scholarly journals Number of Points for Roundness Measurement - Measured Results Comparison

2011 ◽  
Vol 19 (30) ◽  
pp. 19-24
Author(s):  
Augustín Görög
Keyword(s):  
Least Squares ◽  
Coordinate Measuring Machine ◽  
Experimental Results ◽  
Cylindrical Grinding ◽  
Minimum Zone ◽  
Measuring Machine ◽  
Roundness Measurement

Number of Points for Roundness Measurement - Measured Results Comparison Paper deals with filtering roundness. It presents experimental results measured for roundness turning and cylindrical grinding. Roundness was measured using Prismo Navigator 5 coordinate measuring machine. Evaluation was done by four methods: Minimum zone reference circles (MZCI), Least squares reference circle (LSCI), Minimum circumscribed reference circle (MCCI) and Maximum inscribed reference circle (MICI). The filters used were: Gauss, Spline and no filter.

Fitting Weighted Total Least-Squares Planes and Parallel Planes to Support Tolerancing Standards

2012 ◽  
Author(s):  
Craig M. Shakarji ◽  
Vijay Srinivasan
Keyword(s):  
Least Squares ◽  
Point Contact ◽  
Coordinate Measuring Machine ◽  
Total Least Squares ◽  
Point Sampling ◽  
Least Squares Fitting ◽  
Weighted Total Least Squares ◽  
Measuring Machine ◽  
Fitting In ◽  
Value Decomposition

We present elegant algorithms for fitting a plane, two parallel planes (corresponding to a slot or a slab) or many parallel planes in a total (orthogonal) least-squares sense to coordinate data that is weighted. Each of these problems is reduced to a simple 3×3 matrix eigenvalue/eigenvector problem or an equivalent singular value decomposition problem, which can be solved using reliable and readily available commercial software. These methods were numerically verified by comparing them with brute-force minimization searches. We demonstrate the need for such weighted total least-squares fitting in coordinate metrology to support new and emerging tolerancing standards, for instance, ISO 14405-1:2010. The widespread practice of unweighted fitting works well enough when point sampling is controlled and can be made uniform (e.g., using a discrete point contact Coordinate Measuring Machine). However, we demonstrate that nonuniformly sampled points (arising from many new measurement technologies) coupled with unweighted least-squares fitting can lead to erroneous results. When needed, the algorithms presented also solve the unweighted cases simply by assigning the value one to each weight. We additionally prove convergence from the discrete to continuous cases of least-squares fitting as the point sampling becomes dense.

Hardware Design of a Planar Platform for Naro-CMM

2013 ◽  
Vol 706-708 ◽  
pp. 1146-1149
Author(s):  
Hui Zhi Sun
Keyword(s):  
Hardware Design ◽  
Coordinate Measuring Machine ◽  
Modern Technology ◽  
Experimental Results ◽  
Power Module ◽  
Positioning Accuracy ◽  
Technology Platform ◽  
Fast Development ◽  
Measuring Machine ◽  
Planar Mode

Nanometer three Coordinate Measuring Machine (Naro-CMM) has got fast development especially in the advancement of modern technology. Platform is an important part of the Naro-CMM, paper puts forward a new way to drive platform. “Planar” mode is adopted, and the power module is designed based on L6234PD, the experimental results express that the positioning accuracy of the platform reaches nanometer accuracy. So the drive method satisfied the demand of this platform’s movement.

scholarly journals Influence of the probing definition on the flatness measurement

2018 ◽  
Vol 9 ◽  
pp. 15 ◽  
Author(s):  
Djezouli Moulai-khatir ◽  
Eric Pairel ◽  
Hugues Favreliere
Keyword(s):  
Coordinate Measuring Machine ◽  
Minimum Volume ◽  
Analysis Study ◽  
Mechanical Parts ◽  
Minimum Zone ◽  
Cloud Points ◽  
Measuring Machine ◽  
Flatness Defect ◽  
Cloud Of Points ◽  
Flatness Measurement

The quality control of mechanical parts is generally performed on a coordinate measuring machine (CMM). The choice of the number of points to be sampled, their distributions and their positions on the surface, as well as the association criterion remains unresolved. This paper studies the variation of the flatness defect with regard to the number of palpated points. The methodology begins by sampling a cloud of points on a CMM. Then, a modal analysis study is carried out in order to generate a modal surfaces (digitally deformed). Insertion of the coordinate cloud points of these modal surfaces in the GEOVERIF software will allow estimation of the flatness defect. The results of the measured flatness by the three fitting criteria (minimum zone, least squares and minimum volume) are compared.

Theory and Algorithms for Weighted Total Least-Squares Fitting of Lines, Planes, and Parallel Planes to Support Tolerancing Standards

2013 ◽  
Vol 13 (3) ◽  
Author(s):  
Craig M. Shakarji ◽  
Vijay Srinivasan
Keyword(s):  
Least Squares ◽  
Point Contact ◽  
Coordinate Measuring Machine ◽  
Total Least Squares ◽  
Point Sampling ◽  
Least Squares Fitting ◽  
Weighted Total Least Squares ◽  
Measuring Machine ◽  
Fitting In ◽  
Value Decomposition

We present the theory and algorithms for fitting a line, a plane, two parallel planes (corresponding to a slot or a slab), or many parallel planes in a total (orthogonal) least-squares sense to coordinate data that is weighted. Each of these problems is reduced to a simple 3 × 3 matrix eigenvalue/eigenvector problem or an equivalent singular value decomposition problem, which can be solved using reliable and readily available commercial software. These methods were numerically verified by comparing them with brute-force minimization searches. We demonstrate the need for such weighted total least-squares fitting in coordinate metrology to support new and emerging tolerancing standards, for instance, ISO 14405-1:2010. The widespread practice of unweighted fitting works well enough when point sampling is controlled and can be made uniform (e.g., using a discrete point contact coordinate measuring machine). However, we show by example that nonuniformly sampled points (arising from many new measurement technologies) coupled with unweighted least-squares fitting can lead to erroneous results. When needed, the algorithms presented also solve the unweighted cases simply by assigning the value one to each weight. We additionally prove convergence from the discrete to continuous cases of least-squares fitting as the point sampling becomes dense.

A Kinematic Model for Parallel-Joint Coordinate Measuring Machine

2013 ◽  
Vol 5 (4) ◽  
Author(s):  
Jie Li ◽  
Lian-Dong Yu ◽  
Jing-Qi Sun ◽  
Hao-Jie Xia
Keyword(s):  
Mathematical Modeling ◽  
Data Processing ◽  
Newton Method ◽  
Measurement Accuracy ◽  
Kinematic Model ◽  
Coordinate Measuring Machine ◽  
Experimental Results ◽  
Kinematic Modeling ◽  
Kinematic Parameters ◽  
Measuring Machine

The typical nonorthogonal coordinate measuring machine is the portable coordinate measuring machine (PCMM), which is widely applied in manufacturing. In order to improve the measurement accuracy of PCMM, structural designing, data processing, mathematical modeling, and identification of parameters of PCMM, which are essential for the measurement accuracy, should be taken into account during the machine development. In this paper, a kind of PCMM used for detecting the crucial dimension of automobile chassis has been studied and calibrated. The Denavit–Hartenberg (D–H) kinematic modeling method has often been used for modeling traditional robot, but the D–H error representation is ill-conditioned when it is applied to represent parallel joints. A modified four-parameter model combined with D–H model is put forward for this PCMM. Based on the kinematic model, Gauss–Newton method is applied for calibrating the kinematic parameters. The experimental results indicate the improvement of measuring accuracy and the effectiveness of the PCMM based on the proposed method.

An Optimization Strategy for Maximizing Coordinate Measuring Machine Productivity, Part 2: Problem Formulation, Solution, and Experimental Results

1995 ◽  
Vol 117 (4) ◽  
pp. 610-618 ◽  
Author(s):  
S. D. Jones ◽  
A. Galip Ulsoy
Keyword(s):  
Golden Section ◽  
Coordinate Measuring Machine ◽  
Sensitivity Study ◽  
Experimental Results ◽  
Motor Power ◽  
Optimization Strategy ◽  
Connecting Rod ◽  
Measurement Quality ◽  
Machine Productivity ◽  
Measuring Machine

In this, the second of two papers focused on optimizing CMM productivity, a strategy is presented for obtaining operating speeds that maximize CMM throughput. The strategy involves posing the objective and constraints in terms of a nonlinear programming problem. The objective is to minimize measuring time, and constraints are on measurement quality, available motor power and other machine specific characteristics. Solutions to various measurement scenarios are given, computed with a generalized conjugate gradient method that uses a golden section acceptable search method. Also, a sensitivity study is presented that utilizes the optimization strategy to determine how change to a CMM’s design will affect overall productivity. In the final section, experimental results utilizing the optimally computed trajectories for both single axis and multiple axis motion are given. In addition, an example is presented to demonstrate the implementation of the optimization strategy in an actual measuring application. In the example, a connecting-rod is measured at three speeds: the machine’s default speed, a speed constrained by available motor power, and the optimized speed (constrained additionally by measurement quality). The experiment demonstrates a 27 percent reduction in time for the optimized speed compared to the default speed using the Bartlett test for comparing variances in the dimensional data obtained.

scholarly journals MAXIMUM- INSCRIBED AND MINIMUM-CIRCUMSCRIBED FITTING FOR CO-ORDINATE MEASURING MACHINE

2010 ◽  
Vol 13 (3) ◽  
pp. 5-13
Author(s):  
Ha Thi Thu Thai ◽  
Phuoc Hong Nguyen
Keyword(s):  
Least Squares ◽  
Simulated Annealing Algorithm ◽  
Least Squares Method ◽  
Coordinate Measuring Machine ◽  
Data Sets ◽  
Effective Algorithm ◽  
Least Squares Fit ◽  
Measuring Machine ◽  
Annealing Algorithm ◽  
Near Future

This paper describes algorithms that fit geometric shapes to data sets according to maximum- inscribed (MI) and minimum- circumscribed (MC) fit. We use these fits to build the CMM’s (Coordinate Measuring Machine) software in cases of circle, sphere and cylinder. For each case, we obtain the fit by two methods: first, by (relative easy) least squares fit method and then refine by MI and MC fit method. Although, the later method is substantially more complicated than the former one, Its results are used to make comparision with the the results of least squares method in order to give more options in the CMM software. In the near future we will continue to develop MI and MC fit with an effective algorithm- Simulated Annealing algorithm.

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