Study on the P-S-N Curve of Sucker Rod Based on Three-Parameter Weibull Distribution

Abstract

During the oil production process, sucker rods are subjected to cyclic alternating load. After a certain number of cycles, a sucker rod can experience fatigue failure. The number of cycles is called fatigue life (N), and the accurate relationship between maximum stress (S) and fatigue life (N) under a certain reliability (P), namely the P-S-N curve, is an important basis for the reliability analysis and fatigue life prediction of sucker rods. The Basquin model, based on log-normal distribution, is widely used for fitting the P-S-N curves of sucker rods. Due to the limitation of this model, it is difficult to extrapolate the conclusion obtained from a finite fatigue region to the high-cycle or ultra-high-cycle fatigue region, which makes it impossible to estimate the fatigue limit of the sucker rod. Compared to the log-normal distribution, Weibull distribution causes the sucker rod to have a minimum safety life, namely the safety life at 100% survival rate, which complies with the fatigue characteristics of the sucker rod and is more in line with the actual situation. In this study, the fatigue data for ultra-high-strength HL and HY grade sucker rods were obtained through experimental fatigue tests. A new fatigue life model was established and the P-S-N curves of two types of ultra-high strength sucker rods were obtained. For HL- and HY-type ultra-high strength sucker rods, the average error between the fitting result and fatigue test value is 1.25% and 4.39%, respectively. Compared to the S-N curve fitting result obtained from the Basquin model commonly used for sucker rods, the new model based on three-parameter Weibull distribution provides better fitting precision and can estimate fatigue limit more accurately, so this model is more suitable for estimating fatigue life and can better guide the design of ultra-high strength sucker rod strings.

A new multiaxial fatigue life prediction method based on grey theory under small sample condition

“…In fact, the fatigue life of the same specimen under the same load is quite different, showing a certain dispersion, and the S‐N field or ε ‐ N field can be used to describe this dispersion of fatigue life. In recent years, a great deal of work has been done on how to establish accurate P ‐ S‐N curves ( P ‐ ε ‐ N curves) 24–26 . In 2014, Enrique Castillo's team 27 developed a software program ProFatigue for probabilistic assessment of experimental fatigue life, which greatly facilitates the drawing of S‐N field or ε ‐ N field.…”

“…In recent years, a great deal of work has been done on how to establish accurate P-S-N curves (P-ε-N curves). [24][25][26] In 2014, Enrique Castillo's team 27 developed a software program Pro-Fatigue for probabilistic assessment of experimental fatigue life, which greatly facilitates the drawing of S-N field or ε-N field.…”

Research on fatigue life evaluation method of shaft parts based on small sample

“…The maximum likelihood method was used to estimate model parameters, and the results showed that the model can effectively characterize data variability under high cycle fatigue and fatigue limit conditions. Cai et al . (2022) compared the P-S-N curves fitted by the Basquin model and Weibull distribution, and the results showed that the extrapolation of the Weibull distribution fitted in finite fatigue region performed better than the Basquin model in the high and ultra-high cycle fatigue regions.…”

“…The maximum likelihood method was used to estimate model parameters, and the results showed that the model can effectively characterize data variability under high cycle fatigue and fatigue limit conditions. Cai et al (2022) compared the P-S-N curves fitted by the Basquin model and Weibull distribution, and the results showed that the extrapolation of the Weibull distribution fitted in finite fatigue region performed better than the Basquin model in the high and ultra-high cycle fatigue regions. Due to the limitations of the Goodman, Gerber, Soderber and Elliptical failure theories in determining the failure time of mechanical components, Barraza-Contreras et al (2020) combined fatigue life and Weibull distribution to predict the failure time, validated with numerical calculations, finite element analysis results, and static analysis method.…”

A study on modified P‐S‐N curve of notched specimens based on small sample under multiaxial loading

“…Thus, the relationship between stress amplitude and fatigue life cannot be simply represented by a single S‐N curve but should be characterized as a group of S‐N curves under different survival rates, namely, the P‐S‐N curve 3 . P‐S‐N curve is an important tool to describe the relationship of the fatigue failure probability, stress, and fatigue life in engineering, 4 and its drawing usually relies on a large amount of fatigue experimental data. However, the number of available data are often limited in practical engineering due to the high cost of experimental specimens and time, and it is difficult to obtain large sample data to meet the requirements of traditional statistical methods.…”