A high-speed bearing temperature prediction method and device based on a multi-stage exponential decay model

Abstract

This invention relates to the field of bearing temperature monitoring and fault prediction technology, specifically to a high-speed bearing temperature prediction method based on a multi-stage exponential decay model. The method collects outer ring temperature-time series data during high-speed bearing operation, uses a double exponential decay superposition model to fit the temperature curve, and decomposes the temperature rise process into two stages: a period dominated by frictional heat generation and a period of thermal equilibrium establishment. The Levenberg-Marquardt algorithm is used to solve for the model parameters, constructing two derived feature parameters: a time-scale separation factor λ and a thermal dynamic coupling coefficient K. Based on the criteria for these parameters, quantitative assessment and early warning of bearing condition are achieved. This method solves the problems of insufficient fitting accuracy of existing single exponential models and the lag of traditional threshold alarms. It can predict long-term steady-state temperatures in a short time, shorten the test cycle, accurately identify early fault symptoms, and significantly improve the reliability of high-speed bearing temperature prediction and health assessment.

Description

Technical Field

[0001] This invention relates to the field of bearing temperature monitoring and fault prediction technology, specifically to a method and device for predicting the temperature of high-speed bearings based on a multi-stage exponential decay model. Background Technology

[0002] In high-speed rotating machinery such as aero engines, precision machine tools, and high-speed motors, bearings are key core components, and their operating condition directly determines the reliability, accuracy, and lifespan of the entire machine. When bearings operate at high speeds exceeding 10,000 revolutions per minute, they generate a large amount of heat, and temperature rise becomes a major indicator of performance degradation and even failure.

[0003] Most existing bearing temperature monitoring technologies are based on simple threshold alarms, such as absolute temperature thresholds or temperature rise rate thresholds. While simple, this method suffers from significant lag, often triggering alarms only when the fault has already progressed to a considerable extent, failing to provide early warning and accurate condition assessment. Furthermore, some studies have attempted to fit temperature rise curves using single exponential models, but these cannot accurately describe the complex dynamic process of high-speed bearings from startup and stabilization to abnormal temperature rise, resulting in insufficient prediction accuracy.

[0004] Therefore, there is an urgent need for a new temperature monitoring method that can more accurately and earlier reflect the health status of bearings. Summary of the Invention

[0005] This invention aims to overcome the shortcomings of existing technologies and provide a method and device for predicting the temperature of high-speed bearings based on a multi-stage exponential decay model. This method can decompose the temperature-time curve of the bearing outer ring into two stages with clear physical meaning, and introduce derived characteristic parameters such as time scale separation factor and thermal dynamic coupling coefficient to achieve early, accurate and quantitative assessment of the bearing condition, significantly shorten the test cycle and improve the reliability of prediction.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A method for predicting the temperature of high-speed bearings based on a multi-stage exponential decay model includes the following steps: S1. Collect the outer ring temperature-time series data of the high-speed bearing during operation; S2. Based on the temperature-time series data collected in step S1, the temperature-time curve is fitted using a double exponential decay superposition model. The expression for the double exponential decay superposition model is: (1) in, This is the bearing's steady-state temperature, i.e., the final temperature after thermal equilibrium. , These represent the temperature rise values ​​for the first and second stages, indicating the temperature increase from the initial value to the steady state. , The time constants for the first and second stages reflect the speed of the thermal response in that stage. S3. Based on the model parameters obtained from step S2, construct derived feature parameters, including the time scale separation factor λ and the thermal dynamic coupling coefficient K. S4. Based on the derived characteristic parameters obtained in step S3, the lubrication status and thermal dynamic characteristics of the bearing are quantitatively evaluated. When λ and K meet the preset health status criteria, the bearing is determined to be in a healthy state. When λ or K shows an abnormal trend, an early warning signal is issued.

[0007] Furthermore, the formula for calculating the time scale separation factor λ in step S3 is as follows: (2) The timescale separation factor λ is used to quantitatively describe the degree of separation between the first-stage lubricating film formation process and the second-stage thermal equilibrium establishment process on a timescale.

[0008] Furthermore, the health status criteria in step S4 include: when λ≥10, it is determined that the time scales of the first and second stages are sufficiently separated, the identification results of the model parameters are highly stable, and the bearing is in a normal lubrication state; when λ abnormally decreases and approaches 1, it is determined that there are early signs of lubrication failure or abnormal cage movement.

[0009] Furthermore, the formula for calculating the thermal dynamic coupling coefficient K in step S3 is as follows: (3) The thermal dynamic coupling coefficient K is used to reflect the degree to which the overall temperature rise of the bearing is dominated during the thermal equilibrium establishment stage.

[0010] Furthermore, the health status criteria in step S4 also include: when the K value is large and remains stable, the bearing is determined to be in a healthy state; when a continuous downward trend in the K value is detected, it is determined that there are signs of performance degradation such as premature aging of lubricant, abnormal preload, or increased system thermal resistance.

[0011] Furthermore, in step S2, the Levenberg-Marquardt algorithm is used to perform nonlinear least squares fitting on the double exponential decay superposition model, and the optimal parameter set is iteratively solved with equation (1) as the objective function. , , , , This minimizes the sum of squared residuals.

[0012] Furthermore, in step S1, the acquisition duration of the temperature-time series data is a preset short-time test duration, and the acquisition frequency of the temperature-time series data is not less than 1Hz.

[0013] Furthermore, in step S2, the first stage of the double exponential decay superposition model is the period dominated by frictional heat generation, which corresponds to the start-up transient process of the bearing from standstill to high-speed operation. The time constant τ1 reflects the speed of lubricant film establishment. The second stage is the period of thermal equilibrium establishment, which corresponds to the process of heat transfer, storage and tendency to balance in various components of the bearing after stable operation. The time constant τ2 reflects the characteristic time of thermal equilibrium establishment of the system, and τ2 > τ1.

[0014] Furthermore, in step S2, the temperature rise amplitude A1 in the first stage of the double exponential decay superposition model is the temperature rise amplitude generated during the period dominated by frictional heat generation, and the temperature rise amplitude A2 in the second stage is the temperature rise amplitude generated during the period of thermal equilibrium establishment, and A2 accounts for more than 90% of the total temperature rise.

[0015] A device for predicting the temperature of high-speed bearings based on a multi-stage exponential decay model, used in any of the above methods, characterized in that the device is the acquisition device in step S1, which includes a control console, a test shaft system, an electric spindle, a high-temperature gas source, a frequency converter, and a signal processing cabinet, wherein the frequency converter is responsible for adjusting the speed of the electric spindle to realize the speed input, the high-temperature gas source is provided by a heatable air compressor and input into the bearing chamber of the test machine, the electric spindle and the test spindle are connected as a whole by an elastic diaphragm coupling, which are respectively connected to the control console, the high-temperature gas source and the frequency converter, and the frequency converter is connected to the signal processing cabinet; The test shaft system is supported by a bearing testing machine, which includes a testing machine base plate, a bearing base, a bearing cover, a bearing loading mechanism, sensors, and a bearing non-load-bearing side cover. The bearing cover and the bearing non-load-bearing side cover are fixed to the upper surface of the testing machine base plate through the bearing base. A bearing loading mechanism for providing axial loading force is also provided between the bearing non-load-bearing pressure cover and the bearing base. Several sensors are also provided on the bearing base, the bearing non-load-bearing side cover, and the bearing cover.

[0016] The beneficial effects of this invention are: Firstly, this invention constructs a double exponential decay superposition model to decompose the bearing outer ring temperature-time curve into two stages with clear physical meaning: the period dominated by frictional heat generation and the period of thermal equilibrium establishment. This solves the problem that existing single exponential models cannot accurately describe the complex dynamic process of high-speed bearings from startup, stabilization to abnormal temperature rise. It achieves high-precision fitting of bearing temperature change law and short-term prediction of long-term steady-state temperature, significantly shortening the test cycle.

[0017] Secondly, this invention constructs a time-scale separation factor and a thermal dynamic coupling coefficient, and uses the time-scale separation factor and the thermal dynamic coupling coefficient as a joint criterion to comprehensively evaluate the health status of bearings. This solves the problem that a single indicator cannot fully reflect the complex thermal dynamic characteristics of bearings and that traditional threshold alarm methods have obvious lag and cannot achieve early warning. It realizes accurate diagnosis of bearing status from multiple dimensions and angles, greatly improves prediction reliability and fault identification accuracy, and can issue early warning signals in the early stage of fault development.

[0018] Third, this invention solves the problem of computational convergence difficulties caused by multi-parameter coupling during model parameter identification by using the Levenberg-Marquardt algorithm to perform nonlinear least squares fitting on the double exponential decay superposition model, thereby achieving efficient and stable solution of model parameters and ensuring the reliability of the calculation of derived feature parameters. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 The curve of bearing temperature change over time at 7200 r / min; Figure 2 This is a schematic diagram of the on-site layout of the testing machine; Figure 3 This is a schematic diagram of the bearing testing machine used in this invention; Figure 4 The fitted curve is shown at a rotational speed of 17000 r / min; Figure 5 The fitted curve is for a rotational speed of 2000 rpm; Figure 6 The curve shows the bearing temperature change over time at 20000 r / min.

[0021] In the figure, 1-testing machine base plate, 2-bearing base, 3-bearing cover, 4-bearing loading mechanism, 5-sensor, 6-bearing non-load-bearing side cover. Detailed Implementation

[0022] The present invention will now be described in detail through exemplary embodiments. However, it should be understood that, without further description, elements, structures, and features in one embodiment may be advantageously incorporated into other embodiments.

[0023] It should be noted that, unless otherwise defined, the technical or scientific terms used herein should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "a," "an," or "the," and similar words used in the specification and claims of this patent application do not express a limitation of quantity, but rather indicate the presence of at least one; terms such as "comprising" or "including" indicate that the elements or objects preceding "comprising" encompass the elements or objects listed following "comprising" or "including" and their equivalents, but do not exclude other elements or objects having the same function.

[0024] To more clearly describe the working principle of this high-speed bearing temperature prediction method based on a multi-stage exponential decay model, combined with the appendix... Figure 1 -Appendix Figure 6 This embodiment is described as follows: Based on previous temperature testing of a series of angular contact ball bearings, it was found that, under the condition of changing only the bearing speed while keeping other operating conditions constant, the temperature change of the bearing outer ring over time exhibits a highly consistent regularity. For example... Figure 1 As shown, taking the operating data of the 7020C bearing at 7200 r / min as an example, the temperature rise rate gradually slows down over time: the temperature rises sharply in the initial stage of the test (first 60 min), then tends to level off, and finally reaches the steady-state temperature corresponding to this speed.

[0025] This trend closely resembles an exponential function curve. To accurately describe this pattern and achieve the goal of predicting long-term steady-state temperature based on short-term test data and significantly shortening the test cycle, the outer ring temperature-time curve of the high-speed bearing during operation can be precisely fitted by superimposing two consecutive exponentially decaying functions. These two stages correspond to different physical operating states of the bearing. The temperature-time curve fitting model is as follows: (1) in, Let be the temperature of the bearing outer ring at time t; This is the bearing's steady-state temperature, i.e., the final temperature after thermal equilibrium. , These represent the temperature rise values ​​for the first and second stages, indicating the temperature increase from the initial value to the steady state. , The time constants for the first and second stages reflect the speed of the thermal response in that stage.

[0026] Phase 1: Dominant Period of Frictional Heat Generation. This phase corresponds to the transient process of a bearing starting from rest to high-speed operation. At the moment of startup, the rolling elements and the inner and outer raceways are in a state of boundary lubrication or even dry friction. Due to the contact angle, the rolling elements simultaneously bear normal loads and centrifugal forces. Under the action of high-speed centrifugal forces, the lubricant has difficulty quickly entering the contact area, resulting in a significant lag in oil film formation. At this time, frictional heat mainly comes from the solid contact friction between the rolling elements and the raceways. Simultaneously, due to inertial lag, the cage will experience slippage or whirling relative to the rolling elements, and the sliding friction between the cage and the outer ring guide surface further intensifies the initial heat generation. The combined effect of these two mechanisms makes this phase characterized by delayed lubricant film formation and unstable cage movement, constituting the dominant period of frictional heat generation during bearing startup. Time constant This reflects the speed at which the lubricating film forms, and is related to the bearing's inertia, starting torque, rotational speed, and lubricant viscosity. Temperature rise amplitude. This represents the temperature rise during this stage, which is usually small due to the extremely short duration of this stage.

[0027] Phase Two: Thermal Equilibrium Establishment. This phase corresponds to the process after stable operation, where heat is transferred, stored, and tends towards equilibrium in the bearing components. During this phase, the lubricant begins to circulate and distribute evenly, and the frictional heat generation rate tends to be constant. However, due to the continuous input of heat generated by the rolling friction between the rolling elements and the raceway, as well as the oil loss from the cage, the bearing temperature continues to rise. This heat is transferred outward along the path of "rolling elements → raceway → bearing rings → bearing housing → cooling system," while some heat is carried away by the lubricant. Time constant. This reflects the characteristic time required for the system to establish thermal equilibrium, and is related to the heat capacity and thermal resistance of the entire bearing-lubrication-cooling system, typically much longer than... Temperature rise amplitude It is related to the frictional power loss under steady-state conditions and usually accounts for more than 90% of the total temperature rise.

[0028] To further reveal the physical mechanisms underlying the parameters of the double exponential decay model and to achieve a quantitative assessment of the bearing's thermal dynamic state, this invention further constructs two derived feature parameters from the fitted model parameters: a timescale separation factor. Coupling coefficient with thermal dynamics .

[0029] The time scale separation factor is defined as shown in equation (2): (2) This factor quantitatively describes the degree of separation between the lubricating film formation process and the thermal equilibrium establishment process on a time scale. From a physical perspective, if... A larger value means that the lubricating film can be established rapidly in a very short time, while the establishment of thermal equilibrium is a relatively slow process. When When the value is ≥10, the time scales of the two stages are fully separated, and the identification results of the model parameters are highly stable, indicating that the bearing is in a normal lubrication state. Conversely, if... An abnormal decrease, or even approaching 1, indicates lubrication failure or abnormal cage movement. This indicator can be used as a characteristic parameter for early failures.

[0030] The thermal dynamic coupling coefficient is defined as shown in equation (3): (3) This coefficient reflects the degree to which the second stage dominates the overall temperature rise of the bearing. (Molecular) Characterized the cumulative heat effect during the heat equilibrium establishment phase, denominator This characterizes the cumulative thermal effect during the lubrication film formation stage. In healthy bearings, because the frictional heat during startup is minimal and short-lived, while the frictional heat during stable operation is continuous and exhibits significant thermal inertia, there is typically... This means that the temperature rise of the bearing is almost entirely determined by the process of establishing thermal equilibrium. If monitored... A continuous downward trend in the value indicates premature aging of the lubricant, abnormal preload, or increased system thermal resistance. These changes can all serve as quantitative indicators of bearing performance degradation.

[0031] This invention employs a nonlinear least squares method to perform curve fitting on the collected complete temperature-time series data. Specifically, after completing temperature data collection for a preset duration (e.g., 60 minutes), the optimal parameter set is iteratively solved using the Levenberg-Marquardt algorithm with equation (1) as the objective function. , , , , This minimizes the sum of squared residuals. Simultaneously, based on the calculated... and Quantitatively evaluate the lubrication condition and thermodynamic characteristics of the bearing: when When ≥10 and the value is relatively large and When stable, the bearing is considered to be in a healthy condition; when or When abnormal trends occur, an early warning signal is issued. 3. Detailed Implementation Furthermore, step S1 includes the arrangement of the data acquisition device and the assembly of the bearing testing machine, as detailed below: (1) Data acquisition device The data acquisition device is horizontally arranged and includes a control console, test shaft system, electric spindle, high-temperature gas source, frequency converter, and signal processing cabinet. The frequency converter adjusts the electric spindle speed to achieve speed input. The high-temperature gas source is provided by a heatable air compressor and input into the bearing chamber of the testing machine. The electric spindle and test spindle are connected as a whole via a flexible diaphragm coupling, and are respectively connected to the control console, high-temperature gas source, and frequency converter. The frequency converter is connected to the signal processing cabinet. The high-temperature gas source is provided by a heatable air compressor and input into the bearing chamber of the testing machine. The spatial layout of each part is as follows: Figure 2 As shown.

[0033] The test shaft system is supported by two identical bearings. The bearing furthest from the coupling is the test bearing, which is the primary source of test parameters. The bearing closer to the coupling is the auxiliary bearing, which can also be used to collect temperature and axial load data.

[0034] The test shaft system is supported by a bearing testing machine. The base plate 1 of the testing machine is placed on the test table. The bearing base 2 is fixed to the base plate 1 by bolts. The bearing base 2 is machined by horizontal planing and is also connected by bolts. Bearing holes are provided on the bearing base 2 to determine the bearing installation position. A bearing cap 3 is also provided to fix the axial position of the bearing. A bearing loading mechanism 4 with an internal spring is provided between the bearing bearing-bearing side cap 6 and the bearing to apply axial force to the bearing. The bearing cap 3 is in direct contact with the bearing. Additionally, sensor insertion holes are provided on the bearing base 3. The assembly diagram of the bearing base and related components of the testing machine is shown below. Figure 3 As shown.

[0035] (2) Data collection A high-response temperature sensor was installed on the outer ring of the bearing. Data was collected for 60 minutes at a frequency of at least 1Hz, after which the machine was stopped and allowed to cool naturally to room temperature before the next speed point test was conducted. Bearing model: 7006C angular contact ball bearing. Operating conditions: The outer ring of the bearing is fixed, the inner ring rotates, the axial load is 50N, and the inner ring speeds are 17000r / min and 20000r / min respectively.

[0036] (3) Data processing and analysis The collected raw temperature data is first filtered and denoised, and then the nonlinear least squares method is used to fit the curve of the double exponential decay model shown in equation (1) to accurately predict the steady-state temperature at this rotational speed. .

[0037] When the inner ring speed is 17000 r / min, the fitted curve is as follows: =24.027, =-0.125, =-3.999, =2.998, =65.400, curve fitting accuracy The value is 0.9983, and the fitted curve is as follows: Figure 4 As shown.

[0038] When the rotational speed is 17000 r / min, the fitting formula shows that the steady-state temperature of the bearing is 24.027℃ and the total temperature rise is 4.124℃. , The proportion of the total temperature rise indicates that the temperature increases almost entirely during the thermal equilibrium phase; timescale separation factor A value much greater than 10 satisfies the time-scale separation condition, indicating that the lubricating film formation stage and the thermal equilibrium establishment stage are fully separated on a time scale, and the model parameter identification results are highly stable; the thermal dynamic coupling coefficient... A value much greater than 1 indicates that the bearing temperature rise is almost entirely dominated by the second stage.

[0039] From a physical mechanism perspective, at the moment of startup, the rolling elements and raceways are in a boundary lubrication state, with brief metal-to-metal contact. However, since the bearing uses grease lubrication, an initial oil film is already partially present, resulting in low contact stress. Therefore, the elastohydrodynamic lubrication film can be fully formed in a very short time. During this process, the coefficient of friction decreases rapidly, and although the heat generation rate is high, its duration is extremely short, resulting in very little frictional heat. After the lubrication film is formed, the frictional heat generation rate tends to stabilize, mainly originating from the rolling resistance of the rolling elements and the churning loss of the grease. This heat is continuously input into the bearing and transferred along the path of "rolling element → raceway → bearing housing," while some heat is carried away by the grease and surrounding air. Due to the combined effect of the system's heat capacity and thermal resistance, the temperature rise is significantly slower than in the first stage, requiring approximately 3.3 minutes to approach steady state. This stage is the dominant factor in the temperature rise.

[0040] When the inner ring speed is 20000 r / min, the fitted curve is: =25.989, =-0.047, =-5.830, =1.361, =81.710, curve fitting accuracy The value is 0.9998, and the fitted curve is as follows: Figure 5 As shown.

[0041] When the rotational speed increases to 20,000 r / min, the fitted parameters show consistent and reasonable patterns in both numerical changes and physical mechanisms. Compared to 17,000 r / min, the time-scale separation factor at 20,000 r / min is [higher / lower / higher]. The significant increase indicates that the increased rotational speed leads to a more complete separation of the time scales between the two stages; the thermal dynamic coupling coefficient The significant increase indicates that the dominance of the second stage has been further strengthened.

[0042] Comparing the fitted parameters at the two rotational speeds reveals a consistent physical change pattern: as the rotational speed increases from 17000 r / min to 20000 r / min, This decreases accordingly. This change indicates that the increased rotational speed increases the entrainment velocity between the rolling elements and the raceways, thereby accelerating the formation of the elastohydrodynamic lubrication film; simultaneously, since grease lubrication has already pre-existed a base oil film on the raceway surface during assembly, and the centrifugal force at high speeds helps the lubricating oil spread to the contact area, the duration of boundary lubrication is significantly compressed. Therefore, the frictional heat generated by solid contact during the startup phase is minimal. On the other hand, and It increases with increasing rotational speed. Among them, The increase directly reflects the significant rise in rolling friction and churning losses with increasing speed during stable operation, resulting in more frictional heat being continuously input into the bearing system. The increase in grease may be due to the redistribution of grease under centrifugal force at high speeds. Some grease is thrown off the raceway and accumulates on the cage or bearing chamber edge, which increases the mass of the effective medium participating in heat exchange and correspondingly increases the equivalent heat capacity of the system.

[0043] Overall, the increase in rotational speed strengthens the dominance of the second stage in bearing temperature rise, and the time-scale separation factor... The time scale is significantly increased, and the separation is more complete, thus making the parameter identification of the double exponential decay model more stable and reliable.

[0044] (4) Verification To verify the accuracy of the temperature rise prediction model based on 60 minutes of data, a rotation speed of 20,000 r / min was selected as the verification point, and temperature data were continuously collected for 180 minutes under the same operating conditions. Figure 6 As shown, the actual steady-state temperature is 26.631℃, while the model prediction is... The temperature was 25.989℃, with an error of only 0.642℃, verifying the accuracy of the model under high-speed operating conditions.

[0045] It should be noted that although the present invention has been described through the above embodiments, the present invention may have many other embodiments. Without departing from the spirit and scope of the present invention, those skilled in the art can obviously make various corresponding changes and modifications to the present invention, but all such changes and modifications should fall within the scope of protection of the appended claims and their equivalents.

Claims

1. A method for predicting the temperature of high-speed bearings based on a multi-stage exponential decay model, characterized in that, Includes the following steps: S1. Set up a data acquisition device to collect the outer ring temperature-time series data of the high-speed bearing during operation; S2. Based on the temperature-time series data collected in step S1, the temperature-time curve is fitted using a double exponential decay superposition model. The expression for the double exponential decay superposition model is: （1） in, This is the bearing's steady-state temperature, i.e., the final temperature after thermal equilibrium. , These represent the temperature rise values ​​for the first and second stages, indicating the temperature increase from the initial value to the steady state. , The time constants for the first and second stages reflect the speed of the thermal response in that stage. S3. Based on the model parameters obtained from step S2, construct derived feature parameters, including the time scale separation factor λ and the thermal dynamic coupling coefficient K. S4. Based on the derived characteristic parameters obtained in step S3, the lubrication status and thermal dynamic characteristics of the bearing are quantitatively evaluated. When λ and K meet the preset health status criteria, the bearing is determined to be in a healthy state. When λ or K shows an abnormal trend, an early warning signal is issued.

2. The high-speed bearing temperature prediction method based on a multi-stage exponential decay model according to claim 1, characterized in that, The formula for calculating the time scale separation factor λ in step S3 is as follows: （2） The timescale separation factor λ is used to quantitatively describe the degree of separation between the first-stage lubricating film formation process and the second-stage thermal equilibrium establishment process on a timescale.

3. The high-speed bearing temperature prediction method based on a multi-stage exponential decay model according to claim 2, characterized in that, The health status judgment in step S4 is as follows: when λ≥10, it is determined that the time scales of the first and second stages are sufficiently separated, the identification results of the model parameters are highly stable, and the bearing is in a normal lubrication state; when λ decreases and approaches 1, it is determined that there are early signs of lubrication failure or abnormal cage movement.

4. The high-speed bearing temperature prediction method based on a multi-stage exponential decay model according to claim 1, characterized in that, The formula for calculating the thermal dynamic coupling coefficient K in step S3 is as follows: （3） The thermal dynamic coupling coefficient K is used to reflect the degree to which the overall temperature rise of the bearing is dominated during the thermal equilibrium establishment stage.

5. The high-speed bearing temperature prediction method based on a multi-stage exponential decay model according to claim 4, characterized in that, The health status criteria in step S4 also include: when the K value is large and remains stable, the bearing is determined to be in a healthy state; when a continuous downward trend in the K value is detected, it is determined that there are signs of performance degradation such as premature aging of lubricant, abnormal preload, or increased system thermal resistance.

6. The high-speed bearing temperature prediction method based on a multi-stage exponential decay model according to claim 1, characterized in that, In step S2, the Levenberg-Marquardt algorithm is used to perform nonlinear least squares fitting on the double exponential decay superposition model, and the optimal parameter set is iteratively solved with equation (1) as the objective function. , , , , This minimizes the sum of squared residuals.

7. The high-speed bearing temperature prediction method based on a multi-stage exponential decay model according to claim 1, characterized in that, In step S1, the acquisition duration of the temperature-time series data is a preset short-time test duration, and the acquisition frequency of the temperature-time series data is not less than 1Hz.

8. The high-speed bearing temperature prediction method based on a multi-stage exponential decay model according to claim 1, characterized in that, In step S2, the first stage of the double exponential decay superposition model is the period dominated by frictional heat generation, which corresponds to the start-up transient process of the bearing from standstill to high-speed operation. The time constant τ1 reflects the speed of lubrication film establishment. The second stage is the period of thermal equilibrium establishment, which corresponds to the process of heat transfer, storage and tendency to balance in various components of the bearing after stable operation. The time constant τ2 reflects the characteristic time of thermal equilibrium establishment of the system, and τ2 > τ1.

9. The high-speed bearing temperature prediction method based on a multi-stage exponential decay model according to claim 1, characterized in that, In step S2, the temperature rise amplitude A1 in the first stage of the double exponential decay superposition model is the temperature rise amplitude generated during the period dominated by frictional heat generation, and the temperature rise amplitude A2 in the second stage is the temperature rise amplitude generated during the period of thermal equilibrium establishment, and A2 accounts for more than 90% of the total temperature rise.

10. A device for predicting the temperature of high-speed bearings based on a multi-stage exponential decay model, used in the method according to any one of claims 1-9, characterized in that, The device is the acquisition device in step S1, which includes a control console, a test shaft system, an electric spindle, a high-temperature gas source, a frequency converter, and a signal processing cabinet. The frequency converter is responsible for adjusting the speed of the electric spindle to achieve speed input. The high-temperature gas source is provided by a heatable air compressor and input into the bearing chamber of the test machine. The electric spindle and the test spindle are connected as a whole by an elastic diaphragm coupling, which is connected to the control console, the high-temperature gas source, and the frequency converter respectively. The frequency converter is connected to the signal processing cabinet. The test shaft system is supported by a bearing testing machine. The bearing testing machine includes a testing machine base plate (1), a bearing base (2), a bearing cover (3), a bearing loading mechanism (4), a sensor (5), and a bearing non-load-bearing side cover (6). The bearing cover (3) and the bearing non-load-bearing side cover (6) are fixed on the upper surface of the testing machine base plate (1) through the bearing base (2). A bearing loading mechanism (4) for providing axial loading force is also provided between the bearing non-load-bearing side cover (6) and the bearing base (2). Several sensors (5) are also provided on the bearing base (2), the bearing non-load-bearing side cover (6), and the bearing cover (3).

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