<p>Predicting part machining deformation is vital for optimizing design and manufacturing processes, thereby enhancing the quality and performance of heavy machinery parts. Traditional numerical methods, such as the finite element method, are limited by their computational inefficiency. Furthermore, recent data-driven approaches for predicting machining deformation face challenges due to the complex features and variable geometries of parts throughout design iterations and machining processes. To this end, this paper proposes a method, Voxel-FNO, which rapidly predicts machining deformation for parts with variable feature geometry. This method utilizes the Fourier neural operator to capture the underlying mechanistic relationship between residual stress and machining deformation of parts. Both stress and geometry are sampled by voxel into standard domain before being input into the neural network model. This approach ensures efficiency and applicability, even as part geometries change. The proposed method is verified in both simulation and real environment, demonstrating its accuracy, stability, and generalization capability for varying part geometries, compared to the accurate results from the finite element method. It shows prediction max errors of 0.003 mm, 0.002 mm, and 0.018 mm, and RMSE of 0.0003 mm, 0.0002 mm, and 0.0013 mm for deformations in X, Y, and Z directions, respectively, compared with FEM results.</p>