As a new polishing method, bonnet polishing is suitable for polishing the curved surface due to its advantages in flexibility and adaptability of the polishing tool. In the polishing process, the contact state between the bonnet and the curved surface always changes. The traditional polishing tool path with equal interval will inevitably lead to over-polished areas and unpolished areas. In this article, a new tool path for bonnet polishing, which is called the revised Archimedes spiral polishing path, is proposed to ensure the physical uniform coverage of the curved surface in bonnet polishing. The path generation method is based on the modified tool–workpiece contact model and the pointwise searching algorithm. To prove the effectiveness of the revised path, two aspheric workpieces were polished along the traditional Archimedes spiral polishing path and the revised path, respectively. The roughnesses of the two workpieces are 10.94 and 10 nm, and the profile tolerances are 0.4097 and 0.2037 μm, respectively. The experimental results show that the revised path achieves lower roughness and surface tolerance than the traditional Archimedes path, which indicates that the revised path can achieve uniform physical coverage on the surface.

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The high-precision part surfaces are usually finished by the corrective polishing to improve the surface form accuracy. This article proposes a new method to model and optimize the material removal in the polishing process. This method assumes that the material removal rate in polishing follows the Preston’s equation, and the material removal profile is obtained by integrating the material removal index along the tool path at each unit area of the tool/workpiece contact. The focus is on the effect of the sliding velocity on the material removal profile. Results indicate that the shape of the removal profile is affected by the angular spindle velocity, angular feed velocity and tool path radius. A series of simulation and practical polishing experiments were conducted to verify the proposed model. The tending gene of the removal profile is defined and derived. By using the principle of maximum tending gene, the material removal profile is optimized, which is helpful to plan the process parameter properly in polishing.

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In deterministic polishing, solving the dwell time is one of the key factors. Usually, dwell time is solved by the tool influence function (TIF) and residual error. In previous research, single-point TIF (sTIF) is usually used in calculation, but it is not consistent with the TIF in the actual polishing process. In addition, when using the linear equation to solve the dwell time, a large TIF matrix results in a normal computer not having enough memory for calculation. In order to solve the above problems, a continuous TIF (cTIF) that changes with the polishing path is proposed: first, by the discretization method to simulate the continuous movement of the polishing tool in actual polishing, and then an optimized grouped least squares (LSQR) orthogonal decomposition algorithm is proposed to solve the dwell time. In this paper, an x − y polynomial free-form surface with different initial residual errors ( R M S = 30 n m , P V = 120 n m ; R M S = 70 n m , P V = 280 n m ; and R M S = 100 n m P V = 400 n m ) were simulated by the proposed algorithm, respectively. The final residual error was R M S = 1.8 n m , P V = 13.3 n m ; R M S = 2.6 n m , P V = 10.1 n m ; and R M S = 2.8 n m , P V = 17.4 n m , respectively. The convergence rate of RMS and PV basically reached 95%, and the validity of the algorithm is proved.