Design and Error Analysis of Multiball Artifact Composed of Simple Features to Evaluate Pitch Measurement Accuracy

The strength and vibration/noise of gears are influenced by the pitch deviation of micrometer order and therefore, advanced quality control is needed in gear manufacturing processes using measuring instruments. The accuracy of the pitch measuring instrument is verified using a master gear or artifact, but their accuracy is not sufficiently high. An artifact with higher accuracy for the evaluation and calibration of the pitch measurement is necessary in order to respond to the requirement of gear accuracy. In this research, the multiball artifact, a novel high-precision pitch artifact, is proposed for use in the evaluation of pitch measuring instruments. The multiball artifact is composed of balls, a cylinder, and a plane, where the center cylinder or center ball is surrounded by the balls on the plane. The positions of those elements are decided automatically by the contact among those elements. Balls, cylinders, and planes can be manufactured with accuracy on the order of several tens of nanometers. Therefore, this artifact can realize high accuracy. In addition, this artifact does not need advanced techniques in manufacturing and assembly. This leads to the reduction in manufacturing cost. In this report, the concept and structure of the multiball artifact are proposed, and theoretical analysis on the measurement of the artifact is carried out. Feasible angular pitch is analyzed theoretically. For a cylinder-centered artifact, it is easy to realize the target angular pitch by adjusting the cylinder diameter. Ball-centered types suffer from the limitation of the variation in ball diameter if standard balls are used, but an angular pitch close to the target pitch is possible through the selection of an appropriate combination of balls. The effects of the dimensional deviation of the diameter of the center cylinder, the inclination of the center cylinder, the dimensional deviation of the surrounding ball diameters, the sphericity of balls, and the flatness of the base plane are analyzed. Deviations in the cylinder have a comparatively large effect on angular pitch. On the other hand, the effect of the deviation of the ball or base plane is smaller. The feasible angular pitch is clarified, and it is verified that the concept and structure of the multiball artifact are effective. The effects of deviations in the form and dimension of the composing elements are analyzed, and it is clarified that the accuracy of the cylinder is important.