Development of a novel lead master consisting of an offset sphere

During the calibration of gear inspection systems, special calibration masters, or artifacts, are often used. Lead masters are used for adjustment and calibration of the system’s lead generation axes and algorithms. This paper discusses the development of a novel lead master for system calibration consisting of an offset sphere. A curve along the surface of the sphere is used to simulate a helix. The calibration curve for the artifact is formulated. Critical design parameters are specified. In addition, the impact to the calibration curve attributable to measurement uncertainties for the design parameters is assessed. An example design is also presented.     

Three-dimensional surface characterization for orthopaedic joint prostheses

This study attempts to investigate a range of 'better' methods for the characterization of the three-dimensional (3D) surface topography of orthopaedic joint prostheses. In this paper, a new characterization tool for the comprehensive identification and evaluation of functional features of these surface topographies is presented. For identification, the surface topography is investigated in a space-scale space, by employing wavelet analysis. The roughness, waviness and form involved in surface topography are consequently separated and recovered respectively. The multiscalar topographical features are identified and captured. The errors caused as a consequence of three-dimensional measurement methods can be reduced. After identification, the three-dimensional surface assessment techniques previously reported by Stout and co-workers are used for the quantitative evaluation of various surface roughness features of the orthopaedic joint prostheses. Moreover, the functional properties, such as bearing area, material volume and void volume which are significantly effected by large peaks, pits and scratches are studied and the location of isolated peaks, pits and scratches in the different scales is also clearly characterized. In this work, measurement of the femoral heads and acetabular cups is carried out to demonstrate the applicability of the characterization technique for the three-dimensional surface topography of orthopaedic joint prostheses.     

Comparison of chaos optimization functions for performance improvement of fitting of non-linear geometries

Fitting algorithms play an important role in the whole measuring cycle in order to derive a measurement result. They involve associating substitute geometry to a point cloud obtained by an instrument. This situation is more difficult in the case of non-linear geometry fitting since iterative method should be used. This article addresses this problem. Three geometries are selected as relevant case studies: circle, sphere and cylinder. This selection is based on their frequent use in real applications; for example, cylinder is a relevant geometry of an assembly feature such as pin-hole relationship, and spherical geometry is often found as reference geometry in high precision artifacts and mechanisms.In this article, the use of Chaos optimization (CO) to improve the initial solution to feed the iterative Levenberg–Marquardt (LM) algorithm to fit non-linear geometries is considered. A previous paper has shown the performance of this combination in improving the fitting of both complete and incomplete geometries. This article focuses on the comparison of the efficiency of different one-dimensional maps of CO. This study shows that, in general, logistic-map function provides the best solution compared to other types of one-dimensional functions. Finally, case studies on hemispheres and industrial cylinders fitting are presented.     

Sampling uncertainty in coordinate measurement data analysis

There are a number of important software related issues in coordinate metrology. After measurement data are collected in the form of position vectors, the data analysis software must derive the necessary geometric information from the point set, and uncertainty plays an important role in the analysis. When extreme fit approaches (L_−∞ norm estimation approaches) are employed for form error evaluation, the uncertainty is closely related to the sampling process used to gather the data. The measurement points are a subset of the true surface, and, consequently, the extreme fit result differs from the true value. In this paper, we investigate the functional relationship between the uncertainty in an extreme fit and the number of points measured. Two major issues are addressed in this paper. The first addresses and identifies the parameters that affect the functional relationship. The second develops a methodology to apply this relationship to the sampling of measurement points.     

A unified generalized thermoelasticity; solution for cylinders and spheres

A new unified formulation for the generalized theories of the coupled thermoelasticity based on the Lord–Shulman, Green–Lindsay, and Green–Naghdi models is proposed in this paper. The unified form of the governing equations is presented by introducing the unifier parameters. The formulations are derived and given for the anisotropic heterogeneous materials. The unified equations are reduced for the isotropic and homogeneous materials. Transforming the governing equations into the Laplace domain, they are analytically solved in the space domain for a hollow sphere and cylinder, where a parameter is introduced to consolidate the solution for the sphere and cylinder in a unified form. A thermal shock load is applied to the inner surface of the sphere and cylinder and the results are presented using a numerical inversion technique of the Laplace transform. The results are validated with the known data in the literature.     

一种多传感器测量系统全局标定方法

针对复杂曲面零件加工中由触发式测头-关节臂激光扫描仪组成的多传感器测量系统,提出了六面体零件作为模板的全局标定方法,建立了基于单位四元数的全局标定数学模型,并用数学形态学方法在单位四元数球上进行聚类分析以确定最优的刚体变换矩阵。仿真和试验结果表明,该方法应用简单、鲁棒性好、精度高,适用于加工现场的在机测量系统标定。     

The uncertainty of radius estimation in least-squares sphere-fitting,with an introduction to a new summation based method

This paper considers the sensitivity of three sphere-fitting algorithms to real-world measurement errors. It pays particular attention to nominally spherical surfaces, such as those typically measured by tactile and optical profilometers, addressing the limitations of sensor gauge range and angular tolerance. A recently proposed linear circle-fitting algorithm is extended to a sphere-fitting algorithm and its performance compared to two long standing sphere-fitting algorithms; namely linear and non-linear least-squares. Sources of measurement error in optical profilometers are discussed, and user defined scan parameters are optimised based on the results of a designed experiment. The performance of all three sphere-fitting algorithms are tested on a sphere superimposed with varying degrees of surface irregularities in a Monte Carlo simulation; this study shows that both linear routines display a negative skewness in their radius error distribution. Finally, a method of predicting radius uncertainty is offered that considers the surface residual that remains after sphere-fitting and relates this to the radius uncertainty of the chosen algorithm.     

Scanning tunneling microscopy-based on-machine measurement for diamond fly cutting of micro-structured surfaces

This paper presents a new on-machine measuring system based on scanning tunneling microscope principle, in order to meet the demand for precision form control of fabricated micro-structures. It is compactly established and mounted on a diamond turning machine, capable of on-machine measuring microstructures with steep slopes and size of tens of micrometers, which remains a challenge task to accomplish undistorted measurement even for general off-line metrological methods. Fly cutting with V-tip fly-cutter was first applied in two directions with interval angle of 60° to form the crossed micro V-grooves, and then efficient on-machine measurement was carried out to characterize the machined surface form without ending the proceeding of the subsequent fabrication. By depth compensation of fly cutting in 120° direction through feedback of on-machine measured results, the surface of rectangular pyramid array with diamond-shaped feature was successfully generated. Experimental results demonstrate that the proposed measuring system is of significance in the fabrication process, owing to its efficient on-machine characterization capability for generating accurate micro-structured surfaces.     

A method for evaluating spindle rotation errors of machine tools using a laser interferometer

This paper presents a method for assessing radial and axial error motions of spindles. It uses the Hewlett Packard 5529A laser interferometer. The measurement is made using reflection directly from a high-precision sphere. Such object is used as the optical reflector. The sphere is affixed at the end of a wobble device, which is clamped in the spindle. The principle of measurement is similar to that of a linear interferometer, except that the high-precision sphere is used in place of the usual retroreflector. A convergent lens is utilized to focus the laser beam to a small spot on the sphere surface. This minimizes the dispersion of the beam due to the reflection on the spherical surface. A software package has been developed for data acquisition and presentation of the error motion polar plots of the spindle. Application of this spindle error calibrator on a CNC machining centre is undertaken. The results are presented and discussed.     

A New Method of Non-Contact Measurement for Microtopography in Semiconductor Wafer Implementing a New Optical Probe Based on the Precision Defocus Measurement

In this paper, a new method of non-contact measurement has been developed for 3D topography for a semiconductor wafer, implementing a new optical probe based on precision defocus measurement. The developed technique consists of the new optical probe, precision stages, and the measurement/control system. The basic principle of the technique is to use the reflected slit beam from the specimen surface to measure the deviation of the specimen surface. The defocusing distance can be measured by the reflected slit beam, where the defocused image is measured by the proposed optical probe, giving very high resolution. A distance measuring formula has been proposed for the developed probe, using the laws of geometric optics. A precision calibration technique has been applied, giving about 10 nm resolution and 72 nm four-sigma uncertainty. In order to quantitise the micro pattern on the specimen surface, some efficient analysis algorithms have been developed to analyse the 3D topography pattern and some parameters of the surface. The developed system has been successfully applied to measure the wafer surface, demonstrating the line scanning feature and the excellent 3D measurement capability.     

Feature based characterization of worn surfaces for a sliding test

In this paper a novel 3D surface characterization technique—feature based characterization—is applied to analyse worn surfaces from a ball on disc sliding test. This technique concentrates on analysis of surface features that are related to tribological behaviour. The worn surfaces of discs are segmented according to their surface texture primitives in order to analyse the shapes of the asperities. In order to remove shapes and unnecessary features of the ball surfaces, a filtering technique through wavelet analysis is applied. Then the significant features are extracted by means of a marker controlled watershed transformation. As a result, the relationship between the feature based parameters and the tribological behaviour is presented.     

Measurement of form error of a probe tip ball for coordinate measuring machine (CMM) using a rotating reference sphere

This study presents a method of measurement of the form error of the tip ball in the tactile probing systems of a coordinate measuring machine (CMM) by using a rotating reference sphere. The measurement of the form error of the CMM probe tip was conducted without the use of additional external measuring instruments or sensors. The form errors of the probe tip ball and the reference sphere were separated from the probing coordinates of CMM by rotation of the reference sphere. The effectiveness of the proposed method was evaluated based on an uncertainty analysis. The uncertainty in measurement of diameter of the probe tip ball was estimated to be less than 0.5 μm.     

Geometrics of tooth wear

Wear measurement implies the need for comparative measurements based on a reference frame. In this study, part of a tooth surface (common area) is proposed to be a reference frame for the comparative measurement. A registration procedure applies an iterative closest point algorithm for the least square best fit of the two surfaces on this common area. When the common area matches the best fit condition, the difference at the remaining part of the tooth surface represents changes between the two surfaces; in this case signifying tooth wear.The minimum requirements to verify tooth wear results are a three quadrant spherical surface of a molar tooth to be common area, and the fit of the common area needs to be less than 10 μm, to achieve the sensitivity of wear measurement up to the 100 μm level on the occlusal tooth surface. Incise apparatus was used for the digitisation of the tooth surface. Cloud, a 3-D image analysis software package was utilised for visualisation, registration and image analysis. A mathematical scrutiny was applied to validate the findings in theory. The proposed methodology is proven to be adequate to quantify tooth wear.     

The selection of radius correction method in the case of coordinate measurements applicable for turbine blades

The objective of the research presented in the paper is the selection of suitable probe radius correction method in the case of coordinate measurements which can be applied for turbine blades. The investigations are based on theoretical analysis of geometric data and on further computer simulation of measurements and data processing. In the paper two methods for computing coordinates of corrected measured points are verified. Those so-called local methods of probe radius correction are based on Bézier curves. They are dedicated first of all to coordinate measurements of free-form surfaces which are characterized by big values of curvature, e.g. those surrounding the leading and trailing edges of a turbine blade. Numerical simulations are done for several models of the cross-sections of turbine blades with diversified magnitudes of radii of curvature. There are considered both manufacturing deviations and coordinate measurement uncertainty of each examined profile of a turbine blade. Numerical investigations based on the developed analytical models show the advantage of the algorithm which uses the second degree Bézier curves in probe radius correction. Moreover, in the paper there is explained the implementation of the developed algorithms for probe radius correction into the standard CMM software which amplifies the usability of the algorithms.     

微型精密零件图像测量清晰度算法的选择与综合评价算法

随着仪器、设备的日益小型化,微型精密零件应用日益广泛。由于常规测量手段的局限性,光学影像测量方法在微型精密零件测量中成为国内外竞相发展的技术。然而在图像采集过程中对图像清晰度的评价算法虽种类较多但各算法之间缺乏统一。本论文基于微型精密零件的成像测量方法,使用前人制作的图像测量仪,使用远心成像测量系统在不同工作距离处进行图像采集,然后使用相关算法进行清晰度评价,最后对所得数据进行主成分分析和因子分析,从8种图像清晰度评价算法计算出适用于课题使用的评价算法,并建立了综合清晰度评价模型。本文的数据处理模式能够对算法进行选择并解决不同算法间的协调问题。而且本文提出的数据挖掘算法能针对同一要求的不同评价值进行选择及综合,同时能大幅减少后续运算量。     

Calibration of laser beam direction for optical coordinate measuring system

For the purpose of measuring free form surfaces of some key parts in the aviation field accurately and effectively, such as blades, a non-contact optical coordinate measuring system is set up in the paper. A laser displacement sensor is mounted on the Z axis of a CMM via a turntable and adjusted to the suitable orientation according to the shape of the target surface. The combination of optical sensor and CMM can reach the full potential of them both. To enable the laser sensor to perform measurement in every direction, a calibration method used to determine the laser beam direction based on a standard sphere is proposed, the principle of which is analyzed in detail in the paper. In the calibration procedure, the sensor moves at an equal step along X, Y and Z axes respectively and then equation sets are established to calculate the unit direction vector of the line which the laser beam is on. In the process of solving the unknown quantities, a new parameter substitution method is applied. Finally, a gauging block and a sphere with known size are used to verify the method. As the experimental results show, the measuring errors in several directions are all smaller than 0.05 mm, which manifests that the calibration method proposed can meet the requirements of reverse engineering.     

The development of the modified Hurst orientation transform for the characterization of surface topography of wear particles

A modified Hurst orientation transform (HOT) method for characterization of wear particle surfaces is proposed and described in this paper. The method involves the calculation of self-affine Hurst coefficients in all directions and displays the calculated coefficient values in a form of rose plot. The calculation of individual Hurst coefficients, H, is based on the rescale range (r/s) analysis (r(d)/s∼ d ^H ). The rose plot is then used to obtain three texture surface parameters, i.e.: texture aspect ratio, texture minor axis and texture direction. The effectiveness of this modified HOT and resulting surface texture parameters was evaluated. The method was first applied to computer-generated images of isotropic and anisotropic particle fractal surfaces and then to field emission scanning electron microscope images of wear particles found in synovial joints. The ability of the surface parameters to reveal surface isotropy or anisotropy, measure roughness and determine the dominant direction of surface texture was assessed. The effects of measurement conditions such as noise, gain variations and focusing on the surface parameters were also investigated. The results demonstrate that the HOT and surface texture parameters developed can successfully be used in the characterization of wear particle surface topography. This revised version was published online in August 2006 with corrections to the Cover Date.     

A Spindleless Instrument for the Roundness Measurement of Precision Spheres

This paper presents an automated instrument for high-precision roundness measurement of spheres. Instead of a rotating spindle, the surface of the sphere itself is used as a geometrical reference. The measurement method is based on the well-established three-point method. In our design, two points are realized as mechanical contacting points and one as a capacitive gauge that directly faces the surface of the sphere. By this simple design—without any moving parts involved in the probing process—we measured the roundness of 1-inch steel spheres with nanometer resolution. After a short introduction into the basic mathematics of the three-point method, the design of the instrument is presented, including the automation of the measuring process and the means used to minimize environmental effects in an industrial environment. Results are presented that prove the outstanding repeatability and accuracy of the instrument. In a comparison with conventional methods, the advantages and limitation of the method are discussed.     

逆向工程中自由曲面重构的算法探讨

介绍常用的自由曲面反求的几种算法和特点及归类 ,探讨目前曲面重构过程中的难点、热点问题。     

Free knot recursive B-spline for compensation of nonlinear smart sensors

Compensation of nonlinear smart sensors is an important topic that must always be considered to assure the accuracy of measurement systems. Nowadays, with the advent of microprocessor devices in smart sensors, advanced compensation algorithms can be implemented to improve the accuracy of measurement. In this paper, an inverse modeling methodology based on B-spline is proposed for the compensation of nonlinear smart sensors. To avoid complicated least squares solution of the B-spline, a training algorithm in a recursive form is proposed to reduce the training cost and make the on-chip training of B-spline available. Moreover, the choices of B-spline knots and training points are important designed parameters in this methodology. So the free knot insertion algorithm and training points’ selection method are used prior to the training process to improve the accuracy of the inverse models and avoid the under and over fitting. Simulations and results are presented to validate the theoretical expectations.