Extension of the displacement method by measuring reference pieces using multiple sensors for on-machine surface profile measurement

On-machine measurement is crucial in industrial production because it allows the measurement of the surface properties of products without having to remove them from the machine tool; however, measurement results are superimposed with the motion error caused by the table traverse. Therefore, eliminating motion errors is this field's main objective. This paper discusses measuring a surface profile using an extension of the displacement method to eliminate motion errors. The displacement method can separate the surface profile and motion error of the stages in measurement results; however, it introduces a specific cumulative error. The tolerance of the accumulated error was first investigated by simulating a one-axis measurement. The displacement method was extended to a two-axis stage to measure the surface profile and correct the stage tilt to each axis. Moreover, carbon steel finished using a face mill was measured in the experiments, and a coordinate measuring machine was used to compare the results with those of the extended displacement method. It was found that the extended displacement method was able to remove the motion error. Applying the displacement method resulted in an improvement of approximately 88.9%. Error analyses were also formulated and evaluated for sensor drift, reference piece measurement, motion error, table rotation, and thermal expansion, and the percentage of these errors in the total was clarified. The results showed that the motion error and table rotation for the y-axis of the prototype experimental apparatus were larger than the others. These errors are discussed to analyze each error and listed in the error budget. The proposed extended displacement method can eliminate motion errors despite the simplicity of the measurement principle and can be easily integrated into machine tools and other tables.