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Machine and workpiece coordinates

Coordinate systems build on each other

Different coordinate systems are used in coordinate measuring machines for different tasks, e.g. for machine axes, sensor measuring ranges and datum systems on the workpiece and on the CAD model. These coordinate systems are related to each other due to the functional principle of the machines or are deliberately related by the user to solve certain measuring tasks.

Machine and sensor coordinates

The machine coordinate system is a cartesian coordinate system to which the position of the measurement points is related. The sensor position is also defined in this coordinate system. The positions of all machine axes including the workpiece, rotary and tilt axes as well as corrections for geometry, temperature deviations and other effects are taken into account. In the sensor coordinate system, the position of the measurement points in relation to the sensor reference point is primarily captured for measuring sensors. For switching sensors, this is replaced by recognising the reference point of the sensor (trigger point). The coordinates of the measurement points in the device coordinate system are calculated accordingly by superimposing the sensor position in device coordinates with the measurement points in sensor coordinates.

Measurement "on the image"

For sensors with their own multidimensional measuring range, the measurement of features using different sensor positions is called measurement "on the image" as opposed to measurement "in the image" (Fig. 58).

The calculation of sizes or features from the measurement points determined in this way requires the definition of the associated datum systems. These are often specified in the technical drawing of the workpiece or must be defined by the user. The length of a parallel gage block, for example, can only be measured correctly perpendicular to the gauge block surfaces. This is ensured by setting the zero point, the axis direction and the spatial position of the workpiece coordinate system in relation to previously measured features of the workpiece ("workpiece alignment"). The subsequent measurements are now carried out and displayed in this coordinate system (Fig. 59). Different datum systems are often used for different features or feature groups on the same workpiece. In automatic measuring operation, the workpiece coordinates are automatically transformed into machine and axis coordinates for positioning. In order to be able to measure workpieces in different positions with the same programme, the workpiece coordinate system is roughly measured in advance with a few points or defined by recording it in a fixture.

Measurement "on the image"
<p>Fig. 58: Measurement "in the image" and "on the image": The diameter a and the distance b are measured at a sensor position "in the image". The circle with the diameter c is determined from various sensor positions x, y in the machine coordinate system and thus measured "on the image"; the same applies to the distance d.</p>

Workpiece coordinates

The workpiece coordinate system is then defined more precisely as part of the programme. Clear, reproducible and comparable measurement is only possible according to an exact definition of the workpiece coordinate system.

If the information from a CAD data set is to be used for measurement (taking nominal dimensions, controlling the measurement sequence, performing nominal-actual comparison), the CAD data and the measurement points must be brought into the correct position in relation to each other. This alignment can be carried out in various ways:

Workpiece coordinates
<p>Fig. 59: Machine coordinate system (a) and workpiece coordinate system (b) of a skewed object, defined on a cylinder axis (c) for the spatial alignment of the z-axis and the surface normal of a cuboid side surface (d) for the alignment of the x-axis. The position of the y-axis results from the intersection of the cylinder axis with the upper cuboid surface as the coordinate origin (e).</p>

Overlaying the measurement points with CAD data

  • Determination of coordinate systems from the same datum features on the workpiece and the CAD model and subsequent superimposition (zero point, axes)
  • Optimising the position of the measured points relative to the CAD model so that the deviations are as small as possible (BestFit, see Comparing to CAD data, p. 81 ff.)
  • Optimisation of the position of the measured points relative to the CAD model so that the tolerance zones are used or exceeded as little as possible (ToleranceFit®, see Comparisons with CAD data, p. 81 ff.)
  • Determination of the position of defined measurement points on the measuring object and on the CAD model with subsequent fitting, taking into account defined degrees of freedom for these reference points (multi-point alignment, also RPS alignment)

During alignment, the CAD data set is automatically transformed and displayed in the correct position in relation to the measurement points in machine coordinates. Workpiece coordinate systems can then be set as described above. These then apply to both the measurement points and the CAD model.