Gear transmission system dynamic reliability modeling considering multiple failure mode correlation

Abstract

The invention discloses a gear transmission system dynamic reliability modeling considering correlation of multiple failure modes, which comprises the following steps of: 1, identifying and classifying fatigue failure, wear failure and tooth breakage failure of a gear system according to the working state and environmental factors of the gear transmission system; 2, describing the stress process of the gear transmission system by using a random statistic principle, and simplifying the reliability modeling calculation amount of the failure process according to the dynamic stress borne by the gear teeth; 3, describing a gear strength degradation process by adopting a Gamma degradation random process, deducing Gamma distribution parameters in combination with a material P-S-N curve, and establishing a gear reliability model based on strength degradation; the invention provides a dynamic reliability modeling method suitable for a complex gear transmission system by combining failure mode correlation modeling, multi-dimensional dynamic simulation and a reliability evaluation algorithm.

Description

Technical Field

[0001] The present invention relates to the technical field of gear transmission system modeling, and specifically to the dynamic reliability modeling of gear transmission systems considering multiple failure modes. Background Technique

[0002] Gear transmission systems are core components widely used in modern mechanical equipment, and their performance and reliability have important impacts on the safety, stability, and service life of the equipment. However, due to the influence of complex loads and environmental conditions during the long-term operation of gears, various failure modes such as fatigue, wear, and tooth breakage are likely to occur, and there are often coupling relationships between these failure modes, which exacerbates the difficulty of reliability analysis of gear systems.

[0003] Traditional gear reliability analysis methods usually assume that failure modes are independent of each other and adopt static failure probability distribution models. Although this method is simple, it has obvious deficiencies in practical applications. On the one hand, it ignores the mutual influence and dynamic changes between multiple failure modes and cannot truly reflect the reliability changes of gear systems under complex working conditions. On the other hand, traditional methods rely on a large amount of test data and accurate modeling, and it is very difficult to accurately obtain these parameters under complex and variable working conditions. In addition, existing methods are difficult to effectively combine various dynamic characteristics such as gear force characteristics, wear laws, and strength degradation processes, resulting in a large deviation between the reliability assessment results and the actual situation.

[0004] To solve the above problems and improve the reliability prediction accuracy and adaptability of gear transmission systems, there is an urgent need for a dynamic reliability modeling method that can comprehensively consider the coupling effects of multiple failure modes. The present invention proposes a dynamic reliability modeling method based on the correlation analysis of failure modes, which combines advanced technologies such as the principle of random statistics, degradation process modeling, and Copula functions, and can accurately describe the reliability changes of gear transmission systems under complex working conditions. This method can not only meet the high-precision reliability prediction requirements but also provide a scientific basis for the maintenance and optimization of gear systems, and has important engineering application value. Summary of the Invention

[0005] The purpose of the present invention is to provide a dynamic reliability modeling of gear transmission systems considering multiple failure modes, aiming to improve the problem that there is a large deviation between the evaluation results of traditional gear reliability analysis methods and the actual situation.

[0006] The present invention is implemented as follows: A dynamic reliability modeling of gear transmission systems considering multiple failure modes, characterized by including

[0007] Step 1: According to the working state and environmental factors of the gear transmission system, identify and classify the fatigue failure, wear failure, and tooth breakage failure of the gear system;

[0008] Step 2: Describe the force-bearing process of the gear transmission system using the principle of random statistics, and simplify the reliability modeling calculation amount of the failure process for the dynamic stress borne by the gear teeth;

[0009] Step 3: Use the Gamma degradation random process to describe the gear strength degradation process, deduce the Gamma distribution parameters in combination with the material P-S-N curve, and establish a gear reliability model based on strength degradation;

[0010] Step 4: Calculate the wear amount of the gear during continuous operation based on the contact mechanics theory and Hertz's theorem, describe the random impact wear amount caused by external loads through the Poisson process, and construct a wear failure reliability model in combination with the set accuracy threshold;

[0011] Step 5: Use the Copula function to establish a correlation model between failure modes, and by introducing multi-dimensional state variables, integrate the coupling effects of each failure mode into a dynamic reliability model.

[0012] Compared with the prior art, the beneficial effects of the present invention are as follows: By combining failure mode correlation modeling, multi-dimensional dynamic simulation, and reliability evaluation algorithms, the present invention proposes a dynamic reliability modeling method applicable to complex gear transmission systems. This method overcomes the limitation of ignoring the coupling effect of failure modes in traditional methods and can more accurately reflect the reliability changes of gear transmission systems under complex working conditions. By introducing the principle of random statistics and degradation random process modeling, the model complexity is significantly reduced and the calculation efficiency is improved. The application of the Copula function realizes the quantitative modeling of the correlation between multiple failure modes, enhancing the accuracy and practicality of reliability prediction. The present invention provides a scientific basis for fault prediction, maintenance optimization, and reliability improvement of complex gear transmission systems, and has wide engineering application value. Brief Description of the Drawings

[0013] Figure 1 is a schematic diagram of the dynamic reliability modeling process of a gear transmission system considering the correlation of multiple failure modes provided by an embodiment of the present invention.

[0014] Figure 2 is a schematic diagram of the failure mode of an improved stress-strength interference model provided by an embodiment of the present invention.

[0015] Figure 3 is a schematic diagram of the wear-wear threshold failure mode provided by an embodiment of the present invention.

[0016] Figure 4 is a schematic diagram of the dynamic reliability solution of a gear transmission system related to multiple failure modes based on the Copula function provided by an embodiment of the present invention. Detailed Embodiments

[0017] In the present invention, unless otherwise clearly specified and defined, terms such as "installation", "connection", "linkage", "fixation" shall be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or integrated; it may be a mechanical connection or an electrical connection; it may be a direct connection or an indirect connection through an intermediate medium, and it may be the internal communication of two components or the interaction relationship between two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0018] The following further explanations are provided in conjunction with the accompanying drawings and specific embodiments:

[0019] The present invention proposes a dynamic reliability modeling method for a gear transmission system considering multiple failure modes. The following describes the implementation process of the method in detail in conjunction with specific implementation steps.

[0020] Step 1: Failure mode identification. First, for the operating environment and working conditions of the gear transmission system, identify the main modes that may cause system failure, including fatigue failure, wear failure, and tooth breakage failure, etc. Through experimental tests and on-site data collection, obtain the characteristic parameters of different failure modes, such as tooth stress distribution, wear rate, and crack propagation characteristics. At the same time, use the correlation analysis method to quantitatively analyze the mutual coupling effect between failure modes. For example, stress concentration caused by wear may exacerbate fatigue failure, so as to determine the magnitude and direction of the correlation. Obtain the stress time history data of the gear teeth under different working conditions through finite element analysis or dynamic simulation, and use statistical methods to fit the data to construct a random force process model. This model can characterize the influence of load fluctuations on gear failure in a parametric form, such as Gaussian distribution or lognormal distribution. The solution formulas for the contact stress and bending stress of the gear are as follows:

[0021]

[0022] Among them, in the formula: K A is the service factor; K V is the dynamic load factor; K Hβ , K Fβ are the load distribution factors in the tooth direction respectively; K Hα , K Fα are the load distribution factors between teeth; Y F， Y S are the tooth form factor and stress correction factor respectively; Y β is the helix angle factor; Z B is the single pair tooth engagement coefficient; Z H is the nodal region factor; Z E is the elastic coefficient; Z ε is the contact ratio coefficient; Zβ is the helix angle coefficient; d 1 is the pitch circle diameter of the driving gear, and b is the tooth width.

[0023] When the contact stress of the gear or the bending stress of the gear tooth root is greater than the gear strength, it is determined as gear contact failure or gear bending failure. When the tooth surface wear amount of the gear is greater than the wear threshold, it is determined as wear failure.

[0024] Step 2: Model the force-bearing process of the gear transmission system. Use random statistics to describe the force distribution of gear teeth. In actual operation, the loads borne by each component of the mechanical system are not constant, but vary with the influence of the external environment and its own degradation, forming random variables. In addition, components usually bear such random loads multiple times. Using the traditional stress-strength model to evaluate the reliability of components may introduce large errors. Assuming that the degradation of component strength is not considered, when a component does not fail under the maximum load, it will still not fail after n random load applications. Therefore, the reliability of a component after experiencing n random loads can be expressed as follows:

[0025] P(z > s max ) = P(z > s 1 , z > s 2 , …, z > s n )

[0026] where z is the strength, s 1 , s 2 … s n are n load samples, and s max is the maximum value in the load samples. Determine the maximum load in the load samples according to the maximum statistic principle. Let the distribution function of the random load s be F s (s), and the probability density function be f s (s). Then the distribution function and probability density function of the maximum load X when the load acts on the component n times are:

[0027] F X (x) = [F s (x)] n

[0028] f X (x) = n[F s (x)] n-1 f s (x)

[0029] According to the classical stress interference theory, the reliability of the part when the load acts n times is:

[0030]

[0031] Step 3: Gear strength degradation reliability model. The Gamma process describes the process in which the degradation amount gradually accumulates over time, which is exactly applicable to the strength degradation process of mechanical components and has high applicability to degradation phenomena such as fatigue, pitting, and cracks in mechanical components. Therefore, the Gamma process is used to describe the degradation process of components. Let D(t) represent the strength degradation amount of the component and Z represent the initial strength. Then, the strength of the component at any time t is:

[0032] Z(t) = Z - D(t)

[0033] The probability density function of the Gamma process is as follows:

[0034]

[0035] In the formula, v is the shape parameter, u is the scale parameter, and I A (x) is the indicator function.

[0036] Assume that the stress and strength of the part respectively follow the normal distribution: ). Let Y = Z - S, and solve it by the numerical integration method. Then, the reliability of the gear is:

[0037]

[0038] Step 4: Wear failure reliability model. Calculate the surface wear amount caused by the normal working load during the operation of the gear according to the contact mechanics theory, and determine the pressure distribution in the gear meshing area and its contribution to wear in combination with the Hertz contact theory. At the same time, describe the wear caused by external random impact loads through the Poisson process, and construct a reliability model of wear failure in combination with the wear threshold calibrated by experiments (such as gear clearance or surface roughness change). Finally, comprehensively consider the influence of normal wear and impact wear on the system reliability, and dynamically update the failure probability distribution. Use the wear depth to represent the wear amount, and use the preset accuracy standard to determine the wear threshold in the interference model:

[0039] [h] = r b Δθ

[0040] Where: [h] is the wear threshold; r b is the pitch circle radius of the gear; Δθ is the accuracy.

[0041] According to the wear amount formula derived from the solid wear theory and the Hertz contact theory, this wear amount is the normal line wear amount of the contact surface and has a direct relationship with the normal load on the tooth surface. According to the gear contact mechanics model, the normal line wear amount of the tooth surface is:

[0042] h = I n Snt

[0043] Where: h is the normal line wear; I n is the wear characteristic coefficient of the gear; n is the rotational speed; t is the time; S is the sliding friction distance.

[0044] The function of the number of impact actions with respect to time is represented by N(t). Assuming that N(t) follows a Poisson process, then:

[0045] Where: λ is the intensity of the Poisson process.

[0046] Impact wear B(t) is the cumulative effect of each impact. When the number of impact actions is i, then:

[0047]

[0048] Where: Z i is the wear amount caused by each impact; i is the specific value of the number of impact actions; m is the wear amount caused by the i-th impact.

[0049] The failure of the gear is determined by the interference between the cumulative wear and the wear threshold. When the cumulative wear is less than the wear threshold, the gear is considered effective. According to the conditional probability, the reliability R(t) is:

[0050]

[0051] Where: T is the torque magnitude; K is the gear coefficient; m is the wear amount caused by each impact; r b is the pitch circle radius of the gear; Δθ is the accuracy.

[0052] Step 5: Multi-mode dynamic reliability modeling. Use the Copula function to construct the correlation model between multiple failure modes such as fatigue failure, wear failure, and tooth breakage failure. By selecting an appropriate Copula function (such as Gumbel, Clayton, or Frank Copula) and combining the correlation parameters, integrate the probability distributions of each failure mode to form a joint failure probability model. Further introduce multi-dimensional state variables (such as time, load level, and temperature, etc.) to construct a dynamic reliability model for reflecting the changing trend of the system reliability in real time. The solution of the model uses Monte Carlo simulation or numerical integration methods, and verify its accuracy and applicability. According to Sklar's theorem, assume that F(x 1 , x 2 , … x N ) has marginal distributions F 1 (x 1 ), F 2 (x 2 ), …, F N (x N)'s multi-dimensional joint distribution function, there will be a unique Copula function C(,,) such that the following equation holds.

[0053] F(x 1 ,x 2 ,…x N )=C(F 1 (x 1 ),F 2 (x 2 ),…,F N (x N ))

[0054] Through the probability density function C(,,) of the Copula function and the marginal distributions F 1 (x 1 ),F 2 (x 2 ),…,F N (x N ) the N - dimensional distribution function F(x 1 ,x 2 ,…x N )'s probability density function is:

[0055]

[0056] In the context of component reliability, this connection is also called the failure distribution connection. Another type of connection is called the survival connection, such as the following formula:

[0057]

[0058] For a three - dimensional distribution, the failure connection function and the survival connection function have the following relationship:

[0059]

[0060] Let P 1i be the tooth surface contact fatigue failure probability, P 2i be the tooth root bending fatigue failure probability, P 3i be the wear failure probability, then the failure probabilities related to the three failure modes of each gear are:

[0061] P i =P(g 1i ≤0∪g 2i ≤0∪g 3i ≤0)=P(g 1i ≤0)

[0062] +P(g 2i ≤0)+P(g 3i ≤0)-P(g 1i ≤0∩g 2i≤

[0063] 0)-P(g 1i ≤0∩g 3i ≤0)-P(g 2i ≤0∩g 3i ≤

[0064] 0)+P(g 1i ≤0∩g 2i ≤0∩g 3i ≤0)=P 1i +P 2i +

[0065] P 3i -C(P 1i ,P 2i )-C(P 1i ,P 3i )-C(P 2i ,P 3i )+

[0066] C(P 1i ,P 2i ,P 3i )

[0067] R i The reliability related to the three failure modes of the corresponding gear is as follows:

[0068]

[0069] The above is only the preferred embodiment of the present invention and is not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. Dynamic reliability modeling of gear transmission system considering multiple failure modes, characterized by: include Step 1: Identify and classify fatigue failure, wear failure and tooth breakage failure of the gear system according to the working status and environmental factors of the gear transmission system; Step 2: Use the principle of random statistics to describe the force process of the gear transmission system, and simplify the reliability modeling calculation of the failure process based on the dynamic stress borne by the gear teeth; Step 3: Use the Gamma degradation random process to describe the gear strength degradation process, derive the Gamma distribution parameters based on the material PSN curve, and establish a gear reliability model based on strength degradation; Step 4: Based on the contact mechanics theory and Hertz's theorem, the wear amount of the gear during continuous operation is calculated, and the random impact wear amount caused by the external load is described by the Poisson process. Combined with the set accuracy threshold, a wear failure reliability model is constructed; Step 5: Use the Copula function to establish the correlation model between failure modes. By introducing multidimensional state variables, the coupling effects of each failure mode are integrated into a dynamic reliability model.

2. The dynamic reliability modeling of a gear transmission system considering multiple failure modes according to claim 1 is characterized in that: The stress-time history data of the gear teeth under different working conditions are obtained through finite element analysis or dynamic simulation, and the data are fitted using statistical methods to construct a random stress process model.

3. The dynamic reliability modeling of a gear transmission system considering multiple failure modes according to claim 2 is characterized in that: The parametric form is used to construct the force random process model, in which the contact stress and bending stress formulas of the gear are as follows:

4. The dynamic reliability modeling of a gear transmission system considering multiple failure modes according to claim 1 is characterized in that: According to the classical stress interference theory, the reliability of the part when the load acts n times is:

5. The dynamic reliability modeling of a gear transmission system considering multiple failure modes according to claim 1 is characterized in that: The reliability of the gear reliability model based on strength degradation is:

6. The dynamic reliability modeling of a gear transmission system considering multiple failure modes according to claim 1, characterized in that: The failure of the gear is determined by the interference of the accumulated wear and the wear threshold. When the accumulated wear is less than the wear threshold, the gear is considered valid. According to the conditional probability, the reliability R(t) is obtained as:

7. The dynamic reliability modeling of a gear transmission system considering multiple failure modes according to claim 1 is characterized in that: The multidimensional state variables include time, load level, and temperature.

8. The dynamic reliability modeling of a gear transmission system considering multiple failure modes according to claim 1, characterized in that: The reliability of the three failure modes of gear failure is: R i =1-P i =1-[P 1i +P 2i +P 3i -C(P 1i ,P 2i )-C(P 1i ,P 3i )-C(P 2i ,P 3i )+C(P 1i ,P 2i ,P 3i )].

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