ITS Technology Knowledge: Correction Factor a1 for Fatigue Life of Rolling Bearing
Reliability coefficient calculation of rolling bearing
Abstract: the reliability coefficient a of rolling bearing under different reliability and different life dispersion coefficient is deduced and calculated for use in the life calculation of rolling bearing.
Key words: bearing reliablility, bearing life, correction coefficient
1. Introduction
More than 40 years ago, Swedish scholars Lundberg and Palmgrn studied the service life of rolling bearings by using the theory of mathematical statistics. For a batch of bearings, 90% of the service life that can be achieved is called the rated service life, which is represented by L10. The relationship between L10 and bearing load is
C is the basic rated load and P is the equivalent dynamic load.
With the continuous development of science and technology, the requirements for the reliability of rolling bearing are higher and higher, so the accuracy of its calculation is also improved. In addition, with the continuous improvement of bearing steel quality and processing methods, the actual life of the bearing is higher than the calculated rated life. In 1997, the international standard ISO began to modify formula (1), and the modified fatigue life formula is
Ln - Corrected rated life with reliability of (1-N)%
a1 - Reliability coefficient
a2 - Material coefficient
a3 - Service condition or lubrication coefficient
In this paper, the value of life correction coefficient a1 is deduced and calculated.
2. Analysis and Calculation of a1
2.1 Weibull Distribution of Bearing Life
A large number of bearing fatigue tests show that even if the load, speed, lubrication and environmental conditions are exactly the same, the same bearing has different life. Through the statistical analysis of a large number of fatigue life test data of rolling bearings, it is found that the bearing life basically obeys the three parameter Weibull distribution, namely,
F(Ln) - Probability of bearing failure when tested to Ln
Ln - Bearing Life
L0 - Minimum bearing life
Lβ - Bearing characteristic life
e - Base of natural logarithm
α - The smaller the Weibull distribution slope (also known as the discrete coefficient of bearing life) α , the greater the discrete of bearing life; The larger the α, the smaller the dispersion of bearing life. For general bearing steel, α is 1.1 - 1.5. The better the quality of steel, the greater the α, and the larger the α value can be obtained by vacuum smelting steel.
In 1962, American scholar Talian analyzed the test data of the bearing and found that the service probability was 0.40-0.93, the life distribution parameter is very consistent with the two parameter Weibull distribution. Namely,
However, the test data within the range of failure probability F (Ln) > 0.6 and F (Ln) < 0.07 deviate from the two parameter distribution law. Through the test, Taliant found that when the failure probability F (Ln)< 0.1, there is an extremely important minimum life Lmin of the bearing. There are two reasons for the existence of Lmin. One is that it takes a period of time before fatigue pitting corrosion occurs on the surface. The other is that the modern testing technology used in bearing steel smelting and bearing processing can detect the sundries and serious structural defects in the material in advance, So as to eliminate the risk of early fatigue failure. The durability test shows that the minimum service life is about 5% of the rated service life. Namely,
Roller bearing: Lmin=L0=0.053L10
Ball bearing: Lmin=L0=0.05L10
General approximation: Lmin=L0=0.05L10
2.2 Calculation of a l
In order to simplify the calculation, assuming a 2 = a 3 = 1, the two parameter and three parameter distributions are deduced, that is, the expression of a 1 is obtained
The a1 values under different a values and different reliability conditions can be calculated from equations (5) and (6). The A1 values are shown in Table 1.
Table 1 Calculation of a l
It can be seen from Table 1 that when the reliability R is constant, the value of a1 depends on the increase of a, and a1 also increases. When a is constant, a1 decreases with the increase of reliability R, that is, the higher the requirement of reliability R, the smaller the value of a1, and the smaller the rated life of the bearing.
Table 2 a1 values given by ISO
The reliability coefficient a1 recommended by ISO is shown in Table 2. Compared with table 1, the value of a1 in Table 2 is based on a = 1.5 and two parameter Weibull distribution function. It can be seen from table 1 that the value of a1 calculated according to the two parameter distribution is smaller than that calculated according to the three parameter distribution. This is because in the two parameter distribution, it is assumed that L0= 0, that is, the shortest life is 0, but in fact L0 is not 0. Therefore, when the use probability R < 0.99, it is safer to calculate according to the two parameter distribution. If R > = 0.99. The calculated a1 value may be less than 0.5. At this time, it should be calculated as a1 = 0.05, because the non-destructive life of the bearing is 0.5L10. In addition, it should be pointed out that the value of a is related to the material of bearing steel and bearing processing method. a = 1.5 in ISO is taken because the quality and processing level of bearing steel in developed countries are high, but there is still a gap in these aspects in China. A should not be taken as 1.5, which should be selected according to the actual situation.
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