Steven D. Phillips

Error compensation for CMM touch trigger probes

Abstract We present the analysis of a simple mechanical model of a common type of kinematic seat touch trigger probe widely used on modern coordinate measuring machines (CMMs). The model provides a quantitative description of the pretravel variation or “probe-lobing” characteristics that limit the use of such probes for high-accuracy dimensional measurements. We include the effects of stylus bending and the frictional interaction between the stylus ball and the part surface. The model is restricted to probes with simple straight styli, and we demonstrate significant error reduction both for vertically and horizontally oriented styli. In the latter case, gravitational forces are shown to play an important role in probe triggering and pretravel variation. Extensions to arbitrary orientations are discussed.

The estimation of measurement uncertainty of small circular features measured by coordinate measuring machines

Abstract This paper examines the measurement uncertainty of small circular features as a function of the sampling strategy; i.e., the number and distribution of measurement points. Specifically, we examine measuring a circular feature using a three-point sampling strategy in which the angular distance between the points varies from widely spaced, 120°, to closely grouped, a few degrees. Both theoretical and experimental results show that the measurement uncertainty is a strong function of the sampling strategy. The uncertainty is shown to vary by four orders of magnitude as a function of the angular distribution of the measurement points. A conceptual framework for theoretically estimating the measuring uncertainty is described, and good agreement with experiments is obtained when the measurements are consistent with the assumptions of the theoretical model. This paper is an expansion of a previous internal report 1 with additional material on analog probes and probe lobing models.

ASME B89.4.19 Performance Evaluation Tests and Geometric Misalignments in Laser Trackers.

Small and unintended offsets, tilts, and eccentricity of the mechanical and optical components in laser trackers introduce systematic errors in the measured spherical coordinates (angles and range readings) and possibly in the calculated lengths of reference artifacts. It is desirable that the tests described in the ASME B89.4.19 Standard [1] be sensitive to these geometric misalignments so that any resulting systematic errors are identified during performance evaluation. In this paper, we present some analysis, using error models and numerical simulation, of the sensitivity of the length measurement system tests and two-face system tests in the B89.4.19 Standard to misalignments in laser trackers. We highlight key attributes of the testing strategy adopted in the Standard and propose new length measurement system tests that demonstrate improved sensitivity to some misalignments. Experimental results with a tracker that is not properly error corrected for the effects of the misalignments validate claims regarding the proposed new length tests.

A Careful Consideration of the Calibration Concept

This paper presents a detailed discussion of the technical aspects of the calibration process with emphasis on the definition of the measurand, the conditions under which the calibration results are valid, and the subsequent use of the calibration results in measurement uncertainty statements. The concepts of measurement uncertainty, error, systematic error, and reproducibility are also addressed as they pertain to the calibration process.

Calculation of Measurement Uncertainty Using Prior Information

We describe the use of Bayesian inference to include prior information about the value of the measurand in the calculation of measurement uncertainty. Typical examples show this can, in effect, reduce the expanded uncertainty by up to 85 %. The application of the Bayesian approach to proving workpiece conformance to specification (as given by international standard ISO 14253-1) is presented and a procedure for increasing the conformance zone by modifying the expanded uncertainty guard bands is discussed.

Measuring Scale Errors in a Laser Tracker's Horizontal Angle Encoder Through Simple Length Measurement and Two-Face System Tests.

We describe a method to estimate the scale errors in the horizontal angle encoder of a laser tracker in this paper. The method does not require expensive instrumentation such as a rotary stage or even a calibrated artifact. An uncalibrated but stable length is realized between two targets mounted on stands that are at tracker height. The tracker measures the distance between these two targets from different azimuthal positions (say, in intervals of 20° over 360°). Each target is measured in both front face and back face. Low order harmonic scale errors can be estimated from this data and may then be used to correct the encoder’s error map to improve the tracker’s angle measurement accuracy. We have demonstrated this for the second order harmonic in this paper. It is important to compensate for even order harmonics as their influence cannot be removed by averaging front face and back face measurements whereas odd orders can be removed by averaging. We tested six trackers from three different manufacturers. Two of those trackers are newer models introduced at the time of writing of this paper. For older trackers from two manufacturers, the length errors in a 7.75 m horizontal length placed 7 m away from a tracker were of the order of ± 65 μm before correcting the error map. They reduced to less than ± 25 μm after correcting the error map for second order scale errors. Newer trackers from the same manufacturers did not show this error. An older tracker from a third manufacturer also did not show this error.

A novel artifact for testing large coordinate measuring machines

We present a high-accuracy artifact useful for the evaluation of large CMMs. This artifact can be physically probed by the CMM in contrast to conventional techniques that use such purely optical methods as laser interferometers. The system can be used over large distances; for example, over 4 meters, with an uncertainty of less than one part per million. The artifact is relatively inexpensive, robust for use in reasonable industrial environments, and significantly reduces testing time over traditional step gauge measurements.

Assessing ranging errors as a function of azimuth in laser trackers and tracers

Tilt and radial error motion of a laser tracker head as it spins about the two rotation axes result in small but measurable ranging and angle errors. The laser tracer, on the other hand, measures range with respect to the center of a high quality stationary sphere. It is therefore not expected to be influenced by the radial error motions of the carriage that carries the optics and the source, but the form error of the reference sphere and possibly the eccentricity in its placement with respect to the circular path traced by the carriage will be contributors to the ranging errors. In this paper, we describe experiments to assess the magnitude of these ranging errors as a function of the azimuth angle in different laser trackers and a laser tracer.

Properties of free-standing ball bar systems

Abstract This article offers recommendations to coordinate-measuring machine (CMM) buyers, sellers, and users on the design of free-standing ball bar systems used to evaluate the volumetric performance of CMMs according to the ANSI/ASME B89.1.12M standard. These systems are more widely used today than earlier methods such as magnetic ball bars. In this article we study the general design requirements, mechanical deformations under gravity and probing forces, vibrational considerations, and thermal effects on free-standing ball bar systems. We conclude with a summary of the issues in ball bar design, which must be considered in order to maintain an artifact error budget of ∼1 μm.

Performance evaluation of laser trackers

The American Society for Mechanical Engineers (ASME) recently released the ASME B89.4.19 Standard [1] on performance evaluation of spherical coordinate instruments such as laser trackers. At the National Institute of Standards and Technology (NIST), we can perform the complete set of tests described in the Standard, and have done so for a variety of laser trackers. We outline the tests described in the Standard, discuss our capabilities at the large-scale coordinate metrology group, and present results from B89.4.19 tests conducted on a few trackers. We also outline an analysis approach that may be used to evaluate the sensitivity of any measurement, including the tests described in the B89.4.19 Standard, to different geometric misalignments in trackers. We discuss how this approach may be useful in determining optimal placement of reference lengths to be most sensitive to different geometric misalignments.