Erdvinių paviršių geometrinių parametrų matavimo tyrimas ir tobulinimas ; Research and improvement of measuring the geometrical parameters of spatial surfaces
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Erdvinių paviršių geometrinių parametrų matavimo tyrimas ir tobulinimas ; Research and improvement of measuring the geometrical parameters of spatial surfaces

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Darius MARIŪ NAS RESEARCH AND IMPROVEMENT OF MEASURING THE GEOMETRICAL PARAMETERS OF SPATIAL SURFACES Summary of Doctoral Dissertation Technological Sciences, Measurement Engineering (10T) 1156 Vilnius „Technika“ 2005 VILNIUS GEDIMINAS TECHNICAL UNIVERSITY Darius MARIŪ NAS RESEARCH AND IMPROVEMENT OF MEASURING THE GEOMETRICAL PARAMETERS OF SPATIAL SURFACES Summary of Doctoral Dissertation Technological Sciences, Measurement Engineering (10T) Vilnius „Technika“ 2005 Doctoral dissertation was prepared at Vilnius Gediminas Technical University in 2001 – 2005 Scientific Supervisor Prof Dr Habil Vytautas Giniotis (Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T) The Dissertation is being defended at the Council of Scientific Field of Measurement Engineering at Vilnius Gediminas Technical University: Chairman Prof Dr Habil Algimantas ZAKAREVI IUS (Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T) Members: Prof Dr Habil Jonas SKEIVALAS (Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T) Prof Dr Habil Ramutis Petras BANSEVI IUS (Kaunas University of Technology, Technological Sciences, Measurement Engineering – 10T) Prof Dr Habil Vladas VEKTERIS (Vilnius Gediminas Technical University, Technological Sciences,

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Published 01 January 2005
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    Darius MARIŪNAS     RESEARCH AND IMPROVEMENT OF MEASURING THE GEOMETRICAL PARAMETERS OF SPATIAL SURFACES    Summary of Doctoral Dissertation Technological Sciences, Measurement Engineering (10T)         Vilnius „Technika“ 2005
 
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VILNIUS GEDIMINAS TECHNICAL UNIVERSITY          Darius MARIŪNAS      RESEARCH AND IMPROVEMENT OF MEASURING THE GEOMETRICAL PARAMETERS OF SPATIAL SURFACES    Summary of Doctoral Dissertation Technological Sciences, Measurement Engineering (10T)         Vilnius „Technika“ 2005
 
 
Doctoral dissertation was prepared at Vilnius Gediminas Technical University in 2001 – 2005  Scientific Supervisor Prof Dr Habil Vytautas Giniotis (Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T)  The Dissertation is being defended at the Council of Scientific Field of Measurement Engineering at Vilnius Gediminas Technical University: Chairman Prof Dr Habil Algimantas ZAKAREVIČIUS(Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T) Members: Prof Dr Habil Jonas SKEIVALAS(Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T) Prof Dr Habil Ramutis Petras BANSEVIČIUS(Kaunas University of Technology, Technological Sciences, Measurement Engineering – 10T) Prof Dr Habil Vladas VEKTERIS(Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T) Prof Dr Habil Petras ILGAKOJIS(Lithuanian University of Agriculture, Technological Sciences, Mechanical Engineering – 09T) Opponents: Prof Dr Habil Genadijus KULVIETIS(Vilnius Gediminas Technical University, Technological Sciences, Mechanical Engineering – 09T) Prof Dr Habil Vitalijus VOLKOVAS University of (Kaunas Technology, Technological Sciences, Measurement Engineering – 10T)  The dissertation will be defended at the public meeting of the Council of Scientific Field of Measurement Engineering in the Senate Hall of Vilnius Gediminas Technical University at 2 p. m. on 16 September 2005. Address: Saulėtekio al. 11, LT-10223 Vilnius-40, Lithuania Tel.: +370 5 274 49 52, +370 5 274 49 56; fax +370 5 270 01 12; e-mail doktor@adm.vtu.lt  The summary of the doctoral dissertation was distributed on 12 August 2005. A copy of the doctoral dissertation is available for review at the Library of Vilnius Gediminas Technical University (Saulėtekio al. 14, Vilnius, Lithuania)  © Darius Mariūnas, 2005
 
 
VILNIAUS GEDIMINO TECHNIKOS UNIVERSITETAS          Darius MARIŪNAS    ERDVINIŲPAVIRŠIŲGEOMETRINIŲ PARAMETRŲMATAVIMO TYRIMAS IR TOBULINIMAS    Daktaro disertacijos santrauka Technologijos mokslai, Matavimųinžinerija (10T)          Vilnius „Technika“ 2005 
 
 
Disertacija rengta 2001 – 2005 metais Vilniaus Gedimino technikos universitete.   Mokslinis vadovas prof. habil. dr. Vytautas Giniotis (Vilniaus Gedimino technikos universitetas, technologijos mokslai, matavimųinžinerija – 10T).  Disertacija ginama Vilniaus Gedimino technikos universiteto Matavimų inžinerijos mokslo krypties taryboje: Pirmininkas prof. habil. dr. Algimantas ZAKAREVIČIUS(Vilniaus Gedimino technikos universitetas, technologijos mokslai, matavimų inžinerija – 10T). Nariai: prof. habil. dr. Jonas SKEIVALAS(Vilniaus Gedimino technikos universitetas, technologijos mokslai, matavimųinžinerija – 10T), prof. habil. dr. Ramutis Petras BANSEVIČIUS(Kauno technologijos universitetas, technologijos mokslai, matavimųinžinerija – 10T), prof. habil. dr. Vladas VEKTERIS(Vilniaus Gedimino technikos universitetas, technologijos mokslai, matavimųinžinerija – 10T), prof. habil. dr. Petras ILGAKOJIS(Lietuvosžemėsūkio universitetas, technologijos mokslai, mechanikos inžinerija – 09T). Oponentai: prof. habil. dr. Genadijus KULVIETIS(Vilniaus Gedimino technikos universitetas, technologijos mokslai, mechanikos inžinerija – 09T), prof. habil. dr. Vitalijus VOLKOVAS technologijos (Kauno universitetas, technologijos mokslai, matavimųinžinerija – 10T).  Disertacija bus ginama viešame Matavimų inžinerijos mokslo krypties tarybos posėdyje 2005 m. rugsėjo 16 d. 14 val. Vilniaus Gedimino technikos universiteto senato posėdžiųsalėje. Adresas: Saulėtekio al. 11, LT-10223 Vilnius-40, Lietuva. Tel.: +370 5 274 49 52, +370 5 274 49 56; faksas +370 5 270 01 12; el. paštas doktor@adm.vtu.lt  Disertacijos santrauka išsiuntinėta 2005 m. rugpjučio 12 d. Disertaciją galima peržiūrėti Vilniaus Gedimino technikos universiteto bibliotekoje (Saulėtekio al. 14, Vilnius, Lietuva) VGTU leidyklos „Technika“ 1156 mokslo literatūros knyga  © Darius Mariūnas, 2005
 
 
1. General Characteristic of the Dissertation  Topicality of the problema process used to assess the – Measurement is quality either of the whole product released or its constituent. Measurement results are employed for monitoring complex manufacture process lines or other complicated lines of engineering process. Measurement problems become more and more acute in nanotechnologies and other fields of modern technologies since physical and technical characteristics of the end product are found to be greatly dependent on the measurement accuracy. Complex measurements necessitate the introduction of more challenging inputs in terms of much tedious work, time and funds. Bearing this in mind, proper selection of the algorithm or strategy of measurement is of utmost importance. In other words, it is crucial not only properly to select measurement method, measuring means or measurement system but also to have adequately selected the algorithm of control a space or plane during the measuring pitch selection, i.e., discretization procedure. Efforts should be made to reduce the number of measurement points –either in 3D space or on plane in order to cut down measurement time and measurement-related costs.  Aim and tasks of the work – The task of the work is to investigate efficiency and effectiveness of measurement operations due to possibilities to select an optimal pitch of measurement and change it in-operation according to the newly developed algorithm or strategy of measurement. The task of the investigation would also be to present recommendations for measurements of planes or 3D measurements in machine engineering and instrumentation, geodesy and surveying, structure industry. The present work pursues the following objectives: · the analysis of the ways leading to the most cost-effective selection of planar and three-dimensional surface measurement tests; · the identification of optimal frequency in the tested space by determining the measurement discretization pitch and associating its value with the nature of the deviations measured; · cutting down the measurement time without any loss in deviations’ assessment accuracy by undertaking investigations into the effect of the nature of the deviation function upon the value of the discretization pitch as well as by developing new procedures and algorithms to cut down measurement time; · the submission of the recommendations how to reduce the number of measurement tests and ensure optimal measurement time in machine and instrument manufacture process, in construction and geodesy.
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Scientific novelty The following achievements can be regarded as scientific novelty: · The development of integrally and differentially modified space or plane discretization pitch determination methods that allow both for selection of the pitch value against the nature of the deviation function of the surfaces measured and its value and for reduction of the measurement time without any loss in accuracy. · The examination of the recommended methods by employing experimental and mathematical statistics procedures to establish their usability and validity. · The development of algorithms to be applied in the modified methods under discussion and the procedure of their practical realization.  Methodology of research. Theoretical, analytical and experimental work was carried out during this research. It includes calculation methods and methods of experimental research. Results of experimental research are processing of methods of mathematical statistics. Results of experimental research were processed using the methods of mathematical statistics. Features of gradient variation of random function of local deviation were verified by least-squares method. In such a way the differentially modified 3D space or plane discretization were analyzed, allowing to evaluate the quality of measurement of deviations of the surfaces and the time used for this operation. Correlation and spectral analysis were used for quality assessment of modified methods.  The practical value. The integrally and differentially modified discretization methods make it possible to cut down the time of measurement of the object without any loss of quality of the results obtained. The newly developed strategy of measurement and measuring pitch selection were tested using the coordinate measuring machine of high accuracy. The newly developed algorithm of measurement was used for measurement of surface planes. The methods developed were proved as simpler, saving the time for measurements and retaining the same accuracy of measurements performed. The algorithms supporting realization of such modified methods, thus developed, enable the operator to make use of them in various types of automatic measurement equipment.  Presented for the defence · modified plane or 3D surface discretization pitch determinationThe methods that allow to select the pitch value depending on the character of
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the deviation function of the surfaces under measurement. · The methodology of realization of modified 3D or plane discretization strategy based on the pitch determination methods and their validation by analytic and experimental means.  The scope of the scientific work. scientific work consists of the The general characteristic of the dissertation, 4 chapters, conclusions, list of literature, list of publications. The total scope of the dissertation – 109 pages, 63 pictures, 6 tables.  2. Modified methods of discretization and results  2.1 The description of the work performed  Based on the scientific technical literature references, the first chapter covers the analysis of: the methods used for measurement of geometric accuracy parameters; the calibration procedures as applied to measuring means and machines; and measurement algorithms. Following such references, the methods used for measurement of geometric accuracy parameters have been roughly split up into two groups: the methods for spatial accuracy determination and the procedures for measurement periodicity determination. The major focus was on the determination of the discretization pitch value as measured in space or in plane. Also, consideration has been given to the problem how to reduce the duration of time needed to measure the deviations of the surface. The characteristics of gradient of local deviations of the object to be measured in the space using discretization method of variable value of the pitch are expressed:  ræ¶Fr¶Frj¶Fkr D=èçx×i+y×+z×. (1)  HereF=f(x,y,z)– function of deviations of a local surface, thei, andk– unitary vectors. Vector (1) permits to evaluate changes of deviations in measurement volume in directions ofx, yandz-axiswith one integral index. So, in the areas where deviations of the object are growing sharply, scalar value of integral indexD enlarges, and in places, where these values increase not so sharply –
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the indexDsign of change of the scalar vary not so significantly. The  will value of indexD be used for establishing the size of the pitch of could discretization of measuring space. This variation of the pitch of discretization will be called further an integrally modified method of discretizing the measuring space. Choosing the sizeLintof discretization of the pitch of measurement in the space(inversely proportional to the scalar value of integral index, it would be possible to evaluate regularities of change in deviations of geometry of the object. Nevertheless, scalar value of the integral indexD vary in the can interval 0 D  . So, choosing valueLintof the pitch of discretization of the space, it is necessary to use some limitations, indicating maximal and minimal permissible limits, at which the values ofLint be acceptable. Then the would valueLintof the pitch could be calculated:  Lint=qrL. (2) D  r¶F2èøæöF2è2ø. (3) D=æçèxøö+ç÷yFæ+÷çzö÷  These limitations would be as follows: · when inequalityb1£ D £b2is satisfied, then the valueDis such that it is received by calculation according expression (3); · whenD áb1, thenD =b1; ·  whenD >b2, thenD =b2.        (4)  Hereq– the coefficient of proportionality,b1andb2– selected values according to the standards for measurement. Coefficients of proportionalityb1 and b2let us chooseLmin  Lint  Lmaxin the interval, which corresponds to the generalised interval of change of integral indexb1£ D £b2It is necessary to establish values of. b1 andb2 which would define margins of changes ofD. The expression (3) can be transformed to the
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formDr=tg2ax+tg2ay+tg2az=tga, i.e., as the medium square value of a tangent of three different anglestgαx, tgαyirtgαz; andtga–mean square value  ur of anglea that can be calculated asa=arctgD. Taking into account that D =tga, expression (2) will be recomposed as:  Lint=q×Lgta, whenb1£tga£b2. (5)  It is clear from expression (5), that parametersb1 andb2 determine must the variation limits oftga. Methodology that permits to determine the variation values of coefficientsb1,b2,qaccording to the character and size of variation of deviations function is presented in the second chapter of this work. It is necessary to construct an approximate expression of the function of deviations for a comparatively small number of measuring points for calculation of partial derivatives. Further it is called a function of local deviations. To describe its dependences, a polynomial of three variable of the third power will be used:  F = + × + × + × +2× +2× +2× +3× +3×z3+6( . ) a1a2x a3y a4z a5x a6y a7z a8x a9y a10  Two main conditions exist for the polynomial chosen. First, it must filtrate random constituents of deviations and components of measurement of short lengths; second, to describe regularities of changes in local deviations with minimal number of members of the polynomial and securing appropriate accuracy. There are 10 unknown coefficientsa1,a2, ...,a10in polynomial (6), so it is necessary to perform 10 measurements for estimation of its values. A system of 10 algebraic equations must be constructed. The least-square method for calculating coefficientsa1,a2, ...,a10was used:  A=(YTY)-1YTF.(7)  HereAis a column of vector of the coefficients of variablesa1,a2, …,an;Yis a rectangular matrix of experiment (7);Fis a column of vector of the values of errors determined by experimental trials. The different values of pitch of discretization of measuring space in directions of 0x,0yand 0zaxes could be calculated:
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Lx=q×LF,Ly=q×LF,Lz=q×L. (8) ¶F y After the evaluation of limitations when inequalities are satisfied: · whenb1F£x£b2,b1F£y£b2,b1£Fz£b2, thenF;¶F and¶F yvalues are such that they are received by calculation according to the expression (3); · whenxF£b1;Fy£b1;z£Fb1, then all¶F;F andF values of y components are equal to b1; · whenFx£b2;yF£b2;zF£b2, then allF;FyandFvalues of components are equal tob2.  Taking into account that geometrical meaning of the partial derivative is tgα, expression (7) is rearranged as follows:  Lx=q×gtLa,Ly=q×gtLay,Lz=q×Ltga; (9) x  heretgaxF=,tgay=Fy,tgaz=F, whenb1tgαx b2,b1tgαyb2and b1tgαzb2. Analogical dependencies are received in cases of plane and 3D coordinate measurement. So, by using integrally and differentially modified methods of space discretization assessing the properties of local deviations gradient, these methods permit us to choose a value of the pitch of surface measurement. At the same time the characteristics of the function of deviations of geometrical surface are assessed securing the accuracy and overall quality of measurement. The methods of measurement presented here allows to save time for evaluation of 3D or plane surface deviations. They are simple and can be easily realised in the systems of automatic measurements. These methods could be applied in CNC machines and other technological equipment, measuring instruments and coordinate measuring machines as well.
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