Computerized CMMs normally use Least Square Center (LSC) algorithms, although ANSI standards recommend the Minimum Zone Circle (MZC) algorithms. Voronoi Diagrams algorithm were tested against the LSC using various sets of points 'with out-of-roundness values ​​similar to real parts. Results differences and their importance related with uncertainty of the machine were discussed.

Анотація наукової статті за медичними технологіями, автор наукової роботи - Novaski Olivio, Lids Andre, Barczak Chautard

Область наук:
  • Медичні технології
  • Рік видавництва: +1997
    Журнал: Известия Південного федерального університету. Технічні науки

    Наукова стаття на тему 'Measurements of out-of-roundness in computer aided machines using Voronoi diagrams'

    Текст наукової роботи на тему «Measurements of out-of-roundness in computer aided machines using Voronoi diagrams»


    1. Bakoglu, J. T. Walker, and J.D. Meindi, "A Symmetric Clock-Distribution Tree and Optimized High-Speed ​​Interconnections for Reduced Clock Skew in ULSI and WSI Circuits" IEEE International Conference on Computer Design: VLSI in Computers, ICCD 1986, pp. 118-122.

    2. Jackson, A. Srinivasan, and E.S. Kuh, "Clock Routing for High-Performance ICs", IEEE Design Automation Conference, DAC 1990, pp. 573-579.

    3. Kahng, J. Cong, and G. Robins, "High-Performance Clock Routing Based on Recursive Geometric Matching" IEEE Design Automation Conference, DAC 1991 року, pp. 322-327.

    4. Tsay, "Exact Zero Skew" International Conference on Computer Aided Design, ICCAD 1991 року, pp. 336-339

    5. Cong. A. Kahng, and G. Robins, "Matching-Based Methods for High-Performance Clock Routing", to appear in IEEE Transactions on Computer-Aided Design

    y / tfC 658.512.2

    Olivio Novaski, Andre Luis Chautard Barczak

    Measurements of out-of-roundness in computer aided machines using voronoi



    Computerized CMMs normally use Least Square Center (LSC) algorithms, although ANSI standards recommend the Minimum Zone Circle (MZC) algorithms. Voronoi Diagrams algorithm were tested against the LSC using various sets of points 'with out-of-roundness values ​​similar to real parts. Results differences and their importance related with uncertainty of the machine were discussed.


    Tolerancing and metrology allow improving quality. Nevertheless, many of the methods and definitions of these techniques come from industry practice. The case of roundness measuring through Coordinate Measuring Machines (CMM) is an example. The utilization of computerized CMMs and other computer aided measuring instruments permits measure roundness quickly and precisely, and the interpretation is done by algorithms. The algorithm normally used is the least square center (LSC). It does not obtain the minimum tolerance zone the way is defined by the new ANSI 14.5 standards [1,2]. Other algorithms can be developed. For the same set of points, two different algorithms may produce two different results. Considering only the mathematical model, any MZC algorithm should find the same value for a given set.

    The ANSI B89.3.1 [3] suggests four different methods to calculate out-of-roundness. The LSC finds a center of a circle in which the sum of the squares of the distances between each point and the circle has a minimum value. The difference among maximum and minimum radial ordinates, considering that the origin is the found center, defines out-of-roundness. The other three methods are Minimum Zone Circle (MZC), Minimum Circumscribed Circle (MCC) and Maximum Inscribed Circle (MIC).

    The MCC finds the smallest circle which will contain the set of points, and the out-of-roundness is the distance between this circle and the most inward point. In opposition, the MIC method finds the largest circle that will not contain any point of the set, and the most outward point complete the method. The MZC method fits the definition of form errors defined on the ANSI Y14.5. The radial distance between two concentric circles with minimum separation is the out-of roundness value. It is important to emphasizes here that one can demonstrate for some sets that MZC value may coincide with MCC or with MIC.

    Differences in results should exist using LSC or MZC methods. But the errors are not limited to mathematical model. The computational environment also introduces rounding errors that can not be negligible in some cases. Sampling methods and number of points sampled is also important to represent the measured part adequately. In this work only the model will be analyzed.

    Many alternative algorithms have been proposed, emphasizing geometric algorithms. Simplex method, Chebyshev, Monte Carlo simulation and other algorithms were proposed, some of them useful also to other types of form errors. A geometric method like Voronoi Diagrams demonstrates a great potential, in spite of until now its use is limited to roundness assessment.

    After analyzing various types of MZC algorithms, the authors decided to implement the Vorono's one. The main reason was the facility of implementation. Also the assurance of optimization and the low complexity were considered. About 30000 sets of points were simulated. Two parameters (number of points and out-of-roundness magnitude) were varied, so the relationship between the two algorithms could be determined.

    2. The voronoi algorithm

    The Voronoi Diagrams is used in many applications, such as geodesic and visualization algorithms. Roy and Zhang [4,5] improved the method by using two types of diagrams, the farthest and the nearest diagrams to find solutions to MCC and MIC respectively. The intersection of the two diagrams finds a solution that should be compared to the preview [4]. If it is smaller than the preview the MZC solution is on the intersection, otherwise the answer to MZC situation may coincide with MIC or MCC depending on the set. Also examples of the algorithm were showed in their papers to prove the consistency of the method. The points were sparse to allow visualization of the algorithm's work. It seems to be expected that with real points, where the form error may be of order of microns, the error between the methods can be smaller than the uncertainty of the machine. In this case an algorithm LSC would be adequate. There should be a relationship between number of points measured, the order of the out-of-roundness value and the differences between the calculated values. In the most extreme case, a perfect circle "part" (or the equivalent data set) produces a zero out-of-roundness value using any method. Hence it is necessary to determine the behavior of the error caused by method choice, considering the most correct is the MZC algorithms.

    The complexity in the Voronoi algorithm developed is 0 (n2) but it can be improved to 0 (n log nj. It is a comfortable situation because the complexity of a LSC algorithm that utilizes simplified approach is the same 0 (n log n). It can be expected that for a set with a great number of points the time expended by LSC or Voronoi to run in the same environment is very close, j The implementation of the algorithm was relatively simple. There are problems i related with the great number of information that should be stored in the first iteration., considering the computer tends to have more and more memory and considering the | numbers of points measured is limited in practice, this will not be a common situation. Generally the Voronoi algorithm can be used universally.

    3. Simulation results and discussion

    In this research, after analyzing the mathematical model, implementation and algorithm complexity, the Voronoi Diagrams was elected to compare the differences of the results between LSC and minimum zone algorithms. Two programs were developed in the same language and environment. The C language was used with double float variables, and the programs run in DOS. The results of the errors caused by LSC's choice were presented in graphics.

    Another program to generate sets of points was also developed. The user gave a diameter and the number of points (n). The points 'position were calculated and distributed symmetrically for each set. One point of the set was kept in the nominal diameter and another point was moved the same size as the given out-of-roundness magnitude. The other points were moved between the two circles formed by the first two points. The distances were randomized.

    The sets were used to calculate LSC end Voronoi out-of roundness The absolute difference between them were plotted in graphics, where the typical relationship between algorithms could be seen. In figure 3 n is equal to 100 and out-of-roundness varied between 0,1 and 0,001 mm. For each out-of-roundness value 100 sets of points were tested (resulting in 1900 sets for this case). The differences varied from zero to a determined value contained in a triangle region. Note that if more sets were tested, one would expect that all region below this line would be filled. These values ​​indicate the maximum expected error when using LSC type algorithms.

    Considering sets with other n quantities and plotting the twenty greater relative difference for each one, one can see that the maximum differences tends to be greater when n decreases. The angular coefficient increases with lower n.

    When larger n is involved the probability that points are close to the circle's pair found by LSC is bigger. In this case the maximum difference tends to be lower, as the movement of the circle's pair is proportionally smaller. If only LSC algorithms are enabled the use of greater n will improve the results, making a better approximation to MZC algorithms.

    The importance of the difference and the uncertainty of the machine should also be analyzed. Consider, for instance, a Brown & Sharpe CMM (Micro Val model). It has a repeatability value of 0.004 mm related with the position of the measured points, and

    0.006 mm in linear accuracy value (determined following ASME B89.1.12). A 0.010 mm out-of-roundness the difference do not pass 0.002 mm for n = 100, below machine's uncertainty. In this case the uncertainty of the result would not be affected by the algorithm's choice, and the LSC could be used without significant error. For a machine where the measured points are obtained more accurately, the LSC algorithm could affect significantly the final out-of-roundness value. So it is necessary to analyze the machine's uncertainty, the magnitude of the out-of-roundness and the maximum expected difference between the methods to determine if using LSC algorithms are good enough.

    4. Conclusions

    The simulation of Voronoi and LSC algorithms allowed to observe the behavior of the maximum differences between them. The preliminary results showed that: I) the LSC error are negligible in many real case situations. In the case the uncertainty of the machine is greater than the error caused by the mathematical model, the LSC can be used without restrictions with respect to the mathematical model. It may be true for many CMM used in industry. For dedicated machines normally the uncertainty is very smaller, than a better algorithm should be used. The Voronoi Diagrams algorithm is a very powerful method in this case. 2) The maximum error found in the randomized tests showed that the angular coefficient is smaller when n increases. It means that using sets

    with a greater number of measured points the result tends to approximate LSC from MZC methods.

    S. References

    1. Dimensioning and tolerancing, ASME Y14.5M-1994 ASME, NY, 1995.

    2. Mathematical definition of dimensioning and tolerancing principles, ASME Y14.5.1- 1994 ASME, N. Y "тисяча дев'ятсот дев'яносто п'ять.

    3. Measurement of Out-of-Roundness. ASME B89.3.1-1972, ASME, NY »1979.

    4. Roy, U. e Zhang, X., "Development and application of Voronoi Diagrams in the assessment of roundness error in an industrial environment". Computers for Industry Engineering. Vol. 26, pp. 11-26,1994.

    5. Roy, U. e Zhang, X., "Establishment of a pair of concentric circles with the minimum radial separation for assessing roundness error" Computer-aided Design, Vol. 24, pp. 161-168,1992.

    УДК 658.52.011

    Ruey-Shun Chen, Y. S. Yeh A new approach for multiuser access library full-text image cd-rom database via

    campus network


    This paper proposes a approach to solve this problem. A case study is presented that describes the practical design and implementation of an microcomputer system and novell server that allows multiuser access library CD-ROM jukebox database via campus network. The method use microcomputer via standard network interfaces like Ethernet, high speed fiber networks, and standard protocols TCP / IP and IP-tunnel .until login novell server. Its advantages are that it reduces waiting time, improve access speed, reduces the damage incurred by handing jukebox CD-ROM devices in and out, and novell sever with network secure access control to allow many users to retrieving the jukebox CD-ROM from microcomputers. Keywords: Distributed network, CDROM jukebox. Campus network. Microcomputer.

    1. Introduction

    Library automation is a goal for many libraries, the utilization of CDROM in the library and information science area goes back to 1985, when Bibiofile was announced by the library corporation. CDROM provides enormous storage of about 600MB, retrieval capacities, and reasonable price. It has been gradually replacing some of its printed counterparts. Most of European and American universities have used CDROM databases since 1987. A survey of libraries in Taiwan has shown that currently 86% of academic libraries have CDROMs in their library collection [1].

    In fact, one of the greatest limitations is on the use of library stand-alone CDROM database at a time [2], we have solved it. But now we have a large amounts of image CDROMs such as 1ЕЕЕДЕЕ publication ondisc (IPO), Business publication ondisc (BPO), General publication ondisc (GPO). How to network it. As we know, CDROM jukebox can solve it. Campus network can offer other benefits, such as facilitating searching of databases containing more than one disk [3]. For examples, Dartmouth College Library has developed system that uses modem login to file server access an on-

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