Local volumetric error calibration of a weak stiffness on-machine measuring device with a new 3-D calibrator

This paper presents a new local volumetric error calibration method for weak stiffness on-machine measuring (OMM) devices. First, the original volumetric error models’ union is established, and an equivalent dimensionality reduction algorithm is proposed to reduce the dimensionality of the model. As a result, a novel equivalent volumetric error models’ union (EVEMU) is derived, which is more suitable for cases with limited calibration data. For better flexibility and efficiency of error measurements, a new 3-D ball array calibrator is introduced, and its local calibration procedures can be executed directly in the 3-D space. Subsequently, a smoothly clipped absolute deviation (SCAD) regularization algorithm with oracle property is introduced to identify equivalent coefficients as well as select the optimal volumetric error sub-model of EVEMU, which can closely represent the real error state of the weak stiffness OMM device. The experiments demonstrated that the local volumetric error calibration method proposed in this paper is effective and provides new insights for the error compensation of similar devices.