Improved method for constructing rolling bearing dynamics models

Abstract

This invention relates to the field of rotating machinery dynamics modeling technology, and discloses an improved method for constructing a rolling bearing dynamics model. The method includes: acquiring a set of bearing basic structural parameters and a set of operating condition features; establishing a multi-body coupled dynamics basic model based on structural relationships; generating a dynamically corrected parameter set based on operating condition feature vectors; dividing the operating state region based on operating condition discrimination indices and switching parameter update rules; mapping microscopic defects and manufacturing errors to equivalent excitation terms; performing inversion correction on model parameters under physical constraints based on measured response data; and outputting the improved rolling bearing dynamics model.

Description

Technical Field

[0001] This invention relates to the field of rotating machinery dynamics modeling technology, and more specifically to an improved method for constructing a rolling bearing dynamics model. Background Technology

[0002] Rolling bearings are widely used in rotating machinery such as high-speed motors, wind turbines, rail transit traction systems, industrial robot joints, precision machine tool spindles, and gearbox support systems. In actual service, bearings are subjected to complex conditions involving variable speed, variable load, temperature fluctuations, changes in lubrication conditions, assembly deviations, and minor wear.

[0003] Existing rolling bearing dynamics models typically assume constant parameters such as contact stiffness, damping, clearance, and friction coefficient. However, these parameters drift with operating conditions during actual operation, and the assumption of fixed parameters cannot reflect this change. Furthermore, existing models lack closed-loop correction capabilities, and their predictive accuracy decreases with operating time. Therefore, existing technologies suffer from insufficient parameter adaptability and time-dependent degradation of predictive accuracy. Summary of the Invention

[0004] This invention provides an improved method for constructing a rolling bearing dynamic model, which solves the technical problems in related technologies where the rolling bearing dynamic model cannot adapt to multiple working conditions, lacks the ability to characterize microscopic defects, and has insufficient parameter identification accuracy.

[0005] This invention discloses an improved method for constructing a rolling bearing dynamic model, comprising at least the following steps: obtaining a set of basic structural parameters and a working condition feature vector for the rolling bearing, wherein each component of the working condition feature vector is standardized to eliminate dimensional differences; based on the structural relationships between the components in the bearing system, using generalized coordinates to describe the degrees of freedom of each component, and establishing a multi-body coupled dynamic basic model through nonlinear contact deformation relationships; based on the working condition feature vector, performing state-based processing on the contact stiffness, damping, clearance, and friction coefficient in the multi-body coupled dynamic basic model to generate a dynamic correction parameter set; dividing the bearing operating state into at least three working condition regions according to the working condition discrimination index, and adopting different parameter update rules for different working condition regions; mapping microscopic defects and manufacturing errors into equivalent excitation terms and incorporating them into the dynamic equations; and based on measured response data, performing inversion correction on the dynamic correction parameter set under physical constraints to output the improved rolling bearing dynamic model.

[0006] Furthermore, in the fundamental model of multibody coupled dynamics, the normal contact force of each rolling element is determined by the product of the contact stiffness coefficient, the power value of the contact deformation, and the step function; wherein, the step function takes a value of 1 when the contact deformation is greater than zero, and a value of 0 otherwise; the contact deformation is determined by the product of the contact stiffness coefficient, the power value of the contact deformation, and the step function. The effective clearance of each rolling element at the current angular position is obtained by comprehensively solving for the inner ring displacement, outer ring displacement, contact angle deflection, and effective clearance. Number the rolling element.

[0007] Furthermore, the contact deformation is calculated as follows: multiply the radial displacement component of the inner ring relative to the outer ring by the cosine and sine values ​​of the current rolling element angular position, sum them up, multiply by the cosine value of the current contact angle, add the product of the axial displacement component and the sine value of the current contact angle, and subtract the radial clearance. The result is the contact deformation of the rolling element.

[0008] Furthermore, the dynamic correction parameter set includes: an effective contact stiffness correction term, which corrects the contact stiffness coefficient based on load distribution, contact area deformation, and surface roughness; an equivalent damping correction term, which corrects the damping coefficient based on lubrication film thickness, material energy dissipation characteristics, and velocity changes; a thermal clearance correction term, which calculates the actual effective clearance based on temperature rise, coefficient of thermal expansion, and assembly constraints, replacing the initial clearance parameter; a friction coefficient correction term, which corrects the friction coefficient based on lubrication state, rolling ratio, and contact pressure; and a load distribution correction term, which updates the load distribution ratio through self-consistent iteration based on the instantaneous stress state of each rolling element.

[0009] Furthermore, the process of generating the thermal clearance correction term is as follows: obtain the inner ring temperature and outer ring temperature of the bearing, multiply the outer ring material linear expansion coefficient by the outer ring raceway diameter and the outer ring temperature rise to obtain the outer ring thermal expansion, multiply the inner ring material linear expansion coefficient by the inner ring raceway diameter and the inner ring temperature rise to obtain the inner ring thermal expansion, add the outer ring thermal expansion to the initial radial clearance and then subtract the inner ring thermal expansion to obtain the effective clearance under the current temperature condition.

[0010] Furthermore, the operating condition discrimination index is generated as follows: after standardizing the speed change rate, load fluctuation amplitude, temperature rise rate, and impact pulse value respectively, the index is weighted and summed using their respective weighting coefficients to obtain the operating condition discrimination index. Among them, at least three operating condition regions include the start-up transition region, the steady-state operation region, and the abnormal disturbance region. The criteria for determining the start-up transition region are that the standardized speed change rate is greater than the first threshold and the standardized load fluctuation amplitude has not yet reached the standardized value corresponding to the rated load. The criteria for determining the steady-state operation region are that the standardized speed change rate is lower than the second threshold and the standardized temperature rise rate is lower than the third threshold. The criteria for determining the abnormal disturbance region are that the standardized impact pulse value exceeds the fourth threshold or the standardized temperature rise rate exceeds the fifth threshold.

[0011] Furthermore, within the time window when the working condition area label changes, a linear interpolation algorithm is used to perform parameter smoothing transition processing on the parameter sets before and after the change. The input is the two sets of parameter sets before and after the change and the corresponding time nodes, and the output is the smoothed parameter values ​​at each time during the transition period.

[0012] Furthermore, microscopic defects and manufacturing errors are mapped to equivalent excitation terms, including: characterizing periodic errors through harmonic excitation, decomposing waviness and rolling element diameter difference into harmonic components of each order and superimposing them on the contact deformation term; characterizing local defects through pulse-type contact interruption excitation, when the angular position of the rolling element enters the defect angular interval, adding an additional depth disturbance determined by the product of defect depth and defect edge transition shape function to the contact deformation amount; and characterizing assembly deviations through static offset terms and coupled attitude terms, superimposing them on the generalized coordinates with a constant offset.

[0013] Furthermore, based on the measured response data, the dynamic correction parameter set is inverted and corrected under physical constraints. This includes: acquiring vibration and temperature signals during actual operation, and simultaneously acquiring speed and torque signals for the corresponding time periods to generate a measured response dataset; substituting the current model parameters into the dynamic equations for numerical solution to obtain the model's predicted response; calculating the time-domain error and frequency-domain characteristic error between the model's predicted response and the measured response dataset, and weighting the time-domain error, frequency-domain characteristic error, and trend response error with their respective weighting coefficients to generate a comprehensive error index; under physical constraints, a hierarchical optimization strategy is adopted, firstly prioritizing the correction of contact stiffness and clearance to obtain preliminary correction parameters, and then finely correcting damping and friction coefficients to obtain the corrected model parameters with the goal of minimizing the comprehensive error index; the physical constraints include: each contact stiffness correction value does not exceed the stiffness range corresponding to the material's elastic limit, the damping coefficient remains positive and does not exceed the upper limit calculated by fluid lubrication theory, the clearance correction value meets the reasonable range predicted by thermal expansion theory, and the rate of change of parameters between adjacent time steps does not exceed a preset continuity threshold.

[0014] This invention discloses an improved rolling bearing dynamics model construction system for executing the aforementioned improved rolling bearing dynamics model construction method, comprising: a parameter acquisition module for acquiring the basic structural parameter set of the rolling bearing and the standardized operating condition feature vector; a basic model establishment module for establishing a multi-body coupled dynamics basic model based on the structural relationships between components in the bearing system, using generalized coordinates to describe the degrees of freedom of each component, and establishing a multi-body coupled dynamics basic model through nonlinear contact deformation relationships; a dynamic correction module for performing state-based processing on the contact stiffness, damping, clearance, and friction coefficient in the multi-body coupled dynamics basic model based on the operating condition feature vector, generating a dynamic correction parameter set; an operating condition region division module for dividing the bearing operating state into at least three operating condition regions according to the operating condition discrimination index, and switching the corresponding parameter update rules for different operating condition regions; a defect mapping module for mapping microscopic defects and manufacturing errors into equivalent excitation terms and incorporating them into the dynamic equations; and an inversion correction module for performing inversion correction on the dynamic correction parameter set based on measured response data under physical constraints, outputting the improved rolling bearing dynamics model.

[0015] The present invention has the following beneficial effects: Introducing dynamic correction parameters that vary with the characteristic vector of the working condition into the basic model of multibody coupled dynamics enables parameters such as contact stiffness, damping, clearance and friction coefficient to be continuously updated according to the actual operating conditions, thus overcoming the problem of parameter distortion in traditional fixed parameter models under varying working conditions.

[0016] By dividing the operating state into zones and switching the corresponding parameter update rules through operating condition discrimination indicators, the response deviation caused by using uniform parameters under different operating conditions such as start-up impact, short-term overload and thermal drift of a single model is avoided, so that the improved rolling bearing dynamic model can adapt to the dynamic characteristics of different operating stages.

[0017] By mapping micro-defects and manufacturing errors into equivalent excitation terms and incorporating them into the dynamic equation framework, the improved rolling bearing dynamic model can express the influence of local damage and assembly deviations on dynamic response, thus making up for the shortcomings of traditional models in not covering the actual service conditions.

[0018] By performing parameter inversion correction based on measured response under physical constraints, a closed-loop correction process is formed, enabling model parameters to be automatically adjusted according to operating data, reducing reliance on manual parameter tuning; at the same time, physical constraints ensure that the corrected parameters have clear mechanical meaning, maintaining the interpretability of the improved rolling bearing dynamics model. Attached Figure Description

[0019] Figure 1 This is a flowchart of the method for constructing an improved rolling bearing dynamics model provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the normal contact force distribution of each rolling element provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the distribution of standardized values ​​of the working condition feature vector provided in an embodiment of the present invention; Figure 4 This is a schematic diagram comparing parameters before and after dynamic correction provided in an embodiment of the present invention; Figure 5 This is a schematic diagram of the working condition discrimination index Γ at each sampling time provided in the embodiments of the present invention; Figure 6 This is a schematic diagram comparing the operating condition characteristic indicators at different sampling times provided in the embodiments of the present invention; Figure 7 This is a schematic diagram illustrating the changes of various error indices during the inversion correction iteration process provided in this embodiment of the invention; Figure 8 This is a schematic diagram illustrating the change of the comprehensive error E during the inversion correction iteration process provided in an embodiment of the present invention; Figure 9 This is a schematic diagram of the cosine transition shape function curve of the pitting defect in the outer ring provided in an embodiment of the present invention. Detailed Implementation

[0020] Example 1: Rolling bearings are widely used in rotating machinery such as high-speed motors, wind turbines, rail transit traction systems, industrial robot joints, precision machine tool spindles, and gearbox support systems. During actual service, bearings operate under complex conditions involving variable speed, variable load, temperature fluctuations, changes in lubrication conditions, assembly deviations, and minor wear. Existing dynamic models typically set parameters such as contact stiffness, damping, clearance, and friction coefficient as constants, failing to reflect parameter drift due to varying operating conditions. Furthermore, these models lack closed-loop correction capabilities, leading to a decrease in prediction accuracy over time. Therefore, a method for constructing rolling bearing dynamic models that combines adaptability to operating conditions and parameter correctability is needed.

[0021] The improved method for constructing a rolling bearing dynamics model according to Embodiment 1 of the present invention includes the following steps: Step 1: Obtain the bearing foundation structural parameter set and operating condition feature set Obtain the geometric parameters, material parameters, assembly parameters, and operating parameters of the rolling bearing to generate a set of basic bearing structural parameters. The geometric parameters include at least the inner ring diameter, outer ring diameter, rolling element diameter, number of rolling elements, contact angle, and initial clearance; the assembly parameters include at least the preload, coaxiality deviation, and support stiffness; and the operating parameters include at least the rotational speed, external load, temperature, lubrication condition, and vibration response.

[0022] The operating parameters are organized into a condition feature vector to characterize the bearing's state changes at different operating stages. This feature vector serves as input for subsequent dynamic updates of the model parameters. It should be noted that the components in the condition feature vector have different physical dimensions. Before inputting them into subsequent calculations, each component in the condition feature vector is standardized using Z-scores to eliminate the influence of these dimensional differences on the weighted calculations.

[0023] Step 2: Establish a basic model of multibody coupled dynamics based on structural relationships Based on the structural relationships between the shaft, inner ring, outer ring, cage, and rolling elements in a bearing system, a multibody coupled dynamics fundamental model is established. Generalized coordinates are used to describe the translational and rotational degrees of freedom of each component, and contact constraints are used to connect the components into a unified set of equations.

[0024] The normal contact force between the rolling elements and the raceway is described using a nonlinear contact deformation relationship. The contact deformation is determined by relative displacement, contact angle variation, clearance variation, and local elastic deformation. The normal contact force of each rolling element... Represented as: ; in, For contact stiffness coefficient, For the first The contact deformation of each rolling element, in meters. Number the rolling element. For contact index, For step function, when The value is 1 if the condition is met, and 0 otherwise.

[0025] By using nonlinear contact deformation relationships, the source of bearing dynamic response is expanded from a single contact term to a unified expression of structural coupling, contact nonlinearity, and motion constraints.

[0026] It should be noted that the above-mentioned contact deformation amount The calculation is based on the first The results are obtained by comprehensively solving for the inner ring displacement, outer ring displacement, contact angle deflection, and effective clearance of each rolling element at the current angular position. Specifically, It can be represented as: ; in, , , These represent the radial and axial displacement components of the inner ring relative to the outer ring, respectively, in meters. For the first The angular position of each rolling element, in radians, with a range of values ​​of [value missing]. , This is the current contact angle of the rolling element, in radians. The radial clearance is expressed in meters. All terms in the formula have the dimension of length and are dimensionlessly consistent.

[0027] Step 3: Generate dynamic correction parameters based on operating condition feature vectors In the fundamental model of multibody coupled dynamics, a dynamic correction term that varies with the operating conditions is introduced. The following parameters are then treated as states to generate a set of dynamic correction parameters: Effective contact stiffness correction term: The contact stiffness coefficient is corrected based on load distribution, contact area deformation, and surface roughness; Equivalent damping correction term: The damping coefficient is corrected based on the lubricating film thickness, material energy dissipation characteristics, and velocity variation; Thermal clearance correction term: The actual effective clearance is calculated based on temperature rise, coefficient of thermal expansion and assembly constraints, and is used to replace the initial clearance parameter; Friction coefficient correction term: The friction coefficient is corrected based on lubrication conditions, slip-roll ratio, and contact pressure; Load distribution correction term: The load distribution ratio is updated by self-consistent iteration based on the instantaneous force state of each rolling element.

[0028] With the above corrections, the model parameters are no longer fixed as constants, but are dynamically updated as the feature vectors of the operating conditions change.

[0029] It should be noted that the above-mentioned thermal clearance correction term is generated as follows: obtain the bearing inner ring temperature. and outer ring temperature The thermal expansion of the inner and outer rings is calculated separately, and then superimposed with the initial clearance to obtain the effective clearance at the current temperature. : ; in, This represents the initial radial clearance, in meters. and These are the coefficients of linear expansion of the outer and inner ring materials, respectively, in Kelvin (kJ / L). ), and These are the outer raceway diameter and the inner raceway diameter, respectively, in meters. and These represent the temperature rise of the outer and inner rings, respectively, in Kelvin (K). ). (All) The units of measurement are all meters, and The dimensions are consistent, and the dimensions of each term in the formula are matched.

[0030] Step 4: Divide the operating status regions based on the operating condition discrimination indicators and switch the parameter update rules. Based on the speed, load, temperature rise rate, lubrication condition and impact characteristics, the operating condition discrimination index is calculated, and the bearing operating condition is divided into at least three typical regions, generating operating condition region labels.

[0031] When the operating condition discrimination index meets the conditions for the start-up transition zone, the time period is identified as the start-up transition zone, and the parameter update rules corresponding to the start-up transition zone are adopted; when the operating condition discrimination index meets the conditions for the steady-state operation zone, it is identified as the steady-state operation zone; when the operating condition discrimination index exceeds the normal range, it is identified as the abnormal disturbance zone.

[0032] Different parameter update rules or different sub-model expressions are used for different working conditions to achieve partitioned modeling and state switching.

[0033] It should be noted that the above operating condition discrimination index is a weighted comprehensive index based on the speed change rate, load fluctuation amplitude, temperature rise rate, and impact pulse value. Because these four components have different physical dimensions, Z-score standardization is applied to the speed change rate, load fluctuation amplitude, temperature rise rate, and impact pulse value before calculating the operating condition discrimination index to eliminate the influence of dimensional differences on the weighted summation calculation. Operating Condition Discrimination Index Represented as: ; in, The normalized rate of change of rotational speed. This represents the standardized load fluctuation amplitude. The standardized temperature rise rate, This is the standardized impact pulse value. , , , These are the weighting coefficients for the corresponding items, and each weighting coefficient is pre-calibrated based on the sensitivity of different operating conditions. The criteria for determining the start-up transition zone are as follows: Greater than the first threshold and The standardized value corresponding to the rated load has not yet been reached; the criteria for determining the steady-state operating range are: Below the second threshold and Below the third threshold; the criteria for determining the abnormal disturbance zone are: Exceeding the fourth threshold or Exceeding the fifth threshold. The first to fifth thresholds are all indicators for judging operating conditions. The dimensionless judgment boundaries of each component after standardization are pre-calibrated according to the bearing model and operating condition range.

[0034] In this embodiment, to avoid abrupt changes in model parameters during the switching of operating condition regions, a parameter smoothing transition process is introduced during the transition phase between adjacent operating condition regions. Specifically, within the time window when the operating condition region label changes, a linear interpolation algorithm is used to process the parameter sets before and after the switch. The input consists of two sets of parameter sets before and after the switch and their corresponding time nodes, and the output is the smoothed parameter values ​​at each time point during the transition period, thereby eliminating the abrupt change in dynamic response at the switching moment.

[0035] Step 5: Map microscopic defects and manufacturing errors to equivalent excitation terms. Raceway waviness, rolling element diameter difference, eccentricity error, cage fluctuation, local spalling, pitting, and lubrication contamination are converted into equivalent excitation terms and mapped to the external excitation matrix or contact deformation disturbance term in the dynamic equation.

[0036] Among them, periodic error is characterized by harmonic excitation, decomposing waviness and rolling element diameter difference into harmonic components of each order and superimposing them on the contact deformation term; local defects are characterized by pulse-type contact interruption excitation, introducing a sudden drop in contact force and recovery process at the corresponding angular position when the rolling element passes through the defect area; assembly deviation is characterized by static offset term and coupled attitude term, superimposed on the generalized coordinate with a constant offset.

[0037] Through the above mapping, manufacturing errors, assembly errors, and service damage are unified into the same dynamic equation framework.

[0038] It should be noted that the equivalent excitation characterization of the aforementioned localized spalling defects is a perturbation function that converts the geometric parameters of the defect into the contact deformation amount. When the... angular position of each rolling element Entering the defect zone At that time, contact deformation amount An additional depth perturbation is added. Depth disturbance amount Defect depth The shape is determined together with the transition shape of the defect edge, specifically as follows: ; in, The maximum depth of the defect, in meters. The location is the center corner of the defect, in radians. The angular expansion of the defect is expressed in radians. For the first The current angular position of each rolling element, in radians. This is the defect edge transition shape function, whose independent variable is the normalized angular offset, and its value range is... The output is a dimensionless coefficient, making the depth disturbance amount With defect depth All measurements are in the same dimension, measured in meters. When the defect edge is abruptly rectangular... The value is always 1 within the interval; when the defect edge is a cosine transition. Pick ,in This is the normalized angular offset; in practical applications, the corresponding transition shape function is selected based on the defect morphology measurement results.

[0039] Step 6: Invert and correct the model parameters based on the measured response data under physical constraints. Vibration, temperature, speed, and torque signals of the bearing during actual operation are collected to construct an error function between the model output response and the measured response. Under the premise of satisfying material parameter boundary constraints, contact mechanics constraints, energy conservation constraints, and parameter continuity constraints, an iterative optimization method is used to invert and correct the dynamically modified parameter set, generating the corrected model parameters.

[0040] Step 6 may specifically include: Step 601: Acquire vibration and temperature signals during actual operation, and simultaneously acquire speed and torque signals for the corresponding time periods to generate a measured response dataset.

[0041] Step 602: Substitute the current model parameters into the dynamic equations to solve numerically and obtain the model's predicted response.

[0042] Step 603: Calculate the time-domain error and frequency-domain characteristic error between the model's predicted response and the measured response dataset, and generate a comprehensive error index.

[0043] Step 604: Under physical constraints, a multi-objective iterative optimization strategy is adopted to optimize the model parameters, while minimizing the time domain error, frequency domain feature error and trend response error, to obtain the corrected model parameters.

[0044] It should be noted that the above physical constraints include: each contact stiffness correction value does not exceed the stiffness range corresponding to the material's elastic limit; the damping coefficient remains positive and does not exceed the upper limit calculated by fluid lubrication theory; the clearance correction value meets the reasonable range predicted by thermal expansion theory; and the rate of change of parameters between adjacent time steps does not exceed a preset continuity threshold. These physical constraints ensure that the parameters after inversion correction always have physical meaning.

[0045] It should be noted that the above comprehensive error index Due to time domain error Frequency domain characteristic error and trend response error The weighted summation is expressed as: ; in, The root mean square error between the model's predicted response and the measured response dataset in the time domain. The amplitude error between the two at the fault characteristic frequency and its harmonics is given. The difference between the two in the trend of parameter evolution is... , , The weighting coefficients for the corresponding error terms, summing to 1, are pre-calibrated based on the emphasis placed on time-domain accuracy, frequency-domain characteristics, and trend tracking in practical applications. The objective of the multi-objective iterative optimization in step 604 is to minimize the comprehensive error index. That is, solving for the comprehensive error index under physical constraints. The combination of model parameters that yields the minimum value.

[0046] In this embodiment, to improve the convergence efficiency and robustness of the inversion correction, a hierarchical optimization strategy is adopted in step 604. First, parameters with higher sensitivity (contact stiffness and clearance) are preferentially corrected to obtain preliminary correction parameters. Then, based on the preliminary correction parameters, parameters with lower sensitivity (damping and friction coefficient) are finely corrected to obtain the final correction parameters. The hierarchical optimization strategy reduces the search difficulty in the high-dimensional parameter space and improves the iterative convergence speed.

[0047] Step 7: Output the improved rolling bearing dynamics model The dynamic equations, after dynamic parameter updates, operating condition region switching, and defect equivalent excitation mapping, are used as the final model output. The improved rolling bearing dynamic model can be used for bearing dynamic response prediction, load distribution analysis, fault characteristic simulation, life assessment, and structural optimization.

[0048] Technical effects of this embodiment: This implementation introduces dynamic correction parameters that vary with the characteristic vector of the operating condition into the basic model of multibody coupled dynamics. This makes parameters such as contact stiffness, damping, clearance, and friction coefficient no longer fixed as constants, but continuously updated according to the actual operating conditions. Therefore, it overcomes the problem of parameter distortion in traditional fixed parameter models under varying operating conditions.

[0049] By dividing the operating state into zones and switching the corresponding parameter update rules through operating condition discrimination indicators, the response deviation caused by using uniform parameters under different operating conditions such as start-up impact, short-term overload and thermal drift of a single model is avoided, so that the improved rolling bearing dynamic model can adapt to the dynamic characteristics of different operating stages.

[0050] By mapping micro-defects and manufacturing errors into equivalent excitation terms and incorporating them into the dynamic equation framework, the shortcomings of traditional models in covering the actual service conditions are made up for, enabling the improved rolling bearing dynamic model to express the influence of local damage and assembly deviations on dynamic response.

[0051] By performing parameter inversion correction based on measured response under physical constraints, a closed-loop correction process is formed, enabling model parameters to be automatically adjusted according to operating data, reducing reliance on manual parameter tuning. At the same time, physical constraints ensure that the corrected parameters have clear mechanical meaning, maintaining the interpretability of the improved rolling bearing dynamics model.

[0052] Complete application scenario content: The main shaft bearing of a wind turbine at a wind farm entered its operation and maintenance monitoring cycle in year C of 20XX. The turbine has a rated speed of 18 rpm, and the main shaft bearing is a double-row tapered roller bearing that bears the combined load generated by the wind turbine. Due to wind speed fluctuations, the turbine frequently experiences three operating states: start-up transition, steady-state power generation, and gust disturbances. Maintenance personnel deployed vibration sensors, temperature sensors, and a speed encoder at the bearing housing, with a data acquisition frequency of 25.6 kHz, for continuous correction and condition assessment of the bearing dynamics model.

[0053] Implementation of step 1; Bearing basic structural parameters and operating parameters are extracted from the unit's factory records and online sensors to generate a bearing basic structural parameter set and an operating condition feature vector. The operating condition feature vector contains six components: speed, radial load, axial load, bearing housing temperature, lubricating oil temperature, and root mean square value of vibration. After Z-score standardization to eliminate dimensional differences, it serves as a unified input for subsequent dynamic correction parameter generation and operating condition discrimination.

[0054] Table 1 Bearing Foundation Structure Parameter Set

[0055] Table 2 Standardization of Operating Condition Feature Vectors

[0056] Implementation of step 2; Based on the structural relationships between the shaft, inner ring, outer ring, cage, and 18 rolling elements of the wind turbine main shaft bearing, a multibody coupled dynamics model is established. Each component is described using generalized coordinates; the inner ring has radial bidirectional translational degrees of freedom and axial translational degrees of freedom, while the outer ring is fixed to the bearing housing. Taking rolling element number 7 as an example, its current angular position... rad, contact angle rad, relative displacement of the inner ring m、 m、 m, radial clearance m.

[0057] Substituting the above values ​​into the contact deformation formula:

[0058] Calculated m is greater than zero, therefore the step function With the current contact stiffness coefficient N / m Contact Index Substituting, we obtain the normal contact force. N.

[0059] Table 3. Contact Deformation and Normal Contact Force of Some Rolling Elements

[0060] Implementation of step 3; Using the current operating condition feature vector as input, the contact stiffness, damping, clearance, and friction coefficient are dynamically corrected. Taking the thermal clearance correction term as an example, the sensor collects the inner ring temperature... ℃, outer ring temperature ℃, the reference temperature is 20℃, then K, K. Substituting into the effective clearance formula:

[0061] in, For the initial radial clearance, , These are the linear expansion coefficients of the outer and inner rings, respectively. , These are the outer and inner raceway diameters, respectively. , These represent the temperature rise of the outer and inner rings relative to the reference temperature, respectively. The calculation yields... The increase in m compared to the initial clearance reflects the actual state where the thermal expansion of the outer ring is slightly greater than that of the inner ring due to the temperature rise.

[0062] Table 4 Dynamic Correction Parameter Set

[0063] Implementation of step 4; The rotational speed change rate, load fluctuation amplitude, temperature rise rate, and impact pulse value are extracted from real-time sensor data, Z-score standardized, and then the operating condition discrimination index is calculated according to the pre-calibrated weights. Taking a sampling moment during the unit startup phase as an example, the standardized rate of change of rotational speed... Load fluctuation amplitude Temperature rise rate Impact pulse value Weighting coefficient , , , Substituting into the formula, we get:

[0064]

[0065] That moment Exceeding the first threshold (0.80) and The rated load standardization value (1.00) has not yet been reached, so it is determined to be in the start-up transition zone, and the start-up transition zone parameter update rule is activated.

[0066] Steady-state power generation stage It dropped to 0.12, below the second threshold (0.30). The value is 0.18, which is lower than the third threshold (0.50), indicating a switch to the steady-state operating region. During the transition time window between the two regions, linear interpolation is applied to both sets of parameters to eliminate parameter abrupt changes.

[0067] Table 5 Results of Working Condition Zone Identification

[0068] Implementation of step 5; During equipment inspection, a pitting defect was found on the outer raceway. Eddy current testing confirmed the location of the defect's center corner. rad, angular span rad, maximum depth m, the defect edge morphology is close to a cosine transition. When rolling element 11 moves to the angular position... When the angle is in the defect range, the normalized angular offset is calculated using the rad measurement. Substituting the cosine transition shape function:

[0069] Calculated Depth disturbance amount m, superimposed on the contact deformation of rolling element 11, generates a corresponding sudden drop in contact force in the contact deformation disturbance term of the dynamic equation, simulating the pulse excitation when the defect passes through.

[0070] In addition, the difference in rolling element diameter (maximum difference of 0.0000082m) is decomposed into harmonic components of each order superimposed on the contact deformation term, and the assembly coaxiality deviation is superimposed on the generalized coordinate as a static offset. The three types of error sources are uniformly incorporated into the dynamic equation framework.

[0071] Implementation of step 6; Measured response data are collected from vibration and temperature sensors and compared with the predicted response of the current model parameters to generate a comprehensive error index. Under initial parameters, time-domain error mm / s, frequency domain characteristic error dB, trend response error Weighting coefficient , , Substitute into the comprehensive error formula: ; Calculated (Dimensionless composite error after normalization).

[0072] A hierarchical optimization strategy is adopted. First, under physical constraints, the contact stiffness and effective clearance are preferentially modified, and the contact stiffness coefficient is adjusted from... Adjust to N / m 1.5 The effective clearance is adjusted to m; based on this, the damping and friction coefficients are finely corrected. After two rounds of iteration, the overall error is... The value was reduced to 0.19, and the correction values ​​of each parameter all met the material elastic limit, the upper limit of the lubrication theory, and the parameter continuity constraints.

[0073] Table 6 Comparison of comprehensive errors before and after inversion correction

[0074] Implementation of step 7; After the above steps, an improved rolling bearing dynamic model is output. This model includes: dynamically corrected parameters with the modified parameter set in Table 4 as the current state; a partitioned parameter update module with the steady-state operating zone rule at time T3 in Table 5 as the current activation rule; a contact deformation equation with the equivalent excitation of pitting defects on the outer ring as the disturbance term; and a parameter set that converges after the second round of iterations in Table 6. This model was subsequently used for vibration response prediction and remaining life assessment of the unit over the next six months.

[0075] The entire data flow starts with the geometric parameters and standardized operating condition feature vectors in step 1. Step 2 establishes a nonlinear mapping between contact force and displacement. Step 3 transforms temperature, load, and lubrication status into dynamic correction parameters. Step 4 switches parameter rules between three regions based on operating condition discrimination indicators. Step 5 maps pitting defects and diameter differences into contact deformation disturbances. Finally, in step 6, closed-loop inversion correction is completed based on measured vibration signals. The output data of each step serves as the input for the next step, forming a complete data flow chain from structural parameters to predicted response and from measured signals to parameter correction.

[0076] The embodiments of the present invention have been described above. However, the embodiments are not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make more equivalent embodiments under the guidance of the present embodiments, and all of them are within the protection scope of the present embodiments.

Claims

1. Improved method for constructing a dynamic model of a rolling bearing, characterized in that, At least including: Obtain the basic structural parameter set and operating condition feature vector of the rolling bearing, wherein each component of the operating condition feature vector is standardized to eliminate dimensional differences; Based on the structural relationships between the components in the bearing system, generalized coordinates are used to describe the degrees of freedom of each component, and a multibody coupled dynamics basic model is established through nonlinear contact deformation relationships. Based on the working condition feature vector, the contact stiffness, damping, clearance and friction coefficient in the basic model of multibody coupled dynamics are processed into a state and a dynamic correction parameter set is generated. Based on the operating condition discrimination index, the bearing operating status is divided into at least three operating condition zones, and different parameter update rules are adopted for different operating condition zones. Microscopic defects and manufacturing errors are mapped as equivalent excitation terms and incorporated into the dynamic equations; Based on measured response data, the dynamic correction parameter set is inverted and corrected under physical constraints to output an improved rolling bearing dynamic model.

2. The method of constructing an improved rolling bearing dynamics model according to claim 1, characterized in that, In the basic model of multibody coupled dynamics, the normal contact force of each rolling element is determined by the product of the contact stiffness coefficient, the power value of the contact deformation, and the step function; wherein, the step function takes a value of 1 when the contact deformation is greater than zero, and a value of 0 otherwise; the contact deformation is determined by the product of the contact stiffness coefficient, the power value of the contact deformation, and the step function. The effective clearance of each rolling element at the current angular position is obtained by comprehensively solving for the inner ring displacement, outer ring displacement, contact angle deflection, and effective clearance. Number the rolling element.

3. The method of constructing an improved rolling bearing dynamics model according to claim 2, characterized in that, The contact deformation is calculated as follows: multiply the radial displacement component of the inner ring relative to the outer ring by the cosine and sine values ​​of the current rolling element angular position, sum them up, multiply by the cosine value of the current contact angle, add the product of the axial displacement component and the sine value of the current contact angle, and subtract the radial clearance. The result is the contact deformation of the rolling element.

4. The method of constructing an improved rolling bearing dynamics model of claim 1, wherein, The dynamic correction parameter set includes: The effective contact stiffness correction term corrects the contact stiffness coefficient based on load distribution, contact area deformation, and surface roughness. The equivalent damping correction term adjusts the damping coefficient based on the lubrication film thickness, material energy dissipation characteristics, and velocity variation. The thermal clearance correction term calculates the actual effective clearance based on temperature rise, coefficient of thermal expansion, and assembly constraints, replacing the initial clearance parameter. The friction coefficient correction term corrects the friction coefficient based on lubrication conditions, sliding-rolling ratio, and contact pressure. The load distribution correction term updates the load distribution ratio through self-consistent iteration based on the instantaneous force state of each rolling element.

5. The method of constructing an improved rolling bearing dynamics model according to claim 4, characterized in that, The process of generating the thermal clearance correction term is as follows: obtain the inner ring temperature and outer ring temperature of the bearing, multiply the outer ring material linear expansion coefficient by the outer ring raceway diameter and the outer ring temperature rise to obtain the outer ring thermal expansion, multiply the inner ring material linear expansion coefficient by the inner ring raceway diameter and the inner ring temperature rise to obtain the inner ring thermal expansion, add the outer ring thermal expansion to the initial radial clearance and then subtract the inner ring thermal expansion to obtain the effective clearance under the current temperature condition.

6. The method of constructing an improved rolling bearing dynamics model according to claim 1, characterized in that, The operating condition discrimination index is generated as follows: the speed change rate, load fluctuation amplitude, temperature rise rate, and impact pulse value are standardized respectively, and then weighted and summed with their respective weight coefficients to obtain the operating condition discrimination index. Among them, there are at least three types of operating condition regions, including the start-up transition region, the steady-state operation region, and the abnormal disturbance region. The judgment condition for the start-up transition region is that the standardized speed change rate is greater than the first threshold and the standardized load fluctuation amplitude has not yet reached the standardized value corresponding to the rated load. The judgment condition for the steady-state operation region is that the standardized speed change rate is lower than the second threshold and the standardized temperature rise rate is lower than the third threshold. The judgment condition for the abnormal disturbance region is that the standardized impact pulse value exceeds the fourth threshold or the standardized temperature rise rate exceeds the fifth threshold.

7. The method of constructing an improved rolling bearing dynamics model according to claim 6, characterized in that, Within the time window when the working condition area label changes, a linear interpolation algorithm is used to smooth the parameter transition of the parameter sets before and after the change. The input is two sets of parameter sets before and after the change and the corresponding time nodes. The output is the smoothed parameter values ​​at each time point during the transition period.

8. The method of constructing an improved rolling bearing dynamics model of claim 1, wherein, The microscopic defects and manufacturing errors are mapped to equivalent excitation terms, including: characterizing periodic errors through harmonic excitation, decomposing waviness and rolling element diameter difference into harmonic components of each order and superimposing them on the contact deformation term; characterizing local defects through pulse-type contact interruption excitation, when the angular position of the rolling element enters the defect angular interval, adding an additional depth disturbance determined by the product of the defect depth and the transition shape function of the defect edge to the contact deformation amount; and characterizing assembly deviations through static offset terms and coupled attitude terms, superimposed on the generalized coordinates with a constant offset.

9. The method of constructing an improved rolling bearing dynamics model of claim 1, wherein, Based on measured response data, the dynamic correction parameter set is inverted and corrected under physical constraints, including: The vibration and temperature signals during actual operation are acquired, and the speed and torque signals for the corresponding time periods are acquired simultaneously to generate a measured response dataset. Substitute the current model parameters into the dynamic equations and solve numerically to obtain the model's predicted response; The time-domain error and frequency-domain characteristic error between the model's predicted response and the measured response dataset are calculated. The time-domain error, frequency-domain characteristic error, and trend response error are weighted and summed with their respective weighting coefficients to generate a comprehensive error index. Under physical constraints, a hierarchical optimization strategy is adopted. First, the contact stiffness and clearance are preferentially corrected to obtain preliminary correction parameters. Then, the damping and friction coefficient are finely corrected to obtain the corrected model parameters with the goal of minimizing the comprehensive error index. The physical constraints include: each contact stiffness correction value does not exceed the stiffness range corresponding to the material's elastic limit; the damping coefficient remains positive and does not exceed the upper limit calculated by fluid lubrication theory; the clearance correction value meets the reasonable range predicted by thermal expansion theory; and the rate of change of parameters between adjacent time steps does not exceed the preset continuity threshold.

10. A system for constructing an improved dynamic model of a rolling bearing for performing the method for constructing an improved dynamic model of a rolling bearing according to any one of claims 1 to 9, characterized in that, include: The parameter acquisition module is used to acquire the basic structural parameter set of the rolling bearing and the standardized operating condition feature vector. The basic model building module is used to describe the degrees of freedom of each component based on the structural relationship between the components in the bearing system, and to establish a basic model of multibody coupled dynamics through nonlinear contact deformation relationship. The dynamic correction module is used to perform state-based processing on the contact stiffness, damping, clearance and friction coefficient in the basic model of multibody coupled dynamics based on the working condition feature vector, and generate a dynamic correction parameter set. The working condition zone division module is used to divide the bearing operating status into at least three types of working condition zones based on the working condition discrimination index, and switch the corresponding parameter update rules for different working condition zones. The defect mapping module is used to map microscopic defects and manufacturing errors into equivalent excitation terms, which are then incorporated into the dynamic equations. The inversion correction module is used to invert and correct the dynamic correction parameter set based on measured response data under physical constraints, and output the improved rolling bearing dynamic model.

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