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In this work, a special grinding machine tool using a small ball-end grinding wheel is designed to achieve ultra-precision grinding of complex components with small concave surfaces. A comprehensive error propagation model is established, considering kinematic errors, setup errors and structure parameters. Sensitivity analysis is performed by the Sobol' method to quantify the relationship between the errors, structure parameters and geometric accuracy of the machine tool. On this basis, error allocation is carried out, and the inclination angle of the grinding wheel spindle and the working range of the C-axis are optimized to reduce the influence of the setup errors on machining accuracy. Then, the predicted geometric accuracy of the machine is 0.3 μm, contributing only to half of the profile accuracy requirement for peak-to-valley PV

To meet the strict requirements for processing quality, the metal-bonded small ball-end diamond wheel (SBDW) has become a promising choice to process the hard and brittle materials with small concave surface. Unlike conventional diamond wheels, the profile accuracy of SBDW would so greatly affect the form accuracy of ground small concave surfaces that a truing system must be adopted to insure the accuracy of SBDW. Hence, the effects of kinematic parameters of the truing system on the on-machine electric discharge truing (EDT) of SBDW are investigated. The effects of the errors from kinematics, electrode geometry and relative position on truing are analyzed by establishing the mathematical model through screw theory. In the experiments, the effects of spindle speeds of SBDW and tool electrode on truing are investigated and the complex component with small concave surfaces is ground by the optimally trued SBDW. The results indicate that there are more factors affecting the dimension accuracy than profile accuracy of the trued SBDW. Each factor affects dimension accuracy equally, while the radial run-out error of grinding wheel spindle influences profile accuracy more significantly than others. The spindle speed of SBDW affects the profile accuracy more remarkably than that of tool electrode, and the relative speed between them affects the truing efficiency and surface quality of SBDW. The final profile error (PV) and surface roughness (Ra) of the practically ground component are 0.328 μm and 50.2 nm, respectively.

Potassium dihydrogen phosphate (KH2PO4 or KDP) crystal is a typical soft-brittle optical crystal, and the size effect and brittle cutting mode are easy to appear in micro ball end-milling of KDP crystal. In this paper, micro-grooving experiments are conducted to study the size effect and brittle cutting in micro ball end-milling of KDP crystal with different feed rate and depth of cut. The cutting force, machined groove base quality and chip morphology are collected and analyzed carefully. The size effect is discovered by the phenomena of the existence of oscillations and relaxations in cutting force and hyper-proportional increase of specific cutting force, when the ratio of feed per tooth to cutting edge radius ft/re is less than 1. While the brittle cutting mode is detected through the existence of sharp fluctuations in cutting force and cracks on the groove base when the ratio ft/re is larger than 2. From the further comprehensive analysis of cutting force, specific cutting force, machined groove base quality and chip morphology, the cutting parameters with ratios of the maximum undeformed chip thickness in one cutting circle to cutting edge radius hmax/re around 0.14, 0.2 and 0.4 are regarded as size effect, optimal and brittle cutting points, respectively. The size effect, ductile cutting and brittle cutting zones are divided by the size effect and brittle cutting boundaries (points). Among the optimal points, the depth of cut of 2 μm with the ratio ft/re of 1 is the optimal cutting parameter for micro ball end-milling of KDP crystal.

Micro-milling is a promising approach to repair the micro-defects on the surface of KH2PO4 (KDP) crystal. The geometrical parameters of micro ball end mill will greatly influence the repairing process as a result of the soft brittle properties of KDP crystal. Two types of double-edged micro ball end mills were designed and a three-dimensional finite element (FE) model was established to simulate the micro milling process of KDP crystal, which was validated by the milling experiments. The rake angle of −45°, the relief angle of 45° and the cutting edge radius of 1.5–2 μm were suggested to be the optimal geometrical parameters, whereas the rake angle of −25° and the relief angle of 9° were optimal just for micro ball end mill of Type I, the configuration with the rake angles ranging from 0° to 35°, by fully considering the cutting force, and the stress–strain distribution over the entire tool and the cutting zone in the simulation. Moreover, the micro polycrystalline diamond (PCD) ball end mills adopting the obtained optimal parameters were fabricated by wire electro-discharge machining (WEDM) and grinding techniques, with the average surface roughness Ra of tool rake face and tool flank face ∼0.10 μm, and the cutting edge radius of the tool ∼1.6 μm. The influence of tool's geometrical parameters on the finished surface quality was verified by the cutting experiments, and the tool with symmetric structure was found to have a better cutting performance. The repairing outlines with Ra of 31.3 nm were processed by the self-fabricated tool, which could successfully hold the growth of unstable damage sites on KDP crystal.