Quantitative diagnosis of a spall-like fault of a rolling element bearing by empirical mode decomposition and the approximate entropy method

• The EMD and ApEn were utilized in estimation of the size of spall-like fault in a bearing.
• The IMF-ApEn distribution of white noise signals was studied.
• The IMF-ApEn distribution template was developed to extract the EIMF components.
• Model of bearing signal in conditions with variable spall-like fault sizes.

Spalling or pitting is the main manifestation of fault development in a bearing during the earlier stages. Previous studies indicated that the vibration signal of a bearing with a spall-like defect may be composed of two parts; the first part originates from the entry of the rolling element into the spall-like area, and the second part refers to the exit from the fault region. The quantitative diagnosis of a spall-like fault of the rolling element bearing can be realised if the entry–exit event times can be accurately calculated. However, the vibration signal of a faulty bearing is usually non-stationary and non-linear with strong background noise interference. Meanwhile, the signal energy from the early spall region is too low to accurately register the features of the entry–exit event in the time domain. In this work, the approximate entropy (ApEn) method and empirical mode decomposition (EMD) are applied to clearly separate the entry–exit events, and thus the size of the spall-like fault is estimated.First, the original acceleration vibration signal is decomposed by EMD, and some useful intrinsic mode function (IMF) components are obtained. Second, the concept of IMF-ApEn is introduced, which can directly reflect the complexity of the IMFs using the actual vibration signal. The IMF-ApEn distributions of different noise signals illustrate that the process of complexity changes when a full spectrum process is split into its IMFs. Third, a unit white noise IMF-ApEn distribution template serves as a sieve to extract the (effective intrinsic mode functions) EIMF components, and thus the entry and exit events in the response signal are distinguished.The IMF-ApEn method is further compared with a previous method (N. Sawalhi's method) to test its superiority. The dynamic effects are investigated when the ball element enters a spall-like region by computer simulation. The simulation and the experimental results show that the approach to the quantitative diagnosis of a rolling element bearing based on IMF-ApEn has higher veracity and good robustness.