Uncertainty analysis of slot die coater gap width measurement by using a shear mode micro-probing system

A shear mode micro-probing system was constructed for gap measurement of a precision slot die coater with a nominal gap width of 90 μm and a length of 200 mm. A glass micro-stylus with a nominal tip ball diameter of 52.6 μm was oscillated by a tuning fork quartz crystal resonator with its oscillation direction parallel to the measurement surfaces. An on-line qualification setup was established to compensate for the influences of the uncertainty sources, including the water layers on the measurement surfaces. The measurement uncertainty of the measured gap width was estimated to be less than 100 nm.     

Uncertainty analysis for a phase-detector based phase noise measurement system

Phase noise is an important parameter to characterise the frequency stability of oscillators and synthesised signal generators. Accurate measurement of phase noise is required for various applications in radar, communication and navigation systems. A single-channel phase-detector based phase noise measurement system is described. The system’s measurement errors and uncertainties have been analysed in details. The expanded uncertainty is about 2.7 dB for calibrating phase noise of a signal generator at 0.001–1.6 GHz for frequency offsets from 1 Hz to 100 kHz. The uncertainty budget for measuring a signal generator’s phase noise at 640 MHz is also presented.     

High-accuracy displacement metrology and control using a dual Fabry-Perot cavity with an optical frequency comb generator

A displacement metrology and control system using an optical frequency comb generator and a dual Fabry-Perot cavity is developed with sub-nm accuracy. The optical frequency comb generator has expanded the displacement measurement range and the dual cavity system has suppressed the environmental fluctuation. We evaluated the absolute uncertainty of the developed displacement measurement system to be approximately 190 pm for the displacement of 14 μm and the accurate displacement control using a phase-locked loop was demonstrated with a resolution of approximately 24 pm.     

Design and experimental validation of an ultra-precision Abbe-compliant linear encoder-based position measurement system

The design and development of an Abbe-compliant linear encoder-based measurement system for position measurement with a targeted 20 nm uncertainty (k = 2) in machine tools and CMMs is presented. It consists of a linear scale and a capacitive sensor, mounted in line on an interface which is guided in the scale's measurement direction and driven by a linear motor based on the output signal of the capacitive sensor. The capacitive sensor measures the displacement of a target surface on the workpiece table. The functional point, which is the center of a tool or touch probe, is always aligned with the scale and capacitive sensor such that this configuration is compliant with the Abbe principle. Thermal stability is achieved by the application of a thermal center between the scale and capacitive sensor at the tip of the latter, which prevents both components to drift apart. Based on this concept, a prototype of a one-DOF measurement system was developed for a measurement range of 120 mm, together with an experimental setup aimed at verifying the reproducibility of the system for changing ambient conditions of ±0.5 °C and ±5%rh and the repeatability during tracking of a target surface over a short period of time. These experiments have shown that the measurement uncertainty of the one-DOF system is below 29 nm with a 95% confidence level.     

Application of Monte Carlo simulation for estimation of uncertainty of four-point roundness measurements of rolls

Large-scale rotors in the paper and steel industry are called rolls. Rolls are reground at regular intervals and roundness measurements are made throughout the machining process. Measurement systems for roundness and diameter variation of large rolls (diameter <2000 mm) are available on the market, and generally use two to four sensors and a roundness measurement algorithm. These methods are intended to separate roundness of the rotor from its movement. The hybrid four-point method has improved accuracy, even for harmonic component amplitudes. For reliable measurement results, every measurement should be traceable with an estimation of measurement uncertainty. In this paper, the Monte-Carlo method is used for uncertainty evaluation of the harmonic components of the measured roundness profile under typical industrial conditions. According to the evaluation, the standard uncertainties for the harmonic amplitudes with the hybrid method are below 0.5 μm for the even harmonics and from 1.5 μm to 2.5 μm for the odd harmonics, when the standard uncertainty for the four probes is 0.3 μm each. The standard uncertainty for roundness deviation is 3.3 μm.     

Diagonal in space of coordinate measuring machine verification using an optical-comb pulsed interferometer with a ball-lens target

This paper presents a new optical method of coordinate measuring machine (CMM) verification. The proposed system based on a single-mode fiber optical-comb pulsed interferometer with a ball lens of refractive index 2 employed as the target. The target can be used for absolute-length measurements in all directions. The laser source is an optical frequency comb, whose repetition rate is stabilized by a rubidium frequency standard. The measurement range is confirmed to be up to 10 m. The diagonals of a CMM are easier to verify by the proposed method than by the conventional artifact test method. The measurement uncertainty of the proposed method is also smaller than that of the conventional method because the proposed measurement system is less affected by air temperature; it achieves an uncertainty of approximately 7 μm for measuring lengths of 10 m. The experimental results show that the measurement accuracy depends on noise in the interference fringe, which arises from airflow fluctuations and mechanical vibrations.     

International comparison of volume measurement for a 1 kg silicon sphere between KRISS and NMIJ

1 kg single-crystal silicon spheres are presently used as primary density standards in many countries. The absolute density of the spheres is determined from the measurements of their mass and volume in conformity with the definitions of the SI base units. Since the mass of the spheres is almost 1 kg, a mass comparison with the prototype of the kilogram can be performed with very low uncertainty. Absolute volume measurements for the spheres therefore have a crucial role in realizing a reliable density traceability system. To confirm the reliability of the volume measurement, the volume of a silicon sphere was measured independently using optical interferometers at the Korea Research Institute of Standards and Science (KRISS, Korea) and the National Metrology Institute of Japan (NMIJ, Japan). An optical interferometer with an etalon scanning system was used at KRISS. On the other hand, an optical interferometer with an optical frequency scanning system was used at NMIJ. The volume was measured at 20 °C and 0 Pa, and the results are in agreement with each other within their uncertainties. Details of the two interferometers and the comparison results are described.     

Verification of the positioning accuracy of industrial coordinate measuring machine using optical-comb pulsed interferometer with a rough metal ball target

An optical-comb pulsed interferometer was developed for the positioning measurements of the industrial coordinate measuring machine (CMM); a rough metal ball was used as the target of the single-mode optical fiber interferometer. The measurement system is connected through a single-mode fiber more than 100 m long. It is used to connect a laser source from the 10th floor of a building to the proposed measuring system inside a CMM room in the basement of the building. The repetition frequency of a general optical comb is transferred to 1 GHz by an optical fiber-type Fabry–Pérot etalon. Then, a compact absolute position-measuring system is realized for practical non-contact use with a high accuracy of measurement. The measurement uncertainty is approximately 0.6 μm with a confidence level of 95%.     

Towards the standardization of ballistocardiography systems for J-peak timing measurement

There is a growing interest in accurately measuring the timing of the J peak of the ballistocardiogram (BCG) in order to obtain cardiovascular function markers non-invasively, especially in modern home healthcare applications. In this paper we have studied the effect that some common uncertainty sources have in the time measurement of the J peak. This is a necessary step towards the standardization of modern ballistocardiography systems equivalent to that available for ECG systems. We conclude that, to reduce J peak time uncertainty below the measured intrinsic uncertainty of about ±2 ms, the minimal bandwidth should be from 1.5 Hz to 22.5 Hz; the sampling frequency can be decreased up to 50 Hz when using cubic spline interpolation; 5 bits are required to quantify the signal, and signal-to-noise ratio (SNR) and signal-to-interference ratio (SIR) should be over 40 dB and 3 dB respectively.     

Implementation of unscented transform to estimate the uncertainty of a liquid flow standard system

First-order partial derivatives of a mathematical model are an essential part of evaluating the measurement uncertainty of a liquid flow standard system according to the Guide to the expression of uncertainty in measurement (GUM). Although the GUM provides a straight-forward method to evaluate the measurement uncertainty of volume flow rate, the first-order partial derivatives can be complicated. The mathematical model of volume flow rate in a liquid flow standard system has a cross-correlation between liquid density and buoyancy correction factor. This cross-correlation can make derivation of the first-order partial derivatives difficult. Monte Carlo simulation can be used as an alternative method to circumvent the difficulty in partial derivation. However, the Monte Carlo simulation requires large computational resources for a correct simulation because it considers the completeness issue whether an ideal or a real operator conducts an experiment to evaluate the measurement uncertainty. Thus, the Monte Carlo simulation needs a large number of samples to ensure that the uncertainty evaluation is as close to the GUM as possible. Unscented transform can alleviate this problem because unscented transform can be regarded as a Monte Carlo simulation with an infinite number of samples. This idea means that unscented transform considers the uncertainty evaluation with respect to the ideal operator. Thus, unscented transform can evaluate the measurement uncertainty the same as the uncertainty that the GUM provides.     

Adaptive Monte Carlo and GUM methods for the evaluation of measurement uncertainty of cylindricity error

Measurement uncertainty is one of the most important concepts in geometrical product specification (GPS). The “Guide to the expression of uncertainty in measurement (GUM)” is the internationally accepted master document for the evaluation of uncertainty. The GUM method (GUMM) requires the use of a first-order Taylor series expansion for propagating uncertainties. However, when the mathematical model of measurand is strongly non-linear the use of this linear approximation may be inadequate. Supplement 1 to GUM (GUM S1) has recently been proposed based on the basis of probability density functions (PDFs) using the Monte Carlo method (MCM). In order to solve the problem that the number of Monte Carlo trials needs to be selected priori, adaptive Monte Carlo method (AMCM) described in GUM S1 is recommended to control over the quality of the numerical results provided by MCM.The measurement and evaluation of cylindricity errors are essential to ensure proper assembly and good performance. In this paper, the mathematical model of cylindricity error based on the minimum zone condition is established and a quasi particle swarm optimization algorithm (QPSO) is proposed for searching the cylindricity error. Because the model is non-linear, it is necessary to verify whether GUMM is valid for the evaluation of measurement uncertainty of cylindricity error. Then, AMCM and GUMM are developed to estimate the uncertainty. The procedure of AMCM scheme and the validation of GUMM using AMCM are given in detail. Practical example is illustrated and the result shows that GUMM is not completely valid for high-precision evaluation of the measurement uncertainty of cylindricity error if only the first-order terms in the Taylor series approximation are taken into account. Compared with conventional methods, not only the proposed QPSO method can search the minimum zone cylindricity error precisely and rapidly, but also the Monte Carlo simulation is adaptive and AMCM can provide control variables (i.e. expected value, standard uncertainty and lower and higher coverage interval endpoints) with an expected numerical tolerance. The methods can be extended to the evaluation of measurement uncertainty of other form errors such as roundness and sphericity errors.     

Reaffirmation of measurement uncertainty in pressure sensitivity determination of LS2P microphones by reciprocity method

The paper presents the accuracy and precision associated with realization of primary standard of sound using the reciprocity method. An experimental determination of the front cavity volume on Universal Measuring Machine has lead to reaffirmation of measurement uncertainty in pressure sensitivity determination to 0.04–0.15 dB in frequency range 31.5 Hz to 25 kHz. The reduced measurement uncertainty has also been validated from the results of the recent APMP Key comparison and also by comparison to the manufacturer’s value for LS2P microphones. The use of optical method for measuring the front cavity volume has refined the measurement methodology followed with adaptation of a self reliant, traceable and systematic measurement procedure in comparison to the earlier use of nominal values for sensitivity fitting exercise conducted on MP.EXE program. Consequently, the measurement uncertainty associated with the calibration of working standard microphones, multifunction acoustic calibrator and A-weighted sound pressure level measurements is also reduced.     

Designing and producing large-volume liquid gamma-ray standard sources for low radioactive pollution measurements of seawater samples by comparison between experimental and simulation results

In order to in-situ measurement of large volume water samples, using of a portable HPGe detector was considered. Because of necessity of efficiency calibration of the detector for the geometry (100 L), the large volume standard sources were prepared. Before making large volume standard sources (100 L), the Monte Carlo method has been applied in order to optimizing the calibration procedures and in agreement with experiment results, has been caused reducing the amount of produced radioactive wastes. First, the efficiency of the portable coaxial P-type HPGe detector for 1 L liquid standard sources in Marinelli beaker geometry was simulated. Then, the experimental efficiency calibration was carried out using the detector for those 1 L liquid standard sources in Marinelli beaker geometry. The detector dead layer was determined by comparison of the simulation and experimental efficiency curve results. Then, a relation between simulation and experimental measurements, that is, between pulse-height per emitted particle, F8 tally, and estimated amount of spiked radioactive solution into the 1 L distilled water in Marinelli beaker was found. Then, the efficiency calibration of the large volume liquid standard sources was simulated. The estimated amount of spiking radioactive solution into the large volume distilled water (100 L) has been taken into account dividing experimental efficiencies (in Marinelli beaker) by the simulated efficiencies (in 100 L). Finally, by spiking the large volume distilled water with the radioactive solution, efficiency calibration of the potable HPGe detector for 100 L geometry was done.     

Determining environmental noise measurement uncertainty in the context of the Italian legislative framework

This paper aims to demonstrate the importance of uncertainties in the measurement of environmental noise in the context of Italian legislation on noise pollution focusing the attention on the variability of the measurand as a source of uncertainty and offering a proposal for the evaluation of uncertainty for traffic noise measurement. In particular, drawing on a real traffic noise dataset, firstly outliers are eliminated from the actual noise measurements using an outlier detection algorithm based on K-neighbors distance and then uncertainty range is estimated with the bootstrap-t method. Since the original sequence was Gaussian, this range was compared with the confidence interval of the mean ± standard deviation interval and two intervals were almost coincident.     

Validation of the GUM using the Monte Carlo method when applied in the calculation of the measurement uncertainty of a compact prover calibration

This article presents the calibration of a compact prover using the weighing method. An evaluation of measurement uncertainty of the prover calibration has been developed using the GUM and Monte Carlo methodologies. A water draw kit was utilized to direct the liquid flow from the compact prover to a water container in order to weigh the transferred water mass on a balance. This amount of mass was used as reference for the calculation of the prover base volume. A modeling of the flow rate into the water draw kit as a function of time was conceived. This modeling was applied for calculating the error in the liquid volume of the water container due to the switching of two solenoid valves of the water draw kit. A mathematical model of the prover base volume has been developed. This model is non-linear and the two largest sources of uncertainty are related to the balance calibration certificate that together account for 31.84% of the uncertainty budget. This work showed that the GUM approach was validated by Monte Carlo method in the calculation of the measurement uncertainty of the calibration of a compact prover. The absolute differences of the respective endpoints of the coverage intervals of these two methods are less than 0.00023% of estimate of the prover base volume whose value is 151.427 dm³. This result was obtained for a coverage probability of 95% and ${10}^6$ Monte Carlo iterations. The density of the calibration water and its uncertainty have been calculated through an innovative approach.     

A laser-based machine vision measurement system for laser forming

Laser forming continues to be a promising technology in manufacturing due to its fast speed, flexibility, and low-cost. Measurement of deformation after laser forming is widely needed to verify its convergence to the intended shape in academic research. With the development of laser forming, high requirements on the measurement of the deformed work-piece have been sought such as a 3D profile of the deformed surface, a large measuring range, and measuring convenience. In this paper, a laser-based machine vision measurement system was developed to measure the 3D profile of deformed surface by a one-off scanning process. Based on the 3D profile data, the vertical displacement of the deformed plate was calculated for bending analysis. In addition, as one of the important feature parameters, transverse shrinkage was automatically determined through a novel image-based method during the scanning process. A measuring accuracy of 0.03 mm for vertical displacement measurement and 0.0125 mm for transverse shrinkage were achieved in the developed measurement system. This measurement performance is acceptable in most of the laser forming processes currently studied.     

Calibration of a 3D-ball plate

The presented 3D-ball plate is used for testing machine tools with a workspace of 500 mm × 500 mm × 320 mm. The artefact consists of a 2D-ball plate which is either located by a kinematic correct coupling on a base plate or on a spacer. The spacers are placed between the base plate and the ball plate and are also kinematic coupled to the other elements of the artefact. The kinematic couplings provide a high repeatability of the measurement setup. Because of the specific application the known calibration procedures for 2D-ball plates are not applicable.A calibration method for the pseudo-3D-artefact on a coordinate measuring machine (CMM) is presented, with the aim to minimise the influence of geometric CMM errors. Therefore a computer simulation is used to analyse the effects of these disturbing errors on the calibration of the ball plate and the spacers. Using a reversal method, the plate is measured at four different horizontal positions after rotating the ball plate around its vertical axis. A couple of the CMM errors, e.g., a squareness error C0Y between the X- and Y-axis of the CMM, can be eliminated by that method—others have to be determined with additional measurements, e.g., the positioning errors EXX or EYY of the X- and Y-axis, respectively. The paper also contains a measurement uncertainty estimation for the calibration by use of experiments, tolerances and Monte Carlo-simulations. The achieved uncertainty for ball positions in the working volume is less than 2.1 μm (coverage factor k = 2).     

Structural inspection and troubleshooting analysis of a lab-scale distillation column using gamma scanning technique in comparison with Monte Carlo simulations

In the present study, structural inspection and troubleshooting analysis of a lab-scale distillation column has been performed using gamma scanning technique and Monte Carlo simulations. MCNP4C Monte Carlo code has been used for simulations of the column and calculation of the computational density profile. The tested column is a one-pass tray type with 51 cm diameter. A Cs-137 sealed source and a 1 × 1 inch NaI (Tl) detector has been used for this gamma scanning process. According to the results, both experimental and simulation results showed the specification of trays and another section of the column accurately. Also, in addition to the flooding and damaged tray in the column, defects such as foaming with the density of 0.17 g/cm³ can be distinguished using this technique. Based on the results, using photopeak count approach the differences in the material attenuations can be better distinguished. The effectiveness of this approach in determination of malfunctions increases with the density of the material between the source and the detector. Analyzing the experimental and simulation results are indicative of the fact that the procedures and methods used in this work are quite suitable for improving the accuracy of the troubleshooting analysis based on gamma scanning technique.     

Gas Oil Piston Prover,primary reference values for Gas-Volume

The paper describes the design, measurement results and uncertainty analyses of the hydraulic driven piston-prover system which has been in operation at VSL since 2008. The 12-meter long, 0.6 m bore piston-prover is used for the realization of Reference Values for Gas-Volume at pressures between 1 and 65 bar(a) at several gases. The principle is based on the displacement of a piston acting as a Gas–Oil separator. The standard has a flow-rate range from 5 to 230 m³/h. The system is designed to calibrate reference meters. The Calibration and Measurement Capability (CMC) of the system is proven to be smaller than 0.1% (k=2). The paper also explains the coherence between the Gas–Oil piston-prover and other traceability generators and ‘flow rate bootstrapper systems’.     

High-precision radius measurement of ball indenter

To solve the problem of calibrating the radius of a ball indenter in a hardness tester, a laser confocal radius measurement and calibration method for the ball indenter is proposed without separating the ball from the body of the indenter. The laser confocal radius measurement and calibration method uses the maximum of the confocal axial intensity curve to precisely identify the cat’s eye and confocal position of the test ball indenter. The distance between these two positions is then measured to achieve high-precision radius measurement. The theoretical analyses and experimental results indicate that the radius measurement uncertainty of the ball indenter with a diameter of 1.5875 mm is within 0.12 μm.