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A hydrostatic bearing for high speed applications
A hydrostatic bearing for high speed applications The Total Cross Flow hydrostatic bearing M. E. Mohsin* This paper describes a hydrostatic bearing designed for high speed applications: the Total Cross Flow (TCF) bearing x . The design features of this bearing are discussed and compared with conventionally designed hydrostatic bearings. The TCF bearing offers a number of important meritorious properties which are essential for high and ultra-high speed applications
The need for high and ultra-high speedst has recently become an important factor in applying modern technology. For example, the use of exceptionally high speeds for metal cutting operations will be the key to boosting productivity, probably beyond evolutionary increments. Titanium is already being cut at 70 m/s and the ultimate goal is 600 m/s. The machines required to achieve such high cutting speeds will have spindles running in excess of 100 000 rev/min with diameters large enough to secure rigidity, essential for the required accuracy. Energy-storing as a measure of energy saving is another field calling for the use of high and ultra-high speeds. The recently introduced fly-wheel systems, especially when run at sufficiently high speeds, can prove to be much more economical and practical than any other existing system. Such fly-wheel systems use materials with substantially higher strength to weight ratios than steel so that much higher speeds can be attained. This will lead to a high increase in the amount of energy that can be stored in a given volume. Such high speed applications, and many others, require the use of well designed journal, thrust or linear bearings that can achieve the purpose for which they are designed together with • Minimum energy loss • Minimum wear and hence long operational life to avoid expensive overhauls • Maximum rigidity to ensure accuracy and smooth running • Reasonable temperature rise to secure accuracy without the use of expensive cooling equipment • Maximum stability and damping capacity to avoid excessive vibrations, especially when run at high or ultra-high speeds • Stability of sliding motion to avoid stick-slip which is detrimental to controlled positioning tHigh and ultra-high speeds refer, for the purpose of this paper, to peripheral speeds which can be attained by high rotary speeds and/or large diameters XBritish Patent Application No. 7917555 and corresponding applications elsewhere *Manufacturing and Machine Tools Division, Department of Mechanical Engineering, UMIST, PO Box 88, Manchester M60 IQD, UK
0301-679X/81/010047-08 $02.00 © 1981 IPC Business Press
Conventionally lubricated metal-to-metal contact bearings, such as sleeve, ball or roller bearings, as well as hydrodynamic bearings, usually need design alterations and/or running care when used under high speed conditions. For example, the use of lobed bores with either fixed-profile or tilted-pad hydrodynamic bearings is essential to prevent bearing-initiated whirl and laboratory-type care is sometimes essential in lubricating roller bearings under high speed conditions. In some applications, the short operational life of the bearing at high speed necessitates frequent expensive overhauls. Even with care, such bearings may not achieve fully all desirable characteristics. Unlike hydrodynamic bearings, hydrostatically lubricated bearing systems prevent metal-to-metal contact even at zero speed. The bearing floats the moving slide, by means of the pressurised fluid supplied from an external source, thus maintaining a positive clearance between the two moving surfaces. Such a bearing, when well designed, may be able to achieve most, if not all, the desirable characteristics mentioned above, even at high and ultra-high speed.
The hydrostal~c bearing under quasi-static conditions In many applications entailing quasi-static conditions, such as machine tool slideways, the design of hydrostatic bearings represents little difficulty. Many developments have been introduced to improve the performance I and facilitate the production 2 of such bearings. Design methods and techniques have been introduced to optimise bearing characteristics 3-~. The hydrostatic bearing is usually made up of a number of pads. Each pad has a recess in which the fluid is pressurised, under constant supply pressure, through a restrictor which allows the fluid bearing pressure in the recess to vary in order to balance the load on the pad. The fluid beating pressure is separated from the pressure of the surrounding environment (usually atmospheric) by the hydraulic resistance of the close clearance under the lands of the pad. Such lands are usually made up of a flat surface parallel to the supporting bearing surface. Under quasi-static conditions, pads with a high land width ratio have relatively low load carrying capacity but are characterised by a low flow rate and high damping capacity. A compromise is made between these three properties and a preferred land width ratio of 0.25 is commonly used under quasi-static conditionL A clearance of 2 (x 25/am) is usually
TRIBOLOGY international February 1981 47
Mohsin - A hydrostatic bearing for high speed applications
used, under such conditions, to compromise flow rate, machining tolerances, stiffness and damping capacity. A fluid of a kinematic viscosity around 75 x 10-6 m2/s at 25°C is most recommended, especially for machine tool slideways. Hydrostatic bearings, designed in this way, will show the following meritorious properties when used under quasistatic conditions:
Nomenclatu
B b e ]p h ho hp K Lp
• Vanishing coefficient of friction • High stiffness • High damping capacity • Long operational life (virtually no wear) • Consistency of location • High accuracy • High load carrying capacity
Pf Pp Pt p Pb Po Ps
The hydrostatic bearing under high speed conditions Frictional characteristics
Re
Under high speed conditions, hydrostatic bearings show improved characteristics, such as good stiffness at zero eccentricity and operational quietness. Unfortunately, under such conditions, the coefficient of friction does not vanish but grows with speed due tO 6 the pure laminar shearing of the fluid under the lands and the shearing of the fluid in the pressurised recesses which can be either laminar or turbulent. Fig I shows the velocity profile of the fluid under the close clearance as well as that inside the recess.
Close-ended recess (w~thout ERFS) . t
T2 u V y r tt p
re
Pad length Land width Eccentricity ratio Recess friction factor Land clearance Design clearance Recess depth Power ratio = Pt./Pp Recess length Land length Friction drag power Fluid pumping power Total power consumed by bearing Fluid pressure Recess pressure Mean recess pressure Fluid supply pressure Reynolds number Temperature at point 2 on the land (see Fig 2) Flow velocity Relative speed of bearing surfaces Distance from fixed surface Shear stress in fluid Absolute viscosity of fluid Fluid density
For the close clearance (lands), the flow is invariably laminar, hence is pure shear flow and the velocity profile is linear. Then
u = V(ylho)
(1)
and the shear stress is given by r o =/l (du/dy) = IJ(V/ho)
y--
T ~I ~
- - ~~, !
.......... - _
(2)
For the recess, the flow can either be laminar or turbulent, depending on the relative speed V. In the speed range for which the laminar flow prevails, the flow is of the Couette type for which the velocity pattern (Fig 1) is given by 6
Lo
/
u=(y/hp) [ V-(h 2/2/.0 (dp/dx) (1 -y/hp)] (3) Neglecting the end effects and assuming ho/h p < < 1, then
I
(dp/dx) = (Ap/Lp) I
and
Ap = 60 VLp/hp 2 Recess w=th ERFS
1
/ i
(4)
Ap represents the pressure gradient that creates the back flow required by the continuity condition. Such a pressure gradient can be high enough to cause negative gauge pressure near the recess leading edge. Consequent suction of air may lead to poor dynamic response and can cause bearing failure. The critical pressure gradient at which the pressure at the leading edge of the recess becomes atmospheric is given by APcr = 2p o = 6~ VcrLp/hp 2 Hence Vcr = Pohp2/31a Lp
Fig 1 b~ffect of ERFS on fluid flow inside recess
48
TRIBOLOGY international February 1981
(5)
Fig 2(a) shows the pressure distribution, as measured experimentally 7 , at the leading and trailing edges of the pad recess when an opposed multi-pad thrust bearing with flat lands is run at 1000 rev/min (corresponding to a maximum peripheral speed of 15 m/s).
Moh$in Io
From Equations (3) and (4),
u = (Vy/hp) [1-3(l-y/hp)]
(6)
and the shear stress under the recess is
L
rp = At ( du/dy)y=hp = 4 (At V/hp)
(7)
Comparing Equations (2) and (7), under laminar flow conditions, it is clear that the Couette type flow initiates shear stress, and hence drag power, four times that initiated by a linear velocity profile.
The top curve of Fig 3 shows the values of the recess friction factor fp as defined by Equation (8) and calculated from the experimental results obtained by Shinkle and Hornung 6. The figure shows also the value o f f p as determined theoretically by Ng and Pan and explained in the discussion at the end of Reference (6). D y n a m i c characteristics
Leodlng ecRe
o
c
~-~\
I 21
I 22
I I I I\1 25 25 27
4
@
~llF I l 1 1
I 19
14 15 1617 18
L
I 20
Trmhng e ~ e
•
d/
FIOI IOt~S /OOd:4 IO00rev/rr*n Des~gncleorcmce=lSx25/,m ~b,
C C
~_l/~fl i r iJ l
I
I 2 5 4
I
I
1
1 t I NI
,5 6 7 8 No external return flow
9 I01112
I5
/ / / / / / / / / / / / / / / / / / / / / / / ~J~-~/
a
L I-
12
Pod recess
////////////
Leodlng
~--
-~---- -~---
15 16 1718 d
I
19
20
i
~
22
23
~
~
-
25
27
Trailing edge
12
^
8
j/
4
I
0
-~---~------t
21
yrl
//I --~--.~-- Stat,oe~r~
Lo¢¢1= 4 71 toni or ;,L~,w.;land(L0/50~.4£
c ~ OOOmv/~nDe~.c.mnc.= S125pm~
I
I
I
I
1
I 2 3 4
I
5
6
7
8
I
l
L
9 10 II 12 15
WOh external return flow
,/,/,////////////////////.
b
~
/ /
I
/
/
Pad recess / / / /
/
/
/Aec~cdlng W) Shmkleand Ho¢flul~lII
%
//
•
u
i ;
.~
\
1o
1o2
i
io 3 Re
io 4
Io5
Fig 3 Friction factor fp for close-ended and ERFS recess
are being taken : the use of extremely narrow landis and the use of fluids with very low viscosities. Narrow lands will result in the reduction of the damping capacity due to the squeeze action under them, the damping coefficient being directly proportional to the cube of the land width. Reduced viscosity also means lower damping capacity being directly proportional to each other. This may result in the bearing showing poor dynamic response s'9
In an endeavour to reduce the drag power at high speeds under the lands of a hydrostatic bearing, two measures
0
JO-I I-- %
Close - ended recess (mthout ERFS)
I
rp = fp (Re~Z) (At V/hp) (8) where f_ is a recess friction factor to be established experimentallY.
8
~
~-.P'102
In the speed range for which turbulent flow prevails, the shear stress under the recess is 6
2
A hydrostatic bearing for high speed applications
/
Fig 2 Pressure distribution at leading and trailing edges for {a} a conventional hydrostatic bearing and (b) a total cross flow hydrostatic bearing
It has been shown a'9 that the dynamic stiffness of a hydrostatic bearing depends largely on the stiffness of the entrained fluid volume between the restrictor and the bearing film (the compressibility stiffness). Hence, for a certain pad geometry a minimum recess depth h_v will ensure maximum dynamic stiffness. However, in order to reduce the resonance amplitude through increasing the damping ratio, for a fixed bearing damping constant, a certain reduction of the compressibility stiffness may be required. Such a reduction will also secure a certain level for the stability of the bearing system against self-excited vibrations 9. Accordingly, for a fixed bearing design, the recess depth h_e should be tuned to give the compressibility stiffness that ensures the minimum resonance amplitude combined with the maximum dynamic stiffness at other frequencies. If such tuned recess depth contradicts with that required to ensure optimum recess frictional characteristics, other methods 9 are used to increase the compressibility stiffness without changing the recess depth. The churning action of the fluid inside the recess usually causes 'fluid foaming' which can substantially reduce the compressibility stiffness and impair the dynamic response of the bearing s. Turbulence may also increase such foaming and extreme turbulence can lead to complete bearing failure. H y b r i d action
Hydrostatic bearings with flat lands will initiate hydrodynamic effects which increase with the relative speed V and the eccentricity ratio e. Many investigators have shown that such hybrid action, although useful in increasing the load carrying capacity under high speeds and eccentricity ratios, will introduce a number of undesirable characteristics which can cause deterioration in bearing performance if not complete failure under high and ultra-
TRIBOLOGY
international
February
1981
49
Mohsin - A hydrostatic bearing for high speed applications
high speed conditions. Perhaps the most important of such detrimental characteristics are: • The onset of whirl tends to be aggravated by large hydrodynamic contributions, especially when combined with low hydrostatic stiffness and large mass 1~''2. On the other hand, it has been demonstrated that, in the absence of hydrodynamic effects, hydrostatic bearings, pressurised with incompressible fluids, are unconditionally stable • At higher eccentricity ratios, the hydrodynamic wedge has a marked effect on the pressure distribution over the lands (see Fig 2(a))and hence on the degree of cavitationT, 'a
Design techniques Most of the techniques used for the design of hydrostatic bearings under speed conditions use a process of optimisation of the total power consumed by the bearing 3-s . However, it seems that most such techniques, through the optimisation process, disregard the effect of the optimising parameters such as clearance, fluid viscosity, land width etc on the other important characteristics of the bearing such as its static stiffness, damping capacity, dynamic response, ability to dissipate heat generated etc. The optimisation process is, indeed, very complex due to the great number of variables and conditions of optimisation. When running at high or ultra-high speeds, even under optimised conditions of K = 1, the amount of heat generated can be too much for the beating conditions to stabilise at reasonable temperatures. As an example, the allowable beating area could be limited, thus resulting in a higher supply pressure and hence a lower rate of flow for
70
60
.
"x,
"x,
N
N
.
"x.
",,l
'
Fig 50rthotropic land the same pumping power as given by K = 1. A smaller bearing area with a reduced rate of flow can result in higher bearing temperatures which sometimes cannot be stabilised at reasonable levels. This can be illustrated by the following example in which an opposed multi-pad thrust bearing was tested 7 with speed = 1000 rev/min, supply pressure Ps = 50 bars and/fb = 0.2 (fiat lands). The bearing was optimised for K ~ 1 to give: clearance = 2(x 25/am), oil viscosity (Tellus 37) at design temperature of 40°C = 35 × 10-6 m2/s, maximum peripheral speed ~ 15 m/s, calculated friction power consumed by lands (PfL) = 5.8 HP, measured friction power consumed by bearing (Pf) --- 7.0 HP, calculated pumping power (Pp) = 6.2 HP and K = Pf/Pp = 1.13.
Fig 4 shows the maximum temperature of the bearing plotted against time as measured experimentally. After about eight minutes from the start, the bearing temperature reached 70°C and was still rising at the rate of 1.4°C/min. However, when the amount of power consumed by the circumferential lands was reduced by using orthotropic lands (part of the features of the Total Cross-Flow hydrostatic bearing which will be explained later), the bearing temperature stabilised at 55°C. All conditions were kept the same except the clearance = 1.5 (x 25pa'n), calculated friction power consumed by lands (PfL) = 2.5 HP, measured friction power consumed by bearing (Pf) = 4.5 HP, calculated pumping power (Pp) = 2.6 HP and K = Pf/Pp = 1.73. The ratio of the total power consumed by the bearing in the second case (orthotropic lands) to that in the first case (flat lands) is 0.54.
50
The total cross-flow hydrostatic bearing
_=
o E
40
40
30
30
~L
h F
li
20 ho
20
I 2
I
I
I
I
4
6
8
tO
.
I
I
I
12
14
t6
l°
18
Ttn~, rain
Fig 4 Rise of temperature with time for flat and orthotropic lands
50 TRIBOLOGY international February 1981
The Total Cross-Flow (TCF) hydrostatic bearing T M is an extemaUy pressurised bearing with design features to overcome most of the side effects of conventionally designed quasi-static hydrostatic bearings when used under high or ultra-high speed conditions. This is done by designing the beating in exactly the same manner as the well known conventional quasi-static hydrostatic bearing. The design method of such a bearing, as mentioned before, is simple and backed by wide practical experience. The following TCF design features are then added.
Orthotropic circumferential lends The circumferential lands of the beating are grooved (Fig 5) according to preferred profiles t7-19. The specific impedance of such lands to pressure flow is a minimum in the circumferential direction and a maximum in the axial or radial direction. Accordingly, such lands are called
Moh$in - A hydrostatic bearing for high speed applications 'orthotropic'. The impedance and drag characteristics for orthotropic lands, with different groove geometries and pitches ranging between 0.5 mm and 2.0 mm, are well illustrated and explained 1s'~9.
Table 1 Comparison of different land= (based on minimum power assumption)
Under high and ultra-high speed conditions, wide orthotropic lands offer many advantages 7,19 over narrow flat lands having enough width to give the same hydrostatic impedance. In the Appendix, the damping constant for orthotropic lands due to squeeze action has been calculated and compared with that for the narrow flat lands. It must be stated, however, that the analysis given in the Appendix, although it applies to flat thrust bearings, will need to be modified when applied to journal bearings to allow for the effect of opposed pads with common circumferential lands. Further work in this direction is now in progress.
Land
X,"
(1) Flat wide land 1.00 (2) Orthotropic wide land 1.60 (3) Flat narrow land 1.33
Land
The opposed multi-pad thrust bearing which was tested and reported ~'2° was optimised for the following land conditions: (1) flat wide land with land width ratio of 0.20; (2) orthotropic wide land with land width ratio of 0.20 and (3) flat narrow land with land width ratio of 0.09 to give the same impedance as the orthotropic land 2 . The following design conditions are used for the optimisation process: a fluid of Tellus 37 at 25°C, supply pressure Ps = 50 bars, maximum pocket pressure Po = 0.SPs = 40 bars and maximum speed = 2000 rev/min corresponding to a maximum peripheral speed of about 30 m/s.
Flat lands some width as O'thotropic
rev/rain
o
!
%.. o
iL
_oI ~4" =o!--2~.~] ~ . . .. . .. .. . .. L__.~-_--y~-]_
3_,
80
~ _ . . . . i_
J
40
////
/y/
ooo
20
~~'_-_-_~_~_ I
2
-i 3
i
I
i
I
T
I
4
.5
6
7
O
Clearance, h, x 25 /=rn
Fig 6 0 r t h o t r o p i c
versus narrow f l a t lands
Total power,
Xs"
C*"
Pt
1.00 1.48 0.18
1.00 0.61 0.90
(1) Flat wide land 1.00 (2) Orthotropic wide land 1.50 (3) Flat narrow land 1.29
*Assu l i n g equal recess area **The comparison applies only to the case of flat thrust bearings. The case o f inure,hi bearings will be the subject o f another paper
Fig 6 shows the power consumed by the bearing for different clearances, the top figure for a circumferential land according to case (1) above and the bottom figure according to cases (2) and (3).
External return flow system (ERFS)
== ¢== ~
Narrow flat lands (some impedance)//~s~
•- - - - , r - i
Damping constant,
It has been established from Equations (2) and (7), that under laminar flow conditions, the Couette type flow initiated in a closed-ended recess produces four times the drag resistance of a flow with linear velocity profile initiated in a recess with an ERFS.
Orthotroplc lands
•, ' \
Static stiffness,
///
7
•
60
1.00 0.58 0.85
Fig l compares the velocity profile of the drag flow inside a close-ended recess (Couette type flow) with that inside a recess having an external return flow conduit used to transfer the drag flow from the trailing edge of the recess back to its leading edge. The linear velocity profile resulting from the use of an external return flow system (ERFS) is similar to that in the close clearance under the lands. The only difference is that, because of the small ratio of the clearance to the depth of the recess, the flow under the lands is always laminar, unlike the flow in the recess which can be either laminar or turbulent.
•
2 0 0 0 rev/mm
Pt
. .
I00
Q. -r
C**
1.00 1.79 0.20
• They create a negligible level of hydrodynamic action ~, (see Fig 2(b)), thus avoiding all the associated undesirable characteristics and produce almost a pure hydrostatic bearing • Pads with orthotropic lands are less sensitive to tilt 'a49 and hence can adapt more to manufacturing errors and shaft bending, avoid land drying-up and cavitation
,
a:
20
Total power,
Tables 1 and 2 demonstrate the superiority of an orthotropic wide land over a flat narrow one of the same hnpedance not only in nearly having the total power consumed by the bearing, but in all other respects, too. Orthotropic lands have shown other useful characteristics such as:
120
2000
Damping constant,
Table 2 Comparison of different land= (based on K = 1)
The following example compares some of the characteristics of orthotropic lands of flat thrust bearings.
~OO -
Static stiffness,
Hirs 21 has discussed the frictional characteristics of the linear velocity profile drag flow, initiated in a recess with an ERFS, under laminar as well as turbulent conditions.
T R I B O L O G Y international February 1981
51
Moh$in - A hydrostatic bearing for high speed applications
!
The bottom curve of Fig 3 shows the values of the recess friction factor fp as given by Hirs for such conditions.
IO-I ~-
Table 3 shows a comparison between the frictional characteristics due to drag flow in a conventional recess (without ERFS) and that in a recess with an ERFS. It is clear from this table that: For.the same Re, V and h_, a recess with an ERFS will consume one quarter the ~rag frictional power of that consumed by a conventional recess when the flow in both cases is laminar. When the flow is turbulent, the power saving is even higher • For the same Re and recess drag friction (represented by to), a recess with an ERFS could have a depth one quarter that of a conventional recess and in the same time run at four times its relative speed V when the flow in both cases is laminar. When the flow is turbulent, even a shallower recess running at higher speeds could be used.
i Close-ended recess (wzthout ERFS)
•
i r
The ERFS has other useful and important results such as: Since there will be no back flow in the recess when using an ERFS, the pressure differential Ap between the leading and trailing edges will disappear (see Fig 2(b)) except for a negligible pressure differential required to drive the back flow in the return flow conduit. This will substantially reduce the possibility of cavitation as explained before • The ERFS results in a decrease in the amount of flow from one pad recess to the other across the axial or radial lands, llence, the possibility of air in-flow in the recesses will be reduced • There will be negligible churning action with the ERFS and the 'fluid foaming' will practically disappear •
Accord,ng to Ng ond POn
. . . . .
=o,°o0,o
....
o
~ 10-2
[
The second deduction shows that, for the same drag power consumption as a conventional recess, a recess with ERFS will run at much higher speeds without impairing the dynamic response of the bearing and at the same time give room for the 'dynamic turning' explained before. Fig 7 shows the friction factor fp plotted against the dimensionless recess depth hp/(hp)cr for the two cases of a conventional recess and one with an ERFS. It is clear from the figure that at/Lk' = 0.0066 for both recesses as an example, the conventional recess should be made 16.7 times as deep as the recess with an ERFS. In case fp needs to be lower, a much higher ratio will be required. Of course, the depth of the recess, and hence the entrained volume of fluid, is limited by the compressibility stiffness needed for an optimum dynamic response of the bearing.
~
~
Recess . , ' h ERFS
t 10-3L I 0 -I
[
I t
____[
. _ _
I 0
I0
hp /(hp )¢r Fig 7 Close-ended versus ERFS recess-depth ratio for the same drag power Such a flow will also increase the pumping power needed by the bearing and hence the minimum total power consumption. The cross-related pads, on the other hand, have the disadvantage that the fluid recirculation in the bearing may help raise the temperature of the fluid and hence of the bearing. Fig 8 shows an improved recess geometry in which the leading and trailing edges are made in the form of f'mgers which may have, in betweep them, circumferential atmospheric grooves that will allow cross-flow conditions T M of the pressure and drag flows. This type of recess geometry will also accommodate the ERFS and reduce the possibility of air in-flow into the recesses. It will reduce substantially the possibility of cavitation as a result of the edge-effect. Also, in case circumferential atmospheric grooves are used, such a geometry will decrease the amount of drag flow lost to the atmosphere and at the same time will help to stop the recirculation of the fluid, resulting in a cooler bearing.
Conclusions Improved recess geometry The axial or radial lands between the bearing recesses play an important role in the performance of high speed hydrostatic bearings. Two existing designs are now in use: the independent type pads in which axial atmospheric grooves separate the axial lands of adjacent pads and the crossrelated type pads in which the axial lands between the pads are continuous. The first type ensures that the pressure in one recess is not directly influenced by the flow of fluid from an adjacent recess. However, the presence of axial or radial atmospheric grooves may increase the possibility of air in-flow in the recesses. Under high speed conditions, the discharge of fluid ahead of the bearing • surface as it moves across the atmospheric axial grooves, or across the leading and trailing edges of the recesses (edge effect), can produce detrimental cavitation 22 .
52
TRIBOLOGY international February 1981
The Total Cross-Flow (TCF) hydrostatic bearing for high an~t ultra-high speed applications offers the following meritorious properties : •
It substantially reduces the friction coefficient under speed conditions, thus cutting the drag power losses of the bearing and ensuring fast temperature stabilisation at acceptable levels. This will also reduce the total minimum power consumed by the bearing to reasonable values • It practically eliminates the effect of pocket pressure differential and the possibility of land drying-up, thus reducing the possibility of bearing cavitation • It reduces the hydrodynamic effects to negligible values, nearly eliminating all the corresponding disadvantages of the hybrid action such as bearing-whirl and cavitation. The TCF bearing behaves almost as a pure hydrostatic
Mohsin - A hydrostatic bearing for high speed applications
• •
• •
bearing and hence, when pressurised by an incompressible fluid, is unconditionally stable The acquired meritorious characteristics do not lead to substantial reductions in stiffness or damping capacity It can be tuned to give optimum dynamic performance under working conditions by changing the compressibility stiffness without affecting the frictional characteristics It ensures higher capacity of heat dissipation and more uniform temperature distributions 7 It can be easily standardised
£N =/.F. £0
and WN = 8b#V£N3/h 3 = (1.F.)3 (8b/~v~o3/M)
If W is the load due to the squeeze action of a fiat rectangular plate with length 2 ~o then
w0/w= q.F.)
and
WN/W= (/.F.) 3
For an orthotropic plate with grooves 1.0/60/0.0 We/W= 0.438
and
WN/W= 0.085
For an orthotropic plate with grooves 2.0/60/0.0
Appendix
We/W=0.234
and
WN/W=O.OI3
Damping coefficient for orthotropic plates
Consider an orthotropic rectangular plate (Fig 9), with impedance factor 1.F., approaching a large surface with a relative constant velocity v. The ratio b/~ o is assumed large enough such that the flow will be unidirectional along the x-axis.
References 1. Moh~n M.E. The Use of Controlled Rcsttictots for Compensating Hydrosta tic Beatings. Advances hz Machine Tool Design and
Research, 1962, p. 429 Independent pod system
The flow through a differential slot of length dx is:
~llo6wSS {I Pressure flow ~ o I urog r"1o w \\
q = - (1/I.F.) (bh3/121a) (dp/dx) The volume of fluid being forced out through this differential slot is the volume being displaced by the part of the plate x as it approaches the lower flat surface or, assuming an incompressible flow proved to be a viable assumption for practical cases with recommended groove geometries,
ERFS conduits
Drog flow
Return flow
q=vbx ~rcumferentlol atmospheric grOOve
such that Cross- related pad system
vbx = - (1/l.F.) (bh3 / lZla) (dp/dx) or
p = I.F. (6/av/h 3) (£2o-X2) Return flow
Hence, the extra load due to the squeeze action of an orthotropic plate is
from E~FS
Wo = 2~ Op dx = 1. F. (8b/av £o 3/h 3 ) o
•IFS
condu=ts
For an equivalent narrow flat plate with the same impedance as the orthotropic plate
Fig 8 Improved geometry recess
L
7
Table 3 The effect of using an ERFS on the recess frictional characteristics
Case Type of No. recess
Re
V
hp
Relative characteristics fp. = r = r/_~__V f p $ V 2
1
2
Convent- (Re) o V o lanai
(hp) o
ERFS
(Re) o V 0
(hp) O
~-
~-'f o
Convent- (Re) o V o lanai
(hp) o
(fp)o
re
ERFS
(fp)o
2
l lfp) °
1 1 (Re) o n V o n(hp)o n(fp)o
For laminar conditions :n = 4 For turbulent conditions : n > 4
re
For the same (Re) o, V o and (hp)o:
1
(I")ERFS -
dx i
i
1
I
___,
n 70
For the same (Re) 6 and To: (V)ERFS
r O
x
I VelocLty v
= r/V o
1 (hp)ERFS=n(hp)o
T Fig 9 Squeeze action of orthotropic plates
TRIBOLOGY international February 1981
53
Mohsin - A hydrostatic bearing for high speedapplications 2. Hallstedt G. Standardised Hydrostatic Bearing Units. Proceedings Join t Conference on Externally Pressurised Bearings, L Mech. E., 1971, p.422
3. O'Donoghue J.P. and Rowe W.B. Hydrostatic Bearing Design. Tribology, 1969, 2(1), 25--71
4. Rowe W.B., O'Donoghue J.P. and Cameron A. Optimisation of Externally Pressurised Bearings for Minimum Power and Temperature Rise. Tribology, 1970, 3(3), 1 5 3 - 1 5 7 5. Loeb A.M. and Rippel H.C. Determination of Optimum Proportions for Hydrostatic Bearings. Trans. ASLE, 1958, 1,241 6. Shinkle J.N. and Hornung K.G. Frictional Characteristics of Liquid Hydrostatic Journal Beatings. Trans. ASME, Ser.D.Jnl o f Basic Eng., 1965, 87, 163 7. Mohsin M.E. and Sharratt A. The Behaviour of a Total Cross-Flow Hydrostatic Thrust Beating. To be presented at the 21st International MTDR Conference, Swansea, 1980
8. Mohsin M.E. and Morsi S.A. The Dynamic Stiffness of Controlled Hydrostatic Bearings. Trans. ASME, Jnl. o f Lubrication Tech., Paper No. 69-Lub.G. 1969
9. Opitz H., Bottcher R. and Effenberger W. Investigation on the Dynamic Behaviour of Hydrostatic Spindle-Beating Systems. Proc. lOth MTDR Conference, 1969, p.453
10. Ettles C.M.M. and O'Donoghue J.P. Laminar Recess Flow in Liquid Hydrostatic Beatings. Proc. Joint Conference on Externally Pressurised Bearings, L Me ch.E., 19 71, p. 215
11. Rowe W.B. and Stout K.J. Design of Hydrostatic Bearings for Exacting Applications. Proc. 13th International MTDR Con-
12. Davies P.B. Modes of Failure in Multirecess Hydrostatic Journal Bearings. Proe. l Oth International MTDR Conference, 1969, p. 425
13. O'Donoghue J.P., Rowe W.B. and H o o k e C.J. Computer Analysis of Externally Pressurised Journal Bearings. Proc. LMech.E. 1969, 184, 48 14. Opitz H. Pressure Pad Bearings. Proc. LMech.l':. ConJ~ on Lubrication and Wear, 1967. p.67
15. Mohsin M.E. Improvements in or Relating to Bearings. British Patent Application No. 791 7555, 1978
16. Mohsin M.E. Hydrostatische Querstromlager fiir Schnellaufende Gleitfuhrungen. Werkstatt und Betrieb. 1979. 11, 793 17. Mohsin M.E. and Shaheen M.M. Viscous Drag on a Plate Moving Along a Flooded Groove. To be published. 18. Mohsin M.E. The Total Cross Flow Hydrostatic Beating. Development Project htterim Reports, 1979, Manu]acturing and Machine Tools Division, Mech. Eng. Dept., UMIST, 2 and 3
19. Mohsin M.E. and Shartatt A. The Behaviour of llydrostatic Pads with Grooved Lands. Tribology International. b'ebntarv 1981, 14(1), 3 3 - 4 5
20. Mohsin M.E. The Total Cross Flow ttydrostatic Bearing. Development Project Interim Reports, 19 79, Manufacturing and Machbte Tools Division, Mech. Eng. Dept., UMIST. 4
21. Hits G.G. Design Directives for Turbulent Film Bearings. Proc. Joint Conference on Externally Pressurised Bearhzgs, LMech.E., 1971. p.262
22.Wilson R.W. Cavitation Damage in Plane Bearings. Proc. 1st Leeds-Lyon Symposium on Tribology, Leeds, 1974. p. 177
ference, 1972, p.119
Fundamentals of Tribology Edited by Nam. P. Suh and Nannaji Soka This is a report o f the proceedings of a conference held at MIT in June 1978 and contains approximately eighty papers arranged in sixteen groups: Introduction, Surface Topography, Physical Properties, Surface and Interfacial Phenomena, Friction, Wear Mechanisms, Thermo-mechanical Effects, Wear in Processing, Polymer Wear, Wear Monitoring, Wear Prevention, Boundary Lubrication, Elastohydrodynamic Lubrication, Systems Approach and finally Documentation and the Tribology Literature. Each group is headed by an invited keynote paper and some of the following papers in the group, and the limited discussion which is recorded, grow from and refer to these special papers. Books o f this kind can be judged on two standards. First, one can look at them simply as a report of the conference; in this respect the conference can be judged to have been a great success. Second, one can look at the published volume as a contribution to the literature; in this light one can ask to what extent the book will be used in, say, ten years' time. It is this latter function upon which it is right to concentrate this review.
54
In his introductory paper, Douglas Scott points out that entries in the tribological literature are now running at 7000 papers, or so, per year. One must therefore ask what value this volume has in providing a useful and discriminating summary o f the state of the subject in 1976. This is an important question because at a price of more than £50 the main home for this b o o k will be on the shelves of libraries. The answer to the central question posed above is a mixed one. The book is a far more sprawling and discursive discussion than the superb series of Interdisciplinary Discussions sponsored by NASA and edited by the late P.M.Ku. (but judging a volume by P.M.'s superb standards is taking a very hard line). There is much valuable material here. For example, the session on Surface Topography, headed by a fairly comprehensive review by Whitehouse, confirms this reviewer's view o f a subject o f a superbly sophisticated theory still awaiting some solid triboiogical justification. As the list o f paper groupings given above indicates the subject material is strongly biassed towards wear in all
TRIBOLOGY international February 1981
its aspects. This is a welcome change for that Cinderella of the tribological disciplines, but it means that the volume as a whole is not totally representative of tribology in 1976. The papers themselves vary widely in the extent to which they are either a sound survey o f existing knowledge or a sustained and inspired attempt to re-interpret it. This is, of course, inevitable but I missed in this volume of more than 1200 pages the appearance of many startling or thought provoking ideas. I was considerably more excited to read the new review of wear by Dr Tom Childs*. The critical elements in the above review are, perhaps, making excessive demands of a volume of this type. As a summary of large parts of tribology in 1976, and in particular as a summary of many aspects o f wear, it will sit on my bookshelf, among many others, for many years to come. It will provide a very valuable reference, bearing in mind the appearance of the 7000 papers per year to which we referred above. d . F. A r c h a r d
*Childs T.H.C. The Sliding Wear Mechanisms of Metals, Mainly Steels. Tribology International, 1980, 13(6), 285 293 Published by M I T Press, 28 Carleton Street, Cambridge, MA 02142, USA
The need for high and ultra-high speedst has recently become an important factor in applying modern technology. For example, the use of exceptionally high speeds for metal cutting operations will be the key to boosting productivity, probably beyond evolutionary increments. Titanium is already being cut at 70 m/s and the ultimate goal is 600 m/s. The machines required to achieve such high cutting speeds will have spindles running in excess of 100 000 rev/min with diameters large enough to secure rigidity, essential for the required accuracy. Energy-storing as a measure of energy saving is another field calling for the use of high and ultra-high speeds. The recently introduced fly-wheel systems, especially when run at sufficiently high speeds, can prove to be much more economical and practical than any other existing system. Such fly-wheel systems use materials with substantially higher strength to weight ratios than steel so that much higher speeds can be attained. This will lead to a high increase in the amount of energy that can be stored in a given volume. Such high speed applications, and many others, require the use of well designed journal, thrust or linear bearings that can achieve the purpose for which they are designed together with • Minimum energy loss • Minimum wear and hence long operational life to avoid expensive overhauls • Maximum rigidity to ensure accuracy and smooth running • Reasonable temperature rise to secure accuracy without the use of expensive cooling equipment • Maximum stability and damping capacity to avoid excessive vibrations, especially when run at high or ultra-high speeds • Stability of sliding motion to avoid stick-slip which is detrimental to controlled positioning tHigh and ultra-high speeds refer, for the purpose of this paper, to peripheral speeds which can be attained by high rotary speeds and/or large diameters XBritish Patent Application No. 7917555 and corresponding applications elsewhere *Manufacturing and Machine Tools Division, Department of Mechanical Engineering, UMIST, PO Box 88, Manchester M60 IQD, UK
0301-679X/81/010047-08 $02.00 © 1981 IPC Business Press
Conventionally lubricated metal-to-metal contact bearings, such as sleeve, ball or roller bearings, as well as hydrodynamic bearings, usually need design alterations and/or running care when used under high speed conditions. For example, the use of lobed bores with either fixed-profile or tilted-pad hydrodynamic bearings is essential to prevent bearing-initiated whirl and laboratory-type care is sometimes essential in lubricating roller bearings under high speed conditions. In some applications, the short operational life of the bearing at high speed necessitates frequent expensive overhauls. Even with care, such bearings may not achieve fully all desirable characteristics. Unlike hydrodynamic bearings, hydrostatically lubricated bearing systems prevent metal-to-metal contact even at zero speed. The bearing floats the moving slide, by means of the pressurised fluid supplied from an external source, thus maintaining a positive clearance between the two moving surfaces. Such a bearing, when well designed, may be able to achieve most, if not all, the desirable characteristics mentioned above, even at high and ultra-high speed.
The hydrostal~c bearing under quasi-static conditions In many applications entailing quasi-static conditions, such as machine tool slideways, the design of hydrostatic bearings represents little difficulty. Many developments have been introduced to improve the performance I and facilitate the production 2 of such bearings. Design methods and techniques have been introduced to optimise bearing characteristics 3-~. The hydrostatic bearing is usually made up of a number of pads. Each pad has a recess in which the fluid is pressurised, under constant supply pressure, through a restrictor which allows the fluid bearing pressure in the recess to vary in order to balance the load on the pad. The fluid beating pressure is separated from the pressure of the surrounding environment (usually atmospheric) by the hydraulic resistance of the close clearance under the lands of the pad. Such lands are usually made up of a flat surface parallel to the supporting bearing surface. Under quasi-static conditions, pads with a high land width ratio have relatively low load carrying capacity but are characterised by a low flow rate and high damping capacity. A compromise is made between these three properties and a preferred land width ratio of 0.25 is commonly used under quasi-static conditionL A clearance of 2 (x 25/am) is usually
TRIBOLOGY international February 1981 47
Mohsin - A hydrostatic bearing for high speed applications
used, under such conditions, to compromise flow rate, machining tolerances, stiffness and damping capacity. A fluid of a kinematic viscosity around 75 x 10-6 m2/s at 25°C is most recommended, especially for machine tool slideways. Hydrostatic bearings, designed in this way, will show the following meritorious properties when used under quasistatic conditions:
Nomenclatu
B b e ]p h ho hp K Lp
• Vanishing coefficient of friction • High stiffness • High damping capacity • Long operational life (virtually no wear) • Consistency of location • High accuracy • High load carrying capacity
Pf Pp Pt p Pb Po Ps
The hydrostatic bearing under high speed conditions Frictional characteristics
Re
Under high speed conditions, hydrostatic bearings show improved characteristics, such as good stiffness at zero eccentricity and operational quietness. Unfortunately, under such conditions, the coefficient of friction does not vanish but grows with speed due tO 6 the pure laminar shearing of the fluid under the lands and the shearing of the fluid in the pressurised recesses which can be either laminar or turbulent. Fig I shows the velocity profile of the fluid under the close clearance as well as that inside the recess.
Close-ended recess (w~thout ERFS) . t
T2 u V y r tt p
re
Pad length Land width Eccentricity ratio Recess friction factor Land clearance Design clearance Recess depth Power ratio = Pt./Pp Recess length Land length Friction drag power Fluid pumping power Total power consumed by bearing Fluid pressure Recess pressure Mean recess pressure Fluid supply pressure Reynolds number Temperature at point 2 on the land (see Fig 2) Flow velocity Relative speed of bearing surfaces Distance from fixed surface Shear stress in fluid Absolute viscosity of fluid Fluid density
For the close clearance (lands), the flow is invariably laminar, hence is pure shear flow and the velocity profile is linear. Then
u = V(ylho)
(1)
and the shear stress is given by r o =/l (du/dy) = IJ(V/ho)
y--
T ~I ~
- - ~~, !
.......... - _
(2)
For the recess, the flow can either be laminar or turbulent, depending on the relative speed V. In the speed range for which the laminar flow prevails, the flow is of the Couette type for which the velocity pattern (Fig 1) is given by 6
Lo
/
u=(y/hp) [ V-(h 2/2/.0 (dp/dx) (1 -y/hp)] (3) Neglecting the end effects and assuming ho/h p < < 1, then
I
(dp/dx) = (Ap/Lp) I
and
Ap = 60 VLp/hp 2 Recess w=th ERFS
1
/ i
(4)
Ap represents the pressure gradient that creates the back flow required by the continuity condition. Such a pressure gradient can be high enough to cause negative gauge pressure near the recess leading edge. Consequent suction of air may lead to poor dynamic response and can cause bearing failure. The critical pressure gradient at which the pressure at the leading edge of the recess becomes atmospheric is given by APcr = 2p o = 6~ VcrLp/hp 2 Hence Vcr = Pohp2/31a Lp
Fig 1 b~ffect of ERFS on fluid flow inside recess
48
TRIBOLOGY international February 1981
(5)
Fig 2(a) shows the pressure distribution, as measured experimentally 7 , at the leading and trailing edges of the pad recess when an opposed multi-pad thrust bearing with flat lands is run at 1000 rev/min (corresponding to a maximum peripheral speed of 15 m/s).
Moh$in Io
From Equations (3) and (4),
u = (Vy/hp) [1-3(l-y/hp)]
(6)
and the shear stress under the recess is
L
rp = At ( du/dy)y=hp = 4 (At V/hp)
(7)
Comparing Equations (2) and (7), under laminar flow conditions, it is clear that the Couette type flow initiates shear stress, and hence drag power, four times that initiated by a linear velocity profile.
The top curve of Fig 3 shows the values of the recess friction factor fp as defined by Equation (8) and calculated from the experimental results obtained by Shinkle and Hornung 6. The figure shows also the value o f f p as determined theoretically by Ng and Pan and explained in the discussion at the end of Reference (6). D y n a m i c characteristics
Leodlng ecRe
o
c
~-~\
I 21
I 22
I I I I\1 25 25 27
4
@
~llF I l 1 1
I 19
14 15 1617 18
L
I 20
Trmhng e ~ e
•
d/
FIOI IOt~S /OOd:4 IO00rev/rr*n Des~gncleorcmce=lSx25/,m ~b,
C C
~_l/~fl i r iJ l
I
I 2 5 4
I
I
1
1 t I NI
,5 6 7 8 No external return flow
9 I01112
I5
/ / / / / / / / / / / / / / / / / / / / / / / ~J~-~/
a
L I-
12
Pod recess
////////////
Leodlng
~--
-~---- -~---
15 16 1718 d
I
19
20
i
~
22
23
~
~
-
25
27
Trailing edge
12
^
8
j/
4
I
0
-~---~------t
21
yrl
//I --~--.~-- Stat,oe~r~
Lo¢¢1= 4 71 toni or ;,L~,w.;land(L0/50~.4£
c ~ OOOmv/~nDe~.c.mnc.= S125pm~
I
I
I
I
1
I 2 3 4
I
5
6
7
8
I
l
L
9 10 II 12 15
WOh external return flow
,/,/,////////////////////.
b
~
/ /
I
/
/
Pad recess / / / /
/
/
/Aec~cdlng W) Shmkleand Ho¢flul~lII
%
//
•
u
i ;
.~
\
1o
1o2
i
io 3 Re
io 4
Io5
Fig 3 Friction factor fp for close-ended and ERFS recess
are being taken : the use of extremely narrow landis and the use of fluids with very low viscosities. Narrow lands will result in the reduction of the damping capacity due to the squeeze action under them, the damping coefficient being directly proportional to the cube of the land width. Reduced viscosity also means lower damping capacity being directly proportional to each other. This may result in the bearing showing poor dynamic response s'9
In an endeavour to reduce the drag power at high speeds under the lands of a hydrostatic bearing, two measures
0
JO-I I-- %
Close - ended recess (mthout ERFS)
I
rp = fp (Re~Z) (At V/hp) (8) where f_ is a recess friction factor to be established experimentallY.
8
~
~-.P'102
In the speed range for which turbulent flow prevails, the shear stress under the recess is 6
2
A hydrostatic bearing for high speed applications
/
Fig 2 Pressure distribution at leading and trailing edges for {a} a conventional hydrostatic bearing and (b) a total cross flow hydrostatic bearing
It has been shown a'9 that the dynamic stiffness of a hydrostatic bearing depends largely on the stiffness of the entrained fluid volume between the restrictor and the bearing film (the compressibility stiffness). Hence, for a certain pad geometry a minimum recess depth h_v will ensure maximum dynamic stiffness. However, in order to reduce the resonance amplitude through increasing the damping ratio, for a fixed bearing damping constant, a certain reduction of the compressibility stiffness may be required. Such a reduction will also secure a certain level for the stability of the bearing system against self-excited vibrations 9. Accordingly, for a fixed bearing design, the recess depth h_e should be tuned to give the compressibility stiffness that ensures the minimum resonance amplitude combined with the maximum dynamic stiffness at other frequencies. If such tuned recess depth contradicts with that required to ensure optimum recess frictional characteristics, other methods 9 are used to increase the compressibility stiffness without changing the recess depth. The churning action of the fluid inside the recess usually causes 'fluid foaming' which can substantially reduce the compressibility stiffness and impair the dynamic response of the bearing s. Turbulence may also increase such foaming and extreme turbulence can lead to complete bearing failure. H y b r i d action
Hydrostatic bearings with flat lands will initiate hydrodynamic effects which increase with the relative speed V and the eccentricity ratio e. Many investigators have shown that such hybrid action, although useful in increasing the load carrying capacity under high speeds and eccentricity ratios, will introduce a number of undesirable characteristics which can cause deterioration in bearing performance if not complete failure under high and ultra-
TRIBOLOGY
international
February
1981
49
Mohsin - A hydrostatic bearing for high speed applications
high speed conditions. Perhaps the most important of such detrimental characteristics are: • The onset of whirl tends to be aggravated by large hydrodynamic contributions, especially when combined with low hydrostatic stiffness and large mass 1~''2. On the other hand, it has been demonstrated that, in the absence of hydrodynamic effects, hydrostatic bearings, pressurised with incompressible fluids, are unconditionally stable • At higher eccentricity ratios, the hydrodynamic wedge has a marked effect on the pressure distribution over the lands (see Fig 2(a))and hence on the degree of cavitationT, 'a
Design techniques Most of the techniques used for the design of hydrostatic bearings under speed conditions use a process of optimisation of the total power consumed by the bearing 3-s . However, it seems that most such techniques, through the optimisation process, disregard the effect of the optimising parameters such as clearance, fluid viscosity, land width etc on the other important characteristics of the bearing such as its static stiffness, damping capacity, dynamic response, ability to dissipate heat generated etc. The optimisation process is, indeed, very complex due to the great number of variables and conditions of optimisation. When running at high or ultra-high speeds, even under optimised conditions of K = 1, the amount of heat generated can be too much for the beating conditions to stabilise at reasonable temperatures. As an example, the allowable beating area could be limited, thus resulting in a higher supply pressure and hence a lower rate of flow for
70
60
.
"x,
"x,
N
N
.
"x.
",,l
'
Fig 50rthotropic land the same pumping power as given by K = 1. A smaller bearing area with a reduced rate of flow can result in higher bearing temperatures which sometimes cannot be stabilised at reasonable levels. This can be illustrated by the following example in which an opposed multi-pad thrust bearing was tested 7 with speed = 1000 rev/min, supply pressure Ps = 50 bars and/fb = 0.2 (fiat lands). The bearing was optimised for K ~ 1 to give: clearance = 2(x 25/am), oil viscosity (Tellus 37) at design temperature of 40°C = 35 × 10-6 m2/s, maximum peripheral speed ~ 15 m/s, calculated friction power consumed by lands (PfL) = 5.8 HP, measured friction power consumed by bearing (Pf) --- 7.0 HP, calculated pumping power (Pp) = 6.2 HP and K = Pf/Pp = 1.13.
Fig 4 shows the maximum temperature of the bearing plotted against time as measured experimentally. After about eight minutes from the start, the bearing temperature reached 70°C and was still rising at the rate of 1.4°C/min. However, when the amount of power consumed by the circumferential lands was reduced by using orthotropic lands (part of the features of the Total Cross-Flow hydrostatic bearing which will be explained later), the bearing temperature stabilised at 55°C. All conditions were kept the same except the clearance = 1.5 (x 25pa'n), calculated friction power consumed by lands (PfL) = 2.5 HP, measured friction power consumed by bearing (Pf) = 4.5 HP, calculated pumping power (Pp) = 2.6 HP and K = Pf/Pp = 1.73. The ratio of the total power consumed by the bearing in the second case (orthotropic lands) to that in the first case (flat lands) is 0.54.
50
The total cross-flow hydrostatic bearing
_=
o E
40
40
30
30
~L
h F
li
20 ho
20
I 2
I
I
I
I
4
6
8
tO
.
I
I
I
12
14
t6
l°
18
Ttn~, rain
Fig 4 Rise of temperature with time for flat and orthotropic lands
50 TRIBOLOGY international February 1981
The Total Cross-Flow (TCF) hydrostatic bearing T M is an extemaUy pressurised bearing with design features to overcome most of the side effects of conventionally designed quasi-static hydrostatic bearings when used under high or ultra-high speed conditions. This is done by designing the beating in exactly the same manner as the well known conventional quasi-static hydrostatic bearing. The design method of such a bearing, as mentioned before, is simple and backed by wide practical experience. The following TCF design features are then added.
Orthotropic circumferential lends The circumferential lands of the beating are grooved (Fig 5) according to preferred profiles t7-19. The specific impedance of such lands to pressure flow is a minimum in the circumferential direction and a maximum in the axial or radial direction. Accordingly, such lands are called
Moh$in - A hydrostatic bearing for high speed applications 'orthotropic'. The impedance and drag characteristics for orthotropic lands, with different groove geometries and pitches ranging between 0.5 mm and 2.0 mm, are well illustrated and explained 1s'~9.
Table 1 Comparison of different land= (based on minimum power assumption)
Under high and ultra-high speed conditions, wide orthotropic lands offer many advantages 7,19 over narrow flat lands having enough width to give the same hydrostatic impedance. In the Appendix, the damping constant for orthotropic lands due to squeeze action has been calculated and compared with that for the narrow flat lands. It must be stated, however, that the analysis given in the Appendix, although it applies to flat thrust bearings, will need to be modified when applied to journal bearings to allow for the effect of opposed pads with common circumferential lands. Further work in this direction is now in progress.
Land
X,"
(1) Flat wide land 1.00 (2) Orthotropic wide land 1.60 (3) Flat narrow land 1.33
Land
The opposed multi-pad thrust bearing which was tested and reported ~'2° was optimised for the following land conditions: (1) flat wide land with land width ratio of 0.20; (2) orthotropic wide land with land width ratio of 0.20 and (3) flat narrow land with land width ratio of 0.09 to give the same impedance as the orthotropic land 2 . The following design conditions are used for the optimisation process: a fluid of Tellus 37 at 25°C, supply pressure Ps = 50 bars, maximum pocket pressure Po = 0.SPs = 40 bars and maximum speed = 2000 rev/min corresponding to a maximum peripheral speed of about 30 m/s.
Flat lands some width as O'thotropic
rev/rain
o
!
%.. o
iL
_oI ~4" =o!--2~.~] ~ . . .. . .. .. . .. L__.~-_--y~-]_
3_,
80
~ _ . . . . i_
J
40
////
/y/
ooo
20
~~'_-_-_~_~_ I
2
-i 3
i
I
i
I
T
I
4
.5
6
7
O
Clearance, h, x 25 /=rn
Fig 6 0 r t h o t r o p i c
versus narrow f l a t lands
Total power,
Xs"
C*"
Pt
1.00 1.48 0.18
1.00 0.61 0.90
(1) Flat wide land 1.00 (2) Orthotropic wide land 1.50 (3) Flat narrow land 1.29
*Assu l i n g equal recess area **The comparison applies only to the case of flat thrust bearings. The case o f inure,hi bearings will be the subject o f another paper
Fig 6 shows the power consumed by the bearing for different clearances, the top figure for a circumferential land according to case (1) above and the bottom figure according to cases (2) and (3).
External return flow system (ERFS)
== ¢== ~
Narrow flat lands (some impedance)//~s~
•- - - - , r - i
Damping constant,
It has been established from Equations (2) and (7), that under laminar flow conditions, the Couette type flow initiated in a closed-ended recess produces four times the drag resistance of a flow with linear velocity profile initiated in a recess with an ERFS.
Orthotroplc lands
•, ' \
Static stiffness,
///
7
•
60
1.00 0.58 0.85
Fig l compares the velocity profile of the drag flow inside a close-ended recess (Couette type flow) with that inside a recess having an external return flow conduit used to transfer the drag flow from the trailing edge of the recess back to its leading edge. The linear velocity profile resulting from the use of an external return flow system (ERFS) is similar to that in the close clearance under the lands. The only difference is that, because of the small ratio of the clearance to the depth of the recess, the flow under the lands is always laminar, unlike the flow in the recess which can be either laminar or turbulent.
•
2 0 0 0 rev/mm
Pt
. .
I00
Q. -r
C**
1.00 1.79 0.20
• They create a negligible level of hydrodynamic action ~, (see Fig 2(b)), thus avoiding all the associated undesirable characteristics and produce almost a pure hydrostatic bearing • Pads with orthotropic lands are less sensitive to tilt 'a49 and hence can adapt more to manufacturing errors and shaft bending, avoid land drying-up and cavitation
,
a:
20
Total power,
Tables 1 and 2 demonstrate the superiority of an orthotropic wide land over a flat narrow one of the same hnpedance not only in nearly having the total power consumed by the bearing, but in all other respects, too. Orthotropic lands have shown other useful characteristics such as:
120
2000
Damping constant,
Table 2 Comparison of different land= (based on K = 1)
The following example compares some of the characteristics of orthotropic lands of flat thrust bearings.
~OO -
Static stiffness,
Hirs 21 has discussed the frictional characteristics of the linear velocity profile drag flow, initiated in a recess with an ERFS, under laminar as well as turbulent conditions.
T R I B O L O G Y international February 1981
51
Moh$in - A hydrostatic bearing for high speed applications
!
The bottom curve of Fig 3 shows the values of the recess friction factor fp as given by Hirs for such conditions.
IO-I ~-
Table 3 shows a comparison between the frictional characteristics due to drag flow in a conventional recess (without ERFS) and that in a recess with an ERFS. It is clear from this table that: For.the same Re, V and h_, a recess with an ERFS will consume one quarter the ~rag frictional power of that consumed by a conventional recess when the flow in both cases is laminar. When the flow is turbulent, the power saving is even higher • For the same Re and recess drag friction (represented by to), a recess with an ERFS could have a depth one quarter that of a conventional recess and in the same time run at four times its relative speed V when the flow in both cases is laminar. When the flow is turbulent, even a shallower recess running at higher speeds could be used.
i Close-ended recess (wzthout ERFS)
•
i r
The ERFS has other useful and important results such as: Since there will be no back flow in the recess when using an ERFS, the pressure differential Ap between the leading and trailing edges will disappear (see Fig 2(b)) except for a negligible pressure differential required to drive the back flow in the return flow conduit. This will substantially reduce the possibility of cavitation as explained before • The ERFS results in a decrease in the amount of flow from one pad recess to the other across the axial or radial lands, llence, the possibility of air in-flow in the recesses will be reduced • There will be negligible churning action with the ERFS and the 'fluid foaming' will practically disappear •
Accord,ng to Ng ond POn
. . . . .
=o,°o0,o
....
o
~ 10-2
[
The second deduction shows that, for the same drag power consumption as a conventional recess, a recess with ERFS will run at much higher speeds without impairing the dynamic response of the bearing and at the same time give room for the 'dynamic turning' explained before. Fig 7 shows the friction factor fp plotted against the dimensionless recess depth hp/(hp)cr for the two cases of a conventional recess and one with an ERFS. It is clear from the figure that at/Lk' = 0.0066 for both recesses as an example, the conventional recess should be made 16.7 times as deep as the recess with an ERFS. In case fp needs to be lower, a much higher ratio will be required. Of course, the depth of the recess, and hence the entrained volume of fluid, is limited by the compressibility stiffness needed for an optimum dynamic response of the bearing.
~
~
Recess . , ' h ERFS
t 10-3L I 0 -I
[
I t
____[
. _ _
I 0
I0
hp /(hp )¢r Fig 7 Close-ended versus ERFS recess-depth ratio for the same drag power Such a flow will also increase the pumping power needed by the bearing and hence the minimum total power consumption. The cross-related pads, on the other hand, have the disadvantage that the fluid recirculation in the bearing may help raise the temperature of the fluid and hence of the bearing. Fig 8 shows an improved recess geometry in which the leading and trailing edges are made in the form of f'mgers which may have, in betweep them, circumferential atmospheric grooves that will allow cross-flow conditions T M of the pressure and drag flows. This type of recess geometry will also accommodate the ERFS and reduce the possibility of air in-flow into the recesses. It will reduce substantially the possibility of cavitation as a result of the edge-effect. Also, in case circumferential atmospheric grooves are used, such a geometry will decrease the amount of drag flow lost to the atmosphere and at the same time will help to stop the recirculation of the fluid, resulting in a cooler bearing.
Conclusions Improved recess geometry The axial or radial lands between the bearing recesses play an important role in the performance of high speed hydrostatic bearings. Two existing designs are now in use: the independent type pads in which axial atmospheric grooves separate the axial lands of adjacent pads and the crossrelated type pads in which the axial lands between the pads are continuous. The first type ensures that the pressure in one recess is not directly influenced by the flow of fluid from an adjacent recess. However, the presence of axial or radial atmospheric grooves may increase the possibility of air in-flow in the recesses. Under high speed conditions, the discharge of fluid ahead of the bearing • surface as it moves across the atmospheric axial grooves, or across the leading and trailing edges of the recesses (edge effect), can produce detrimental cavitation 22 .
52
TRIBOLOGY international February 1981
The Total Cross-Flow (TCF) hydrostatic bearing for high an~t ultra-high speed applications offers the following meritorious properties : •
It substantially reduces the friction coefficient under speed conditions, thus cutting the drag power losses of the bearing and ensuring fast temperature stabilisation at acceptable levels. This will also reduce the total minimum power consumed by the bearing to reasonable values • It practically eliminates the effect of pocket pressure differential and the possibility of land drying-up, thus reducing the possibility of bearing cavitation • It reduces the hydrodynamic effects to negligible values, nearly eliminating all the corresponding disadvantages of the hybrid action such as bearing-whirl and cavitation. The TCF bearing behaves almost as a pure hydrostatic
Mohsin - A hydrostatic bearing for high speed applications
• •
• •
bearing and hence, when pressurised by an incompressible fluid, is unconditionally stable The acquired meritorious characteristics do not lead to substantial reductions in stiffness or damping capacity It can be tuned to give optimum dynamic performance under working conditions by changing the compressibility stiffness without affecting the frictional characteristics It ensures higher capacity of heat dissipation and more uniform temperature distributions 7 It can be easily standardised
£N =/.F. £0
and WN = 8b#V£N3/h 3 = (1.F.)3 (8b/~v~o3/M)
If W is the load due to the squeeze action of a fiat rectangular plate with length 2 ~o then
w0/w= q.F.)
and
WN/W= (/.F.) 3
For an orthotropic plate with grooves 1.0/60/0.0 We/W= 0.438
and
WN/W= 0.085
For an orthotropic plate with grooves 2.0/60/0.0
Appendix
We/W=0.234
and
WN/W=O.OI3
Damping coefficient for orthotropic plates
Consider an orthotropic rectangular plate (Fig 9), with impedance factor 1.F., approaching a large surface with a relative constant velocity v. The ratio b/~ o is assumed large enough such that the flow will be unidirectional along the x-axis.
References 1. Moh~n M.E. The Use of Controlled Rcsttictots for Compensating Hydrosta tic Beatings. Advances hz Machine Tool Design and
Research, 1962, p. 429 Independent pod system
The flow through a differential slot of length dx is:
~llo6wSS {I Pressure flow ~ o I urog r"1o w \\
q = - (1/I.F.) (bh3/121a) (dp/dx) The volume of fluid being forced out through this differential slot is the volume being displaced by the part of the plate x as it approaches the lower flat surface or, assuming an incompressible flow proved to be a viable assumption for practical cases with recommended groove geometries,
ERFS conduits
Drog flow
Return flow
q=vbx ~rcumferentlol atmospheric grOOve
such that Cross- related pad system
vbx = - (1/l.F.) (bh3 / lZla) (dp/dx) or
p = I.F. (6/av/h 3) (£2o-X2) Return flow
Hence, the extra load due to the squeeze action of an orthotropic plate is
from E~FS
Wo = 2~ Op dx = 1. F. (8b/av £o 3/h 3 ) o
•IFS
condu=ts
For an equivalent narrow flat plate with the same impedance as the orthotropic plate
Fig 8 Improved geometry recess
L
7
Table 3 The effect of using an ERFS on the recess frictional characteristics
Case Type of No. recess
Re
V
hp
Relative characteristics fp. = r = r/_~__V f p $ V 2
1
2
Convent- (Re) o V o lanai
(hp) o
ERFS
(Re) o V 0
(hp) O
~-
~-'f o
Convent- (Re) o V o lanai
(hp) o
(fp)o
re
ERFS
(fp)o
2
l lfp) °
1 1 (Re) o n V o n(hp)o n(fp)o
For laminar conditions :n = 4 For turbulent conditions : n > 4
re
For the same (Re) o, V o and (hp)o:
1
(I")ERFS -
dx i
i
1
I
___,
n 70
For the same (Re) 6 and To: (V)ERFS
r O
x
I VelocLty v
= r/V o
1 (hp)ERFS=n(hp)o
T Fig 9 Squeeze action of orthotropic plates
TRIBOLOGY international February 1981
53
Mohsin - A hydrostatic bearing for high speedapplications 2. Hallstedt G. Standardised Hydrostatic Bearing Units. Proceedings Join t Conference on Externally Pressurised Bearings, L Mech. E., 1971, p.422
3. O'Donoghue J.P. and Rowe W.B. Hydrostatic Bearing Design. Tribology, 1969, 2(1), 25--71
4. Rowe W.B., O'Donoghue J.P. and Cameron A. Optimisation of Externally Pressurised Bearings for Minimum Power and Temperature Rise. Tribology, 1970, 3(3), 1 5 3 - 1 5 7 5. Loeb A.M. and Rippel H.C. Determination of Optimum Proportions for Hydrostatic Bearings. Trans. ASLE, 1958, 1,241 6. Shinkle J.N. and Hornung K.G. Frictional Characteristics of Liquid Hydrostatic Journal Beatings. Trans. ASME, Ser.D.Jnl o f Basic Eng., 1965, 87, 163 7. Mohsin M.E. and Sharratt A. The Behaviour of a Total Cross-Flow Hydrostatic Thrust Beating. To be presented at the 21st International MTDR Conference, Swansea, 1980
8. Mohsin M.E. and Morsi S.A. The Dynamic Stiffness of Controlled Hydrostatic Bearings. Trans. ASME, Jnl. o f Lubrication Tech., Paper No. 69-Lub.G. 1969
9. Opitz H., Bottcher R. and Effenberger W. Investigation on the Dynamic Behaviour of Hydrostatic Spindle-Beating Systems. Proc. lOth MTDR Conference, 1969, p.453
10. Ettles C.M.M. and O'Donoghue J.P. Laminar Recess Flow in Liquid Hydrostatic Beatings. Proc. Joint Conference on Externally Pressurised Bearings, L Me ch.E., 19 71, p. 215
11. Rowe W.B. and Stout K.J. Design of Hydrostatic Bearings for Exacting Applications. Proc. 13th International MTDR Con-
12. Davies P.B. Modes of Failure in Multirecess Hydrostatic Journal Bearings. Proe. l Oth International MTDR Conference, 1969, p. 425
13. O'Donoghue J.P., Rowe W.B. and H o o k e C.J. Computer Analysis of Externally Pressurised Journal Bearings. Proc. LMech.E. 1969, 184, 48 14. Opitz H. Pressure Pad Bearings. Proc. LMech.l':. ConJ~ on Lubrication and Wear, 1967. p.67
15. Mohsin M.E. Improvements in or Relating to Bearings. British Patent Application No. 791 7555, 1978
16. Mohsin M.E. Hydrostatische Querstromlager fiir Schnellaufende Gleitfuhrungen. Werkstatt und Betrieb. 1979. 11, 793 17. Mohsin M.E. and Shaheen M.M. Viscous Drag on a Plate Moving Along a Flooded Groove. To be published. 18. Mohsin M.E. The Total Cross Flow Hydrostatic Beating. Development Project htterim Reports, 1979, Manu]acturing and Machine Tools Division, Mech. Eng. Dept., UMIST, 2 and 3
19. Mohsin M.E. and Shartatt A. The Behaviour of llydrostatic Pads with Grooved Lands. Tribology International. b'ebntarv 1981, 14(1), 3 3 - 4 5
20. Mohsin M.E. The Total Cross Flow ttydrostatic Bearing. Development Project Interim Reports, 19 79, Manufacturing and Machbte Tools Division, Mech. Eng. Dept., UMIST. 4
21. Hits G.G. Design Directives for Turbulent Film Bearings. Proc. Joint Conference on Externally Pressurised Bearhzgs, LMech.E., 1971. p.262
22.Wilson R.W. Cavitation Damage in Plane Bearings. Proc. 1st Leeds-Lyon Symposium on Tribology, Leeds, 1974. p. 177
ference, 1972, p.119
Fundamentals of Tribology Edited by Nam. P. Suh and Nannaji Soka This is a report o f the proceedings of a conference held at MIT in June 1978 and contains approximately eighty papers arranged in sixteen groups: Introduction, Surface Topography, Physical Properties, Surface and Interfacial Phenomena, Friction, Wear Mechanisms, Thermo-mechanical Effects, Wear in Processing, Polymer Wear, Wear Monitoring, Wear Prevention, Boundary Lubrication, Elastohydrodynamic Lubrication, Systems Approach and finally Documentation and the Tribology Literature. Each group is headed by an invited keynote paper and some of the following papers in the group, and the limited discussion which is recorded, grow from and refer to these special papers. Books o f this kind can be judged on two standards. First, one can look at them simply as a report of the conference; in this respect the conference can be judged to have been a great success. Second, one can look at the published volume as a contribution to the literature; in this light one can ask to what extent the book will be used in, say, ten years' time. It is this latter function upon which it is right to concentrate this review.
54
In his introductory paper, Douglas Scott points out that entries in the tribological literature are now running at 7000 papers, or so, per year. One must therefore ask what value this volume has in providing a useful and discriminating summary o f the state of the subject in 1976. This is an important question because at a price of more than £50 the main home for this b o o k will be on the shelves of libraries. The answer to the central question posed above is a mixed one. The book is a far more sprawling and discursive discussion than the superb series of Interdisciplinary Discussions sponsored by NASA and edited by the late P.M.Ku. (but judging a volume by P.M.'s superb standards is taking a very hard line). There is much valuable material here. For example, the session on Surface Topography, headed by a fairly comprehensive review by Whitehouse, confirms this reviewer's view o f a subject o f a superbly sophisticated theory still awaiting some solid triboiogical justification. As the list o f paper groupings given above indicates the subject material is strongly biassed towards wear in all
TRIBOLOGY international February 1981
its aspects. This is a welcome change for that Cinderella of the tribological disciplines, but it means that the volume as a whole is not totally representative of tribology in 1976. The papers themselves vary widely in the extent to which they are either a sound survey o f existing knowledge or a sustained and inspired attempt to re-interpret it. This is, of course, inevitable but I missed in this volume of more than 1200 pages the appearance of many startling or thought provoking ideas. I was considerably more excited to read the new review of wear by Dr Tom Childs*. The critical elements in the above review are, perhaps, making excessive demands of a volume of this type. As a summary of large parts of tribology in 1976, and in particular as a summary of many aspects o f wear, it will sit on my bookshelf, among many others, for many years to come. It will provide a very valuable reference, bearing in mind the appearance of the 7000 papers per year to which we referred above. d . F. A r c h a r d
*Childs T.H.C. The Sliding Wear Mechanisms of Metals, Mainly Steels. Tribology International, 1980, 13(6), 285 293 Published by M I T Press, 28 Carleton Street, Cambridge, MA 02142, USA