A kind of disc spring device and disc spring compression performance prediction method
By setting radial stress relief grooves and flexible strain sensors on the conical surface of the disc spring body, and combining ABAQUS finite element simulation with BP neural network, the stress concentration problem of traditional disc springs is solved, enabling accurate performance prediction and real-time monitoring, improving the life and reliability of the spring, and adapting to complex working conditions.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- DONGTAI JINZHIZE METAL PROD CO LTD
- Filing Date
- 2026-03-07
- Publication Date
- 2026-06-09
AI Technical Summary
The conical structure of traditional disc springs leads to stress concentration, which can easily cause early fatigue cracks. Furthermore, existing performance prediction methods fail to effectively consider structural parameter coupling, material nonlinearity, and environmental factors, resulting in large prediction errors and difficulty in adapting to complex working conditions.
A radial stress relief groove is set on the conical surface of the disc spring body, and the bottom of the groove is an arc structure. Combined with a flexible strain sensor, the stress state is monitored in real time. By integrating the influence of multiple parameters through ABAQUS finite element simulation and BP neural network prediction model, an accurate performance prediction method is constructed.
It significantly improves the service life and operational reliability of springs, reduces prediction errors to within 5%, adapts to complex working conditions, reduces maintenance costs and failure risks, and realizes a closed-loop design of structural optimization and real-time monitoring.
Smart Images

Figure CN122170185A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of disc spring technology, and in particular to a disc spring device and a method for predicting the compressive performance of a disc spring. Background Technology
[0002] Disc springs, as elastic elements with high stiffness and small deformation characteristics, are widely used in machinery, aerospace, and automotive fields, primarily for applications such as damping, load compensation, and sealing. Traditional disc springs typically employ a conical thin-walled structure, relying on axial compression to generate elastic deformation for energy storage and release. Their design and performance evaluation are largely based on traditional materials mechanics theories, such as the Belleville spring formula, deriving load-displacement relationships by simplifying structural parameters. However, with the development of industrial equipment towards higher precision and reliability, higher requirements are being placed on the load-bearing capacity, fatigue life, and dynamic response characteristics of disc springs.
[0003] In existing technologies, the conical surface structure of traditional disc springs causes stress concentration on the upper inner surface and the lower outer surface under compression, which easily leads to early fatigue cracks, severely shortens service life and reduces operational reliability. Furthermore, there is a lack of effective means to monitor stress state in real time. In addition, traditional performance prediction methods rely on simplified calculations based on theoretical formulas, without fully considering the coupling of structural parameters, material nonlinearity and the influence of environmental factors, resulting in large prediction errors. These methods are also difficult to cover complex working conditions such as bidirectional compression and variable frequency vibration, and cannot provide accurate support for the optimized design and life assessment of springs. Therefore, this invention proposes a disc spring device and a method for predicting the compression performance of disc springs to solve the problems existing in the prior art. Summary of the Invention
[0004] To address the aforementioned problems, this invention proposes a disc spring device and a method for predicting the compressive performance of disc springs. A radial stress relief groove is set on the conical surface of the disc spring body, and the bottom of the groove adopts an arc-shaped structure to eliminate stress concentration at sharp corners. This solves the problem of early fatigue cracks caused by stress concentration on the inner edge of traditional disc springs from a structural design perspective. At the same time, a flexible strain sensor is used to realize real-time monitoring of stress state, providing real-time data support for performance evaluation, which significantly improves the service life and operational reliability of the spring.
[0005] To achieve the objective of this invention, the invention is implemented through the following technical solution: a disc spring device, comprising at least one disc spring body and a data acquisition and processing unit, wherein a stress relief groove extending radially is provided on the conical surface of the disc spring body; and an annular groove is provided on the upper surface of the disc spring body, wherein a flexible strain sensor is embedded in the annular groove.
[0006] The flexible strain sensor is electrically connected to the data acquisition and processing unit and is used to acquire and process strain signals.
[0007] A further improvement is that the stress relief grooves are evenly distributed in several groups along the circumference of the disc spring body, and the bottom of the stress relief grooves is an arc-shaped structure.
[0008] A further improvement is that the annular groove is located near the neutral ring of the disc spring body, and the flexible strain sensor is a fiber optic grating sensor or a printed resistance strain gauge.
[0009] A further improvement is that the data acquisition and processing unit includes a signal conditioning module, an analog-to-digital conversion module, and a microprocessor, wherein the microprocessor has a pre-stored disc spring performance prediction model trained based on machine learning.
[0010] Further improvements are made in that: the signal conditioning module is used to filter and amplify the analog signal acquired by the flexible strain sensor, and the analog-to-digital conversion module converts the processed analog signal into a digital signal and transmits it to the microprocessor.
[0011] A method for predicting the compressive performance of a disc spring includes the following steps:
[0012] S1: Construct a multi-parameter set for the disc spring, which includes structural parameters, material property parameters, and environmental parameters;
[0013] S2: Construct a finite element model of a disc spring based on ABAQUS, import the actual material constitutive model, set contact conditions and boundary constraints, simulate displacement loading, and output load-displacement curves and hysteresis curves.
[0014] S3: Integrate the multi-parameter set of S1 with the finite element simulation data of S2, and combine it with physical experimental data to construct a BP neural network prediction model;
[0015] S4: The BP neural network prediction model is trained and corrected using physical test data to obtain an optimized pressure performance prediction model;
[0016] S5: Input the multiple parameters of the disc spring to be predicted into the optimized prediction model, and output the elastic deformation, ultimate bearing pressure and fatigue life.
[0017] A further improvement is made in S3, where the training process of the BP neural network prediction model includes: dividing the physical experiment data into a training set and a test set in a 7:3 ratio, setting the learning rate to 0.01-0.05, the number of iterations to 500-1000, using the mean squared error (MSE) as the loss function, and adjusting the weight coefficients and bias terms through the backpropagation algorithm until the model converges.
[0018] A further improvement is made in S5, where the prediction formula for the elastic deformation Δ is:
[0019] ,
[0020] in: denoted as the elastic deformation of the disc spring (mm); n represents the number of neurons in the input layer (corresponding to the number of parameters in the multi-parameter set). The weight coefficients for the j-th input parameter (obtained through model training); For the j-th input parameter (normalized value of structural / material / environmental parameter); This is the hidden layer bias term (obtained through model training); The sigmoid function is used as the activation function. .
[0021] A further improvement lies in: in S5, the ultimate bearing pressure The prediction formula is:
[0022] ,
[0023] in: The ultimate bearing pressure (N); The yield strength (MPa) of the disc spring material; The effective bearing area of the disc spring k is the structural correction factor (determined based on the number and size of stress relief grooves, with a value range of 0.85-0.95); m is the number of neurons in the hidden layer. The weight coefficients of the k-th hidden layer neuron (obtained through model training); This represents the output value of the k-th hidden layer neuron. This is the output layer bias term (obtained through model training); The activation function for the output layer is a linear function: g(z) = z.
[0024] A further improvement is made in S5, where the formula for predicting fatigue life N is:
[0025] ,
[0026] Where: N is the total fatigue life (times) of the disc spring; i is the number of load levels; The actual number of cycles (times) under the i-th level load; The predicted fatigue life (times) under the i-th level load is output by the BP neural network. Environmental correction factor (temperature effect factor) Humidity Influence Coefficient The product of T is the ambient temperature (°C), and H is the ambient humidity (%RH).
[0027] The beneficial effects of this invention are as follows:
[0028] 1. This invention provides a radial stress relief groove on the conical surface of the disc spring body. The bottom of the groove adopts an arc-shaped structure to eliminate stress concentration at sharp corners. From the structural design level, it solves the problem of early fatigue cracks caused by stress concentration on the inner edge of the traditional disc spring. At the same time, it realizes real-time monitoring of stress state through a flexible strain sensor, providing real-time data support for performance evaluation, and significantly improving the service life and operational reliability of the spring.
[0029] 2. This invention integrates the coupling effects of multiple parameters of structure, materials, and environment, and combines the complex working condition adaptability of ABAQUS finite element simulation with the nonlinear mapping advantage of BP neural network. Compared with traditional theoretical calculation methods, the prediction error is reduced to less than 5%, and it can effectively cover complex working conditions such as bidirectional pressure and variable frequency vibration, filling the application gap of traditional prediction methods in complex scenarios.
[0030] 3. This invention realizes a closed-loop design of structural optimization, real-time monitoring, and accurate prediction. The stress relief structure and sensor monitoring function of the device provide real working condition data for the prediction model. The output of the prediction model can guide the optimization of the device's structural parameters, forming a synergistic effect, further improving the overall performance of the disc spring, and reducing maintenance costs and failure risks in engineering applications. Attached Figure Description
[0031] Figure 1 This is a front view of the device of the present invention;
[0032] Figure 2 This is a schematic diagram of the method of the present invention.
[0033] The components include: 1. Disc spring body; 2. Stress relief groove; 3. Annular groove; 4. Flexible strain sensor. Detailed Implementation
[0034] To enhance understanding of the present invention, the present invention will be further described in detail below with reference to embodiments. These embodiments are only used to explain the present invention and do not constitute a limitation on the scope of protection of the present invention.
[0035] Example 1
[0036] according to Figure 1 , 2 As shown, this embodiment proposes a disc spring device, including at least one disc spring body 1 and a data acquisition and processing unit. The disc spring body 1 has a stress relief groove 2 extending radially on its conical surface; the upper surface of the disc spring body has an annular groove 3, and a flexible strain sensor 4 is embedded in the annular groove 3.
[0037] The flexible strain sensor 4 is electrically connected to the data acquisition and processing unit to acquire and process strain signals. The combined design of the stress relief groove and the flexible strain sensor optimizes stress distribution at the structural level and enables real-time acquisition of strain signals, providing first-hand data for performance evaluation. This integrated design eliminates the need for additional external monitoring components, is compact, adaptable to various installation scenarios, and enhances the device's practicality.
[0038] The stress relief grooves 2 are evenly distributed in several groups along the circumference of the disc spring body 1, and the bottom of the stress relief grooves 2 is an arc-shaped structure. The evenly distributed stress relief grooves can evenly distribute the stress in the circumferential direction and avoid local overload; the arc-shaped groove bottom completely eliminates the stress concentration at sharp corners, and compared with the right-angle groove bottom, the risk of crack initiation is reduced by more than 60%, significantly extending the fatigue life of the spring.
[0039] The annular groove 3 is located near the neutral ring of the disc spring body 1, and the flexible strain sensor 4 is a fiber optic grating sensor or a printed resistance strain gauge. The strain change near the neutral ring is stable and representative, which can accurately reflect the overall stress state of the spring and improve the effectiveness of the monitoring data; both sensors have flexible adaptability, can fit closely to the groove structure, and have strong anti-interference ability, making them suitable for use in harsh working conditions.
[0040] The data acquisition and processing unit includes a signal conditioning module, an analog-to-digital conversion module, and a microprocessor. The microprocessor pre-stores a disc spring performance prediction model trained based on machine learning. The modular design clearly defines the division of labor in the signal processing flow, improving data processing efficiency and stability. The pre-stored prediction model can directly interface with sensor data to achieve real-time calculation of performance parameters without relying on external computing devices, enhancing the independence of the device.
[0041] The signal conditioning module is used to filter and amplify the analog signal acquired by the flexible strain sensor 4. The analog-to-digital conversion module converts the processed analog signal into a digital signal and transmits it to the microprocessor. Filtering and amplification can effectively remove environmental interference signals and ensure the accuracy of the original data; analog-to-digital conversion realizes the accurate conversion of analog signals into digital signals, providing high-quality input for the microprocessor's model calculation and improving the accuracy of performance prediction.
[0042] A method for predicting the compressive performance of a disc spring includes the following steps:
[0043] S1: Construct a multi-parameter set for the disc spring, which includes structural parameters, material property parameters, and environmental parameters;
[0044] S2: Construct a finite element model of a disc spring based on ABAQUS, import the actual material constitutive model, set contact conditions and boundary constraints, simulate displacement loading, and output load-displacement curves and hysteresis curves.
[0045] S3: Integrating the multi-parameter set of S1 and the finite element simulation data of S2, combined with physical experimental data, a BP neural network prediction model is constructed. The training process of the BP neural network prediction model includes: dividing the physical experimental data into training and test sets in a 7:3 ratio, setting the learning rate to 0.01-0.05, the number of iterations to 500-1000, using the mean squared error (MSE) as the loss function, and adjusting the weight coefficients and bias terms through the backpropagation algorithm until the model converges. The 7:3 dataset division ratio ensures sufficient training data and effective validation of the test set, balancing the model's training effect and generalization ability; reasonable learning rate and iteration number settings avoid overfitting or slow convergence; the mean squared error loss function accurately measures prediction bias and improves model optimization efficiency.
[0046] S4: The BP neural network prediction model is trained and corrected using physical test data to obtain an optimized pressure performance prediction model;
[0047] S5: Input the multiple parameters of the disc spring to be predicted into the optimized prediction model, and output the elastic deformation, ultimate bearing pressure and fatigue life.
[0048] The formula for predicting the elastic deformation Δ is:
[0049] ,
[0050] in: denoted as the elastic deformation of the disc spring (mm); n represents the number of neurons in the input layer (corresponding to the number of parameters in the multi-parameter set). The weight coefficients for the j-th input parameter (obtained through model training); For the j-th input parameter (normalized value of structural / material / environmental parameter); This is the hidden layer bias term (obtained through model training); The sigmoid function is used as the activation function. Standardized input parameters can eliminate the influence of dimensional differences on prediction results and improve the stability of formula calculation; the sigmoid activation function can effectively fit the nonlinear characteristics of elastic deformation, and compared with linear functions, the deformation prediction error is reduced by more than 30%.
[0051] Ultimate bearing pressure The prediction formula is:
[0052] ,
[0053] in: The ultimate bearing pressure (N); The yield strength (MPa) of the disc spring material; The effective bearing area of the disc spring k is the structural correction factor (determined based on the number and size of stress relief grooves, with a value range of 0.85-0.95); m is the number of neurons in the hidden layer. The weight coefficients of the k-th hidden layer neuron (obtained through model training); This represents the output value of the k-th hidden layer neuron. This is the output layer bias term (obtained through model training); The output layer activation function is a linear function: g(z) = z. Introducing a structural correction coefficient allows for precise matching of the structural optimization effect of the stress relief groove, ensuring the formula closely aligns with the actual load-bearing characteristics of the device. The linear activation function guarantees that the calculated ultimate bearing pressure is consistent with actual mechanical laws, avoiding extreme value deviations caused by nonlinear fitting.
[0054] The formula for predicting fatigue life N is:
[0055] ,
[0056] Where: N is the total fatigue life (times) of the disc spring; i is the number of load levels; The actual number of cycles (times) under the i-th level load; The predicted fatigue life (times) under the i-th level load is output by the BP neural network. Environmental correction factor (temperature effect factor) With humidity influence coefficient K h The product of T represents ambient temperature (°C), and H represents ambient humidity (%RH). By weighting the number of cycles under multiple load levels, the fatigue cumulative effect under actual working conditions is accurately reflected, improving the accuracy of life prediction. The environmental correction coefficient quantifies the impact of temperature and humidity on fatigue life, filling the gap in traditional methods that ignore environmental factors.
[0057] Example 2
[0058] according to Figure 1 , 2 As shown, this embodiment proposes a disc spring device and a method for predicting the compressive performance of the disc spring. The disc spring body is made of 60Si2MnA spring steel, with an outer diameter D=80mm, an inner diameter d=40mm, a thickness t=5mm, and a cone angle of [missing information]. Eight radial stress relief grooves are evenly distributed along the circumference of the conical surface. The groove width w = 3 mm, the groove depth h = 2 mm, and the radius of the bottom arc r = 1.5 mm to eliminate stress concentration at sharp corners. An annular groove with a width of 2 mm and a depth of 1 mm is formed near the neutral ring of the disc spring body (15 mm from the inner edge). A fiber optic strain sensor (range -2000~2000 με, accuracy...) is embedded in the groove. The sensor is connected to the data acquisition and processing unit via a shielded cable. The data acquisition and processing unit includes an AD8421 signal conditioning module, an ADS1256 analog-to-digital converter module, and an STM32H743 microprocessor. The microprocessor has a pre-stored BP neural network performance prediction model to realize real-time acquisition of strain signals and calculation of performance parameters.
[0059] Example 3
[0060] according to Figure 1 , 2 As shown, this embodiment proposes a disc spring device and a method for predicting the compressive performance of the disc spring. A finite element model of the disc spring described in Embodiment 1 is constructed using ABAQUS: a C3D8R solid element mesh is used, with a mesh size of 20,000; the material constitutive model of 60Si2MnA (elastic modulus E = 206 GPa, Poisson's ratio) is imported. Yield strength =1500MPa); set the guide rail-spring contact condition to surface-to-surface contact, friction coefficient 0.15; boundary constraint is fixed inner diameter end face, apply axial displacement load to the lower end face (loading rate 0.1mm / s, maximum displacement 10mm); simulate bidirectional pressure condition (additional radial pressure 5MPa) and variable frequency vibration condition (frequency 5-50Hz), output load-displacement curve and hysteresis curve, extract key data such as elastic deformation and energy consumption value, and provide training samples for BP neural network model.
[0061] Example 4
[0062] according to Figure 1 , 2 As shown, this embodiment proposes a disc spring device and a method for predicting the compressive performance of the disc spring. The BP neural network model adopts a three-layer structure of "input layer-hidden layer-output layer": the number of neurons in the input layer n=8 (corresponding structural parameters: outer diameter D, inner diameter d, thickness t, cone angle). Number of stress relief grooves Groove width w, groove depth h; Material parameters: elastic modulus E, yield strength Environmental parameters: temperature T, humidity H, a total of 10 parameters, n=10); number of hidden layer neurons m=20; number of output layer neurons 3 (corresponding to elastic deformation Δ, ultimate bearing pressure). Fatigue life (N). 100 sets of physical test data were collected (covering different structural parameters, temperatures from -20 to 80℃, and humidity from 30% to 90%), with 70 sets used as the training set and 30 sets as the test set. The learning rate was set to 0.03, the number of iterations to 800, and the mean squared error (MSE) was used as the loss function. The model was trained using the backpropagation algorithm until MSE ≤ 0.001, at which point the model converged. The parameters of the disc spring to be predicted (D = 70mm, d = 35mm, t = 4mm) were used. , =6, w=2.5mm, h=1.8mm, E=206GPa, Input the model with a strength of 1500MPa, a temperature of 25℃, and a humidity of 50%, and output the elastic deformation. =8.2mm, ultimate bearing pressure =12500N, fatigue life Second-rate.
[0063] Validation data
[0064] A comparative test was conducted on the disc spring device of Example 2 and a traditional disc spring without a stress relief groove. Under the same working conditions (axial load 8000N, cycle frequency 10Hz, temperature 25℃), the fatigue life of the traditional disc spring was [missing information]. Next, the fatigue life of the device of the present invention is The lifespan is improved by 33.3%; stress tests show that the maximum stress on the inner edge of the device is 850 MPa, while that of a traditional spring is 1200 MPa, resulting in a 29.2% reduction in stress concentration. The monitoring error of the flexible strain sensor... The data acquisition frequency can reach 100Hz, meeting the needs of real-time monitoring.
[0065] The prediction errors of the prediction method of this invention are compared with those of the traditional Belleville formula and the single finite element method. The results are shown in the table below:
[0066]
[0067] As shown in the table, the prediction error of each performance parameter of the prediction method of the present invention is controlled within 5%, which is significantly better than the traditional method. Moreover, under bidirectional pressure and variable frequency vibration conditions, the error of the traditional method further increases (≥25%), while the error of the method of the present invention is still ≤5%, which is suitable for the prediction needs of complex working conditions.
[0068] This invention features a radial stress relief groove 2 on the conical surface of the disc spring body 1. The groove bottom employs an arc-shaped structure to eliminate stress concentration at sharp corners. This structural design addresses the early fatigue cracking problem caused by stress concentration on the inner surface of traditional disc springs. Simultaneously, a flexible strain sensor 4 enables real-time monitoring of the stress state, providing real-time data support for performance evaluation and significantly improving the spring's service life and operational reliability. Furthermore, this invention integrates the coupled effects of multiple parameters related to structure, materials, and environment. Combining the complex condition adaptability of ABAQUS finite element simulation with the nonlinear mapping advantages of BP neural networks, the prediction error is reduced to less than 5% compared to traditional theoretical calculation methods. It can effectively cover complex conditions such as bidirectional compression and variable frequency vibration, filling the application gap of traditional prediction methods in complex scenarios. Moreover, this invention achieves a closed-loop design of structural optimization, real-time monitoring, and accurate prediction. The stress relief structure and sensor monitoring function of the device provide real-world data for the prediction model, and the output of the prediction model can guide the optimization of the device's structural parameters, creating synergistic effects and further improving the overall performance of the disc spring, while reducing maintenance costs and failure risks in engineering applications.
[0069] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.
Claims
1. A disc spring device, comprising at least one disc spring body (1) and a data acquisition and processing unit, characterized in that: The disc spring body (1) has a radially extending stress relief groove (2) on its conical surface; the upper surface of the disc spring body has an annular groove (3), and a flexible strain sensor (4) is embedded in the annular groove (3). The flexible strain sensor (4) is electrically connected to the data acquisition and processing unit and is used to acquire and process strain signals.
2. The disc spring device according to claim 1, characterized in that: The stress relief grooves (2) are evenly distributed in several groups along the circumference of the disc spring body (1), and the bottom of the stress relief grooves (2) is an arc-shaped structure.
3. The disc spring device according to claim 1, characterized in that: The annular groove (3) is located near the neutral ring of the disc spring body (1), and the flexible strain sensor (4) is a fiber optic grating sensor or a printed resistance strain gauge.
4. The disc spring device according to claim 1, characterized in that: The data acquisition and processing unit includes a signal conditioning module, an analog-to-digital conversion module, and a microprocessor. The microprocessor has a pre-stored disc spring performance prediction model trained based on machine learning.
5. A disc spring device according to claim 4, characterized in that: The signal conditioning module is used to filter and amplify the analog signal collected by the flexible strain sensor (4), and the analog-to-digital conversion module converts the processed analog signal into a digital signal and transmits it to the microprocessor.
6. A method for predicting the compressive performance of a disc spring, applied to a disc spring device according to any one of claims 1-5, characterized in that, Includes the following steps: S1: Construct a multi-parameter set for the disc spring, which includes structural parameters, material property parameters, and environmental parameters; S2: Construct a finite element model of a disc spring based on ABAQUS, import the actual material constitutive model, set contact conditions and boundary constraints, simulate displacement loading, and output load-displacement curves and hysteresis curves. S3: Integrate the multi-parameter set of S1 with the finite element simulation data of S2, and combine it with physical experimental data to construct a BP neural network prediction model; S4: The BP neural network prediction model is trained and corrected using physical test data to obtain an optimized pressure performance prediction model; S5: Input the multiple parameters of the disc spring to be predicted into the optimized prediction model, and output the elastic deformation, ultimate bearing pressure and fatigue life.
7. The method for predicting the compressive performance of a disc spring according to claim 6, characterized in that: In S3, the training process of the BP neural network prediction model includes: dividing the physical experiment data into a training set and a test set in a 7:3 ratio, setting the learning rate to 0.01-0.05, the number of iterations to 500-1000, using the mean squared error (MSE) as the loss function, and adjusting the weight coefficients and bias terms through the backpropagation algorithm until the model converges.
8. The method for predicting the compressive performance of a disc spring according to claim 6, characterized in that: In S5, the formula for predicting the elastic deformation Δ is: , in: denoted as the elastic deformation of the disc spring (mm); n represents the number of neurons in the input layer (corresponding to the number of parameters in the multi-parameter set). The weight coefficients for the j-th input parameter (obtained through model training); For the j-th input parameter (normalized value of structural / material / environmental parameter); This is the hidden layer bias term (obtained through model training); The sigmoid function is used as the activation function. .
9. The method for predicting the compressive performance of a disc spring according to claim 8, characterized in that: In S5, the ultimate bearing pressure The prediction formula is: , in: The ultimate bearing pressure (N); The yield strength (MPa) of the disc spring material; denoted as , where is the effective bearing area of the disc spring (mm²); k is the structural correction coefficient (determined based on the number and size of stress relief grooves, ranging from 0.85 to 0.95); m is the number of neurons in the hidden layer. The weight coefficients of the k-th hidden layer neuron (obtained through model training); This represents the output value of the k-th hidden layer neuron. This is the output layer bias term (obtained through model training); The activation function for the output layer is a linear function: g(z) = z.
10. The method for predicting the compressive performance of a disc spring according to claim 9, characterized in that: In S5, the formula for predicting fatigue life N is: , Where: N is the total fatigue life of the disc spring (times); i is the number of load levels; The actual number of cycles (times) under the i-th level load; The predicted fatigue life (times) under the i-th level load is output by the BP neural network. Environmental correction factor (temperature effect factor) Humidity Influence Coefficient The product of T is the ambient temperature (°C), and H is the ambient humidity (%RH).