The advantages are discussed of hydrostatic, high pressure bearings as providers of higher margin of stability to the rotor/bearing systems. It is apparent that deliberate use of hydrostatic bearing high pressure lubricated (any gas or liquid) can easily be used to build higher stability margin into rotating machinery, in spite of the thirty years bias against high pressure lubrication. Since this supply pressure is controllable (the Direct Dynamic Stiffness at lower eccentricity is also controllable) so that within some rotor system limits, the stability margin and dynamic response of the rotor system is more readily controllable. It may be possible to take advantage of this effect in the various seals, as well as the bearings, to assist with stability margin and dynamic response of rotating machinery. The stability of the bearing can be additionally improved by taking advantage of the anti-swirling concept. The high pressure fluid supply inlets should be located tangentially at the bearing circumference and directed against rotation. The incoming fluid flow creates stability by reducing the swirling rate

Bently, D. E.

Muszynska, A.

English

NASA Technical Reports Server

WHY HAVE HYDROSTATIC BEARINGS BEEN AVOIDED AS A 
STABILIZING ELEMENT FOR ROTATING MACHINES? 
Donald E. Bently and Agnes Huszynska 
Bently Rotor Dynamics Research Corporation 
H i  nden, Nevada 09423 
The paper discusses the advantages of hydrostatic, high pressure bearings as provid- 
ing higher margin of stability to the rotodbearing systems. 
INTRODUCTION 
Despite the fact that the hydrostatic bearing was invented in 1862 by L. Girard, it 
appears to have been carefully avoided as a means of stabilizing rotor systems. 
This is very interesting because it is perfectly obvious that if a cylindrical 
bearing could provide a higher Direct Dynamic Stiffness term (see Appendix) in the 
low eccentricity region, then the stability of a rotor system is, in normal situa- 
tions, greatly enhanced. 
term easily, it may also supply its controllability. 
It is an interesting exercise to examine the history of rotor dynamics and lubrica- 
tion theory to guess what went right and what went wrong, and for what reasons. In 
this instance, as is typical in other such histories, there appears to be other 
engineering considerations which caused the path to go in the wrong direction. 
Very early in lubrication theory (in 1919), Harrison correctly pointed out that a 
fully lubricated cylindrical bearing is inherently unstable. As a result of this 
natural behavior, Newkirk and Kimball introduced the pressure dam modification in 
order to provide a static load to the bearing to alleviate the instability when 
they showed the basic rules of oil whirl and oil whip in 1924. Numerous research 
since that time deals with stabilization by means of static loading, and this 
method of static load to a seal or bearing to hold it at high eccentricity 
position. At high eccentricity position, of course, the Direct Dynamic Stiffness 
term is always very high, thus providing stability to the system. 
In addition to internal static loading (the pressure dam) and external static 
loading (by whatever means, such as gravity or deliberate misalignment), there has 
been a great deal of work on various modifications of the cylindrical form of 
bearings. It is the author's observation that all of these modifications are 
helpful for the simple reason that they provide a modification of the flow pattern, 
as a pure cylinder inside a cylinder is the worst possible situation, if stability 
is desired. There are lobe bearings, offset halves, tapered land, and hundreds of 
other helpful geometric modifications of bearings. These methods, however, cannot 
be applied to seals. 
With all these studies and designs, surely someone must have tried .hydrostatic 
principles on the basic bearing. 
The hydrostatic principle not only provides this stiffness 
Even so, the only known high pressure lubrication 
59 
https://ntrs.nasa.gov/search.jsp?R=19860020693 2020-03-20T14:40:18+00:00Z
systems fo r  ro tat ing machinery a r e  very successful designs by a few manufacturers 
using a combination o f  tapered land bearings plus high pressure supply. 
these, the f i e l d  appears barren. 
Beyond 
As nearly as can be reconstructed, the blockade against hydrostatics occurred i n  
the 1950s. 
unstable i f  the bearing was 360' ( f u l l y )  lubricated, but was stable wi th pa r t i a l  
lubrication. 
wi th par t ia l  lubrication. ) The obvious and unfortunate conclusion, however, 
appears t o  have been tha t  high pressure o i l  supply can cause 360' lubr icat ion,  
therefore, use only low pressure o i l  supply! 
Thus, while correct i n  i t s  own context, t h i s  conclusion apparently blocked the use 
o f  Girard's great invention. It i s  in terest ing t o  note tha t  Rayleigh followed upon 
the or ig ina l  hydrostatic bearing t o  make the f i r s t  o f  the more widely used hydro- 
s ta t i c  thrust  bearing, but no one applied t h i s  idea t o  o i l  and gas-lubricated rad ia l  
bearings [l] . 
Papers published i n  t h i s  period noted tha t  the sleeve bearing went 
(This i s  more o r  less correct; there usually i s  wider s t a b i l i t y  margin 
HIGH PRESSURE BEARING RESULTS 
The p lo ts  o f  the Direct  Dynamic Sti f fness as a function o f  s ta t i c  load-related 
eccentr ic i ty r a t i o  (a) f o r  a bearing wi th  "normal" o i l  supply, i.e., wi th hydro- 
dynamic pressure o r  about 20 psi ,  and (b) f o r  the same bearing with four o i l  supply 
ports and four hydrostatic segments generating pressure about ten times high i s  
shown i n  Figure 1. The increase o f  the Di rect  Dynamic Sti f fness, especially f o r  l o w  
eccentr ic i ty rat ios, i s  very s igni f icant,  as t h i s  increase powerfully increases the 
s t a b i l i t y  margin o f  the ro to r  system i f  the values are s igni f icant,  especially for 
low eccentr ic i ty rat io.  
The Quadrature Dynamic St i f fness (see Appendix) i s  v i r t u a l l y  unaffected by the 
addit ion of the hydrostatic bearing, exhib i ts  very regular relat ionship wi th the 
eccentr ic i ty r a t i o  for various values o f  ro ta t i ve  speed and c i rcu la r  preloads, as 
shown i n  Figure 2. 
For a more dramatic presentation o f  the extent o f  control over i n s t a b i l i t y  a t  the 
bearing, the Direct  Dynamic Sti f fness as a function o f  perturbation frequency 
yielded from perturbation tes t ing  i s  shown f o r  the same bearing a t  low, medium, and 
high o i l  supply pressures i n  Figure 3a. 
Figure 3b shows the Quadrature Dynamic Stiffness. 
tests, essent ia l ly  independent of o i l  supply pressure. 
Very s imi lar  t o  the high pressure bearing e f fec t  was described i n  the paper [e] 
reviewing the Lomakin effect. A l l  tha t  i s  required t o  match up t o  Lomakin effect 
i s  tha t  the f l u i d  pressure t o  the seals (or other r o t o d s t a t o r  periphery) goes up 
w i th  the square o f  ro ta t i ve  speed, because the hydrostatic s t i f fness increases 
1 i nearly w i th  o i  1 pressure. Obviously t h i s  creates a D i  r ec t  Dynamic S t i f f  ness 
which increases wi th  square o f  speed, therefore looks l i k e  the Lomakin e f fec t  o f  the 
"negative mass." 
It is ,  as i n  the steady-state 
CONCLUSIONS 
The conclusions are as follows: 
60 
1. 
lubr icated (any gas o r  l i q u i d )  can easi ly be used t o  b u i l d  higher s t a b i l i t y  margin 
i n t o  ro ta t i ng  machinery, i n  sp i te  o f  the t h i r t y  years bias against high pressure 
1 ubr i  c a t i  on. 
It i s  readi ly  apparent t h a t  deliberate use o f  hydrostat ic bearing high pressure 
2. Since t h i s  supply pressure i n  controllable, the Di rect  Dynamic Sti f fness a t  
lower eccentr ic i ty  i s  also controllable, so tha t  wi th in  some ro to r  system l i m i t s ,  
the s t a b i l i t y  margin and dynamic response o f  the ro to r  system i s  more readi ly  
control lable. 
3. 
well as the bearings, t o  ass is t  with s t a b i l i t y  margin and dynamic response o f  
ro ta t i ng  machinery. 
4. 
o f  the ant i -swi r l ing concept. 
located tangent ia l ly  a t  the bearing circumference and directed against rotat ion. 
The incoming f l u i d  f l o w  creates s t a b i l i t y  by reducing the sw i r l i ng  rate. 
It may be possible t o  take advantage o f  t h i s  e f f e c t  i n  the vacious seals, as 
The s t a b i l i t y  o f  the bearing can be addi t ional ly  improved by taking advantage 
The high pressure f l u i d  supply i n l e t s  should be 
REFERENCES 
1. Cameron, A.: Basic Lubrication Theory. Third Edition, John Wil ley & Sons, 
1981. 
2. Gopalakrishnan, S. Fehlau, R., Lorett, J. :  C r i t i c a l  Speed i n  Centrifugal 
Pumps. ASME 82-GT-277, 1982. 
APPENDIX 
It i s  the easiest t o  explain Dynamic Sti f fness terms on the example o f  a one-degree- 
o f  freedom mechanical osc i l l a to r ,  modelled by the equation: 
where M i s  mass, D i s  damping coeff ic ient ,  K i s  s t i f fness coeff ic ient ,  x i s  
vibrat ional displacement and F represents the amplitude o f  the periodic exc i t ing 
force with frequency w. Dots indicate derivation with respect t o  time, t. 
The forced response o f  the 
where 
I n  the expression (2) A i s  
osci 11 ator has the fo l  1 owi ng form: 
(2) 
the amplitude o f  the v ibrat ion response, 01 i s  the phase 
o f  response wi th  respect t o  the forcing function F. The product AeJ" has a name o f  
the Complex Response Vector. 
inverse proportional t o  the Complex Dynamic Stiffness: 
It i s  proportional t o  the exc i ta t ion amplitude F and 
61 
Complex Dynamic Stiffness = K - Mu2 + Dju (4) 
Complex Dynamic Stiffness has the components: 
Direct Dynamic Stiffness = K - Mu2 
Quadrature Dynamic Stiffness = Du, 
and 
The equation (3) yields 
(7) F Direct Dynamic Stiffness = A cos a 
( 8 )  F 
The expressions (5) through (8) are used for the identification of the system 
parameters. 
Plotted versus excitation frequency w the Direct Dynamic Stiffness is a symmetric 
parabola; the Quadrature Dynamic Stiffness is a straight line crossing the origin 
of the coordinates. 
Similar formulation of the Dynamic Stiffness terms can be applied t o  the systems 
model led by more sophisticated equations. 
In particular, for a symmetric rotor supported in' one rigid and one f l u i d  
lubricated bearing t h e  model is as follows: 
Quadrature Dynamic Stiffness = - A sin a 
M4 + Mf(Z-2jhwR;-A2wR2z) + D(;-jhwRz) + k + Kbz = Fe j w t  
z = x + + y  j = f i  
where M, K are rotor mass and stiffness respectively, M , D, Kb are bearing fluid 
inertia,  radial damping, and radial stiffness corresponhngly, wR is  rotative 
speed, A i s  the average o i l  swir l ing ratio,  w is perturbation (excitation) 
frequency. 
w i t h  the horizontal (x) and vertical (y) displacements. 
The variable z = z ( t )  represents the rotor radial displacement composed 
For the steady-state periodic response 
z = Ae j bt+d 
the Direct and Quadrature Dynamic Stiffnesses for the rotor model (9) are as 
follows: 
F (1'1) 
(12) 
Direct Dynamic Stiffness = A cos a = K - bz - Mf(~-AwR)2 + Kb 
Quadrature Dynamic Stiffness = - A sin a = D(whwR) F 
The Direct Dynamic Stiffness versus frequency w is  a parabola shifted from the 
symmetric origin due t o  fluidic inertia. The effect  of higher pressure, which 
causes an increase of K is shown i n  Figure 3. For small values of K + Kb the 
Direct Dynamic Stiffnesl? a t  zero frequency w can be negative (Fig. 3). 
62 
The Quadrature Dynamic Stiffness versus frequency ut i s  a straight line crossing the 
vertical axis at  i t s  negative side. 
stiffness coefficient, -0hwR, Fig. 3b. 
This value i s  equal to the bearing "cross" 
-- 
I - l- 
I 
I -- 
600 
500 
400 
300 
200 
100 
-1, 
I 
-I- 
I 
I 
-_  
Figure 1. - Direct dynamic stiffness versus eccentricity rat io for a hydrodynamic bearing (a) and a 
hydrostatic bearing (b). (Eccentricity rat io Z: rat io of journal displacement to radial clearance). 
700 - 
SO0 - 
500 - 
400 
300 - 5, KO0 
0 
0 0.5 e 1.0 
EcCEMRlCfly WHO 
Figure 2- - Experimentally obtained quadrature dynamic stiffness versus eccentricity ratio, indicating 
insensitivity to oil pressure. 
63 
Figure 3. - Dynanic stiffnesses versus frequency for several values of oil supply pressure, indicating 
stabi 1 i t y  margins . 
64 


Why have hydrostatic bearings been avoided as a stabilizing element for rotating machines

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