Hydrodynamic Journal Bearing

Hydrodynamic Journal Bearing

The Hydrodynamic lubricant bearing is also called Thick film lubricant Bearing. The thick film bearings are those in which the working surfaces are completely separated from each other by the lubricant. 

History of lubrication theory

O. Reynolds published famous equation of thin fluid film flow in the narrow gap between two solids (Reynolds 1886). This equation carries his name and forms a foundation of the lubrication theory. 

Hydrodynamic Journal Bearing-

A little consideration will show that when the bearing is supplied with sufficient lubricant, a pressure is build up in the clearance space when the journal is rotating about an axis that is eccentric with the bearing axis. The load can be supported by this fluid pressure without any actual contact between the journal and bearing. The load carrying ability of a hydrodynamic bearing arises simply because a viscous fluid resists being pushed around. Under the proper conditions, this resistance to motion will develop a pressure distribution in the lubricant film that can support a useful load. The load supporting pressure in hydrodynamic bearings arises from either

1. The flow of a viscous fluid in a converging channel (known as wedge film lubrication).

2. The resistance of a viscous fluid to being squeezed out from between approaching surfaces (known as squeeze film lubrication).

Assumptions in Hydrodynamic Lubricated Bearings 

The following are the basic assumptions used in the theory of hydrodynamic lubricated bearings:

1. The lubricant obeys Newton's law of viscous flow.
2. The pressure is assumed to be constant throughout the film thickness.
3. The lubricant is assumed to be incompressible.
4. The viscosity is assumed to be constant throughout the film.
5. The flow is one dimensional, i.e. the side leakage is neglected.

Important Factors for the Formation of Thick Oil Film in Hydrodynamic Lubricated Bearings 

According to Reynolds, the following factors are essential for the formation of a thick film of oil in hydrodynamic lubricated bearings : 

1. A continuous supply of oil. 

2. A relative motion between the two surfaces in a direction approximately tangential to the surfaces. 3. The ability of one of the surfaces to take up a small inclination to the other surface in the direction of the relative motion. 

4. The line of action of resultant oil pressure must coincide with the line of action of the external load between the surfaces. 

1. Wedge Film Journal Bearings 

The load carrying ability of a wedge-film journal bearing results when the journal and/or the bearing rotates relative to the load. The most common case is that of a steady load, a fixed (nonrotating) bearing and a rotating journal. 

Fig.(a) shows a journal at rest with metal to metal contact at A on the line of action of the supported load. When the journal rotates slowly in the anticlockwise direction, as shown in Fig.(b), the point of contact will move to B, so that the angle AOB is the angle of sliding friction of the surfaces in contact at B. In the absence of a lubricant, there will be dry metal to metal friction. If a lubricant is present in the clearance space of the bearing and journal, then a thin adsorbed film of the lubricant may partly separate the surface, but a continuous fluid film completely separating the surfaces will not exist because of slow speed.

When the speed of the journal is increased, a continuous fluid film is established as in Fig. (c). The centre of the journal has moved so that the minimum film thickness is at C. It may be noted that from D to C in the direction of motion, the film is continually narrowing and hence is a converging film. The curved converging film may be considered as a wedge shaped film of a slipper bearing wrapped around the journal. 

2. Squeeze Film Journal Bearing 

The wedge film journal bearing, the bearing carries a steady load and the journal rotates relative to the bearing. But in certain cases, the bearings oscillate or rotate so slowly that the wedge film cannot provide a satisfactory film thickness. If the load is uniform or varying in magnitude while acting in a constant direction, this becomes a thin film or possibly a zero film problem. But if the load reverses its direction, the squeeze film may develop sufficient capacity to carry the dynamic loads without contact between the journal and the bearing. Such bearings are known as squeeze film journal bearing.

Terms used in Hydrodynamic Journal Bearing

A hydrodynamic journal bearing is shown in Fig , in which O is the centre of the journal and O′ is the centre of the bearing. 

Let D = Diameter of the bearing, 

d = Diameter of the journal, and 

l = Length of the bearing. 

1. Diametral clearance- It the difference between the diameters of the bearing and the journal. Mathematically, diametral clearance, 

c = D – d 

2. Radial clearance- It is the difference between the radii of the bearing and the journal. Mathematically, radial clearance,

c1 = R - r

3. Diametral clearance ratio-  It is the ratio of the diametral clearance to the diameter of the journal. Mathematically, diametral clearance ratio

 c/d = D-d / d

4. Eccentricity- It is the radial distance between the centre (O) of the bearing and the displaced centre (O′) of the bearing under load. It is denoted by e. 

5. Minimum oil film thickness-  It is the minimum distance between the bearing and the journal, under complete lubrication condition. It is denoted by h0 and occurs at the line of centres as shown in Fig. Its value may be assumed as c / 4. 

6. Attitude or eccentricity ratio- It is the ratio of the eccentricity to the radial clearance. Mathematically, attitude or eccentricity ratio,

ε = e / c1

7. Short and long bearing- If the ratio of the length to the diameter of the journal (i.e. l / d) is less than 1, then the bearing is said to be short bearing. On the other hand, if l/d is greater than 1, then the bearing is known as long bearing. When the length of the journal (l ) is equal to the diameter of the journal (d ), then the bearing is called square bearing. 

Bearing Characteristic Number and Bearing Modulus for Journal Bearings 

The coefficient of friction in design of bearings is of great importance, because it affords a means for determining the loss of power due to bearing friction. It has been shown by experiments that the coefficient of friction for a full lubricated journal bearing is a function of three variables, i.e.

(i)  ZN/p

(ii)  d/c

(iii) l/d 

Therefore the coefficient of friction may be expressed as

where μ = Coefficient of friction

φ = A functional relationship

Z = Absolute viscosity of the lubricant, in kg / m-s 

N = Speed of the journal in r.p.m.

p = Bearing pressure on the projected bearing area in MPa, = Load on the journal ÷ l × d 

d = Diameter of the journal

l = Length of the bearing

c = Diametral clearance. 

The factor ZN / p is termed as bearing characteristic number and is a dimensionless number. The variation of coefficient of friction with the operating values of bearing characteristic number (ZN / p) as obtained by McKee brothers (S.A. McKee and T.R. McKee) in an actual test of friction is shown in Fig. The factor ZN/p helps to predict the performance of a bearing.

The part of the curve PQ represents the region of thick film lubrication. Between Q and R, the viscosity (Z) or the speed (N) are so low, or the pressure ( p) is so great that their combination ZN / p will reduce the film thickness so that partial metal to metal contact will result. The thin film or boundary lubrication or imperfect lubrication exists between R and S on the curve. This is the region where the viscosity of the lubricant ceases to be a measure of friction characteristics but the oiliness of the lubricant is effective in preventing complete metal to metal contact and seizure of the parts. It may be noted that the part PQ of the curve represents stable operating conditions, since from any point of stability, a decrease in viscosity (Z) will reduce ZN / p. This will result in a decrease in coefficient of friction (μ) followed by a lowering of bearing temperature that will raise the viscosity (Z ). From Fig. we see that the minimum amount of friction occurs at A and at this point the value of ZN / p is known as bearing modulus which is denoted by K. 

The bearing should not be operated at this value of bearing modulus, because a slight decrease in speed or slight increase in pressure will break the oil film and make the journal to operate with metal to metal contact. This will result in high friction, wear and heating. In order to prevent such conditions, the bearing should be designed for a value of ZN / p at least three times the minimum value of bearing modulus (K). If the bearing is subjected to large fluctuations of load and heavy impacts, the value of ZN / p = 15 K may be used.

Critical Pressure of the Journal Bearing 

The pressure at which the oil film breaks down so that metal to metal contact begins, is known as critical pressure or the minimum operating pressure of the bearing. It may be obtained by the following empirical relation, i.e. Critical pressure or minimum operating pressure,

Design Procedure for Journal Bearing

The following procedure may be adopted in designing journal bearings, when the bearing load, the diameter and the speed of the shaft are known.

1. Determine the bearing length by choosing a ratio of l/d.

2. Check the bearing pressure, p = W / l.d for probable satisfactory value. 

3. Assume a lubricant and its operating temperature (t0). This temperature should be between 26.5°C and 60°C with 82°C as a maximum for high temperature installations such as steam turbines. 

4. Determine the operating value of ZN / p for the assumed bearing temperature and check this value with corresponding values in Table, to determine the possibility of maintaining fluid film operation. 

5. Assume a clearance ratio c/d.

6. Determine the coefficient of friction (μ). 

k = Factor to correct for end leakage. It depends upon the ratio of length to the diameter of the bearing (i.e. l/d). = 0.002 for l/d ratios of 0.75 to 2.8. 

7. Determine the heat generated by using the relation

Qg = μ.W.V N-m/s or J/s or watts 

where μ = Coefficient of friction

W = Load on the bearing in N

V = Rubbing velocity in m/s =πdN/60

N = Speed of the journal in r.p.m. 

8. Determine the heat dissipated by using the relation

Qd = C.A (tb – ta) J/s or W 

where C = Heat dissipation coefficient in W/m2/°C, 

For unventilated bearings (Still air) = 140 to 420 W/m2/°C 

For well ventilated bearings = 490 to 1400 W/m2/°C 

A = Projected area of the bearing in m2 = l × d, 

tb = Temperature of the bearing surface in °C

ta = Temperature of the surrounding air in °C. 

9. Determine the thermal equilibrium to see that the heat dissipated becomes at least equal to the heat generated. In case the heat generated is more than the heat dissipated then either the bearing is redesigned or it is artificially cooled by water. 

Qt = m.S.t J/s or watts 

where m = Mass of the oil in kg / s 

S = Specific heat of the oil. 

Its value may be taken as 1840 to 2100 J / kg / °C

t = Difference between outlet and inlet temperature of the oil in °C. 

Advantages of Hydrodynamic Lubricant Journal Bearing

1. Very low friction (hydrodynamic means that there is a full film of oil between the bearing and race components).

2. Lower wear and longer life than standard bearings (no metal-metal contact within the wearing portions of the bearing).

3. Should run cooler since there is less friction and mainly viscous loss to the oil.

Disadvantages of Hydrodynamic Lubricant Journal Bearing

1. Hydrodynamic bearings require forced lubrication to maintain the full film.

2. The correct viscosity of oil is required to avoid contact between metal pieces (temperature and load play into that).

3. More costly than standard bearings.