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Investigation of recessed hydrostatic and slot-entry journal bearings for hybrid hydrodynamic and hydrostatic operation
55
Wear, 43 (19’77) 55 - 69 Q Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands
INVESTIGATION OF RECESSED HYDROSTATIC AND SLOT-ENTRY JOURNAL BEATINGS FOR HYBRID HYDRODYNAMIC AND HYDROSTATIC OPERATION*
W. B. ROWE and D. KOSHAL Department of Mechanical, Liverpool (Ct. Britain)
Marine and Production
Engineering,
Liverpool
Polytechnic,
K. J. STOUT School of ‘mechanical and Production (Gt. Britain)
Engineering,
Leicester
Potytechnjc,
Leicester
(Received December 3, 1976)
Summary Results of investigations into recessed hydrostatic bearings and slotentry hydrostatic bearings are presented. Initial comparative results show that there are certain conditions under which slot-entry bearings may have marked advantages. Results are given for such parameters as load, torque and flow rate under hydrostatic (i.e. zero speed) conditions and also under hybrid hydrodynamic/hydros~tic operating conditions.
Introduction The development of externally pressurised bearings has progressed over approximately 120 years since Girard [l] first obtained a patent. Since the 1950s externally pressurised journal bearings have increased in use in engineering applications such as machine tools, test equipment, medical equipment, measuring instruments, radio telescopes and in the aerospace industry. Their popularity is attributed to their high load-carrying capacity, zero starting friction and low friction at low speeds, nominally zero wear and hence long life, good rotational accuracy and excellent stiffness and damping. Externally pressurised bearings can be applied to many engineering situations and the detailed design of the bearing depends on the specification of such factors as the type of operation (hybrid, hydrostatic), the choice of bearing geometry (recessed, slot), the type of restrictor (capillary, orifice, slot, diaphragm), the type of loading (static, dynamic), the operating speed, the flow rate and the temperature rise. *Paper presented at the 2nd Israel Tribology Conference, Haifa, October 20 - 22, 1976.
56
(a) Fig. 1. A recessed
(b) bearing.
Typically a hydrostatic journal bearing (Fig. 1) consists of three rings fitted into a sleeve. The middle ring has axial grooves to form recesses separated by axial lands. A ring is fitted on each side of the middle ring to form the two circumferential lands. The lubricant is supplied to each recess through a separate restrictor such as a capillary or an orifice. Recesses which are introduced into the bearing surface of hydrostatic journal bearings are a means of reducing friction and a method of increasing load support. Bearings generally contain four recesses but five, six or even more recesses may be employed, particularly for values of the L/D ratio less than unity. Slot-entry bearings (Fig. 2) used in applications such as machine tool spindles consist of a bearing body which is recessed on either side to accommodate slotted shims. The shims are held in position by retaining rings. The assembly is clamped together with bolts that pass through the body and the retaining rings. The oil enters through holes leading into an annulus and escapes to the bearing clearance through slots which act as laminar restrictors.
(a) Fig. 2. A double
(b) slot-entry
bearing.
The increased land area due to the absence of recesses is an advantage for hydrodynamic and dynamic performance of a bearing [2]. Cowley and Kher [ 31 gave results for one capillary-controlled fourpocket recessed bearing. Hunt and Ahmed [4] investigated the effect of rotation in a six-pocket hydrostatic journal bearing with capillary compensation Ghosh [ 51 extended these results for other bearings and varied design factors at constant speed, Results were presented by Davis et al. [6] for orifice-controlled bearings and included some results for misalignment. The present paper extends the experimental knowledge. It deals with four- and six-pocket bearings with capillary control. Parameters varied include the speed, alignment, pressure ratio and direction of loading. Load power, stiffness and frictional torque have been measured. Some load and friction results are also presented for plain slot-fed journal bearings.
The test rig Two rigs have been used to investigate bearing characteristics. The rig used for early work was based on a shaft of diameter 1 in and the later rig was designed for a shaft nominally 40 mm in diameter. Figure 3 shows the test rig based on a set-up with a shaft of diameter 1 in for loading tests and torque measurement tests respectively. The rig is similar to that described earlier [ 71 with improvements in the loading ~rangement and control of misali~ment. This general purpose hybrid bearing test rig was developed to test hydrostatic journal bearings or hydrodynamic jaumal bearings and was designed to control the load, shaft torque, shaft speed, film thickness, lubricant pressure and lubricant outlet temperature. The test shaft was driven by a variable speed motor up to a speed of 2000 rev min-I. The test shaft contained an inductive transducer and a pressure transducer. The signals from the rotating shaft were brought out to the stationary signal conditioning equipment by slip rings. The shaft could be moved axially through the bearing by a small leadscrew and cradle. The bearing was fed by a gear pump through a 3 pm (absolute) filter at pressures up to 400 lb in2. The load was applied to the bearing in an upward direction. To align the bearing with the axis of the shaft a misalignment jig [8] was employed. The hybrid bearing test rig based on a 40 mm diameter shaft was designed for improved rigidity and instrumentation to test bearings at higher eccentricity ratios and speeds.
Test procedure Figure 3(a) shows the rig set up for a loading test. The bearing was aligned with the axis of the shaft using the misalignment jig. The misalignment
(a)
(b) Fig. 3. The test rig showing ment.
(a) the load test arrangement
and (b) the torque
test arrangc-
was checked by moving the test shaft axially through the bearing from one end to the other and observing the output from the film thickness transducer. The shaft was rotated and a load was applied. As the attitude angle varies with load in the experiment, it is necessary to solve the computer program
59
for several attitude angles in order to obtain theoretical results which correspond to a particular experimental point. Thus it is tedious to obtain correlation between experimental and theoretical results. Figure 3(b) shows the rig set up for torque measurement. Three arms were screwed into the bearing housing. The two horizontal arms on each side of the bearing housing were used to hang pans for weights. At zero speed the position of the vertical arm was noted. The speed was varied from 0 to 2000 rev min- l and at each speed setting the vertical arm was brought back to the null position by adding weights in the appropriate pan. The outlet temperature of the oil was measured as close to the bearing as possible.
Some theoretical bearing designs
results comparing
load/eccentricity
ratios for various
Figure 4 compares the theoretical performance characteristics of three types of bearings. A four-pocket recessed bearing is compared with a slot-fed bearing and also with the common axial groove hydrodynamic bearing. The basis of comparison is the Sommerfeld number. As expected, the axial groove hydrodynamic bearing gives lower load support than the four-pocket recessed bearing at low eccentricity ratio but gives better performance at higher eccentricity ratio. The slot-fed bearing gives improved performance over both bearings through the operating range from zero eccentricity up to e = 0.8.
-
SLOT atLzO.1
14. ----AXIAL
HYBRID
LID=l.O
Kz1.0
bO.5
GROOVE HYDRODYNAMIC
12----RECESS
L/D=l.O
BEARING L/D=%0
O/L.O.25
IOW -?fLDN
C& z 0 D 6.
0.2
0.3
0x3
c
0.5
0.6
0.7
04
Fig. 4. A comparison of the theoretical results for a slot-entry bearing with those for recessed and axial groove bearings.
60
Experimental
results
Load characteristics for recessed bearings Figure 5 shows the direction of loading and the attitude angle convention for the recessed bearings used. Figure 6(a) shows the load support obtained for varying eccentricity ratio when the load is applied towards the midrecess position, i.e. $’ = 0”. At a speed corresponding to the optimum for minimum power dissipation (i.e. K = 1 and SH = 0.053) there is an improvement in load support compared with the zero speed case (i.e. K = 0) due to the hydrodynamic effects, particularly at high eccentricity ratios. Figure 6(b) shows the corresponding cases for loading towards the mid-land position, i.e. @’= 45”. The load support is inferior at zero speed but there is a larger improvement at X: = 1 in the direction of loading. Figure 6(c) compares some results for a four-pocket recessed bearing with those for a six-pocket recessed bearing and shows the advantage of the increased number of recesses. Whereas all the previous results have been for a pressure ratio p close to the recommended value of 0.5, Fig. 6(d) shows some results for differing values of p. These values show how the hydrostatic load support is seriously reduced as p is increased above 0.5. A more comprehensive picture of the pressure ratio effect is shown in Fig. 8. Figure 6(e) shows the effect of misalignment on bearing performance. The degree of misalignment is characterised by the percentage tilt. This parameter combines the effect of the angle of tilt with the effect of clearance. Thus a 10% tilt corresponds to a condition where the eccentricity at one end of the bearing deviates from the eccentricity at the middle of the bearing by 10% of the concentric clearance. These results show that the effect on load is most serious owing to the geometrical change of eccentricity since the film thickness is correspondingly reduced. However the load support for a given value of eccentricity ratio at the mid-plane of the bearing is little affected. This can be verified by noting that the slopes of the three lines are
Fig. 5. The direction af loading and the attitude angle convention.
61
w p,LD 02
0 0
0.2
0.L
E
0.6
0.8
1.0
(bf
(a)
0.3 w pS LD
0.2
w pSLD 0.2
Of
01
0
02
0
0.4
E
06
08
0
10
0
0.2
OL
0
0.2
0.4
E
0.6
0.8
2.0
0.6
0.8
1.0
(d)
(cl 05
4 4.0
EXPERIMENTAL
x
0.L fd =0505 ” :I W p,LD
0.3
0.2
0.1
0 Cl
0.2
0.6
0.6 E max.
0.8
E
(f)
(e)
Fig. 6. Experimental
f.D
results showing
the variation
of the load with the eccentricity
ratio.
62
0.5
0.4
0.4
03
0.3 ic
3 0.2
0.2
0.1
0.1
0 0
0 0.2
0.1
E
0.6
0.8
1.0
0
Fig. 7. The variation of the stiffness with the eccentricity bearings: L/D = 1.0; a/L = 0.25; S, = 0.0; n = 4; Q,= 0.0.
0.2
0.1
0.6
0.8
10
P
ratio for recessed
Fig. 8. The variation of the load parameter with the pressure bearings: L/D= 1.0; a/L = 0.25; SH = 0.0; n = 4.
journal
ratio for recessed
journal
substantially the same, whereas there is a significant change in the intercept with the horizontal axis corresponding to the change of eccentricity ratio (E max.) at one end of the bearing. Figure 6(f) shows the effect on load support of the number of recesses at a value of the speed parameter which is above the optimum and corresponds to a power ratio (K) value of 3.28. At a value of the eccentricity ratio exceeding 0.5 the six-recess bearing shows advantage over the four-pocket recessed bearing. Figure 7 shows the variation of stiffness with eccentricity ratio. Stiffness reduces with increasing eccentricity at zero speed for p = 0.5. The results also show that the stiffness decreases when the pressure ratio 13is increased above 0.5. Figure 8 shows that the optimum value of the pressure ratio 0 is near 0.5 and that a permissible range of p between 0.4 and 0.7 leads to high load capacity and high stiffness. Load characteristics for slot-en try bearings Experimental work into slot-entry bearings is continuing. However, initial results (Fig. 9) indicate that load support from a slot-entry bearing is in line with theoretical predictions. This suggests that slot-entry bearings have better performance characteristics at zero speed than recessed bearings and this may be explained by the greater number of pressure sources. Figure 10 shows theoretical results for load against a/L when the bearing operates at a speed co~esponding to K = 3. Load increases rapidly as a/L
06 5,zoo 2.0
0.5 w %LD
W
0.L
1.5
0.3
1.0
0.i
0.5
P, E =0.25
0.1 o
~
0
,
0.2
,
OL
0.6
,
,
08
10
E
' 0'
01
0.126
0.2
;
0,089
0.3
04
O-5
0.073
0.063
0.059
5,
Fig. 9. The variation of the load with the eccentricity: -+slot-entry bearing, L/D = 0.525, a/L = 0.25, fl= 0.34; -*recessed bearing, L/D = 1, a/L = 0.25, fi = 0.5; -Aslot-entry bearing, L/D = 1, a/L = 0.25, p = 0.86. Fig. 10. The variation of the load parameter bearing with LID = 1.0, fi = 0.5, K = 3.
with a/L and S, for a double
entry journal
diminishes to 0.1. This is where performance differs markedly from the experience with recessed journal bearings. The difference is due to the significant advantage to be obtained from hydrodynamic effects at higher eccentricities. Variation of load support with the pressure ratio p for slot-entry bearings is shown in Fig. 11. These characteristics differ from those of the recessed bearing shown in Fig. 8.
Friction
and torque
As rotating machines become larger and operate at high speeds friction losses become important in bearing performance. An increase in friction losses results in undesired increased power losses. Some of the major bearing friction effects [9] that need to be taken into account when designing bearings operating in the laminar regime may be summarised as follows.
64
L/D ~1.0 I 2.5 I
W p,LD
Fig. 11. The variation journal bearing with
of the load parameter
with the pressure
ratio for a double
entry
L/D = 1.0,a/L = 0.1,K = 1.
Petroff friction torque The viscous friction torque in a non-recessed ing concentrically with laminar flow is given by
cylindrical
bearing operat-
QAUD Tp = ~ CD Friction torque due to eccentricity (laminar flow) With increasing eccentricity it is necessary to take into account the varying clearance and also the effect of pressure-induced flow on the friction torque. For non-recessed bearings with non-cavitating conditions it is possible to write a reasonable approximation for friction ignoring pressure-induced flow:
CDTE _= vAUD
1 (1 - e2)1’2
For strongly cavitating bearings at values of eccentricity less than 0.6, the Petroff formula for friction torque may be a better approximation. Friction torque due to recirculation in the recesses Where the bearing has recesses it is necessary to take into account recirculation effects on recess friction. Flow continuity must be applied at the boundaries. If the recess is sufficiently deep it is justifiable to treat the recess as a sealed system for evaluation of the friction [lo] . A reasonable approximation for non-turbulent recesses is
(2)
65
(3) It may be found that recess effects are the dominant thin-land bearings.
cause of friction
in some
Momentum torque Usually the torque required to accelerate the fluid entering the bearing is neglected but it has been shown that friction torque increases with flow rate [II]. For liquid lubrication the contribution of momentum torque may be evaluated from the following expression : CD
CDTM
4 -
TjAUD =‘DA
%K -
K
(4)
Re
where Re = p UCn 1277
I(
=
2qA, U2 psqcD
Recess flow becomes turbulent at much lower speeds than flow under the lands of a recessed bearing. Shinkle and Hornung [lo] presented a simple basis for evaluating turbulent recess friction. The total friction torque for the lands and the recesses in a concentric bearing is expressed as
TR
cD -~l--~+-
VAUD
AR
fp
AR _
2 A
ha
-ReR
hR
(5)
fp needs to be determined for superlaminar conditions. In order to appreciate the different friction effects consider the following example calculations. A bearing may be proportioned so that L/D = 1 either with or without recesses. The dimensions of the recessed bearing are such that 90% of the axial length in the recesses and 93% of the circumferential length is relieved. All values are divided by the term CDT/~AUD so as to introduce a sense of scale. The ratio of pocket depth to concentric film thickness is 20. The pressure ratio p is 0.5. The results are shown in Fig. 12 as a simple presen~tion of the range of friction values which could arise in practice. Each different case is compared with the value that would result from the Petroff torque in a plain nonrecessed bearing. The effect of incre~ing the eccentricity ratio from zero to 0.5 is to increase the friction torque in a non-recessed bearing by approximately 15%. This range of eccentricity is a normal design range for satisfactory operation. In a recessed bearing the effect of increasing eccentricity
where
66
“SAUD i
0*2
0.4
TORQUE WITH
LAND
z-o*,
EQZENTRRICITY
1.0
NON-RECESSED
1.2
I BEARING
E=0.5
RECESSES
TORQUE DUE TO RECIRCULATION
RECESSED
BEARKG
+o.oS
$20
E=O.O
MOMENTUM
TORQUE
RECESSED
TORQUE
NON-RECESSED
BEARING
R&XXI
*
S,zO.i46
I ~MENTUM
BEARING
R do00
SJ0.0&4
Fig. 12. Typical values of comparative torques.
ratio is comparatively smaller. The case of a recessed bearing operating eccentrically is not shown in the diagram. However for this case the calculation would normally be based on the concentric case owing to the complexity of coping with ~ccent~city in the recessed bearing. The example shown for a recessed bearing operating concentrically applies to a bearing with very thin lands, Fe. a/L = 0.05. This probably represents an extreme condition since it is unlikely that a value less than a/L = 0.05 would be employed in practice. It would however be possible to increase the value of the recess depth ratio beyond the value hR /ho to reduce further the effect of recess friction. For this example the friction torque value is approximately one-gird of the Petroff value of a plain bearing. In practice the difference in operational friction values would be much smaller owing to the compensating adjustments resulting from the optimisation procedure which requires the total power to be minimised. The momentum torque example as illustrated is likely to be greater than that which would be achieved in most bearings owing to the thin landwidth ratio and high Reynolds number, i.e. Re = 1000. The momentum
67
torque for the recessed bearing reaches some 50% of the viscous shear losses in a recessed bearing. For the plain bearing the momentum torque is not greater than 25% of the Petroff torque.
Experimental
results of friction
and torque
Figures 13(a) and 13(b) show torque results for two recessed bearings; at high speeds the friction parameter apparently falls below the value given by eqn. (3). This discrepancy has not been fully explained but is attributed to the difference in the temperature inside the bearing and the temperature of the expelled oil, since it is expected that a greater proportion of the heat will be dissipated by the bearing as the speed increases. Figure 14 shows torque results for a double entry slot bearing. The friction has slightly exceeded the value given by the Petroff formula and, as with the recessed bearings, the discrepancy is due to the measurement of the temperature of the oil. While slot-entry bearings appear to involve a much higher friction torque value the comparison is not quite so simple. With correct hybrid bearing design it is found that the slot-entry bearing gives greater load capacity for a given power consumption. Figure 15 shows the variation of power with the optimisation parameter Sn , It should be noted that the calculated value of the optimum speed parameter Sn, for this recessed bearing is 0.084 while the measured value of Sn at which pumping power equals the friction power occurs at approximately 0.1.
__ 1.0
1.0
()* --_- -
_d--_*a
*
.
.
-a<
0.8 -
06-
0.6 -
0.1 -
0.4 r___.,,~.f--r.L--______
0.2 -
0.2 -
0. 0
* 0.M
0.02
0.03
0.04
0.05
0
006
0
SH (a)
01
0.2
03
0.6
6H (b)
Fig. 13. The variation of the torque with S H, as a result of recirculation, for recessed journal bearings with L/D = 1, n = 4 and e = 0.0; - - - theoretical, . . . experimental. In (a) a/L = 0.25, CD = 0.119 mm and h&h, = 14; in (b) a/L = 0.1, CD = 0.0533 mm and h,/h, = 38.
(
8 POWER 0.6
_
IWATTS)
_.w_ “lAUD
02 /
o0
OOL
0.06
012
016
C120
SH
Fig. 14. Variation of the torque with SH for a double slot liquid fed journal bearing: L/D = 0.830; a/L = 0.25;CD = 0.0737 mm. - - - theoretical, -*-b-experimental; Fig. 15. Variation of the power with SH: L/D = 1; a/L = 0.1; CD = 0.0533 0.084; p = 0.55; n = 4.
mm; SH, =
Conclusions The experimental results show the effect of power factor, pressure ratio, number of pockets and misalignment on the load-carrying ability of recessed hydrostatic bearings and they show friction effects in recessed and nonrecessed bearings. From studies and initial experimental results there are areas of operation where slot-feed journal bearings have considerable advantages over recessed bearings. Slot-entry bearings should be more suitable for heavily loaded conditions including high dynamic loading.
The authors thank the Science Research Council for the support given to the project and Horstman Gauges Ltd. for their cooperation.
Nomenclature
lj, Ar
A, CD
axial flow land width ?rDL, bearing area friction area bearing recess area dimetral clearance
69
D
ha h, R L
FJ PS q Re
bearing diameter radial clearance under axial land recess depth Hp/Hf,power ratio (optimum range 1 Q K < 3) bearing length number of recesses speed of rotation supply pressure bearing flow rate Reynolds’ number optimisation
SH TE TM TP TR u T E 9 P 2 Ic,
parameter
used as a measure
of speed
friction torque due to eccentricity friction torque due to momentum Petroff friction torque friction torque due to recirculation in the recess shaft speed bearing load pressure ratio eccentricity ratio dynamic viscosity density of the oil angle of eccentricity relative to mid-recess angle of load relative to mid-recess attitude angle between the load and eccentricity
References des Surfaces Glissantes, Bachelier, Paris, 1863. 1 L. D. Girard, Application pressurised bearings - design for manufacture, 2 K. J. Stout and W. B. Rowe, Externally parts 1 - 3, Tribol. Int., 7 (3) (1974) 98 - 106; 7 (4) (1974) 169 - 180; 7 (5) (1974) 195 - 212. 3 A. K. Kher and A. Cowley, The design and performance characteristics of a capillary compensated hydrostatic journal bearing, 8th Int. Machine Tool Development and Research Conf., Manchester, 1967, pp. 397 - 418. 4 J. B. Hunt and K. M. Ahmed, Load capacity, stiffness and flow characteristics of a hydrostatically lubricated six-pocket journal bearing supporting a rotating spindle, Proc. Inst. Mech. Eng., London, Part 3N, 182 (1967 - 68) 53 - 62. 5 B. Ghosh, Load and flow characteristics of a capillary-compensated hydrostatic journal bearing, Wear, 23 (1973) 377 - 386. journal 6 P. B. Davis and T. A. Andvig, The behaviour of a multirecess hydrostatic bearing in the presence of severe shaft bending, 9th Int. Machine Tool Development and Research Conf., Manchester, 1968. 7 W. B. Rowe, D. Koshal and K. J. Stout, Slot-entry bearings for hybrid hydrodynamic and hydrostatic operation, J, Mech. Eng. Sci., 18 (2) (1976) 73 - 78. 8 K. J. Stout, The performance of externally pressurised bearings with particular reference to manufacturing variations, Ph. D. Thesis, Lanchester Polytechnic, Gt. Britain, 1973. 9 W. B. Rowe, D. Koshal, R. L. Aston and K. J. Stout, Friction and torque charaeteristics of liquid film journal bearings, 2nd Leeds- Lyon Symp., Lyon, France, 1975. 10 J. N. Shinkle and K. G. Hornung, Friction characteristics of liquid hydrostatic journal bearings, J. Basic. Eng., 87 (1965) 163 - 169. 11 J. Bennet and H. Marsh, The frictional torque in externally pressurised bearings, 6th Int. Gas Bearing Symp., University of Southampton, March 1974.
Wear, 43 (19’77) 55 - 69 Q Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands
INVESTIGATION OF RECESSED HYDROSTATIC AND SLOT-ENTRY JOURNAL BEATINGS FOR HYBRID HYDRODYNAMIC AND HYDROSTATIC OPERATION*
W. B. ROWE and D. KOSHAL Department of Mechanical, Liverpool (Ct. Britain)
Marine and Production
Engineering,
Liverpool
Polytechnic,
K. J. STOUT School of ‘mechanical and Production (Gt. Britain)
Engineering,
Leicester
Potytechnjc,
Leicester
(Received December 3, 1976)
Summary Results of investigations into recessed hydrostatic bearings and slotentry hydrostatic bearings are presented. Initial comparative results show that there are certain conditions under which slot-entry bearings may have marked advantages. Results are given for such parameters as load, torque and flow rate under hydrostatic (i.e. zero speed) conditions and also under hybrid hydrodynamic/hydros~tic operating conditions.
Introduction The development of externally pressurised bearings has progressed over approximately 120 years since Girard [l] first obtained a patent. Since the 1950s externally pressurised journal bearings have increased in use in engineering applications such as machine tools, test equipment, medical equipment, measuring instruments, radio telescopes and in the aerospace industry. Their popularity is attributed to their high load-carrying capacity, zero starting friction and low friction at low speeds, nominally zero wear and hence long life, good rotational accuracy and excellent stiffness and damping. Externally pressurised bearings can be applied to many engineering situations and the detailed design of the bearing depends on the specification of such factors as the type of operation (hybrid, hydrostatic), the choice of bearing geometry (recessed, slot), the type of restrictor (capillary, orifice, slot, diaphragm), the type of loading (static, dynamic), the operating speed, the flow rate and the temperature rise. *Paper presented at the 2nd Israel Tribology Conference, Haifa, October 20 - 22, 1976.
56
(a) Fig. 1. A recessed
(b) bearing.
Typically a hydrostatic journal bearing (Fig. 1) consists of three rings fitted into a sleeve. The middle ring has axial grooves to form recesses separated by axial lands. A ring is fitted on each side of the middle ring to form the two circumferential lands. The lubricant is supplied to each recess through a separate restrictor such as a capillary or an orifice. Recesses which are introduced into the bearing surface of hydrostatic journal bearings are a means of reducing friction and a method of increasing load support. Bearings generally contain four recesses but five, six or even more recesses may be employed, particularly for values of the L/D ratio less than unity. Slot-entry bearings (Fig. 2) used in applications such as machine tool spindles consist of a bearing body which is recessed on either side to accommodate slotted shims. The shims are held in position by retaining rings. The assembly is clamped together with bolts that pass through the body and the retaining rings. The oil enters through holes leading into an annulus and escapes to the bearing clearance through slots which act as laminar restrictors.
(a) Fig. 2. A double
(b) slot-entry
bearing.
The increased land area due to the absence of recesses is an advantage for hydrodynamic and dynamic performance of a bearing [2]. Cowley and Kher [ 31 gave results for one capillary-controlled fourpocket recessed bearing. Hunt and Ahmed [4] investigated the effect of rotation in a six-pocket hydrostatic journal bearing with capillary compensation Ghosh [ 51 extended these results for other bearings and varied design factors at constant speed, Results were presented by Davis et al. [6] for orifice-controlled bearings and included some results for misalignment. The present paper extends the experimental knowledge. It deals with four- and six-pocket bearings with capillary control. Parameters varied include the speed, alignment, pressure ratio and direction of loading. Load power, stiffness and frictional torque have been measured. Some load and friction results are also presented for plain slot-fed journal bearings.
The test rig Two rigs have been used to investigate bearing characteristics. The rig used for early work was based on a shaft of diameter 1 in and the later rig was designed for a shaft nominally 40 mm in diameter. Figure 3 shows the test rig based on a set-up with a shaft of diameter 1 in for loading tests and torque measurement tests respectively. The rig is similar to that described earlier [ 71 with improvements in the loading ~rangement and control of misali~ment. This general purpose hybrid bearing test rig was developed to test hydrostatic journal bearings or hydrodynamic jaumal bearings and was designed to control the load, shaft torque, shaft speed, film thickness, lubricant pressure and lubricant outlet temperature. The test shaft was driven by a variable speed motor up to a speed of 2000 rev min-I. The test shaft contained an inductive transducer and a pressure transducer. The signals from the rotating shaft were brought out to the stationary signal conditioning equipment by slip rings. The shaft could be moved axially through the bearing by a small leadscrew and cradle. The bearing was fed by a gear pump through a 3 pm (absolute) filter at pressures up to 400 lb in2. The load was applied to the bearing in an upward direction. To align the bearing with the axis of the shaft a misalignment jig [8] was employed. The hybrid bearing test rig based on a 40 mm diameter shaft was designed for improved rigidity and instrumentation to test bearings at higher eccentricity ratios and speeds.
Test procedure Figure 3(a) shows the rig set up for a loading test. The bearing was aligned with the axis of the shaft using the misalignment jig. The misalignment
(a)
(b) Fig. 3. The test rig showing ment.
(a) the load test arrangement
and (b) the torque
test arrangc-
was checked by moving the test shaft axially through the bearing from one end to the other and observing the output from the film thickness transducer. The shaft was rotated and a load was applied. As the attitude angle varies with load in the experiment, it is necessary to solve the computer program
59
for several attitude angles in order to obtain theoretical results which correspond to a particular experimental point. Thus it is tedious to obtain correlation between experimental and theoretical results. Figure 3(b) shows the rig set up for torque measurement. Three arms were screwed into the bearing housing. The two horizontal arms on each side of the bearing housing were used to hang pans for weights. At zero speed the position of the vertical arm was noted. The speed was varied from 0 to 2000 rev min- l and at each speed setting the vertical arm was brought back to the null position by adding weights in the appropriate pan. The outlet temperature of the oil was measured as close to the bearing as possible.
Some theoretical bearing designs
results comparing
load/eccentricity
ratios for various
Figure 4 compares the theoretical performance characteristics of three types of bearings. A four-pocket recessed bearing is compared with a slot-fed bearing and also with the common axial groove hydrodynamic bearing. The basis of comparison is the Sommerfeld number. As expected, the axial groove hydrodynamic bearing gives lower load support than the four-pocket recessed bearing at low eccentricity ratio but gives better performance at higher eccentricity ratio. The slot-fed bearing gives improved performance over both bearings through the operating range from zero eccentricity up to e = 0.8.
-
SLOT atLzO.1
14. ----AXIAL
HYBRID
LID=l.O
Kz1.0
bO.5
GROOVE HYDRODYNAMIC
12----RECESS
L/D=l.O
BEARING L/D=%0
O/L.O.25
IOW -?fLDN
C& z 0 D 6.
0.2
0.3
0x3
c
0.5
0.6
0.7
04
Fig. 4. A comparison of the theoretical results for a slot-entry bearing with those for recessed and axial groove bearings.
60
Experimental
results
Load characteristics for recessed bearings Figure 5 shows the direction of loading and the attitude angle convention for the recessed bearings used. Figure 6(a) shows the load support obtained for varying eccentricity ratio when the load is applied towards the midrecess position, i.e. $’ = 0”. At a speed corresponding to the optimum for minimum power dissipation (i.e. K = 1 and SH = 0.053) there is an improvement in load support compared with the zero speed case (i.e. K = 0) due to the hydrodynamic effects, particularly at high eccentricity ratios. Figure 6(b) shows the corresponding cases for loading towards the mid-land position, i.e. @’= 45”. The load support is inferior at zero speed but there is a larger improvement at X: = 1 in the direction of loading. Figure 6(c) compares some results for a four-pocket recessed bearing with those for a six-pocket recessed bearing and shows the advantage of the increased number of recesses. Whereas all the previous results have been for a pressure ratio p close to the recommended value of 0.5, Fig. 6(d) shows some results for differing values of p. These values show how the hydrostatic load support is seriously reduced as p is increased above 0.5. A more comprehensive picture of the pressure ratio effect is shown in Fig. 8. Figure 6(e) shows the effect of misalignment on bearing performance. The degree of misalignment is characterised by the percentage tilt. This parameter combines the effect of the angle of tilt with the effect of clearance. Thus a 10% tilt corresponds to a condition where the eccentricity at one end of the bearing deviates from the eccentricity at the middle of the bearing by 10% of the concentric clearance. These results show that the effect on load is most serious owing to the geometrical change of eccentricity since the film thickness is correspondingly reduced. However the load support for a given value of eccentricity ratio at the mid-plane of the bearing is little affected. This can be verified by noting that the slopes of the three lines are
Fig. 5. The direction af loading and the attitude angle convention.
61
w p,LD 02
0 0
0.2
0.L
E
0.6
0.8
1.0
(bf
(a)
0.3 w pS LD
0.2
w pSLD 0.2
Of
01
0
02
0
0.4
E
06
08
0
10
0
0.2
OL
0
0.2
0.4
E
0.6
0.8
2.0
0.6
0.8
1.0
(d)
(cl 05
4 4.0
EXPERIMENTAL
x
0.L fd =0505 ” :I W p,LD
0.3
0.2
0.1
0 Cl
0.2
0.6
0.6 E max.
0.8
E
(f)
(e)
Fig. 6. Experimental
f.D
results showing
the variation
of the load with the eccentricity
ratio.
62
0.5
0.4
0.4
03
0.3 ic
3 0.2
0.2
0.1
0.1
0 0
0 0.2
0.1
E
0.6
0.8
1.0
0
Fig. 7. The variation of the stiffness with the eccentricity bearings: L/D = 1.0; a/L = 0.25; S, = 0.0; n = 4; Q,= 0.0.
0.2
0.1
0.6
0.8
10
P
ratio for recessed
Fig. 8. The variation of the load parameter with the pressure bearings: L/D= 1.0; a/L = 0.25; SH = 0.0; n = 4.
journal
ratio for recessed
journal
substantially the same, whereas there is a significant change in the intercept with the horizontal axis corresponding to the change of eccentricity ratio (E max.) at one end of the bearing. Figure 6(f) shows the effect on load support of the number of recesses at a value of the speed parameter which is above the optimum and corresponds to a power ratio (K) value of 3.28. At a value of the eccentricity ratio exceeding 0.5 the six-recess bearing shows advantage over the four-pocket recessed bearing. Figure 7 shows the variation of stiffness with eccentricity ratio. Stiffness reduces with increasing eccentricity at zero speed for p = 0.5. The results also show that the stiffness decreases when the pressure ratio 13is increased above 0.5. Figure 8 shows that the optimum value of the pressure ratio 0 is near 0.5 and that a permissible range of p between 0.4 and 0.7 leads to high load capacity and high stiffness. Load characteristics for slot-en try bearings Experimental work into slot-entry bearings is continuing. However, initial results (Fig. 9) indicate that load support from a slot-entry bearing is in line with theoretical predictions. This suggests that slot-entry bearings have better performance characteristics at zero speed than recessed bearings and this may be explained by the greater number of pressure sources. Figure 10 shows theoretical results for load against a/L when the bearing operates at a speed co~esponding to K = 3. Load increases rapidly as a/L
06 5,zoo 2.0
0.5 w %LD
W
0.L
1.5
0.3
1.0
0.i
0.5
P, E =0.25
0.1 o
~
0
,
0.2
,
OL
0.6
,
,
08
10
E
' 0'
01
0.126
0.2
;
0,089
0.3
04
O-5
0.073
0.063
0.059
5,
Fig. 9. The variation of the load with the eccentricity: -+slot-entry bearing, L/D = 0.525, a/L = 0.25, fl= 0.34; -*recessed bearing, L/D = 1, a/L = 0.25, fi = 0.5; -Aslot-entry bearing, L/D = 1, a/L = 0.25, p = 0.86. Fig. 10. The variation of the load parameter bearing with LID = 1.0, fi = 0.5, K = 3.
with a/L and S, for a double
entry journal
diminishes to 0.1. This is where performance differs markedly from the experience with recessed journal bearings. The difference is due to the significant advantage to be obtained from hydrodynamic effects at higher eccentricities. Variation of load support with the pressure ratio p for slot-entry bearings is shown in Fig. 11. These characteristics differ from those of the recessed bearing shown in Fig. 8.
Friction
and torque
As rotating machines become larger and operate at high speeds friction losses become important in bearing performance. An increase in friction losses results in undesired increased power losses. Some of the major bearing friction effects [9] that need to be taken into account when designing bearings operating in the laminar regime may be summarised as follows.
64
L/D ~1.0 I 2.5 I
W p,LD
Fig. 11. The variation journal bearing with
of the load parameter
with the pressure
ratio for a double
entry
L/D = 1.0,a/L = 0.1,K = 1.
Petroff friction torque The viscous friction torque in a non-recessed ing concentrically with laminar flow is given by
cylindrical
bearing operat-
QAUD Tp = ~ CD Friction torque due to eccentricity (laminar flow) With increasing eccentricity it is necessary to take into account the varying clearance and also the effect of pressure-induced flow on the friction torque. For non-recessed bearings with non-cavitating conditions it is possible to write a reasonable approximation for friction ignoring pressure-induced flow:
CDTE _= vAUD
1 (1 - e2)1’2
For strongly cavitating bearings at values of eccentricity less than 0.6, the Petroff formula for friction torque may be a better approximation. Friction torque due to recirculation in the recesses Where the bearing has recesses it is necessary to take into account recirculation effects on recess friction. Flow continuity must be applied at the boundaries. If the recess is sufficiently deep it is justifiable to treat the recess as a sealed system for evaluation of the friction [lo] . A reasonable approximation for non-turbulent recesses is
(2)
65
(3) It may be found that recess effects are the dominant thin-land bearings.
cause of friction
in some
Momentum torque Usually the torque required to accelerate the fluid entering the bearing is neglected but it has been shown that friction torque increases with flow rate [II]. For liquid lubrication the contribution of momentum torque may be evaluated from the following expression : CD
CDTM
4 -
TjAUD =‘DA
%K -
K
(4)
Re
where Re = p UCn 1277
I(
=
2qA, U2 psqcD
Recess flow becomes turbulent at much lower speeds than flow under the lands of a recessed bearing. Shinkle and Hornung [lo] presented a simple basis for evaluating turbulent recess friction. The total friction torque for the lands and the recesses in a concentric bearing is expressed as
TR
cD -~l--~+-
VAUD
AR
fp
AR _
2 A
ha
-ReR
hR
(5)
fp needs to be determined for superlaminar conditions. In order to appreciate the different friction effects consider the following example calculations. A bearing may be proportioned so that L/D = 1 either with or without recesses. The dimensions of the recessed bearing are such that 90% of the axial length in the recesses and 93% of the circumferential length is relieved. All values are divided by the term CDT/~AUD so as to introduce a sense of scale. The ratio of pocket depth to concentric film thickness is 20. The pressure ratio p is 0.5. The results are shown in Fig. 12 as a simple presen~tion of the range of friction values which could arise in practice. Each different case is compared with the value that would result from the Petroff torque in a plain nonrecessed bearing. The effect of incre~ing the eccentricity ratio from zero to 0.5 is to increase the friction torque in a non-recessed bearing by approximately 15%. This range of eccentricity is a normal design range for satisfactory operation. In a recessed bearing the effect of increasing eccentricity
where
66
“SAUD i
0*2
0.4
TORQUE WITH
LAND
z-o*,
EQZENTRRICITY
1.0
NON-RECESSED
1.2
I BEARING
E=0.5
RECESSES
TORQUE DUE TO RECIRCULATION
RECESSED
BEARKG
+o.oS
$20
E=O.O
MOMENTUM
TORQUE
RECESSED
TORQUE
NON-RECESSED
BEARING
R&XXI
*
S,zO.i46
I ~MENTUM
BEARING
R do00
SJ0.0&4
Fig. 12. Typical values of comparative torques.
ratio is comparatively smaller. The case of a recessed bearing operating eccentrically is not shown in the diagram. However for this case the calculation would normally be based on the concentric case owing to the complexity of coping with ~ccent~city in the recessed bearing. The example shown for a recessed bearing operating concentrically applies to a bearing with very thin lands, Fe. a/L = 0.05. This probably represents an extreme condition since it is unlikely that a value less than a/L = 0.05 would be employed in practice. It would however be possible to increase the value of the recess depth ratio beyond the value hR /ho to reduce further the effect of recess friction. For this example the friction torque value is approximately one-gird of the Petroff value of a plain bearing. In practice the difference in operational friction values would be much smaller owing to the compensating adjustments resulting from the optimisation procedure which requires the total power to be minimised. The momentum torque example as illustrated is likely to be greater than that which would be achieved in most bearings owing to the thin landwidth ratio and high Reynolds number, i.e. Re = 1000. The momentum
67
torque for the recessed bearing reaches some 50% of the viscous shear losses in a recessed bearing. For the plain bearing the momentum torque is not greater than 25% of the Petroff torque.
Experimental
results of friction
and torque
Figures 13(a) and 13(b) show torque results for two recessed bearings; at high speeds the friction parameter apparently falls below the value given by eqn. (3). This discrepancy has not been fully explained but is attributed to the difference in the temperature inside the bearing and the temperature of the expelled oil, since it is expected that a greater proportion of the heat will be dissipated by the bearing as the speed increases. Figure 14 shows torque results for a double entry slot bearing. The friction has slightly exceeded the value given by the Petroff formula and, as with the recessed bearings, the discrepancy is due to the measurement of the temperature of the oil. While slot-entry bearings appear to involve a much higher friction torque value the comparison is not quite so simple. With correct hybrid bearing design it is found that the slot-entry bearing gives greater load capacity for a given power consumption. Figure 15 shows the variation of power with the optimisation parameter Sn , It should be noted that the calculated value of the optimum speed parameter Sn, for this recessed bearing is 0.084 while the measured value of Sn at which pumping power equals the friction power occurs at approximately 0.1.
__ 1.0
1.0
()* --_- -
_d--_*a
*
.
.
-a<
0.8 -
06-
0.6 -
0.1 -
0.4 r___.,,~.f--r.L--______
0.2 -
0.2 -
0. 0
* 0.M
0.02
0.03
0.04
0.05
0
006
0
SH (a)
01
0.2
03
0.6
6H (b)
Fig. 13. The variation of the torque with S H, as a result of recirculation, for recessed journal bearings with L/D = 1, n = 4 and e = 0.0; - - - theoretical, . . . experimental. In (a) a/L = 0.25, CD = 0.119 mm and h&h, = 14; in (b) a/L = 0.1, CD = 0.0533 mm and h,/h, = 38.
(
8 POWER 0.6
_
IWATTS)
_.w_ “lAUD
02 /
o0
OOL
0.06
012
016
C120
SH
Fig. 14. Variation of the torque with SH for a double slot liquid fed journal bearing: L/D = 0.830; a/L = 0.25;CD = 0.0737 mm. - - - theoretical, -*-b-experimental; Fig. 15. Variation of the power with SH: L/D = 1; a/L = 0.1; CD = 0.0533 0.084; p = 0.55; n = 4.
mm; SH, =
Conclusions The experimental results show the effect of power factor, pressure ratio, number of pockets and misalignment on the load-carrying ability of recessed hydrostatic bearings and they show friction effects in recessed and nonrecessed bearings. From studies and initial experimental results there are areas of operation where slot-feed journal bearings have considerable advantages over recessed bearings. Slot-entry bearings should be more suitable for heavily loaded conditions including high dynamic loading.
The authors thank the Science Research Council for the support given to the project and Horstman Gauges Ltd. for their cooperation.
Nomenclature
lj, Ar
A, CD
axial flow land width ?rDL, bearing area friction area bearing recess area dimetral clearance
69
D
ha h, R L
FJ PS q Re
bearing diameter radial clearance under axial land recess depth Hp/Hf,power ratio (optimum range 1 Q K < 3) bearing length number of recesses speed of rotation supply pressure bearing flow rate Reynolds’ number optimisation
SH TE TM TP TR u T E 9 P 2 Ic,
parameter
used as a measure
of speed
friction torque due to eccentricity friction torque due to momentum Petroff friction torque friction torque due to recirculation in the recess shaft speed bearing load pressure ratio eccentricity ratio dynamic viscosity density of the oil angle of eccentricity relative to mid-recess angle of load relative to mid-recess attitude angle between the load and eccentricity
References des Surfaces Glissantes, Bachelier, Paris, 1863. 1 L. D. Girard, Application pressurised bearings - design for manufacture, 2 K. J. Stout and W. B. Rowe, Externally parts 1 - 3, Tribol. Int., 7 (3) (1974) 98 - 106; 7 (4) (1974) 169 - 180; 7 (5) (1974) 195 - 212. 3 A. K. Kher and A. Cowley, The design and performance characteristics of a capillary compensated hydrostatic journal bearing, 8th Int. Machine Tool Development and Research Conf., Manchester, 1967, pp. 397 - 418. 4 J. B. Hunt and K. M. Ahmed, Load capacity, stiffness and flow characteristics of a hydrostatically lubricated six-pocket journal bearing supporting a rotating spindle, Proc. Inst. Mech. Eng., London, Part 3N, 182 (1967 - 68) 53 - 62. 5 B. Ghosh, Load and flow characteristics of a capillary-compensated hydrostatic journal bearing, Wear, 23 (1973) 377 - 386. journal 6 P. B. Davis and T. A. Andvig, The behaviour of a multirecess hydrostatic bearing in the presence of severe shaft bending, 9th Int. Machine Tool Development and Research Conf., Manchester, 1968. 7 W. B. Rowe, D. Koshal and K. J. Stout, Slot-entry bearings for hybrid hydrodynamic and hydrostatic operation, J, Mech. Eng. Sci., 18 (2) (1976) 73 - 78. 8 K. J. Stout, The performance of externally pressurised bearings with particular reference to manufacturing variations, Ph. D. Thesis, Lanchester Polytechnic, Gt. Britain, 1973. 9 W. B. Rowe, D. Koshal, R. L. Aston and K. J. Stout, Friction and torque charaeteristics of liquid film journal bearings, 2nd Leeds- Lyon Symp., Lyon, France, 1975. 10 J. N. Shinkle and K. G. Hornung, Friction characteristics of liquid hydrostatic journal bearings, J. Basic. Eng., 87 (1965) 163 - 169. 11 J. Bennet and H. Marsh, The frictional torque in externally pressurised bearings, 6th Int. Gas Bearing Symp., University of Southampton, March 1974.