**6.3. Conclusion**

88 Performance Evaluation of Bearings





0

25

50

75

100

**Frequency Calculated Experimental Difference**  f1 (Hz) 1 201 940 +27,8 % f2 (Hz) 1 727 1610 +7,3 %

f3 (Hz) 10 605 - -

The results can be considered as correct, in spite of the relatively large difference in values (28 %) in the first frequency. This is as a result of the fact that the dimensions of the additional rotating parts are not included. If these parts were included in the calculation, the

An example of the graphic output of calculated values is shown in Figure 35, [23]. The chart shows the dynamic deflection of the spindle reduced to three masses. The first two resonant

I.nf II.nf I.nf - I.natural (resonant) frequency

**deflections y1, y2, y3 (um)** radial part of cutting force Fr=1000N

DEFLECTIONS UNDER MASSES Y1=f(f), Y2=f(f), Y3=f(f)

0 200 400 600 800 1000 1200 1400 1600 1800 2000

**Figure 35.** Dynamic deflections of the spindle according to research findings [7]

1201 1727

spindle Lee **frequency f(Hz)**

**Table 3.** Experimental and calculated values of frequencies

values of the calculated natural frequencies would be smaller.

frequencies of the optimized spindle are marked on the chart.

II.nf - II.natural (resonant) frequency

deflection y2 deflection y3

deflection y1

One of the main requirements in designing new spindle housing systems is the ability of the design to be quickly applied to real world practice. The methodologies of calculation that were created must be verified, and models must be adapted into a suitable user friendly, computerized format. The models must illustrate the real characteristics of a spindle housing system.

In this design process, only one variable or parameter was changed and the optimal configuration was identified. The results calculated for a static analysis of the SBL Headstock are presented in Table 2 and Figure 33. The dynamic analysis results are presented in Table 3 and Figure 35. The calculated results were verified with experimental measurements. The difference between measured and calculated values is relatively small.

There is no doubt that the re-design has been a success story, and has proven to be highly effective in the identification of optimal SBS design. More detailed information can be read in [22], [23] and its application can be seen in the machine tools made by TRENS Inc., The SBL Lathe was presented in the Mechanical Engineering Exhibition in Nitra in 2010 and in the EMO Exhibition in Düseldorf in 2011.
