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Comparison of slot-entry and orifice-compensated gas journal bearings
Wear, 51 (1978) 137 - 145 0 Elsevier Sequoia S.A., Lausanne
137 - Printed
COMPARISON OF SLOT-ENTRY JOURNAL BEARINGS
K. J. STOUT,
in the Netherlands
AND ORIFrCE-COMPENSATED
GAS
E. G. PINK and M. TAWFIK
F~~~~ty of Techno~5gy, Leicester Po~ytec~~ie, Leicester (Gt. Britain) (Received
April 18,1978)
Summary
Controversy concerning the relative merits of gas journal bearings employing slot and orifice restrictors led to an experimental and theoretical study to determine the relative merits of the two types of bearing. This paper is an interim report on the programme and shows that slot-entry bearings yield greater load capacity at high eccentricity ratios, whilst orifice-compensated bearings have greater stiffness up to E = 0.35.
1. Introduction Slot-entry bearings and orifice bearings are shown in Fig. 1. Figure l(a) shows the general arrangement of a double-entry orifice bearing, where the orifices are jewels pressed to an appropriate depth below the bearing bore. Figure l(b) shows the general form of the slot-entry bearing. The entry slots are provided by suitably prepared shims which are located between the concentric cylinders which form the bearing. For most gas bearing applications, the shims employed are typically 0.5 X low3 in thick (0.0125 mm), Manufacturing techniques and areas which could adversely affect the bearing performance for both types of bearings have previously been discussed [ 11.
2. Comparison
of experimental
results
The experimental test rig previously described [ 21 was employed for comparison of the two bearing geometries. The advantage of using this rig was that pressure profiles and clearances could be determined both axially and circumferentially in the bearing. Figure 2 shows the losses due to circumferential flow and dispersion. The diagram indicates that the axial flow model for an orifice-compensated
(a) Fig. 1. Bearing geometries:
(b) (a) orifice compensated;
(b) slot compensated.
Fig. 2. Losses in the load capacity of double-entry orifice-fed and slot-fed bearings: a/L = 0.25; E = 0.5; K = 0.5. *Additional discrepancies include the effects of (a) variation of Cd with P&Pa, (%) en t rance loss effects and (c) pressure recovery in the pocket.
bearing yields a significantly higher load parameter than the corresponding slot-entry bearing. Both types of bearing suffer from a reduction in load parameter due to circumferential flow. These losses are of a similar magnitude. Additional losses are experienced with orifice-compensated journal bearings because of dispersion and entrance loss effects; these losses are the reason why the load parameters of both types of bearing are approximately similar.
139
Fig. 3. The radial load capacity plotted against I&_, for a double-slot-entry L/D = 1: - . -, existing theory for values of PO/P, of 2 and 6. Experiment: and6;X,&=0.25;o,f=:0.5;+,E=0.8.
bearing with PO/P, = 2, 4
Figure 3 is a complete load map for slot-entry bearings showing the radial load capacity plotted against I& (bearing pressure ratio). The theoretical results are presented for values of PO/P, of 2 and 6. The value PO/P, = 2 yields the higher load parameter [ 31. Experimental values are plotted on this figure for values of PO/Pa of 2,4 and 6. The experimental results show good correlation with theory over the full experimental range even at high eccentricity ratios (e = 0.8). Some discrepancy does exist at high I&, values, but some of this may be due to errors in estimating the exact R,, value of the experiment. The methods of adjusting the design K,, value were limited to varying bearing supply pressure, shim thickness, slot length y and radial clearance h,, . A similar diagram for orifice-compensated journal bearings is presented in Fig. 4. The experimental values are compared with theoretical predictions given in ref. 4. These theoretical predictions are only available for eccentricity ratios up to E = 0.5. The results show that correlation between theory and experiment is not as good as for slot-entry bearings. The results of ref. 4 tend to underestimate the load capacity, whilst Fig. 3 shows that the theory for slot-entry bearings tends to overestimate slightly the load capacity. The experimental results obtained at an eccentricity ratio of e = 0.8 have been included on the figure. For this case, a best fit line has been drawn through the experimental results to indicate more clearly the trend of load parameter against K,, . A more specific comparison of double-entry slot and orifice bearings is presented in Fig. 5. The experimental curves show that at low eccentricity
0
G--+--------i-.__.+_----c--_-+-
0
a2
____e
0.4
0.6
Kg,
___--+-_-c_
0.8
Fig. 4. The radial load capacity plotted against R,, for double-orifice bearings with L/l3= 1: - .-, predictions from ref. 4 for values of PO/P, of 2 and 10. Experiment: Pa/Pa = 1.7 7.8;x,~=O.25;0,~=0.5;~,~=0.8.
ratios the load and stiffness of orifice bearings are superior to the slot bearing. As the eccentricity ratio approaches E = 0.5, the load parameter has approximately the same value. It should be remembered that this is the value at which many data are presented and the reader could be misled into thinking that both bearings yield the same characteristics from the concentric position through to e = 0.5. As the eccentricity ratio increases, the slot-entry bearing has maximum load parameter. The experimental results show that slot-entry bearings do not exhibit the static instability known as negative stiffness. The orifice bearing, in contrast, does exhibit negative stiffness and collapse occurs at an eccentricity ratio of E = 0.8. This negative stiffness or lock up occurs because orifices are a discrete inlet source. Since entry slots are a line inlet source slot-entry bearings do not generally suffer from this problem. A further point of note is the hysteresis in the load line for orifice bearings. Figure 6 compares the experimental performance of single-entry bearings. Again, orifice bearings have greater load capacity and stiffness at low eccentricity ratios. Experimental results were obtained for orifice bearings having both eight and sixteen entries. The sixteen-entry bearing has a greater load capacity since it is less susceptible to dispersion losses and approaches a line source bearing. It compares very favourably with the slot-entry bearing up to an eccentricity ratio of E = 0.8. Figure 6 again indicates that orificecompensated bearings suffer from lock up and although this is significantly reduced when the number of entries is increased to sixteen the effect is nevertheless still present.
141
0
0.2
0.4
0.6
E
____ 08
I
Fig. 5. A comparison of slot-fed and orifice-compensated bearings (experimental load us. deflection curves) for double-entry bearings with L/D = 1 and a/L = 0.25: -, optimized orifice bearing ((\,t = 0.45), n = 8, slot bearing (K,, = 0.5), n = 12;- . -, optimized pocketed orifices.
Stiffness parameters are presented in Fig. 7 for both bearing types. As indicated in Fig. 5, orifice bearings have a greater stiffness at the concentric condition and at low eccentricity ratios. As the eccentricity ratios increase above E = 0.35, the stiffness of the slot-entry bearings becomes greater and the difference increases dramatically beyond E = 0.6. At e = 0.8 the stiffness of the orifice bearing becomes negative. Figure 8 shows dimensionless stiffness plotted against dimensionless load parameter and may be useful for the designer in determining the stiffness at any particular load. This chart is difficult to use for design as it does not give the designer any indication of the operating eccentricity ratio. Its advantage is that the stiffness can be obtained from the load which is appliec to the bearing and which is normally known or can be calculated.
3. Discussion
theory
of results
The results presented indicate that there is accurate correlation between and experiment for slot-entry bearings (the maximum divergence is of
142
0
0.2
0.4
0.6
1
Fig. 6. A comparison of slot-fed and orifice-compensated bearings (experimental radial Ioad US. deffection curves] for single-entry bearings with L/D = I : -, optimized slot bearing (K%, = 0.5), R = 12; - * -, optimized arifice bearing {h& = 0.51, n = 8 and n = 16, pocketed orifices.
the order of rt 10%) whilst the orifice-compensated bearings are less well predicted. At the present time there appears to be a lack of information on the characteristics of orifice bearings at high eccentricity ratios, This inaccuracy has fed to the development of new theories for orifice-compensated bearings which will be presented in a further paper. From the results obtained, some general conclusions may be drawn as to the suitability of orifice and slot bearings in service. These conclusions are summarized in Table 1. The experimental programme has for the first time yielded accurate results for both orifice-compensated and slot-entry bearings. These tests have been conducted on the same test rig under rigorously controlled experimental conditions and hence these results can be regarded with a high degree of confidence. Some of the experimental errors may be due to factors such as tilt, ellipticity and slight mismatch in contra1 devices and errors in orifice diameters [I, 53 . These effects have all been computed and the magnitude of the discrepancy in the load and stiffness parameters are within the range which may be associated with Lhe small deviations from the design conditions found experimentally.
143
, c3
0.8 t
I
i/D-l
I
0
0.2
0.6
0.6
I
\ ; \ 0.8 E
+ I
Fig. 7. A comparison of slot-fed and orifice-compensated bearings (experimental radial stiffness against E) for double-entry bearings with L/D = 1 and a/L = 0.25: -, optimized orifice bearing (A,.$ = 0.45), n = 8, slot bearing (K,, = 0.5), n = 12; - . -, optimized pocketed orifices. TABLE
1
Attribute
Slot
Low load capacity
and high stiffness
Ease of manufacture combined moderate load capacity
Shock
at high eccentricity
load protection
Orifice
bearing
J
with
High load capacity High stiffness
bearing
J J
ratio
4 J
Acknowledgments
The authors acknowledge the cooperation they have received from Southampton University, in particular for the loan of the test rig on which the experiments were conducted. The authors acknowledge the financial
0
0.1
0.2
I : 0.3
I 0.6
b
0.5
“=* 0 z Fig. 8. A comparison of slot-fed and orifice-compensated bearings (experimental radial stiffness against load) for double-entry bearings with L/D = 1 and a/L = 0.25: -, optimized slot bearing (K,, = 0.5), n = 12; - . -, optimized orifice bearing (iz,t = 0.45), n = 8, pocketed orifices.
support they have received from the Science enabled this project to be carried out.
Nomenclature distance from control device to edge of bearing slot width orifice diameter do bearing diameter D e displacement from the concentric position concentric clearance ho K g0 (Pd--P,)/(Po -Pa), design pressure ratio bearing length L number of entries per row ambient pressure PO supply pressure W bearing load w dimensionless load parameter
(I
as
1:,
Research
Council which has
145 slot length slot thickness e/ho, eccentricity viscosity
Y
z E 77
67)nd;(R1’)1/2 M
3
4Poho h_R XR
stiffness dimensionless
ratio L feeding
parameter
0’ stiffness
parameter
REFERENCES E. G. Pink and M. Tawfik, The effect of errors in manufacturing on aerostatic bearing performance, Paper F2, 1st Joint Polytechnic Symp. on Manufacturing Engineering, June 1977, Leicester Polytechnic. E. G. Pink, An experimental investigation of externally pressurised gas journal bearings and comparison with design method predictions, Paper G3, Gas Bearing Symp., Cambridge University, BHRA, 1976. W. B. Rowe and K. J. Stout, Design of externally pressurised gas-fed journal bearings employing slot restrictors, Tribology, 6 (1973) 140 - 144. D. F. Wilcock (ed.), Design of Gas Bearings, Mechanical Technology Inc., Latham, N.Y., 1967 E. G. Pink and K. J. Stout, Design procedures for orifice compensated gas journal bearings based on experimental data, Tribol. Int., 11 (1978) 63 - 75.
137 - Printed
COMPARISON OF SLOT-ENTRY JOURNAL BEARINGS
K. J. STOUT,
in the Netherlands
AND ORIFrCE-COMPENSATED
GAS
E. G. PINK and M. TAWFIK
F~~~~ty of Techno~5gy, Leicester Po~ytec~~ie, Leicester (Gt. Britain) (Received
April 18,1978)
Summary
Controversy concerning the relative merits of gas journal bearings employing slot and orifice restrictors led to an experimental and theoretical study to determine the relative merits of the two types of bearing. This paper is an interim report on the programme and shows that slot-entry bearings yield greater load capacity at high eccentricity ratios, whilst orifice-compensated bearings have greater stiffness up to E = 0.35.
1. Introduction Slot-entry bearings and orifice bearings are shown in Fig. 1. Figure l(a) shows the general arrangement of a double-entry orifice bearing, where the orifices are jewels pressed to an appropriate depth below the bearing bore. Figure l(b) shows the general form of the slot-entry bearing. The entry slots are provided by suitably prepared shims which are located between the concentric cylinders which form the bearing. For most gas bearing applications, the shims employed are typically 0.5 X low3 in thick (0.0125 mm), Manufacturing techniques and areas which could adversely affect the bearing performance for both types of bearings have previously been discussed [ 11.
2. Comparison
of experimental
results
The experimental test rig previously described [ 21 was employed for comparison of the two bearing geometries. The advantage of using this rig was that pressure profiles and clearances could be determined both axially and circumferentially in the bearing. Figure 2 shows the losses due to circumferential flow and dispersion. The diagram indicates that the axial flow model for an orifice-compensated
(a) Fig. 1. Bearing geometries:
(b) (a) orifice compensated;
(b) slot compensated.
Fig. 2. Losses in the load capacity of double-entry orifice-fed and slot-fed bearings: a/L = 0.25; E = 0.5; K = 0.5. *Additional discrepancies include the effects of (a) variation of Cd with P&Pa, (%) en t rance loss effects and (c) pressure recovery in the pocket.
bearing yields a significantly higher load parameter than the corresponding slot-entry bearing. Both types of bearing suffer from a reduction in load parameter due to circumferential flow. These losses are of a similar magnitude. Additional losses are experienced with orifice-compensated journal bearings because of dispersion and entrance loss effects; these losses are the reason why the load parameters of both types of bearing are approximately similar.
139
Fig. 3. The radial load capacity plotted against I&_, for a double-slot-entry L/D = 1: - . -, existing theory for values of PO/P, of 2 and 6. Experiment: and6;X,&=0.25;o,f=:0.5;+,E=0.8.
bearing with PO/P, = 2, 4
Figure 3 is a complete load map for slot-entry bearings showing the radial load capacity plotted against I& (bearing pressure ratio). The theoretical results are presented for values of PO/P, of 2 and 6. The value PO/P, = 2 yields the higher load parameter [ 31. Experimental values are plotted on this figure for values of PO/Pa of 2,4 and 6. The experimental results show good correlation with theory over the full experimental range even at high eccentricity ratios (e = 0.8). Some discrepancy does exist at high I&, values, but some of this may be due to errors in estimating the exact R,, value of the experiment. The methods of adjusting the design K,, value were limited to varying bearing supply pressure, shim thickness, slot length y and radial clearance h,, . A similar diagram for orifice-compensated journal bearings is presented in Fig. 4. The experimental values are compared with theoretical predictions given in ref. 4. These theoretical predictions are only available for eccentricity ratios up to E = 0.5. The results show that correlation between theory and experiment is not as good as for slot-entry bearings. The results of ref. 4 tend to underestimate the load capacity, whilst Fig. 3 shows that the theory for slot-entry bearings tends to overestimate slightly the load capacity. The experimental results obtained at an eccentricity ratio of e = 0.8 have been included on the figure. For this case, a best fit line has been drawn through the experimental results to indicate more clearly the trend of load parameter against K,, . A more specific comparison of double-entry slot and orifice bearings is presented in Fig. 5. The experimental curves show that at low eccentricity
0
G--+--------i-.__.+_----c--_-+-
0
a2
____e
0.4
0.6
Kg,
___--+-_-c_
0.8
Fig. 4. The radial load capacity plotted against R,, for double-orifice bearings with L/l3= 1: - .-, predictions from ref. 4 for values of PO/P, of 2 and 10. Experiment: Pa/Pa = 1.7 7.8;x,~=O.25;0,~=0.5;~,~=0.8.
ratios the load and stiffness of orifice bearings are superior to the slot bearing. As the eccentricity ratio approaches E = 0.5, the load parameter has approximately the same value. It should be remembered that this is the value at which many data are presented and the reader could be misled into thinking that both bearings yield the same characteristics from the concentric position through to e = 0.5. As the eccentricity ratio increases, the slot-entry bearing has maximum load parameter. The experimental results show that slot-entry bearings do not exhibit the static instability known as negative stiffness. The orifice bearing, in contrast, does exhibit negative stiffness and collapse occurs at an eccentricity ratio of E = 0.8. This negative stiffness or lock up occurs because orifices are a discrete inlet source. Since entry slots are a line inlet source slot-entry bearings do not generally suffer from this problem. A further point of note is the hysteresis in the load line for orifice bearings. Figure 6 compares the experimental performance of single-entry bearings. Again, orifice bearings have greater load capacity and stiffness at low eccentricity ratios. Experimental results were obtained for orifice bearings having both eight and sixteen entries. The sixteen-entry bearing has a greater load capacity since it is less susceptible to dispersion losses and approaches a line source bearing. It compares very favourably with the slot-entry bearing up to an eccentricity ratio of E = 0.8. Figure 6 again indicates that orificecompensated bearings suffer from lock up and although this is significantly reduced when the number of entries is increased to sixteen the effect is nevertheless still present.
141
0
0.2
0.4
0.6
E
____ 08
I
Fig. 5. A comparison of slot-fed and orifice-compensated bearings (experimental load us. deflection curves) for double-entry bearings with L/D = 1 and a/L = 0.25: -, optimized orifice bearing ((\,t = 0.45), n = 8, slot bearing (K,, = 0.5), n = 12;- . -, optimized pocketed orifices.
Stiffness parameters are presented in Fig. 7 for both bearing types. As indicated in Fig. 5, orifice bearings have a greater stiffness at the concentric condition and at low eccentricity ratios. As the eccentricity ratios increase above E = 0.35, the stiffness of the slot-entry bearings becomes greater and the difference increases dramatically beyond E = 0.6. At e = 0.8 the stiffness of the orifice bearing becomes negative. Figure 8 shows dimensionless stiffness plotted against dimensionless load parameter and may be useful for the designer in determining the stiffness at any particular load. This chart is difficult to use for design as it does not give the designer any indication of the operating eccentricity ratio. Its advantage is that the stiffness can be obtained from the load which is appliec to the bearing and which is normally known or can be calculated.
3. Discussion
theory
of results
The results presented indicate that there is accurate correlation between and experiment for slot-entry bearings (the maximum divergence is of
142
0
0.2
0.4
0.6
1
Fig. 6. A comparison of slot-fed and orifice-compensated bearings (experimental radial Ioad US. deffection curves] for single-entry bearings with L/D = I : -, optimized slot bearing (K%, = 0.5), R = 12; - * -, optimized arifice bearing {h& = 0.51, n = 8 and n = 16, pocketed orifices.
the order of rt 10%) whilst the orifice-compensated bearings are less well predicted. At the present time there appears to be a lack of information on the characteristics of orifice bearings at high eccentricity ratios, This inaccuracy has fed to the development of new theories for orifice-compensated bearings which will be presented in a further paper. From the results obtained, some general conclusions may be drawn as to the suitability of orifice and slot bearings in service. These conclusions are summarized in Table 1. The experimental programme has for the first time yielded accurate results for both orifice-compensated and slot-entry bearings. These tests have been conducted on the same test rig under rigorously controlled experimental conditions and hence these results can be regarded with a high degree of confidence. Some of the experimental errors may be due to factors such as tilt, ellipticity and slight mismatch in contra1 devices and errors in orifice diameters [I, 53 . These effects have all been computed and the magnitude of the discrepancy in the load and stiffness parameters are within the range which may be associated with Lhe small deviations from the design conditions found experimentally.
143
, c3
0.8 t
I
i/D-l
I
0
0.2
0.6
0.6
I
\ ; \ 0.8 E
+ I
Fig. 7. A comparison of slot-fed and orifice-compensated bearings (experimental radial stiffness against E) for double-entry bearings with L/D = 1 and a/L = 0.25: -, optimized orifice bearing (A,.$ = 0.45), n = 8, slot bearing (K,, = 0.5), n = 12; - . -, optimized pocketed orifices. TABLE
1
Attribute
Slot
Low load capacity
and high stiffness
Ease of manufacture combined moderate load capacity
Shock
at high eccentricity
load protection
Orifice
bearing
J
with
High load capacity High stiffness
bearing
J J
ratio
4 J
Acknowledgments
The authors acknowledge the cooperation they have received from Southampton University, in particular for the loan of the test rig on which the experiments were conducted. The authors acknowledge the financial
0
0.1
0.2
I : 0.3
I 0.6
b
0.5
“=* 0 z Fig. 8. A comparison of slot-fed and orifice-compensated bearings (experimental radial stiffness against load) for double-entry bearings with L/D = 1 and a/L = 0.25: -, optimized slot bearing (K,, = 0.5), n = 12; - . -, optimized orifice bearing (iz,t = 0.45), n = 8, pocketed orifices.
support they have received from the Science enabled this project to be carried out.
Nomenclature distance from control device to edge of bearing slot width orifice diameter do bearing diameter D e displacement from the concentric position concentric clearance ho K g0 (Pd--P,)/(Po -Pa), design pressure ratio bearing length L number of entries per row ambient pressure PO supply pressure W bearing load w dimensionless load parameter
(I
as
1:,
Research
Council which has
145 slot length slot thickness e/ho, eccentricity viscosity
Y
z E 77
67)nd;(R1’)1/2 M
3
4Poho h_R XR
stiffness dimensionless
ratio L feeding
parameter
0’ stiffness
parameter
REFERENCES E. G. Pink and M. Tawfik, The effect of errors in manufacturing on aerostatic bearing performance, Paper F2, 1st Joint Polytechnic Symp. on Manufacturing Engineering, June 1977, Leicester Polytechnic. E. G. Pink, An experimental investigation of externally pressurised gas journal bearings and comparison with design method predictions, Paper G3, Gas Bearing Symp., Cambridge University, BHRA, 1976. W. B. Rowe and K. J. Stout, Design of externally pressurised gas-fed journal bearings employing slot restrictors, Tribology, 6 (1973) 140 - 144. D. F. Wilcock (ed.), Design of Gas Bearings, Mechanical Technology Inc., Latham, N.Y., 1967 E. G. Pink and K. J. Stout, Design procedures for orifice compensated gas journal bearings based on experimental data, Tribol. Int., 11 (1978) 63 - 75.