This paper aims at diagnosing the fault of rolling bearings and establishes the system of dynamics model with the consideration of rolling bearing with nonlinear bearing force, the radial clearance, and other nonlinear factors, using Runge-Kutla such as Hertzian elastic contactforce and internal radial clearance, which are solved by the Runge-Kutta method. Using simulated data of the normal state, a self-adaptive alarm method for bearing condition based on one-class support vector machine is proposed. Test samples were diagnosed with a recognition accuracy over 90%. The present method is further applied to the vibration monitoring of rolling bearings. The alarms under the actual abnormal condition meet the demand of bearings monitoring.

Rolling bearings are widely used in high-end CNC machine tools, aircraft engines, measuring instruments, and other valuable equipment. It plays a key role for the entire work of the host. Carrying out the bearing condition monitoring and fault diagnosis is important to ensure that the equipment is in good working condition. Since fault-prone of early rolling bearing easily exists in most of the bearing work cycle, and most of them are potential problem. Therefore, bearing failure abnormality diagnosis has been a research hotspot [

About anomaly identification bearing, which is combined with failure mechanism analysis and intelligent diagnosis, this paper first built a physical model of the rolling bearing normal state, and obtain the system response by numerical methods. By dimensionless indicators as characteristic quantities such as kurtosis and peak and building up the bearing diagnosis model based on a class support vector machine, the test bearing diagnosis results show the effectiveness of this method.

The structural vibration model of ball bearings can be developed for the rigid rotor system that with the outer ring fixed, the inner ring is equivalent to the concentrated mass. As Figure

Ball bearing dynamics model.

In the above formula,

Through Hertz theory, the Eschmann had given the expression of elastic deformation of the two-solid-point touching,

Here,

Therefore, coefficient of nonlinear deformation of point contacting is

The calculation methods of curvature about contact surfaces and

In this paper, bearings used FUKATA is calculated in order to verify the correctness of ball bearing model and Table

Ball bearings parameter table.

Bearings parameter | Numerical |
---|---|

The bearing pitch circle diameter | 58.8 mm |

Ball diameter | 11.9062 mm |

Number of balls | 8 |

Clearance | 40 um |

The quality of the rotor (inner ring) | 16 kg |

External load | 58.8 N |

Bearing damping | 2940 Ns/m |

Time-domain waveform.

The calculated results of FUKATA.

One-class support vector machine is an unsupervised learning method based on statistical learning theory, having no prior knowledge, structural risk minimization, and so forth. Its purpose is to effectively distinguish the target class samples and other samples. The basic principle of one-class support vector machine is as follows [

In formula (

In formula (

The nature of the fault diagnosis is pattern recognition problem. In this paper, through numerical simulation to build a normal state of the sample, thus eliminate the problem by failure data. However the kurtosis, waveform, margin, peak and skewness of five dimensionless index [

Class support vector machine diagnosis flowchart.

An experimental study of the vibrated signal in the bearing test, which used to judge the bearing working state. Using SonyEX data acquisition system to get the signal, the sampling frequency is 10 kHz. Figure

Abnormal rate of diagnosis of each state.

Bearing condition | Correct rate |
---|---|

Inner ring defect | 94.3% |

Outer ring defect | 90.6% |

Ball defects | 91.7% |

Normal signal waveform and power spectra.

This paper presents a model-based ball bearing fault diagnosis method. It is through the use of dynamic models to get the timing of data reconstruction, thus taking advantage of the dimensionless indicators eigenvectors training one-class support vector machine to discover abnormal state. Engineering experiments show the feasibility and effectiveness of this method with the diagnosis rate being up to more than 90%. This results meet the actual monitoring needs of the industrial field.

The authors declare that there is no conflict of interests.

The authors would like to thank the Research Project of National Torch Plan in 2012 (2010GH041809).