Rotor reliability constrained rolling bearing assembly parameter robust design method

Abstract

The invention discloses a rotor reliability constrained rolling bearing assembly parameter robust design method. The method comprises the following steps: constructing a dynamic model for an actual rotor-bearing system; constructing an uncertainty parameter vector and a design variable vector; a target function based on robustness and a constraint function based on reliability are constructed, so that an uncertainty optimization model is obtained; constructing an augmented input variable, and establishing a candidate orthogonal polynomial basis function set; on the basis, constructing and evaluating polynomial chaos-Kriging models for the target function and the constraint function respectively, and screening out an optimal polynomial chaos-Kriging model; calculating the expectation and the standard deviation of the target function and the failure probability of the constraint function under each design variable vector; and converting the uncertainty optimization model into an unconstrained single-target optimization model, randomly generating population individuals of a heuristic optimization algorithm in a feasible region of design variables, and iteratively searching an optimal solution of the unconstrained single-target optimization model as a rolling bearing assembly scheme.

Description

Technical Field

[0001] This invention relates to the field of dynamics and reliability design technology of rotating machinery systems, and in particular to a method for optimizing the design of rolling bearing assembly parameters under multi-source uncertainties such as geometric errors, material dispersion, and assembly errors, with reliability as a constraint and robustness as an objective. Background Technology

[0002] As a core component of rotating machinery, the rotor-bearing system undertakes key functions such as power transmission, maintaining motion accuracy, and ensuring efficient and stable operation of equipment. It is widely used in important fields such as aerospace, marine propulsion, energy equipment, and high-end manufacturing. With the development of modern equipment towards higher speed, higher precision, and higher reliability, higher requirements are placed on the dynamic performance and operational stability of rotor-bearing systems.

[0003] As a key component supporting the rotor, the assembly parameters of rolling bearings (such as preload, clearance, mounting angle, and position) have a decisive impact on the stiffness, damping characteristics, critical speed distribution, and overall stability of the rotor-bearing system. A reasonable configuration of rolling bearing assembly parameters can effectively improve the system's dynamic response, enhance load-bearing capacity, and improve disturbance rejection; conversely, improper parameter selection can lead to serious problems such as resonance, instability, or even failure. Therefore, optimizing the design of rolling bearing assembly parameters is an important means of improving the performance of the rotor-bearing system.

[0004] In practical engineering applications, rotor-bearing systems are inevitably affected by various uncertainties, including geometric deviations, material property fluctuations, assembly errors, changes in lubrication conditions, and external load disturbances. These uncertainties can cause system performance to deviate from design expectations, resulting in increased vibration, decreased reliability, or even sudden failures, seriously affecting the safety and availability of the equipment. Traditional deterministic optimization methods are usually based on ideal models and fixed parameter assumptions, which are difficult to cope with performance fluctuations under real operating conditions, and have insufficient robustness and reliability risks. Summary of the Invention

[0005] The purpose of this invention is to provide a robust design method for rolling bearing assembly parameters with rotor reliability constraints, aiming to solve the problem that existing methods are unable to simultaneously satisfy system reliability and robustness under the influence of multi-source uncertainties.

[0006] To achieve the above objectives, the present invention employs the following technical solution: A robust design method for rolling bearing assembly parameters under rotor reliability constraints includes: Based on the actual rotor-bearing system structure, a dynamic model of the rotor-bearing system is constructed, and the dynamic model is calibrated through experimental verification and parameter identification. Identify the sources of uncertainty parameters in the rotor-bearing system and model them based on probability distributions, constructing an uncertainty parameter vector; simultaneously determine the design variables, construct a design variable vector, and set its upper and lower limits. Based on the uncertainty parameter vector and design variable vector, and combined with the dynamic performance requirements of the rotor-bearing system, a robust objective function and a reliability-based constraint function are constructed to obtain an uncertainty optimization model. By constructing augmented input variables using uncertainty parameter vectors and design variable vectors, a candidate set of orthogonal polynomial basis functions is established. Based on this, polynomial chaos-kriging models are constructed and evaluated for the objective function and constraint function, and the optimal polynomial chaos-kriging model is selected. Using the optimal polynomial chaotic-Kriging model corresponding to the constructed objective function and constraint function, the expected value and standard deviation of the objective function and the failure probability of the constraint function are calculated under each design variable vector. The uncertain optimization model is transformed into an unconstrained single-objective optimization model using the linear weighted sum and penalty function method. By randomly generating a population of individuals for the heuristic optimization algorithm within the feasible region of the design variable vector, the optimal solution of the unconstrained single-objective optimization model is iteratively searched as the rolling bearing assembly scheme.

[0007] Furthermore, the unbalanced response of the rotor-bearing system at the critical speed is taken as the objective function, and the optimization objective is to minimize the mathematical expectation and standard deviation of the unbalanced response. With the first The critical speed is used as a constraint function, requiring that the failure probability of it being less than a given threshold does not exceed a preset allowable upper limit; The uncertainty optimization model is as follows:

[0008] in, For the uncertain parameter vector, To design variable vectors, and Design upper and lower limits for variables; and These represent the expected value and standard deviation, respectively. Let be the objective function. For constraint functions; Given a threshold, This is the maximum allowed limit; Indicates the first The failure probability of a constraint. This represents the total number of constraints. This represents a probability and statistics function.

[0009] Furthermore, by constructing augmented input variables using the uncertainty parameter vector and the design variable vector, a set of candidate orthogonal polynomial basis functions is established, including: Uncertainty parameter vector and design variable vector Combined to form augmented input variables ; Latin hypercube sampling is used to generate parameters within the augmented input variable parameter space. training samples Constructing a training sample set By solving the dynamic model of the rotor-bearing system, the corresponding objective function value is obtained. With constraint function values ; Based on the distribution type of each augmented input variable, select the corresponding orthogonal polynomial basis functions to construct a cutoff order of... The set of candidate orthogonal polynomial basis functions ,in Orthogonal polynomial basis functions For multidimensional indexes, Each element This represents the order of the basis functions of the candidate orthogonal polynomials in different dimensions. A collection of multidimensional indexes.

[0010] Furthermore, multinomial chaotic-kriging models are constructed and evaluated for the objective function and constraint functions, respectively, and the optimal multinomial chaotic-kriging model is selected, including: The method combines minimum angle regression and cross-validation, with the objective function being... and constraint functions From the basis function set of candidate orthogonal polynomials The important terms are selected step by step and used to construct a polynomial chaos-kriging model. Leave-one-out cross-validation is used to evaluate the performance of the polynomial chaos-kriging model and find the optimal polynomial chaos-kriging model.

[0011] Furthermore, the specific process of finding the optimal polynomial chaotic-Kriging model is as follows: Step 4-4-1, for constructing the objective function The polynomial chaotic-Kriging agent model, assuming the training input set The corresponding training output set ; Step 4-4-2, for each multidimensional index that has not been selected Calculate the basis functions of its corresponding orthogonal polynomial. Value vector on training samples ;calculate With the current number The residual of the next iteration correlation Selecting relevance Multidimensional index at maximum Join the The selected basis function index set of the next iteration ; Step 4-4-3, using the least squares method on the ... The set of orthogonal polynomial basis functions for each iteration Fit a polynomial chaotic expansion model and update the residuals. ; Step 4-4-4: Repeat steps 4-4-2 to 4-4-3 until the number of selected orthogonal polynomial basis functions reaches the preset upper limit. This ultimately yields a sparse polynomial basis function set. This includes selecting sequentially. The corresponding orthogonal polynomial basis functions; Step 4-4-5, from the sparse polynomial basis function set Take the front Construct a polynomial chaos-Kriging model using orthogonal polynomial basis functions; Step 4-4-6: For each constructed polynomial chaotic-Kriging model, calculate its leave-one error; in all... Among the polynomial chaotic-Kriging models, the one with the smallest leave-one error is selected as the final optimal polynomial chaotic-Kriging model.

[0012] Furthermore, after determining the corresponding optimal polynomial chaotic-Kriging surrogate model for both the objective function and the constraint function, multiple test samples are generated in the parameter space of the augmented input variables using Latin hypercube sampling to construct a test sample set; the true response corresponding to the test sample set is calculated, i.e., the corresponding set of objective function values ​​and set of constraint function values; the response under the test sample is predicted using the optimal polynomial chaotic-Kriging model; and the coefficient of determination is calculated to evaluate the predictive performance of the model. If the determination coefficients corresponding to all optimal polynomial chaotic-Kriging models are greater than the preset threshold, proceed to the next step; otherwise, add the test set to the training sample set and increase the order of the candidate orthogonal polynomial basis functions to redetermine the optimal polynomial chaotic-Kriging model.

[0013] Furthermore, using the optimal polynomial chaotic-Kriging model corresponding to the constructed objective function and constraint functions, the expected value and standard deviation of the objective function and the failure probability of the constraint functions under each design variable vector are calculated, including: Multiple random samples are generated in the parameter space of the uncertain parameters by Latin hypercube sampling to construct a random sample set. The deterministic design variable vector is concatenated with each random sample to form an augmented input. The optimal polynomial chaos-Kriging model is used to predict the objective function response and constraint function response under each augmented input. Calculate the expected value and standard deviation of the objective function under any set of design variable vectors; at the same time, use Monte Carlo simulation to estimate the failure probability of each constraint function.

[0014] Furthermore, a heuristic optimization algorithm is employed, setting the population size, maximum number of iterations, and convergence criteria. The combination of design variable vectors is used as the individuals in the population, and the design variable vector population is initialized accordingly. The algorithm is then used to calculate the value of each individual. Iteratively update the population until the preset convergence condition is met, and output the optimal individual. The optimal individual component is selected as the rolling bearing assembly scheme that meets the requirements of reliability and robustness. ;in, This means that the uncertain optimization model is transformed into the objective function in the unconstrained single-objective optimization model using the linear weighted sum penalty function method.

[0015] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, it implements a robust design method for rolling bearing assembly parameters under rotor reliability constraints.

[0016] A computer-readable storage medium storing a computer program; when executed by a processor, the computer program implements a robust design method for rolling bearing assembly parameters that addresses rotor reliability constraints.

[0017] Compared with the prior art, the present invention has the following technical features: This invention introduces an adaptive surrogate model technique to replace the traditional high-fidelity finite element model for performance prediction and reliability assessment, significantly reducing the computational cost and convergence difficulty in the multi-nested optimization process. Addressing the critical impact of rolling bearing assembly parameters on the performance and reliability of rotor-bearing systems, a robust optimization design framework that balances failure probability constraints and performance objectives is constructed, ensuring good operational stability and a long service life under various assembly deviations and uncertainties. Combining heuristic intelligent optimization algorithms and experimental verification methods, efficient optimization of rolling bearing assembly parameters and verification of engineering feasibility are achieved, forming a closed-loop design process from modeling and optimization to verification. In summary, this invention provides a systematic solution for the reliability and robustness design of complex rotor-bearing systems considering the uncertainties of rolling bearing assembly, possessing significant engineering application value and promising prospects for widespread adoption. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating the method of the present invention.

[0019] Figure 2 This is a schematic diagram of a rotor-bearing system and vibration testing system according to one embodiment of the present invention; wherein the reference numerals are: 1 angular contact ball bearing, 2 rotating shaft, 3 turbine disk, 4 fiber optic sensor, 5 data acquisition unit, 6. computer; Figure 3(a) is a regression plot of the first-order critical speed predicted by the optimal polynomial chaotic-Kriging surrogate model in one embodiment of the present invention; Figure 3(b) is a regression diagram of the steady-state response amplitude predicted by the optimal polynomial chaotic-Kriging surrogate model at the first-order resonance frequency in one embodiment of the present invention. Figure 4(a) is the iterative curve of the standardized objective function during optimization design in one embodiment of the present invention; Figure 4(b) is an iterative curve of the expected value and standard deviation of the steady-state response amplitude at the first-order resonant frequency during optimization design in one embodiment of the present invention; Figure 5 This is a comparison chart of Campbell plot confidence intervals before and after optimization in one embodiment of the present invention.

[0020] Figure 6 This is a comparison diagram of the steady-state time-domain response confidence intervals at the first-order resonant frequency before and after optimization in one embodiment of the present invention. Detailed Implementation

[0021] To address the shortcomings of existing technologies, research on the optimization design of rolling bearing assembly parameters considering uncertainties is of great significance. By introducing reliability constraints and robustness indices, an optimization framework that balances system performance stability and failure probability control is constructed, enabling the optimal configuration of rolling bearing assembly parameters under complex and variable real-world operating environments. This method not only helps reduce the system's sensitivity to uncertainties but also effectively improves its safety margin and operational consistency, possessing significant engineering application value for ensuring the high performance, long lifespan, and high reliability of rotating machinery systems.

[0022] This invention provides a robust design method for rolling bearing assembly parameters under rotor reliability constraints, comprising the following steps: Step 1: Based on the actual rotor-bearing system structure, construct a dynamic model of the rotor-bearing system, and adjust the dynamic model through experimental verification and parameter identification.

[0023] Step 1-1: Based on the structural characteristics of the rotor-bearing system, the rotating shaft is divided into multiple one-dimensional Timoshenko beam elements along the axial direction, and the lumped mass components such as the turntable are discretized into lumped mass elements considering rotational inertia; based on the finite element method, the mass matrix of each beam element is calculated. Stiffness matrix Damping matrix and gyroscope matrix Further calculate the mass matrix of the lumped mass element. and gyroscope matrix .

[0024] Steps 1-2: Based on the type of rolling bearing used (e.g., angular contact ball bearing, cylindrical roller bearing, etc.) and its geometric and structural parameters, derive the equivalent stiffness and damping parameters of the rolling bearing unit, and establish the stiffness matrix of the rolling bearing unit. and damping matrix .

[0025] Steps 1-3: Based on the degree-of-freedom mapping relationship, assemble the mass matrix, stiffness matrix, damping matrix, and gyroscope matrix of the beam element, lumped mass element, and rolling bearing element into the global mass matrix of the rotor-bearing system. Global stiffness matrix Global gyroscope matrix With the global damping matrix The dynamic model of the rotor-bearing system can be expressed as: (1) in, Let be the system's generalized displacement vector. and These are the velocity and acceleration vectors, respectively. For external excitation, the global gyroscope matrix The rotational speed of each rotating component (shaft and turntable) The gyroscopic effect generated is determined by the above vectors, which are all related to the design variable vector. Uncertainty parameter vector and time Related, global quality matrix Global stiffness matrix Global gyroscope matrix With global damping matrix With design variable vector Uncertainty parameter vector Related.

[0026] Step 2: After completing the establishment and calibration of the dynamic model, identify the sources of uncertainty parameters in the rotor-bearing system and model them based on probability distribution, constructing an uncertainty parameter vector; at the same time, determine the design variables, construct a design variable vector, and set its upper and lower limits.

[0027] Specifically, key uncertainty parameters are identified, such as material elastic modulus, density, and geometric dimensional deviations. Based on their statistical characteristics and engineering experience, models are constructed using normal distribution, uniform distribution, or other suitable probability distributions to form an uncertainty parameter vector. ,in For a vector space, It is the dimension of the uncertain parameter vector.

[0028] Design variables are selected from adjustable assembly parameters, including the installation position of the rolling bearing, axial preload, and interference fit of the outer ring, to form a design variable vector. And set its feasible region, that is, its upper and lower limits. and ;in It is the dimension of the design variable vector; the identified uncertainty parameter vector. With design variable vector They will be used together as inputs to the subsequent objective function and constraint functions.

[0029] Step 3: Based on the uncertainty parameter vector and design variable vector, and combined with the dynamic performance requirements of the rotor-bearing system, construct a robust objective function and a reliability-based constraint function, thereby obtaining the uncertainty optimization model; the specific steps are as follows: Step 3-1: Use the unbalanced response of the rotor-bearing system at the critical speed as the objective function. The optimization objective is to minimize the expected value and standard deviation of the imbalanced response, i.e.: (2) in, and These represent the uncertainty parameter vectors respectively. Objective function under action The expected value and standard deviation of the mathematical expression.

[0030] Step 3-2, with the first First critical speed as constraint function It is required that it be below a given threshold. The failure probability does not exceed the preset allowable upper limit. ,Right now: (3) in, Indicates the first The failure probability of a constraint. Represents a probability and statistics function. This represents the total number of constraints. Step 3-3: Combining the above objectives and constraints, construct a multi-objective, multi-constraint uncertainty optimization model: (4) Step 4: Construct augmented input variables using the step deterministic parameter vector and design variable vector to establish a candidate set of orthogonal polynomial basis functions; on this basis, construct and evaluate polynomial chaotic-kriging models for the objective function and constraint functions respectively, and select the optimal polynomial chaotic-kriging model.

[0031] To avoid the computational cost of directly solving the optimization model under high-dimensional uncertainty, this step uses an adaptive polynomial chaos-Kriging surrogate model to efficiently approximate the objective function and the constraint function.

[0032] Step 4-1, convert the uncertainty parameter vector and design variable vector Combined to form augmented input variables ,in To broaden the dimensionality of the input variables and to improve the approximate accuracy of the boundary region, the boundaries of the uncertainty parameters and design variables are extended outward by 1%.

[0033] Step 4-2: Generate parameters using Latin hypercube sampling within the parameter space of the augmented input variables. training samples Constructing a training sample set By solving the dynamic model equation (1) of the rotor-bearing system, the corresponding objective function value is obtained. With constraint function values The number of sampling points Conditions must be met: (5) Step 4-3: Select the corresponding orthogonal polynomial basis functions according to the distribution type of each augmented input variable. For example, a Gaussian distribution corresponds to the Hermite polynomial, and a uniform distribution corresponds to the Legendre polynomial; construct a cutoff order of... The set of candidate orthogonal polynomial basis functions ,in Orthogonal polynomial basis functions For multidimensional indexes, Each element This represents the order of the candidate orthogonal polynomial basis functions in different dimensions, and is a set of multidimensional indices. ,in It represents the set of natural numbers.

[0034] Step 4-4 employs a combination of minimum angle regression and cross-validation, with the objective function being... and constraint functions From the basis function set of candidate orthogonal polynomials The process involves progressively selecting important terms and constructing a multinomial chaotic-kriging model. Leave-one-out cross-validation is then used to evaluate the performance of the multinomial chaotic-kriging model, ultimately identifying the optimal model. The specific steps are as follows: Step 4-4-1, to construct the objective function Taking the polynomial chaotic-Kriging agent model as an example, let the training input set be... The corresponding training output set Initialize the number of iterations. residual and the selected basis function index set The maximum number of candidate basis functions is The upper limit of the target sparse term number is .

[0035] Step 4-4-2, for each multidimensional index that has not been selected Calculate the basis functions of its corresponding orthogonal polynomial. The value vector on the training samples: (6) in, Indicates the first The values ​​of the orthogonal polynomial basis functions corresponding to each training sample. , where the parameter superscript This indicates transposition, and the same applies below.

[0036] calculate With the current number The residual of the next iteration Correlation: (7) Select correlation Multidimensional index at maximum Join the The selected basis function index set of the next iteration , can be represented as: (8) in For the current number The set of selected basis function indices for the next iteration.

[0037] Step 4-4-3, using the least squares method on the ... The set of orthogonal polynomial basis functions for each iteration Fitting a polynomial chaotic expansion model: (9) Among them, the The coefficient vector of the next iteration It was obtained by solving using the least squares method, superscript Indicates transpose, here Update residuals: (10) in, It is the first The next iteration feeds the training input set into the output of the multinomial chaotic expansion model.

[0038] Step 4-4-4: Repeat steps 4-4-2 to 4-4-3 until the number of selected orthogonal polynomial basis functions reaches the preset upper limit. This ultimately yields a sparse polynomial basis function set. ,in It is selected step by step in sequence. The corresponding orthogonal polynomial basis functions, For the set of A number of orthogonal polynomial basis functions.

[0039] Step 4-4-5, for each From the set of sparse polynomial basis functions Take the front Constructing a polynomial chaos-Kriging model using orthogonal polynomial basis functions: (11) in, This represents a polynomial chaos-Kriging model. It is the trend term of the chaotic-Kriging model expressed by the polynomial chaotic expansion model (9). It is the fitting residual in the chaos-Kriging model.

[0040] Step 4-4-6, for each of the polynomial chaotic-Kriging models constructed in step 4-4-5 Calculate its leave-one error: (12) in, It is the training output set The first in One training output, To remove the first The multinomial chaotic-Kriging surrogate model trained after the nth training sample is used for the th... Predicted values ​​for each training sample; in all Among the polynomial chaotic-Kriging models, the one with the smallest leave-one error is selected as the final optimal polynomial chaotic-Kriging model.

[0041] Steps 4-5, after performing step 4-4 on both the objective function and constraint functions, yield the corresponding optimal polynomial chaotic-Kriging surrogate model; with augmented input variables... Generate in parameter space using Latin hypercube sampling M test samples Constructing a test sample set ;calculate The corresponding true response, i.e., the set of corresponding objective function values. Constraint function value set The optimal polynomial chaotic-Kriging model is used to predict the response under test samples, and the coefficient of determination is calculated. To evaluate the predictive performance of the model: (13) in, For the first The set of objective function values ​​corresponding to each test sample or set of constraint function values The first in One value, For the first The response value predicted for each test sample using the corresponding optimal polynomial chaotic-Kriging model. This represents the mathematical expectation of the true response corresponding to the test sample.

[0042] If the coefficients of determination for all optimal polynomial chaotic-Kriging models are... If all values ​​are greater than the preset threshold, proceed to step 5; otherwise, return to step 4-2 to add the test set to the training sample set, increase the order of the candidate orthogonal polynomial basis functions in step 4-3, and repeat steps 4-4 and 4-5 until the determination coefficients of all models are obtained. The requirements are met.

[0043] Step 5, utilize the constructed objective function and constraint functions The corresponding optimal polynomial chaotic-Kriging model is used to calculate arbitrary design variable vectors. Lower objective function Expectations Standard deviation and constraint functions failure probability The details are as follows: Step 5-1: Generate parameters in the parameter space of the uncertainty parameters using Latin hypercube sampling. random samples Constructing a random sample set ,in The vector of design variables should be large enough to ensure statistical stability; With each random sample Serial connection to form augmented input Predicting each augmented input using an optimal polynomial chaotic-Kriging model. The objective function response and constraint function response .

[0044] Step 5-2: Calculate any set of design variable vectors based on the prediction results. Lower objective function Expectations with standard deviation : (14) Meanwhile, Monte Carlo simulation was used to estimate the first... The failure probability of each constraint function: (15) in, It is an indicator function that takes the value 1 if the condition is met, and 0 otherwise.

[0045] Step 6: Since multi-objective and multi-constraint optimization problems are difficult to solve due to conflicts in non-convex objectives, the uncertain optimization model (4) is transformed into an unconstrained single-objective optimization model using the linear weighted sum penalty function method: (16) in, This represents the transformed objective function. These are the weighting coefficients used to adjust the expected value and standard deviation; These are parameters that ensure the objective function is non-negative; and These are two regularization factors; These are penalty factors; their function is to ensure that the objectives and constraints are of the same magnitude and can be optimized simultaneously. The constraint violation function is defined as follows: (17) Step 7: Using a heuristic optimization algorithm (such as genetic algorithm, particle swarm optimization, etc.), set the population size, maximum number of iterations, and convergence conditions. Use the combination of design variable vectors as individuals in the population, and randomly generate individuals within the feasible region of the calculation variable vectors to initialize the population. Calculate the objective function corresponding to each individual by repeatedly executing steps 5-6. Iteratively update the population until the preset convergence condition is met (such as reaching the maximum number of iterations), and output the optimal individual. The optimal individual component is selected as the rolling bearing assembly scheme that meets the requirements of reliability and robustness. Based on the optimization results, process control strategies and improvement plans for key assembly parameters were formulated. Furthermore, vibration tests and finite element simulations under typical operating conditions were used to verify the dynamic performance and reliability of the optimized system, achieving closed-loop feedback and continuous optimization.

[0046] Example: This embodiment uses Figure 2 The design method of the present invention will be described using the rotor-bearing system and vibration testing system shown in the figure as examples.

[0047] Step 1: The rotor-bearing system studied in this embodiment is a cantilever rotor-bearing structure. Based on its geometric configuration and mass distribution, the finite element method is used for modeling. The shaft is divided into multiple one-dimensional Timoshenko beam elements along the axial direction. The turbine component is simplified into a lumped mass element that considers mass, diameter moment of inertia, and polar moment of inertia. The angular contact ball bearing is simplified into a spring-damped element with equivalent stiffness and damping characteristics.

[0048] For angular contact ball bearings, their radial stiffness is established based on Hertzian contact theory. and damping Mathematical model (18) in, For the number of rolling elements, and They are respectively the inner circle and the outer circle and the first Radial contact stiffness of each rolling element and The first Oil film damping between each rolling element and the inner and outer rings and The first The contact angle between the rolling element and the inner and outer rings after being loaded.

[0049] After calculating the element matrices for each component (shaft, turntable, bearing), they are assembled into a global mass matrix based on the system's degree-of-freedom mapping relationship. Stiffness matrix Damping matrix and gyroscope matrix Thus, the global dynamic equation of the system as shown in equation (1) is constructed, and its prediction accuracy is ensured through parameter identification.

[0050] Step 2: Based on factors such as the structural design tolerances, manufacturing and assembly errors, and the dispersion of material properties of the rotor-bearing system, identify and select uncertain parameters that have a significant impact on the system's dynamic characteristics. In this embodiment, the following parameter is selected as a random uncertain variable, and it is assumed that it follows a uniform distribution: Young's modulus. exist The change between them, Poisson's ratio exist Fluctuations within the range; turbine eccentricity exist The variation between these values, turbine mass Diameter Moment of Inertia and polar moment of inertia Based on the nominal value Fluctuations within a certain range. The uncertainty parameter vector can be represented as... .

[0051] Simultaneously, considering the adjustability of the structural design and the controllability of the assembly process, the rolling bearing assembly parameters, which have a significant regulatory effect on system performance, are selected as design variables. In this embodiment, the design variables and their value ranges are: the deviation of the installation positions of the two bearings. The interference fit of the outer rings of the two bearings ; and the axial preload of the two rolling bearings. The design variable vector can be represented as... .

[0052] Step 3: To improve vibration stability, in this embodiment, the steady-state response amplitude at the first-order resonant frequency is selected. As a performance metric, the optimization objective is to minimize the mathematical expectation of the response. with standard deviation Meanwhile, based on the API 684 standard's requirements for "avoidance rate," a first-order critical speed is set. This is a critical constraint. It requires the value to be below a given threshold. The failure probability does not exceed In summary, a multi-objective, multi-constraint uncertainty optimization model of the form (4) is constructed.

[0053] Step 4: Analyze the steady-state response amplitude at the first-order resonant frequency. and critical speed Construct an adaptive multinomial chaos-Kriging proxy model.

[0054] First, design the variable vector. With uncertainty parameter vector Combined to form augmented input variables To improve the approximation accuracy of the boundary region, each augmented input variable is extended outward by 1% from the original parameter boundaries. Within the augmented input space, Latin hypercube sampling is used to generate... training samples By solving the high-fidelity finite element model shown in equation (1) constructed in step 1, the objective function value corresponding to each sample is calculated. and constraint function values .

[0055] Set the initial cutoff order of the polynomial basis functions Select the appropriate orthogonal polynomial basis functions based on the distribution type of each input variable: uniformly distributed variables correspond to Legendre polynomials. Construct a set of candidate basis functions. A method combining minimum angular regression and cross-validation is employed to screen important terms from candidate basis functions, construct a sparse multinomial chaotic expansion surrogate model, and further build a multinomial chaotic-Kriging model. The specific process follows the algorithm in step 4-4 of the invention description.

[0056] To verify the accuracy of the surrogate model, it was regenerated in the augmented input space. For each test sample, calculate the coefficient of determination between the actual response and the predicted value of the multinomial chaos-Kriging model in equation (13). .according to By adaptively increasing the number of training samples and the truncation order of the polynomial chaotic expansion, the polynomial chaotic-Kriging model ultimately meets the accuracy requirements.

[0057] In this embodiment, the first-order critical speed With the amplitude of the first-order resonant response Proxy model regression plot and coefficient of determination As shown in Figures 3(a) and 3(b) respectively, All values ​​reached 1.0, which is higher than the preset threshold such as 0.99, indicating that the model has extremely high prediction accuracy and meets the needs of subsequent optimization.

[0058] Step 5, in the uncertainty parameter vector Within the parameter space, generated through Latin hyperlegal sampling Sample Each With fixed design variables splicing for augmented input Fast prediction of objective function response using optimal polynomial chaotic-Kriging model With constraint function response Based on the prediction results, the expectation of the objective function is estimated using equation (14). with standard deviation Similarly, equation (15) can be used to estimate the failure probability of the first-order critical speed constraint. .

[0059] Step 6: In this embodiment, as shown in equation (16), this type of problem is transformed into an unconstrained single-objective optimization problem by using linear weighting of the objective and constraint penalty. (19) This allows for the use of more mature and efficient single-objective optimization algorithms, thereby improving computational efficiency and convergence speed, and facilitating engineering implementation and practical applications. In this embodiment, the weighting coefficients... Adjust parameters Normalization coefficient , Sum of penalty coefficients Set them to 0.5, 0, and respectively. , And 100.

[0060] Step 7: Solve equation (19) using the heuristic intelligent optimization algorithm—the snake optimization algorithm. Specific parameter settings are as follows: population size is 30, maximum number of iterations is 100, and other parameters use default values. In each iteration, repeat steps 5 and 6 to calculate the corresponding values ​​for each individual (combination of design variables). The population is then updated until the convergence condition is met. Finally, the optimal combination of rolling bearing assembly parameters is obtained. In this example, the standardized objective function and steady-state peak value at the first-order resonant frequency The iterative curves of the expected value and standard deviation are shown in Figure 4(a) and Figure 4(b), respectively.

[0061] The optimal bearing parameter combination obtained through optimization is input into the finite element simulation model. Dynamic response analysis is performed under typical load conditions. In addition, vibration tests are conducted on the actual prototype using a vibration testing system to measure its key response indicators, thereby verifying the performance improvement and reliability level of the optimized system.

[0062] In this embodiment, the confidence intervals of the Campbell plot before and after optimization are as follows: Figure 5 As shown, the confidence interval of the steady-state time-domain response at the first-order resonant frequency is as follows: Figure 6 As shown above, the robust optimization design method effectively improves the dynamic performance and reliability of the rotor-bearing system, and the optimized design scheme has good engineering applicability and robustness.

[0063] This invention effectively overcomes the limitations of traditional deterministic and uncertain rolling bearing assembly parameter optimization design methods. By introducing adaptive surrogate modeling technology, combined with reliability theory and multi-objective optimization methods, robust optimization of rolling bearing assembly parameters is rapidly achieved, effectively enhancing the robustness and operational safety of the rotor-bearing system. The optimization process system provided by this invention is complete, logically clear, and possesses good engineering feasibility. The above description is only a preferred embodiment of this invention, and this invention is not limited to the design optimization of rotor-bearing systems in high-end rotating machinery such as aero-engines, gas turbines, and steam turbines.

[0064] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A robust design method for rolling bearing assembly parameters under rotor reliability constraints, characterized in that, include: Based on the actual rotor-bearing system structure, a dynamic model of the rotor-bearing system is constructed, and the dynamic model is calibrated through experimental verification and parameter identification. Identify the sources of uncertainty parameters in the rotor-bearing system and model them based on probability distributions, constructing an uncertainty parameter vector; simultaneously determine the design variables, construct a design variable vector, and set its upper and lower limits. Based on the uncertainty parameter vector and design variable vector, and combined with the dynamic performance requirements of the rotor-bearing system, a robust objective function and a reliability-based constraint function are constructed to obtain an uncertainty optimization model. By constructing augmented input variables using uncertainty parameter vectors and design variable vectors, a candidate set of orthogonal polynomial basis functions is established. Based on this, polynomial chaos-kriging models are constructed and evaluated for the objective function and constraint function, and the optimal polynomial chaos-kriging model is selected. Using the optimal polynomial chaotic-Kriging model corresponding to the constructed objective function and constraint function, the expected value and standard deviation of the objective function and the failure probability of the constraint function are calculated under each design variable vector. The uncertain optimization model is transformed into an unconstrained single-objective optimization model using the linear weighted sum and penalty function method. The combination of design variable vectors is used as an individual in the heuristic algorithm, and the optimal individual is selected as the rolling bearing assembly scheme using the unconstrained single-objective optimization model.

2. The robust design method for rolling bearing assembly parameters with rotor reliability constraints according to claim 1, characterized in that, The unbalanced response of the rotor-bearing system at the critical speed is used as the objective function, and the optimization objective is to minimize the mathematical expectation and standard deviation of the unbalanced response. With the first The critical speed is used as a constraint function, requiring that the failure probability below a given threshold does not exceed a preset allowable upper limit; The uncertainty optimization model is as follows: in, For the uncertain parameter vector, To design variable vectors, and Design upper and lower limits for variables; and These represent the expected value and standard deviation, respectively. Let be the objective function. For constraint functions; Given a threshold, This is the maximum allowed limit; Indicates the first The failure probability of a constraint. This represents the total number of constraints. This represents a probability and statistics function.

3. The robust design method for rolling bearing assembly parameters under rotor reliability constraints according to claim 1, characterized in that, By constructing augmented input variables using uncertainty parameter vectors and design variable vectors, a set of candidate orthogonal polynomial basis functions is established, including: Uncertainty parameter vector and design variable vector Combined to form augmented input variables ; Latin hypercube sampling is used to generate parameters within the augmented input variable parameter space. training samples Constructing a training sample set By solving the dynamic model of the rotor-bearing system, the corresponding objective function value is obtained. With constraint function values ; Based on the distribution type of each augmented input variable, select the corresponding orthogonal polynomial basis functions to construct a cutoff order of... The set of candidate orthogonal polynomial basis functions ,in Orthogonal polynomial basis functions For multidimensional indexes, Each element This represents the order of the basis functions of the candidate orthogonal polynomials in different dimensions. A collection of multidimensional indexes.

4. The robust design method for rolling bearing assembly parameters with rotor reliability constraints according to claim 1, characterized in that, Multinomial chaotic-kriging models are constructed and evaluated for the objective function and constraint functions, respectively, and the optimal multinomial chaotic-kriging model is selected, including: The method combines minimum angle regression and cross-validation, with the objective function being... and constraint functions From the basis function set of candidate orthogonal polynomials The important terms are selected step by step and used to construct a polynomial chaos-kriging model. Leave-one-out cross-validation is used to evaluate the performance of the polynomial chaos-kriging model and find the optimal polynomial chaos-kriging model.

5. The robust design method for rolling bearing assembly parameters under rotor reliability constraints according to claim 1, characterized in that, The specific process for determining the optimal polynomial chaotic-Kriging model is as follows: Step 4-4-1, for constructing the objective function The polynomial chaotic-Kriging agent model, assuming the training input set The corresponding training output set ; Step 4-4-2, for each multidimensional index that has not been selected Calculate the basis functions of its corresponding orthogonal polynomial. Value vector on training samples ;calculate With the current number The residual of the next iteration correlation Selecting relevance Multidimensional index at maximum Join the The selected basis function index set of the next iteration ; Step 4-4-3, using the least squares method on the ... The set of orthogonal polynomial basis functions for each iteration Fit a polynomial chaotic expansion model and update the residuals. ; Step 4-4-4: Repeat steps 4-4-2 to 4-4-3 until the number of selected orthogonal polynomial basis functions reaches the preset upper limit. This ultimately yields a sparse polynomial basis function set. This includes selecting sequentially. The corresponding orthogonal polynomial basis functions; Step 4-4-5, from the sparse polynomial basis function set Take the front Construct a polynomial chaos-Kriging model using orthogonal polynomial basis functions; Step 4-4-6: For each constructed polynomial chaotic-Kriging model, calculate its leave-one error; in all... Among the polynomial chaotic-Kriging models, the one with the smallest leave-one error is selected as the final optimal polynomial chaotic-Kriging model.

6. The robust design method for rolling bearing assembly parameters under rotor reliability constraints according to claim 1, characterized in that, After determining the corresponding optimal polynomial chaotic-Kriging surrogate model for both the objective function and the constraint function, multiple test samples are generated in the parameter space of the augmented input variables using Latin hypercube sampling to construct a test sample set. Calculate the true response corresponding to the test sample set, i.e. the set of objective function values ​​and the set of constraint function values, and use the optimal polynomial chaotic-Kriging model to predict the response under the test sample. Calculate the coefficient of determination to evaluate the predictive performance of the model. If the determination coefficients corresponding to all optimal polynomial chaotic-Kriging models are greater than the preset threshold, proceed to the next step; otherwise, add the test set to the training sample set and increase the order of the candidate orthogonal polynomial basis functions to redetermine the optimal polynomial chaotic-Kriging model.

7. The robust design method for rolling bearing assembly parameters under rotor reliability constraints according to claim 1, characterized in that, Using the constructed optimal polynomial chaotic-Kriging model corresponding to the objective function and constraint functions, the expected value and standard deviation of the objective function and the failure probability of the constraint functions are calculated for each design variable vector, including: Multiple random samples are generated in the parameter space of the uncertain parameters by Latin hypercube sampling to construct a random sample set. The deterministic design variable vector is concatenated with each random sample to form an augmented input. The optimal polynomial chaos-Kriging model is used to predict the objective function response and constraint function response under each augmented input. Calculate the expected value and standard deviation of the objective function under any set of design variable vectors; at the same time, use Monte Carlo simulation to estimate the failure probability of each constraint function.

8. The robust design method for rolling bearing assembly parameters under rotor reliability constraints according to claim 1, characterized in that, A heuristic optimization algorithm is employed, setting the population size, maximum number of iterations, and convergence criteria. The combination of design variable vectors is used as the individuals in the population, and the population is initialized accordingly. The algorithm then calculates the values ​​corresponding to each individual. Iteratively update the population until the preset convergence condition is met, and output the optimal individual. The optimal individual component is selected as the rolling bearing assembly scheme that meets the requirements of reliability and robustness. ;in, This means that the uncertain optimization model is transformed into the objective function in the unconstrained single-objective optimization model using the linear weighted sum penalty function method.

9. A terminal device, comprising a processor, a memory, and a computer program stored in the memory; characterized in that, When the processor executes the computer program, it implements the robust design method for rolling bearing assembly parameters with rotor reliability constraints as described in any one of claims 1-8.

10. A computer-readable storage medium storing a computer program; characterized in that, When the computer program is executed by the processor, it implements the robust design method for rolling bearing assembly parameters with rotor reliability constraints as described in any one of claims 1-8.

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