{'fraction_non_alphanumeric': 0.02326869806094183, 'fraction_numerical': 0.006648199445983379, 'mean_word_length': 5.336842105263158, 'pattern_counts': {'":': 0, '<': 1, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Nano-level instrumentation for analyzing the dynamic accuracy of a rolling element bearing.

The rotational performance of high-precision rolling bearings is fundamental to the overall accuracy of complex mechanical systems. A nano-level instrument to analyze rotational accuracy of high-precision bearings of machine tools under working conditions was developed. In this instrument, a high-precision (error motion < 0.15 μm) and high-stiffness (2600 N axial loading capacity) aerostatic spindle was applied to spin the test bearing. Operating conditions could be simulated effectively because of the large axial loading capacity. An air-cylinder, controlled by a proportional pressure regulator, was applied to drive an air-bearing subjected to non-contact and precise loaded axial forces. The measurement results on axial loading and rotation constraint with five remaining degrees of freedom were completely unconstrained and uninfluenced by the instrument's structure. Dual capacity displacement sensors with 10 nm resolution were applied to measure the error motion of the spindle using a double-probe error separation method. This enabled the separation of the spindle's error motion from the measurement results of the test bearing which were measured using two orthogonal laser displacement sensors with 5 nm resolution. Finally, a Lissajous figure was used to evaluate the non-repetitive run-out (NRRO) of the bearing at different axial forces and speeds. The measurement results at various axial loadings and speeds showed the standard deviations of the measurements' repeatability and accuracy were less than 1% and 2%. Future studies will analyze the relationship between geometrical errors and NRRO, such as the ball diameter differences of and the geometrical errors in the grooves of rings.