Friction in Journal bearings

1
Friction in Journal bearings

• From Newtons law of friction, the stress t on
  any layer is
• From Reynolds equations it was found that
• We need to find the friction stress at the 2
  surfaces, i.e. z 0 and z h

2

• Therefore
• The positive sign is for z h (bearing surface)
  and the negative for z 0 (shaft surface). The
  total drag F on the whole bearing under
  consideration, of extent B and L (length), in the
  x and y directions is

Where 2pR B
3

• Now h c(1ecosq) and dh/dq -cesinq, so
  integrating the first term by parts gives
• The first of these terms is zero, as p must be
  zero at q 0, and 2p (Sommerfelds condition)
• For the second term the integral is solved using
  the relation

4

• The third term should be taken under two separate
  conditons. This is because the viscosity is not
  constant around the whole circumference. If there
  is cavitation in some part of the bearing a
  different law will apply.
• At the moment the bearing will be assumed to be
  full of a liquid with one single viscosity. Thus,
  using Sommerfelds substitution
• The expression for friction then becomes

The positive sign in front of the first term is
when z h (at the bearing surface), and the
negative sign when z 0 (at the shaft surface)
5

• The integrated oil forces on the shaft and
  bearing act through their respective centers.
• These are in the direction of the load, a
  distance esiny apart, and there will be a couple
  set up of magnitude Wesiny Wcesiny
• This corresponds to a frictional force of
  Wcesiny/R at the surface of the shaft. This force
  is added to the friction at the shaft surface h
  0, so that

Bearing
e
y
esiny
W
Oil film height h
Shaft
6

• This is exactly equal to the friction Fh, when z
  h. Therefore
• for both surfaces. Of these two terms, the first
  arises from the offset between the center of the
  shaft and that of the bearing. The second is the
  simple Newtonian friction.
• Petroff analysis of friction gives friction as
• The term 1/(1-e2)1/2 is a multiplier to take into
  account the eccentric running of the shaft

7
Journal- Narrow bearings

• Assumption Length L is much smaller compared to
  radius R. The flow in the y direction will
  therefore be much more significant than the flow
  in the x (or q) direction
• Equation for flow in the x direction is given by
• In the axial (y) direction it is given by

Bearing
R
L
shaft
8

• The continuity equation is
• If the average pressure in the lubricant is p,
  then
• is of the order of pressure/circumference or
• p/2pR and is of the order pressure/length or p/L.
• As RgtgtL , ltlt as x Rq and L is in
  the y direction
• Furthermore, the term in qx is also taken
  to be much
• small compared to Uh/2

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Pressure change with y

• Thus the continuity equation reads
• Now h varies with x only (assuming no tilt in the
  shaft). Therefore the equation can be written as
• Or

10

• This equation can be integrated to give
• And again to give
• Where C1 and C2 are constants of integration.
• The pressure is zero at either side of the
  bearing. i.e. if the length is L, p is zero at y
  L/2, and y -L/2

R
Bearing
-L/2
L/2
0
11

• Due to symmetry dp/dy must be zero on the center
  line (y0). Therefore C1 0 as dp/dy 0, at y
  0
• From the former condition C2 must equal
• Hence we get the pressure as
• Now h c(1 ecosq) and x Rq, therefore

12

• Therefore
• and
• From this equation, it is clear that the pressure
  varies with
• Giving a positive pressure between 0 an p and
  negative from p to 2p.

13
Narrow bearing load
Wx

• The load components Wx and Wy are derived by
  applyling a double integral as the pressure
  varies in the q as well as y directions. Wx is
  the component along the line of centers and Wy is
  the component normal to it.

Bearing
Rdq
q
y
Wy
Shaft
W
Line of centers
Pressure curve
14

• Therefore
• And
• Substituting the expression for p we get
• and

15

• The following integrals can be evaluated to give
• And
• Thus
• And

16

• The resultant load
• Or
• Now 16/p2)-1 0.6211, therefore
• The group on the left is similar to Sommerfelds
  variable, except that it has L2 in it instead of
  R2. If top and bottom are divided by R2 and the 4
  is taken from the right hand side, then
• Where D is the Sommerfeld variable and D is the
  diameter 2R

17
Attitude angle

• The attitude angle is given by
• TanY Wy/-Wx
• Therefore
• For narrow bearings, the volume flow in the
  circumferential direction is given by
  per unit width.
• The make up oil or the total side leakage, Qc is
  the difference between the oil flowing in at the
  start of the pressure curve and out at its end.

18

• It is given by
• h c(1ecosq), therefore
• And
• Therefore
• Therefore the non-dimensional side flow is
  defined as
• Therefore Qc 2e

19
Detergent additives

• To clean undesired substances (mostly oxidation
  products and contaminants) from the surfaces and
  passages of a lubricating system
• Detergent additives are soaps of high molecular
  weight, soluble in oil
• Consist of a metal and organic component
• Ashless (without metal) detergents are also
  employed leaving no metallic residue

20
Detergent additives
Binding agent
Deposit particles that agglomerate due to binding
agent
Detergent
Detergent
Detergent bound to binding agent
Particles remain free
Detergent
Detergent
OR Envelope the particles, preventing them from
forming deposits

• Make the binding agents in deposits less
  effective
• Particles remain in suspension and can be drained
  or filtered off
• Envelope the deposit particles and prevent them
  from agglomerating with other particles
• E.g. metal phosphonates, sulphonates

21
Dispersant additives

• Particles separated by detergents are to be
  prevented from accumulating (usually at lower
  temperature)
• Dispersants isolate the particles from each other
  and disperse them in the lubricant
• Form a coating on particles and due to the polar
  nature, tend to repel each other
• E.g. pollymethacrylates, polyamine succimides

22
Dispersants- mechanism
Dispersant particles (same charge on outside)
Separated and suspended particles due to
detergent action


Detergent
Detergent


Detergent
Detergent
Like charges repel, hence there is dispersion
23
Pour point depressants

• Pour point is the lowest temperature at which the
  lubricant will flow
• Forms waxy crystals at lower temperatures
• Pour point depressants reduce the pour point and
  are therefore required when operating at lower
  temperatures
• E.g. methacrylate polymers, polyalkylphenol esters

24
Pour point depressant- mechanism
WAX CRYSTAL
WAX CRYSTAL
WAX CRYSTAL
WAX CRYSTAL
Crystal growth
WAX CRYSTAL
POR POINT DEPRESSANT
WAX CRYSTAL
POR POINT DEPRESSANT
Encapsulate crystal so that it cannot grow
WAX CRYSTAL
OR change the structure of crystals making them
amorphous (crystals of different shapes and sizes)
WAX CRYSTAL
25
Viscosity index improvement

• Remove aromatics (low VI) during refining stage
• Blending with high viscous oil
• Using polymeric additives that cause an increase
  in viscosity with temperature due to chain
  unwinding
• E.g. polyisobutenes, ethylene/propylene
  copolymers,

26
VI improvement using polymeric additives
Polymer chains
Temperature increase

• As the temperature increases, the polymer chains
  tend to uncoil.
• In the uncoiled form, they tend to increase the
  viscosity thereby compensating for the decrease
  in viscosity of the oil

27
Boundary and extreme pressure additives

• Reduce friction, control wear, and protect
  surfaces from severe damage
• Used in highly stressed machinery where there is
  metal to metal contact leading to boundary
  lubrication
• Chemically react with sliding metal surfaces to
  form films which are insoluble in the lubricant
• Have low shear strength than the metal
• These layers are more easily sheared in
  preference to the metal

28
Anti-foaming agents

• Foaming is the formation of air bubbles in the
  lubricant
• Interfere with flow and heat transfer
• The additives lower the surface tension between
  the air and liquid to the point where bubbles
  collapse
• E.g. silicone polymers, polymethacrylates

29
Friction modifiers

• In boundary lubrication there is poor film
  strength, there is surface to surface contact
• These modifiers are polar materials such as fatty
  oils, acids and esters having long chains
• Form an adsorbed film on the metal surfaces with
  the polar ends projecting like carpet fibers
• Provide a cushioning effect and keep metal
  surfaces apart from each other