*Article* **Automatic Error Compensation for Free-Form Surfaces by Using On-Machine Measurement Data**

#### **Wei-chen Lee \*, Yu-tzu Lee and Ching-Chih Wei**

Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei 10607, Taiwan

**\*** Correspondence: wclee@mail.ntust.edu.tw; Tel.: +886-2-2737-6478

Received: 15 June 2019; Accepted: 28 July 2019; Published: 30 July 2019

#### **Featured Application: The algorithm of the research can be applied to machining industry to reduce the variation of the product dimensions.**

**Abstract:** Currently, most computer numerical control (CNC) controllers lack the function needed to compensate machining errors for free-form surfaces. The objective of this research was to enhance the accuracy and precision of the machined free-form surfaces of a workpiece using the mirror compensation method with the on-measurement data. By mirroring the points measured after semi-finishing, a new free-form surface for finishing machining can be automatically reconstructed. The surface can then be used to generate the cutting tool path to reduce the errors during finishing machining. In this research, three di fferent types of surfaces were used for evaluating the proposed method. The results show that the proposed method reduced the standard deviations of the three surface geometries by 61%, 61%, and 32%, respectively. We also evaluated the tool radius modification method commonly used in the industry for error compensation and found that there is no substantial reduction on standard deviation. Therefore, the e ffectiveness of the error compensation method proposed in this research is evident.

**Keywords:** error compensation; free-form surface; on-machine measurement; mirror compensation method
