design of HYDRODYNAMIC JOURNAL BEARING

HYDRODYNAMIC JOURNAL BEARING

D  Diameter of bearing

d   Diameter of journal

l    Length of bearing

1. Diameteral  clearance : It is the difference between the diameters of the bearing and journal.

          C - D - d

2. Radial clearance : It is the difference between the radie of bearing and journal.

         

3. Eecentricity : It is the radical distance between the centre (o) of the bearing and the displaced centre(o’) of the bearing under load.

4. Short and long bearing: If the ratio of the length to diameter of the journal (i.e., )

(i)      Minimum Oil Film Thickness. It determines the closest approach of the journal and the bearing surfaces with complete lubrication. Its value depends upon the degree of finish of these surfaces and the rigidity of the journal and bearing construction, and on the size and kind of the dirt particles present in the oil. If the bearing construction is quite rigid and if the oil is kept clean, then the minimum oil film thickness for hydrodynamic lubrication, must be equal to or greater than the sum of the average peak to valley roughness of the journal and bearing surface i.e.

C_p = roughness peak factor

= ratio of peak to average roughness

 = bearing and journal roughness respectively, mm.

To take into account, the dirt particles, shaft deflection, etc., a factor called “clearance factor” is incorporated to increase the specified minimum film thickness, so

, where C_e = clearance factor.

For ordinary Babbitt lined bearings the film thickness should not be less than 0.02 mm. On larger power machinery, the minimum film thickness may be limited to 0.025 to 0.15 mm. one rule of the thumb is to limit the minimum film thickness to 0.00025D.

It has been found by investigators that, for bearings of certain geometry, the minimum oil film thickness is a function of Bearing Modulus or Bearing service characteristic number (defined ahead as equal to Zn/p), that is,

\  For hydro-dynamic lubrication to occur.

1.        Wedge-shaped gap should be formed between the sliding surfaces.

2.        A lubricant of adequate viscosity should continually be introduced into the gap.

3.        The relative speed of the journal should be enough to create the hydro-dynamic pressure in the fluid film necessary to balance the external load.

Roughness Peak Factor C_p

Metallic Finish	Average Value, Cp	Typical range, Cp
Ground	4.5	3.5 – 5.0
Hydrolapped	6.5	5.5 – 7.5
Loose abrasive lapped	10.0	7.5 – 13.0
Sand papered	7.0	5.5 – 9.0
Super finished	7.0	5.5 – 9.5
Turned	5.0	3.5 – 8.0

Bearing Surface Roughness mm rms

Type of surface	Surface Roughness
High Precision Journal	0.125 – 0.2
High Precision Bearing	0.125 – 0.5
Medium Precision Journal	0.4
Medium Precision Bearing	0.8
Commercial Grinding	0.4 – 1.6
Broaching, Reaming, Boring, Finish Turning	0.8 – 1.6

(ii)     Bearing Modulus: It is designated as “C” and is defined as;

Bearing Modulus =        (8)

The bearing modulus is of special interest in bearing design. Its variation with co-efficient of friction is shown in Fig. 17.11. For any given bearing, there is a value for bearing modulus indicated by C, for which the co-efficient of friction is minimum. The bearing should not be operated at this value of bearing modulus, since a slight decreases in speed or a slight increase in pressure will make the journal to operate in the partial lubrication state resulting in high friction, heating and wear.

To prevent this, the average value of

Bearing modulus should be,

The values of C are given in Table 17.11.

p is in MPa

For large fluctuations and heavy impact loads,

The design data for Journal bearings is listed in Table 17.12

Values of C

Shaft	Bearing	C
Hardened and ground steel	Babbitt	2.85
Machined soft steel	Babbitt	3.60
Hardened and ground steel	Plastic Bronze	4.30
Machined soft steel	Plastic Bronze	5.00
Hardened and ground steel	Rigid Bronze	5.70
Machined soft steel	Rigid Bronze	7.00

Design Data  for Journal Bearings

Bearing Types	p MN/m2	Z kg/ms
Axles:
Locomotive	3.85	0.600	4.5 – 7.35	0.001 max.	1.6 – 1.8
Railway Car	2.1 – 3.5	0.500	7.00 – 14.30	0.001 max.	1.8 – 2.0
Crankpins:
Aircraft	5.25 – 35	0.008	1.5	-	0.5 – 1.5
Automobile	10.5 – 24.5	0.008	1.5	0.001 max.	0.5 – 1.4
Diesel	10.35 – 28	0.020 – 0.060	0.75 – 1.43	0.001	0.8 – 1.5
Gas	8.4 – 12.6	0.020 – 0.60	1.43 – 2.85	0.001	0.8 – 1.5
Steam (HS)	2.8 – 8.4	0.030	0.85 – 2.14	0.001 max.	1
Steam (LS)	5.6 – 1.5	0.080	0.85 – 1.14	0.001 max.	1 – 1.25
Shears, Punches	35 – 56	0.100	-	0.001	1- 2
Crank shaft, main bearing
Aircraft	4.2 – 12.6	0.025 – 0.030	2.25 – 3.00	0.001 max.	0.6 – 1.5
Automobile	2.1 – 12.6	0.025 – 0.0030	2.85 – 4.30	0.001 max	0.8 – 1.5
Diesel	2.45 – 8.4	0.022 – 0.060	2.14 – 2.85	0.001 max	0.8 – 1.5
Gas	3.5 – 7	0.020 – 0.060	2.85 – 4.30	0.001 max.	0.4 – 2.4
Steam (HS)	0.42 – 3.5	0.15 – 0.030	3.60 – 4.30	0.001 max.	1.3 – 1.7
Steam (LS)	0.56 – 2.8	0.070	2.85 – 4.30	0.001 max.	1.2 – 1.6
Shears, Punches	14.0 – 28.0	0.100	-	0.001	1-2
Wrist Pins:
Aircraft	20-70	0.007-0.008	1.14-2.14	0.001 max	0.6-1.5
Automobile	10.5-35	0.007-0.008	1.14-2.14	0.001 max.	0.8-1.5
Diesel	8.4-12.6	0.020-0.060	2.85-3.60	0.001 max.	0.8-1.4
Gas	8.4-14	0.020-0.060	0.75-1.43	0.001 max.	0.8-1.25
Steam (HS)	10.5-12.6	0.025	0.75	0.001	1.4-1.6
Steam (LS)	7-10.5	0.070	0.75	0.001	1.2-1.5
Generators	0.7 – 1.4	0.025	28.50	0.001	1-2
Motors Pumps
Line shafts	0.105 – 1.05	0.025-0.060	4.30-14.30	0.001	2.5-3
Reducing Gears	0.56-17.5	0.030-0.050	5.70-43.00	0.001	2-4
Machine Tools	0.35 – 2.1	0.040	0.3 – 1.43	0.001	1-3
Steam Turbines	0.55-2.1	0.010-0.20	14.30-28.50	0.001	1-2
Rolling mills	21	0.050	14.30	0.0015	1.1-1.5

(iii)    Sommerfeld number or Bearing Characteristic Number: This is also a very useful number in the design of sleeve bearings. It is defined as:

          (9) n’ is rev/s and r is in N/m².

Fig. 17.12 shows the graphs of the minimum film ratio  versus Sommerfeld number, S for bearings having various length diameter ratio . These graphs can be easily used for the design of sleeve bearings. For example, corresponding to a known minimum permissible oil film thickness h0 and an assumed radial clearance Cf a specific value of S can be obtained. Then if certain quantities in Eqn. (17.9) are known, the remaining can be found out. Curves showing variation of co-efficient of friction variable, oil flow variable, Temperature rise variable are also available.

(iv)    Operating pressures: The minimum operating pressure known as “critical pressure” is the pressure at which the oil film breaks down and metal to metal contact begins. It is given empirically as:

     (10)

In the above equation, it is assumed that

(v) Coefficient of Friction: The co-efficient of friction is of great significance in bearing design. Its value can’t be determined very accurately since the degree of lubrication is generally not known. For self contained full bearings, for hydrodynamic lubrication, the co-efficient of friction is given empirically as:

            (11)

Where k_f = factor to correct for end leakage. Its value varies with  Ratio.

Its value may be taken as 0.002 for . Its value can also be found out from Fig. 17.13.

For pressure fed hydrodynamic bearings, and hydrostatic bearings, the correction factor is not considered, and, therefore, the co-efficient of friction is given as:

The co-efficient of friction for these conditions, is generally below than 0.001.

For lightly loaded bearings, the co-efficient of friction may be approximately calculated from petroff’s equation:

(13)

here p is N/m².

When the bearing operate at boundary lubrication or partial lubrication conditions, the values of ‘f’ may be taken from table, which is due to Fuller.

Co-efficient of friction for partial lubrication conditions

Condition	f
Boundary lubricated, regularly attended	0.02 – 0.08
Bearing dried out containing a bare film of oil	0.08 – 0.14
Bearing completely dry with contamination and burned off	0.25 – 0.40

(vi)    Heating of Bearings: The factional work is converted into heat- This heat must be dissipated from the bearing house to avoid its overheating because at high temperatures the oil viscosity will decrease, making the oil to squeeze out resulting in negligible lubrication and consequently seizing of the bearing. The usual operating temperature for bearings varies from 50 to 80°C, The heal generated due to friction is given as :

Hg = f . F. V watts

where F = load in N = pLD, p in N/m², L and D in m.

and V = Rubbing velocity, m/s

f will correspond to the type state of lubrication.

\ Heat generated is:

            (14)

After thermal equilibrium, the heat will be dissipated at the same rate at which it is generated. The heat dissipation will depend upon the method of lubrication

(a)     Self-contained bearings: In such bearings, the heat generated in the oil will be transmitted to the bearing body from where it must be dissipated into the surrounding area. The amount of heat dissipated will depend upon the temperature difference, size and mass of the radiating surface, and on the air flow around the bearing. The rate of heat dissipation is given as :

H_d = k_d DL(t_b – t_a)    (15)

where t_b =  temperature of bearing ^oC

t_a = temperature of surrounding, ^oC

where k_d =  energy dissipation co-efficient, W/m^2oC Table 14.

Energy dissipation coefficient

Bearing Condition	kd
1)      Simple Pillow – block bearings:          Quiet Air          Air at 2.5 m/s	146.56 to 244.23 488.50 to 767.60
2)      Heavy duty self aligning ring-oil lubricated:          Quiet Air          Air at 2.5 m/s	293.00 to 390.77 879.23 to 1228.13

The bearing temperature t_b is frequently assumed to be the mean between the average oil temperature t₀ and the temperature of surroundings i.e.

 For usual industrial applications, the upper limit of permissible oil temperatures ranges from 70°C to 1°.C. If the temperature is higher, bearing is cooled by water circulating through oils built in the bearing or sing pressure feeding of the lubricant.

(b) Pressure Fed Bearings: The amount of heat removed by the circulating oil is:

          H₀ = r . f . (t₀ . t_e), watts         *17)

where r = density of oil = 900 kg/m3.

          f = specific heat of oil = 1.84 to 2.05 kJ/kg^oC

          Q = quantity of oil, m³/s

          t₀ – t_e = outlet temperature of oil – entrance temperature of oil) ^oC

The average oil film temperature may be taken as:

The upper limit of the permissible oil temperature for usual industrial applications ranges from about 70° to 82Q C. If this temperature is exceeded, either the oil feed pressure or oil viscosity must be changed. The oil '' is usually circulated through the bearings at pressures ranging from 0.07 to 0.7 N/mm². Another method to  avoid overheating of oil is to circulate 3 to 5 times the amount of oil calculated from the equation (17.17). (vii) Design Procedure: There is no one design procedure for the design of journal bearings. There can be unlimited design procedures. Sommerfeld number, as discussed earlier, may be used for the bearing design. The design usually involves :

1. Optimising clearance.

2. Optimizing bearing length, lubricating inlet slots, and

3. Calculation of energy balance.

Before we give the design procedure, the following design considerations should be kept in mind : -

1.       Lubricants: The lubricant to be used can be either liquid, solid or gas. The choice will depend upon such factors as type of machine, method of lubricant supply and load characteristics.

2.       Bearing load: The load coming on a bearing is usually specified. However, its value per projected area can be determined by suitably selecting length and diameter of the bearing. The value of load per projected area will depend upon the bearing life desired. It is clear that smaller the load per projected area, the greater the bearing life and vice versa.

3.       Length to Diameter Ratio: This is a very important parameter in bearing design. Its value lies between 0.8 and 1.5, with a value of unity being most common. Long bearing (L/D ratio greater than 1) is used where misalignment must be avoided and a reduced load carrying capacity can be tolerated, In short bearings (L/D<1), the danger of metal to metal contact due to large shaft deflections is greatly reduced. So, a rought rule | for choosing a L/D ratio is:

(i) Use preferably, L/D =1.0

(ii) Use L/D<1 .0, if, deflections are expected to be severe

(ii)     Use L/D>1 .0, if shaft alignment is important

4. Clearance: The value of journal bearing clearance depends on: materials, manufacturing accuracy, load carrying capacity, minimum film clearance, oil flow, film temperature etc. Large clearance will allow foreign material to pass-easily through the bearing, the increased oil flow will reduce film temperature and thus increase the bearings life. But a large clearance will result in a loose, noisy bearing and a resulting decrease in minimum film thickness. A reasonable clearance ratio (Cd/D) equal to 0.001 is most common.

When the bearing load, the diameter and speed of the shaft are known, the following design procedure may be followed:

Design Procedure for Journal Bearing

When the bearing load, the diameter and speed of the shaft are known the following design procedure may be followed.

(1)        Determine the bearing length by choosing a ratio of

(2)        Check the bearing pressure  from table for probable sales  factory value

(3)        Assume a clearance ratio  from table

(4)     Assume a lubricant ail from table, and its operating temp, the ranged which has already been mentioned from graph find the value of Z corresponding to the operating temp. assumed for the selected oil.

(5)     Find and check this value with corresponding values in table to determine the possibility of maintaining fluid film  lubrication.

(6)     Determine coefficient of friction

(7)     Determine heat generated

(8)     Determine hat drum palled

(9)     Determine the thermal equilibrium to see that heat dissipated become at least equal to heal  generated.

References

1.      Mechanical Engineering Design – Joseph Shigley

2.      Machine Design – Mubeen

3.      Machine Design – Black

4.      Principles of Lubrication – Cameron A.