Normally, contouring errors are usually generated when a machine tool controlled by numerical controller moves with a reference trajectory. These errors are due to delays of the motors, acceleration and deceleration of the numerical controller, vibration of the machine among others. For researchers to study this error, its magnification is deemed necessary since, its size in comparison to the reference trajectory, is very small. Currently, cross-grid encoders are the most popular tools used to measure these errors in two dimensional trajectories in machine tools and robots. Conventionally, this technique has an inherent set back in that the contouring error inside a corner is discontinuously magnified and represented. This in return makes it difficult to visually comprehend the manner in which the error occurred at the corner. More so, errors during the discontinuity cannot be quantitatively detected. Past scholars have proposed other techniques for solving this problem but a majority of those methods have critical drawbacks, which are complicated settings or restrictions on the reference trajectory, thereby triggering the need for a more practical and universal technique of utmost precision and minimal inhibitions.
Toshiaki Otsuki and colleagues at Tokyo University of Agriculture and Technology and Kobe University in Japan proposed a new method for continuously calculating the contouring error inside a corner, including the corner vertex without restrictions to magnify and represent the error. They aimed at applying the proposed technique to measure the results of an actual machining center. Their research work is now published in the journal, Precision Engineering.
To begin with, the research team undertook calculations for error propagation when assuming the case of a shorter measured trajectory length. This was accomplished by computing the error from the reference trajectory towards the measured trajectory since, generally, the reference trajectory is longer than the measured trajectory. Secondly, the team, for the alternative case where the measured trajectory is longer than the reference trajectory due to overshooting or vibration, undertook the error computations from the measured trajectory towards the reference trajectory as was previous done in the convectional method.
The authors of this paper observed that for the shorter measured trajectory length the direction of the error obtained was continuously changing before and after the corner and the magnified error trajectory was continuous. Of crucial importance, the team noted that the novel technique was both practical and universal and needed not any complicated settings or restrictions on the reference trajectory. More so, they realized that the technique could be used to calculate the error continuously even inside corners; particularly at the corner vertex.
Herein, a practical and universal novel technique namely: the inward direction error calculation method (the ID method), has been presented. This technique can be used to compute and magnify the contouring error inside the corner continuously without being restricted by settings or conditions on the reference trajectories. Its usefulness has been confirmed by its application on actual measurement of machine tool. Additionally, the technique can be used to accurately obtain the maximum error and the average error of an entire reference trajectory.
Toshiaki Otsuki, Hiroyuki Sasahara, Ryuta Sato. A method for the evaluation and magnified representation of two-dimensional contouring error. Precision Engineering volume 50 (2017) pages 433–439
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