Next, we consider four kinds of rol

Next, we consider four kinds of rolling bearing data under the same rotor speed 1730 r/min and load 3 HP but different fault locations with pitting size 0.1778 mm. The data includes vibration signals of normal bearings and bearings with outer race fault, inner race fault and ball element fault (i.e. Norm4, IR1, BE and OR) and their time domain waveforms are given in Fig. 9, from which it is difficult to differ them from each other. Then CMFE is employed to analyze these four kinds of rolling bearing vibration signals. Three samples of each kind are used and thus CMFEs of totally twelve sample signals are calculated and shown in Fig. 11, from which the following results can be concluded. First of all, the CMFEs of vibration signals from normal rolling bearing in most scale factor are larger than those of faulty rolling bearings. And they change smoothly and fluctuate around a constant with the increase of scale factor while the CMFEs of vibration signal of three fault rolling bearings have an apparently decreasing. This can be explained that the vibration is random when the rolling bearing works on a healthy condition. However, this randomness is like the 1/f noise's (by observing their CMFEs) other than white noise's, which means that it still contains much important information of mechanical systems. Once the rolling bearing works with fault, the failure position will become a drive source to continuously generating a regular and periodic impact. Therefore, the obtained vibration signals have an evident regularity and increasing selfsimilarity, which results in an decreasing complexity and thus an increasing FuzzyEns. Therefore, CMFE is very suitable for rolling bearing fault detection and diagnosis and is an effective tool for machinery fault diagnosis and condition monitoring. In addition, at most scale factors, the CMFE of vibration signal collected from rolling bearing with ball element fault is larger than that of rolling bearing with inner race fault, which is larger than that of rolling bearing with outer race fault. This is mainly because when a failure occurs, the vibration signal of system has obvious impact characteristics and different fault locations have different impact frequencies and therefore faults in different locations result in vibration signals with different complexities. Since the outer race of rolling bearing is fixed on the bearing housing and when the failure occurs in outer race, the impact characteristic frequency of vibration signal is single and simple. Besides, compared with the inner race and ball element fault, the characteristic frequency of outer race fault is the smallest and hence its self-similarity and regularity also is the most obvious, which results in its CMFE curve of vibration signal drops fastest with the increase of scale factor. Since inner race rotates with the rotation axis and rolling element revolves round the shaft and on its own axis, the fault characteristic frequency of ball element is larger than that of inner race (and outer race), hence, in theory the vibration signals of rolling element with ball element fault is more complex than those of inner race and outer race. This is why the CMFE of vibration signal of roller bearing with ball element fault in most scales is greater than those of inner race and outer race. Third, CMFE in a single scale can not effectively distinguish fault category. When the scale factor equals to 1, the CMFE of original vibration signal will degenerate into FuzzyEn. It can be seen from the Fig. 10 that the FuzzyEn of vibration signal from normal rolling bearing is smaller than those of vibration signals from faulty rolling bearings, from which it is easy to come a preposterous result that the vibration signal of faulty rolling bearings is much more complex than that of normal rolling bearing. Therefore, compared with the traditional single scale based fuzzy entropy analysis, CMFE can reflect the failure nature better. To sum up, the above analysis indicates that CMFE is an effective tool for rolling bearing fault detection and diagnosis.