Distribution Characterisation of Coil Spring Strain Histories Using Mixed Weibull Analysis

  • Authors

    • M Mahmud
    • S Abdullah
    • S S. K. Singh
    • A K. Ariffin
    • Z M. Nopiah
    • A Arifin
    2018-08-01
    https://doi.org/10.14419/ijet.v7i3.17.16632
  • Coil Spring, Distribution, Mixed Weibull, Strain Signal, Suspension.

  • Abstract

    This paper investigates the scatter of strain histories obtained from coil spring of a vehicle suspension system. Statistical characterisation is essential in fatigue analysis due to the random nature of fatigue process. The element of uncertainty can be dealt with appropriately by applying probabilistic approach. In this study, four different road profiles were used to obtain strain signal data. Initial description of the strain histories was achieved by computing the global statistics values. The strain range data was calculated from the counted fatigue cycle and distribution fitting was performed using the Anderson Darling test. Four different types of distribution; the exponent, Gamma, 3P-Weibull, and 2P-Weibull; were compared to find the appropriate fit to model the strain range data. The results showed that strain range data are highly skewed with thick-tailed indicating a non-Gaussian distribution. All four tested distribution turned out to be insignificance, with the closest p-value of 0.01 produced by the 2P-Weibull distribution at significance level of 0.05. Due to the non-straight probability plot of data, the mixed Weibull distribution was chosen to model the data. The campus area and highway profiles follow this distribution with 2 sub-populations while rural and housing area resulted in 3 sub-populations. Finally, this distribution is found suitable for analysing the strain range data of vehicle coil spring and hence can be used in time-domain fatigue life evaluation.

     

     

  • References

    1. [1] [1] Y. Wang and L. Susmel. 2016. The Modified Manson–Coffin Curve Method to estimate fatigue lifetime under complex constant and variable amplitude multiaxial fatigue loading. International Journal of Fatigue. 83(2): 135-149.

      [2] [2] S. P. Zhu, Q. Lei, H. Z. Huang, Y. J. Yang, and W. Peng. 2016. Mean stress effect correction in strain energy-based fatigue life prediction of metals. International Journal of Damage Mechanics. 31(11): 1-23.

      [3] [3] S.-P. Zhu, H.-Z. Huang, W. Peng, H.-K. Wang, and S. Mahadevan. 2016. Probabilistic Physics of Failure-based framework for fatigue life prediction of aircraft gas turbine discs under uncertainty. Reliability Engineering & System Safety. 146: 1-12.

      [4] [4] A. Fernández-Canteli, C. Przybilla, M. Nogal, M. L. Aenlle, and E. Castillo. 2014. ProFatigue: A Software Program for Probabilistic Assessment of Experimental Fatigue Data Sets. Procedia Engineering. 74: 236-241.

      [5]

      International Journal of Engineering & Technology

      117

      [5] Z. Lu and Y. Liu. 2011. Experimental investigation of random loading sequence effect on fatigue crack growth. Materials & Design. 32(10): 4773-4785.

      [6] [6] R. F. Sanches, A. M. P. de Jesus, J. A. F. O. Correia, A. L. L. da Silva, and A. A. Fernandes. 2015. A probabilistic fatigue approach for riveted joints using Monte Carlo simulation. Journal of Constructional Steel Research. 110: 149-162.

      [7] [7] C. Baptista, A. Reis, and A. Nussbaumer. 2017. Probabilistic S-N curves for constant and variable amplitude. International Journal of Fatigue. 101(2): 312-327.

      [8] [8] E. Olsson, A. Olander, and M. Öberg. 2016. Fatigue of gears in the finite life regime — Experiments and probabilistic modelling. Engineering Failure Analysis. 62: 276-286.

      [9] [9] J. Klemenc and M. Fajdiga. 2013. Joint estimation of E–N curves and their scatter using evolutionary algorithms. International Journal of Fatigue. 56: 42-53.

      [10] [10] D. S. Paolino, G. Chiandussi, and G. Belingardi. 2013. Uncertainty in fatigue loading: Consequences on statistical evaluation of reliability in service. Probabilistic Engineering Mechanics. 33: 38-46.

      [11] [11] A. Fernández-Canteli, E. Castillo, M. López-Aenlle, and S. Seitl. 2010. Using statistical compatibility to derive advanced probabilistic fatigue models. Procedia Engineering. 2(1): 1131-1140.

      [12] [12] J. Yu, G. Marquis, and T. Björk. 2011. Development of data sheets for statistical evaluation of fatigue data. Journal of Iron and Steel Research, International. 18(5): 70-78.

      [13] [13] D. Benasciutti and R. Tovo. 2010. On fatigue cycle distribution in non-stationary switching loadings with Markov chain structure. Probabilistic Engineering Mechanics. 25: 406–418.

      [14] [14] M. F. M. Yunoh, S. Abdullah, Z. M. Nopiah, and M. Z. Nuawi. 2013. A review of localised time-frequency features classification associated to fatigue data analysis. International Review of Mechanical Engineering. 7(5): 960-976.

      [15] [15] D. Benasciutti and R. Tovo. 2006. Fatigue life assessment in non-Gaussian random loadings. International Journal of Fatigue. 28: 733–746.

      [16] [16] T. Zhang and M. Xie. 2011. On the upper truncated Weibull distribution and its reliability implications. Reliability Engineering & System Safety. 96(1): 194-200.

      [17] [17] J. Schijve. 2005. Statistical distribution functions and fatigue of structures. International Journal of Fatigue. 27(9): 1031-1039.

      [18] [18] E. E. Elmahdy and A. W. Aboutahoun. 2013. A new approach for parameter estimation of finite Weibull mixture distributions for reliability modeling. Applied Mathematical Modelling. 37(4): 1800-1810.

      [19] [19] C. B. Patel, P. P. Gohil, and B. Borhade. 2010. Modeling and vibration analysis of road profile measuring system. International Journal of Automotive and Mechanical Engineering. 1: 13-28.

      [20] [20] T. E. Putra, S. Abdullah, D. Schramm, M. Z. Nuawi, and T. Bruckmann. 2017. The need to generate realistic strain signals at an automotive coil spring for durability simulation leading to fatigue life assessment. Mechanical Systems and Signal Processing. 94: 432-447.

      [21] [21] M. Haiba, D. C. Barton, P. C. Brooks, and M. C. Levesley. 2003. The development of an optimisation algorithm based on fatigue life. International Journal of Fatigue. 25: 299-310.

      [22] [22] S. Abdullah, C. K. E. Nizwan, M. F. M. Yunoh, M. Z. Nuawi, and Z. M. Nopiah. 2013. Fatigue features extraction of road load time data using the S-transform. International Journal of Automotive Technology. 14(5): 805−815.

      [23] [23] H. F. S. G. Pereira, D. L. DuQuesnay, A. M. P. De Jesus, and A. L. L. Silva. 2009. Analysis of variable amplitude fatigue data of the P355NL1 steel using the effective strain damage model. Journal of Pressure Vessel Technology. 131(5): 87-96.

      [24] [24] J. Klemenc and M. Fajdiga. 2008. Improved modelling of the loading spectra using a mixture model approach. International Journal of Fatigue. 30: 1298–1313.

      [25] [25] R. Tovo. 2002. Cycle distribution and fatigue damage under broad band random loading. International Journal of Fatigue. 24: 1137-1147.

  • Downloads

  • How to Cite

    Mahmud, M., Abdullah, S., S. K. Singh, S., K. Ariffin, A., M. Nopiah, Z., & Arifin, A. (2018). Distribution Characterisation of Coil Spring Strain Histories Using Mixed Weibull Analysis. International Journal of Engineering & Technology, 7(3.17), 110-117. https://doi.org/10.14419/ijet.v7i3.17.16632

    Received date: 2018-07-31

    Accepted date: 2018-07-31

    Published date: 2018-08-01