Precision Lifetime Analysis of High-Speed Machine Tool Bearings Based on Quasi-Static and Mixed Thermal Elastohydrodynamic Lubrication Models

The spindle bearing is one of the key components of a high-precision and high-speed machine tool, and thus its rotational accuracy is a crucial factor that ensures the reliability of machining precision. Therefore, the effective evaluation of the precision lifetime of spindle bearings is particularly important. Currently, most life models focus on bearing fatigue failure rather than bearing precision failure. Consequently, in order to predict the lifetime of bearing due to the working precision lost, a framework is established based on the Archard wear theory. Since the bearing mechanical theoretical model generally ignores the influence of lubricating oil film stiffness, a novel coupling analysis algorithm of the quasi-static model and the mixed thermal elastohydrodynamic lubrication (mixed-TEHL) model is proposed, based on which the functional relationship between raceway contact load and oil film thickness can be redefined by the partial differential method. Then, in order to verify the coupling model, the simulated oil film thickness results were compared with the Hamrock-Dowson (H-D) formula calculation results and the experiment data measured by the resistance capacitance oscillation method. It was found that, compared with the H-D formula, the simulation results of the coupling algorithm were in good agreement with the experimental data. The accuracy of the coupling analysis model was proven. Considering that the wear coefficient of bearing steel was not obtained by theoretical calculation, this paper introduced the quantitative function relationship between the wear coefficient of GCr15 bearing steel and oil film parameters obtained by the ball-disc wear test, which could evaluate the wear resistance of bearing steel under various lubrication environments. After this, the oil film thickness, wear coefficient, contact load, and other key state parameters of bearings could be obtained, and then combined with the Archard theory formula, the bearing precision lifetime prediction model was constructed, which comprehensively considered the bearing mechanical state, lubrication performance, and bearing steel anti-wear performance. In order to verify the model, the predicted precision lifetime results were compared with the published experimental data of bearing lifetime, which proved the feasibility of the bearing precision lifetime prediction model constructed in this paper. The contact load and entrainment velocity between balls and raceways were obtained by the quasi-static model of the bearing. Meanwhile, the oil film thickness, oil film pressure, and oil film temperature were calculated by the mixed-TEHL model. In order to accelerate the contact deformation calculation, the discrete convolution Fourier Transform method was applied. To ensure the stability of the iterative process of the Reynolds equation, the semi-system method was used. The temperature field was computed through the column scanning and chase-after methods. The non-Newtonian fluid characteristics were simulated by the Ree-Eyring model, and contact surface roughness was simulated by 2D digital filter technology. Finally, the influence of the thermal effect, non-Newtonian fluid characteristics, surface roughness parameters, and operation conditions on bearing precision lifetime was analyzed. The numerical results showed that the increase of oil film temperature would significantly weaken the lubrication performance, resulting in a significant reduction of the bearing precision lifetime. The root-mean-square (RMS) of surface roughness determined the height of surface fluctuation. With the increase of RMS, the extreme value of oil film pressure increased, the lubrication performance deteriorates, and the bearing precision lifetime decreased. Considering the non-Newtonian fluid characteristics of the lubricant, the oil viscosity was reduced, the oil film was slightly thinned, and the bearing precision life time was slightly reduced. With the increase of axial and radial load on the bearing, the working condition became harsher, and the bearing precision lifetime decreased significantly. In particular, it was found that when the rotation speed was increased, the precision lifetime showed a trend of short increase and then decrease. The proposed bearing precision lifetime prediction model could provide a theoretical basis for the service performance evaluation of bearing precision and therefore guide the optimization of bearing structure design.