GEOMETRIC ERRORS OF MACHINES

Axes



X, Y, and Z are primary linear motions

A, B and C define rotary axes about linear axes X, Y and Z respectively.

Positive A, B and C are clockwise about the linear axes looking along the linear axes in the positive direction

U, V, and W are secondary linear axes parallel to the X, Y, and Z axes, respectively

P, Q, and R are tertiary linear axes parallel to the X, Y, and Z axes, respectively

Definitions



Axis Average Line - XX

Angular Error Motion of a Linear Axis - rotational motions of the carriage about each linear axis as it traverses along its nominal trajectory

Linear Positioning Error Motion - unwanted linear motion along the direction of nominal motion

Linear Positioning Deviation - actual position minus target position

Straightness Error Motion - unwanted linear motion in one of the two directionis orthogonal to the direction of nominal motion

Straightness Deviation - distance the functional point is from the reference straight line that is fitted to the axis trajectory

Rotary Axis Error Motions



Axis Average Line - XX

Axis Shift - quasi-static change in location and orientation of the axis average line due to a change in conditions

Angular Positioning Error Motion - unwanted motion along the direction of rotation that results in the actual angular position reached by the rotating component differing from the local commanded position

Angular Positioning Deviation - actual angular position reached by the rotating component minus the commanded/target position

Axial Error Motion - error motion coaxial with the axis average line

Radial Error Motion - error motion in a direction perpendicular to the axis average line at a specified axial location

Tilt Error Motions - error motion in an angular direction relative to the axis average line

XXX



Pitch - rotation around an axis in the horizontal plane perpendicular to the direction of travel

Roll - rotation around an axis in the horizontal plane parallel to the direction of travel

Yaw - rotation around an axis in the vertical plane perpendicular to the direction of travel

A-axis Errors

  • EAA - angular positioning error of A
  • EBA - tilt error of A about the Y-axis
  • ECA - tilt error of A about the Z-axis
  • EXA - axial linear error of A n the X-axis direction
  • EYA - radial error motion of A in the Y-axis direction
  • EZA - radial error motion of A in the Z-axis direction

B-axis Errors

  • EAB - tilt error of B about the X-axis
  • EBB - angular positioning error of B
  • ECB - tilt error of B about the Z-axis
  • EXB - radial error motion of B in the X-axis direction
  • EYB - axial linear error of B n the Y-axis direction
  • EZB - radial error motion of B in the Z-axis directio

C-axis Errors

  • EAC - tilt error of C about the X-axis
  • EBC - tilt error of C about the Y-axis
  • ECC - angular positioning error of C
  • EXC - radial error motion of C in the X-axis direction
  • EYC - radial error motion of C in the Y-axis direction
  • EZC - axial linear error motion of C in the Z-axis direction
A picture of two people looking at a cell phone

X-axis Errors

  • EAX - angular error motion of X about the X-axis - roll
  • EBX - angular error motion of X about the Y-axis - pitch
  • ECX - angular error motion of X about the Z-axis - yaw
  • EXX - linear positioning error of X
  • EYX - linear error motion of X in the Y-axis direction
  • EZX - linear error motion of X in the Z-axis direction
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Y-axis Errors

  • EAY - angular error motion of Y about the X-axis - X
  • EBY - angular error motion of Y about the Y-axis - X
  • ECY - angular error motion of Y about the Z-axis - X
  • EXY - linear error motion of Y in the X-axis direction
  • EYY - linear positioning error of Y
  • EZY - linear error motion of Y in the Z-axis direction
A picture of two people looking at a cell phone

Z-axis Errors

  • EAZ - angular error motion of Z about the X-axis - X
  • EBZ - angular error motion of Z about the Y-axis - X
  • ECZ - angular error motion of Z about the Z-axis - X
  • EXZ - linear error motion of Z in the X-axis direction
  • EYZ - linear error motion of Z in the Y-axis direction
  • EZZ - linear positioning error of Z
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Linear Axis Squareness Error Terms

  • EAOY - squareness of Y to Z
  • EAOZ - squareness of Z to Y
  • EBOX - squareness of X to Z
  • EBOZ - squareness of Z to X
  • ECOY - squareness of Y to X
  • ECOX - squareness of X to Y

Rotary Axis Offset Error Terms

  • EXOB - error of the position of B in X-axis direction
  • EXOC - error of the position of C in X-axis direction
  • EYOA - error of the position of A in Y-axis direction
  • EYOC - error of the position of C in Y-axis direction
  • EZOA - error of the position of A in Z-axis direction
  • EZOB - error of the position of B in Z-axis direction

Orientation Error Terms

  • EAOB - error of the orientation of B in the A-axis direction; squareness of B to Y
  • EAOC - error of the orientation of C in the A-axis direction; squareness of C to Y
  • EAO(C) - error of the orientation of the spindle (C) in the A-axis direction; squareness of (C) to Y
  • EBOA - error of the orientation of A in the B-axis direction; squareness of B to Y
  • EBOC - error of the orientation of C in the B-axis direction; squareness of C to X
  • EBO(C) - error of the orientation of the spindle (C) in the B-axis direction; squareness of (C) to X
  • ECOA - error of the orientation of A in the C-axis direction; squareness of A to Y
  • ECOB - error of the orientation of B in the C-axis direction; squareness of B to X

Workpiece Error Terms

  • EAOw - error of the orientation of the workpiece w about the X-axis
  • EBOw - error of the orientation of the workpiece w aboutthe Y-axis
  • ECOw - error of the orientation of the workpiece w about the Z-axis
  • EXOw - error of the position of the workpiece w in X-axis direction
  • EYOw - error of the position of the workpiece w in Y-axis direction
  • EZOw - error of the position of the workpiece w in Z-axis direction

Tool Error Terms

  • EAOt - error of the orientation of the tool t about the X-axis
  • EBOt - error of the orientation of the tool t about the Y-axis
  • ECOt - error of the orientation of the tool t about the Z-axis
  • EXOt - error of the position of the tool t in X-axis direction
  • EYOt - error of the position of the tool t in Y-axis direction
  • EZOt - error of the position of the tool t in Z-axis direction

References

  1. ASME B5.54, 2005, Methods for Performance Evaluation of Computer Numerically Controlled Machining Centers
  2. ISO 230-2:2006(E), Test code for machine tools – Part 2: Determination of accuracy and repeatability of positioning numerically controlled axes
  3. IS0/TR 230-9:2005(E), Test code for machine tools – Part 9: Estimation of measurement uncertainty for machine tool tests according to series ISO 230, basic equations
  4. JCGM 100:2008, Evaluation of measurement data – Guide to the expression of uncertainty in measurement, 2008