The design and kinematic modelling of a novel single-sensor three-dimensional coordinate measuring machine

Abstract

Traditional measuring equipment such as callipers, gauges and micrometres are well-known measuring instruments and they have been trusted for decades by industries to perform dimensional measurements. However, in situations where complex shapes or less uncertainty is required a unique but more advanced metrology system such as a coordinate measuring machine (CMM) is employed to provide a solution. CMMs are highly recommended measuring equipment because of their versatile capabilities, measuring flexibility and measurement setup that is easy to perform. They have displayed potential for automated measurement, reverse engineering, and the ability to be integrated with computer design and manufacturing systems. The new developments towards miniaturization and the changes in technical specifications from foundries and aerospace, automotive, medical, semiconductor, electronic, and other manufacturing industries have driven the need for CMMs with less uncertainty. Therefore, to keep up with miniaturization and the technical specification changes of parts, a fast three-dimensional (3D) CMM with acceptable uncertainty becomes necessary. The industry has presented unique developments of CMMs with great speed at micro and nanometres accuracy. These designs have demonstrated potential for further innovation(s) to reduce the manufacturing cost of the machines. Thus, this study proposes a novel CMM design that has the potential to measure 3D objects using only one displacement sensor without compromising the Abbe principle. The novel CMM design discussed in this study considers the conceptual bases of the ultra-precision CMM by reducing the number of displacement sensors or interferometers from three to one while achieving micrometre measurement uncertainty. To satisfy these conditions, the design incorporates Abbe's principle as the fundamental basis to achieve positioning accuracy. Also, the metrology frame and structural frame are separated to allow for optimising the design. The design suggests a workpiece supported by the mirror table and is translated into the x and y-axis by the manipulation system. The mirror is positioned at 45o to the vertical axis of the mirror table, and towards each plane surface of the coordinate system. The displacement sensor is mounted at 45o at the lower end of the vertical member of the metrology frame while the probe is fixed at the horizontal end. The functional line (laser beam) of the displacement sensor is always fixed to the tip of the probe. This configuration allows the alignment to be maintained and fulfil Abbe's fundamental requirements in all translations of the machine in a global coordinate system. The mirror is perpendicular and always intersects the laser beam at a gap distance between the displacement sensor and the probe. The kinematic and error modelling were developed to determine the positioning of the probe and the out-of-squareness of the mirror respectively. During the measurement process, the probe approaches the workpiece at a gradually decreased speed. This is achieved by dividing the travel distance until the probe contacts the workpiece, and a signal will command the motor to stop. The position of the probe is computed after every movement by solving a kinematic model. This is supported by understanding the direction of the translation, and the distance between the displacement sensor and the mirror. Therefore, the experiment was performed to validate the proposed kinematic model and the out-of-squareness of the mirror. During the experiment, the machine was employed to measure a calibrated gauge block from Matrix-Pitter with Grade 1. The developed kinematic model was proven to be relevant in determining the position of the probe. With a measurement standard deviation of 0.012, 0.016, and 0.018 mm on the x, y, and z-axis respectively.