On-Machine Measurement of Profile and Concentricity for Ultra-Precision Grinding of Hemispherical Shells

Abstract

The profile and concentricity of hemispherical shells affect the frequency split and quality factor of hemispherical resonators. To compensate for machining errors caused by tool wear and tool setting, an on-machine measurement (OMM) method for the profile and concentricity of hemispherical shells in ultra-precision grinding was developed without the removal of workpieces from the machine tool. The OMM utilizes an inductive lever probe to test the inner and outer surfaces of the shell. A standard sphere is utilized to calibrate the relative position of the inductive lever probe at the two different work positions. To enhance the test accuracy of the OMM, a zero-position trigger-sampling method for the inductive lever probe was developed. It was verified to achieve a stable repeatability accuracy of 0.04 μm when using the OMM to realize a single-point sampling. Hemispherical shells were tested using the proposed OMM method. The concentricity test’s accuracy was verified to achieve accuracy better than 1 μm using a coordinate measuring machine and a standard sphere. The accuracy was 0.26 μm for testing the profiles of the hemispherical shell. The proposed OMM system was integrated with an ultra-precision machine tool. It is hoped that this method can help realize the integration function of machining-measurement-compensation.

A normal tracking differential confocal measurement method for multiple geometric parameters of hemispherical shell resonator with a common reference

“…Figure 18 shows the measurement results for the equatorial thickness of the HSR shell; the average shell thickness T is 835.726 µm. According to equations ( 5) and (10), the inside surface curvature radius R I of the equatorial cross-section of the HSR is 10 109.012 µm; the thickness uniformity t u of this section is 0.819 µm.…”

“…It cannot accurately represent the inside and outside surface profiles or the shell thickness of the HSR. Wang et al [10] used a contact probe to measure the inside and outside surface profiles and concentricity of the HSR online during processing. De Podesta et al [11] used a coordinate measurement machine to measure the profiles of quasi-spherical resonators.…”

Unified framework for geometric error compensation and shape-adaptive scanning in five-axis metrology systems

“…Upon constructing the geometric error model, the compensated measurement points W Q compensate are obtained by correcting the original measurement points W Q measure using the synthesized error δ, as articulated in equation ( 10), This establishes a one-to-one mapping between W Q measure and W Q compensate , thereby completing the error compensation process. It is crucial to differentiate between the roles of equations ( 9) and (10). The former refers to the analytical expression for the geometric error model, while the latter provides a numerical calculation methodology for correcting the actual measurement points 1, 2, .…”

“…After computing the compensated data W Q compensate from equation (10), it becomes essential to construct the theoretical surface W Q theory to serve as a reference for evaluating deviations in the compensated measurements. Following the idea of surface construction via forward kinematics, the theoretical surface is generated from equation ( 11) by nulling geometric errors and surface deviations.…”

“…The advent of complex optical surfaces, such as conformal domes [9], hemisphere resonators [10], and freeform surfaces [11,12], poses significant challenges to both of these metrology approaches [13]. These intricate components demand measurement techniques that synergize flexibility with high accuracy.…”