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Fig. 3. Error motions for the z-axis. Fig. 4. Circle-diamond-—square workpiece dimensions (all values in mm).

Figure 3 Error motions for the z-axis. Fig. 4. Circle-diamond-—square workpiece dimensions (all values in mm).

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Fig. 1. Error motions for the x-axis. Five repetitions were completed; both the forward and reverse directions are shown.
Fig. 1. Error motions for the x-axis. Five repetitions were completed; both the forward and reverse directions are shown.
Axis orthogonality errors Table | nality errors are determined from best-fit lines to the measured tool point coordinates along each axis of actuation. The LBB was not able to measure the entire machine work volume in a single setup due to limitations in its maximum and minimum lengths (the maximum x, y, and z-axes machine travels were {600, 450, and 450} mm, respectively). However, all subsequent thermal, contouring, and cutting force error measurements were carried out within the LBB measurement volume so the indi- vidual effects could be compared. Machining tests were also completed at the same axis locations as the contouring error grid plate measurements.
Axis orthogonality errors Table | nality errors are determined from best-fit lines to the measured tool point coordinates along each axis of actuation. The LBB was not able to measure the entire machine work volume in a single setup due to limitations in its maximum and minimum lengths (the maximum x, y, and z-axes machine travels were {600, 450, and 450} mm, respectively). However, all subsequent thermal, contouring, and cutting force error measurements were carried out within the LBB measurement volume so the indi- vidual effects could be compared. Machining tests were also completed at the same axis locations as the contouring error grid plate measurements.
Fig. 2. Error motions for the y-axis.
Fig. 2. Error motions for the y-axis.
Examples of the T and E matrices for the x-axis are provided in Eq. (2), where xcommand is the nominal motion in the x direction, the € terms are the rotation errors, and the 6 values are the trans- lation errors. The matrices for the y and z-axes were defined in a similar manner. Note that non-orthogonality between the axes were included as linear terms in the appropriate straightness error functions. The measured errors shown in Figs. 1-3 were used in con- junction with the HTM model to predict tool path errors due to machine geometry errors. In order to incorporate the statistical variation in the measurement results, the HTM model was evalu- ated within a Monte Carlo simulation to determine the resulting spread in machine positioning errors at each commanded point along the tool path. At increments of 2-5 mm along the tool path, a value for each of the 18 (six errors for each of the three machine axes) machine geometric error components was selected from a
Examples of the T and E matrices for the x-axis are provided in Eq. (2), where xcommand is the nominal motion in the x direction, the € terms are the rotation errors, and the 6 values are the trans- lation errors. The matrices for the y and z-axes were defined in a similar manner. Note that non-orthogonality between the axes were included as linear terms in the appropriate straightness error functions. The measured errors shown in Figs. 1-3 were used in con- junction with the HTM model to predict tool path errors due to machine geometry errors. In order to incorporate the statistical variation in the measurement results, the HTM model was evalu- ated within a Monte Carlo simulation to determine the resulting spread in machine positioning errors at each commanded point along the tool path. At increments of 2-5 mm along the tool path, a value for each of the 18 (six errors for each of the three machine axes) machine geometric error components was selected from a
Fig. 6. Spindle thermal growth. The left column provides results for 5000 rpm (top panel is translation errors, the bottom panel is rotation errors); the right column shows results for 15,000 rpm. normal distribution with the mean and standard deviation com- puted from the five measurement values shown in Figs. 1-3 (at the appropriate axis location). The normal distance from the resulting tool point location to the nominal path was then com- puted and saved. After many iterations, the spread in error at points along the tool path were computed and the mean value was plotted; see Fig. 5 (a 2000 error magnification has been applied for viewing purposes).
Fig. 6. Spindle thermal growth. The left column provides results for 5000 rpm (top panel is translation errors, the bottom panel is rotation errors); the right column shows results for 15,000 rpm. normal distribution with the mean and standard deviation com- puted from the five measurement values shown in Figs. 1-3 (at the appropriate axis location). The normal distance from the resulting tool point location to the nominal path was then com- puted and saved. After many iterations, the spread in error at points along the tool path were computed and the mean value was plotted; see Fig. 5 (a 2000 error magnification has been applied for viewing purposes).
Fig. 7. Predicted tool path errors including thermal effects (2000 magnifica- tion).
Fig. 7. Predicted tool path errors including thermal effects (2000 magnifica- tion).
Fig. 8. Grid plate encoder for dynamic, two-dimensional tool trajectory mea- surements.
Fig. 8. Grid plate encoder for dynamic, two-dimensional tool trajectory mea- surements.
Fig. 9. Tool path measured by grid plate encoder for two feed rates: (left) 150 mm/min and (right) 8000 mm/min.
Fig. 9. Tool path measured by grid plate encoder for two feed rates: (left) 150 mm/min and (right) 8000 mm/min.
Fig. 10. Undercut surface in down milling due to the cutter vibration state at cu exit. The error is dominated by y direction vibrations.
Fig. 10. Undercut surface in down milling due to the cutter vibration state at cu exit. The error is dominated by y direction vibrations.
Fig. 11. SLE results for circle, diamond, and square. The data are normalized to the top spindle speed of 14,000rpm. For all features the SLE is strongly dependent on spindle speed.
Fig. 11. SLE results for circle, diamond, and square. The data are normalized to the top spindle speed of 14,000rpm. For all features the SLE is strongly dependent on spindle speed.
Fig. 12. Comparison of tool path (grey solid line), nominal path (dashed) and actual part errors for two spindle speeds—11,500 rpm (dotted) and 14,000 rpm (solid). The error magnification is 250x.
Fig. 12. Comparison of tool path (grey solid line), nominal path (dashed) and actual part errors for two spindle speeds—11,500 rpm (dotted) and 14,000 rpm (solid). The error magnification is 250x.
Fig. 13. Percent contribution of error sources to workpiece accuracy.
Fig. 13. Percent contribution of error sources to workpiece accuracy.
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