The limit state equations of each gear tooth and each failure mode contain a common random variable T, which acts as the failure common factor [3], which triggers the failure correlation of each module of the equivalent system. The research results of the application literature [4] and the literature [5] can be seen that the gear tooth state (reliable or failure) is statistically related due to the common torque T, and the degree of failure correlation is related to the dispersion of the working torque and the dispersion of the strength of each tooth. It is proportional to the variance of the working torque and inversely proportional to the variance of the strength of each tooth. Only when the working torque is constant (variance of zero) and the strength of each tooth is independent, the state of each tooth is statistically independent.
The failure correlation of each tooth state leads to an increase in the probability that each tooth has an anti-root root bending fatigue safety margin Gi1 and an anti-tooth surface contact fatigue safety margin Gi2 in the probability space, so that each tooth and each mode The combined failure probability and joint reliability probability increase simultaneously, which has a great impact on gear reliability analysis. Since the equivalent system of the gear is a series system, and the reliability of the series system is equal to the joint reliability probability of each module, the failure correlation will lead to an increase in gear reliability compared with the failure independent assumption. When the failure is completely correlated, the gear reliability Reaches the maximum value. Usually, the degree of failure correlation is between statistical independence and complete correlation, so the actual reliability of the gear should be between the reliability of the module independent hypothesis and the assumption of complete correlation of the module. Gear strength reliability analysis model According to the load) strength interference theory, the damage of each unit in the structure is the result of the load greater than its strength. The structural reliability is the reflection of the contradictory effect of each unit performance and environmental load on the probability measure space. . Let the intensity of each tooth be independent and identically distributed. Under the assumption of failure independence, the gear strength reliability R=[F2j=1Q]0fT(T)Qsij(T)0fRij(rij)drijdT]n can be obtained from equation (1). 6) where fT(T) shows the probability density function of the working torque T.
The discrete value T of a gear transmission torque T is 110000, 259260, 275670, 292080, 320000 (Nmm). The probability values ​​corresponding to each discrete value are 0105, 0110, 0160, 0115, 0110. Pinion speed n1= 970r/min, tooth width b=35mm, gear ratio L=3, number of teeth z1=25, modulus m=3mm, size gear material is 40Cr steel, root bending fatigue strength r1 obeys mean value, standard deviation is 680MPa, The normal distribution of 85MPa, the correlation coefficient is 0187; the contact fatigue strength r2 of the tooth surface obeys the normal distribution with the mean and standard deviation of 1035MPa and 56MPa respectively, the correlation coefficient is 0192. The manufacturing precision is 7 and the gear surface roughness is Rz=312Lm. The load has a small impact, one-way transmission, when the 50e is selected, the kinematic viscosity is 810@10-7m2/s, and the reliability of the gear is calculated.
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