A Numerical Model for the Identification of the Structural Damages in Rolling Contact Bearings Using Matrix Method of Dimensional Analysis

Abstract

The damages to the structural elements, viz., inner race, outer race, rollers, cage, etc., of rolling contact bearings if not detected in time can cause tragic failures of the machineries supported by these bearings. The operating parameters like variations in the machinery speed, unbalance, operating load, etc., can cause a bearing to vibrate at higher energy levels and consequently will accelerate its wear. An attempt is made in this study, and a generalized model is developed using matrix method of dimensional analysis (MMDA) that predicted the response and correlated the dependent parameter, i.e., response with the significant independent parameters. Combined use of response surface methodology (RSM) is made to explore the dependence of various factors such as size of the defect, unbalance, speed, and their interactions on the vibration characteristics of the bearings. It is observed from the study that the model developed based on the MMDA has provided an efficient approach in recognizing the damaged bearing state, which can be easily implemented in the condition-based preventive maintenance strategies. Also, the effectiveness of MMDA as compared to the conventional Buckingham's pi theorem in the dimensional analysis (DA) practice, especially in the problems involving multiple variables, is shown in this study.

An overview of dynamic modeling of rolling-element bearings

“…In addition, the limited study of the dynamic behavior of the REB under the influence of defect size, speed, and unbalance and their interface is supported by Jamadar and Vakharia. 175 In this, Jamadar and Vakharia 176 developed a universal model using a MMDA to forecast the response with substantial independent parameters. In addition, the dependency of several factors such as the size of the defect, rotational speed, unbalance, and mutual interaction with the vibration characteristics of the REB is sighted by using the RSM.…”

“…Former vibrational study of REB using DA considering FLT method was done for single and multiple faults on races, which forms a gap to investigate the effect of spall on rollers using the FLT system. Hence, an extension to Jamadar and Vakharia; 176 Jamadar and Vakharia 177 developed MMDA-based theoretical model to inspect the effect of defect size, rotational speed, load, unbalance, lubricant properties, and a number of rolling elements on the vibration amplitude. The interaction of the inner and outer race of the bearing with a damaged rolling element is considered to foster the model equation which successfully correlates the level of rolling element damage with the amplitude of the vibration.…”

Dynamic response analysis of unbalanced rotor-bearing system with internal radial clearance

“…However, a more reliable FLTθ system is used for this model. Jamadar and Vakharia [20] developed a mathematical model for bearing vibration response analysis using the Matrix Method of Dimensional Analysis (MMDA). The model was validated using RSM and experimental results.…”

Influence of roller defect and coupled roller–inner–outer race defects on the performance of cylindrical roller bearing

“…Under lubricating condition, the analysis of roller–race contact presented by Kushwaha and Rahnejat, 35 where coupled rolling and tilting of roller takes place when roller moves from unloaded to loaded section. A model using matrix method was described by Jamadar and Vakharia, 36 for the prediction of response and correlated it with the dependent parameters like defect size, unbalance, and speed. A model based on the dimensional analysis method for the improvement of the computational efficiency for the nonlinear dynamic analysis of rolling contact was described by Jamadar and Vakharia, 37 which is used to the predict the vibration behavior of faulty bearing.…”