A new method for directly measuring the position errors of a three-axis machine. Part 1: theory

This paper presents a measurement method and instrument to measure position changes in a three-axis machine workspace. The proposed instrument, named 3D step gauge, includes two parts. One is composed of three LVDTs and installed in the main spindle. The other is a plate that is fixed on the worktable. Many triangular pyramids are distributed on the plate. Each pyramid profile plane is the basic measurement plane for the LVDTs. When the spindle moves relative to the plate, the LVDTs’ tip ends slide on the pyramid profile planes. From the datum measured by the LVDTs, the differential position changes of the spindle can be obtained by the pyramid’s constructional parameters. In addition, the error effect analysis is used to investigate the accuracy of the method with respect to the factor of the device constructional parameters. Part 1 of this paper gives the basic theory of measuring the differential position changes in the multi-axis machine workspace. Part 2 gives the application of this theory and so the position error in the multi-axis machine workspace can be directly measured. This proposed method and the instrument have been tested using an actual machine tool. The measurement results show good repeatability and high accuracy.