On-machine measurement and temperature compensation method of NURBS surface interpolation for semicircular narrow neck thickness based on ultra-precision machine tool

Flexible joint is a typical low-rigidity micro part, which has four narrow neck structures evenly distributed around its central axis. In the ultra-precision machining process, it is crucial to control the dimensional accuracy of the narrow necks to improve stiffness consistency. However, the limited space of the neck structures and the high accuracy requirements bring extremely difficulties to the measuring process. In this paper, a novel on-machine measurement method for the semicircular narrow necks was presented and a measuring device was developed based on the combination of high linearity incremental measurement method and on-machine measurement technology. Moreover, the uncertainty of measurement error was analyzed in detail. In view of the measurement error caused by temperature drift, a compensation method based on non-uniform rational B-spline surface interpolation was used to enhance the measurement accuracy. The experimental results showed that the measurement accuracy enhanced over 30% after compensation, which met the measuring requirement of flexible joint.