Coordinate measuring machine

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Conventional coordinate measuring system in portal design

A coordinate measuring machine based on the principle of the coordinate measuring technology and includes a product suitable for the measurement of spatial coordinates measuring system . It consists of a measuring head system (switching or measuring sensor ), the measuring range of which is extended by a movement or positioning system with incremental displacement or angle sensors. In addition, additional software and hardware components are required for evaluating the recorded coordinate values, for correcting systematic measurement errors mathematically and for controlling the travel axes.

A purely mechanical analog forerunner is the coordinatograph .

Basic principle and areas of application

Basic types

A coordinate measuring system has a CNC -controlled positioning system or a hand-operated movement system with which the measuring head system (sensor) and the measuring object are moved in their spatial position relative to one another in order to record the respective measuring points. Each travel axis of the positioning system is assigned at least one length measuring system that measures the respective position with fine resolution. Due to the known positions of the positioning unit, individual sensor measuring points can thus be transformed into a common coordinate system and linked to one another.

Usually, incremental length measuring systems with electronic data acquisition and measuring standards on a material (e.g. glass scale) or optical (e.g. laser interferometer) basis serve as length measuring systems for determining the relative position of the axes .

The measuring range and the device coordinate system are determined by the traversing axes and their guides, drives and incremental measuring systems. Coordinate measuring systems of conventional design have a Cartesian device coordinate system . Coordinate measuring systems, the guides of which span a cylinder or spherical coordinate system, are also widespread and work with a combination of incremental displacement and angle sensors.

Conventional construction - Cartesian device coordinate system

The most commonly used “classic” devices are Cartesian right-angled coordinate measuring systems. The orthogonal guides span a Cartesian coordinate system. The main structural and functional groups of a Cartesian coordinate measuring machine are:

Open storage of a coordinate measuring system. a) Incremental scale, b) air bearings, c) granite guideway
  • Measuring table: mostly hard rock
  • Material measures for the individual axes: z. B. Photoelectric incremental length measuring system with Zerodur scales (low thermal expansion coefficient ).
  • Storage of the individual axes: z. B. aerostatic bearings (air bearings) to achieve low friction between the individual moving components. Guideways made of hard stone (granite).
  • Drive: z. For example, with CNC-controlled CMMs, the movement of the axes is implemented by electric drives (including gearboxes and vibration-damping elements) in a closed control loop. The task of the drive system is only to move the axes, not to provide information about the position of the axes. This task is taken over by the length measuring system, which transmits the current position to the control (for positioning) and evaluation computer (for calculating the scanned coordinate values).
  • Measuring and probe systems: see section Sensors
  • Control and evaluation computer: To control the measuring process and the traversing movements, to regulate the position or trajectory (e.g. variation of the traversing speed), to manipulate the measured values ​​with regard to a computational correction of systematic measurement deviations (with the help of previously determined calibration values) and with regard to the Transformation of the coordinate values ​​and the evaluation of the measuring points according to the assigned geometry element.
Basic structure of a conventional Cartesian portal coordinate measuring device: 1 - drive for X axis; 2 - reading system for the X axis; 3 - Measuring standard for the X axis; 4 - push button; 5 - 3D probe head; 6 - bearing for Y-axis; 7 - display; 8 - control and adjustment electronics; 9 - control panel; 10 - workpiece holder; 11 - device base

According to DIN EN ISO 10360-1: 2003, a distinction is made between the following basic designs for the implementation of three guides that can move at right angles to each other:

  • Cantilever design: A cantilever arm to which the measuring head system is attached can be moved in the vertical direction. Two further axes can each be moved perpendicular to one another in the horizontal direction. The horizontal movement can be implemented either by a movable table or, in the case of a stationary table, by movable structural elements of the boom. This design is mostly used for measuring devices with a small measuring range but very good measuring accuracy.
  • Bridge construction: The movable axes and the clamping area are separated from each other. The bridge, which can be moved in the horizontal direction, carries the quill with the measuring head system, which can be moved in the horizontal direction along the bridge and in the vertical direction. Coordinate measuring machines in bridge construction allow a large measuring range and thus the acquisition of very large workpieces up to entire vehicles or components from aircraft construction.
  • Portal design: The quill carrying the measuring head system (vertical movement) is arranged on the portal crossbeam, which is movable in the horizontal direction along the portal crossbeam. The portal is mounted with two feet on the edges of the device table and can be moved in the horizontal direction along the device table. Construction methods with a fixed portal and movable equipment table are also widespread. Coordinate measuring systems in portal design offer low measurement deviations with good accessibility and a sufficiently large measuring range. They are therefore the most common type of construction. A measuring range of around 1 m³ is common.
  • Stand construction: With a coordinate measuring system in stand construction with horizontal arm, the quill with the measuring head system can be moved in the horizontal direction, which can be moved along a stand (also called a column) in the vertical direction. The second horizontal movement can be realized by moving the stand along the measuring table or by a movable table. This type of construction is often used to measure car bodies and large sheet metal components, as three sides of the measuring area are freely accessible.
  • Basic types of coordinate measuring systems according to DIN EN ISO 10360-1: 2003

  • Cantilever design

  • Bridge construction

  • Portal construction

  • Stand construction

Unconventional design - cylindrical or spherical coordinate system

Coordinate measuring systems of unconventional design measure in cylindrical or spherical coordinates. These include laser trackers , articulated arm measuring devices and X-ray computed tomography .

Unconventional design - micro and nano coordinate measuring systems

To reduce the measurement deviations - caused by random and systematic rotational guidance deviations - unconventional arrangements of the length measurement and drive systems are used in micro and nano coordinate measuring devices. By implementing the abbe comparator principle in several measuring axes, the use of laser interferometric length measuring systems and a parallel metrology, which measures all position values ​​directly on the sensor that is movable in all three axes or the platform with the measuring object that is movable in all three axes, the measurement deviations and measurement uncertainties can be significant to reduce.

Extensions

By using an additional turntable or a turn-swivel device, measuring elements that are not ideally located can also be touched. With such extensions, the workpiece can be rotated in one or more axes. The changed position of the workpiece is taken into account when calculating and transforming the measured coordinate values into the workpiece coordinate system . Alternatively or in addition, rotary-swivel devices are also used for the sensors.

Sensors

Sensors for coordinate measuring machines - broken down according to the mode of operation (for reasons of clarity, the contrast methods that are basically assigned to the triangulation methods are listed separately; there are no electrically probing sensors).

Coordinate measuring systems can be equipped with switching and measuring sensors. Switching sensors only supply a trigger signal when a measuring point is recorded , which initiates the reading out of the length measuring systems. Measuring sensors, on the other hand, have their own internal measuring range of a few millimeters. The internally measured sensor value is superimposed with the position of the sensor determined by the length measuring systems.

Sensors for coordinate measuring systems can also be subdivided according to their physical principle. Until the 1990s, tactile sensors were the most commonly used touch sensors in coordinate measuring machines. With improved sensor technology, more powerful computing technology and increased requirements, optical, opto-tactile and X-ray sensors are increasingly being used today. An overview of sensors in coordinate measuring systems is also given in.

In order to increase the universality of coordinate measuring systems, several different sensor principles can also be combined in one coordinate measuring system. These coordinate measuring systems are called multi-sensor coordinate measuring systems.

Since it is not possible to solve all measuring tasks with a single sensor or button, it is possible to exchange them with most coordinate measuring systems. The change can be integrated into the automatic measuring process with probe change devices.

Mechanical (tactile) probing

Measuring probe with ruby ball as measuring tip

Measuring head systems with tactile sensors are divided into switching systems (e.g. based on the electro-mechanical principle) and measuring systems (e.g. with inductive or capacitive measuring sensors).

The probing on the workpiece surface is carried out by measuring probes. Depending on the measuring task, different geometric shapes of the probe element (mostly spheres) and materials (often industrial ruby, hard metal, silicon nitride ) can be used.

Since a measuring force in the order of magnitude of 0.01 N to 0.2 N acts when probing, the stylus bends, which must be taken into account when measuring. The curvature of the stylus is taken into account when measuring the stylus (stylus calibration, stylus qualification) and automatically corrected for the following measurements. In addition, the diameter is determined when the probe is calibrated and, in the case of several probe elements, the relationship to one another is established (e.g. the distances between the center points of the probe balls for star probes). The probe is calibrated on a very precise spherical standard (shape deviation <0.2 µm), which is probed with each probe used at at least five or more points in accordance with a calibration strategy defined by the device manufacturer.

The point-by-point recording of the workpiece surface is essentially comparable to drawing a sample from the infinitely large total of all surface points. The areas between the recorded measuring points are not recorded and consequently are not taken into account in the evaluation. The more measuring points are recorded, the more information about the surface of the workpiece is recorded and included in the evaluation (the scope of the sample becomes larger). If there are large numbers of measuring points, probing individual points requires considerable, mostly unacceptable measuring times.

When scanning, the probe ball is moved along the surface of the workpiece with the help of special control functions. Measured values ​​are continuously adopted during the movement. Newer devices allow high scanning speeds with which, as with form metrology, very large numbers of measuring points can be achieved in a short measuring time. This can lead to increased reliability of the statement, although the single point uncertainty is significantly greater when scanning than when probing individual points. Scanning is therefore becoming more and more important compared to single point operation.

Standards and guidelines that deal directly with tactile probing during coordinate measurements are DIN EN ISO 10360-4: 2002, DIN EN ISO 10360-5: 2010 and VDI / VDE 2617 sheet 12.1.

Contactless probing

Optical, electrical and X-ray tomographic sensors can be used for contactless probing. In principle, any electrical or optical sensor can be used in coordinate measuring systems in order to expand its measuring range with the aid of the positioning system.

Optical distance sensors

Electric distance sensors

X-ray tomographic sensors

Standards and guidelines that deal with non-contact probing for coordinate measurements are DIN EN ISO 10360-7: 2011, DIN EN ISO 10360-8: 2012, VDI / VDE 2617 sheet 6.1 and VDI / VDE 2617 sheet 6.2.

Advanced device technology

Multi-sensor coordinate measuring devices - measuring with several sensors

Multi-sensor coordinate measuring device with a) image processing sensor, b) tactile-optical button and c) tactile button

A particularly high universality is achieved by combining several different sensors in one coordinate measuring machine. The optimal sensor can be selected for each feature to be measured. The measurement results of the different sensors are available in a common coordinate system. For this purpose, the position of the sensors is measured in relation to one another in advance. This makes it possible to combine the results of different sensors in order to measure features that cannot or only poorly be measured with one sensor alone.

The various sensors are either attached to a change interface on the quill of the coordinate measuring machine and automatically exchanged one after the other during the measuring process (sensor changer), or are permanently arranged next to one another on the vertically positionable quill. Devices with several quills, which allow separate vertical positioning of the individual sensors, reduce the risk of collision. Likewise, sensors are also attached to the quill by means of retraction axes and only extended when necessary, which prevents collisions.

Standards and guidelines with direct reference to coordinate measuring systems with multi-sensors are DIN EN ISO 10360-9: 2011 and VDI / VDE 2617 sheet 6.3.

Portable coordinate measuring machines

While conventional coordinate measuring machines (CMMs) use a probe that moves on three Cartesian axes to measure physical properties of an object, portable CMMs use either articulated arms or, in the case of optical coordinate measuring machines, arm-free scanning systems that use optical triangulation methods and have unrestricted freedom of movement allow around the object. Portable CMMs with articulated arms have six or seven axes that are equipped with rotary encoders instead of linear axes. Portable measuring arms are lightweight (typically less than 20 pounds) and can be carried and used almost anywhere. However, optical coordinate measuring machines are increasingly being used in industry. They are equipped with compact linear or matrix array cameras (like the Microsoft Kinect) and are smaller than portable CMMs with arms. They work wirelessly and allow users to quickly and easily take 3D measurements of all types of objects practically anywhere. Portable CMMs are particularly suitable for certain, non-repetitive applications in reverse engineering, rapid prototyping and for the inspection of large components. The advantages of portable CMMs are many. Users can measure any type of part in 3D even in the most remote and difficult environments. The optical measurement systems are easy to use and do not require a controlled environment for accurate measurements. In addition, portable coordinate measuring machines cost less than conventional CMMs.

Compromises have to be made with portable CMMs: a user is required for manual handling. In addition, the overall accuracy can be somewhat less precise than with a permanently installed portal measuring machine. In addition, the portable CMM is less suitable for some applications.  

X-ray computed tomography

In addition to tactile and optical sensors, which, apart from the layer thickness measurement, always record the external geometry, the X-ray computer tomography method can be used to measure the internal geometry of a workpiece in addition to the external geometry. When measuring with these sensors, numerous influences (ring artifacts, wobble artifacts, cone beam / Feldkamp artifacts, beam hardening, partial or partial volume artifacts) affect the accuracy of the measurement result. By using additional tactile sensors, systematic measurement deviations of the tomography can be partially corrected. Since a component always has to be completely irradiated during tomography, its use for solid components or for components with very different absorption coefficients (due to areas that are not irradiated and overexposed) is limited.

VDI / VDE 2617 sheet 13 and VDI / VDE 2630 sheet 1.1, 1.2, 1.4 and 2.1 are guidelines with direct reference to X-ray computed tomography for coordinate measurements.

While coordinate measuring systems based on X-ray computed tomography are commercially available for industrial use, industrial coordinate measuring systems based on ultrasonic computed tomography (USCT) and neutron computed tomography (NCT) are still in the research stage.

Laser tracker

See tracking interferometer . Standards and guidelines with a direct reference to laser trackers for coordinate measurements are DIN EN ISO 10360-10: 2012, VDI / VDE 2617 sheet 10 and VDI / VDE 2617 sheet 10.1.

Machine-integrated measurement technology

Tool gauges are specialized solutions for the testing, adjustment, alignment and adjustment of cutting tools. There are different variants, the design of which corresponds to the requirements of the specialization.

For the milling manufacturing process, i.e. for rotating tools such as twist drills or cutter heads , only two longitudinal axes (tool height and width) and one axis of rotation are required to check the tool length, tool diameter and runout .
Instead of a measuring sensor for contact measurement on a surface, tool measuring devices usually have an overhead projector that can be moved in two axes and that shows the shadow or the profile of the tool on a large projection screen with crosshairs . During the measurement, the projection unit is moved so that the edge or a corner of the tool lies in the crosshairs . The tool length or diameter results from the travel path. By aligning it with the crosshair and then rotating it, the runout can be checked and corrected until the rotation shows no deviation from the shadow edge on the crosshair.

Tool measuring devices for cutting tools for the turning manufacturing process formally manage with two axes, but usually have three in order to also be able to check the height of the tool cutting edge (for so-called "turning above or below center") in relation to the tool holder plane to the axis of rotation on the lathe .

Causes and measures to reduce measurement errors

With every measurement there are deviations between the measured value displayed by the measuring device and the actual value of the geometric variable (reference value). These measurement errors can be divided into random and systematic measurement errors. In the case of coordinate measuring systems, many constructive and computational measures are used to keep measurement deviations to a minimum. While systematic measurement errors can be corrected mathematically, random measurement errors make the measurement result uncertain . Standardized procedures for determining the measurement and test uncertainty of coordinate measuring systems are presented in DIN EN ISO 15530-3: 2011, VDI / VDE 2617 sheet 7, VDI / VDE 2617 sheet 11 and in DIN ISO / TS 23165: 2008.

Influences that can lead to measurement deviations in coordinate measurements (numbers = weighting of the influences)

Important causes of measurement errors in coordinate measuring machines are:

  • Ambient conditions: temperature (temperature fluctuations, gradients, radiation), vibrations, humidity, dirt
  • Workpiece, measurement object: form deviations, micro-shape (roughness), material (modulus of elasticity with tactile probing), degree of reflection (with optical probing), dimensions / weight, temperature, flexibility (e.g. filigree structures), cleanliness
  • Measuring device: structural design, guide deviations, probe system, probing force and direction, measuring and evaluation software
  • Measurement strategy: probing mode, number and distribution of measurement points, measurement process, evaluation criteria, filters
  • Operator: care, clamping, probe configuration, probe calibration, monitoring of the CMM

Constructive measures against temperature-related measurement deviations

  • Precisely manufactured guide bodies with good thermal properties.
  • The quill and traverse of the portal made of materials with high thermal conductivity (e.g. aluminum). The high thermal conductivity shortens the adjustment time to restore accuracy after temperature fluctuations.
  • Compliance with the internationally agreed reference temperature of 20 ° C through an air-conditioned measuring room, temperature control of the measuring objects and avoidance of a temperature change on the measuring device (thermal insulation of the device structure; avoidance of direct hand warmth through thermal gloves, avoidance of radiation from lighting and sun, etc.)
  • Rulers made of materials with a minimal thermal expansion coefficient
  • Temperature monitoring of the measuring room, the measuring range, the measuring object and measuring system elements

Constructive measures against vibrations

  • In order to reduce the vibrations from the environment on the measuring equipment, a solid concrete slab can serve as a foundation on which all the equipment relevant to the measurement stand, which in turn is separated from the ground by a gravel bed and an insulating damping layer (special polymer). A circumferential separating joint decouples the floor slab from the rest of the building. With these measures, the maximum permissible vibration amplitudes according to VDI / VDE 2627 can be maintained.
  • A system for passive (or active) pneumatic vibration damping that is integrated in the coordinate measuring system minimizes the transfer of floor vibrations and levels the device table in the event of an asymmetrical load from the workpiece weight.

Mathematical measures

  • Mathematical correction of static and dynamic influences of all 21 control deviations (regular monitoring and, if necessary, recalibration to avoid drift)
  • Existing plate deformations on the measuring table - caused by temperature gradients - are compensated for by measuring the temperature difference between the top and bottom of the plate.
  • Computational correction of the probe deflection caused by contact forces (with tactile sensors)
  • Computational correction of temperature deviations of the workpiece and individual components (e.g. the scales) of the coordinate measuring system

Acceptance and confirmation tests

To confirm the performance of a measuring system as determined by the manufacturer, acceptance tests are carried out and confirmation tests are carried out at regular intervals. With the help of calibrated test specimens (step gauge, ball plate, perforated plate, etc.), length measurement deviations according to DIN EN ISO 10360-2: 2010 and VDI / VDE 2617 sheet 2.1 and probing deviations according to DIN EN ISO 10360-5: 2010 can be checked. VDI / VDE 2617 Part 5 and Part 5.1 specifically deal with individual test specimens.

Terminology

The term "measuring machine" (or "coordinate measuring machine") should always be avoided. The designation “measuring device” (or “coordinate measuring machine ”) is correct, since in technology a “ device ” is defined as a signal-converting or information processing system to increase the sensory or mental performance of a person, while a “machine” is an energy- or a metabolic system for increasing the physical performance of a person.

Since devices for coordinate measurements are now complex systems, i. H. represent a network of several devices, an international agreement was reached in 2013 within the framework of ISO / TC 213 WG10 that in future only the term “coordinate measuring system” will be used in standards.

Standards and guidelines

  • DIN EN ISO 10360 series: Geometrical Product Specifications (GPS) - Acceptance and confirmation tests for coordinate measuring machines (CMM). An overview is given on the homepage of ISO / TC 213.
  • VDI / VDE 2617 series: Accuracy of coordinate measuring machines - parameters and their testing. An overview is given on the GMA FA homepage “3.31 Coordinate Measuring Machines”.

literature

  • Albert Weckenmann (Ed.): Coordinate measuring technology: Flexible strategies for functional and production-oriented testing. 2nd Edition. Hanser, 2012.
  • Robert J. Hocken, Paulo H. Pereira (Eds.): Coordinate Measuring Machines and Systems (Manufacturing, Engineering and Materials Processing) . CRC Press, 2011.
  • Wolfgang Dutschke, Claus P. Keferstein: Production metrology: Practice-oriented principles, modern measuring methods. 5th edition. Vieweg + Teubner, 2005.
  • Ralf Christoph, Hans J. Neumann: Multi-sensor coordinate measuring technology - production-related, optical-tactile measurement, shape and position determination . (= The Library of Technology. Volume 248). Verlag Moderne Industrie, 2006.

Web links

Individual evidence

  1. ↑ a b DIN EN ISO 10360-1: 2003: Geometrical product specifications (GPS) - Acceptance test and confirmation test for coordinate measuring machines (CMM) - Part 1: Terms
  2. ↑ VDI / VDE 2617 sheet 9: Accuracy of coordinate measuring machines - parameters and their testing - acceptance and confirmation testing of articulated arm coordinate measuring machines, 2009.
  3. ↑ a b coordinatenmesstechnik.de
  4. ↑ Sensors - button changing device. ( Memento from November 12, 2013 in the Internet Archive ) aukom-ev.de
  5. ^ A b Albert Weckenmann (ed.): Coordinate measuring technology: Flexible strategies for functional and production-oriented testing. 2nd Edition. Hanser, 2012.
  6. ↑ DIN EN ISO 10360-4: 2002: Geometrical product specification (GPS) - acceptance test and confirmation test for coordinate measuring machines (CMM) - Part 4: CMM in scanning mode
  7. ↑ a b DIN EN ISO 10360-5: 2010: Geometrical product specification (GPS) - acceptance test and confirmation test for coordinate measuring machines (CMM) - verification of the probing deviations of CMMs with contacting measuring head systems
  8. ↑ VDI / VDE 2617 sheet 12.1: Accuracy of coordinate measuring machines - parameters and their testing - acceptance and confirmation tests for coordinate measuring machines for tactile measurement of micro-geometries
  9. ↑ DIN EN ISO 10360-7: 2011: Geometrical product specification (GPS) - acceptance test and confirmation test for coordinate measuring machines (CMM) - CMM with image processing systems
  10. ↑ DIN EN ISO 10360-8: 2012: Geometrical product specification (GPS) - acceptance test and confirmation test for coordinate measuring machines (CMM) - CMM with optical distance sensors
  11. ↑ VDI / VDE 2617 sheet 6.1: Accuracy of coordinate measuring machines - parameters and their testing - guidelines for the application of DIN EN ISO 10360 for coordinate measuring machines with optical sensors for lateral structures, 2007.
  12. ↑ VDI / VDE 2617 sheet 6.2: Accuracy of coordinate measuring machines - parameters and their testing - guidelines for the application of DIN EN ISO 10360 for coordinate measuring machines with optical distance sensors, 2005.
  13. ↑ DIN EN ISO 10360-9: 2011: Geometrical product specification (GPS) - acceptance test and confirmation test for coordinate measuring machines (CMM) - CMM with multi-sensors
  14. ↑ VDI / VDE 2617 sheet 6.3: Accuracy of coordinate measuring machines - parameters and their testing - coordinate measuring machines with multi-sensors, 2008.
  15. ↑ Philipp Krämer: Simulation-based estimation of the accuracy of measurements with X-ray computed tomography . Dissertation Friedrich-Alexander-Universität Erlangen-Nürnberg, Shaker, 2012.
  16. ↑ coordinatenmesstechnik.de
  17. ↑ VDI / VDE 2617 sheet 13: Accuracy of coordinate measuring machines - parameters and their testing - guidelines for the application of DIN EN ISO 10360 for coordinate measuring machines with CT sensors, 2011.
  18. ↑ VDI / VDE 2630 sheet 1.1: Computed tomography in dimensional measurement technology - basics and definitions, 2009.
  19. ↑ VDI / VDE 2630 sheet 1.2: Computed tomography in dimensional measurement technology - influencing variables on the measurement result and recommendations for dimensional computed tomography measurements, 2010.
  20. ↑ VDI / VDE 2630 sheet 1.4: Computed tomography in dimensional measurement technology - comparison of different dimensional measurement methods, 2010.
  21. ↑ VDI / VDE 2630 sheet 2.1: Computed tomography in dimensional metrology - determination of the measurement uncertainty and the test process suitability of coordinate measuring machines with CT sensors, 2013.
  22. ↑ DIN EN ISO 10360-10: 2012: Geometrical product specifications (GPS) - Acceptance test and confirmation test for coordinate measuring machines (CMM) - Part 10: Laser trackers
  23. ↑ VDI / VDE 2617 sheet 10: Accuracy of coordinate measuring machines - parameters and their testing - acceptance and confirmation testing of laser trackers, 2011.
  24. ↑ VDI / VDE 2617 sheet 10.1: Accuracy of coordinate measuring machines - parameters and their testing - laser trackers with multi-sensors, 2012.
  25. ↑ DIN EN ISO 15530-3: 2011: Geometrical product specification and testing (GPS) - Procedure for determining the measurement uncertainty of coordinate measuring machines (CMM) - Part 3: Use of calibrated workpieces or standards
  26. ↑ VDI / VDE 2617 sheet 7: Determination of the uncertainty of measurements on coordinate measuring machines by simulation, 2008.
  27. ↑ VDI / VDE 2617 sheet 11: Determination of the uncertainty of measurements on coordinate measuring machines through measurement uncertainty balances, 2011.
  28. ↑ DIN ISO / TS 23165: 2008: Geometrical Product Specifications (GPS) - Guidelines for determining the test uncertainty of coordinate measuring machines
  29. ↑ DIN EN ISO 10360-2: 2010: Geometrical product specifications (GPS) - Acceptance test and confirmation test for coordinate measuring machines (CMM) - Part 2: CMM used for length measurements
  30. ↑ VDI / VDE 2617 sheet 2.1: Accuracy of coordinate measuring machines - parameters and their testing - guidelines for the application of DIN EN ISO 10360-2 for the measurement of linear dimensions
  31. ↑ VDI / VDE 2617 sheet 5: Accuracy of coordinate measuring machines - parameters and their testing - monitoring by test bodies, 2010.
  32. ↑ VDI / VDE 2617 sheet 5.1: Accuracy of coordinate measuring machines - parameters and their testing - monitoring with spherical plates, 2011.
  33. ↑ iso.org
  34. ↑ vdi.de