For measuring machines and machine tools, geometrical accuracy is a key performance criterion. While numerical compensation is well established for CMMs, it is increasingly used on machine tools in addition to mechanical accuracy. This paper is an update on the CIRP keynote paper by Sartori and Zhang from 1995 [Sartori S, Zhang GX (1995) Geometric error measurement and compensation of machines, Annals of the CIRP 44(2):599–609]. Since then, numerical error compensation has gained immense importance for precision machining. This paper reviews the fundamentals of numerical error compensation and the available methods for measuring the geometrical errors of a machine. It discusses the uncertainties involved in different mapping methods and their application characteristics. Furthermore, the challenges for the use of numerical compensation for manufacturing machines are specified. Based on technology and market development, this work aims at giving a perspective for the role of numerical compensation in the future.

Geometric error measurement and compensation of machines : an update

Accuracy of machined components is one of the most critical considerations for any manufacturer. Many key factors like cutting tools and machining conditions, resolution of the machine tool, the type of workpiece etc., play an important role. However, once these are decided upon, the consistent performance of the machine tool depends upon its ability to accurately position the tool tip vis-a-vis the required workpiece dimension. This task is greatly constrained by errors either built into the machine or occurring on a periodic basis on account of temperature changes or variation in cutting forces. The three major types of error are geometric, thermal and cutting-force induced errors. Geometric errors make up the major part of the inaccuracy of a machine tool, the error caused by cutting forces depending on the type of tool and workpiece and the cutting conditions adopted. This part of the paper attempts to review the work done in analysing the various sources of geometric errors that are usually encountered on machine tools and the methods of elimination or compensation employed in these machines. A brief study of cutting-force induced errors and other errors is also made towards the end of this paper.

Error compensation in machine tools — a review: Part I: geometric, cutting-force induced and fixture-dependent errors

International Status of Thermal Error Research (1990)

The paper gives a survey of the upcoming use of X-ray computed tomography (CT) for dimensional quality control purposes: i.e. for traceable measurement of dimensions of technical (mechanical) components and for tolerance verification of such components. It describes the basic principles of CT metrology, putting emphasis on issues as accuracy, traceability to the unit of length (the meter) and measurement uncertainty. It provides a state of the art (anno 2011) and application examples, showing the aptitude of CT metrology to: (i) check internal dimensions that cannot be measured using traditional coordinate measuring machines and (ii) combine dimensional quality control with material quality control in one single quality inspection run.

Computed tomography for dimensional metrology

One of the major errors in machine tools namely geometric/kinematic errors was discussed at length in Part I of this paper. Here, in Part II, another major source of inaccuracy, namely thermal error that occurs due to extended usage of the machine is analysed. Continuous usage of a machine tool causes heat generation at the moving elements and this heat causes expansion of the various structural elements of the machine tool. It is this expansion of the structural linkages of the machine that leads to inaccuracy in the positioning of the tool. Such errors are called thermal errors and constitute a significant portion of the total error in a machine tool. Thus the overall volumetric error of a machine tool is not only dependent on errors due to the assembly and the specific kinematic structure of the machine but also on the thermal errors. In Part II of this paper, an attempt is made to review the work carried out over the last decade in the estimation and compensation of temperature dependent errors.

Error compensation in machine tools — a review: Part II: thermal errors

In recent years there has been an increasing interest in suitable techniques for evaluating the uncertainties of measurement values yielded by CMMs. Among others, simulation techniques appear to suit the versatility of CMMs and to keep the CMM user involvement to a minimum. The paper outlines the Monte Carlo-based technique under development at the IMGC and illustrates its modular approach which enables a separate treatment of the various uncertainty sources. The importance of measurement correlation is pointed out and a medium-complexity example is given in the case of geometrical errors.

Evaluation of CMM Uncertainty Through Monte Carlo Simulations

A Method for Thermal-Deformation Corrections of CMMs

Dimensional artefacts to achieve metrological traceability in advanced manufacturing

Results of the CIRP-Euromet Intercomparison of Ball Plate-Based Techniques for Determining CMM Parametric Errors

A method of determining geometric errors in a machine tool or measuring machine having a mobile unit for moving a target within a measuring volume, the method including the steps of determining a first direction within the measuring volume; moving the target into a number of points along the direction by means of the mobile unit; measuring, by means of a measuring device, the abscissa of each of the points from an origin located along the first direction; acquiring the coordinates of each of the points by means of the machine; repeating the foregoing steps for a number of directions within the measuring volume; and determining error parameters of the machine on the basis of the abscissas measured by the measuring device, and the coordinates of the points acquired by the machine.

Alessandro Balsamo

Papers

Evaluation of CMM Uncertainty Through Monte Carlo Simulations

A Method for Thermal-Deformation Corrections of CMMs

Dimensional artefacts to achieve metrological traceability in advanced manufacturing

Results of the CIRP-Euromet Intercomparison of Ball Plate-Based Techniques for Determining CMM Parametric Errors

Method of determining geometric errors in a machine tool or measuring machine