Nonlinear time-controlled grinding method for micron-accuracy machining of complex curved surfaces

The growing demand for complex curved optical components has exposed the limitations of existing micron-scale machining methods. In the conventional grinding–lapping–polishing process, precision grinding only achieves an accuracy of tens of micrometers, failing to meet the entry requirements for polishing. Although lapping can serve as a transition to polishing, it suffers from low accuracy and long cycle time due to poor conformal contact and edge effects. Ultra-precision grinding (UPG) reaches micron-level accuracy but introduces deep grinding marks that are difficult to eliminate via polishing, still necessitating lapping and thus further degrading the accuracy. To address these issues, this paper introduces a time-controlled grinding (TCG) machine tool and further proposes a nonlinear TCG method. The nonlinear geometric modulation of the gravity component through the local surface slope is modeled explicitly, and a position-dependent nonlinear compensation factor together with a force–position coupling compensation model is established, while the material removal itself retains a linear Preston dependence on the contact force. Experimental verification on a 330 − mm off-axis aspheric mirror shows that the surface profile accuracy is improved from a PV value of 23.224 μ m after lapping to 8.413 μ m , achieving accuracy comparable to UPG without severe grinding marks. Power spectral density analysis indicates a significant reduction in low-frequency errors, satisfying the polishing entrance condition and markedly outperforming conventional lapping. This work provides an effective approach to breaking through the contradiction between accuracy and efficiency in the manufacturing of complex curved surfaces. • The time-controlled grinding (TCG) machine tool and its working principle are introduced in detail. • Nonlinear TCG is elaborated and applied to address the challenge of efficient, micron-precision manufacturing of complex curved surfaces. • Nonlinear TCG achieves machining accuracy comparable to ultra-precision grinding, while producing shallower grinding marks. • Compared with lapping, nonlinear TCG exhibits advantages in both machining efficiency and accuracy.