Modeling of Fault Frequencies for Distributed Damages in Bearing Raceways

Abstract

There are two types of damages in the inner ring and outer ring of the bearing. One is names as localized damage and second is known as distributed damage. These damages in inner ring or outer ring create bearing faults and causes breakdown on machine. To avoid the unplanned shutdown, various type of preventive maintenance techniques such as thermal analysis, acoustic emission and vibration analysis are used in the industry. However, these conventional methods use costly sensors and require experts for data interpretation and analysis. Recently, an alternative approach has been proposed by researchers which is known as Park analysis technique. The data collection and analysis through Park analysis technique is cheaper and easier as compared to thermal analysis, acoustic emission and vibration analysis techniques. However, Park analysis technique utilizes the frequency domain analysis and need a frequency information of the fault to locate fault amplitude on the spectrum. The frequency models are only available for the bearing localized damages and the frequency model for the bearing distributed damages are still unknown. Thus, derivation of frequency model for bearing distributed damage is required to enhance the fault diagnosing capability of the Park analysis technique. Hence, this research paper aims to derive a mathematical model of the fault frequencies related to bearing distributed damages. The developed model will be experimentally verified through experiments performed on the custom designed test-setup.

Appendix

$$ \begin{aligned} {\text{Fit factor}} & = 1 + \frac{{{\text{D}}_{{{\text{ir}}}} }}{{1.8\left( {{\text{D}}_{{{\text{or}}}} - {\text{D}}_{{{\text{ir}}}} } \right) + 6{\text{D}}_{{{\text{ir}}}} }} \\ & = 1 + \frac{{15}}{{1.8\left( {35 - 15} \right) + 90}} = 1.12 \\ \end{aligned} $$

${\text{F}}_{\text{ddi}}$ for the no load:

$$ {\text{F}}_{\text{ddi}} \left( {\text{Higher limit}} \right) = {\text{F}}_{\text{ddi}} * {\text{Fit factor}} = { 89}. 2* 1. 1 2 { } = { 1}00{\text{ Hz}} $$

$$ {\text{F}}_{\text{ddi}} \left( {\text{Lower limit}} \right) = {\text{F}}_{\text{ddi}} /{\text{Fit factor}} = { 89}. 2/ 1. 1 2 { } = { 79}. 6 {\text{ Hz}} $$

Thus, the ${\text{F}}_{\text{ddi}}$ under no load condition should be in the range of 79 Hz to 100 Hz

${\text{F}}_{\text{ddi}}$ for the full load:

$$ {\text{F}}_{\text{ddi}} \left( {\text{Higher limit}} \right) = {\text{F}}_{\text{ddi}} * {\text{Fit factor}} = { 83}. 3 6* 1. 1 2 { } = { 93}. 3 6 {\text{ Hz}} $$

$$ {\text{F}}_{\text{ddi}} \left( {\text{Lower limit}} \right) = {\text{F}}_{\text{ddi}} /{\text{Fit factor}} = { 83}. 3 6/ 1. 1 2 { } = { 74}. 4 {\text{ Hz}} $$

Thus, the ${\text{F}}_{\text{ddi}}$ under full load condition should be in the range of 74–93 Hz

${\text{F}}_{\text{ddo}}$ for the no load:

$$ {\text{F}}_{\text{ddo}} \left( {\text{Higher limit}} \right) = {\text{F}}_{\text{ddo}} * {\text{Fit factor}} = { 2}0. 50* 1. 1 2 { } = {\text{ 23 Hz}} $$

$$ {\text{F}}_{\text{ddo}} \left( {\text{Lower limit}} \right) = {\text{F}}_{\text{ddo}} /{\text{Fit factor}} = { 2}0. 50/ 1. 1 2 { } = {\text{ 18 Hz}} $$

Thus, the ${\text{F}}_{\text{ddo}}$ under no load condition should be in the range of 18–23 Hz

${\text{F}}_{{{\text{dd}}0}}$ for the full load:

$$ {\text{F}}_{{{\text{dd}}0}} \left( {\text{Higher limit}} \right) = {\text{F}}_{\text{ddo}} * {\text{Fit factor}} = { 19}. 1 4* 1. 1 2 { } = { 21}. 4 {\text{ Hz}} $$

$$ {\text{F}}_{\text{ddo}} \left( {\text{Lower limit}} \right) = {\text{F}}_{\text{ddo}} /{\text{Fit factor}} = { 19}. 1 4/ 1. 1 2 { } = {\text{ 17 Hz}} $$

Thus, the ${\text{F}}_{\text{ddo}}$ under full load condition should be in the range of 17 Hz to 21 Hz