Dynamic Evaluation of the Degradation Process of Vibration Performance for Machine Tool Spindle Bearings

Abstract

Real-time condition monitoring and fault diagnosis of spindle bearings are critical to the normal operation of the matching machine tool. In this work, considering the interference of random factors, the uncertainty of the vibration performance maintaining reliability (VPMR) is introduced for machine tool spindle bearings (MTSB). The maximum entropy method and Poisson counting principle are combined to solve the variation probability, so as to accurately characterize the degradation process of the optimal vibration performance state (OVPS) for MTSB. The dynamic mean uncertainty calculated using the least-squares method by polynomial fitting, fused into the grey bootstrap maximum entropy method, is utilized to evaluate the random fluctuation state of OVPS. Then, the VPMR is calculated, which is used to dynamically evaluate the failure degree of accuracy for MTSB. The results show that the maximum relative errors between the estimated true value and the actual value of the VPMR are 6.55% and 9.91%, and appropriate remedial measures should be taken before 6773 min and 5134 min for the MTSB in Case 1 and Case 2, respectively, so as to avoid serious safety accidents that are caused by the failure of OVPS.

Keywords: degradation probability; machine tool spindle bearings; optimal performance state; uncertainty; vibration performance maintaining reliability.

Figure 1

Performance degradation and reliability evaluation process of rolling bearings.

Figure 2

Flow diagram of proposed method.

Figure 3

Vibration signals of MTSB.

Figure 4

Probability density function of data samples of intrinsic series.

Figure 5

Variation probability curve.

Figure 6

Variation probability curve fitting using least-square method.

Figure 7

Sample data generated using grey bootstrap method.

Figure 8

Maximum entropy probability density function of grey bootstrap samples.

Figure 9

Estimated results of degradation probability of OVPS of MTSB.

Figure 10

Dynamic evaluation results of PMR.

Figure 11

Error bars of PMR.

Figure 12

Dynamic evaluation results of PMRR.

Figure 13

Vibration signals of bearing performance (Case 2).

Figure 14

Probability density function of data samples of intrinsic series (Case 2).

Figure 15

Variation probability curve (Case 2).

Figure 16

Variation probability curve fitting using least-square method (Case 2).

Figure 17

Sample data using grey bootstrap method (Case 2).

Figure 18

Maximum entropy probability density function of grey bootstrap samples (Case 2).

Figure 19

Estimated results of degradation probability of OVPS of MTSB (Case 2).

Figure 20

Dynamic evaluation results of PMR (Case 2).

Figure 21

Error bars of PMR (Case 2).

Figure 22

Dynamic evaluation results of PMRR (Case 2).