Yohan Kondo

Traceability strategy for gear-pitch-measuring instruments: development and calibration of a multiball artifact

There is a strong demand to ensure the traceability of gear-measuring instruments (GMIs). We propose a multiball artifact (MBA) for the evaluation of pitch-measuring accuracy. The aim of the MBA is to transfer the minimum uncertainty from a calibrated value at the National Metrology Institute of Japan (NMIJ) to a measured value of GMIs at a shop floor. The MBA is composed of equally spaced high-accuracy balls around an axis. The pitch-measuring accuracy of GMIs is evaluated by measuring the angular pitch deviation of the balls instead of the angular pitch deviation of a gear. We calibrated the angular pitch deviation using a coordinate measuring instrument (CMM) at the NMIJ and adapting a multiple-orientation technique. We proposed a calibration strategy of the angular pitch deviation. The calibration value of the pitch deviation for the MBA at the NMIJ was obtained with a measurement uncertainty (U95) of 0.2 µm. We evaluated the pitch-measuring accuracy of a GMI using the calibrated MBA. Each value of U95 for the cumulative and single pitch deviations for the left and right flanks was less than or equal to 0.5 µm. The small uncertainty was transferred from the NMIJ to the GMI.

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. DOI: 10.1115/1.3087535

Development of a Novel Artifact as a Reference for Gear Pitch Measuring Instruments

The pitch accuracy of a gear is graded on the order of 0.1 μm in ISO 1328-1; therefore, it is necessary for gear measuring instruments (GMIs) to be able to measure gears with the required high accuracy. GMIs are evaluated by measuring a calibrated gear or a gearlike artifact. It is, however, difficult to obtain a measurement uncertainty of less than 0.1 μm. The reason for this difficulty is that a gear artifact has a form error and surface roughness, and that the measurement position on the gear face differs slightly from the calibrated position. In view of this situation, we propose a novel multiball artifact (MBA), which is composed of equally spaced pitch balls, a centering ball, and a datum plane. The pitch balls are assumed to act as gear teeth by calibrating the angular pitch between the centers of each pitch ball. The centering ball and the datum plane are used to set a reference axis of the virtual gear. We manufactured an MBA with the pitch balls arranged on a curvic coupling. The angular pitch deviation between the centers of each pitch ball was calibrated using a coordinate measuring machine (CMM) and adopting the multiple-orientation technique. A master gear was also calibrated for comparison. The measurement uncertainty for the cumulative angular pitch deviation was 0.45 arc sec for the MBA and 1.58 arc sec for the master gear. The MBA could be calibrated with small uncertainty compared with the master gear. After the calibration, a virtual gear of the MBA was built using the calibration value. The virtual gear was measured using the gear-measuring software on the CMM. The measurement value was equal within the range of uncertainty of calibration value. It is verified that the superiority of the MBA to the gear artifact is due to the following reasons: (1) The balls can be manufactured with an accuracy of several tens of nanometers. (2) The calibrated result for the MBA is almost independent of a probe-positioning error because the centers of each pitch ball can be measured at multiple points. (3) In setting the reference axis, the gear artifact generally uses a datum cylinder, in contrast, the MBA uses more accurate ball.

Design Method of Double Ball Artifact for Use in Evaluating the Accuracy of a Gear-Measuring Instrument

Vibration of gears is a serious problem in mechanical devices. The characteristics of these vibrations are strongly affected by tooth flank form deviation of micrometer or submicrometer order. The quality of manufactured gears is controlled by a gear-measuring instrument. The accuracy of the profile measurement by such an instrument is evaluated using a master gear or an involute artifact. However, it is difficult to manufacture gears with high accuracy because the involute is a complicated geometrical form. To solve this problem, the double ball artifact (DBA) has been proposed as a means to evaluate the profile measurement accuracy. The application of the DBA requires a DBA design method so that the DBA can be applied to a wide variety of gear dimensions in the industrial field and can realize high-precision evaluation. In the present study, a design method is proposed for the DBA, and the dimensions, tolerance, and material of the DBA are determined. A DBA is designed and manufactured according to the proposed design method and the effectiveness of the manufactured DBA is verified experimentally using a gear-measuring instrument.

Artifact Design and Measurement Error Analysis in the Evaluation of Lead Measurement Accuracy of Helical Gear Using Wedge Artifact

The reduction in the vibration and noise of gears is an important issue in mechanical devices such as vehicles and wind turbines. The characteristics of the vibration and noise of gears are markedly affected by deviations of the tooth flank form of micrometer order; therefore, strict quality control of the tooth flank form is required. The accuracy of the lead measurement for a gear-measuring instrument is usually evaluated using a helicoid artifact. However, it is difficult to manufacture it with high accuracy because the helix is a complicated geometrical form. To solve this problem, a method of evaluating a gear-measuring instrument using a wedge artifact, which includes a highly precise plane surface, has been proposed. In this research, to put the wedge artifact into practice, a design method of the wedge artifact is developed. In addition, the effects of the measuring condition and the setting error of the wedge artifact on the measurement result are investigated. The uncertainty for the evaluation method using a wedge artifact is assessed by a measurement experiment and simulation.

Optimized measurement strategy for multiple-orientation technique on coordinate-measuring machines

Coordinate-measuring machines (CMMs) are widely used to measure the characteristics of various geometrical features. The measurement results using CMMs include systematic errors. To eliminate the systematic errors, the multiple-orientation technique is effective for rotationally symmetric workpieces such as cylinders or gears. However, there are Fourier components of the calibration curve that cannot be analyzed on the basis of the number of orientations; therefore, the number of orientations was set to be larger than the number of required Fourier components. Such a method takes, however, a very long time and it is difficult to maintain a stable environment during the measurement. In this paper, we propose a new measurement strategy for reducing the total number of orientations by compensating the deficient Fourier components using the measurement result with another number of orientations. When the lowest common multiple of integers m and n is set to be larger than the number of required Fourier components, the calibration result can be obtained from m + n − 1 orientations. To select m and n most efficiently, the combination should not include a common prime number. The effectiveness of the combination measurement strategy for the multiple-orientation technique was demonstrated by calibrating a multiball artifact and a gear.

Evaluation of the deformation value of an optical flat under gravity

The flatness of an optical surface can be evaluated using a Fizeau interferometer. There is strong demand for ensuring that the measurement uncertainty of flatness is of nanometer order over a measurement range of 300?mm or more; however, the measurement range and measurement uncertainty of flatness at the National Metrology Institute of Japan (NMIJ) are 300?mm and 10?nm, respectively. In a Fizeau flatness interferometer, the gap distance between the reference flat and the specimen is measured. To obtain the absolute profile of the specimen, the absolute profile of the reference flat should be measured in advance. The three-flat test is one of the methods used to measure the absolute profile of a reference flat. The reference flat, however, deforms under the force of gravity, and its absolute deformation value cannot be determined by the three-flat test. The deformation value of the reference flat can be corrected by the finite element method (FEM) analysis; however, it is difficult to ensure the validity of the analysis and there is a large uncertainty component of the Fizeau flatness interferometer. To verify the FEM analysis, we developed a scanning deflectometric profiler (SDP) that does not require a reference flat and can directly measure a profile. We calibrated an optical flat using a Fizeau flatness interferometer and the SDP. Finally, the deformation value of the reference flat under the force of gravity was evaluated by comparing the measurement results.

High-lateral-resolution scanning deflectometric profiler using a commercially available autocollimator

The lateral resolution of the angle-based deflectometric surface profiler using a commercially available autocollimator has been improved by introducing a novel null instrument. The proposed null instrument is simple, inexpensive, and has a short response time. High-accuracy flatness measurements of low-reflective surfaces have been successfully demonstrated using a laser beam with a spot size of 1 mm. The repeatability of the surface profile measurement is better than ±0.6 nm.

Evaluation of a high-precision gear measuring machine for helix measurement using helix and wedge artifacts

High-precision gears are required for advanced motion and power transmission. The reliability of the measured value becomes important as the gear accuracy increases, and the establishment of a traceability system is needed. Therefore, a high-precision gear measuring machine (GMM) with a smaller uncertainty is expected to improve the gear calibration uncertainty. For this purpose, we developed a prototype of a high-precision GMM that adopts a direct drive mechanism and other features. Then, the high measurement capability of the developed GMM was verified using gear artifacts. Recently, some new measurement methods using simple shapes such as spheres and planes have been proposed as standards. We have verified the tooth profile measurement using a sphere artifact and reported the results that the developed GMM had a high capability in tooth profile measurement. Therefore, we attempted to devise a new evaluation method for helix measurement using a wedge artifact (WA) whose plane was treated as the tooth flank, and the high measurement capability of the developed GMM was verified. The results will provide a part of information to fully assess measurement uncertainty as our future work. This paper describes the evaluation results of the developed GMM for helix measurement using both a helix artifact and the WA, and discusses the effectiveness of the WA as a new artifact to evaluate the GMMs.