Correcting the roundness profile basing on elements of the wavelets analysis

W artykule przedstawiono procedurę eliminacji z pomiarów zarysów okrągłości błędu systematycznego określanego mianem pełzania sygnału. Trójetapowa procedura korygowania błędu pełzania sygnału obejmuje filtrację górnoprzepustową zmierzonego sygnału za pomocą transformaty falkowej, wyznaczanie wielomianu interpolacyjnego pomiędzy punktami końcowymi zarysu dla odszumiania przy wysokim poziomie dekompozycji oraz korekcję wykresu wyznaczonym wielomianem. Przeprowadzona ocena efektywności zaproponowanej procedury zrealizowana za pomocą rachunku korelacyjnego wykazała wysoki stopień korelacji pomiędzy skorygowanymi wykresami obarczonymi wcześniej błędem pełzania sygnału a wykresem, w którym ten efekt nie występował.The paper presents a procedure of elimination of the systematic error known as signal creeping from the roundness profiles. This error is revealed in the measurement of roundness by discontinuity of measurements, and in the graph by discontinuity of a profile. A three-step procedure for correcting the creep signal error includes: high-pass filtration of the measurement signal with use of the wavelet transform, calculation of polynomial interpolation between the terminal points of the profile to remove the noise at high levels of decomposition as well as correction of the graph with the specified polynomial. The evaluation of the effectiveness of the proposed procedure realized by the correlation demonstrated a high level of correlation between the corrected graphs loaded with the creep signal error and the graph without this error. The proposed procedure has good properties for correcting the error with maintaining the characteristics and features of the measured roundness profile

Force analysis and simulation – experimental research on the measurement of cylindrical surface profiles

The results of tests presented herein can have practical applications for the adjustment of rotary speed to ensure constant contact between the measuring sensor’s spindle tip and the crankshaft journal of a piston energy converter, whose roundness profile is being measured. Analytical considerations have been supported by the results of simulations as well as experimental tests. The research has also shown that an increase in rotary speed affects the obtained profile shape and the value of determined roundness deviation

Applying Harmonic Analysis in the Measurements of Geometrical Deviations of the Crankshafts – Selecting Support Conditions

The article presents principles of the most suitable support conditions which enable elimination of deflections and elastic deformations of crankshafts under their self-weight. On the basis of the formulated principles sample calculations of force values of support reactions were performed. This guarantees zero value of deflections on main journals depending on the angle of rotation of the shaft, applying available programme of strength calculations Nastran FX 2010. The obtained results have been approximated with a mathematical equation applying the calculating method based on the harmonic analysis theory. Then a comparative assessment of the force diagram (the forces were obtained via strength calculations and mathematical model including so called mutual inter-correlation coefficient) was made. The obtained results of comparative analysis showed high correspondence between the compared diagrams. Presented procedures of determining the required forces ensuring elimination of deflections and elastic deformations can be applied to measurements of crankshaft geometrical deviations realized on the basis of a measuring system with, so called, flexible support of a measured object

A new approach to mathematical description of roundness shape by two-prism support

W artykule przedstawiono nowe ujęcie matematycznego zapisu zarysu okrągłości odpowiadające pomiarom cylindrycznych elementów maszyn podpartych w dwóch pryzmach. W oparciu o opracowany schemat pomia-rów odniesieniowych, uwzględniający związki kątowe pomiędzy promie-niem zarysów okrągłości wyprowadzone zostały wzory mające zastoso-wanie w symulacyjnych obliczeniach mierzonej odchyłki okrągłości Dz3 oraz wartości współczynnika wykrywalności kn3.In the paper was shown a new approach to mathematical description of roundness shape corresponding to measurements of cylindrical machinery parts supported onto two prisms. Basing on reference measurement schema, taking in regard angular relations between radius of roundness shape, the formulae used in simulating computations of measured roundness deviation Dz3 as well as detectability coefficient kn3 were presented

A Force-Sensor-Based Method to Eliminate Deformation of Large Crankshafts during Measurements of Their Geometric Condition

This article describes an innovative method for eliminating deformation in large crankshafts during measurement of their geometric condition. The currently available techniques for measuring crankshaft geometry are introduced and classified according to their applicability and the method of measurement. The drawbacks of the methods have been identified and a solution to these problems has been proposed. The influence of the rigid support of a shaft on its deformation, and thus on the reduction in the accuracy of crankshaft geometry measurements, has also been investigated. The concept and main versions of the proposed measuring system with active compensation for shaft deflection, by means of actuators cooperating with force transducers monitoring the deflection of individual crank journals of a crankshaft being measured, have been presented and the flexible support control system has also been described. The problems relating to the operation of the control system have been furnished along with a way to solve them, including the issue of noise reduction in the signal from the force transducer and the influence of the controller parameters on the operation of the flexible support. The computer system that controls the flexible supports has been briefly characterized, and the performance of the prototype system and the model reference system has been compared. The results have shown that the system is able to effectively eliminate the deflection and elastic deformation of the crankshaft under the influence of its own weight

Problems of support and elastics strains of a measured object

The author presents the results of research aimed at determining the best conditions of supporting large and elastic machine elements such as crankshafts. A number of simulation tests were performed with variable shaft support conditions changed using the author’s system of elastic support of crankshafts. The selection criteria were established for support parameters. Meeting these criteria guarantees that shaft elastic deflections and strains are eliminated. Consequently, such strains will not affect the estimation of geometrical deviations of the measured object

Analysis of the axis deviation measurement error caused by deviation resulting from eccentricity displacement of the measured profile center

W artykule przedstawiono wyniki analizy błędu pomiaru odchyłek położenia osi cylindrycznych elementów maszyn bazowanych w pryzmach, spowodowanego wynikającą z tych odchyłek mimośrodowością przemieszczania się osi zespołu powierzchni cylindrycznych tak bazowanych elementów. Wyprowadzone zostały zależności matematyczne umożliwiające uwzględnienie tego błędu w postaci poprawek w zależności od kąta obrotu przedmiotu mierzonego. Przeprowadzona analiza wykazała nieznaczny wpływ rozpatrywanego błędu pomiaru na wartość mierzonych odchyłek geometrycznych, potwierdzając przydatność wykorzystania metod odniesieniowych do kompleksowych pomiarów stanu geometrycznego elementów maszyn bazowanych w pryzmach.In the paper there is presented analysis of the error measurement of the position axis deviation of machine elements based in prisms caused by eccentricity deviations of mutually movement of the based in prisms elements cylindrical surfaces. Basing on the support scheme assumed for theoretical consideration, the mathematical relationships describing changes of the investigated measurement error value as a function of the measured object rotation angle were derived. When determining the measured error values, there was also taken into account possibility of influencing the measurement results by an additional eccentricity caused by the error of the measuring sensor position in relation to the rotation axis realised by the measurement system. The analysis results showed a very small impact of the considered error on the described geometrical deviation values on condition that the eccentricity caused by the error of the measuring sensor position was eliminated before. The analysis results also confirmed usefulness of the referencing methods used for complex measurements of the geometrical state of large cylindrical mechanical elements such as crankshafts or distribution shafts which are often placed in prism during measurements

Wyznaczanie i analiza złożonej niepewności pomiarowej odchyłki okrągłości

This author presents the results of an analysis of the effect of directly measured quantities and their measurement (standard) deviations on the value of the total measurement uncertainty of roundness deviation. The methods described refer to the determination of roundness deviation based on the mean square element and basic mathematical transformations and relationships that provided a basis for the analysis. Its results are given in the form of diagrams followed by final conclusions.W artykule zaprezentowane zostały wyniki analizy wpływu wielkości mierzonych bezpośrednio oraz ich niepewności pomiarowych (standardowych) na wartość złożonej niepewności pomiarowej odchyłki okrągłości. Przedstawiona została metodyka wyznaczania odchyłki okrągłości według elementu średniokwadratowego oraz podstawowe przekształcenia i zależności matematyczne, w oparciu o które dokonano wspomnianej analizy. Wyniki analizy zapisano w postaci wykresów i sformułowanych wniosków końcowych

Harmonic analysis and methodology of determining the deviations in shape and axis location for a set of cylindrical surfaces with use of DEVFORMLOC-NKŁN computer program

W artykule przedstawiona została metodyka pomiaru i wyznaczania odchyłek kształtu oraz położenia osi według elementu średniokwadratowego, dla zespołu powierzchni cylindrycznych obiektu ustalonego w dwóch pryzmach. W metodyce tej wykorzystane zostały elementy teorii analizy harmonicznej zarysów okrągłości. Przedstawiony został również autorki program obliczeniowy realizujący obliczenia według zaproponowanej metodyki .Measurements of geometrical errors of large size cylindrical machinery parts based in V-blocks belong to a group of the so-called reference measurements. During them a based element is displaced. The existing mathematical models, developed for a case of basing the detail in a single V-block, make it possible to transform the measured shape into the so-called transformed real shape as well as to determine unknown parameters of the measured roundness shape [4]. The paper presents the method for measuring and determining the shape deviations as well as axis location of the measured system of surfaces of cylindrical machinery parts based in two V-blocks. For measurements of this kind there was worked out a mathematical model, based on the theory of roundness shape harmonic analysis, for transformation from the measured to transformed real shape [6]. The mentioned model makes it possible to express harmonic components of the real shape as a function of parameters of the measured detail and measuring system. As a final result, there was developed by author the computer program DEVFORMLOC-NKŁN by the author. It is destined for numerical computations of estimated parameters of the measured cylindrical surfaces system and presented in the paper asa flow-chart

Determination of harmonic components of transformed shape roundness

W artykule przedstawione zostały zagadnienia związane z procedurą transformacji i wyznaczania ze zmierzonego zarysu okrągłości parametrów rzeczywistego zarysu okrągłości dla pomiarów części maszyn ustalonych w dwóch pryzmach. Procedura ta jest niezbędna dla prawidłowej oceny rzeczywistego zarysu okrągłości, który podczas pomiarów ulega zniekształceniu z uwagi na występujące przemieszczenia tak bazowanego elementu. Przedstawione zostały podstawy matematyczne tej procedury oraz przykładowe wyniki obliczeń symulacyjnych zrealizowanych w oparciu o opracowaną procedurę transformacji. Uzyskane wyniki potwierdziły poprawność przyjętych założeń, prawidłowość dokonanych przekształceń i słuszność wyprowadzonych zależności.Measurements of geometrical errors of large size machinery parts fixed in V-blocks are belonging to group of reference method measurements. One of the properties of mentioned method is such, that points of contact between shapes of measured detail and V-block are immovable, which causes displacement of based in V-block part. An existing mathematical model, developed for cases of fixing details in the single V-block makes possible to convert the measured shape onto so called transformed real shape and to deter-mine the unknown parameters of estimation measured shape with use the theory of harmonic analysis of roundness shape [1]. The paper presents problems related with procedure of transformation and determination of parameters of real roundness shape basing on measured roundness shape for measurements of large size machinery parts fixed in two V-blocks (e.g. crankshafts or cam shafts). In the paper the mathematical foundations of such procedure were also described. It was proved, that amplitude values of harmonic components for particular indices n3 of measured shape ARn3, BRn3 are in dependence on following factors: amplitudes of harmonic components of measured shape AFn3, BFn3, amplitudes of harmonic components of measured shape tangent with shapes of V-blocks AFn1, BFn1, AFn2, BFn2 as well as parameters of measuring system and measured detail (angles ? and ? and coordinates li and l) (formulae (12) and (13)). The paper contains also examples of simulation results based on previous developed procedure of transformation. Obtained results confirmed, that assumptions, performed transformations and proven dependencies were correctly