Machine design and cad ii presentation

Machine Design
and CAD-II
Presentation by Group(F)
Chapter No. 26

Group Members
Bahar-u-din 2K19-ME-12
Alam Khan 2K19-ME-14
Abdul Basit 2K19-ME16
M. Sohail 2K19-ME-26
M Nasir Mumtaz 2K19-ME29

List of topics
 Terms used in Hydrodynamic Journal Bearing
 Bearing Characteristic Number and Bearing Modulus for Journal
Bearings
 Coefficient of Friction for Journal Bearings
 Critical Pressure of the Journal Bearing
 Sommerfeld Number
 Heat Generated in a Journal Bearing
 Design Procedure for Journal Bearing
 And Examples from 26.1 to 26.5

1) Terms used in Hydrodynamic Journal Bearing
 In Figure O is the Centre of the journal and O′ is the center of the
bearing.
Let D = Diameter of the bearing,
d = Diameter of the journal,
And l = Length of the bearing.

Terms used in Hydrodynamic Journal Bearing
Diametral Clearance
It the difference between the diameters of the bearing and the
journal.
c = D – d
Where,
c is the diametral clearance
D is the diameter of the bearing
And, d is the diameter of the journal

Radial clearance
It is the difference between the radii of the bearing and the journal.
Diametral clearance ratio
It is the ratio of the diametral clearance to the diameter of the journal.
Diametral clearance ratio

Eccentricity
It is the radial distance between the center (O) of the bearing and the displaced center
(O′) of the bearing under load. It is denoted by “e”.
e = c1 –h0
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 it occurs at the line of centers

Attitude or eccentricity ratio
It is the ratio of the eccentricity to the radial clearance.
It is denoted by “ε”

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.
 If the ratio of the length to the diameter of the journal (i.e. l / d) is
greater than 1, then the bearing is said to be long bearing.

2) 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.
1) ZN/ p 2) d /c 3) l /d
coefficient of friction expressed as

Bearing Characteristic Number and Bearing Modulus for
Journal Bearings
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 N/mm2, = Load
on the journal ÷ l × d,
d = Diameter of the journal,
l = Length of the bearing, and
c = Diametral clearance.
The factor ZN / p is termed as bearing characteristic number and is a
dimensionless number.
The factor ZN/p helps to predict the performance of a bearing.

Bearing Characteristic Number and Bearing Modulus for Journal
Bearings
 The curve PQ represents the thick film lubrication.
 The curve Q and R, between this the
Viscosity or the speed (N) are so low, or the
Pressure P is also great that their
Combination ZN/P will reduce the film
Thickness so that partial metal to metal
Contact will occurs.
 The curve △R represents the thin film
Or boundary lubrication or impact lubricant
Exist.
 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.

Continue……
 To prevent this condition the bearing should be designed for a value of ZN/P at
least3 times the minimum value of bearing modulus K.
 If the bearing is subjected large fluctuation of load and heavy impact, the value
ZN/P=15K is used.

3) Coefficient of Friction for Journal Bearings
In order to determine the coefficient of friction for well lubricated full journal
bearings, the following empirical relation established by McKee based on the
experimental data
Coefficient of friction
Where, Z is absolute viscosity of Lubricant in Kg/m-s
P is Bearing pressure on projected in N/mm2
N is the speed of journal in r.p.m.
d is the diameter of journal.
c is the diametral clearance
K is the factor to correct for end leakage.it depend upon the l/d
of the bearing.

4) 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
Where , Z is in kg / m-s

5) Sommerfeld Number
It is a dimensionless parameter used extensively in the design of
journal bearings.
Sommerfeld Number

6) Heat Generated in a Journal Bearing
The heat generated in a bearing is due to the fluid friction of the part having
relative motion .
Heat generated in bearing;
Qg = μ.W.V N-m/s or J/s or watts
where
μ = Coefficient of friction,
W = Load on the bearing in N,
= Pressure on the bearing in N/mm2 × Projected area of the bearing in mm2
= p (l × d)
V = Rubbing velocity in m/s = πd N/60 ,d is in meters
N = Speed of the journal in r.p.m

Continue…
 After the thermal equilibrium has been reached,
 Heat will be dissipated at the outer surface of the bearing at the
same rate at which it is generated in the oil film.
Heat dissipated by the bearing(Qd);
Qd= C.A (t b – t a) J/s Or W i.e. (j/s=W)
Where,
C = Heat dissipation coefficient in W/m2/°C,
A = Projected area of the bearing in m2 = l × d,
tb= Temperature of the bearing surface in °C, and
ta = Temperature of the surrounding air in °C.

Continue…
It has been shown by experiments that the temperature of the bearing (tb) is
approximately mid-way between the temperature of the oil film (t0 ) and the
temperature of the outside air (ta).

7) Design procedure for journal bearing
We know that when journal rotates in a bearing then large amount of heat gets
generated in a bearing due to fraction.
For the safe design of the journal bearing the dimension, speed of etc.
Dimension of journal and the type of
lubricant all should be selected in such a way
That the heat dissipation is maximum
Step for design of journal bearing
 To determine the bearing length by choosing a ratio
Of l/d from table (26.3) for the desired application.
 Check the bearing pressure with the corresponding (Pmaxi)value from table (26.3)
P=W/l.d <Pmaxi
 According to the application the type and lubricant and its operating temp. (t0)
Can be selected from the table..,
For safe operation of journal bearing , the temperature should b/w 26.5°C ≤ to
≤60°C , with maximum temperature (t0) 82°C.

Continue …
 Condition of lubricant will be determine from the bearing characteristic number ;
ZN/P compare this value with the minimum value of bearing Modulus(K) at minimum
point of friction
K= 1/3(ZN/P)
The value of ZN/P should be taken from the table (26.3)
a) if ZN/P <K , this for thin film or hydrostatic lubrication
b) if ZN/P > K ,this For Thick film or Hydrodynamic lubrication.
 Determine coefficient of friction is given by;
µ=33/108 (ZN/P)(c/d)+K
The value of the c/d should be taken from the the table (26.3) .
 Determine the heat generated in the bearing is given by
Qg = µ.V.W
where, V= velocity of rubbing ,
V= πdN/60, m/s

Continue….
 Determine the heat dissipated from the bearing is given by;
Qd =C.A (t0 - ta )
Qd =C.l.d [1/2(t0 - ta )]
 Determine the thermal equilibrium to see that the heat dissipate becomes at least
equal to the heat generated . In case of the heat generated is more then the heat
dissipated then either the bearing is redesigned or it is artificially cooled by water.
 Artificial cooling (Qg > Qd ) is given by
Qt= m.s.t (mass. Specific .Temperature )

Given; W = 20 000 N ; N = 900 r.p.m, t0 = 55°C ; Z = 0.017 kg/m-s ; ta = 15.5°C ; p = 1.5 N/mm2 ; t
= 10°C ; C = 1232 W/m2/°C.
Solution :1) let us find the length of the journal ( l ), Assume the d of the journal ( d ) as 100 mm
l = 1.6 d = 1.6 × 100 = 160 mm …………Ans.
2) Bearing Pressure
p= 20 000 /160* 150=1.25
Z.N /p= 0.017 *900/ 1.25 =12.24
3)
From Table 26.3, we find that the operating value of
ZN/p=28
The minimum value of the bearing modulus at which the oil film will break is given by
3K=ZN/p
k = 1/3*(28)=9.33
Since the calculated value of bearing characteristic number 12.24 is more then 9.33
So, the bearing will operate under hydrodynamic conditions.

4)
From Table 26.3, the clearance ratio (c/d) = 0.0013
5) coefficient of friction,
= 0.0031 + 0.002 = 0.0051 …… . [From Art. 26.13, k = 0.002]
6) Heat generated,
7) . Heat dissipated
… ( d” taken in meters)

We see that the heat generated is greater than the heat dissipated which
indicates that the bearing is warming up.
Therefore, either the bearing should be redesigned by taking t 0 = 63°C or the
bearing should be cooled artificially. We know that the amount of artificial
cooling required
= Heat generated – Heat dissipated
= Qg – Qd
= 480.7 – 389.3
= 91.4 W
>Mass of lubricating oil required for artificial cooling
Let m = Mass of the lubricating oil required for artificial cooling in kg / s.
We know that the heat taken away by the oil,
Qt = m.S.t = m × 1900 × 10= 19 000 m W
Equating this to the amount of artificial cooling required,
we have 19 000 m = 91.4
∴ m = 91.4 / 19 000 = 0.0048 kg / s = 0.288 kg / min Ans

Example 26.2. The load on the journal bearing is 150 kN due to turbine shaft of 300
mm diameter running at 1800 r.p.m. Determine the following 1. Length of the
bearing if the allowable bearing pressure is 1.6 N/mm2, and 2. Amount of heat to
be removed by the lubricant per minute if the bearing temperature is 60°C and
viscosity of the oil at 60°C is 0.02 kg/m-s and the bearing clearance is 0.25 mm.
Solution. Given : W = 150 kN = 150 × 103 N; d = 300 mm = 0.3 m ; N = 1800
r.p.m. ; p = 1.6 N/mm2 ; Z = 0.02 kg / m-s ; c = 0.25 mm
Length of the bearing
Let l = Length of the bearing in mm.
We know that projected bearing area,
A = l × d = l × 300 = 300 l mm2
and allowable bearing pressure ( p)

2) Amount of heat to be removed by the lubricant

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