A collaborative optimization method for topology and dimension of machine tool spindle system considering the modal-thermal deformation correlation criterion

To address the challenges in meeting the comprehensive performance requirements of high-speed and high-precision machine tool spindle systems, which demand superior dynamic characteristics (modal) and thermal stability (thermal deformation), and to overcome the limitations of traditional optimization methods (where modal analysis is decoupled from thermal deformation analysis, and singleobjective optimization struggles to balance multiple performances), this study proposes a collaborative topology and dimension optimization method that integrates a modalthermal deformation correlation criterion. Firstly, a 3D finite element model of the machine tool spindle system is established, followed by multi-physics field simulations to perform temperature field, thermal deformation, and modal analyses. Secondly, using performance data obtained under multi-rotational speed working conditions, the coupling effects of temperature on elastic modulus and thermal deformation on geometric stiffness are quantified. Subsequently, a modal-thermal deformation correlation criterion is derived and verified. Finally, with the derived criterion acting as a constraint, and aiming to maximize the first-order natural frequency while suppressing thermal deformation, topology optimization is first implemented using the SIMP interpolation model and the MMA algorithm to determine the optimal material distribution. Subsequently, dimension optimization is performed by combining optimal Latin hypercube design, response surface methodology (RSM), and a multi-island genetic algorithm (MIGA). Verification on a specific spindle system demonstrates that after optimization, the spindle's first-order natural frequency increases from 326.8 Hz to 346.8 Hz, its maximum thermal deformation decreases from 0.022911 mm to 0.0182 mm, and structural lightweighting is simultaneously achieved. These research results offer theoretical support and practical engineering methods for the multi-performance collaborative optimization of machine tool spindle systems.