A time-varying reliability assessment method for fatigue fracture of surface-strengthened gear tooth surfaces

Abstract

The present invention discloses a method for evaluating the time-varying reliability of the fatigue fracture of the tooth surface of a surface-strengthened gear, including: calculating the surface contact pressure of the gear according to the tooth surface load sequence, and obtaining the mean and variance of the surface contact pressure distribution of the gear by fitting with the normal distribution function; determining the functional relationship between the principal shear stress and the pressure distribution; calculating the fatigue fracture risk position of the tooth surface according to the tooth surface pressure and the performance parameters of the gear hardened layer, and obtaining the depth Z of the position with the maximum failure risk max ; calculating the equivalent stress distribution at the position with the maximum failure risk; determining the initial local shear strength of the gear, and the local shear strength of the fatigue fracture of the tooth surface can be expressed as a function of hardness; establishing a gear strength degradation function according to the damage accumulation criterion and the strength degradation theory; calculating the time-varying reliability of the fatigue fracture of the gear tooth surface according to the stress-strength interference theory and the fuzzy number function. The present invention is helpful for the anti-fatigue design of surface-strengthened gears and can improve the safety and reliability of the transmission system of high-end equipment.

Description

Technical Field

[0001] The present invention relates to the technical field of gear transmission, and in particular to a method for evaluating the reliability of tooth surface fatigue fracture of surface-strengthened gears represented by carburizing, nitriding, etc. in the gear transmission reliability evaluation technology. Background Art

[0002] As large-modulus surface-strengthened gears represented by wind turbine gears develop towards high load and high torque density, higher requirements are placed on the reliability of gear transmission. Tooth surface fatigue fracture, as a fatigue failure form unique to surface-strengthened gears, is significantly different from contact fatigue failures such as micropitting and spalling. The main crack of tooth surface fracture damage initiates deep below the tooth surface, then expands toward the surface and core, and eventually leads to complete damage to the entire gear tooth. Even if the pitting and bending fatigue strength design standard loads are within the allowable value range, tooth surface fatigue fracture failure will still occur, posing a serious threat to the reliability of the gear transmission system. There are relatively mature methods for traditional contact and bending fatigue reliability assessment, but there are few reports on tooth surface fatigue fracture reliability calculation methods. High-reliability and high-torque density wind turbine gearboxes are indispensable core components of large-megawatt wind turbines. The reliability assessment of gear transmission needs to fully consider the influence of multiple failure forms such as contact fatigue, bending fatigue and tooth surface fatigue fracture. The development of tooth surface fatigue fracture reliability calculation methods is of great significance to the reliability assessment and optimization of gearbox transmission systems. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a time-varying reliability assessment method for fatigue fracture of surface-strengthened gear tooth surfaces, which is helpful for the anti-fatigue design of surface-strengthened gears and can improve the safety and reliability of transmission systems of high-end equipment, in view of the shortcomings of the existing technology.

[0004] In order to solve the above technical problems, the present invention adopts the following technical solutions.

[0005] A time-varying reliability assessment method for fatigue fracture of surface-strengthened gear tooth surface comprises the following steps:

[0006] Step S1, calculating the gear surface contact pressure according to the tooth surface load sequence obtained from the fan load spectrum, and obtaining the mean and variance of the gear surface contact pressure distribution by fitting the normal distribution function;

[0007] Step S2, calculating the stress function inside the gear according to the elastic contact stress theory in contact mechanics, the stress function represents the mapping relationship between any point inside the gear and the surface pressure, and combining with the maximum principal shear stress criterion, determining the functional relationship between the principal shear stress and the pressure distribution, and further obtaining the distribution of the principal shear stress;

[0008] Step S3: Calculate the risk position of fatigue fracture of the tooth surface according to the tooth surface pressure and the performance parameters of the gear hardened layer, and obtain the depth Z of the position with the maximum failure risk. max ;

[0009] Step S4: according to the depth Z max and the stress function, calculating the equivalent stress distribution at the location of the maximum failure risk;

[0010] Step S5, determining the initial local shear strength of the gear, the local shear strength of the tooth surface fatigue fracture can be expressed as a function of hardness;

[0011] Step S6, establishing a gear strength degradation function according to the damage accumulation criterion and the strength degradation theory;

[0012] Step S7: Calculate the time-varying gear surface fatigue fracture reliability according to stress-strength interference theory and fuzzy number function.

[0013] In the time-varying reliability assessment method for fatigue fracture of surface-strengthened gear tooth surface disclosed in the present invention, the risk position along the depth direction of the tooth surface is found by calculating the material exposure coefficient, the equivalent shear stress of the point is calculated, and the fatigue fracture reliability of the tooth surface is calculated by combining the residual stress and the local strength degradation curve through a fuzzy function. Compared with the prior art, the beneficial effect of the present invention is that: since the influence of the tooth surface pressure distribution, the hardness of the gear hardened layer and the residual stress in the tooth surface fatigue fracture is taken into account, the present invention can incorporate the geometric design parameters and heat treatment process parameters of the gear into the reliability analysis of tooth surface fatigue fracture, optimize the gear design method and manufacturing process through time-varying reliability assessment, effectively improve the anti-fatigue performance of the gear, and promote the improvement of the load-bearing capacity and safety of the gear transmission system. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 is a flow chart of the evaluation method of the present invention;

[0015] Figure 2 is the time series loading diagram;

[0016] Figure 3 is a functional diagram of the principal shear stress and pressure distribution;

[0017] Figure 4 It is the risk factor diagram of fatigue fracture of tooth surface;

[0018] Figure 5 It is the reliability diagram of tooth surface fatigue fracture with different tooth surface hardness;

[0019] Figure 6 It is the fatigue fracture reliability diagram of tooth surface with different core hardness;

[0020] Figure 7This is the fatigue fracture reliability diagram of the tooth surface with different hardened layer depths. DETAILED DESCRIPTION

[0021] The present invention is described in more detail below with reference to the accompanying drawings and embodiments.

[0022] The present invention discloses a time-varying reliability assessment method for fatigue fracture of surface-strengthened gear tooth surface, see Figure 1 , which includes the following steps:

[0023] Step S1, calculating the gear surface contact pressure according to the tooth surface load sequence obtained from the fan load spectrum, and obtaining the mean and variance of the gear surface contact pressure distribution by fitting the normal distribution function;

[0024] Step S2, calculating the stress function inside the gear according to the elastic contact stress theory in contact mechanics, the stress function represents the mapping relationship between any point inside the gear and the surface pressure, and combining with the maximum principal shear stress criterion, determining the functional relationship between the principal shear stress and the pressure distribution, and further obtaining the distribution of the principal shear stress;

[0025] Step S3: Calculate the risk position of fatigue fracture of the tooth surface according to the tooth surface pressure and the performance parameters of the gear hardened layer, and obtain the depth Z of the position with the maximum failure risk. max ;

[0026] Step S4: according to the depth Z max and the stress function, calculating the equivalent stress distribution at the location of the maximum failure risk;

[0027] Step S5, determining the initial local shear strength of the gear, the local shear strength of the tooth surface fatigue fracture can be expressed as a function of hardness;

[0028] Step S6, establishing a gear strength degradation function according to the damage accumulation criterion and the strength degradation theory;

[0029] Step S7: Calculate the time-varying gear surface fatigue fracture reliability according to stress-strength interference theory and fuzzy number function.

[0030] In the above method, the risk position along the depth direction of the tooth surface is found by calculating the material exposure coefficient, the equivalent shear stress at the point is calculated, and the fatigue fracture reliability of the tooth surface is calculated by combining the residual stress and the local strength degradation curve through the fuzzy function. Compared with the prior art, the beneficial effect of the present invention is that: since the influence of the tooth surface pressure distribution, the hardness of the gear hardened layer and the residual stress in the tooth surface fatigue fracture is taken into account, the geometric design parameters and heat treatment process parameters of the gear can be incorporated into the tooth surface fatigue fracture reliability analysis, and the gear design method and manufacturing process can be optimized through time-varying reliability evaluation, which effectively improves the anti-fatigue performance of the gear and promotes the improvement of the load-bearing capacity and safety of the gear transmission system.

[0031] For step S1, the gear surface contact pressure is calculated according to the tooth surface load sequence obtained from the fan load spectrum, and the gear surface pressure distribution p is obtained by fitting the normal distribution function. H The mean μ 1 With variance s 1 , the distribution is expressed as:

[0032] p H ~N(μ 1 ,s 1 2 );

[0033] For step S2, the stress function inside the gear is calculated according to the elastic contact stress theory in contact mechanics. The stress function represents the mapping relationship between any point inside the gear and the surface pressure. Combined with the maximum principal shear stress criterion, the functional relationship between the principal shear stress and the surface pressure can be determined as follows:

[0034] τ H =k 1 (x,z)p H ;

[0035] Where z represents the coordinate along the depth direction;

[0036] According to the operational properties of normal distribution, for any given point, the distribution of the principal shear stress can be determined as:

[0037] τ H ~N(k 1 μ 1 , (k 1 s 1 ) 2 );

[0038] Where N represents the standard normal distribution, k 1 It represents the mapping relationship between stress components and surface pressure, which can be specifically expressed as:

[0039]

[0040] x and z represent the coordinates of any point on the subsurface in the horizontal direction and depth direction respectively. The stress components can be further expressed by coefficients m and n as follows:

[0041]

[0042] In step S3, the risk position of fatigue fracture of the tooth surface is calculated according to the tooth surface pressure and the performance parameters of the gear hardened layer, and the depth Z of the position with the maximum failure risk is obtained. maxThe risk position of tooth surface fatigue fracture failure is recorded in ISO / TS6336-4 Calculation of load capacity of spur gears and helical gears - Calculation of load capacity of tooth surface fatigue fracture max evaluation method.

[0043] As a preferred method, in step S4, according to the depth Z max and stress function, calculate the equivalent stress distribution at the location with the maximum failure risk. The relationship between the equivalent stress, surface pressure and principal shear stress is: Therefore, the equivalent stress distribution established is:

[0044] τ eq ~N[(k 2 +k 3 )μ 1 , (k 2 2 +k 3 2 )s 1 2 ] (3)

[0045] Among them, k 2 =0.149 / (0.4Z max +1.54), k 3 =k 1 k 2 .

[0046] In step S5 of this embodiment, the initial local shear strength of the gear is determined, and the local shear strength of the tooth surface fatigue fracture is expressed as a function of hardness:

[0047] r(0)=0.416HV(z) (4)

[0048] Among them, z represents the coordinate along the depth direction, HV(z) is the hardness gradient function, which can be directly measured by a microhardness tester or formulated according to an empirical formula. The empirical formula of the hardness gradient function is recorded in the document "ISO / TS6336-4 Calculation of load-bearing capacity of spur gears and helical gears - Calculation of load-bearing capacity of tooth surface fatigue fracture".

[0049] For step S6, a gear strength degradation function is established according to the damage accumulation criterion and strength degradation theory:

[0050]

[0051] Through this formula, we can get the function of strength r changing with time, which is the source of time-varying reliability in this embodiment. Where t represents the time the gear has been running, L sIt represents the design life of the gear, which is usually 25 years for offshore wind power gearboxes. m is a parameter representing the degradation of material properties. For commonly used gear steels, m=0.023. The method for obtaining the material parameters is recorded in Copula-function-basedanalysis model and dynamic reliability of a gear transmission system considering failure correlations, Wei et al., Fatigue Fract Eng Mater Struct. 42: 114-128, 2019. (Copula-function-based analysis model and dynamic reliability of a gear transmission system considering failure correlations, Wei et al., Fatigue Fract Eng Mater Struct. 42: 114-128, 2019.)

[0052] Regarding step S7, the time-varying tooth surface fatigue fracture reliability of the gear is calculated according to the stress-strength interference theory and the fuzzy number function. The calculation formula is as follows:

[0053]

[0054] Where Φ(·) represents the standard normal distribution function, μ and s represent the mean and variance of the gear equivalent stress distribution, respectively.

[0055] Based on the above technical solution, the present invention provides the following embodiments:

[0056] Embodiment 1

[0057] The first parallel gear pair of a 2MW wind turbine gearbox is selected, and the main geometric and operating parameters of the gear are as follows:

[0058]

[0059]

[0060] Specifically in this embodiment:

[0061] Step S1, according to Figure 2 The time series load shown is used to calculate the gear surface contact pressure. The mean of the tooth surface contact pressure distribution is 714.7 and the variance is 175.1 through normal distribution function fitting. The tooth surface pressure can be divided into p H ~N(714.7,175.1 2 );

[0062] Step S2, calculate the gear stress component according to formula (3), and combine the maximum principal shear stress criterion to obtain the functional relationship between the principal shear stress and the pressure distribution, such as Figure 3 As shown;

[0063] Step S3, calculate the risk position of tooth surface fatigue fracture according to the tooth surface pressure and gear hardening layer performance parameters, such as Figure 4 As shown, the depth Z of the location with the maximum failure risk can be obtained. max =3.6mm.

[0064] Step S4: according to the depth Z max and the maximum principal shear stress distribution, calculate the equivalent stress distribution at the location of the maximum failure risk, and Figure 3 The stress function relationship in the depth Z max The relationship between the principal shear stress and the tooth surface pressure is τ H =0.12p H , then according to formula (3), the equivalent stress distribution can be calculated as τ eq ~N[40.02,8.82 2 ];

[0065] Step S5, according to the empirical formula of hardness gradient function recorded in the document "ISO / TS6336-4 Calculation of load capacity of spur gears and helical gears - Calculation of load capacity of tooth surface fatigue fracture", given the surface hardness, core hardness and effective hardened layer depth, calculate the hardness gradient function, and obtain the local strength distribution according to the hardness gradient;

[0066] Step S6, calculate the strength degradation function according to formula (5):

[0067]

[0068] Where HV(3.6) represents the hardness value at a depth of 3.6 mm, σ max Indicates the peak cyclic stress, L s Indicates life span.

[0069] Step S7, calculate the time-varying tooth surface fatigue fracture reliability of the gear according to formula (6), take the surface hardness (HVCASE) of 680HV, 700HV, 720HV, the core hardness (HVCORE) of 380HV, 400HV, 440HV, the effective hardened layer depth (CHD) of 2.0mm, 2.2mm, 2.4mm, and obtain nine groups of different hardness gradient data. The corresponding time-varying tooth surface fatigue fracture degree distribution is calculated as follows: Figure 5-Figure 7As shown. When the surface hardness is 680HV and the core hardness is 420HV, the depth of the hardened layer decreases from 2.4mm to 2.0mm, and the corresponding initial tooth surface fatigue fracture reliability decreases from 0.999985 to 0.999229. The reliability changes to 0.999971 and 0.998729 after 25 years. When the depth of the hardened layer is 2.2mm and the core hardness is 420HV, the initial tooth surface fatigue fracture reliability under the three parameters of surface hardness 680HV, 700HV and 720HV are 0.999877, 0.999623 and 0.999092 respectively, and the reliability changes to 0.999775, 0.999354 and 0.998523 after 25 years. When the surface hardness is 680HV and the depth of the hardened layer is 2.2mm, the initial tooth surface fatigue fracture reliability under the three parameters of surface hardness 380HV, 400HV and 420HV are 0.999912, 0.999905 and 0.999877 respectively, and the reliability changes after 25 years are 0.999863, 0.999838 and 0.999775. It can be seen that the influence of hardened layer parameters on the tooth surface fatigue fracture reliability is consistent with the change trend in engineering practice.

[0070] Based on the above scheme, it can be seen that the present invention takes into account the influence of tooth surface pressure distribution, gear hardening layer hardness and residual stress in tooth surface fatigue fracture, and can incorporate the geometric design parameters and heat treatment process parameters of the gear into the tooth surface fatigue fracture reliability analysis. Through time-varying reliability evaluation, the gear design method and manufacturing process are optimized, which effectively improves the gear fatigue resistance and promotes the improvement of the load-bearing capacity and safety of the gear transmission system.

[0071] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions or improvements made within the technical scope of the present invention should be included in the scope of protection of the present invention.

Claims

1. A time-varying reliability assessment method for fatigue fracture of surface-strengthened gear tooth surface. It is characterized in that The steps include: Step S1, calculating the gear surface contact pressure according to the tooth surface load sequence obtained from the fan load spectrum, and obtaining the mean and variance of the gear surface contact pressure distribution by fitting the normal distribution function; Step S2, calculating the stress function inside the gear according to the elastic contact stress theory, combining the maximum principal shear stress criterion, determining the functional relationship between the principal shear stress and the pressure distribution, and further obtaining the distribution of the principal shear stress; Step S3: Calculate the risk position of fatigue fracture of the tooth surface according to the tooth surface pressure and the performance parameters of the gear hardened layer, and obtain the depth Z of the position with the maximum failure risk. max ; Step S4: according to the depth Z max and the stress function, calculating the equivalent stress distribution at the location of the maximum failure risk; Step S5, determining the initial local shear strength of the gear, the local shear strength of the tooth surface fatigue fracture can be expressed as a function of hardness; Step S6, establishing a gear strength degradation function according to the damage accumulation criterion and the strength degradation theory; Step S7: Calculate the time-varying gear surface fatigue fracture reliability according to stress-strength interference theory and fuzzy number function.

2. The time-varying reliability evaluation method for fatigue fracture of surface-strengthened gear tooth surface according to claim 1, It is characterized in that In step S1, the gear surface pressure distribution p is obtained by fitting the normal distribution function. H The mean μ 1 With variance s 1 , the distribution is expressed as: p H ~N(μ 1 ,s 1 2 )。 3. The time-varying reliability evaluation method for fatigue fracture of surface-strengthened gear tooth surface according to claim 1, It is characterized in that In step S2, the functional relationship between the principal shear stress and the surface pressure is determined as: τ H =k 1 (x,z)p H 4 According to the operational properties of normal distribution, for any given point, the distribution of the principal shear stress can be determined as: t H ~N(k 1 m 1 ,(k 1 s 1 ) 2 ); Where N represents the standard normal distribution, k 1 It represents the mapping relationship between stress components and surface pressure, which can be specifically expressed as: x and z represent the coordinates of any point on the subsurface in the horizontal direction and depth direction respectively. The stress components can be further expressed by coefficients m and n as follows:

4. The time-varying reliability evaluation method for fatigue fracture of surface-strengthened gear tooth surface according to claim 1, It is characterized in that In step S4, according to the relationship between the equivalent stress, the surface pressure and the principal shear stress, the equivalent stress distribution is established as follows: t eq ~N[(k 2 +k 3 )m 1 ,(k 2 2 +k 3 2 )s 1 2 ]; Among them, k 2 =0.149 / (0.4Z max +1.54), k 3 =k 1 k 2 .

5. The time-varying reliability evaluation method for fatigue fracture of surface-strengthened gear tooth surface according to claim 3, It is characterized in that In step S5, the initial local shear strength of the gear is determined. The local shear strength of the tooth surface fatigue fracture can be expressed as a function of the hardness: r(0)=0.416HV(z); Where HV(z) is the hardness gradient function.

6. The time-varying reliability evaluation method for fatigue fracture of surface-strengthened gear tooth surface according to claim 1, It is characterized in that In step S6, the gear strength degradation function established according to the damage accumulation criterion and the strength degradation theory is: Where t represents the time the gear has been running, σ max Indicates the peak stress, L s represents the design life of the gear, and m represents the material performance degradation parameter.

7. The time-varying reliability evaluation method for fatigue fracture of surface-strengthened gear tooth surface according to claim 1, It is characterized in that In step S7, the calculation formula for the time-varying tooth surface fatigue fracture reliability of the gear is: Where Φ(·) represents the standard normal distribution function, μ and s represent the mean and variance of the gear equivalent stress distribution, respectively.

Images