An inverse method for estimating heat sources in a high speed spindle

• Time-varying heat sources in a spindle are estimated by using an inverse method.
• The inverse method is established by a combination of CGM and ANSYS software.
• The heat sources are accurately estimate based on only two measured temperatures.
• Inverse results agree well with given solutions even involved measurement noise.

This article presents an inverse method for estimating time-varying heat sources in a high speed spindle under various working conditions. The method is established by developing a numerical code combining the mechanical ANSYS parametric design language and the conjugate gradient method. The proposed method features a high efficiency solution to direct and inverse problems. It requires a small number of iterations for the computational algorithm, while provides excellent accuracy in temperature and heat source estimations. Computational time is also taken into account through choosing the best form of conjugation coefficient as well as mesh size. Results show that based on only two measurement points, the proposed method can accurately obtain inverse results that agree well with exact solutions even if measurement noise is involved. These results also indicate that the proposed method has a strong potential for estimating the heat sources in a complex structure which is combined different materials.