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Geometric error, mainly due to imperfect geometry and dimensions of machine components, is one of the major error sources of machine tools. Considering that geometric error has significant effects on the machining quality of manufactured parts, it has been a popular topic for academic and industrial research for many years. A great deal of research work has been carried out since the 1970 s for solving the problem and improving the machining accuracy. Researchers have studied how to measure, detect, model, identify, reduce, and compensate the geometric errors. This paper presents a thorough review of the latest research activities and gives an overview of the state of the art in understanding changes in machine tool performance due to geometric errors. Recent advances in measuring the geometrical errors of machine tools are summarized, and different kinds of error identification methods of translational axes and rotation axes are illustrated respectively. Besides, volumetric geometric error modeling, tracing, and compensation techniques for five-axis machine tools are emphatically introduced. Finally, research challenges in order to improve the volumetric accuracy of machine tools are also highlighted. © 2023 Chinese Society of Aeronautics and Astronautics

In this article two complementary methods are developed. Firstly, a method to add precision in large machine tools with modular lightweight structures (APLM), which performs the compensation of geometrics and dynamics errors using embedded intelligence, and secondly, an alternative polishing method called selective polishing (SP). This systematic process comprehends measurement tools and algorithm resources. Phenomena occurred in the machine structure, due to interaction between the cutting tools and the petrous materials in the grinding and polishing processes are modeled mathematically. Using validated flatness models, the variables and parameters were discretized to determine the errors with respect to the Z axis. To validate the method, a test machine of 3m(2) workspace with a multi-body lightweight structure design was built. The geometrical errors were determined using precision instruments and those were compared with a pattern surface. A higher flatness is achieved through a combined grinding-traditional polishing and selective polishing process using the same machine. This method saves time and energy consumption.

Imagination of earth-surface’s objects is contaminated with errors by sensor to target acquisition systems in the satellite remote sensing. Movement of the sensor and displacement of the target are propagated geometric error on the imagery. Systematic errors could be removed by trajectory model and rigorous sensor model; however, random errors are existed that in which is difficult to remove without affecting to image geometry. The study introduced geometric error assessment (GEA) on image objects to understand the error geometries from the imagery. At first, ground control points (GCP) and check points (CP) are scattered in all direction of the image. Then, errors are generated seeding the GCP location using Box-Muller method. The method produced simulated GCP contaminated with errors. Random errors are subtraction from simulated GCP by the true one. The study found that the error of CP is approached to zero when the CP closed to GCP. The corrected image would be applied for GIS analysis such as land-use/land-cover mapping and management, disaster risk mapping and management, urbanization prediction and management, water resource management.

Робота виконана на кафедрі металорізальних верстатів та систем Центральноукраїнського національного технічного університету та у відділі №20 «Перспективних ресурсозберігаючих технологій обробки» Інституту надтвердих матеріалів імені В. Н. Бакуля., У дисертації вирішена науково-технічна проблема, що полягає в розробці науково-обґрунтованих технологічних методів управління параметрами точності при деформуючому протягуванні. Розроблена на основі енергетичних принципів математична модель осередку деформації, що дозволила визначити закономірності деформування в осередку деформації та встановити, що інтенсивне утворення похибок отвору відбувається в позаконтактних зонах осередку деформації. Проведені експериментальні дослідження деформацій оброблених заготовок. Це дозволило розробити аналітично-експериментальну модель викривлення осі обробленої деталі. Представлені результати вивчення деформуючого протягування різнотовщинних заготовок. Розроблені науково-обґрунтовані алгоритми технологічного управління параметрами точності, які використовуються при розробці технологічних процесів на основі деформуючого протягування, а також нові схеми, способи та інструменти, які зменшують похибки обробки.

Робота виконана на кафедрі металорізальних верстатів та систем Центральноукраїнського національного технічного університету та у відділі №20 «Перспективних ресурсозберігаючих технологій обробки» Інституту надтвердих матеріалів імені В. Н. Бакуля., У дисертації вирішена науково-технічна проблема, що полягає в розробці науково-обґрунтованих технологічних методів управління параметрами точності при деформуючому протягуванні. Розроблена на основі енергетичних принципів математична модель осередку деформації, що дозволила визначити закономірності деформування в осередку деформації та встановити, що інтенсивне утворення похибок отвору відбувається в позаконтактних зонах осередку деформації. Проведені експериментальні дослідження деформацій оброблених заготовок. Це дозволило розробити аналітично-експериментальну модель викривлення осі обробленої деталі. Представлені результати вивчення деформуючого протягування різнотовщинних заготовок. Розроблені науково-обґрунтовані алгоритми технологічного управління параметрами точності, які використовуються при розробці технологічних процесів на основі деформуючого протягування, а також нові схеми, способи та інструменти, які зменшують похибки обробки., The thesis solves the scientific and technical problem in the development of science-based technological methods of control parameters of the precision when deforming broaching. The mathematical model of deformation zone has been developed on the basis of energy principles, which allowed to determine the patterns of deformation in the deformation zone and to establish that the intense formation of errors in the hole occurs in the non-contact zones of the deformation zone. Experimental studies of deformations of processed workpieces have been carried out. This allowed to develop an analytical-experimental model of the curvature of the axis of the machined part. The results of the study of deforming broaching of multi-thickness billets are presented. The scientifically grounded algorithms of technological control of precision parameters, which are used in the development of technological processes on the basis of deformation broaching, as well as new circuits, methods and tools that reduce processing errors are developed., В диссертации решена научно-техническая проблема, заключающаяся в разработке научно обоснованных технологических методов управления параметрами точности, позволяющего обеспечить геометрическую точность изделий, обработанных деформирующим протягиванием. Для заготовок с небольшой толстостенностью разработана с использованием энергетических принципов математическая модель очага деформации, состоящего из участка контакта и двух внеконтактных зон, примыкающих к нему. Модель позволила установить закономерности деформирования в очаге деформации и обосновать важное научно-технологическое положение: интенсивное образование погрешностей происходит у внеконтактных зонах. Проведены экспериментальные исследования осевых деформаций обработанных заготовок, установлены причины образования погрешности в зоне контакта. Они обусловлены вариацией осевых деформаций участков разнотолщинных в окружном направлении заготовок. Это позволило разработать аналитически-экспериментальную модель искривления оси обработанных деталей. Разработана математическая модель раздачи разнотолщинной заготовки, которая позволила установить связь между величиной раздачи отверстия и угловым размером пластической области поперечного сечения заготовки. Определены оптимальные области изменения технологических факторов, обеспечивающих отсутствие браковочных признаков у обработанных изделий. Предложен способ раздачи с гарантированной локализацией пластической деформации за счет создания в неравножесткой заготовке жестких и пластических участков, а также разработана теоретическая модель раздачи такой трубы. Определены кинематические, геометрические и энергетические параметры очага деформации. Показано, что протяженность контактной зоны необходимо рассчитывать по двум моделям очага деформации, которые отличаются между собой учетом влияния локальной зоны пластического деформирования. Расчеты по разработанной модели позволили уточнить влияние режимов протягивания и геометрии инструмента на мощность формоизменения и обос

Machine tool testing and accuracy analysis has become increasingly important over the years as it offers machine tool manufacturers and end-users updated information on a machine’s capability. A machine tooĺs capability may be determined by mapping the distribution of deformations and their variation range, in the machine tool workspace, under the cumulative effect of thermal and mechanical loads. This paper proposes a novel procedure for the prediction of machine tool errors under quasi-static and loaded conditions. Geometric errors and spatial variation of static stiffness in the work volume of machines are captured and described through the synthesis of bottom-up and top-down model building approaches. The bottom-up approach, determining individual axis errors using direct measurements, is applied to estimate the geometric errors in unloaded condition utilizing homogeneous transformation matrix theory. The top-down approach, capturing aggregated quasi-static deviations using indirect measurements, estimates through an analytical procedure the resultant deviations under loaded conditions. The study introduces a characterization of the position and direction dependent static stiffness and presents the identification how the quasi-static behavior of the machine tool affects the part accuracy. The methodology was implemented in a case study, identifying a variation of up to 27% in the stiffness response of the machine tool. The prediction results were experimentally validated through cutting tests and the uncertainty of the measurements and the applied methodology was investigated to determine the reliability of the predicted errors., QC 20171206

The geometrical errors of determination the coordinates of the goods are considered in this article. This determination of coordinates based on the use of digital video images of these goods in automated systems. Mathematical models of distortion and projection components geometrical errors are presented for contour points of goods. Numerical simulation and experimental study of geometric errors are executed.In the article the geometric errors of determination of the goods coordinates in automated systems are considered. The digital video images of these goods are used for determination of coordinates. The geometric errors of coordinates are stipulated by a distortion of video images in an optical system and errors of orientation and arrangement of goods by the digital video camera. The mathematical models are obtained for these errors. The numerical simulation and experimental researches are executed for these making a geometric error. Because of outcomes of researches the algorithmic compensation of geometric errors are executed. This result is proved increase of accuracy of measurement of geometric parameters goods, which are inspected by an automated system. For example, it can be goods from a natural stone.

When machining optical part, the surface geometric error cannot be avoided and it can affect optical properties of optical part significantly. So it has far-reaching meanings to study the influence of surface geometric error on optical properties. Based on the evaluation indexes i.e. wavefront aberration, point spread function and modulation transfer function, this paper establishes a model of optical part only with surface error to study the influence of surface error on optical properties with a piece of ring curved lens. The study result indicates with the increment of surface error, the value of wavefront aberration increment increases. Moreover, the transfer capacity of demonstrating object contour decreases. © (2013) Trans Tech Publications, Switzerland.

When machining optical part, the surface geometric error cannot be avoided and it can affect optical properties of optical part significantly. So it has far-reaching meanings to study the influence of surface geometric error on optical properties. Based on the evaluation indexes i.e. wavefront aberration, point spread function and modulation transfer function, this paper establishes a model of optical part only with surface error to study the influence of surface error on optical properties with a piece of ring curved lens. The study result indicates with the increment of surface error, the value of wavefront aberration increment increases. Moreover, the transfer capacity of demonstrating object contour decreases. © (2013) Trans Tech Publications, Switzerland.

When machining optical part, the surface geometric error cannot be avoided and it can affect optical properties of optical part significantly. So it has far-reaching meanings to study the influence of surface geometric error on optical properties. Based on the evaluation indexes i.e. wavefront aberration, point spread function and modulation transfer function, this paper establishes a model of optical part only with surface error to study the influence of surface error on optical properties with a piece of ring curved lens. The study result indicates with the increment of surface error, the value of wavefront aberration increment increases. Moreover, the transfer capacity of demonstrating object contour decreases. © (2013) Trans Tech Publications, Switzerland.

Imagination of earth-surface’s objects is contaminated with errors by sensor to target acquisition systems in the satellite remote sensing. Movement of the sensor and displacement of the target are propagated geometric error on the imagery. Systematic errors could be removed by trajectory model and rigorous sensor model; however, random errors are existed that in which is difficult to remove without affecting to image geometry. The study introduced geometric error assessment (GEA) on image objects to understand the error geometries from the imagery. At first, ground control points (GCP) and check points (CP) are scattered in all direction of the image. Then, errors are generated seeding the GCP location using Box-Muller method. The method produced simulated GCP contaminated with errors. Random errors are subtraction from simulated GCP by the true one. The study found that the error of CP is approached to zero when the CP closed to GCP. The corrected image would be applied for GIS analysis such as land-use/land-cover mapping and management, disaster risk mapping and management, urbanization prediction and management, water resource management., conference paper

This study proposes a measurement and improvement system for the consistency of machined diameter by a CNC lathe with referring the external shape of a machined workpiece. Under the assumption that the external shape of the workpiece is axial symmetrical, the axis of symmetry equivalent to the axial line between the spindle nose and the tailstock can be regarded as the compensatory reference for the straight line motion in turning. This axis in ZX plane can be represented as the successive change of center position of the both external profiles with use of a laser scan sensor traversing in the lathe. For the compensatory machining, the CL data is modified and applied by taking account of the magnitude of machining error from the compensatory reference. As the results of the compensatory machining, the accuracy of finishing has been highly improved as precise as the positioning accuracy of the lathe.

Diplomová práce má za úkol popsat vlivy vybraných výrobních technologií na geometrickou a rozměrovou přesnost obrobků. V práci jsou charakterizovány konkrétní technologie, tedy soustružení, frézování a broušení, a jednotlivé stroje, na kterých budou tyto technologie prováděny, jedná se o svislý soustruh, portálovou frézku a hrotovou brusku. Dále je navržen postup, jak sčítat jednotlivé geometrické chyby na trojosém obráběcím stroji, aby bylo možné popsat celý pracovní prostor stroje z hlediska chyb. Následně je pak pro každý stroj vytvořena analýza jednotlivých geometrických chyb a jejich vliv na výsledný obrobek., The aim of the diploma thesis is to describe influences of selected production technologies on geometrical and dimensional accuracy of workpieces. Specific technologies - turning, milling and grinding and the machines on which these technologies will be implemented - a vertical lathe, a portal milling machine and a center grinder are described in this thesis. Additionally a procedure is created for adding geometric errors to a tri-axial machine tool to describe the entire working area of the machine in terms of errors. Subsequently an analysis of each geometric error is created for each machine and their influence on the resulting workpiece is determined.

A major uncertainty contributor to the on-machine probing is linear axis kinematic errors. This paper proposes a novel self-calibration scheme to separate the workpiece geometry and machine tool kinematic errors from the probed profiles. Many self-calibration schemes have been well developed, but they are limited to either of the straightness, roundness, and two-dimensional (2D) grid point positions, since they require the probed points being in a closed set, as the workpiece is rotated or translated. This paper proposes its extension to a free-form 2D geometry. A key idea is on the assumption that the machine tool’s positioning error is in accordance with the rigid-body kinematic model. It makes linear axis error motions, represented in a look-up table format, be in a closed set. Two experimental case studies are presented. The uncertainty assessment is essential to investigate the effectiveness of the proposed scheme for the given workpiece geometry.

A calibration scheme of position and orientation errors of rotary axis average lines based on touch-trigger probing is widely available on many commercial five-axis machine tools. Such a measurement is influenced by error motions of both linear and rotary axes. This paper proposes a novel scheme to separately identify linear and rotary axis geometric errors by using a touch-trigger probe and an uncalibrated test piece. Whereas the proposed scheme is based on well-developed self-calibration schemes for the circularity measurement, an original contribution is that it is applied to separate linear and rotary axis geometric errors. Two case studies are presented. First, the proposed tests are performed on the same five-axis machine tool for half a year to observe a long-term change in linear and rotary axis geometric errors. The second case study investigates the influence of room temperature change on linear axis and rotary axis error motions.

Diplomová práce má za úkol popsat vlivy vybraných výrobních technologií na geometrickou a rozměrovou přesnost obrobků. V práci jsou charakterizovány konkrétní technologie, tedy soustružení, frézování a broušení, a jednotlivé stroje, na kterých budou tyto technologie prováděny, jedná se o svislý soustruh, portálovou frézku a hrotovou brusku. Dále je navržen postup, jak sčítat jednotlivé geometrické chyby na trojosém obráběcím stroji, aby bylo možné popsat celý pracovní prostor stroje z hlediska chyb. Následně je pak pro každý stroj vytvořena analýza jednotlivých geometrických chyb a jejich vliv na výsledný obrobek., The aim of the diploma thesis is to describe influences of selected production technologies on geometrical and dimensional accuracy of workpieces. Specific technologies - turning, milling and grinding and the machines on which these technologies will be implemented - a vertical lathe, a portal milling machine and a center grinder are described in this thesis. Additionally a procedure is created for adding geometric errors to a tri-axial machine tool to describe the entire working area of the machine in terms of errors. Subsequently an analysis of each geometric error is created for each machine and their influence on the resulting workpiece is determined.

Lately, a cylindrical workpiece of relatively large diameter is often machined by turning operations by a swiveling rotary table in a five-axis machining center. This paper presents a machining test containing features finished by a turning operation by a swiveling rotary table. Unlike conventional machining tests for turning operations described in ISO 13041-6:2009, the present machining test can identify a complete set of position and orientation errors of the axis average line of rotary axes from the geometry of the finished test piece. The radial and axial error motions of the rotary table can be also observed when the swiveling axis is positioned horizontal (A = 0°) and vertical (A = -90°). Experimental demonstration is presented. The rotary axis geometric errors identified from the finished test piece's geometry are compared with those estimated by a conventional error calibration test using a touch-triggered probe and a precision sphere. The uncertainty analysis for the present machining test is also presented.

Efficient, precise and automated in-process calibration schemes are essential to improve the accuracy and productivity of five-axis machine tools. This paper presents a new calibration approach, which combines an on-machine measurement cycle and self-calibration techniques, to evaluate the position errors and the error motions of a rotary axis using a touch trigger probe and an uncalibrated cylindrical artefact. This significantly reduces the downtime of machine tools required for the calibration process. In contrast to many common calibration strategies for rotary axes of five-axis machine tools, the presented self-calibration concept does not neglect the positioning errors of the linear axes when identifying the position errors and the error motions of the rotary axis. The self-calibration procedure is able to separate the positioning errors of the linear axes in radial direction, and the radial error motions and the position errors of a rotary axis, as well as the errors related to the uncalibrated artefact. This error separation is realized by a test cycle consisting of four tests in which the measurements are conducted by particular axis movements. Furthermore, an uncertainty analysis of the self-calibration concept is conducted to visualize the uncertainty propagation within the mathematical model. The self-calibration procedure is analyzed by an experimental evaluation, which includes a comparison between the results of the self-calibration approach and an R-Test. This comparison shows that the results of both measurement procedures are consistent.

Diplomová práce má za úkol popsat vlivy vybraných výrobních technologií na geometrickou a rozměrovou přesnost obrobků. V práci jsou charakterizovány konkrétní technologie, tedy soustružení, frézování a broušení, a jednotlivé stroje, na kterých budou tyto technologie prováděny, jedná se o svislý soustruh, portálovou frézku a hrotovou brusku. Dále je navržen postup, jak sčítat jednotlivé geometrické chyby na trojosém obráběcím stroji, aby bylo možné popsat celý pracovní prostor stroje z hlediska chyb. Následně je pak pro každý stroj vytvořena analýza jednotlivých geometrických chyb a jejich vliv na výsledný obrobek., The aim of the diploma thesis is to describe influences of selected production technologies on geometrical and dimensional accuracy of workpieces. Specific technologies - turning, milling and grinding and the machines on which these technologies will be implemented - a vertical lathe, a portal milling machine and a center grinder are described in this thesis. Additionally a procedure is created for adding geometric errors to a tri-axial machine tool to describe the entire working area of the machine in terms of errors. Subsequently an analysis of each geometric error is created for each machine and their influence on the resulting workpiece is determined.

Diplomová práce má za úkol popsat vlivy vybraných výrobních technologií na geometrickou a rozměrovou přesnost obrobků. V práci jsou charakterizovány konkrétní technologie, tedy soustružení, frézování a broušení, a jednotlivé stroje, na kterých budou tyto technologie prováděny, jedná se o svislý soustruh, portálovou frézku a hrotovou brusku. Dále je navržen postup, jak sčítat jednotlivé geometrické chyby na trojosém obráběcím stroji, aby bylo možné popsat celý pracovní prostor stroje z hlediska chyb. Následně je pak pro každý stroj vytvořena analýza jednotlivých geometrických chyb a jejich vliv na výsledný obrobek., The aim of the diploma thesis is to describe influences of selected production technologies on geometrical and dimensional accuracy of workpieces. Specific technologies - turning, milling and grinding and the machines on which these technologies will be implemented - a vertical lathe, a portal milling machine and a center grinder are described in this thesis. Additionally a procedure is created for adding geometric errors to a tri-axial machine tool to describe the entire working area of the machine in terms of errors. Subsequently an analysis of each geometric error is created for each machine and their influence on the resulting workpiece is determined.

Diplomová práce má za úkol popsat vlivy vybraných výrobních technologií na geometrickou a rozměrovou přesnost obrobků. V práci jsou charakterizovány konkrétní technologie, tedy soustružení, frézování a broušení, a jednotlivé stroje, na kterých budou tyto technologie prováděny, jedná se o svislý soustruh, portálovou frézku a hrotovou brusku. Dále je navržen postup, jak sčítat jednotlivé geometrické chyby na trojosém obráběcím stroji, aby bylo možné popsat celý pracovní prostor stroje z hlediska chyb. Následně je pak pro každý stroj vytvořena analýza jednotlivých geometrických chyb a jejich vliv na výsledný obrobek., The aim of the diploma thesis is to describe influences of selected production technologies on geometrical and dimensional accuracy of workpieces. Specific technologies - turning, milling and grinding and the machines on which these technologies will be implemented - a vertical lathe, a portal milling machine and a center grinder are described in this thesis. Additionally a procedure is created for adding geometric errors to a tri-axial machine tool to describe the entire working area of the machine in terms of errors. Subsequently an analysis of each geometric error is created for each machine and their influence on the resulting workpiece is determined.

Diplomová práce má za úkol popsat vlivy vybraných výrobních technologií na geometrickou a rozměrovou přesnost obrobků. V práci jsou charakterizovány konkrétní technologie, tedy soustružení, frézování a broušení, a jednotlivé stroje, na kterých budou tyto technologie prováděny, jedná se o svislý soustruh, portálovou frézku a hrotovou brusku. Dále je navržen postup, jak sčítat jednotlivé geometrické chyby na trojosém obráběcím stroji, aby bylo možné popsat celý pracovní prostor stroje z hlediska chyb. Následně je pak pro každý stroj vytvořena analýza jednotlivých geometrických chyb a jejich vliv na výsledný obrobek., The aim of the diploma thesis is to describe influences of selected production technologies on geometrical and dimensional accuracy of workpieces. Specific technologies - turning, milling and grinding and the machines on which these technologies will be implemented - a vertical lathe, a portal milling machine and a center grinder are described in this thesis. Additionally a procedure is created for adding geometric errors to a tri-axial machine tool to describe the entire working area of the machine in terms of errors. Subsequently an analysis of each geometric error is created for each machine and their influence on the resulting workpiece is determined.