Topology optimization of cooling elements for worm wheel gear grinding machine tool bed under non-uniform heat sources

In high-performance gear manufacturing, thermal deformation of machine tool beds poses a critical challenge that directly affects machining accuracy and system reliability of the whole worm wheel gear grinding machine tool. Long-term operation and localized heat accumulation around the workpiece and grinding wheel spindles often result in uneven temperature fields and thermal error of the whole machine tool. Conventional cooling methods-typically relying on empirically designed serpentine or U-shaped channels-struggle are used to reduce temperature and thermal deformation. But uneven temperature distribution and significant pressure drop exist. Moreover, many topology optimization studies in cooling design assume idealized conditions, such as uniform heat sources and horizontal channel configurations, which limit their applicability in real-world vertical systems. To address these issues, a topology optimization-based design method of cooling elements is proposed for machine tool beds subjected to spatially varying heat sources and vertical installation constraints. A two-dimensional steady-state thermal-fluid model is established using the Brinkman penalization method to simulate flow in porous media. Gravity is incorporated into the momentum conservation equation to reflect real-world conditions and a multi-objective function is formulated to simultaneously minimize average temperature, temperature gradient, and pressure drop. The governing equations are further simplified to improve convergence rate by 20 %. Comparative simulations and experimental validations demonstrate that the designed topology-optimized cooling plate outperforms conventional designs in thermal uniformity and energy efficiency. Specifically, the topology optimized channel is able to reduce average temperature of the machine tool bed by over 10 %, Z-direction thermal deformation by 32 %, and pressure loss by up to 57.7 % compared to traditional cooling strategies. The practical application yields a substantial reduction in maximal errors for both left and right tooth flanks, diminishing from 18.5 μm to 6.3 μm and from 16.7 μm to 5.4 μm, respectively. This culminates in a notable enhancement of the worm wheel gear grinding machine tool’s accuracy, by approximately 65 %. These improvements significantly enhance the thermal stability and machining accuracy of gear grinding systems, offering a robust solution for next-generation precision machine tool design.