The tool influence function (TIF) modelling for magnetorheological finishing (MRF) is crucial for ultra-precision fabrication of aspheric cylindrical components, and has been widely studied. Nonetheless, the existing TIF modelling methods for MRF suffer from several shortcoming when applied in industry, including the need for physicochemical measurements, the unanalytical hydrodynamics, and the inaccurate calibration of influence coefficient, unresolved coupling between physicochemical and geometric factors, and inapplicability to complex surfaces. To overcome those deficiencies, this work proposes an exponential-trigonometric-spline (ETS) based TIF modelling method for MRF of aspheric cylinder incorporating full decoupling, analytical hydrodynamics, and nonlinear calibration. First, the influences of physicochemical and geometric factors on the TIF for cylindrical surface are decoupled. An ETS-based model for pressure and shear stress is established, and the TIF is reconstructed through nonlinear calibration of the influence coefficient. Then the roles of morphological coefficients in the TIF formation mechanism for MRF are elucidated, and the evolution law of those coefficients with respect to curvature and immersion depth is modelled using a stepwise bivariate Hermite interpolation (SBHI) algorithm. Finally, an efficient deduction method based on an iterative contact-adaptive matching (ICAM) algorithm is proposed. Compared with existing methods, the proposed approach exempts physicochemical measurements, fully decouples physicochemical and geometric factors, and significantly improves adaptability to the contact area on aspheric cylinder. Simulation and experimental results demonstrate that the proposed method significantly improves the accuracy and reliability of TIF reconstruction and deduction compared with conventional methods. For TIF reconstruction, APRRE, AVRRE, and ACE are reduced by 69.63∼96.59%, 30.33∼67.75%, and 25.55∼50.67%, respectively. For TIF deduction, corresponding reductions of 10.74∼84.16%, 8.59∼51.24%, and 12.63∼55.29% are achieved. This work provides important technical support for improving the precision and determinism of MRF for complex surface.
Multiplicative speckle noise is a major challenge in coherent imaging modalities such as synthetic aperture radar (SAR) and ultrasound imaging, where effective noise suppression must be achieved without compromising structural and textural details. In this work, we propose a texture-preserving Caputo fractional-order telegraph diffusion model for image despeckling. The proposed formulation incorporates a Caputo time-fractional derivative into a nonlinear telegraph diffusion framework, combining nonlocal temporal memory effects with wave-like propagation behavior. The resulting fractional dynamics provide enhanced control of the diffusion process while reducing numerical dissipation compared with classical integer-order models. Furthermore, the telegraph diffusion mechanism preserves oscillatory structures and high-frequency image features, mitigating the excessive smoothing commonly encountered in standard parabolic diffusion approaches. We establish a maximum-principle property that guarantees the solution remains bounded by the initial image data and develop a semi-implicit finite difference scheme based on the Caputo L1 approximation, which is proved to be unconditionally stable. Extensive experiments on natural, texture, SAR, MRI and ultrasound images demonstrate that the proposed method effectively suppresses multiplicative speckle noise while preserving important image features. Quantitative and visual comparisons show that the proposed approach reliably outperforms several classical PDE-based methods and relevant recent despeckling approaches.
