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Geometric Errors of Machines

Error sources and description

Machine tools and measuring machines with 3 to 5 axes can be found in vast numbers and all areas of modern production: from automotive to aerospace, from the production of consumer goods to medical goods. Accurate parts can only be achieved by a controlled and deterministic manufacturing process. While the repeatability of the machine is a necessary requirement for a well-controlled process, the geometric accuracy of the part can be achieved either by a feedback loop through part metrology or by accurately calibrated machine tools. Due to shorter product life cycles and small series production, the absolute accuracy of machine tools is of increasing importance.

Sources of geometry errors

The accuracy of machine tools and CMMs is affected by many error sources. The following reported error sources may affect the accuracy of the machined part:

  1. Kinematic errors: Kinematic errors are errors due to imperfect geometry, alignment and dimensions of machine components. They are stable or changing slowly over time e.g. due to foundation drifts, wear or material aging. But also collisions can change these errors.
  2. Thermo-mechanical errors: Internal and external heat sources in the machine may lead to thermo-mechanical deformation of machine components and therefore change of kinematic errors. The time constant and the amplitude of the geometric changes depends on the time constant of the causes, but also on the thermal mass and the damping of the machine structure.
  3. Loads: In some cases, the weight and position of a workpiece have a significant influence on the machine’s geometry. Reproducible deformations due to workpiece mass may be covered by the kinematic error description of the machine, but sometimes may also need additional modelling and measurement.
  4. Dynamic forces: The trajectory to be realized by a machine is also affected by the dynamic stiffness of the machine’s structural loop. In this case varying forces such as machining forces or forces caused by accelerations or decelerations are causing deformations. However, precision machining or measuring is often carried out at small feed speeds, with small acceleration and decelerations as well as small cutting forces.

Kinematic structures of machines

The kinematic structure is defined by the layout of machine components and their axes. Most machine tools and measuring machines have a serial structure: One axis of motion is building up on another. A notation based on Schwerd can be used to describe the serial kinematic structure from the tool to the workpiece [FIGURE 1].

Description of geometric errors

Relevant errors of a machine tool are relative error motions between the tool and the workpiece. Each movement of a machine axis can be described by six degrees of freedom: three translations and three rotations. The notation of an axis movement is standardized in ISO 841: X, Y, and Z denote the linear movements, A, B, and C the rotations around X, Y, and Z respectively.

For a nominal linear movement, the six component errors are the position error, two straightness error motions, roll error motion and two tilt error motions, which are called pitch and yaw error motion for horizontal axes. Under the assumption of rigid body behaviour, these errors are functions of the nominal movement only and do not depend on the location of the other axes (see animations).

For a nominal rotational movement, the six component errors are two radial error motions, one axial error motion, the angular position error, and two tilt error motions. Figure 6 shows these component errors for a C movement [FIGURE 3].

Etalon offers an effective and accurate way to measure and compensate these errors.


Deviations of the X-Axis

The following animations show the single error components. The error components are listed with the res-pective abbreviations from the standards (VDI 2617/ISO 230-1).

Position deviation in X-direction (XTX, EXX) Straightness deviation in Y-direction (XTY, EYX) Straightness deviation in Z-direction (XTZ, EZX) Roll around X-axis (XRX, EAX) Pitch around Y-axis (XRY, EBX) Yaw around Z-axis (XRZ, ECX)
Deviations of the Y-axis
Position deviation in Y-direction (YTY, EYY) Straightness deviation in X-direction (YTX, EXY) Straightness deviation in Z-direction (YTZ, EZY) Roll around Y-axis (YRY, EBY) Pitch around X-axis (YRX, EAY) Yaw around Z-axis (YRZ, ECY)
Deviations of the Z-axis
Position deviation in Z-direction (ZTZ, EZZ) Straightness deviation in X-direction (ZTX, EXZ) Straightness deviation in Y-direction (ZTY, EYZ) Roll around Z-axis (ZRZ, ECZ) Pitch around X-axis (ZRX, EAZ) Yaw around Y-axis (ZRY, EBZ)
Deviations of a rotary axis
Positionierabweichung / Positioning error Axialbewegung/Hub / axial motion Radialbewegung / radial motion Taumeln / tilt motion
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