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Hydrostatic journal bearing without pressure chambers between bearing surfaces
Wear, 1.59 (1992)
31-38
31
Hydrostatic journal bearing without pressure chambers between bearing surfaces A. Palzewicz Institute of Fluid-Flow Machinery of the Polish Academy of Sciences, Gdansk (Poland) (Received
March
15, 1991; revised and accepted
February
11, 1992)
Abstract This paper presents calculated and experimental test results of a specific radial bearing of good hybrid properties. The bearing can be used efficiently as a bearing of hydrostatic load carrying capacity when the velocity of the
surface of the bush is zero and the velocity of the surface of the journal is zero or very small. It can also operate as a bearing of hydrodynamic carrying capacity when the velocity of the surface of the bush is zero and velocity of the surface of the journal is large.
1. Introduction
Slider bearings with a hydrostatic oil film have been known for over a century. As early as 1865 the French engineer Girard was granted a patent for his design of a bearing [l]. Currently, hydrostatic bearings are very often applied in various technological fields especially where one has to deal with carrying of heavy loads per unit area. In a typical design of a hydrostatic bearing, the bearing surfaces are separated by a thin layer of oil which flows out of pressure chambers, into which it has been pumped by a special feeding system [2, 31. The pressure chambers are located in the space between the surfaces of the bearing. This limits the possibility of a spontaneous creation in the bearing of a hydrodynamic oil film, even if there is large difference of speed between the bearing surfaces. In this work, a method of calculation for the operational parameters of bearings will be presented for the case of bearings which can work hydrostatically during start up and stopping and as bearings with a hydrodynamic oil film after reaching full speed work. Such bearings do not have pressure chambers in the clearance between the bush and the journal. The pressurized oil is pumped into at least one pressure chamber placed on the outer surface of the bush, from which it flows out through many capillary, radially directed, orifices into the clearance between the bush and the journal (Fig. 1) [4, 51. A pressure drop occurs in the oil on its way through the bearing, and then in the clearance between the journal of the shaft and the bush. In a bearing of such design every change in the relative position of the journal with respect to the bush causes a change in
0043-1648/92/$5.00
L
‘
Fig. 1. Axial cross-section of a simplified model of a transverse hydrostatic bearing with one pressure chamber.
the distribution of the pressure in the oil clearance. The resultant pressure of the oil, which fills the clearance, on the journal of the shaft amounts to the load carrying force of the bearing. If the surface of the journal of the shaft does not shift with respect to the surface of the bush, the distribution of the pressure in the clearance of the bearing, resulting from the unevenness of the throttling, is the only cause bf the bearing force. The inlet orifices are distributed on the surface of the bush with their relative distances much greater than their diameter, and their total area is not more than 1% of the total area of the bush. If one employs capillary glands with a unidirectional flow, which exclude the possibility of a reverse flow, a hydrodynamic oil film can easily develop in the bearing.
0 1992 - Elsevier
Sequoia.
All rights reserved
A. Pabewicz / A hydrostatic journal bearing without pressure
32
It is generated by the motion of the surface of the journal with respect to the surface of the bush.
chambers
between surfaces
If we insert B=2rrR, L =d,, AP=dp into eqn. (2) then the discharge of the flat-ring clearance is given by
2. Theory Assumptions for a calculation and calculation model are presented here for the case of a hydrostatic transverse bearing with a cylindrical bush and parallel axes of the journal and the bush. On the external surface of the bush the bearing has one external pressure chamber with an angle of 360” (Fig. 1). The oil is supplied to the clearance between the journal and the bush from the external chamber via a multiple radial throttling system which consists of a capillary and orifice placed on the surface of the bush. This throttling system, combined with the circular clearance portion around the orifice, is the total serial throttling system. First, let us consider the throttling of the flow in the isolated serial system (Fig. 2). By using the Hagen-Poiseuille equations [6] for the discharge of the capillary we obtain
Assuming that QSp= constant, H = constant and n = constant, we can write
s
PW
6.77.12
9=-$
R= 1
p
s RW
PO
and after integrating pw-po=
3
.ln
($5)
(6)
w
from the condition of the continuity of the flow, as well as eqns. (l), (3) and (6), we obtain the following formula: AP,=AP.k
(7)
where k=
(1) for an infinitely long flat clearance
QS=
AP;B.H3
(2)
12.7j.L
For the system shown in Fig. 1 some assumptions can be made. If
When the dimensionless coefficient k is determined, the part of the total pressure drop contributed by the flat ring clearance is known. Experimental data [7] show good agreement with the results of the calculations [8] for (Lk/Dk) > 12 and (RJR,)
&>2 LI
andR W>D
k
then the drop in pressure in zone 2 (Fig. 2) is AR, -SZ AR, and can be disregarded. For such a case the drop of pressure in the throttling system amounts to: AP=P,-P,=P,-P,+-P,-PO WM
(3)
>2
In Fig. 3 exemplary runs of the value of k are presented for various proportions of the dimensions of the throttling system of Fig. 2. In the case of a bearing of the type shown in Fig. 1, the diameter of the capillary orifice is at least one hundred times smaller than the diameter of the bush. For technological reasons the orifice diameter is about twice as large as the capillary diameter. Around each outlet orifice one can define a clearance zone, which will be treated as a flat ring clearance of a serial throttling system. With the given ratios of the dimensions H/D, and L,lD,, which are defined by the construction of the bearing, and if (Lk/Dk) > 12 and 1 < (RJD,)
<2
we can find that the main share of the pressure drop
in the flat ring clearance occurs in the radius zone With the diameter of the capillary orifine Dk=O.5 mm, this radius zone is about 3 mm. Taking into account the dimensions of the bush, we can assume a constant height H, in the whole inlet zone, equal to the height of the clearance at the axis of the inlet hole. With such assumptions we can estimate the coefficient
R,< (3R,).
Fig. 2. Schematic axial cross-section of a serial of capillary orifice flat clearance type.
throttling
system
A. Palzewicz I A hydrostatic journal bearing without pressure chambers between surfaces
33
k IO
e5
Fig. 4. Developed of flow.
view of a bush with marked symmetric
zones
04
03
42
01
oc
Fig. 3. Changes of the coefficient k for various parameters of the serial throttling system; R,/R,=2.718..., Dt=0.5 mm: curve 1, L,JD,= 12; curve 2, L,JDt=20; curve 3, L,lD,=28.
k by using eqn. 8. The distribution of the pressure in the oil clearance of the bearing is determined by the way the oil is supplied to the bearing. The oil is supplied by a multiple serial throttling system distributed throughout the bush surface. The basic difficulty lies in the determination of the counter pressures on the boundaries of the outlet zones of every source. Those counter pressures depend upon the flow of oil coming from each source. The determination of the pressure in the clearance around each serial throttling system is necessary for the estimate of the amount of the oil flowing out of the source as a result of the difference of the pressure between the external pressure chamber and the outlet zone in the clearance of the bearing. A discretization of the surface has been performed in order to facilitate the calculations. On the developed view of the surface of the bush two axes of division into symmetric zones of the flow were located (Fig. 4). This was done on the grounds of the assumption made earlier, that the axes of symmetry of the journal and the bush are parallel. Taking into account the small height of the clearance, it has been assumed, that we are dealing with only laminar flows (Fig. 5). In Fig. 6 is shown the rectangular discrete element of the clear-
55.EL PI
Fig. 5. Flow at the edges of the rectangular the clearance.
discrete
,
PfJii,
element
of
7+f)
_CSfJ+f,Z
‘Put+,
7)
Fig. 6. Rectangular discrete element of the clearance with the bordering elements. Possible directions of the flow through the walls are marked. Before starting a calculation at least one direction of flow has to be excluded.
34
A. Pakewicz
I A hydrostatic
journal
bearing
without pressure
chambers
between
surfaces
ante with those bordering it. The problem was solved by an iteration of the equations of the average flows through the side walls of every element up to their full balancing, with simultaneous equilibrium of the amount of oil entering the clearance from all the sources with the oil outflowing by the side edges of the bearing. The distribution of the pressure in the clearance at the moment of flow equilibrium has been taken as the basis for the calculation of the resultant thrust of the oil in the clearance between the journal and the bush [9, 101.
3. An example of the calculation Examples of hydrostatic calculations of a journal bearing with zero rotation speed of the journal with respect to the bush and a uniform distribution of the inlet orifices at the bush circumference are presented. If in a bearing of this kind the journal axis is parallel to that of the bush, and the shape of both surfaces generating the bearing clearance is kept ideally cylindrical then, assuming constant oil pressure (PJ in the external chamber and steady thermal conditions of the bearing, the value of the journal and bush axis aligning force (SJ depends on the radial distance between them. The value of the (S,J force does not depend in such a case on the angle of journal revolution with respect to the bush. The calculation examples presented concern two cases of relative eccentricity, i.e., E= 0.0 and E= 0.9 in a bearing of the design under investigation. The diameter of the bush D,= 0.05600 m; the diameter of the journal D,= 0.05580 m, 0.05560 m, 0.0550 m; the width of the bush L,=O.O9200 m; 24 glands were distributed in 4 rows of 60” on the perimeter of the bush. The parameters of the capillary L, =0.014 m; D,=O.OOOSm. The measured pressures are in good agreement with those calculated. Generally, they do not differ by more than 10-45%. Similar results were obtained with the measured and calculated outflow of the oil through the side edges of the bearing. In Figs. 7 and 8 examples are shown of the calculated distribution of the pressure for two eccentricities of the shaft. If we assume that the pressure in the pressure chamber is
Fig. 7. Distribution of pressures in one of the symmetric parts of the clearance in the developed view. The parameters of the bearing are E= 0.0, P= Pip,. -x-=visible pressure line, - * -= hidden pressure line, fB=oil outlet from bush in segment.
Fig. 8. of the bearing hidden
Distribution of pressures in one of the symmetric parts clearance in the developed view. The parameters of the are E= 0.9, p= Pip,. -x- = visible pressure line, - * - = pressure line, El =oil outlet from bush in segment.
P, = 7 MPa and 77= 0.0495 Nm SK’ then for E= 0.0 (Fig. 7), S, = 0.0 N; Q= 0.144 dcm3 S - '; for ~=0.9 (Fig. 8) .S, = 15000 N; Q, = 0.152 dcm3 S -', where S,, is the resultant force of oil thrust on the bush of the bearing and QC is the total outflow of the oil from the bearing. It follows from the calculation results presented that even in the case of a uniform distribution of inlet orifices at the bush circumference (undesirable from
the viewpoint of effective utilization of oil delivered under pressure to the external chamber) a significant pressure differentation in the oil clearance of a bearing with a journal-bush misalignment takes place. This differentiation results in the force (Sn) being capable of attaining high values.
A. Palzewicz / A hydrostatic journal
bearing without pressure
chambers
between surfaces
35
4. Comparison between the results of experiment and calculation In order to verify calculation results by comparing them with the experimental measurement data, a measuring head shown in Fig. 9 has been designed and constructed (Fig. 10). The structure and the shape of both the bush and the test journal result exclusively from the need for frequent head assembling and disassembling. An industrial hydrostatic bearing of the same operating principle can be a much less complex structure. In Fig. 11 an axial section of the test head is shown. The head consists of the following main components: journal (1) with holes used to measure pressure in the bearing clearance; bush (2) with capillary glands mounted; covers (3) and (4) forming collectors of oil flowing out of the peripheral bush clearances; casing (6). Between the casing (6) and the external side of bush (2) there is an external pressure chamber (7) to which oil is pumped. In this chamber, inlets to all capillary glands are placed. In Fig. 12 a part of the A-A section of Fig. 11 is shown. (1) is a capillary gland with the inlet being opened or closed by means of hood (2).
Fig. 10. A photograph
of the test head.
Fig. 11. An axial section of the test head. (1) is the journal with holes used to measure pressure in the bearing clearance; (2) is the bush with capillary glands; (3) and (4) are covers forming oil collectors for outward flowing oil; (5) is the capillary insert; (6) is the case; (7) is the external pressure chamber.
SR
c
4 56.02+
Fig. 9. A scheme of the journal for investigation the measurements are shown in Table 2).
(the results of
(3) is a pusher sealed by means of a ring (4). This pusher, used together with a screw (5), is applied to set the minimum height of the clearance between the
36
A. Palzewicz
/ A hydrostatic
journal
bearing without pressure
chambers
between
sur$aces
TABLE 1. Results of the measurement of the journal for investigation Part of the journal
4
Angle (“)
0
of the D, and D, diameters
Section A
Section M
(mm)
(mm)
Section B (mm)
(bush)
45 90 13.5
56.00 56.02 56.01 56.01
56.01 56.02 56.03 56.03
56.02 56.02 56.02 56.02
DC (journal)
0 45 90 135
55.76 55.76 55.76 55.76
55.76 55.76 55.76 55.76
55.76 55.76 55.76 55.76
Fig. 12. A part of A-A section (from Fig. 11). (1) is the capillary insert; (2) the capillary hood (when inlet to the capillary is open the hood is out); (3) pusher; (4) O-ring; (5) pusher adjusting screw; (6) plug; (7) external oil chamber; (8) bearing clearance; (9) orifice.
bush and the journal. (6) is a cover allowing access to the screw (5). In the schematic shown in Fig. 9 the distribution of fixing sets SR at the test bearing bush can be seen. In section A-A of this schematic numbers (l-5) denote the outlets of holes situated in the bearing journal and used to measure oil pressure in the bearing clearance. Pressure measurement is carried out at a journal position fixed permanently with respect to the bush by means of the SR fixing sets. In order to rotate the journal by some angle respective to the bush it is sufficient to loosen one of SR sets in each fixing plane. The technique of oil pressure measurement in individual zones of the bearing clearance required the following procedure: (i) setting and fixing the journal in the bush in an appropriate position, with the initial clearance being set using the pusher and clearance gauge; (ii) opening of compressed oil access to the external chamber; (iii) reading out the oil pressure value in the clearance zones opposite to the measuring holes inlets in the journal; (iv) cutting off the oil access to the external chamber and then following the procedure required to rotate the journal with respect to the bush by a given angle without changing the journal and bush axis; (v) repeating the above sequence in order to attain a new measuring hole position. Exemplary results of measurements conducted both for the journal and the bush of dimensions shown in Table 1 and Fig. 13 are put together in Table 2. In the table heading constant values of experimental parameters are given and in rows l-5 the measured pressures are given in form of dimensional (upper part) and dimensionless values (lower part). A similar pres-
Fig. 13. A scheme for Table 1.
sure distribution in clearance zones opposite to holes (4) and (5) in d ica t es a parallel positioning of the bush and journal. The measured oil outflow along the bearing sides was Q= 156 cm3 s-l. In Fig. 14 the calculated pressure distribution of the oil in the clearance quarter is of the same dimensions and operating parameters as shown in Table 2. The relative eccentricity of the bearing is l=0.36 which corresponds to the S, =5260 N lift produced by the oil flow through the clearance and to the QC= 172 cm3 outflow through the side edges. S --I
5. Discussion
and conclusions
In the experiment presented above a satisfying conformity between the calculation results and those of measurements has been obtained. The divergence does not exceed 10-45%. This proves that the correct choice of simplifying assumptions was made when developing the computation model. In the experimental bearing presented, despite a uniform distribution of inlet orifices at the bush surface,
A. Palzewicz
TABLE 2. Exemplary
calculated
/A
hydrostatic
pressure
journal
distribution
bearing
without pressure
chambers
and results of measurements
between
of the pressure
surfaces
37
distribution
in slot of the journal
Number of a measuring orifice
Angle (“) 0
30
60
90
120
150
180
210
240
270
300
330
1
0.373 0.464
0.520 0.518
0.435 0.464
0.373 0.442
0.328 0.385
0.255 0.378
0.223 0.343
0.255 0.350
0.328 0.343
0.373 0.386
0.435 0.429
0.520 0.471
2
0.350 0.307
0.493 0.379
0.350 0.329
0.278 0.329
0.261 0.271
0.235 0.285
0.210 0.257
0.235 0.271
0.261 0.264
0.278 0.300
0.350 0.329
0.493 0.371
3
0.261 0.307
0.301 0.371
0.230 0.321
0.210 0.329
0.202 0.271
0.172 0.285
0.150 0.257
0.172 0.271
0.202 0.264
0.210 0.30
0.230 0.329
0.301 0.371
4
0.092 0.064
0.093 0.071
0.071 0.071
0.068 0.057
0.057 0.057
0.050 0.050
0.050 0.057
0.050 0.057
0.057 0.057
0.068 0.057
0.071 0.057
0.093 0.057
5
0.092 0.079
0.093 0.079
0.071 0.079
0.068 0.079
0.057 0.079
0.050 0.064
0.050 0.057
0.050 0.050
0.057 0.057
0.068 0.057
0.071 0.064
0.093 0.071
MPa and Table 1, n =0.058 Ns m-* and Fig. 9; Lk= 14 mm; Dk =0.5 Top lines are calculated values, lower lines are measured values.
P,=7
nm; H,,= 0.08 mm; P=P/P,
(dimensionless
inlets to the clearance can be set perpendicular oil delivery holes.
pressure).
to the
References D. Dowson, History of Tiibology, Langman, London and New York, 1979. F. T. Barwell, Eojskowanie, WNT, Warsaw, 1984. W. B. Rowe, Hydrostatic and Hybrid Bearing Design, Butterworth, London, 1983. A. Paliewicz, Hydrostatishe Radialgleitlager ohne Schmiennittehaschen, Tribo 88, 19th Int. Symp., Schmierungstechnik KarlMarx-Stadt. Bezkomorowa, Report 5 A. Paliewicz, Podpora Hydrostatycrna No. 25647, Gdansk PoIytechnic, 1988. 6 0. R. Lang and W. Steinhilper, Berechung und Konstruktion von Gleitlagem
Fig. 14. The calculated pressure distribution in oil in the clearance quarter of the same dimensions and operating parameters as those in Table 2: l=0.36; P=P/P,. -x-=visible pressure line; - * - = hidden pressure line; kIJ= oil outlet from bush in segment; 0, 0, 0, @ = trajectory of the measured orifice.
ineffectively utilizing the compressed oil energy, the journal-bush alignment force was found to be of a significant value. This force results from the pressure difference between individual zones of the bearing clearance due to oil flow between the external pressure chamber and the bearing side surfaces. The presented hydrostatic mechanism of carrying the journal when a machine is being started can be applied by modifying the design of bearings with hydrodynamic carrying capacity. This does not require any major reconstruction, as the pressure chamber and the glands can be situated at the bush side surfaces and the oil
mit Konstanten
und
Veranderlicher
Belastung
Springer-Verlag, Berlin, Heidelberg, New York, 1978. A. Palzewicz, BW-855280, unpublished paper, Gdansk Polytechnic, 1986. Computer Program, 1988. 8 A. Paliewicz, TARCZA3I 9 A. Paliewicz, SITO354, Computer Program, 1989. 10 A. Cameron, The Principles of Lubrication Longman Green, London, 1966.
Appendix:
B
DC 4
DP H
HO H k
Inax
Nomenclature
mean flow through the lateral walls of the discrete element width of the flat slot diameter of journal diameter of capillary gland diameter of bush thickness of slot minimum thickness of slot maximum thickness of slot dimensionless coefficient
38
A. Pakewicz
/ A hydrostatic
journal
length of flat slot length of exit hole length of capillary gland pressure out bearing pressure pressure in chamber oil flow source flow into element total oil outflow from the bearing oil outflow from capillary gland oil outflow from rand-flat slot
bearing without pressure
R RW RZ &
chambers
between
surfaces
radius inside radius outside radius bush aligning force
Greek symbols Al’,, AP2, Al’, difference
of pressures between inflow and outflow zones (l), (2), (3) (Fig. 2). pressure sink in capillary gland pressure sink in flat slot eccentricity ratio dynamic viscosity
31-38
31
Hydrostatic journal bearing without pressure chambers between bearing surfaces A. Palzewicz Institute of Fluid-Flow Machinery of the Polish Academy of Sciences, Gdansk (Poland) (Received
March
15, 1991; revised and accepted
February
11, 1992)
Abstract This paper presents calculated and experimental test results of a specific radial bearing of good hybrid properties. The bearing can be used efficiently as a bearing of hydrostatic load carrying capacity when the velocity of the
surface of the bush is zero and the velocity of the surface of the journal is zero or very small. It can also operate as a bearing of hydrodynamic carrying capacity when the velocity of the surface of the bush is zero and velocity of the surface of the journal is large.
1. Introduction
Slider bearings with a hydrostatic oil film have been known for over a century. As early as 1865 the French engineer Girard was granted a patent for his design of a bearing [l]. Currently, hydrostatic bearings are very often applied in various technological fields especially where one has to deal with carrying of heavy loads per unit area. In a typical design of a hydrostatic bearing, the bearing surfaces are separated by a thin layer of oil which flows out of pressure chambers, into which it has been pumped by a special feeding system [2, 31. The pressure chambers are located in the space between the surfaces of the bearing. This limits the possibility of a spontaneous creation in the bearing of a hydrodynamic oil film, even if there is large difference of speed between the bearing surfaces. In this work, a method of calculation for the operational parameters of bearings will be presented for the case of bearings which can work hydrostatically during start up and stopping and as bearings with a hydrodynamic oil film after reaching full speed work. Such bearings do not have pressure chambers in the clearance between the bush and the journal. The pressurized oil is pumped into at least one pressure chamber placed on the outer surface of the bush, from which it flows out through many capillary, radially directed, orifices into the clearance between the bush and the journal (Fig. 1) [4, 51. A pressure drop occurs in the oil on its way through the bearing, and then in the clearance between the journal of the shaft and the bush. In a bearing of such design every change in the relative position of the journal with respect to the bush causes a change in
0043-1648/92/$5.00
L
‘
Fig. 1. Axial cross-section of a simplified model of a transverse hydrostatic bearing with one pressure chamber.
the distribution of the pressure in the oil clearance. The resultant pressure of the oil, which fills the clearance, on the journal of the shaft amounts to the load carrying force of the bearing. If the surface of the journal of the shaft does not shift with respect to the surface of the bush, the distribution of the pressure in the clearance of the bearing, resulting from the unevenness of the throttling, is the only cause bf the bearing force. The inlet orifices are distributed on the surface of the bush with their relative distances much greater than their diameter, and their total area is not more than 1% of the total area of the bush. If one employs capillary glands with a unidirectional flow, which exclude the possibility of a reverse flow, a hydrodynamic oil film can easily develop in the bearing.
0 1992 - Elsevier
Sequoia.
All rights reserved
A. Pabewicz / A hydrostatic journal bearing without pressure
32
It is generated by the motion of the surface of the journal with respect to the surface of the bush.
chambers
between surfaces
If we insert B=2rrR, L =d,, AP=dp into eqn. (2) then the discharge of the flat-ring clearance is given by
2. Theory Assumptions for a calculation and calculation model are presented here for the case of a hydrostatic transverse bearing with a cylindrical bush and parallel axes of the journal and the bush. On the external surface of the bush the bearing has one external pressure chamber with an angle of 360” (Fig. 1). The oil is supplied to the clearance between the journal and the bush from the external chamber via a multiple radial throttling system which consists of a capillary and orifice placed on the surface of the bush. This throttling system, combined with the circular clearance portion around the orifice, is the total serial throttling system. First, let us consider the throttling of the flow in the isolated serial system (Fig. 2). By using the Hagen-Poiseuille equations [6] for the discharge of the capillary we obtain
Assuming that QSp= constant, H = constant and n = constant, we can write
s
PW
6.77.12
9=-$
R= 1
p
s RW
PO
and after integrating pw-po=
3
.ln
($5)
(6)
w
from the condition of the continuity of the flow, as well as eqns. (l), (3) and (6), we obtain the following formula: AP,=AP.k
(7)
where k=
(1) for an infinitely long flat clearance
QS=
AP;B.H3
(2)
12.7j.L
For the system shown in Fig. 1 some assumptions can be made. If
When the dimensionless coefficient k is determined, the part of the total pressure drop contributed by the flat ring clearance is known. Experimental data [7] show good agreement with the results of the calculations [8] for (Lk/Dk) > 12 and (RJR,)
&>2 LI
andR W>D
k
then the drop in pressure in zone 2 (Fig. 2) is AR, -SZ AR, and can be disregarded. For such a case the drop of pressure in the throttling system amounts to: AP=P,-P,=P,-P,+-P,-PO WM
(3)
>2
In Fig. 3 exemplary runs of the value of k are presented for various proportions of the dimensions of the throttling system of Fig. 2. In the case of a bearing of the type shown in Fig. 1, the diameter of the capillary orifice is at least one hundred times smaller than the diameter of the bush. For technological reasons the orifice diameter is about twice as large as the capillary diameter. Around each outlet orifice one can define a clearance zone, which will be treated as a flat ring clearance of a serial throttling system. With the given ratios of the dimensions H/D, and L,lD,, which are defined by the construction of the bearing, and if (Lk/Dk) > 12 and 1 < (RJD,)
<2
we can find that the main share of the pressure drop
in the flat ring clearance occurs in the radius zone With the diameter of the capillary orifine Dk=O.5 mm, this radius zone is about 3 mm. Taking into account the dimensions of the bush, we can assume a constant height H, in the whole inlet zone, equal to the height of the clearance at the axis of the inlet hole. With such assumptions we can estimate the coefficient
R,< (3R,).
Fig. 2. Schematic axial cross-section of a serial of capillary orifice flat clearance type.
throttling
system
A. Palzewicz I A hydrostatic journal bearing without pressure chambers between surfaces
33
k IO
e5
Fig. 4. Developed of flow.
view of a bush with marked symmetric
zones
04
03
42
01
oc
Fig. 3. Changes of the coefficient k for various parameters of the serial throttling system; R,/R,=2.718..., Dt=0.5 mm: curve 1, L,JD,= 12; curve 2, L,JDt=20; curve 3, L,lD,=28.
k by using eqn. 8. The distribution of the pressure in the oil clearance of the bearing is determined by the way the oil is supplied to the bearing. The oil is supplied by a multiple serial throttling system distributed throughout the bush surface. The basic difficulty lies in the determination of the counter pressures on the boundaries of the outlet zones of every source. Those counter pressures depend upon the flow of oil coming from each source. The determination of the pressure in the clearance around each serial throttling system is necessary for the estimate of the amount of the oil flowing out of the source as a result of the difference of the pressure between the external pressure chamber and the outlet zone in the clearance of the bearing. A discretization of the surface has been performed in order to facilitate the calculations. On the developed view of the surface of the bush two axes of division into symmetric zones of the flow were located (Fig. 4). This was done on the grounds of the assumption made earlier, that the axes of symmetry of the journal and the bush are parallel. Taking into account the small height of the clearance, it has been assumed, that we are dealing with only laminar flows (Fig. 5). In Fig. 6 is shown the rectangular discrete element of the clear-
55.EL PI
Fig. 5. Flow at the edges of the rectangular the clearance.
discrete
,
PfJii,
element
of
7+f)
_CSfJ+f,Z
‘Put+,
7)
Fig. 6. Rectangular discrete element of the clearance with the bordering elements. Possible directions of the flow through the walls are marked. Before starting a calculation at least one direction of flow has to be excluded.
34
A. Pakewicz
I A hydrostatic
journal
bearing
without pressure
chambers
between
surfaces
ante with those bordering it. The problem was solved by an iteration of the equations of the average flows through the side walls of every element up to their full balancing, with simultaneous equilibrium of the amount of oil entering the clearance from all the sources with the oil outflowing by the side edges of the bearing. The distribution of the pressure in the clearance at the moment of flow equilibrium has been taken as the basis for the calculation of the resultant thrust of the oil in the clearance between the journal and the bush [9, 101.
3. An example of the calculation Examples of hydrostatic calculations of a journal bearing with zero rotation speed of the journal with respect to the bush and a uniform distribution of the inlet orifices at the bush circumference are presented. If in a bearing of this kind the journal axis is parallel to that of the bush, and the shape of both surfaces generating the bearing clearance is kept ideally cylindrical then, assuming constant oil pressure (PJ in the external chamber and steady thermal conditions of the bearing, the value of the journal and bush axis aligning force (SJ depends on the radial distance between them. The value of the (S,J force does not depend in such a case on the angle of journal revolution with respect to the bush. The calculation examples presented concern two cases of relative eccentricity, i.e., E= 0.0 and E= 0.9 in a bearing of the design under investigation. The diameter of the bush D,= 0.05600 m; the diameter of the journal D,= 0.05580 m, 0.05560 m, 0.0550 m; the width of the bush L,=O.O9200 m; 24 glands were distributed in 4 rows of 60” on the perimeter of the bush. The parameters of the capillary L, =0.014 m; D,=O.OOOSm. The measured pressures are in good agreement with those calculated. Generally, they do not differ by more than 10-45%. Similar results were obtained with the measured and calculated outflow of the oil through the side edges of the bearing. In Figs. 7 and 8 examples are shown of the calculated distribution of the pressure for two eccentricities of the shaft. If we assume that the pressure in the pressure chamber is
Fig. 7. Distribution of pressures in one of the symmetric parts of the clearance in the developed view. The parameters of the bearing are E= 0.0, P= Pip,. -x-=visible pressure line, - * -= hidden pressure line, fB=oil outlet from bush in segment.
Fig. 8. of the bearing hidden
Distribution of pressures in one of the symmetric parts clearance in the developed view. The parameters of the are E= 0.9, p= Pip,. -x- = visible pressure line, - * - = pressure line, El =oil outlet from bush in segment.
P, = 7 MPa and 77= 0.0495 Nm SK’ then for E= 0.0 (Fig. 7), S, = 0.0 N; Q= 0.144 dcm3 S - '; for ~=0.9 (Fig. 8) .S, = 15000 N; Q, = 0.152 dcm3 S -', where S,, is the resultant force of oil thrust on the bush of the bearing and QC is the total outflow of the oil from the bearing. It follows from the calculation results presented that even in the case of a uniform distribution of inlet orifices at the bush circumference (undesirable from
the viewpoint of effective utilization of oil delivered under pressure to the external chamber) a significant pressure differentation in the oil clearance of a bearing with a journal-bush misalignment takes place. This differentiation results in the force (Sn) being capable of attaining high values.
A. Palzewicz / A hydrostatic journal
bearing without pressure
chambers
between surfaces
35
4. Comparison between the results of experiment and calculation In order to verify calculation results by comparing them with the experimental measurement data, a measuring head shown in Fig. 9 has been designed and constructed (Fig. 10). The structure and the shape of both the bush and the test journal result exclusively from the need for frequent head assembling and disassembling. An industrial hydrostatic bearing of the same operating principle can be a much less complex structure. In Fig. 11 an axial section of the test head is shown. The head consists of the following main components: journal (1) with holes used to measure pressure in the bearing clearance; bush (2) with capillary glands mounted; covers (3) and (4) forming collectors of oil flowing out of the peripheral bush clearances; casing (6). Between the casing (6) and the external side of bush (2) there is an external pressure chamber (7) to which oil is pumped. In this chamber, inlets to all capillary glands are placed. In Fig. 12 a part of the A-A section of Fig. 11 is shown. (1) is a capillary gland with the inlet being opened or closed by means of hood (2).
Fig. 10. A photograph
of the test head.
Fig. 11. An axial section of the test head. (1) is the journal with holes used to measure pressure in the bearing clearance; (2) is the bush with capillary glands; (3) and (4) are covers forming oil collectors for outward flowing oil; (5) is the capillary insert; (6) is the case; (7) is the external pressure chamber.
SR
c
4 56.02+
Fig. 9. A scheme of the journal for investigation the measurements are shown in Table 2).
(the results of
(3) is a pusher sealed by means of a ring (4). This pusher, used together with a screw (5), is applied to set the minimum height of the clearance between the
36
A. Palzewicz
/ A hydrostatic
journal
bearing without pressure
chambers
between
sur$aces
TABLE 1. Results of the measurement of the journal for investigation Part of the journal
4
Angle (“)
0
of the D, and D, diameters
Section A
Section M
(mm)
(mm)
Section B (mm)
(bush)
45 90 13.5
56.00 56.02 56.01 56.01
56.01 56.02 56.03 56.03
56.02 56.02 56.02 56.02
DC (journal)
0 45 90 135
55.76 55.76 55.76 55.76
55.76 55.76 55.76 55.76
55.76 55.76 55.76 55.76
Fig. 12. A part of A-A section (from Fig. 11). (1) is the capillary insert; (2) the capillary hood (when inlet to the capillary is open the hood is out); (3) pusher; (4) O-ring; (5) pusher adjusting screw; (6) plug; (7) external oil chamber; (8) bearing clearance; (9) orifice.
bush and the journal. (6) is a cover allowing access to the screw (5). In the schematic shown in Fig. 9 the distribution of fixing sets SR at the test bearing bush can be seen. In section A-A of this schematic numbers (l-5) denote the outlets of holes situated in the bearing journal and used to measure oil pressure in the bearing clearance. Pressure measurement is carried out at a journal position fixed permanently with respect to the bush by means of the SR fixing sets. In order to rotate the journal by some angle respective to the bush it is sufficient to loosen one of SR sets in each fixing plane. The technique of oil pressure measurement in individual zones of the bearing clearance required the following procedure: (i) setting and fixing the journal in the bush in an appropriate position, with the initial clearance being set using the pusher and clearance gauge; (ii) opening of compressed oil access to the external chamber; (iii) reading out the oil pressure value in the clearance zones opposite to the measuring holes inlets in the journal; (iv) cutting off the oil access to the external chamber and then following the procedure required to rotate the journal with respect to the bush by a given angle without changing the journal and bush axis; (v) repeating the above sequence in order to attain a new measuring hole position. Exemplary results of measurements conducted both for the journal and the bush of dimensions shown in Table 1 and Fig. 13 are put together in Table 2. In the table heading constant values of experimental parameters are given and in rows l-5 the measured pressures are given in form of dimensional (upper part) and dimensionless values (lower part). A similar pres-
Fig. 13. A scheme for Table 1.
sure distribution in clearance zones opposite to holes (4) and (5) in d ica t es a parallel positioning of the bush and journal. The measured oil outflow along the bearing sides was Q= 156 cm3 s-l. In Fig. 14 the calculated pressure distribution of the oil in the clearance quarter is of the same dimensions and operating parameters as shown in Table 2. The relative eccentricity of the bearing is l=0.36 which corresponds to the S, =5260 N lift produced by the oil flow through the clearance and to the QC= 172 cm3 outflow through the side edges. S --I
5. Discussion
and conclusions
In the experiment presented above a satisfying conformity between the calculation results and those of measurements has been obtained. The divergence does not exceed 10-45%. This proves that the correct choice of simplifying assumptions was made when developing the computation model. In the experimental bearing presented, despite a uniform distribution of inlet orifices at the bush surface,
A. Palzewicz
TABLE 2. Exemplary
calculated
/A
hydrostatic
pressure
journal
distribution
bearing
without pressure
chambers
and results of measurements
between
of the pressure
surfaces
37
distribution
in slot of the journal
Number of a measuring orifice
Angle (“) 0
30
60
90
120
150
180
210
240
270
300
330
1
0.373 0.464
0.520 0.518
0.435 0.464
0.373 0.442
0.328 0.385
0.255 0.378
0.223 0.343
0.255 0.350
0.328 0.343
0.373 0.386
0.435 0.429
0.520 0.471
2
0.350 0.307
0.493 0.379
0.350 0.329
0.278 0.329
0.261 0.271
0.235 0.285
0.210 0.257
0.235 0.271
0.261 0.264
0.278 0.300
0.350 0.329
0.493 0.371
3
0.261 0.307
0.301 0.371
0.230 0.321
0.210 0.329
0.202 0.271
0.172 0.285
0.150 0.257
0.172 0.271
0.202 0.264
0.210 0.30
0.230 0.329
0.301 0.371
4
0.092 0.064
0.093 0.071
0.071 0.071
0.068 0.057
0.057 0.057
0.050 0.050
0.050 0.057
0.050 0.057
0.057 0.057
0.068 0.057
0.071 0.057
0.093 0.057
5
0.092 0.079
0.093 0.079
0.071 0.079
0.068 0.079
0.057 0.079
0.050 0.064
0.050 0.057
0.050 0.050
0.057 0.057
0.068 0.057
0.071 0.064
0.093 0.071
MPa and Table 1, n =0.058 Ns m-* and Fig. 9; Lk= 14 mm; Dk =0.5 Top lines are calculated values, lower lines are measured values.
P,=7
nm; H,,= 0.08 mm; P=P/P,
(dimensionless
inlets to the clearance can be set perpendicular oil delivery holes.
pressure).
to the
References D. Dowson, History of Tiibology, Langman, London and New York, 1979. F. T. Barwell, Eojskowanie, WNT, Warsaw, 1984. W. B. Rowe, Hydrostatic and Hybrid Bearing Design, Butterworth, London, 1983. A. Paliewicz, Hydrostatishe Radialgleitlager ohne Schmiennittehaschen, Tribo 88, 19th Int. Symp., Schmierungstechnik KarlMarx-Stadt. Bezkomorowa, Report 5 A. Paliewicz, Podpora Hydrostatycrna No. 25647, Gdansk PoIytechnic, 1988. 6 0. R. Lang and W. Steinhilper, Berechung und Konstruktion von Gleitlagem
Fig. 14. The calculated pressure distribution in oil in the clearance quarter of the same dimensions and operating parameters as those in Table 2: l=0.36; P=P/P,. -x-=visible pressure line; - * - = hidden pressure line; kIJ= oil outlet from bush in segment; 0, 0, 0, @ = trajectory of the measured orifice.
ineffectively utilizing the compressed oil energy, the journal-bush alignment force was found to be of a significant value. This force results from the pressure difference between individual zones of the bearing clearance due to oil flow between the external pressure chamber and the bearing side surfaces. The presented hydrostatic mechanism of carrying the journal when a machine is being started can be applied by modifying the design of bearings with hydrodynamic carrying capacity. This does not require any major reconstruction, as the pressure chamber and the glands can be situated at the bush side surfaces and the oil
mit Konstanten
und
Veranderlicher
Belastung
Springer-Verlag, Berlin, Heidelberg, New York, 1978. A. Palzewicz, BW-855280, unpublished paper, Gdansk Polytechnic, 1986. Computer Program, 1988. 8 A. Paliewicz, TARCZA3I 9 A. Paliewicz, SITO354, Computer Program, 1989. 10 A. Cameron, The Principles of Lubrication Longman Green, London, 1966.
Appendix:
B
DC 4
DP H
HO H k
Inax
Nomenclature
mean flow through the lateral walls of the discrete element width of the flat slot diameter of journal diameter of capillary gland diameter of bush thickness of slot minimum thickness of slot maximum thickness of slot dimensionless coefficient
38
A. Pakewicz
/ A hydrostatic
journal
length of flat slot length of exit hole length of capillary gland pressure out bearing pressure pressure in chamber oil flow source flow into element total oil outflow from the bearing oil outflow from capillary gland oil outflow from rand-flat slot
bearing without pressure
R RW RZ &
chambers
between
surfaces
radius inside radius outside radius bush aligning force
Greek symbols Al’,, AP2, Al’, difference
of pressures between inflow and outflow zones (l), (2), (3) (Fig. 2). pressure sink in capillary gland pressure sink in flat slot eccentricity ratio dynamic viscosity