0187] Step S202, solving the equilibrium equation of the rectangular splicing piece to obtain an approximate solution of the physical quantity.

[0188] It is necessary to explain that due to the complexity of actual problems, it is sometimes impossible to directly obtain an exact solution, and it is necessary to use approximate methods to obtain solutions close to the true value. Approximate solutions of physical quantities refer to approximate values ​​of physical quantities that describe the state of the system obtained by some method (such as numerical methods, optimization algorithms, etc.). These physical quantities may include displacement, velocity, acceleration, force, stress, etc.

[0189] Step S203, calculating a chaotic analytical function based on the approximate solution of the physical quantity, and determining a chaotic vibration condition by comparing the value of the chaotic analytical function with a preset critical value.

[0190] It can be understood that the approximate solution of the physical quantity is substituted into the chaotic analytical function, and the function value is obtained through mathematical operations. The calculated chaotic analytical function value reflects the degree of chaos or the characteristics of chaotic behavior of the system under specific conditions.

[0191] It should be noted that the preset critical value is a pre-set threshold used to determine whether the system meets the conditions for chaotic vibration. This critical value is usually determined based on factors such as the system's physical characteristics, design requirements, and safety standards. It may be a fixed value or a dynamic value related to the system state.

[0192] It should be understood that the calculated chaos analysis function value is compared with the preset critical value. If the chaos analysis function value is greater than or equal to the preset critical value, it is judged that the system meets the conditions of chaotic vibration, that is, the system may be in a chaotic state. If the chaos analysis function value is less than the preset critical value, it is judged that the system does not meet the conditions of chaotic vibration, that is, the system may be in a stable state or other non-chaotic state.

[0193] Step S204, calculating the vibration behavior under the milling force by a high-precision numerical integration method.

[0194] It should be noted that high-precision numerical integration methods are an important means for solving integral problems in mathematics and engineering, such as the fourth-order Runge-Kutta method (RK method). Compared with traditional numerical integration methods, high-precision numerical integration methods have higher calculation accuracy and stronger applicability.

[0195] Step S205, in the nonlinear dynamic system, combining the chaotic vibration condition and the vibration behavior, obtaining a bifurcation diagram and a maximum Lyapunov index diagram of the rectangular splicing piece under the milling force.

[0196] The step S205 may further include:

[0197] Under the nonlinear dynamic system, an integral tolerance error is set, which varies with the process parameters of the milling process according to the vibration behavior analysis;

[0198] Combining the variation of the process parameters during the milling process and the chaotic vibration conditions, a bifurcation diagram of the rectangular splicing piece under the milling force is obtained;

[0199] The degree of chaos is evaluated based on the vibration behavior and a maximum Lyapunov exponent diagram is obtained.

[0200] It should be noted that when performing numerical integration, due to the limitations of calculation accuracy and calculation time, an integral tolerance error is usually set. This error is used to control the accuracy of numerical integration and ensure that the calculation results are within an acceptable range. In the analysis of nonlinear dynamic systems, the setting of the integral tolerance error is crucial to the accuracy of the results.

[0201] It is understandable that during the milling process, changes in process parameters (such as spindle speed, feed rate, cutting depth, etc.) will affect the vibration behavior of the rectangular splice. Through vibration behavior analysis, the impact of these parameter changes on the dynamic behavior of the system can be understood.

[0202] Combine vibration behavior analysis with chaotic vibration conditions to understand the dynamic behavior characteristics of the system under different parameters. Based on the analysis results, draw a bifurcation diagram to show how the system's dynamic behavior changes with parameters. Evaluate the degree of chaos of the system based on the vibration behavior, and draw a maximum Lyapunov index diagram to quantify the degree of chaos of the system.

[0203] For ease of understanding, combined Figure 7 and Figure 8 This invention is provided for illustration, but is not intended to limit the present application. Figure 7 is the system vibration bifurcation diagram and maximum Lyapunov index diagram as the spindle speed changes. Figure 8 is the system vibration bifurcation diagram and maximum Lyapunov index diagram with milling depth. Assuming that the mold splicing material is Cr12MoV, the relevant structural dimensions, physical properties and initial conditions are shown in Table 3. Substitute the above parameters into formula (17) and use the fourth-order RK method to program and calculate, where the integral tolerance error is 10 -6 , through programming calculation, the bifurcation diagram and maximum Lyapunov index diagram of the system vibration are obtained.

[0204] Table 3 Dimensions, physical properties and initial conditions of mold assembly parts

[0205]

[0206] This embodiment simplifies the milling dynamics equation into a nonlinear dynamic system for the milling of a single-degree-of-freedom rectangular mold assembly through a variational method, solves the equilibrium equation of the rectangular assembly, obtains the approximate solution of the physical quantity, and then calculates the chaotic analytical function, determines the chaotic vibration condition, and combines the chaotic vibration condition and the vibration behavior to generate a bifurcation diagram and a maximum Lyapunov index diagram. The chaotic vibration behavior of the rectangular assembly during the milling process can be accurately predicted. By generating a bifurcation diagram and a maximum Lyapunov index diagram, the dynamic characteristics of the system can be intuitively understood, which helps to avoid the adverse effects of chaotic vibration and improve processing stability and reliability.

[0207] It should be noted that the above examples are only used to understand the present application and do not constitute a limitation on the nonlinear vibration suppression method of the present application. More simple transformations based on this technical concept are all within the protection scope of the present application.

[0208] The present application also provides a nonlinear vibration suppression device, please refer to Fig. 9 , the nonlinear vibration suppression device comprises:

[0209] A model building module 10 is used to build an instantaneous milling force model at the joint, and to build a milling dynamics equation of the rectangular joint under the action of thermal-mechanical coupling based on the instantaneous milling force model;

[0210] A chaos judgment module 20 is used to judge the chaotic vibration condition through a chaotic analytical function, and solve the bifurcation diagram of the rectangular splicing piece under the milling force according to the milling dynamics equation and the chaotic vibration condition;

[0211] The vibration suppression module 30 is used to analyze the influence of the milling process parameters on the vibration behavior, and to make a stable prediction of the nonlinear dynamic system by combining the influence law and the bifurcation diagram, and to suppress vibration based on the stable prediction.

[0212] The nonlinear vibration suppression device provided by the present application adopts the nonlinear vibration suppression method in the above embodiment, which can solve the technical problem of low processing quality and processing accuracy due to large milling vibration in the mold processing process. Compared with the prior art, the beneficial effects of the nonlinear vibration suppression device provided by the present application are the same as the beneficial effects of the nonlinear vibration suppression method provided by the above embodiment, and other technical features in the nonlinear vibration suppression device are the same as the features disclosed in the above embodiment method, which will not be repeated here.

[0213] The present application provides a nonlinear vibration suppression device, which includes: at least one processor; and a memory that is communicatively connected to the at least one processor; wherein the memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the nonlinear vibration suppression method in the above-mentioned embodiment 1.

[0214] Reference below Fig.10 , which shows a schematic diagram of the structure of a nonlinear vibration suppression device suitable for implementing the embodiment of the present application. The nonlinear vibration suppression device in the embodiment of the present application may include but is not limited to mobile terminals such as mobile phones, laptop computers, digital broadcast receivers, PDAs (Personal Digital Assistants), PADs (Portable Application Descriptions: tablet computers), PMPs (Portable Media Players: portable multimedia players), vehicle-mounted terminals (such as vehicle-mounted navigation terminals), etc., and fixed terminals such as digital TVs, desktop computers, etc. Fig.10 The nonlinear vibration suppression device shown is only an example and should not bring any limitation to the functions and scope of use of the embodiments of the present application.

[0215] like Fig.10As shown, the nonlinear vibration suppression device may include a processing device 1001 (e.g., a central processing unit, a graphics processor, etc.), which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 1002 or a program loaded from a storage device 1003 to a random access memory (RAM) 1004. In the RAM 1004, various programs and data required for the operation of the nonlinear vibration suppression system are also stored. The processing device 1001, the ROM 1002, and the RAM 1004 are connected to each other through a bus 1005. An input / output (I / O) interface 1006 is also connected to the bus. Generally, the following systems can be connected to the I / O interface 1006: an input device 1007 including, for example, a touch screen, a touch pad, a keyboard, a mouse, an image sensor, a microphone, an accelerometer, a gyroscope, etc.; an output device 1008 including, for example, a liquid crystal display (LCD), a speaker, a vibrator, etc.; a storage device 1003 including, for example, a magnetic tape, a hard disk, etc.; and a communication device 1009. The communication device 1009 can allow the nonlinear vibration suppression device to communicate with other systems wirelessly or by wire to exchange data. Although the nonlinear vibration suppression device with various systems is shown in the figure, it should be understood that it is not required to implement or have all the systems shown. More or fewer systems can be implemented or have instead.

[0216] In particular, according to the embodiments disclosed in the present application, the process described above with reference to the flowchart can be implemented as a computer software program. For example, the embodiments disclosed in the present application include a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program includes a program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network through a communication device, or installed from a storage device 1003, or installed from a ROM 1002. When the computer program is executed by the processing device 1001, the above-mentioned functions defined in the method of the embodiment disclosed in the present application are executed.

[0217] The nonlinear vibration suppression device provided by the present application adopts the nonlinear vibration suppression method in the above embodiment, which can solve the technical problem of low processing quality and processing accuracy due to large milling vibration in the mold processing process. Compared with the prior art, the beneficial effects of the nonlinear vibration suppression device provided by the present application are the same as the beneficial effects of the nonlinear vibration suppression method provided by the above embodiment, and other technical features of the nonlinear vibration suppression system are the same as the features disclosed in the method of the previous embodiment, which will not be repeated here.

[0218] It should be understood that the various parts disclosed in this application can be implemented by hardware, software, firmware or a combination thereof. In the description of the above embodiments, specific features, structures, materials or characteristics can be combined in any one or more embodiments or examples in a suitable manner.

[0219] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

[0220] The present application provides a computer-readable storage medium having computer-readable program instructions (ie, computer programs) stored thereon, and the computer-readable program instructions are used to execute the nonlinear vibration suppression method in the above-mentioned embodiment.

[0221] The computer-readable storage medium provided in the present application may be, for example, a USB flash drive, but is not limited to electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, systems or devices, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In this embodiment, the computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in combination with an instruction execution system, system or device. The program code contained on the computer-readable storage medium may be transmitted using any appropriate medium, including but not limited to: wires, optical cables, RF (Radio Frequency), etc., or any suitable combination of the above.

[0222] The computer-readable storage medium may be included in the nonlinear vibration suppression device; or may exist independently without being assembled into the nonlinear vibration suppression device.

[0223] The above-mentioned computer-readable storage medium carries one or more programs. When the above-mentioned one or more programs are executed by the nonlinear vibration suppression device, the nonlinear vibration suppression device: establishes an instantaneous milling force model at the splicing seam, and establishes the milling dynamics equation of the rectangular splicing piece under the action of thermal-mechanical coupling based on the instantaneous milling force model, judges the chaotic vibration condition through the chaotic analytical function, and solves the bifurcation diagram of the rectangular splicing piece under the action of milling force according to the milling dynamics equation and the chaotic vibration condition, analyzes the influence of the process parameters of the milling process on the vibration behavior, and performs stable prediction of the nonlinear dynamic system by combining the influence law and the bifurcation diagram, and performs vibration suppression based on the stable prediction.

[0224] Computer program code for performing the operations of the present application may be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, C++, and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user's computer, partially on the user's computer, as a separate software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0225] The flow chart and block diagram in the accompanying drawings illustrate the possible architecture, function and operation of the system, method and computer program product according to various embodiments of the present application. In this regard, each square box in the flow chart or block diagram can represent a module, a program segment or a part of a code, and the module, the program segment or a part of the code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the square box can also occur in a sequence different from that marked in the accompanying drawings. For example, two square boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each square box in the block diagram and / or flow chart, and the combination of the square boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs a specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0226] The modules involved in the embodiments described in this application may be implemented by software or hardware, wherein the name of the module does not constitute a limitation on the unit itself in some cases.

[0227] The readable storage medium provided by the present application is a computer-readable storage medium, which stores computer-readable program instructions (i.e., computer programs) for executing the above-mentioned nonlinear vibration suppression method, and can solve the technical problem of low processing quality and processing accuracy due to large milling vibration during mold processing. Compared with the prior art, the beneficial effects of the computer-readable storage medium provided by the present application are the same as the beneficial effects of the nonlinear vibration suppression method provided by the above-mentioned embodiment, and will not be repeated here.

[0228] The present application also provides a computer program product, comprising a computer program, wherein when the computer program is executed by a processor, the steps of the nonlinear vibration suppression method as described above are implemented.

[0229] The computer program product provided by the present application can solve the technical problem of low processing quality and processing accuracy due to large milling vibration in the mold processing process. Compared with the prior art, the beneficial effects of the computer program product provided by the present application are the same as the beneficial effects of the nonlinear vibration suppression method provided by the above embodiment, which will not be described in detail here.

[0230] The above descriptions are only some embodiments of the present application, and are not intended to limit the patent scope of the present application. All equivalent structural changes made using the contents of the present application specification and drawings under the technical concept of the present application, or direct / indirect applications in other related technical fields are included in the patent protection scope of the present application.

Claims

1. A nonlinear vibration suppression method, characterized in that: The method comprises the following steps: Establishing an instantaneous milling force model at the joint, and establishing a milling dynamics equation of the rectangular joint under the action of thermal-mechanical coupling based on the instantaneous milling force model; The chaotic vibration condition is determined by a chaotic analytical function, and the bifurcation diagram of the rectangular splicing piece under the milling force is solved according to the milling dynamics equation and the chaotic vibration condition; The influence of the milling process parameters on the vibration behavior is analyzed, and a stable prediction of the nonlinear dynamic system is performed by combining the influence law and the bifurcation diagram, and vibration suppression is performed based on the stable prediction.

2. The nonlinear vibration suppression method according to claim 1, characterized in that: The step of establishing an instantaneous milling force model at the joint, and establishing a milling dynamics equation of the rectangular joint under the action of thermal-mechanical coupling based on the instantaneous milling force model, comprises: The contact collision process is simplified by assuming that the tool-workpiece contact model is a single-degree-of-freedom collision model, and the contact collision process is further simplified by adopting an equivalent spring-damper model to describe the collision force; Based on the contact collision process, an instantaneous milling force model at the joint seam is established, and an instantaneous milling force model under secondary impact force is established by combining the instantaneous milling force model and the secondary cutting impact force; Based on the instantaneous milling force model under the secondary impact force, the milling dynamics equation of the rectangular splicing part under the action of thermal-mechanical coupling is established.

3. The nonlinear vibration suppression method according to claim 2, characterized in that: The step of establishing the milling dynamics equation of the rectangular splicing piece under the action of thermal-mechanical coupling based on the instantaneous milling force model under the secondary impact force includes: Based on the instantaneous milling force model under the secondary impact force, the equilibrium equation of the rectangular splicing piece under the action of thermal-mechanical coupling and the dynamic displacement in the modal direction are established; The milling dynamics equation of the rectangular splicing piece under the action of thermal-mechanical coupling is established according to the equilibrium equation and the dynamic displacement.

4. The nonlinear vibration suppression method according to any one of claims 1 to 3, characterized in that: The step of judging the chaotic vibration condition by using the chaotic analytical function and solving the bifurcation diagram of the rectangular splicing piece under the milling force according to the milling dynamics equation and the chaotic vibration condition comprises: By using the variational method, the milling dynamics equation is simplified into a nonlinear dynamic system for milling of a single-degree-of-freedom rectangular mold assembly. Solve the equilibrium equations of the rectangular spliced ​​pieces to obtain approximate solutions of physical quantities; Calculating a chaotic analytical function based on the approximate solution of the physical quantity, and judging a chaotic vibration condition by comparing the value of the chaotic analytical function with a preset critical value; The vibration behavior under the milling force is calculated by high-precision numerical integration method; Under the nonlinear dynamic system, the chaotic vibration condition and the vibration behavior are combined to obtain a bifurcation diagram and a maximum Lyapunov index diagram of a rectangular splicing piece under the milling force.

5. The nonlinear vibration suppression method according to claim 4, characterized in that: The step of obtaining the bifurcation diagram and the maximum Lyapunov index diagram of the rectangular splicing piece under the milling force in combination with the chaotic vibration condition and the vibration behavior under the nonlinear dynamic system includes: Under the nonlinear dynamic system, an integral tolerance error is set, which varies with the process parameters of the milling process according to the vibration behavior analysis; Combining the variation of the process parameters during the milling process and the chaotic vibration conditions, a bifurcation diagram of the rectangular splicing piece under the milling force is obtained; The degree of chaos is evaluated based on the vibration behavior and a maximum Lyapunov exponent diagram is obtained.

6. The nonlinear vibration suppression method according to claim 1, characterized in that: The step of analyzing the influence of milling process parameters on vibration behavior, performing a stable prediction of the nonlinear dynamic system by combining the influence law and the bifurcation diagram, and performing vibration suppression based on the stable prediction includes: Analyze the influence of milling process parameters on vibration behavior through experimental methods and / or simulation methods, wherein the milling process parameters include cutting depth and spindle speed; Combining the influence law and the bifurcation diagram, a stable prediction is performed on the nonlinear dynamic system to obtain a stable prediction result; Based on the stability prediction result, vibration suppression is performed by optimizing the cutting depth and / or the spindle speed.

7. A nonlinear vibration suppression device, characterized in that: The nonlinear vibration suppression device comprises: A model building module, used to build an instantaneous milling force model at the joint, and to build a milling dynamics equation of the rectangular joint under the action of thermal-mechanical coupling based on the instantaneous milling force model; A chaos judgment module is used to judge the chaotic vibration condition through a chaotic analytical function, and solve the bifurcation diagram of the rectangular splicing piece under the milling force according to the milling dynamics equation and the chaotic vibration condition; The vibration suppression module is used to analyze the influence of the milling process parameters on the vibration behavior, and to make a stable prediction of the nonlinear dynamic system by combining the influence law and the bifurcation diagram, and to suppress the vibration based on the stable prediction.

8. A nonlinear vibration suppression device, characterized in that: The nonlinear vibration suppression device comprises: a memory, a processor, and a nonlinear vibration suppression program stored in the memory and executable on the processor. When the nonlinear vibration suppression program is executed by the processor, the nonlinear vibration suppression method according to any one of claims 1 to 6 is implemented.

9. A storage medium, characterized in that: The storage medium stores a nonlinear vibration suppression program, and when the nonlinear vibration suppression program is executed by the processor, the nonlinear vibration suppression method according to any one of claims 1 to 6 is implemented.

10. A computer program product, characterized in that The computer program product includes a nonlinear vibration suppression program, and when the nonlinear vibration suppression program is executed by a processor, the nonlinear vibration suppression method according to any one of claims 1 to 6 is implemented.

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