This section contains the measured dynamic results for the bearing with and without jacking-oil ports. Dynamic coefficients are presented as frequency-independent stiffness, damping, and virtual-mass coefficients. Dynamic-stiffness measurements will be shown for select test conditions to discuss the validity of the [K][C][M] model. As discussed in the Uncertainty Analysis section, the dynamic-stiffness plots have error bars showing twice the standard deviation, and the dynamic coefficient plots have error bars representing the coefficient uncertainty or goodness of the curve fit.
Dynamic coefficients of a TPJ bearing depend on the bearing clearance. They will be presented as dimensionless quantities (Eqs. (29)-(31)) to allow for a direct comparison between the bearing with and without jacking-oil ports without the effects of the increased clearance. Both dimensional and dimensionless dynamic coefficients are listed in Appendix E.
[K][C][M] Model
Dynamic-stiffness measurements for the bearing with and without jacking-oil ports
are both fit reasonably well by the [K][C][M] model. Figure 25shows the imaginary part
of Hxx and Hxy and the linear curve fit for both bearings. The jacking-oil ports did not
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Figure 25. Im(Hij) with and without ports at 6,800 rpm and 1.452 MPa (210.5 psi)
Figure 26shows the real part of Hxx and Hxy and the respective curve fits with stiffness
and virtual-mass for the bearing with and without jacking-oil ports.
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Adding jacking-oil ports changed the real part of dynamic-stiffness. The direct
dynamic-stiffness terms, Hxx and Hyy, are reduced at high excitation frequencies. This data
can still be modeled well by constant stiffness and virtual-mass term. This is discussed further in the Virtual-Mass Coefficients section.
For certain operating conditions, including the data shown in Figure 26, the direct stiffness data could be accurately modelled with only a constant stiffness value. For consistency, the [K][C][M] model was still used in these cases with a negligible (nearly zero) virtual-mass coefficient.
Baseline Dynamic-Stiffness
Separate baseline tests were conducted for the original and modified bearing to account for any changes in the bearing assembly such as the added shims and jacking-oil hardware. The baseline for each bearing assembly is used to adjust the dynamic-stiffness values for all sixteen operating conditions. All dynamic-stiffness data in the remainder of this thesis have been adjusted with their respective baselines. Figure 27 and Figure 28 show the baseline data for the original bearing recorded by Tschoepe. Figure 29 and Figure
30show the baseline data for the bearing after adding jacking-oil ports. These values and
uncertainties are listed in Appendix F.
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Figure 28. Baseline dynamic-stiffness Re(Hij) for the original bearing
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Figure 30. Baseline dynamic-stiffness Re(Hij) for the modified bearing
Stiffness Coefficients
Dynamic coefficients are plotted versus unit load. Each figure contains four subplots which are labeled with the associated shaft speed. The error bars shown include the uncertainty from both the linear regression and the standard deviation of shaft speed, static load, and bearing clearance. The measured dynamic conditions and uncertainties are
presented inAppendix D. For all measured dynamic results, circular data points connected
by solid lines indicate the original bearing data taken from Tschoepe’s thesis. Square data points connected by dashed lines indicate the modified bearing data.
Figure 31 and Figure 32 show direct stiffness in the y-direction and x-direction
respectively. Figure 33 and Figure 34 show the cross-coupled stiffness, kxy and kyx,
respectively. Stiffness coefficients and their uncertainties can also be found in Appendix E.
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Figure 31. Direct stiffness coefficients kyy (load direction)
Figure 32. Direct stiffness coefficients kxx
Adding jacking-oil ports had no significant effect on the direct stiffness coefficients regardless of shaft speed and unit load. The change in dimensionless stiffness range from
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-9.1% to +0.6% in the y-direction, and from -4.8% to +11.1% in the x-direction. For both bearings, direct stiffness increased with increasing shaft speed and load, and the
coefficients kyy and kxx were similar in magnitude.
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Figure 34. Cross-coupled stiffness ceofficients kyx
The dimensionless cross-coupled stiffness coefficients, kxy and kyx, showed an increase
in magnitude for most operating conditions. However, the large confidence intervals prevent any definite relation between the two bearing tests. These results show that adding jacking-oil ports to a TPJ bearing did not markedly change the magnitude or sign of the
cross-coupled stiffness coefficients. For both bearings, kxy and kyx are both negative,
similar in magnitude, and less than 35% of the magnitude of the direct stiffness kyy and kxx.
Damping Coefficients
Figure 35 and Figure 36 show the direct damping in the y-direction and x-direction
respectively. Figure 37 and Figure 38 show the cross-coupled damping, cxy and cyx. The
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Figure 35. Direct damping coefficients cyy (load direction)
Figure 36. Direct damping coefficients cxx
Direct damping decreased with the addition of jacking-oil ports in both the x-direction and y-direction. The load direction (y-direction) showed a larger decrease than the
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orthogonal (x) direction. The change in the dimensionless direct damping coefficients cyy
ranged from -35% to -16%, with and average decrease of -25.5%. Dimensionless damping
in the x-direction, cxx, changed between +1% and -16%, with an average change of -9.2%.
This decrease depended on unit load, with the largest changes occurring at the highest unit loads and smallest changes occurring at low loads.
Direct damping coefficients showed the same trends for both the original and modified bearing. Damping decreased with increasing shaft speed and load. Direct damping coefficients were very similar in magnitude for the original bearing, while the modified
bearing had an average of 20% less damping in y-direction (cyy) than the x-direction (cxx).
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Figure 38. Cross-coupled damping coefficients cyx
Adding jacking-oil ports caused no significant changes to the cross-coupled damping.
All coefficients cxy and cyx are negative, providing dissipative damping, and small in
magnitude compared to the direct damping. Virtual-Mass Coefficients
Figure 39 and Figure 40 show the direct virtual-mass coefficients, mxx and myy, in the
y-direction and x-direction respectively. Figure 42 and Figure 43 show the cross-coupled
virtual-mass, mxy and myx. These dimensionless coefficients and their uncertainties, as well
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Figure 39. Direct virtual-mass coefficients myy
Figure 40. Direct virtual-Mass coefficients mxx
The original bearing had negative direct virtual-mass coefficients. Adding jacking-oil
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positive). The modified bearing had some positive virtual-mass terms, occurring mostly at high loads.
Recall that the virtual-mass coefficients were used to model the frequency-dependent
dynamic-stiffness, Re(Hij) = Kij - MijΩ2. Positive coefficients describe a “softening” effect
or reduced bearing stiffness at high excitation frequencies. Negative coefficients describe a “stiffening” of the bearing at high excitation frequencies. Figure 41 shows the dynamic-
stiffness Re(Hij) for both bearings at 6,800 rpm and 2.177 MPa (315.8 psi).
Figure 41. Re(Hij) with and without ports at 6,800 rpm and 2.177 MPa (315.8 psi)
The addition of jacking-oil ports has the greatest effect on the bearing dynamic
performance at high excitation frequencies. The dimensionless dynamic-stiffness Re(hxx)
at 244 Hz (14,640rpm) is decreased by 18% by adding jacking-oil ports.
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Figure 42. Cross-coupled virtual-mass coefficients mxy
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For both bearings (original and modified), the cross coupled virtual-mass coefficients
are of equal magnitude and both negative, indicating that mxy and myx are not destabilizing.
The coefficients mxy and myx were largely unaffected by the addition of jacking-oil ports.
Closure
This section compared the measured dynamic results for the bearing with and without jacking-oil ports. The [K][C][M] model was found sufficient to model both bearings. Data
was presented as dimensionless dynamic coefficients (kij, cij, and mij) to account for the
difference in bearing clearance.
The largest effect of adding jacking-oil ports to this TPJ bearing was on the direct damping and direct virtual-mass. Damping in the load direction (y-direction) showed a larger decrease than in the orthogonal (x) direction. Direct damping coefficients were
reduced by an average of -25.5% in the load direction, cyy, and as much an average of -
9.2% in the orthogonal direction cxx. Direct virtual-mass coefficient mxx and myy of the
original bearing were all negative. The bearing with jacking-oil ports showed an increase
in mxx and myy. For many operating conditions, these coefficients were near zero, and some
operating conditions had positive virtual-mass. Accounting for jacking-oil ports is of increased importance at increased excitation frequencies.
One concern that arise when adding large jacking-oil ports is the effects of fluid compressibility. Compressibility has been shown to significantly impact the dynamic coefficients of multi-recess hybrid journal bearings [27]. Ghosh showed that fluid compressibility causes a decrease in the direct damping coefficients for increasing excitation frequency. The test results show that direct damping decreased with the addition of the jacking-oil ports. However, damping does not become frequency dependent within the test range of 10 to 250 Hz. For this TPJ bearing, these frequency dependent fluid compressibility effects were not observed.
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