Efficient boundary conditions identification in thermal simulation of the spindle system with reduced order model and differential evolution algorithm

Abstract

The boundary conditions in thermal simulation of the spindle system are very complicated and the empirically calculated ones will usually result in a significant discrepancy between experiment and simulation. Thus, the optimal boundary conditions were identified by treating it as an inverse optimization problem in this paper. Moreover, to advance the optimization efficiency, a reduced order model is established to replace the time-consuming thermal simulation of the spindle system. By superposition of truncated eigenmodes and accurately predicted modal coefficients, the reduced order model can reconstruct the field very similar to thermal simulation. Experimental reconstruction of both the temperature field and thermal deformation field by the reduced order model demonstrated its at least 360 times speedup with 99.8 % accuracy compared to the actual thermal simulation. With the accurate reduced order model as a lightweight digital twin and using the differential evolution algorithm, three types of boundary conditions, i.e., the heat generation rates, the convective heat transfer coefficients and the thermal contact resistances, under the shaft rotation speed of 4,000r/min were identified within 11s. The maximum temperature simulation error was reduced from 85.6 % to 6.6 % and the thermal deformation simulation error was reduced from 60.9 % to 10.8 %.

Keywords

• Thermal errors
• Boundary conditions optimization
• Reduced order model
• Proper orthogonal decomposition
• Machine tool