Multi-objective optimisation of machine tool error mapping using automated planning

Error mapping of machine tools is a multi-measurement task that is planned based on expert knowledge. There are no intelligent tools aiding the production of optimal measurement plans. In previous work, a method of intelligently constructing measurement plans demonstrated that it is feasible to optimise the plans either to reduce machine tool downtime or the estimated uncertainty of measurement due to the plan schedule. However, production scheduling and a continuously changing environment can impose conflicting constraints on downtime and the uncertainty of measurement. In this paper, the use of the produced measurement model to minimise machine tool downtime, the uncertainty of measurement and the arithmetic mean of both is investigated and discussed through the use of twelve different error mapping instances. The multi-objective search plans on average have a 3% reduction in the time metric when compared to the downtime of the uncertainty optimised plan and a 23% improvement in estimated uncertainty of measurement metric when compared to the uncertainty of the temporally optimised plan. Further experiments on a High Performance Computing (HPC) architecture demonstrated that there is on average a 3% improvement in optimality when compared with the experiments performed on the PC architecture. This demonstrates that even though a 4% improvement is beneficial, in most applications a standard PC architecture will result in valid error mapping plan

Determination of measurement uncertainty by Monte Carlo simulation

Modern coordinate measurement machines (CMM) are universal tools to measure geometric features of complex three-dimensional workpieces. To use them as reliable means of quality control, the suitability of the device for the specific measurement task has to be proven. Therefore, the ISO 14253 standard requires, knowledge of the measurement uncertainty and, that it is in reasonable relation with the specified tolerances. Hence, the determination of the measurement uncertainty, which is a complex and also costly task, is of utmost importance. The measurement uncertainty is usually influenced by several contributions of various sources. Among those of the machine itself, e.g., guideway errors and the influence of the probe and styli play an important role. Furthermore, several properties of the workpiece, such as its form deviations and surface roughness, have to be considered. Also the environmental conditions, i.e., temperature and its gradients, pressure, relative humidity and others contribute to the overall measurement uncertainty. Currently, there are different approaches to determine task-specific measurement uncertainties. This work reports on recent advancements extending the well-established method of PTB's Virtual Coordinate Measuring Machine (VCMM) to suit present-day needs in industrial applications. The VCMM utilizes numerical simulations to determine the task-specific measurement uncertainty incorporating broad knowledge about the contributions of, e.g., the used CMM, the environment and the workpiece

Comparison of Volumetric Analysis Methods for Machine Tools with Rotary Axes

Confidence in the ability of a production machine to meet manufacturing tolerances requires a full understanding of the accuracy of the machine. However, the definition of “the accuracy of the machine” is open to interpretation. Historically, this has been in terms of linear positioning accuracy of an axis with no regard for the other errors of the machine. Industry awareness of the three-dimensional positioning accuracy of a machine over its working envelope has slowly developed to an extent that people are aware that “volumetric accuracy” gives a better estimation of machine performance. However, at present there is no common standard for volumetric errors of machine tools, although several researchers have developed models to predict the effect of the combined errors. The error model for machines with three Cartesian axes has been well addressed, for example by the use of homogenous transformation matrices. Intuitively, the number of error sources increases with the number of axes present on the machine. The effect of the individual axis geometric errors can become increasingly significant as the chain of dependent axes is extended. Measurement of the “volumetric error” or its constituents is often restricted to a subset of the errors of the Cartesian axes by solely relying on a laser interferometer for measurement. This leads to a volumetric accuracy figure that neglects the misalignment errors of rotary axes. In more advanced models the accuracy of the rotary axes are considered as a separate geometric problem whose volumetric accuracy is then added to the volumetric accuracy of the Cartesian axes. This paper considers the geometric errors of some typical machine configurations with both Cartesian and non-Cartesian axes and uses case studies to emphasise the importance of measurement of all the error constituents. Furthermore, it shows the misrepresentation when modelling a five-axis machine as a three-plus-two error problem. A method by which the five-axis model can be analysed to better represent the machine performance is introduced. Consideration is also given for thermal and non-rigid influences on the machine volumetric accuracy analysis, both in terms of the uncertainty of the model and the uncertainty during the measurement. The magnitude of these errors can be unexpectedly high and needs to be carefully considered whenever testing volumetric accuracy, with additional tests being recommended

Geometrical Product Specification and Verification as toolbox to meet up-to-date technical requirements

The ISO standards for the Geometrical Product Specification and Verification (GPS) define an internationally uniform description language, that allows expressing unambiguously and completely all requirements for the geometry of a product with the corresponding requirements for the inspection process in technical drawings, taking into account current possibilities of measurement and testing technology. The practice shows that the university curricula of the mechanical engineering faculties often include only limited classes on the GPS, mostly as part of curriculum of subjects like Metrology or Fundamentals of Machine Design. This does not allow students to gain enough knowledge on the subject. Currently there is no coherent EU-wide provision for vocational training (VET) in this area. Consortium, members of which are the authors of this paper, is preparing a proposal of an EU project aiming to develop appropriate course

Numerical investigation of the real and ideal gap profiles in the calculation of the pressure distortion coefficient and piston fall rate of an LNE 200 MPa pressure balance

This paper aims to investigate, by means of numerical simulation, the effect of gap profiles on the calculation of the pressure distortion coefficient (λ) and the piston fall rate (vf) of two piston-cylinder units used in a Laboratoire National de Métrologie et d'Essais (LNE) 200 MPa pressure balance. The ideal mean gap width between the piston and the cylinder was obtained after measuring the piston fall rate at a low pressure, while the piston radius was obtained from the cross-float experiments at a low pressure. The real gap width was obtained from dimensional measurements by measuring the diameter and straightness of the piston and the cylinder. The piston and cylinder radial distortions were calculated using the finite element method. The pressure distribution in the gap was calculated on the basis of the Navier-Stokes equation for Newtonian viscous flow. The results such as pressure distributions, radial distortions, the pressure distortion coefficient and the piston fall rate were presented for the free-deformation operating mode of the assemblies. The calculation resulted in ideal and real gap profiles indicating that the average pressure distortion coefficient was in good agreement within 0.017 × 10-6 MPa-1 and the calculations of piston fall rate depended on the gap profile especially at the inlet and outlet zones of the engagement length.Laboratoire National de Métrologie et d'Essai

Measuring sensors calibration in worm gear rolling testers

The ISO standard regulating gear-rolling measurement does not specify in detail the calibration and verification procedures for this type of equipment. This may be one of the reasons for the lack of reproducibility in these rolling tests. The uncertainty budget method, which is the most appropriate way to know the accuracy of this dynamic measurement, shows that the measuring sensors’ accuracy is only a part of the total measurement process uncertainty. In this work, a new calibration and verification procedure for a worm gear rolling tester is presented, based on machine tool, coordinate measuring machine and gear measuring instruments’ calibration techniques. After compensating numerically for the measuring instruments, it has been evaluated how the error components of each movement affect the meshing point, a fundamental factor to ensure a good gear transmission. The study shows that there are unintentional position variations, not detected by the measuring sensors, that have to be identified and quantified in the calibration for their later inclusion in the uncertainty budget. In this way, the measurement uncertainty could be reduced, and thus improve the reproducibility of these testers, as a preliminary stage to the development of optimized rolling measurement equipment to solve current limitations

Measurement method for 2-dimensional coordinate system

The subject of this Master’s of Science Thesis is to study suitability of predefined technologies and development of a measurement system for measuring Cartesian style robot’s positioning accuracy within its x/y-plane. The methods currently used for measuring and calibrating robot positioning are based on commercial solutions or measurement systems developed internally. Both of these have their non-beneficial properties that lead to the commissioning of this thesis work. The commercial system provides a high accuracy and repeatability performance but are often costly and difficult or impossible to integrate to the robot system in question. The second mentioned measurement system has much lower building costs but it only measures in one axis at a time and thus, it doesn’t see the possible orthogonality errors. This problem was approached with three methodologies covering the theoretical background of the main geometrical error sources, some basics of the theory of measurement uncertainty, evaluation procedure for evaluating suitability of technologies for measuring positioning and developing a measurement system with the selected technology based on the evaluation results. The technologies are evaluated with a scoring system based on criterion that sets a range of requirements for e.g. accuracy performance and other functionality. The goal of this thesis was to develop a low cost, system integrable positioning measurement system and study its performance and usability by comparing it to commercial measurement systems and systems design and developed internally. After conducting evaluation of the technologies, a camera-based technology was selected for development phase. This technology solution includes a camera and optics that are the robots standard equipment and thus won’t add any additional costs. This solution requires a measurement target which is used with the camera to detect motion and algorithms for camera calibration and for calculating motion increments from the captured images. With the combination of camera, optics and the measurement target a value of 55.2 pixels per millimeter was obtained which translates to 17.9 μm ± 0.001-pixel size in the measurement images

CALIBRATION OF CAPACITIVE SENSORS AND ELECTRONIC LEVELS FOR THE STRAIGHTNESS MEASUREMENTS USING MULTIPROBE METHOD

In this work, the straightness length 300 mm measurement under nanometer uncertainty. The proposed methodology represents a process known as propagation using the assumption of small displacement which leads to solving an overdetermined linear system. The experimental studies were carried out on the capacitive sensors and electronic levels. The least squares mathematic method is apply to calculate the optimal solution. This method requires taking into account the uncertainties of the two different types of sensors leads to method of weighted least squares. The first step is to calibrate the sensors and to estimate the effect on the calculated straightness

Effective Product Lifecycle Management: the role of uncertainties in addressing design, manufacturing and verification processes

The aim of this thesis is to use the concept of uncertainty to improve the effectiveness of Product Lifecycle Management (PLM) systems. Uncertainty is a rather new concept in PLM that has been introduced with the new technical language, drawn by ISO, to manage Geometrical Product Specification and Verification (GPS) in the challenging environment of modern manufacturing. GPS standards regard in particular design and verification environments, and want to guarantee consistence of information through a technical language which define both specification and verification on sound logical and mathematical bases. In this context, uncertainty is introduced as the instrument that measures consistency: between the designer intentions (specifications) and the manufactured artefact (as it is observed through measurement) as well as between the measurand definition provided by designers (the specification again) and that used by metrologists. The implications of such an approach have been analyzed through a case study dealing with flatness tolerance and paying particular attention to the verification processes based on Coordinate Measuring Machines (CMM). A Design of Experiment (DoE) has been used and results have been analyzed and used to build a regression model that allows generalization in the experiment validity domain. Then, using Category Theory, a categorical data model has been defined which represents the operation based structure of GPS language and uses the flatness research results in order to design a software able to concretize the GPS vision of geometrical product specifications management. This software is able to translate specification requirements into verification instructions, estimate the uncertainty introduced by simplified verification operations and evaluate costs and risks of verification operations. It provides an important tool for designers, as it allows a responsible definition of specifications (designer can simulate the interpretation of specifications and have an idea of the costs related with their verification), and for metrologist, as it can be a guide for designing GPS compliant verification missions or handling the usual verification procedures according to the GPS standards. However, during the study, it has been matured the consciousness that this approach, even if correct and valuable, was not the most suitable to fully exploit the real potential of CMM. Then, aside the GPS oriented work, an adaptive sampling strategy, based on Kriging modelization, has been proposed with very encouraging result