A Mathematical Model for Measuring the Static Geometry Errors of a Machine Tool with a Laser Tracker System

• Main Authors: Jui-Liang Her, 何瑞樑
• Other Authors: Chien-Chang Lin
• Format: Others
• Language: en_US
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/62949295940909540817

博士 === 國立中興大學 === 應用數學系 === 92 === This dissertation proposes a mathematical model for measuring the static geometry errors of a machine tool. The mathematical model consists of a triangular plate with three caves on it and a pyramid is imagined on one of the three caves. The model is based on the measurement behavior of a laser tracker system. Three caves are then needed on the plate for putting sensor ball on the three specific points there. If there exits another suitable instrument that can measure the three specific points on the plate, then the caves must be changed to fit the new requirement. The static geometry errors include nine linear errors and nine angular ones. The linear error δ j (i) is defined as the linear error happened in j-axis direction due to the step movement in i-axis direction. And the angular error ε j (i) is defined as the angle error rotated about j-axis due to the step movement in i-axis direction. The static geometry errors of a machine tool can be calculated with the turning over rigid body motion of the plate and the imagined pyramid. The plate is fixed on the machine spindle and moves with it steps by steps toward the diagonal of the working space. After setup, the plate is moved to the place where the location is wanted and then stops there. Then a sensor ball is put into the three caves on the plate sequentially and slowly. When the sensor ball moves from one cave to the other, the laser tracker will rotate automatically with it and then detect the coordinates of each cave. There is an imagined pyramid created on one of the three caves. The movement and rotation of the plate can be calculated by means of the coordinates of the three caves and the imagined pyramids before and after the plate’s rigid body motion. Then the eighteen static geometry errors including linear positional errors and angular pitch, roll, yaw errors of the machine tool at that position can be calibrated. The body diagonal measurement has been recommended for a quick check of the volumetric accuracy in the ASME B5.54 standard [1], section 5.9.2. This is because the body diagonal measurement is sensitive to all the errors such as the position errors, straightness errors, squareness errors, and the angular errors. Thus, it is a good way to check the volumetric accuracy. The measurements in this dissertation is just completed by moving the machine spindle from one lower corner of the working space to the opposite upper corner along the diagonal line steps by steps. The real paths of movements are moving in x, y, z-axis direction, respectively. The simulation proves the correctness of the mathematical model in a CAD/CAM system named CATIA. The method proposed here has the merits of easy setup, quick measurement and accuracy. The model of laser tracker system and triangular plate is also proposed to measure the geometry errors on a circle path and the angular errors of a rotary index table. The flatness situation of a machine table is also studied. The further work of experiment is expected to be finished recently. In the experimental study, some topics will be discussed, including measurement errors and uncertainty analysis, etc. The method is expected to measure the squareness errors in the future. And the on-line or off-line compensation can also be considered together in the final system.