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For a lightweight and accurate description of bearing temperature, this paper aims to present an efficient semi-empirical model with oil–air two-phase flow and gray-box model.

First, the role of lubricant/coolant in bearing temperature was discussed separately, and the gray-box models on the heat convection inside a bearing cavity were also created. Next, the bearing node setting scheme was optimized. Consequently, a novel semi-empirical two-phase flow thermal grid for high-speed angular contact ball bearings was planned. With this model, the thermal network for the selected motored spindle was built, and the numerical solutions for bearing temperature rise were obtained and contrasted with the experimental values for validation. The polynomial interpolation on test data, meanwhile, was also performed to help us observe the temperature change trend. Finally, the simulations based on the current models of bearings were implemented, whose corresponding results were also compared with our research work.

The validation result indicates that the thermal prediction is more accurate and efficient when the developed semi-empirical oil–air two-phase flow model is employed to assess the thermal change of bearings. Clearly, we provide a more proper model for the thermal assessment of bearing and even spindle heating.

To the best of the authors’ knowledge, this paper introduced the oil–air separation and gray-box model for the first time to describe the heat exchange inside bearing cavities and accordingly presents an efficient semi-empirical oil–air two-phase flow model to evaluate the bearing temperature variation by using thermal network method.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-06-2023-0180/

This paper aims to devote to the experimental analysis and modeling on the heat generation of angular contact ball bearings under vibration.

The experiments about vibration effect on bearing temperature are implemented. To explore the causes of bearing temperature rise, the shaft-bearing system is first simplified to a forced vibration model to analyze the bearing loads in vibration. Next, the vibratory-induced additional load is proposed and the spin power loss of balls is re-derived under vibration. The vibration-induced heat is integrated into a novel forecasting model of bearing power loss. For validation, the muti-node model for angular contact ball bearings is referred to create the thermal network of spindle front bearing, and then the contrast and discussion is done.

The simulation and test results both indicate that more energy is expended and more heat is generated with vibration. And the further quantitative comparisons between simulation results and experimental values of bearing temperature demonstrate the rationality and availability of constructed model on bearing heat generation.

The vibration-induced additional load is proposed and modeled, and the novel forecasting model for heat generation for high-speed angular contact ball bearings with vibration is constructed and validated.