Optimization Design Method and Storage Medium for the Feed System of CNC Machine Tools Based on Cooperative Optimization Strategy

Abstract

The present invention belongs to the technical field of machine tool design, and specifically discloses an optimization design method and a storage medium for a numerical control machine tool feed system based on a collaborative optimization strategy. The method is to determine the design indicators and complete the pre-selection of the main equipment; based on the collaborative optimization method, establish a sub-discipline analysis unit in the MDO framework module of the numerical control machine tool feed system; combine the constructed sub-discipline analysis unit to create optimization models for each discipline; establish a surrogate model for the structural discipline analysis unit; determine the mutual influence and transfer relationship of each sub-discipline analysis unit, and combine the constructed optimization models and surrogate models for each discipline to create a system-level optimization model and a discipline optimization model under the collaborative optimization framework, and carry out the collaborative cyclic optimization of the discipline-level optimization model and the system-level optimization model until the system-level optimization target converges, and obtain the final optimization result and output. The present invention has the characteristics of simple operation, high design efficiency, and significantly improved reliability and flexibility.

Description

Technical Field

[0001] The present invention relates to the technical field of machine tool design, and particularly relates to an optimized design method and a storage medium for a feed system of a numerically controlled machine tool based on a collaborative optimization strategy, which are simple to operate, have high design efficiency, and significantly improved reliability and flexibility. Background Art

[0002] In the development process of the design and manufacturing of numerically controlled machine tools towards lean, global, collaborative, service-oriented, green, and intelligent directions, the traditional design mode of numerically controlled machine tools dominated by experience and analogy is gradually transitioning to a design mode dominated by modeling, simulation, optimization, and analysis. As a core component of a numerically controlled machine tool, the motion accuracy, response speed, stability, etc. of the feed system are directly related to the machining accuracy and efficiency of the machine tool. Under the new design mode, a large number of studies have been carried out at home and abroad on the design and optimization of the structure and control system of the feed system of numerically controlled machine tools: For example, in terms of structural optimization design, mainly for the moving components, load-bearing components, etc. in the feed system, methods such as shape optimization, topology optimization, size optimization, and bionic design are used to improve the static and dynamic characteristics, reliability, energy efficiency, etc. of the feed system; while in terms of control system design, artificial intelligence algorithms such as particle swarm optimization algorithm and genetic algorithm are used to design the optimal control parameters of the system to improve performance indicators such as the anti-interference ability, dynamic response characteristics, stability, and accuracy of the feed system.

[0003] However, the above studies have the following limitations: (1) In terms of the design object, the feed system is a typical complex system integrating mechanics, electronics, hydraulics, and control. Its performance not only depends on the characteristics of each subsystem but also on the interaction between each subsystem, which makes it impossible to achieve the maximum performance of the feed system through the design methods of components or subsystems; (2) In terms of the design process, the traditional feed design process of numerically controlled machine tools adopts a serial design mode, where different disciplines are selected to design the feed system at different design stages, and each discipline operates relatively independently. Although the design results can meet the requirements, the design cycle of the process is long, the calculation efficiency is low, and the economic cost is also high.

[0004] As an effective optimization technology for the design of complex engineering systems with multidisciplinary attributes, Multidisciplinary Design Optimization (MDO) has been widely applied in fields such as automobiles, aircraft, and ships. It can shorten the design cycle by implementing modular parallel design of each discipline, explore design potential by considering the mutual coupling between disciplines, achieve automated design of products through highly integrated systems, improve reliability by comprehensively considering each discipline, and reduce development costs through multidisciplinary integrated design. In the prior art, although there are cases of using MDO for collaborative optimization design such as the machine tool bed and floor, the relationship between the bed and the floor is relatively simple, and its collaborative optimization design method is difficult to apply to the feed system of machine tools.

[0005] Therefore, in order to design a high-performance CNC machine tool feed system, it is necessary to utilize the latest achievements of complex engineering system design methods, starting from the perspective of the overall optimal performance of the system, fully considering the coupling relationship between disciplines, and conducting research on new theoretical methods for the overall design of the feed system. Summary of the Invention

[0006] Aiming at the deficiencies in the prior art, the present invention provides an optimized design method for a CNC machine tool feed system based on a collaborative optimization strategy with simple operation, high design efficiency, and significantly improved reliability and flexibility. The present invention also provides a storage medium.

[0007] The optimized design method for a CNC machine tool feed system based on a collaborative optimization strategy of the present invention is implemented as follows: including equipment selection, construction of a sub-discipline analysis unit, establishment of a sub-discipline level optimization model, construction of a structural discipline surrogate model, and collaborative optimization steps. The specific process is as follows:

[0008] A. Equipment selection: Determine the design indicators of the CNC machine tool feed system and complete the preliminary selection of the main equipment;

[0009] B. Construction of a sub-discipline analysis unit: Based on the collaborative optimization method, establish a sub-discipline analysis unit in the MDO framework module of the CNC machine tool feed system. The sub-discipline analysis unit includes a structural discipline analysis unit, a transmission discipline analysis unit, a fluid mechanics discipline analysis unit, and a control discipline analysis unit;

[0010] C. Establishment of a sub-discipline level optimization model: Combine the sub-discipline analysis unit constructed in step B to create optimization models for each discipline;

[0011] D. Construction of a structural discipline surrogate model: Establish a surrogate model for the structural discipline analysis unit. The establishment of the surrogate model includes steps of experimental design, DOE sampling calculation, finite element calculation, judgment of model accuracy, and output of the surrogate model with the highest fitting accuracy;

[0012] E. Collaborative optimization: Determine the mutual influence and transfer relationships among the disciplinary analysis units, and combine the disciplinary optimization models constructed in step C and the surrogate models constructed in step D to create a system-level optimization model and disciplinary optimization models under the collaborative optimization framework. Then, carry out the collaborative cyclic optimization of the disciplinary optimization models and the system-level optimization model until the system-level optimization goal converges, and obtain and output the final optimization result.

[0013] Further, in step A, the design indicators of the CNC machine tool feed system include the maximum rapid traverse speed, acceleration, maximum load capacity, table size, and / or moving stroke, and the preliminary selection of the main equipment includes motors and multi-head pumps.

[0014] Further, the specific process of step B is as follows:

[0015] B10. In the structural discipline analysis unit, analyze the moving components of the feed system using the finite element method; the input parameters include structural dimensions, maximum load capacity, and / or structural material properties, and the output parameters include the mass of the moving components and the maximum deformation.

[0016] B20. In the transmission discipline analysis unit, analyze the motion characteristics of the transmission chain, the mechanical characteristics, and the dynamic characteristics of the ball screw of the feed system; the input parameters include the lead, diameter of the ball screw, the mass of the moving components, the relevant parameters of the selected motor, the maximum rapid traverse speed, and / or acceleration. The output parameters of the transmission chain motion characteristics analysis include the maximum torque, effective torque, maximum speed, and / or load inertia. The output parameters of the mechanical characteristics of the ball screw include the critical speed and the maximum axial load. The dynamic characteristics are modeled using the lumped mass method, and the output parameter is the low-order response characteristics of the transmission chain.

[0017] B30. In the fluid mechanics discipline analysis unit, analyze the working characteristics of the hydrostatic guide; the input parameters include the oil cavity size, oil pad size, and / or multi-head pump selection parameters, and the output parameters include the no-load W min 、 maximum load W max 、 oil cavity pressure under no-load and maximum load p 0 and p 1、 guide lift under no-load and maximum load h 0 and h 1、 average static stiffness j e ;

[0018] In the control discipline analysis unit, the response characteristics of the control system are analyzed, and a control system considering the position loop and the speed loop is established based on step B20. The input parameters include the position loop proportional gain, the speed loop proportional gain, the speed loop integral constant, the motor selection parameters, the transmission parameters, and / or the controlled object parameters. A closed-loop control transfer function is established for the input parameters, and then the aforementioned transfer function is analyzed, and the ITAE index, the Routh criterion, the phase margin, and the amplitude margin are used as output parameters.

[0019] Furthermore, the specific sub-discipline analysis units in step B are as follows:

[0020] The structural discipline analysis unit performs analysis through the finite element method. The structural parameters and material parameters of the moving parts are imported, and then mesh division, constraints, and loads are applied to obtain the weight M of the moving parts and the maximum deformation of the model workbench under typical working conditions σ max , and finally, finite element calculation is performed;

[0021] The transmission discipline analysis unit takes the maximum torque T max , the effective torque Trms , the maximum speed N M , the load inertia γ as the results for motion characteristic analysis, as shown in Equation (1):

[0022] ,

[0023] In the formula: T c is the cutting load torque of the machine tool, J l is the moment of inertia of the coupling, J r is the moment of inertia of the reducer, J s is the moment of inertia of the lead screw, J m is the moment of inertia of the motor, T sp is the additional torque of the lead screw preload force, T f the frictional torque, T e is the equivalent inertia torque of the mechanism, Ta and ta are the acceleration torque and the acceleration time respectively, Tt and tb are the constant-speed torque and the constant-speed time respectively, Td and td are the deceleration torque and the deceleration time respectively, PB is the lead of the lead screw, i is the reduction ratio of the speed reducer, M t is the moving mass of the worktable, M h is the additional workpiece mass, tc is the cycle time, V max is the maximum rapid traverse speed of the feed system;

[0024] The hydrodynamic discipline analysis unit is designed for the feed system equipped with a hydrostatic guideway; due to the heavy load and low-speed working characteristics of heavy-duty CNC machine tools, considering the static characteristics, the no-load W min , maximum load W max oil cavity pressure p 0, p 1, the guideway lift h 0, h 1 and the average static stiffness j e are analyzed and calculated as shown in Equation (2):

[0025] ,

[0026] In the formula: A e is the effective bearing area, is the hydrostatic cavity structure coefficient, b , l are the oil cavity dimensions respectively, B , L are the oil pad dimensions respectively, μ is the dynamic viscosity of the fluid, and Q is the single-head flow rate of the multi-head pump;

[0027] The control discipline analysis unit establishes a control model considering the elasticity of the mechanical subsystem. Considering that the frequency bandwidth of the current loop is much larger than that of the speed loop, the current loop is equivalent to 1, and a proportional-integral-derivative controller and a speed loop with PI control and a position loop with P control are used to establish a control model, and the closed-loop control transfer function is obtained:

[0028] ,

[0029] ,

[0030] In the formula: s is a complex variable, K m is the motor torque constant, K p is the proportional gain of the position loop, Kvp is the speed loop proportional gain, K vi is the speed loop integral time constant, K S is the equivalent rigidity, i is the motion conversion coefficient, B is the system damping, J l is the equivalent load inertia, J m motor inertia;

[0031] Based on the above closed-loop control transfer function, with K p , K vp and T s analyze the stability, phase margin, and amplitude margin of the control system;

[0032] For the said stability, based on the Routh criterion, determine whether Equation (5) satisfies the following inequality. If it does not satisfy, it is unstable; if it satisfies, it is stable:

[0033] ,

[0034] The said phase margin and amplitude margin are obtained by automatically calculating the transfer function imported into MATLAB through the margin() function;

[0035] The said ITAE index is shown in Equation (6) and is used to analyze the rapidity and smoothness of the control discipline through the ITAE index:

[0036] ,

[0037] In the formula: t is the time variable, t a is the response time, E rr (t) is the system error.

[0038] Furthermore, the critical speed V c contained in the mechanical characteristics of the ball screw in the B20 step, the maximum allowable axial buckling load F c1 、 the maximum axial bending load F c2 are calculated as follows:

[0039] ,

[0040] ，

[0041] Wherein: λ is the support bearing coefficient, L is the installation spacing of the lead screw, ρ is the density of the lead screw, E is the Young's modulus of the lead screw, J is the parameter related to the moment of inertia of the lead screw, P B is the lead of the lead screw, d s is the diameter of the lead screw, σ is the allowable tensile and compressive force of the lead screw, A is the cross-sectional area of the lead screw equal to , η 1 is the support coefficient;

[0042] The dynamic characteristics are modeled by the lumped mass method, and the dynamic equation of the feed system is established according to the Lagrangian energy method and written in matrix form:

[0043] ,

[0044] Wherein: ; ;

[0045] ,

[0046] ,

[0047] Wherein: T is the matrix transpose, θ M is the rotation angle of the servo motor, θ S is the rotation angle of the ball screw at the workbench position, X S is the axial displacement of the ball screw at the nut position, X T is the workbench displacement, Q is the cutting force; J M is the moment of inertia of the servo motor, J S is the equivalent moment of inertia of the ball screw, M S 、 M T are the equivalent mass of the ball screw and the moving mass of the workbench respectively; k rot is the torsional stiffness of the ball screw feed system, k axis the axial stiffness of the ball screw feed system, K n is the contact stiffness of the screw nut, α is the equivalent friction coefficient tangent to the rotation direction of the screw shaft, i is the axial displacement generated by the nut per revolution of the screw ;

[0048] Solve the eigenvalue of the dynamic equation of the feed system as shown in Equation (12) to obtain the natural frequency of the system;

[0049] ,

[0050] In the formula: ω is the natural frequency of the system to be obtained.

[0051] Furthermore, the C step is based on each discipline analysis unit to determine the local design variables, design constraints, and design objectives at the discipline level, and establish a discipline optimization model including the aforementioned design variables, design constraints, and design objectives:

[0052] The structural discipline includes:

[0053] Design variables DV : The geometric dimensions of the workbench x 1j , where j is the number of dimensional parameters;

[0054] Design constraints s.t. : The maximum deformation of the workbench σ max is less than the allowable deformation σ’ ;

[0055] Design objective: Minimize the weight of the moving parts M ; Establish a discipline optimization model:

[0056] ,

[0057] The transmission discipline includes:

[0058] Design variables DV : The lead of the ball screw P B , diameter d s ;

[0059] Design constraints s.t. : The load is reduced to the motor end, and the speed, maximum torque, rated torque, and inertia are matched; The maximum design speed of the ball screw V s_max should be less than the critical speed of the screw V c, the designed maximum axial load F max should be less than the maximum axial buckling load and the maximum axial bending load allowed by the lead screw F c1 ; F c2 ;

[0060] Design objective: the first natural frequency of the maximum transmission chain f ;

[0061] ,

[0062] where: N 0 is the maximum rotational speed of the motor, V max is the maximum rapid traverse speed of the worktable, P B is the lead of the lead screw, T max is the maximum torque required for work, T rms is the rated torque required for work, T motor_max is the maximum torque of the motor, T motor_rms is the rated torque of the motor, γ _max is the maximum inertia ratio, γ _min is the minimum inertia ratio, γ is the inertia ratio;

[0063] The discipline of fluid mechanics includes:

[0064] Design variables DV : oil cavity size b , l , oil pad size B , L ;

[0065] Design constraints s.t. : the maximum pressure of the oil pad p max should be less than the maximum oil supply pressure of the selected multi-head pump p c , and the oil film thickness h 0, h 1 should meet the design requirements;

[0066] Design objective: the average stiffness of the oil film j e is the largest; Establish the discipline optimization model:

[0067] ,

[0068] The control discipline includes:

[0069] Design variables DV : The input is the position loop proportional gain K p and the speed loop proportional gain K vp and the speed loop integral constant T S ;

[0070] Design constraints s.t. : To ensure the stability of the system, the control system should satisfy the Routh stability criterion, the gain margin is greater than the design requirement A m_c and the phase margin is greater than the design requirement P m_c and the overshoot should meet the design requirements M c ;

[0071] Design objective: J ITAE Minimum; Establish an optimization model for the discipline:

[0072] ,

[0073] Where: G 1 is the stability constraint based on the Routh criterion, a 0, a 1, a 2, a 3, a 4, a 5 are the denominator coefficients of the transfer function in equations (3) and (4), G 2 is the gain margin and phase margin constraint, G 3 is the overshoot constraint, A m is the system amplitude margin, P m is the system phase margin, M p is the system overshoot.

[0074] Furthermore, the process of establishing the surrogate model of the structural discipline analysis unit in step D is as follows: Use the Latin hypercube sampling method to uniformly extract sample points from the structural discipline-related design parameter space to generate a sampling set of design parameters, substitute the sampling set into the finite element model, complete the finite element calculation of the structural discipline, and output with mass characteristics and maximum deformation as responses; Subsequently, with the sampling results as input and the calculation results as output, use the following methods to fit the surrogate model: Build surrogate models using Kriging model, radial basis function model, and polynomial response surface model respectively, and use the multiple correlation coefficient R2 , the global accuracy metrics root mean square error RMSE and maximum absolute error MAE are used to judge the fitting accuracy of the surrogate model; the closer the R 2 value is to 1, the better the model fitting effect. The smaller the RMSE value, the closer the model prediction value is to the true value. The smaller the value, the lower the worst prediction error of the MAE; select the surrogate model with the highest fitting accuracy for output; R 2 , the calculation formulas for RMSE and MAE are:

[0075] ,

[0076] In the formula: y i is the response value of the i-th sample state variable, is the approximate value of the i-th sample state variable, is the mean value of the i-th sample response, n represents the number of samples.

[0077] Further, the specific process of the E step is as follows:

[0078] E10. Given the expected value of the system-level design variable Z ij , and transfer the expected value Z ij to each disciplinary-level optimization model respectively;

[0079] E20. After the system-level transfers the expected value of the design variable to each disciplinary-level Z ij , the disciplinary analysis unit connected to each disciplinary-level optimization module performs disciplinary analysis based on the design variables provided by the former x i to obtain the difference x i between the design variable Z ij and the expected value of the system-level design variable J i , where i represents the i-th discipline among structure, control, fluid mechanics, and transmission, and j represents the j-th design variable in that discipline, i = 1, 2, 3, j = 1, 2, 3;

[0080] E30. Each disciplinary-level uses the disciplinary-level optimization model established in the C step to perform disciplinary-level optimization of the corresponding discipline. Under the condition of satisfying its own constraint conditions, minimize J i , and calculate and obtain the optimal values of the disciplinary-level design variables Y ij , i = 1, 2, 3, j = 1, 2, 3;

[0081] E40. Return the optimal values of the design variables at the disciplinary level obtained through optimization Y ij to the system level. Based on the optimal values of the design variables at the disciplinary level Y ij , construct the inter-disciplinary consistency constraint G for system-level optimization;

[0082] E50. Using the disciplinary-level optimization model established in step E30, under the condition of satisfying the inter-disciplinary consistency constraint, obtain the optimal solutions for the moving mass M of the workbench, f the first-order natural frequency, J ITAE the ITAE index, j e the average oil film stiffness; Then, after system-level optimization, obtain the optimal values of the system-level design variables Z ij ' . Take the optimal values Z ij ' as the expected value of the new system-level design vector Z ij and transfer it to each disciplinary level;

[0083] E60. Repeat the above steps E10 to E50 until the system-level optimization goal converges, obtain the final optimization result and output it.

[0084] Furthermore, the structural disciplinary-level optimization model under the collaborative optimization framework in step E30 is:

[0085] ,

[0086] where: J 1 is the difference between the disciplinary design variables and the expected value of the system-level design variables in the structural discipline.

[0087] The transmission disciplinary-level optimization model under the collaborative optimization framework in step E30 is:

[0088] ,

[0089] where: J 2 is the difference between the disciplinary design variables and the expected value of the system-level design variables in the transmission discipline.

[0090] The fluid mechanics disciplinary-level optimization model under the collaborative optimization framework in step E30 is:

[0091] ,

[0092] where: J3 is the difference between the disciplinary design variables and the expected values of the system-level design variables in the field of fluid mechanics.

[0093] The disciplinary-level optimization model of control theory under the collaborative optimization framework in the E30 step is as follows:

[0094] ,

[0095] In the formula: J 4 is the difference between the disciplinary design variables and the expected values of the system-level design variables in the field of control theory.

[0096] The system-level optimization model under the collaborative optimization framework in the E30 step and the inter-disciplinary consistency constraint G of the E40 system-level optimization are as follows:

[0097] ,

[0098] In the formula: J 1 ',J 2 ',J 3 ',J 4 ' represents the inter-disciplinary consistency constraint function of each system-level discipline; the subscript ' quantity represents the optimal value passed from each disciplinary level to the system level, J 1 '= ( Z 1j - Y 1j ) 2 ; J 2 '= ( Z 41 - Y 21 ) 2 +( Z 42 - Y 22 ) 2 +( Z 43 - Y 23 ) 2 ; J 3 '= ( Z 31 - Y 31 ) 2 +( Z 32 - Y 32 ) 2 +( Z33 - Y 33 ) 2 +( Z 34 - Y 34 ) 2 ; J 4 '= ( Z 41 - Y 41 ) 2 +( Z 42 - Y 42 ) 2 +( Z 43 - Y 43 ) 2 is the sum of the consistency constraint functions between disciplines, τ is the relaxation factor, generally taking 10 -3 to 10 -5 .

[0099] The storage medium of the present invention is implemented as follows: A computer program is stored thereon, and the computer program can be executed by one or more processors to implement the foregoing optimization design method for the feed system of a numerically controlled machine tool based on a collaborative optimization strategy.

[0100] Compared with the prior art, the beneficial effects of the present invention are:

[0101] 1. By establishing a system-level optimization model for the multi-unit design of the feed system of a numerically controlled machine tool, as well as discipline-level optimization models for the structural unit, transmission unit, fluid mechanics unit, and control unit, and analyzing the design variables and design constraints of each unit, the present invention forms a systematic and integrated design method, and can obtain the optimal comprehensive performance of the feed system of a numerically controlled machine tool.

[0102] 2. Aiming at the integrity of the design domain of the design object of the feed system of a numerically controlled machine tool, the present invention provides an analysis model for the disciplines of the structure, control, transmission, and fluid mechanics of the feed system of a numerically controlled machine tool, and improves the overall design model.

[0103] 3. Aiming at the design process of the feed system of a numerically controlled machine tool, the present invention provides a collaborative optimization process, which coordinates and unifies the analysis models of the disciplines of structure, control, transmission, and fluid mechanics. In addition, the disciplines can perform parallel analysis and optimization, thereby improving the design efficiency.

[0104] 4. Aiming at the complexity of the design of the CNC machine tool feed system, the present invention provides a disciplinary analysis method based on the surrogate model. By constructing the surrogate model, the calculation time can be shortened to improve the design efficiency.

[0105] To sum up, the present invention has the characteristics of simple operation, high design efficiency, and significantly improved reliability and flexibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0106] Figure 1 is the flow chart of the present invention;

[0107] Figure 2 is the flow chart of constructing the surrogate model of the structural discipline analysis unit for the embodiment;

[0108] Figure 3 is the flow chart of the collaborative optimization steps for the embodiment;

[0109] Figure 4 is the prediction effect diagram of the maximum deformation of the workbench by the second-order RSM surrogate model for the embodiment

[0110] Figure 5 is the prediction effect diagram of the moving quality of the workbench by the second-order RSM surrogate model for the embodiment;

[0111] Figure 6 is the schematic diagram of the Isight collaborative optimization framework for the embodiment;

[0112] Figure 7 is the comparison diagram of the optimization iteration of each optimization objective for the embodiment;

[0113] Figure 8 is the Pareto solution set diagram for the embodiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0114] In order to make the purpose, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

[0115] As Figures 1 to 6 shown, the optimization design method of the CNC machine tool feed system based on the collaborative optimization strategy of the present invention includes equipment selection, construction of sub-disciplinary analysis units, establishment of sub-disciplinary level optimization models, construction of structural discipline surrogate models, and collaborative optimization steps. The specific process is as follows:

[0116] A. Equipment selection: Determine the design indicators of the CNC machine tool feed system and complete the preliminary selection of the main equipment;

[0117] B. Construction of Sub - discipline Analysis Units: Based on the collaborative optimization method, establish the sub - discipline analysis units in the MDO framework module of the CNC machine tool feed system. The sub - discipline analysis units include a structural discipline analysis unit, a transmission discipline analysis unit, a fluid mechanics discipline analysis unit, and a control discipline analysis unit;

[0118] C. Establishment of Sub - discipline - level Optimization Models: Combine the sub - discipline analysis units constructed in step B to create optimization models for each discipline;

[0119] D. Construction of a Structural Discipline Surrogate Model: Establish a surrogate model for the structural discipline analysis unit. The establishment of the surrogate model includes steps of experimental design, DOE sampling calculation, finite element calculation, judgment of model accuracy, and output of the surrogate model with the highest fitting accuracy;

[0120] E. Collaborative Optimization: Determine the mutual influence and transfer relationships among the sub - discipline analysis units. Combine the optimization models for each discipline constructed in step C and the surrogate model constructed in step D to create a system - level optimization model and discipline - level optimization models under the collaborative optimization framework. Then carry out the collaborative cyclic optimization of the discipline - level optimization models and the system - level optimization model until the system - level optimization goal converges, and obtain and output the final optimization result.

[0121] In step A, the design indicators of the CNC machine tool feed system include the maximum rapid traverse speed, acceleration, maximum load capacity, table size, and / or moving stroke. The preliminary selection of the main equipment includes motors and multi - head pumps.

[0122] The specific process of step B is as follows:

[0123] B10. In the structural discipline analysis unit, analyze the moving components of the feed system using the finite element method; the input parameters include structural dimensions, maximum load capacity (design requirements), and / or structural material properties, and the output parameters include the mass of the moving components and the maximum deformation;

[0124] B20. In the transmission discipline analysis unit, analyze the motion characteristics of the transmission chain, the mechanical characteristics of the ball screw, and the dynamic characteristics of the feed system; the input parameters include the lead, diameter of the ball screw, the mass of the moving components, the relevant parameters of the selected motor (including rated speed, peak torque, rated torque, rotor inertia), the maximum rapid traverse speed, and / or acceleration (design requirements). The analysis of the motion characteristics of the transmission chain takes the maximum torque, effective torque, maximum speed, and / or load inertia as output parameters. The mechanical characteristics of the ball screw take the critical speed and the maximum axial load as output parameters. The dynamic characteristics are modeled using the lumped mass method and take the low - order response characteristics of the transmission chain as output parameters;

[0125] B30. In the hydrodynamic discipline analysis unit, analyze the working characteristics of the hydrostatic guideway. The input parameters include oil cavity size, oil pad size, and / or multi-head pump selection parameters (including the number of oil outlets, flow rate per outlet, and outlet pressure), and the output parameters include the no-load W min , maximum load W max , oil cavity pressure under no-load and maximum load p 0 and p 1, guideway lift under no-load and maximum load h 0 and h 1, average static stiffness j e ;

[0126] B40. In the control discipline analysis unit, analyze the response characteristics of the control system, and establish a control system considering the position loop and speed loop based on the steps in B20. The input parameters include the position loop proportional gain, speed loop proportional gain, speed loop integral constant, motor selection parameters (including torque constant, motor rotor inertia), transmission parameters (including transmission chain effective stiffness, ball screw lead), and / or controlled object parameters. Establish a closed-loop control transfer function for the input parameters, and then analyze the aforementioned transfer function and use the ITAE index (Integral of Time and Absolute Error), Routh criterion, phase margin, and amplitude margin as output parameters.

[0127] The specific sub-discipline analysis units in the B step are as follows:

[0128] The structural discipline analysis unit is analyzed by the finite element method. Import the structural parameters and material parameters of the moving part, and then perform mesh division, apply constraints and loads to obtain the weight M of the moving part and the maximum deformation of the model workbench under typical working conditions σ max , and finally perform finite element calculation;

[0129] The transmission discipline analysis unit performs kinematic characteristic analysis with the maximum torque T max , effective torque Trms , maximum speed N M , load inertia γ as the results, as shown in Equation (1):

[0130] ,

[0131] In the formula: T c is the cutting load torque of the machine tool, Jl is the moment of inertia of the coupling J r is the moment of inertia of the reducer J s is the moment of inertia of the lead screw J m is the moment of inertia of the motor T sp is the additional torque of the lead screw preload force T f frictional torque T e is the equivalent inertia torque of the mechanism Ta and ta are the acceleration torque and acceleration time respectively Tt and tb are the constant-speed torque and constant-speed time respectively Td and td are the deceleration torque and deceleration time respectively P B is the lead of the lead screw i is the reduction ratio of the reducer M t is the moving mass of the worktable M h is the additional workpiece mass tc is the cycle time V max is the maximum rapid traverse speed of the feed system;

[0132] The hydrodynamic discipline analysis unit is designed for the feed system equipped with a hydrostatic guideway; due to the heavy-load and low-speed working characteristics of heavy-duty CNC machine tools, considering the static characteristics, the no-load W min , maximum load W max oil cavity pressure p 0, p 1, the guideway lift h 0, h 1 and the average static stiffness j e are analyzed and calculated as shown in Equation (2):

[0133] ,

[0134] In the formula: A e is the effective bearing area is the structural coefficient of the hydrostatic cavity b , l are the oil cavity sizes respectively B , L are the oil pad sizes respectivelyμ is the hydrodynamic viscosity, and Q is the flow rate of a single head of the multi-head pump;

[0135] The control discipline analysis unit establishes a control model considering the elasticity of the mechanical subsystem. Considering that the frequency bandwidth of the current loop is much larger than that of the speed loop, the current loop is equivalent to 1. A control model is established using a proportional-integration-differentiation (PID) controller and a speed loop with PI control and a position loop with P control, and the closed-loop control transfer function is obtained:

[0136] ,

[0137] ,

[0138] In the formula: s is a complex variable, K m is the motor torque constant, K p is the proportional gain of the position loop, K vp is the proportional gain of the speed loop, K vi is the integral time constant of the speed loop, K S is the equivalent rigidity, i is the motion conversion coefficient, B is the system damping, J l is the equivalent load inertia, J m motor inertia;

[0139] Based on the above closed-loop control transfer function, with K p , K vp and T s the stability, phase margin, and amplitude margin of the control system are analyzed;

[0140] Regarding the stability, based on the ROUTH criterion, it is judged whether Equation (5) satisfies the following inequality. If it does not satisfy, it is unstable; if it satisfies, it is stable:

[0141] ,

[0142] The phase margin and amplitude margin are obtained by automatically calculating the transfer function imported into MATLAB through the margin() function;

[0143] The ITAE index is shown in Equation (6) and is used to analyze the rapidity and stability of the control discipline through the ITAE index:

[0144] ,

[0145] where: t is the time variable, t a is the response time, E rr (t) is the system error.

[0146] The critical speed included in the mechanical characteristics of the ball screw in the B20 step V c , the maximum allowable axial buckling load F c1 、 The maximum axial bending load F c2 is calculated as follows:

[0147] ,

[0148] ，

[0149] where: λ is the support bearing coefficient, L is the screw installation spacing, ρ is the density of the screw, E is the Young's modulus of the screw, J is the parameter related to the moment of inertia of the screw, P B is the lead of the screw, d s is the diameter of the screw, σ is the allowable tensile and compressive force of the screw, A The cross-sectional area of the screw is equal to , η 1 is the support coefficient;

[0150] The dynamic characteristics are modeled using the lumped mass method, and the dynamic equation of the feed system is established according to the Lagrangian energy method and written in matrix form:

[0151] ,

[0152] where: ; ;

[0153] ,

[0154] ,

[0155] In the formula: T is the matrix transpose, θ M is the rotation angle of the servo motor, θ S is the rotation angle of the ball screw at the workbench position, X S is the axial displacement of the ball screw at the nut position, X T is the workbench displacement, Q is the cutting force; J M is the moment of inertia of the servo motor, J S is the equivalent moment of inertia of the ball screw, M S , M T are respectively the equivalent mass of the ball screw and the moving mass of the workbench; k rot is the torsional stiffness of the ball screw feed system, k ax is the axial stiffness of the ball screw feed system, K n is the contact stiffness of the screw nut, α is the equivalent friction coefficient tangent to the rotation direction of the screw axis, i is the axial displacement generated by the nut for each revolution of the screw ;

[0156] Solve the eigenvalue of the dynamic equation of the feed system as shown in Equation (12) to obtain the natural frequency of the system;

[0157] ,

[0158] In the formula: ω is the natural frequency of the system to be obtained.

[0159] The C step is based on each discipline analysis unit to determine the local design variables, design constraints, and design objectives at the discipline level, and establish a discipline optimization model including the aforementioned design variables, design constraints, and design objectives:

[0160] The structural discipline includes:

[0161] Design variables DV : The geometric dimensions of the workbench x 1j where j is the number of dimensional parameters;

[0162] Design constraints s.t. : The maximum deformation of the workbench σmax Less than the allowable deformation σ’ ;

[0163] Design goal: Minimize the weight of the moving parts M ; Establish a disciplinary optimization model:

[0164] ,

[0165] The transmission discipline includes:

[0166] Design variables DV : Ball screw lead P B , diameter d s ;

[0167] Design constraints s.t. : The load is reduced to the motor end, with speed matching, maximum torque matching, rated torque matching, and inertia matching; The maximum design speed of the ball screw V s_max should be less than the critical speed of the screw V c , The maximum design axial load F max should be less than the maximum allowable axial buckling load of the screw F c1 and the maximum axial bending load F c2 ;

[0168] Design goal: The first natural frequency of the maximum transmission chain f ;

[0169] ,

[0170] Where: N 0 is the maximum speed of the motor, V max is the maximum rapid traverse speed of the workbench, P B is the lead of the screw, T max is the maximum torque required for work, T rms is the rated torque required for work, T motor_max is the maximum torque of the motor, T motor_rms is the rated torque of the motor, γ _max is the maximum inertia ratio, γ _min is the minimum inertia ratio, γ is the inertia ratio;

[0171] The fluid mechanics discipline includes:

[0172] Design variables DV : Oil cavity size b , l , oil pad size B , L ;

[0173] Design constraints s.t. : The maximum oil pad pressure p max should be less than the maximum oil supply pressure of the selected multi-head pump p c , oil film thickness h 0, h 1 should meet the design requirements;

[0174] Design objective: Average oil film stiffness j e Maximum; Establish a discipline optimization model:

[0175] ,

[0176] The control discipline includes:

[0177] Design variables DV : The inputs are the position loop proportional gain K p , speed loop proportional gain K vp , speed loop integral constant T S ;

[0178] Design constraints s.t. : To ensure the stability of the system, the control system should meet the Routh stability criterion, gain margin greater than the design requirements A m_c , phase margin greater than the design requirements P m_c , overshoot should meet the design requirements M c ;

[0179] Design objective: J _ITAE Minimum; Establish a discipline optimization model:

[0180] ,

[0181] Where: G 1 is the stability constraint based on the ROUTH criterion, a 0, a 1, a 2, a 3, a 4,a 5 is the denominator coefficient of the transfer function in equations (3) and (4), G 2 is the gain margin and phase margin constraint, G 3 is the overshoot constraint, A m is the system amplitude margin, P m is the system phase margin, M p is the system overshoot.

[0182] The process of establishing the surrogate model of the structural discipline analysis unit in step D is as follows: Use the Latin hypercube sampling method to uniformly extract sample points from the structural discipline-related design parameter space to generate a sampling set of design parameters. Substitute the sampling set into the finite element model to complete the finite element calculation of the structural discipline, and output with mass characteristics and maximum deformation as responses. Subsequently, with the sampling results as input and the calculation results as output, use the following methods to fit the surrogate model: Build surrogate models using Kriging model, radial basis function model, and polynomial response surface model respectively, and use the multiple correlation coefficient R 2 , the global accuracy index root mean square error RMSE, and the maximum absolute error MAE to judge the fitting accuracy of the surrogate model; The closer the R 2 value is to 1, the better the model fitting effect. The smaller the RMSE value, the closer the model prediction value is to the true value. The smaller the MAE value, the lower the worst prediction error of the model; Select the surrogate model with the highest fitting accuracy for output; The calculation formulas for R 2 , RMSE, and MAE are:

[0183] ,

[0184] In the formula: y i is the response value of the i-th sample state variable, is the approximate value of the i-th sample state variable, is the mean value of the i-th sample response, n represents the number of samples.

[0185] The specific process of step E is as follows:

[0186] E10. Given the expected value Z ij of the system-level design variable, and pass the expected value Z ij to each discipline-level optimization model respectively;

[0187] E20. After the system-level passes the expected value Z ij of the design variable to each discipline-level, the discipline analysis unit connected to each discipline-level optimization module, according to the design variables provided by the formerx i Perform disciplinary analysis to obtain design variables x i And the expected value of the system-level design variables Z ij The difference between J i , where i represents the i-th discipline among structure, control, fluid mechanics, and transmission, and j represents the j-th design variable in that discipline, i = 1, 2, 3, j = 1, 2, 3;

[0188] E30. For each discipline level, use the disciplinary optimization model established in step C to perform disciplinary optimization of the corresponding discipline. Under the condition of meeting its own constraint conditions, minimize J i , and calculate the optimal values of the design variables at each discipline level Y ij , i = 1, 2, 3, j = 1, 2, 3;

[0189] E40. Return the optimal values of the design variables at each discipline level obtained by optimization Y ij To the system level. The system level constructs the inter-disciplinary consistency constraint G for system-level optimization according to the optimal values of the design variables at each discipline level Y ij .

[0190] E50. Using the disciplinary optimization model established in step E30, under the condition of meeting the inter-disciplinary consistency constraint, obtain the optimal solutions for the moving mass of the workbench M , the first-order natural frequency f , the ITAE index J ITAE , the average stiffness of the oil film j e ; Then, after system-level optimization, obtain the optimal values of the system-level design variables Z ij ' , and use the optimal values Z ij ' As the new expected value of the system-level design vector Z ij And transfer it to each discipline level;

[0191] E60. Repeat the above steps E10 to E50 until the system-level optimization goal converges, and obtain the final optimization result and output it.

[0192] The structural discipline-level optimization model in the collaborative optimization framework in step E30 is as follows:

[0193] ,

[0194] wherein: J 1 is the difference between the disciplinary design variables and the expected values of the system-level design variables in the structural discipline.

[0195] The disciplinary-level optimization model of the transmission discipline under the collaborative optimization framework in the E30 step is:[[]]

[0196] ,

[0197] wherein: J 2 is the difference between the disciplinary design variables and the expected values of the system-level design variables in the transmission discipline.

[0198] The disciplinary-level optimization model of the fluid mechanics discipline under the collaborative optimization framework in the E30 step is:[[]]

[0199] ,

[0200] wherein: J 3 is the difference between the disciplinary design variables and the expected values of the system-level design variables in the fluid mechanics discipline.

[0201] The disciplinary-level optimization model of the control discipline under the collaborative optimization framework in the E30 step is:[[]]

[0202] ,

[0203] wherein: J 4 is the difference between the disciplinary design variables and the expected values of the system-level design variables in the control discipline.

[0204] The system-level optimization model under the collaborative optimization framework in the E30 step and the inter-disciplinary consistency constraint G of the E40 system-level optimization are:[[]]

[0205] ,

[0206] wherein: J 1 ',J 2 ',J 3 ',J 4 ' represents the inter-disciplinary consistency constraint function of each system-level discipline; the subscript ' quantity represents the optimal value passed from each disciplinary level to the system level, J 1 '= ( Z 1j - Y 1j ) 2 ; J 2 '= ( Z41 - Y 21 ) 2 +( Z 42 - Y 22 ) 2 +( Z 43 - Y 23 ) 2 ; J 3 '= ( Z 31 - Y 31 ) 2 +( Z 32 - Y 32 ) 2 +( Z 33 - Y 33 ) 2 +( Z 34 - Y 34 ) 2 ; J 4 '= ( Z 41 - Y 41 ) 2 +( Z 42 - Y 42 ) 2 +( Z 43 - Y 43 ) 2 Sum the consistency constraint functions between disciplines, τ is the relaxation factor, usually 10 -3 Up to 10 -5 .

[0207] The storage medium of the present invention stores a computer program thereon, and the computer program can be executed by one or more processors to implement the aforementioned CNC machine tool feed system optimization design method based on the collaborative optimization strategy. Example

[0208] like Figures 1 to 8As shown in the figure, an optimization design is carried out for the feed system of a certain heavy-duty gantry machining center, and an optimization design is carried out for its X-axis feed system. The main drive of the X-axis feed system of the target heavy-duty CNC machine tool adopts a ball screw and a servo motor, is equipped with a full-closed-loop control system, the guide rail type is an open hydrostatic guide rail, and the guide rail structure is one V-shaped and one flat. Based on the MDO idea, the design optimization problem is divided into 4 sub-problem of structural discipline, transmission discipline, fluid mechanics discipline and control discipline. The optimization design process is as follows:

[0209] S100. Determine the design indexes of the CNC machine tool feed system (including the maximum rapid traverse speed, acceleration, maximum load, table size and / or moving stroke), complete the selection of the main equipment, and complete the preliminary selection of the main equipment as shown in Table 1.

[0210] Table 1 Main design indexes of the X-axis of the feed system

[0211]

[0212] S200: Based on the collaborative optimization method, establish the sub-discipline analysis units in the MDO framework module of the CNC machine tool feed system. The sub-discipline analysis units include the structural discipline analysis unit, the transmission discipline analysis unit, the fluid mechanics discipline analysis unit, and the control discipline analysis unit; the structural discipline analysis unit conducts analysis based on ANASYS, and the transmission discipline analysis unit, the fluid mechanics discipline analysis unit, and the control discipline analysis unit conduct analysis based on MATLAB respectively.

[0213] S300: Combine the sub-discipline analysis units constructed in step S200, determine the mutual influence and transfer relationship of each discipline analysis unit, determine the local design variables, design constraints, and design objectives at the discipline level, and establish the optimization models at the discipline level in the MDO framework module of the CNC machine tool feed system. The local design variables and ranges at the discipline level are shown in Table 2.

[0214] Table 2 Local design variables and ranges at the discipline level

[0215]

[0216] Combined with the actual design requirements, establish the sub-discipline level optimization model:

[0217] (1) In order to ensure the static stiffness of the workbench, under typical working conditions, the maximum deformation of the workbench should be less than the design requirement of 0.03 mm. Taking the lightweight design as the criterion and minimizing the mass of the moving parts of the workbench M as the goal, establish the structural discipline optimization model:

[0218] ,

[0219] In the formula: x 11is the thickness of the workbench structure board, x 12 is the width of the longitudinal reinforcement of the workbench structure, x 13 is the width of the transverse reinforcement of the workbench structure, x 14 is the width of the longitudinal reinforcement of the workbench structure; σ max is the maximum deformation of the workbench, σ’ is the allowable deformation of the workbench;

[0220] (2) When the system is working, it is necessary to meet the rotational speed matching, maximum torque matching, rated torque matching, and inertia matching from the motor to the load end. The designed maximum rotational speed of the ball screw should be less than the critical speed of the screw, and the designed maximum axial load should be less than the maximum buckling load allowed by the screw F c1 , maximum bending load F c2 , with high anti-vibration performance as the design criterion, maximizing the first natural frequency of the feed system f as the goal.

[0221] ,

[0222] In the formula: P B is the lead of the ball screw, d s is the diameter of the ball screw; V s_max is the designed maximum rotational speed of the ball screw, V c is the critical speed of the screw; F max is the designed maximum axial load of the screw, F c1 is the maximum axial buckling load allowed by the screw, F c2 is the maximum axial bending load allowed by the screw; N 0 is the maximum rotational speed of the motor, V max is the maximum rapid traverse speed of the workbench, P B is the lead of the screw, T max is the maximum torque required for work, T rms is the rated torque required for work, T motor_max is the maximum torque of the motor, T motor_rms is the rated torque of the motor, γ _max is the maximum inertia ratio, γ_min is the minimum inertia ratio, γ is the inertia ratio.

[0223] (3) In the design of the hydrostatic guideway, the maximum pressure of the oil pad should be less than the maximum oil supply pressure of the selected multi-head pump. Considering the pipeline pressure loss, the maximum pressure is taken as 1 Mpa, and the oil film thickness is taken as 0.03 - 0.06 mm according to the recommended values for medium and heavy machine tools. With high load-bearing rigidity as the design criterion, the average stiffness of the hydrostatic guideway oil film is maximized j e as the goal.

[0224] ,

[0225] In the formula: b , l are the oil cavity sizes, B , L are the oil pad sizes; p max is the maximum pressure of the oil pad, p c is the maximum oil supply pressure of the selected multi-head pump; h 0, h 1 is the oil film thickness, j e is the average stiffness of the oil film.

[0226] (4) To ensure the stability of the system, the coefficients of the system characteristic polynomial should satisfy the Routh stability criterion. To ensure the robustness of the system, the gain margin and phase margin should be greater than 5 db and 40°. To ensure the stable operation of the system, the overshoot of the system should be less than 5%. With high precision and high response as the design criterion, the performance index ITAE of minimizing the absolute value of the error multiplied by the time integral is adopted:

[0227] .

[0228] In the formula: G1 is the stability constraint based on the ROUTH criterion, a 0, a 1, a 2, a 3, a 4, a 5 are the denominator coefficients of the transfer function in equations (3) and (4), G 2 is the gain margin and phase margin constraint, G 3 is the overshoot constraint, A m is the amplitude margin of the system, P m is the phase margin of the system, M p is the overshoot of the system.

[0229] S400: Establish a surrogate model for the structural discipline analysis unit. Establishing the surrogate model includes steps of experimental design, DOE sampling calculation, finite element calculation, judging the model accuracy, and outputting the surrogate model with the highest fitting accuracy.

[0230] The steps of the experimental design and finite element calculation are as follows: According to the initially determined design indicators, determine the initial values and upper and lower limits of the design variables as shown in Table 2; adopt the orthogonal experimental design method, and use the uniform Latin hypercube method to sample 50 times respectively for the maximum deformation of the workbench and the weight of the workbench in the structural subsystem. The numerical results of the experimental design are shown in Table 3.

[0231] Table 3 Numerical results of experimental design

[0232]

[0233] The steps of judging the model accuracy and outputting the surrogate model with the highest fitting accuracy are as follows: For the 50 groups of sample points of the above structural unit, use the Kriging model, Radial-Basis Function (RBF) model, and Response Surface Methodology (RSM) to construct surrogate models respectively, and use the multiple correlation coefficient R 2 (Coefficient of Determination), the root mean square error (RMSE) of the global accuracy index, and the maximum absolute error (MAE) to judge the fitting accuracy of the surrogate model. The expressions of R 2 , RMSE, and MAE are respectively:

[0234] ,

[0235] In the formula: y i is the response value of the i-th sample state variable, is the approximate value of the i-th sample state variable, is the mean value of the i-th sample state response, n represents the number of samples.

[0236] The accuracy of the surrogate model for the maximum deformation of the workbench is shown in Table 4.

[0237] Table 4 Accuracy of the surrogate model for the maximum deformation of the workbench

[0238]

[0239] It can be seen from Table 4 that σ maxThe RMSE and MAE of the second-order RSM surrogate model are the smallest, and R 2 is closest to 1. Therefore, the second-order RSM surrogate model has the best predictive ability for the two response values. Figure 4 Shows the prediction effect of the second-order RSM surrogate model on the maximum deformation of the workbench.

[0240] Similarly, a surrogate model for the moving mass of the workbench is established according to the above process. Figure 5 Shows the prediction effect and model accuracy of the surrogate model for the moving mass of the workbench.

[0241] S500: Determine the mutual influence and transfer relationship between the analysis units of each discipline. Combine the optimization models of each discipline constructed in step S300 and the surrogate models constructed in step S400 to create a system-level optimization model and a discipline-level optimization model under the collaborative optimization framework. Then, carry out the collaborative cyclic optimization of the discipline-level optimization model and the system-level optimization model until the system-level optimization goal converges, and obtain the final optimization result and output it.

[0242] The structural discipline-level optimization model under the collaborative optimization framework is:

[0243] ,

[0244] Where: J 1 is the difference between the discipline design variables and the expected values of the system-level design variables in the structural discipline.

[0245] The transmission discipline-level optimization model under the collaborative optimization framework is:

[0246] ,

[0247] Where: J 2 is the difference between the discipline design variables and the expected values of the system-level design variables in the transmission discipline.

[0248] The fluid mechanics discipline-level optimization model under the collaborative optimization framework is:

[0249] ,

[0250] Where: J 3 is the difference between the discipline design variables and the expected values of the system-level design variables in the fluid mechanics discipline.

[0251] The control discipline-level optimization model under the collaborative optimization framework is:

[0252] ,

[0253] Where: J 4 is the difference between the discipline design variables and the expected values of the system-level design variables in the control discipline.

[0254] The system-level optimization model and the interdisciplinary consistency constraint G for system-level optimization under the collaborative optimization framework are as follows:

[0255] ,

[0256] In the formula: J 1 ',J 2 ',J 3 ',J 4 ' represents the consistency constraint function between disciplines at the system level; the subscript ' represents the optimal value passed from each discipline level to the system level, J 1 '= ( Z 1j - Y 1j ) 2 ; J 2 '= ( Z 41 - Y 21 ) 2 +( Z 42 - Y 22 ) 2 +( Z 43 - Y 23 ) 2 ; J 3 '= ( Z 31 - Y 31 ) 2 +( Z 32 - Y 32 ) 2 +( Z 33 - Y 33 ) 2 +( Z 34 - Y 34 ) 2 ; J 4 '= ( Z 41 - Y 41 ) 2+( Z 42 - Y 42 ) 2 +( Z 43 - Y 43 ) 2 is the sum of the consistency constraint functions among various disciplines. τ is the relaxation factor, generally taking a value from 10 -3 to 10 -5 .

[0257] The collaborative optimization framework is implemented using Isight in the prior art as shown in Figure 6 .

[0258] Result output: The comparison of four objective optimization iterations is as shown in Figure 7 ; The optimized four-objective optimal Pareto solution set obtained by using NSGA-II is as shown in Figure 8 .

[0259] Select a satisfactory optimal solution from the Pareto front. Extract the final optimization plan and adjust the optimization plan considering manufacturability. The comparison between the initial plan and the optimized design plan is listed in Table 5.

[0260] Table 5 Comparison between the optimized plan and the initial plan

[0261]

[0262] As can be seen from Table 5: Compared with the initial plan, the optimized final plan reduces the moving mass of the workbench from 2904 kg to 2636 kg, achieving a weight reduction of 9.22%. On the basis of ensuring the static rigidity of the workbench, the lightweight design of the structure is realized. In addition, the JITAE index is reduced by 68.44%, and the first-order natural frequency f and the average oil film stiffness j e are increased by 1.4% and 13.5% respectively, realizing the optimization of the comprehensive performance of the system.

[0263] The above are only the preferred specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. An optimization design method for a CNC machine tool feed system based on a collaborative optimization strategy, characterized in that: Including equipment selection, construction of sub-discipline analysis units, establishment of sub-discipline-level optimization models, construction of structural discipline agent models, and collaborative optimization steps. The specific process is as follows: A. Equipment selection: Determine the design indicators of the CNC machine tool feed system and complete the pre-selection of major equipment; B. Constructing sub-discipline analysis units: Based on the collaborative optimization method, sub-discipline analysis units in the MDO framework module of the CNC machine tool feed system are established, and the sub-discipline analysis units include a structure discipline analysis unit, a transmission discipline analysis unit, a fluid mechanics discipline analysis unit, and a control discipline analysis unit; C. Establishment of sub-discipline optimization model: Combine the sub-discipline analysis units constructed in step B to create optimization models for each discipline; D. Constructing a proxy model for structural disciplines: Establishing a proxy model for the structural discipline analysis unit. Establishing the proxy model includes experimental design, DOE sampling calculation, finite element calculation, judging model accuracy, and outputting the proxy model with the highest fitting accuracy. E. Collaborative optimization: Determine the mutual influence and transmission relationship between the analysis units of each discipline, combine the optimization models of each discipline constructed in step C and the proxy model constructed in step D, create a system-level optimization model and a discipline optimization model under the collaborative optimization framework, and then carry out collaborative cycle optimization of the discipline-level optimization model and the system-level optimization model until the system-level optimization target converges, obtain the final optimization result and output it; The specific process of step B is as follows: B10, in the structural subject analysis unit, the moving parts of the feed system are analyzed using the finite element method; wherein the input parameters include the structural size, the maximum load and / or the structural material properties, and the output parameters include the mass of the moving parts and the maximum deformation; B20, in the transmission discipline analysis unit, the transmission chain motion characteristics, ball screw mechanical characteristics, and dynamic characteristics of the feed system are analyzed; wherein the input parameters include the ball screw lead, diameter, moving part mass, selected motor related parameters, maximum fast moving speed and / or acceleration; the transmission chain motion characteristics analysis uses the maximum torque, effective torque, maximum speed and / or load inertia as output parameters; the ball screw mechanical characteristics use the critical speed and maximum axial load as output parameters; the dynamic characteristics are modeled using the concentrated mass method with the transmission chain low-order response characteristics as output parameters; B30. In the fluid mechanics analysis unit, the working characteristics of the hydrostatic guide rail are analyzed; the input parameters include the oil chamber size, the oil pad size and / or the multi-head pump selection parameters, and the output parameters include the single oil pad no-load W min , Maximum load W max , oil chamber pressure under no load and maximum load p 0 and p 1 , guide rail floating under no load and maximum load h 0 and h 1 , average static stiffness j e ; B40, in the control subject analysis unit, the response characteristics of the control system are analyzed, and a control system considering the position loop and the speed loop is established on the basis of step B20; the input parameters include the position loop proportional gain, the speed loop proportional gain, the speed loop integral constant, the motor selection parameters, the transmission parameters and / or the controlled object parameters, and a closed-loop control transfer function is established for the input parameters, and then the aforementioned transfer function is analyzed and the ITAE index, ROUTH criterion, phase margin and amplitude margin are used as output parameters; The specific sub-discipline analysis units in step B are as follows: The structural analysis unit is analyzed by the finite element method, importing the structural parameters and material parameters of the moving parts, and then performing meshing, applying constraints and loads to obtain the weight M of the moving parts, the maximum deformation of the model workbench under typical working conditions, and the maximum deformation of the model workbench under typical working conditions. σ max , and finally perform finite element calculation; The transmission discipline analysis unit is based on the maximum torque T max , effective torque Trms , Maximum speed N M , Load inertia γ The motion characteristics analysis is performed for the results, as shown in formula (1): ， Where: T c is the cutting load torque of the machine tool, J l is the moment of inertia of the coupling, J r is the moment of inertia of the reducer, J s is the screw moment of inertia, J m is the motor moment of inertia, T sp The additional torque for the screw preload is T f Friction torque, T e is the equivalent inertia moment of the mechanism, Ta and ta They are acceleration torque and acceleration time respectively. Tt and tb are uniform torque and uniform time respectively, Td and td They are deceleration torque and deceleration time respectively. P B is the screw lead, i is the reduction ratio of the reducer, M t is the moving mass of the workbench, M h For additional workpiece mass, tc is the cycle time, V max The maximum rapid moving speed of the feed system; The fluid mechanics analysis unit is designed for a feed system equipped with a hydrostatic guide rail; Heavy-duty CNC machine tools have heavy-load and low-speed working characteristics. Considering the static characteristics, a single oil pad is unloaded. W min , Maximum load W max Oil chamber pressure under p 0 , p 1 , guide rail floating under no load and maximum load h 0 , h 1 and average static stiffness j e Perform analytical calculations, as shown in formula (2): ， Where: A e is the effective bearing area, is the static pressure chamber structural coefficient, b , l They are the oil chamber size, B , L The oil pad size is respectively, μ is the dynamic viscosity of the fluid, Q is the flow rate of a single head of a multi-head pump; The control discipline analysis unit is to establish a control model that takes into account the elasticity of the mechanical subsystem. Considering that the frequency bandwidth of the current loop is much larger than the bandwidth of the speed loop, the current loop is equivalent to 1, and a proportional-integral-differential controller and a PI-controlled speed loop and a P-controlled position loop are used to establish a control model, and a closed-loop control transfer function is obtained: ， ， Where: s is a complex variable, K m is the motor torque constant, K p is the position loop proportional gain, K vp is the speed loop proportional gain, K vi is the speed loop integral time constant, K S is the equivalent rigidity, i is the motion conversion coefficient, B is the system damping, J l is the equivalent load inertia, J m Motor inertia; Based on the above closed-loop control transfer function, K p , K vp and T s Analyze the stability, phase margin, and amplitude margin of the control system; The stability is based on the ROUTH criterion, which determines whether equation (5) satisfies the following inequality. If not, it is unstable, and if it is, it is stable: ， The phase margin and amplitude margin are obtained by importing the transfer function into MATLAB and automatically calculating it through the margin() function; The ITAE index is shown in formula (6), which is used to analyze the rapidity and stability of the control subject through the ITAE index: ， Where: t is the time variable, t a is the response time, E rr (t) is the system error; The critical speed included in the mechanical characteristics of the ball screw in step B20 V c , the maximum allowable axial buckling load F c1 、 Maximum axial bending load F c2 Perform the calculation: ， ， Where: λ is the support bearing coefficient, L is the screw installation distance, ρ is the density of the screw, E is the Young's modulus of the screw, J are the parameters related to the screw moment of inertia, P B is the screw lead, d s is the screw diameter, σ The allowable pulling pressure of the screw is A The cross-sectional area of ​​the screw is equal to , η 1 is the support coefficient; The dynamic characteristics are mathematically modeled using the lumped mass method, and the dynamic equations of the feeding system are established according to the Lagrangian energy method and written in the form of a matrix: ， in: ; ; ， ， Where: T is the matrix transpose, θ M is the servo motor rotation angle, θ S is the rotation angle of the ball screw at the worktable position, X S is the axial displacement of the ball screw at the nut position, X T is the displacement of the worktable, Q is the cutting force; J M is the servo motor moment of inertia, J S is the equivalent moment of inertia of the ball screw, M S , M T They are the equivalent mass of the ball screw and the moving mass of the worktable respectively; k rot is the torsional stiffness of the ball screw feed system, k ax is the axial stiffness of the ball screw feed system, K n Contact stiffness of the screw nut, α is the equivalent friction coefficient tangential to the direction of rotation of the screw shaft, i The axial displacement of the nut produced by each turn of the screw ; Solve the characteristic value of the dynamic equation of the feed system as shown in formula (12) to obtain the natural frequency of the system; ， Where: ω is the required system natural frequency; The above step C is based on the analysis units of each discipline, determines the local design variables, design constraints, and design goals at the discipline level, and establishes a discipline optimization model including the above-mentioned design variables, design constraints, and design goals: Structural disciplines include: Design variables DV :Workbench geometry x 1j ,in j is the number of size parameters; Design constraints st : Maximum deformation of the workbench σ max Less than allowable deformation σ' ; Design goal: Minimize the weight of moving parts M ; Establish a discipline optimization model: ， Transmission disciplines include: Design variables DV : Ball screw lead P B ,diameter d s ; Design constraints st : Load converted to the motor end, speed matching, maximum torque matching, rated torque matching, inertia matching; ball screw design maximum speed V s_max Should be less than the critical speed of the screw V c , designed maximum axial load F max Should be less than the maximum axial buckling load allowed by the screw F c1 and maximum axial bending load F c2 ; Design goal: Maximum first-order natural frequency of the transmission chain f ; ， Where: N 0 is the maximum speed of the motor, V max is the maximum rapid moving speed of the workbench, P B is the screw lead, T max is the maximum torque required for work, T rms is the rated torque required for work, T motor_max is the maximum torque of the motor, T motor_rms is the rated torque of the motor, γ _max is the maximum inertia ratio, γ _min is the minimum inertia ratio, γ is the inertia ratio; Fluid mechanics disciplines include: Design variables DV :Oil chamber size b , l , Oil pad size B , L ; Design constraints st : Maximum oil pad pressure p max Should be less than the maximum oil supply pressure of the selected multi-head pump p c , oil film thickness h 0 , h 1 Should meet the design requirements; Design target: average oil film stiffness j e Maximum; Establish discipline optimization model: ， Control disciplines include: Design variables DV : Input is the position loop proportional gain K p , speed loop proportional gain K vp , speed loop integral constant T S ; Design constraints st :To ensure the stability of the system, the control system should meet the Routh stability criterion and the gain margin should be greater than the design requirements A m_c , the phase margin is greater than the design requirement P m_c , overshoot should meet the design requirements M c ; Design goals: J ITAE Minimum; Establish discipline optimization model: ， Where: G 1 is the stability constraint based on ROUTH criterion, a0, a1, a2, a3, a4, a5 are the denominator coefficients of the transfer function in equations (3) and (4), G 2 is the gain margin and phase margin constraints, G 3 is the overshoot constraint, A m is the system amplitude margin, P m is the system phase margin, M p is the system overshoot; The establishment process of the proxy model of the structural discipline analysis unit in step D is as follows: using the Latin hypercube sampling method to uniformly extract sample points from the structural discipline-related design parameter space, generating a sampling set of design parameters, substituting the sampling set into the finite element model, completing the finite element calculation of the structural discipline, and outputting the mass characteristics and maximum deformation as responses; then using the sampling results as input and the calculation results as output, fitting the proxy model using the following methods: constructing the proxy model using the Kriging model, radial basis function model, and polynomial response surface model respectively, and using the complex correlation coefficient R 2 , global accuracy indicators root mean square error RMSE, maximum absolute error MAE to judge the fitting accuracy of the proxy model; R 2 The closer the value is to 1, the better the model fitting effect is, the smaller the RMSE value is, the closer the model prediction value is to the true value, and the smaller the MAE value is, the lower the worst prediction error of the model is; the surrogate model with the highest fitting accuracy is selected for output; R 2 The calculation formulas for , RMSE and MAE are: ， Where: y i is the response value of the i-th sample state variable, is the approximate value of the state variable of the ith sample, is the mean of the ith sample response, n Indicates the number of samples; The specific process of step E is as follows: E10. Given the expected value of system-level design variables Z ij , and the expected value Z ij Pass them to each discipline-level optimization model respectively; E20. Expected values ​​of design variables transferred from the system level to each discipline level Z ij After that, the subject analysis units connected to each subject-level optimization module are connected according to the design variables provided by the former. x i Conduct subject analysis to obtain design variables x i and expected values ​​of system-level design variables Z ij The difference between J i , where i represents the i-th subject in structure, control, fluid mechanics, and transmission, and j represents the j-th design variable in the subject, i=1,2,3, j=1,2,3; E30. Each discipline uses the discipline-level optimization model established in step C to perform discipline-level optimization of the corresponding discipline, minimizing the J i , calculate and obtain the optimal value of each subject-level design variable Y ij ,i=1,2,3,j=1,2,3; E40. Optimize the optimal values ​​of each discipline-level design variable Y ij Return to the system level, the system level according to the optimal value of each subject level design variable Y ij , construct the inter-disciplinary consistency constraint G for system-level optimization; E50: Using the discipline-level optimization model established in step E30, the quality of workbench movement is obtained under the condition of satisfying the consistency constraints between disciplines. M , first-order natural frequency f 、ITAE index J ITAE , average stiffness of oil film j e The optimal solution of the system-level design variable is obtained after system-level optimization. Z ij ' , the optimal value Z ij ' As a new system-level design vector expectation value Z ij Delivered to each subject level; E60, repeat the above steps E10 to E50 until the system-level optimization target converges, obtain the final optimization result and output it; The structural discipline-level optimization model under the collaborative optimization framework in the E30 step is: ， Where: J 1 is the difference between the expected values ​​of the discipline design variables and the system-level design variables in the structural discipline; The transmission discipline-level optimization model under the collaborative optimization framework in the E30 step is: ， Where: J 2 is the difference between the expected values ​​of the subject design variables and the system-level design variables in the transmission discipline; The fluid mechanics discipline-level optimization model under the collaborative optimization framework in the E30 step is: ， Where: J 3 is the difference between the expected values ​​of the subject design variables and the system-level design variables in fluid mechanics; The control discipline-level optimization model under the collaborative optimization framework in step E30 is: ， Where: J 4 is the difference between the expected values ​​of the subject design variables and the system-level design variables in the control discipline; The system-level optimization model under the collaborative optimization framework in the E30 step and the inter-disciplinary consistency constraint G of the E40 system-level optimization are: ， Where: J 1 ',J 2 ',J 3 ',J 4 ' Indicates the consistency constraint function between disciplines at the system level; ' The quantity represents the optimal value transmitted from each subject level to the system level. J 1 '= ( Z 1j - Y 1j ) 2 ; J 2 '= ( Z 41 - Y 21 ) 2 +( Z 42 - Y 22 ) 2 +( Z 43 - Y 23 ) 2 ; J 3 ' = ( Z 31 - Y 31 ) 2 +( Z 32 - Y 32 ) 2 +( Z 33 - Y 33 ) 2 +( Z 34 - Y 34 ) 2 ; J 4 '= ( Z 41 - Y 41 ) 2 +( Z 42 - Y 42 ) 2 +( Z 43 - Y 43 ) 2 Sum the consistency constraint functions between disciplines, τ is the relaxation factor, usually 10 -3 Up to 10 -5 .

2. The CNC machine tool feed system optimization design method based on collaborative optimization strategy according to claim 1 is characterized in that: In step A, the design indicators of the CNC machine tool feed system include maximum rapid moving speed, acceleration, maximum load, table size and / or moving stroke, and the main equipment pre-selection includes motors and multi-head pumps.

3. A storage medium having a computer program stored thereon, characterized in that: The computer program can be executed by one or more processors to implement the CNC machine tool feed system optimization design method based on collaborative optimization strategy as described in claim 1 or 2.

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