Gear bending fatigue prediction method, gear contact fatigue prediction method and gear service life prediction method

Abstract

The invention relates to the field of gears. A residual stress intensity factor is introduced into a Walker model, the influence of residual stress on the crack propagation residual life is analyzed, then a crack closing coefficient is introduced to correct the Walker model, and the bending fatigue life of the gear is obtained. The roughness and the dynamic meshing force are added into the model, the dynamic abrasion loss of the gear is calculated according to the improved Archard model, and the contact fatigue life of the gear is obtained; and finally, combining the gear bending fatigue reliability distribution function with the contact fatigue reliability distribution function by adopting a Copula function, and analyzing a competitive failure relationship among different failure forms by utilizing the combined distribution function to obtain a competitive failure reliability model so as to analyze the service life of the gear. According to the technical scheme, the technical problem of comprehensively describing the reliability of the gear is solved, accurate prediction of the reliability of the gear is achieved, and research, development and design of the gear are facilitated.

Description

Technical Field

[0001] The invention relates to the field of gears, and in particular to a method for predicting gear bending fatigue, contact fatigue and gear life for automobile transmission gears. Background Art

[0002] Traditionally, the stress-strength interference theory is mainly used for reliability design. Under a certain reliability, the minimum strength (resistance) on the dangerous section of the part is guaranteed to be no less than the maximum stress. However, stress and strength are not a definite value, but a multivariate random function composed of several random variables, which shows a certain statistical distribution law. As time goes by, due to changes in various factors, the strength of the product degrades, resulting in interference between the stress and strength distribution that the product will bear at a certain time. Since the stress also changes with the use environment, it presents a certain statistical distribution; in the area where the stress and strength distribution overlap, the product will fail. The core of reliability is to complete the specified function, which depends on the result of the mutual interference between stress and strength. Therefore, traditionally, when conducting reliability prediction, the reliability of mechanical products is predicted by establishing a stress-strength interference model.

[0003] Competing failure analysis is a special type of life data analysis whose purpose is to estimate the probability of failure of a product in the presence of competing modes.

[0004] For automotive gear products, the stress distribution analysis required by traditional methods is very complicated in different situations and is affected by many factors. Therefore, the current automotive gears are more directly based on life tests and reliability evaluation based on the overall design of the application location. Since the life of the gear is affected by many factors, and the influence of bending fatigue life and contact fatigue life need to be considered at the same time, it is difficult for common reliability calculation methods to comprehensively describe the reliability of the gear. At the same time, traditional methods often ignore stress cycles, fatigue effects, and wear effects during the working process of the gear. In addition, traditional methods lack consideration of multiple failure forms, but these failure forms often affect each other. Therefore, it is difficult for traditional methods to comprehensively and accurately analyze the failure probability of the gear. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method for predicting gear bending fatigue, contact fatigue and gear life, so as to solve the technical problem that the practice of using stress-strength interference prediction methods for gear and other parts products in the prior art is very complicated, so it is rare to predict the reliability and life of gears alone, and it is also difficult to comprehensively describe the reliability of gears.

[0006] Technical Solution

[0007] A gear bending fatigue prediction method is characterized in that: a Walker model is introduced into a parameter to describe the influence of stress ratio on material fatigue life, thereby providing a more accurate fatigue life prediction, comprising the following steps: firstly, a residual stress intensity factor is introduced into the Walker model by using a superposition method, and the influence of residual stress on the remaining life of crack propagation is analyzed, and then a crack closure coefficient is introduced to correct the Walker model, and the bending fatigue life of the gear is obtained according to the improved Walker model.

[0008] During the crack propagation process, the plastic zone perpendicular to the crack direction will elongate. The growing plastic deformation has a greater impact on the stress intensity factor. The crack tends to close, making the actual load range at the crack front smaller than the theoretical load range. Therefore, the crack closure coefficient can be obtained.

[0009] Through the effective stress ratio R eff By correcting the crack closure coefficient U, the closure effect and residual stress can be considered at the same time. After considering the crack closure effect and residual stress, the fatigue crack growth residual life expression is:

[0010]

[0011] Where C' is the material coefficient, Y' is the component geometry factor, U' is the corrected crack closure coefficient, R eff is the effective stress ratio, a is the crack extension size, a c is the critical crack extension size, n' and m' are also material coefficients, σ F is the bending stress.

[0012] A gear contact fatigue prediction method is characterized in that: on the basis of the traditional Archard wear equation, roughness and dynamic meshing force are added to the model, and the dynamic wear amount of the gear is calculated according to the improved Archard model, so as to obtain the contact fatigue life of the gear.

[0013] First, the tooth profile is discretized, and the meshing point near the tooth root is taken as the starting point, and the tooth top is taken as the meshing point of the gear. The points on the involute tooth profile are discretized into multiple points according to the gear radius. Then the roughness is analyzed, and the dynamic wear coefficient considering the influence of roughness is introduced, and the dynamic meshing force is introduced into the Archard model. After a preliminary calculation of the wear amount of a certain point on the gear tooth surface in one cycle, the overall calculation is combined with the wear amount of multiple discrete points to obtain the dynamic wear amount of the gear calculated by the improved Archard model, thereby obtaining the contact fatigue life of the gear.

[0014] The steps of introducing the dynamic meshing force into the Archard model include: (1) analyzing the dynamic model of the mutual meshing action between the driving wheel and the driven wheel; (2) calculating the dynamic meshing force of the gear, the gear deformation and the ability of the gear structure to resist elastic deformation when subjected to force during one cycle according to the simulated system dynamics equation; (3) analyzing and fitting the changes of various coefficients and parameters over time from the meshing point to the meshing point, that is, the position from the root to the top of the tooth during one cycle of the gear; (4) after one cycle, using the Archard model that considers the influence of dynamic meshing force and roughness to calculate the wear of each point on the tooth surface, and using the position of the point with the largest wear to calculate the contact fatigue life of the gear.

[0015] The dynamic model of the mutual meshing action of a pair of the driving wheel and the driven wheel is simulated by using a spring model connected in parallel with each other.

[0016] A method for predicting the life of gears using the above method, characterized in that: combining the improved Walker model as described in claim 1 and the improved Archard model as described in claim 4, the bending fatigue reliability distribution function and the contact fatigue reliability distribution function of the gear are derived, and then the Copula function is used to combine the gear bending fatigue reliability distribution function and the contact fatigue reliability distribution function, and the Copula function is used to combine the derived distribution functions to analyze the competitive failure relationship between different failure forms, and a competitive failure reliability model considering gear bending and contact fatigue is obtained, and the life of the gear is analyzed based on the model.

[0017] Beneficial Effects

[0018] The present invention introduces the residual stress intensity factor into the Walker model to analyze the influence of residual stress on the remaining life of crack propagation, then introduces the crack closure coefficient to correct the Walker model, and obtains the bending fatigue life of the gear according to the improved Walker model; adds the roughness and dynamic meshing force into the model, calculates the dynamic wear of the gear according to the improved Archard model, and thus obtains the contact fatigue life of the gear; finally, the Copula function is used to combine the gear bending fatigue reliability distribution function and the contact fatigue reliability distribution function, and the combined distribution function is used to analyze the competitive failure relationship between different failure forms, and obtain a competitive failure reliability model considering gear bending and contact fatigue, so as to analyze the life of the gear. The technical solution of the present invention solves the technical problem of comprehensively describing the reliability of the gear, and at the same time, the life obtained by the competitive failure method is less than the life obtained by analyzing a certain failure form of the gear alone. This is because the method considers the mutual influence between multiple failure forms and more restores the working conditions of the gear in the actual situation. The competition of multiple failure forms will shorten the life of the gear, so the life obtained by the analysis is closer to the actual life, and the accurate prediction of the reliability of the gear is achieved, which is beneficial to the prior life prediction of the research and development design of the gear and improves the design reliability of the product. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 Schematic diagram of gear crack.

[0020] Figure 2 Schematic diagram of the relationship between crack size a and remaining life.

[0021] Figure 3 The relationship between a pair of gear pairs is simplified to a schematic diagram of a simulated spring model connected in parallel.

[0022] Figure 4 Schematic diagram of the change of driving wheel slip coefficient ∈ with time.

[0023] Figure 5 Schematic diagram of the deformation variation with time.

[0024] Figure 6 is the equivalent meshing damping c i (t) Schematic diagram of changes with time.

[0025] Figure 7 is the dynamic meshing force F i Schematic diagram of changes over time.

[0026] Figure 8 Schematic diagram of gear wear variation over time.

[0027] Fig. 9 Schematic diagram of the relationship between reliability and life of gears considering competing failures.

[0028] Fig.10 Schematic diagram of the method flow for gear life prediction. DETAILED DESCRIPTION

[0029] The present invention is further described below in conjunction with specific embodiments and drawings.

[0030] In order to solve the problems of the prior art, the inventor team of this application conducted relevant analysis specifically on gear products based on the theory of competitive failure, and proposed a method for gear bending fatigue prediction, contact fatigue prediction and gear life prediction.

[0031] Competing failure analysis is a special type of life data analysis whose purpose is to estimate the probability of failure of a product in the presence of competing modes.

[0032] Gear-type automotive parts are mainly affected by the impact stress on the fatigue life of the material itself, which is manifested in the influence of the residual stress and crack closure effect of the material after the impact on the gear crack growth rate, as well as the impact of dynamic wear of daily contact wear on the life.

[0033] Regarding the prediction of gear bending fatigue, the Walker model can be considered. The Walker model is a model used to describe the fatigue life of materials under cyclic stress, especially in the application of high-cycle fatigue and low-cycle fatigue conditions.

[0034] However, the Walker model alone cannot accurately describe the changes in stress effects. Therefore, the present invention proposes to introduce a parameter into the Walker model to describe the effect of stress ratio on material fatigue life, thereby providing a more accurate fatigue life prediction. First, the residual stress intensity factor is introduced into the Walker model using the superposition method to analyze the effect of residual stress on the remaining life of crack propagation. Then, the crack closure coefficient is introduced to correct the Walker model, and the bending fatigue life of the gear is obtained according to the improved Walker model.

[0035] Regarding the prediction of gear contact fatigue, the Archard wear equation can be considered. The Archard model is a classic model used to describe and predict material wear. The basic idea of ​​the model is that the wear volume is proportional to the positive load and sliding distance, and inversely proportional to the material hardness. This means that under the same load and sliding distance, materials with lower hardness will have higher wear volumes. However, the wear coefficient in the wear equation will change dynamically. Therefore, based on the traditional wear equation, the present invention adds roughness and dynamic meshing force into the model considerations, and obtains the contact fatigue life of the gear according to the improved Archard model.

[0036] Finally, combining the improved Walker model and the improved Archard model, the bending fatigue reliability distribution function and contact fatigue reliability distribution function of the gear are derived. Then, the Copula function is used to combine the gear bending fatigue reliability distribution function and the contact fatigue reliability distribution function. The Copula function is used to combine the distribution functions derived to analyze the competitive failure relationship between different failure forms, and a competitive failure reliability model considering gear bending and contact fatigue is obtained. Based on this model, the life of the gear is analyzed.

[0037] The specific process is as follows:

[0038] 1. Improve the Walker model to analyze the bending fatigue life of gears

[0039] The current Walker model introduces the stress ratio into the expression of crack growth rate, and the expression of fatigue crack growth remaining life can be obtained as:

[0040]

[0041] Among them, R' is the stress ratio, C' is the material coefficient, Y' is the component geometry factor, a is the crack extension size, a c is the critical crack extension size, n' and m' are also material coefficients, σ F is the bending stress.

[0042] However, after removing the external force and uneven temperature field, the internal stress remaining in the gear is called residual stress, and it may be generated during the production process. Studies have shown that residual stress will affect the service life of the gear. Residual tensile stress promotes the growth of gear cracks. The fracture propagation rate near the large end of the gear is higher than that of the small end. It is very important to consider residual stress when calculating the fatigue life of the gear. A large amount of residual stress will be generated inside the gear after quenching, and a large amount of residual stress will be eliminated by tempering. After heat treatment, the internal residual stress of the gear is about 50MPa.

[0043] Residual stress and external load do not change the magnitude of the stress intensity factor, but only the maximum stress factor and the effective stress ratio. res,le The effective stress ratio R eff Instead of the stress ratio of the Walker model, the magnitude of the stress intensity factor ΔK I , effective stress ratio R eff The expression is as follows: ΔK I =(K max +K res,le )-(K min +K res,le )=K max -K min ,

[0044] Among them, Kmax and Kmin are the maximum and minimum stress intensity factor values ​​at the crack.

[0045] The modified Walker formula after residual stress is as follows:

[0046]

[0047] According to the fracture characteristics of most gears, fracture usually occurs at the root of the tooth. The crack diagram is shown in the attached figure. Figure 1 As shown in the figure, the residual stress intensity factor is related to the crack length a and the coordinate x. By calculating the value of the residual stress intensity factor, the influence of residual stress on fatigue life at the x position is analyzed. Its expression is:

[0048]

[0049] Where m(x,a) is the weight function of the crack length a and the coordinate x, σ R (x) is the initial longitudinal residual stress distribution on the crack surface.

[0050] The weight function proposed by Kaya and Erodogan is used to calculate K res,le .

[0051] During the crack propagation process, the plastic zone perpendicular to the crack direction will elongate. The increasing plastic deformation has a greater impact on the stress intensity factor. The crack tends to close, making the actual load range at the front end of the crack smaller than the theoretical load range. Therefore, the crack closure coefficient U can be obtained:

[0052]

[0053] ΔK eff =U·ΔK I

[0054] In the formula, ΔK eff is the effective stress intensity factor, K eff is the stress intensity factor required for crack closure and opening, Δσ eff is the effective stress amplitude at the crack, and F is the geometric correction factor, which is used to correct the stress distribution of the crack.

[0055] According to the actual stress, when the stress ratio R' value is larger, the crack closure effect is smaller. Schijve corrected U based on the 2024-T3 aluminum alloy experiment and obtained: U = 0.55 + 0.35R' + 0.1R' 2 .

[0056] The present invention uses the effective stress ratio R effBy correcting the crack closure coefficient U, it is possible to consider both the closure effect and the residual stress effect. The crack closure coefficient U' considering the residual stress can be expressed as: U' = 0.55 + 0.35R eff +0.1R eff 2 .

[0057]

[0058] After considering the crack closure effect and residual stress, the fatigue crack growth remaining life expression is:

[0059]

[0060] Where U' is the corrected crack closure coefficient, R eff is the effective stress ratio, σ F is the bending stress.

[0061] The following is a comparative analysis of the improved Walker model, the traditional Walker model and the Walker model considering only residual stress after considering crack closure effect and residual stress. The variation trend of instantaneous residual life with crack size a is shown in the attached figure. Figure 2 C' is the material coefficient, which is 3.8461*10^-19 in this embodiment, and n' and m' are also material coefficients, which are 1.6 and 4.76 in this embodiment.

[0062] From the figure, it can be concluded that the fatigue crack growth stage life calculated by the Walker model is 189020 times, the fatigue crack growth stage life calculated by the Walker model considering residual stress is 188918 times, and the fatigue crack growth stage life calculated by the Walker model considering closure effect and residual stress is 253757 times.

[0063] The results of each model are shown in Table 1:

[0064] Table 1 Critical crack size and remaining crack growth life

[0065]

[0066] The predicted value of gear crack growth life predicted by the Walker model considering the closure effect and residual stress is too large. The main reason is that the closure effect will also extend the crack growth life of the gear. The calculated life of the gear will be longer than the life calculated by the original model. Therefore, it also proves that the improved Walker model is more accurate.

[0067] 2. Improve the Archard model and analyze the contact fatigue life of gears

[0068] The simulation results using the Archard wear equation are roughly close to the actual results and are widely used in the prediction of gear wear. The classic Archard wear equation is as follows:

[0069]

[0070] In the formula, h w is the wear depth, s is the sliding distance, p is the m is the average pressure in the local contact state, and k is the wear coefficient.

[0071] In order to facilitate numerical calculation, the tooth profile is discretized, the meshing point near the tooth root is taken as the starting point, the tooth top is taken as the meshing point of the gear, and the points on the involute tooth profile are discretized into 100 according to the gear radius. The wear amount of a certain point on the gear tooth surface in one cycle is expressed as:

[0072]

[0073] Where ∈ is the gear sliding coefficient, b is the tooth width, H is the hardness, and Fn is the nominal normal load of the gear tooth.

[0074] The sliding coefficients of the driving and driven gears are different. The wear amount of the entire gear after one cycle is h wone for:

[0075] Based on the classic Archard model, roughness is introduced. The volume wear caused by unit load displacement distance is expressed as the wear coefficient. As the tooth surface wears, the value of the wear coefficient also changes in real time. It is necessary to establish a dynamic wear coefficient to describe the change of the wear coefficient. The minimum oil film thickness and the root mean square of the tooth surface roughness of the master and slave gears are the main factors affecting the gear wear coefficient. Dynamic wear coefficient k w The value of can be expressed by the following formula:

[0076]

[0077] Where k0 is the wear coefficient under boundary lubrication, λ is the minimum oil film thickness H at the contact point min and the root mean square of the tooth surface roughness of the driving and driven gears The ratio of, that is:

[0078] In the formula, H min =3.63RU' 0.68 G 0.49 W -0.073 (1-e -0.68κ ),

[0079] Where R is the equivalent radius, U' is the dimensionless velocity, G is the material parameter, W is the load parameter, κ is the ellipticity factor, which can be assumed to be infinite for any spur gear contact, and R a1 , R a2 They are the tooth surface roughness of the driving and driven gears respectively.

[0080] The roughness has a great influence on the performance and service life of the parts: the rougher the surface of the gear, the greater the wear coefficient and the faster the wear. A too smooth surface will also cause the lubricant to squeeze out, increase the friction resistance and accelerate the wear. It is necessary to consider the effect of roughness on wear. When calculating the wear life of the gear, the first consideration is the effect of roughness on the wear coefficient. Dynamic wear coefficient k' considering the effect of roughness W It can be expressed as: k' W =K r k w , where K r is the surface roughness coefficient, k w is the dynamic wear coefficient.

[0081] The embodiment of the present invention adopts material 20MnCr5, which is a kind of steel material, and the relationship between its surface roughness coefficient and surface roughness factor is:

[0082]

[0083] Among them, σ b is the tensile strength, R m,N,min is the minimum tensile strength, a R is a constant, Ra is the gear tooth surface roughness, and a is taken according to the material of the embodiment. R =0.22,R m,N,min =400MPa.

[0084] Then the dynamic meshing force is introduced into the model. During the meshing process, the number of tooth pairs involved in the meshing changes with time, and the deformation of the gear also changes with the meshing position, resulting in the dynamic meshing force F i This change is evaluated by using dynamic mesh force instead of nominal normal force when calculating gear wear.

[0085] First, simplify the relationship between a pair of gear pairs into a parallel spring model, as shown in the attached figure. Figure 3 The simulated spring model is shown.

[0086] As attached Figure 3 As shown in the figure, n1 and n2 are the average speeds of the driving and driven wheels respectively; e(t) is the tooth profile error, which is the deviation of the tooth profile from the ideal involute caused by tooth profile modification, processing error and wear; δ m is the gear system clearance function; b' is the tooth side clearance; kn (t) and c i (t) are the equivalent meshing stiffness and damping of the system. Considering the friction torque, the dynamic differential equation of the system is established.

[0087] The system dynamics equation is:

[0088]

[0089] Where I1 and I2 are the moments of inertia of the driving and driven wheels, θ1(t) and θ2(t) are the angular displacements of the driving and driven wheels, T1 and T2 are the input and output torques, respectively. z Indicates the maximum number of gear pairs that are simultaneously engaged, Λ i is the symbolic function, ρ 1i , 2i are the friction arms of the driving and driven wheels at the meshing point, μ i Friction coefficient, F i is the dynamic meshing force, r b1 and r b2 The base circle radius of the master and driven wheels.

[0090] Λ j It is used to characterize the direction of the friction torque, which is consistent with the above Λ i The subscript j represents the jth pair of teeth that are simultaneously engaged.

[0091] By establishing a system dynamics equation of a spring model simulating the relationship between gear pairs, the force on the gear is calculated, as well as the deformation of each part after the force is applied, such as bending deformation of the rectangular part, bending deformation of the trapezoidal part, shear deformation, tilt deformation and contact deformation, and the ability of the gear structure to resist elastic deformation when subjected to force.

[0092] Considering the influence of dynamic meshing force and roughness on gear wear, the wear amount h' of a certain point on the tooth surface in one cycle wi The expression is:

[0093] Fi is the dynamic meshing force, k' W is the dynamic wear coefficient;

[0094] After considering the dynamic meshing force of the gear, the wear amount after one cycle is h wonei for:

[0095]

[0096] The dynamic changes of the parameters in the above formula are analyzed based on the situation of each point on the gear in a cycle of meshing. The sliding coefficient can represent the degree of relative sliding between the tooth surfaces. The change of the sliding coefficient ∈ with time is as follows Figure 4The time starts from the meshing point and ends at the meshing point, that is, the position from the tooth root to the tooth tip. Figure 5 The schematic diagram of the deformation variation over time is shown in Figure 5. The bending deformation of the rectangular part of the gear is δ Br , the bending deformation of the trapezoidal part δ Bt , shear deformation δ S , tilt deformation δ G , the gear deformation δ changes with time as shown in the figure, and the deformation increases with time. Figure 6 is the equivalent meshing damping c i (t) Schematic diagram of changes with time, Figure 7 Schematic diagram of the dynamic meshing force Fi changing with time.

[0097] After one cycle, the wear of each point on the tooth surface is calculated using the Archard model that considers the influence of dynamic meshing force and roughness. Figure 8 As shown. Figure 8 It can be seen that the wear of the gear is the largest at the starting point, that is, the meshing point at the root of the tooth. The wear of the driving gear at the starting point is 1.0252×10 -11 m, the wear amount of the driven gear at the starting point is 1.8152×10 - 13 m. The wear amount of the driving gear is greater than that of the driven gear. The wear life of the gear is calculated based on the wear amount of the driving gear.

[0098] The gear life is calculated by the wear amount of the gear at the starting point. -6 m is considered to be failed. The contact fatigue life calculated by the Archard model is 134911 times, the contact fatigue life calculated by the Archard model considering the influence of roughness is 91481 times, and the contact fatigue life calculated by the Archard model considering the influence of dynamic meshing force and roughness is 585227 times. The results of each model are shown in Table 2:

[0099] Table 2 Wear loss and contact fatigue life of each model

[0100]

[0101] The first gear of the dual-clutch automatic transmission was replaced after 480,000 runs. The gear contact fatigue life calculated by the Archard model taking into account the effects of dynamic meshing force and roughness was more realistic than that without improvement, and the gear wear life was also predicted more accurately.

[0102] 3. Combining the two improved models, introducing the Copula function joint analysis, and deriving the gear reliability model

[0103] Since the life of gears is affected by many factors, and the influence of bending fatigue life and contact fatigue life need to be considered at the same time, it is difficult for general reliability calculation methods to comprehensively describe the reliability of gears. The Copula function is introduced to simultaneously judge the bending fatigue and contact fatigue reliability of transmission gears and analyze the competitive failure reliability of gears.

[0104] Copula functions are mainly divided into three categories: Archimedean Copula functions, elliptic Copula functions, and extreme value Copula functions. Archimedean Copula functions can be further divided into Gumbel Copula, Frank Copula, and Clayton Copula according to the different generators. These three Copula functions have their own applicable intervals. The Gumbel Copula function is more sensitive to the maximum interval, the Clayton Copula function is more sensitive to the minimum interval, and the Frank Copula function is more applicable to the situation where the maximum and minimum values ​​appear at the same time. The elliptic Copula function is mainly divided into Gaussian Copula function and t Copula function. These two functions are determined according to the normal distribution and are more applicable to the situation where the maximum and minimum values ​​appear at the same time. The extreme value Copula function expands to high dimensions to construct functions based on extreme values.

[0105] The present invention uses the Gumbel Copula function to analyze the competitive failure reliability of gears, and the expression is:

[0106]

[0107] Where θ is the parameter of the Copula function, and its value range is [1,+∞).

[0108] When calculating the Copula function, we need to analyze the θ value. This step is parameter estimation. The present invention adopts the maximum likelihood estimation method as the parameter estimation method.

[0109] The competitive failure reliability of gears is analyzed by introducing the Copula function to analyze the correlation between the bending fatigue failure reliability and the contact fatigue failure reliability of gears. The gear reliability Rc after considering competitive failure can be expressed as:

[0110] R c =1-P f1 -P f2 +C(P f1 , P f2 )

[0111] Where P f1 , P f2 is the gear bending fatigue failure unreliability and contact fatigue failure unreliability, which together with the reliability Rf1 , R f2 The relationship between them is: f1 =1-R f1 , P f2 =1-R f2

[0112] In the automotive industry, when the reliability of automotive parts reaches 95% or higher, the parts are in a relatively safe working state. After analysis and calculation, when the reliability of the gear is 100%, the life is 254355 times. When the failure reliability reaches below 95% for the first time, the gear life at this time is 329541 times, which is the gear life determined based on the competitive failure method. The relationship between gear competitive failure reliability and life is as follows Fig. 9 Indicates.

[0113] After calculation, the life of the first gear is shown in Table 3:

[0114] Table 3 Life of first gear

[0115]

[0116]

[0117] As shown in Table 3, the life of the first gear driving gear of the dual clutch automatic transmission determined by the competitive failure method is shorter than the life obtained by analyzing a certain failure mode of the gear alone. The competition of multiple failure modes of the gear will shorten the gear life, making the actual gear life shorter than the life obtained by analyzing a single failure mode. The gear life determined based on the competitive failure reliability method is more accurate, which proves the correctness of the proposed method in estimating the gear life.

[0118] The method proposed in the present invention is used to analyze the life of other gears in the automatic transmission, and the specific values ​​are shown in Table 4.

[0119] Table 4 Life of gears in other gears

[0120]

[0121] The above values ​​have been verified to be consistent with the expected requirements and actual conditions. The predictions obtained using the method of the present invention are more accurate and can be of great help in part design.

[0122] The parameters of the car and gear used in this embodiment are as follows:

[0123] Main parameters of the vehicle

[0124]

[0125] Gear material parameters

[0126]

[0127] Basic parameters of gear

[0128]

[0129]

[0130] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A gear bending fatigue prediction method, characterized by: The Walker model introduces a parameter to describe the influence of stress ratio on material fatigue life, thereby providing a more accurate fatigue life prediction, including the following steps: the first step is to introduce the residual stress intensity factor into the Walker model using the superposition method, and analyze the influence of residual stress on the remaining life of crack propagation; the second step is to introduce the crack closure coefficient into the Walker model, and analyze the influence of crack closure effect on the bending fatigue life of gears, so as to modify the model; the third step is to obtain the bending fatigue life of gears according to the improved Walker model.

2. The gear bending fatigue prediction method according to claim 1, characterized in that: In the second step, during the crack propagation process, the plastic zone perpendicular to the crack direction will elongate, and the growing plastic deformation will have a greater impact on the stress intensity factor. The crack tends to close, making the actual load range at the front end of the crack smaller than the theoretical load range. Therefore, the crack closure coefficient can be obtained.

3. The gear bending fatigue prediction method according to claim 2, characterized in that: Through the effective stress ratio R eff By correcting the crack closure coefficient U, the closure effect and residual stress can be considered at the same time. After considering the crack closure effect and residual stress, the fatigue crack growth residual life expression is: Where C' is the material coefficient, Y' is the component geometry factor, U' is the corrected crack closure coefficient, R eff is the effective stress ratio, a is the crack extension size, a c is the critical crack extension size, n' and m' are also material coefficients, σ F is the bending stress.

4. A gear contact fatigue prediction method, characterized in that: On the basis of the traditional Archard wear equation, roughness and dynamic meshing force are added to the model. The dynamic wear of the gear is calculated according to the improved Archard model, so as to obtain the contact fatigue life of the gear.

5. The gear contact fatigue prediction method according to claim 4, characterized in that: First, the tooth profile is discretized, and the meshing point near the tooth root is taken as the starting point, and the tooth top is taken as the meshing point of the gear. The points on the involute tooth profile are discretized into multiple points according to the gear radius. Then the roughness is analyzed, and the dynamic wear coefficient considering the influence of roughness is introduced, and the dynamic meshing force is introduced into the Archard model. After a preliminary calculation of the wear amount of a certain point on the gear tooth surface in one cycle, the overall calculation is combined with the wear amount of multiple discrete points to obtain the dynamic wear amount of the gear calculated by the improved Archard model, thereby obtaining the contact fatigue life of the gear.

6. The gear contact fatigue prediction method according to claim 5, characterized in that: The steps of introducing the dynamic meshing force into the Archard model include: (1) analyzing the dynamic model of the mutual meshing action between the driving wheel and the driven wheel; (2) calculating the dynamic meshing force of the gear, the gear deformation and the ability of the gear structure to resist elastic deformation when subjected to force during one cycle according to the simulated system dynamics equation; (3) analyzing and fitting the changes of various coefficients and parameters over time from the meshing point to the meshing point, that is, the position from the root to the top of the tooth during one cycle of the gear; (4) after one cycle, using the Archard model that considers the influence of dynamic meshing force and roughness to calculate the wear of each point on the tooth surface, and using the position of the point with the largest wear to calculate the contact fatigue life of the gear.

7. The gear contact fatigue prediction method according to claim 6, characterized in that: The dynamic model of the mutual meshing action of a pair of the driving wheel and the driven wheel is simulated by using a spring model connected in parallel with each other.

8. A method for predicting gear life using the method according to claims 1 and 4, characterized in that: In combination with the improved Walker model as described in claim 1 and the improved Archard model as described in claim 4, the bending fatigue reliability distribution function and the contact fatigue reliability distribution function of the gear are derived. Then, the Copula function is used to combine the gear bending fatigue reliability distribution function and the contact fatigue reliability distribution function. The Copula function is used to combine the derived distribution functions to analyze the competitive failure relationship between different failure forms, and a competitive failure reliability model considering gear bending and contact fatigue is obtained. Based on this model, the life of the gear is analyzed.

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