Chapter 4 Process Parameter Selection for Clinical Implementation
4.6 Absolute Maximums of Vibration
4.6.1
Heuristic Filtering Results
The heuristic filtering method led to fixing the factors of rotational speed, feed rate, and overlap at levels of 75,000 rpm, 6 mm/s, and 10% which produced absolute maximums of vibration. The remaining factors (tool type, diameter, tilt angle, inclination angle, and depth of cut) were not fixed and comprised of the reduced sample set that was analyzed in the MANOVA. Each of the factors were found to produce statistically significant differences at the multivariate level (p<0.001) (Table 4.4).
4.6.2
Vibration
A cylinder tool decreased the average vibration by 0.59±0.31 g-rms compared to the sphere tool (p<0.001). A +40 degrees inclination decreased the average vibration by 0.95±0.47 g-rms (p<0.001) and 0.34±0.47 g-rms (p=0.247) compared to 0 and -40 degree inclination angles.
4.6.3
Temperature
A sphere tool produced an average of 4.8±0.6 ᴼC less than the cylinder tool (p<0.001). An inclination angle of +40 degrees produced an average temperature of 30.2±0.6 ᴼC whereas a 0 and -40 degree inclination angles produced average temperatures of 37.9±0.6 ᴼC (p<0.001) and 36.4±0.6 ᴼC (p<0.001).
Table 4.4: Summary of statistical analysis for process parameters that resulted in absolute maximums of vibration
Absolute Maximums of Vibration - Factors Fixed (Rotational Speed = 75,000 rpm, Feed Rate = 6 mm/s, Overlap = 10%) Multivariate Analysis - Main Effects
Tool Type Diameter Tilt Angle Inclination Angle Depth of Cut
p<0.001 p<0.001 p<0.001 p<0.001 p<0.001 Univariate Analysis - Main Effects
Temperature (ᴼC) Vibration (g-rms)
Tool Type Diameter Tilt Angle Inclination
Angle Depth of Cut Tool Type Diameter Tilt Angle
Inclination
Angle Depth of Cut
p<0.001 p<0.001 p<0.001 p<0.001 p<0.001 p<0.001 p=0.063 p=0.041 p<0.001 p=0.013
Pairwise Comparison
Level-1 32.4±0.4 33.3±0.4 37.0±0.4 37.9±0.5 33.1±0.4 6.60±0.22 6.15±0.22 6.46±0.22 6.82±0.27 6.10±0.22 Level-2 37.2±0.4 36.3 ±0.4 32.6±0.4 30.2±0.5 36.5±0.4 6.00±0.22 6.45±0.22 6.14±0.22 5.87±0.27 6.50±0.22 Level-3 - - - 36.4±0.5 - - - - 6.21±0.27 -
Table 4.4 outlines the MANOVA results for the reduced sample set that resulted from locking certain factors that led to absolute maximums for
vibration (rotational speed = 75,000 rpm, feed rate = 6 mm/s, overlap = 10%). The multivariate and univariate results are outlined in the above table. Temperature and vibration measurements are outlined (mean ± 95% confidence interval) at each of the levels of the associated process parameter.
Vib ratio n Me asu rem en t (g -r m s) T em p er atu re Me asu rem en t ( ᴼ C) Vib ratio n Me asu rem en t (g -r m s) T em p er atu re Me asu rem en t ( ᴼ C) Burring Trail (#) Temperature Vibration
Figure 4.5: Absolute maximums of temperature and vibration
The outcome measurements (temperature and vibration) of all combinations of process parameters within the reduced sample sets that led to maximums of temperature and vibration is shown above. By choosing an inclination and tilt angle of 0 degrees, coupled with a cylinder tool; an average temperature of 53±6 ᴼC was induced regardless of the selection of other parameters. Likewise, fixing the burring process at a rotational speed of 75,000 rpm, feed rate of 6 mm/s and overlap of 10% resulted in an average vibration 6.3±1.6 g-rms. A full list of the corresponding burring trial numbers can found be in Appendix D.
Absolute Maximums of Temperature
Burring Trail (#)
4.7
Chapter Summary
The experimental matrix which was comprised of each outcome measurement for all combinations of parameters was narrowed down to reduced sample sets. This was done to aid in the selection of process parameters associated with the bone burring process.
Selecting a rotational speed of 15,000 rpm with a 2 mm/s feed rate and 50% overlap was found to provide optimal process parameters that led regions of minimums of temperature (<30 °C) and vibration (<3 g-rms). Selection of a rotational speed of 75,000 rpm, inclination angle of 0°, and an overlap of 10%, resulted in a condition where no combination of the remaining parameters produced low temperature and low vibration. This was also indicated by the larger average magnitudes of the main effects pairwise in comparing the optimal to suboptimal parameter set (Table 4.1 and Table 4.2).
The findings that certain sets of parameters can produce optimal or suboptimal outcome measurements with statistical significance, fully supports the second hypothesis. Additionally, the initial trends of increasing the material removal rate increases the process outcomes mostly agreed as indicated by the pairwise comparison trends in Table 4.1 and Table 4.2. However, the only factor that contradicted this hypothesis, was that although a higher feed rate resulted in higher dynamic effects, it did not necessarily result in higher temperatures as indicated by the results in Table 4.3. This contradiction is believed to be due to the reduced time to allow for heat conduction between the tool- workpiece interface previously established by Shin et al.[40].
Additionally, Chapter 4 investigated certain parameters that should not be jointly constrained, if the objective is to avoid high temperatures or high dynamic effects.
Selection of a cylinder tool with 0 inclination and 0 tilt angle resulted in temperatures of greater than 40 ᴼC regardless of how the remaining process parameters were selected. Selecting a rotational speed of 75,000 rpm, feed rate of 6 mm/s, and overlap of 10% resulted in high vibrations for combinations of remaining parameters (6.3±1.6 g-rms). To allow for the design of the tool path trajectory to have the fewest constraints, these parameters should be avoided, as they do not offer any advantages in the context of avoiding high temperatures and high vibrations.
A sensitivity analysis of the tool's response to changes in angles was also performed. The analysis found that the cylinder produced larger differences in inclination angles and tilt angles. The cylinder tool produced the highest temperatures at a 0 degree inclination angle. Therefore, to use the cylinder tool safely, the tool should enter the burring process with a positive or negative inclination angle; although preference would be given to a positive angle as it produced the lowest temperature and vibration as indicated by Figure 4.3.
By performing the large experimental matrix with 864 unique parameter combinations, a select few have been distinguished to be optimal in providing low temperature generation as well as low dynamic effects. The sawbone analog was useful in this analysis because its uniformity allowed for the identification of process trends, while its availability made the large number of trials possible. While the absolute levels of temperature and vibrations are likely different in real bone, it is reasonable to anticipate that these same trends will be relevant, given that the trends are a function of the process parameters. However, it is valuable to know the absolute levels of temperature and vibration for
burring real bone, and so moving forward, the selection of optimal process parameters should be validated on cancellous bone specimens.