One of the last tendencies in modern machine engineering is application of innovative "closed" bearing units with increased service intervals and warranty period that correspond to the top requirements in regard to reliability and durability. To get high performance figures of such bearing units it is required to use modern technologies and advanced equipment during their production. Problems in development of mathematical model and numerical methods for calculation of physical and mechanical parameters of material of cassette bearing rings during and after electric induction hardening and optimization of its modes to provide required picture of hardening, residual stresses and austenite are considered in this paper. The obtained results can be used during creation of industrial technology and equipment for application during mass production of cassette bearings.
In the work, a mathematical multi-physical model is obtained, consisting of the interconnected equations of the Maxwell electromagnetic field and the Fourier heat equations with the corresponding boundary conditions, supplemented by relations modeling the transformation of the microstructure of steel from one state to another during heat treatment.
The mathematical model was verified on test problems, and also “tuned to bearing steel” (according to the results of solving test problems, the missing characteristics of steel were identified).
The research solved the problems of modeling one-step volumetric hardening of the inner ring and three-stage volumetric-surface hardening of the outer cassette bearing with optimization of hardening conditions based on the conditions for ensuring hardness on the surface 59<HRC<63 (with a layer depth s > 2 mm) and in the core of the workpiece - HRC<45 with a minimum of energy consumption.