A Neural Network-Assisted Boussinesq pressure bulb model for load assessment of cylindrical rolling element bearings

• A NN-assisted pressure bulb model was proposed for load assessment of roller bearings. • The accuracy of the Boussinesq pressure bulb model was investigated. • Two NNs were integrated into the model to enhance accuracy. • High accuracy was validated through simulations and experiments. The accurate assessment of contact forces and radial load is critical for the performance and reliability of the cylindrical rolling element bearings. The current theoretical models based on Hertzian theory are challenging since the deformation is relatively small to measure, and installing sensors on the contact area is difficult. This paper introduced the Boussinesq pressure bulb model for bearing load assessment and found that the original model had a maximum of 33% error because it did not consider the boundary effects and material properties. To improve accuracy, a Neural Network-assisted Boussinesq model is proposed by integrating two Neural Networks (NNs) with the original Boussinesq model. The first NN accurately transfers strain measurements from Fiber Bragg Grating (FBG) optical sensors into stresses at the point of interest, while measuring strain is easier in practical applications. The second NN provides an accurate tuning factor to address errors in the original model. The NN-assisted Boussinesq model greatly outperforms the original model and shows an error below 3.73%. The performance of the proposed model is validated through simulations and experiments. In simulations, errors were below 1% when the outer race and housing were made of the same material, 6.7% for a GCr15 steel outer race with a spheroidal graphite iron housing, and 11.6% for a GCr15 steel outer race with a grey cast iron housing; the latter remains acceptable for non-precision applications. In experiments, radial load estimation errors were below 3% in static tests and 4.6% in dynamic tests. All these simulations and experiments demonstrated the superiority of the proposed method. Moreover, it is practical and easy to implement in real-time bearing stress and load measurements.