Rolling Contact Fatigue Life Test Design and Result Interpretation Methods Maintaining Compatibility of Efficiency and Reliability
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1 Rolling Contact Fatigue Life Test Design and Result Interpretation Methods Maintaining Compatibility of Efficiency and Reliability Takumi FUJITA L 1 L 5 L 1 L 5 L 1 L 5 L 1 L 1 L 1 L 5 In this report, several methods for both RCF life test design and result interpretation are introduced. These methods generate results using random numbers followed by Weibull distribution. The first method makes clear the relationship of arbitrary reliability between the minimum test numbers and the suspending time in fixed time test required at L 1 and L 5 lives. This relationship is useful to maintain the qualitative reliability and avoid excessive quantitative testing. The second method can clarify the relationship of arbitrary reliability between given test numbers and a resultant significant difference at L 1 and L 5 lives in accelerated testing. This relationship is also useful to estimate the test number based on statistical logic. Of note, applying calculations allows for estimates of the test results. The third method enables the calculations of the range of L 1 and L 5 lives with significant reliability even if the test numbers are too small to estimate L 1 or L 5 lives employing Weibull plots. The fourth method can determine the significant difference of L 1 and L 5 lives between two lots and allow the quantitative estimation of the minimum difference between their lives from data obtained by experiments. These methods provide techniques that are easier to understand as compared with the recent mathematical model, and they show enough flexibility to apply to almost all type of the testing. These new system will therefore eliminate the need for qualified experiences in the statistical design and result interpretation of RCF life test. -31-
2 L 1 e g(x)= e 1 L 1 2 L 1 L =.5 L 1 (2) L 1 L 1 L 1 g(x)= x e 1 x 5 1/ exp x 1/9 1/9 exp e x 5 72 (1) (3) Applicable contents of this method -32-
3 .95 L 1 (L 1 ) = (4) 1/e ln (1/9) G (x) = 1 exp x L 1 e L 1 L 1 e el 1 e (5) L 1 L 1 Probability 1L 1 e Flowchart to design test number in fixed time test Time (h) L1e Weibull probability density distribution for L1=5h and e=1/9-33-
4 h Time (h) L1e distribution to estimate suspending time prior to failure (Required L1 life=5h, e=1/9, Test number=6) L 1 L 1 1L 1 L 1 e L 1 L L 1 L 1 L 1 L 1 L 1 L 1 L 1 L h L 1 Life (h) L1 e distribution to estimate L1 life from the suspending time prior to failure ( e=1/9, Test number=6) 5 4 Flowchart to estimate L1 life from suspending time prior to failure -34-
5 L 1 L 1 L 1 L 1 L 1 L 1 L 1 L 1 1L 1 e L 1 L 1 L (x, y)=(.42,.5) (x, y)=(21.8,.95) L 1 life ratio 4 5 L1 e distribution of L1 life ratio ( e=1/9, Test number=3) L 1 L L 1 L L 1 Required significant difference of L1 and L5 life ratios L 5 L L 1 4 L 1 Flowchart to determine test numbers on accelerated test Test number L1L5 e Relationship between test number and required significant difference of L1 and L5 life ratios ( e=1/9) -35-
6 L 1 L 1 L 1 L 1 L 1 L 1 L 1 1L 1 e L 1 L 1 L 1 L 1 L 1 L 1 L 1 L (x, y)=(4.9,.95).2 (x, y)=(.181,.5) L 1 life ratio L1 e distribution of L1 life ratio ( e=1/9, Test number=1) 2 1L 1 L L 1 L L 1 L 1 L L 1 L 1 Flowchart to estimate the minimum life difference with respect to accelerated test results of 2 lots (x, y)=(1,.95).2 (x, y)=(.41,.5) L 1 life ratio 4 5 L1 el1 distribution of L1 life ratio ( e=1/9, Test number=1, Difference of L1 life=2.1) -36-
7 Minimum differences of L1 and L5 lives L 5 L 1 and L 5 life ratio e e e e e P e e e e e L L1L5 ( e Diagram to estimate the minimum differences of L1 and L5 lives with respect to accelerated test results of 2 lots ( e=1/9, Test number=1) e e of failure (%) Dispersion limits of Weibull slope e= Life (Loading Cycle) Pmax Example of RCF life test result (Point contact, Pmax=5.88GPa) lower limit upper limit Test number e Relationship between test number and dispersion of Weibull slope (The result is conducted as e=1/9 of life distribution) -37-
8 Normalized differential value of dispersion limits of Weibull slope lower limit upper limit Test number (a) e=1/9 Normalized differential value of dispersion limits of Weibull slope lower limit upper limit Test number (b) e=3 e e Normalized differential value of dispersion limits of Weibull slope depending on test number (e=1/9 and 3) -38-
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