FACULTY OF MECHANICAL ENGINEERING

SKMM 4353 LUBRICATION

CASE STUDY 1

MUHAMMAD NADZMI BIN MOHAMMAD NAZARI

A11KM0260

SECTION 01

EN. MOHD. ZUBIL BIN BAHAK

1

TABLE OF CONTENTS

1.0 INTRODUCTION ............................................................................................ 2

2.0 PROBLEM ANALYSIS ................................................................................... 2

3.0 ANALYSIS ....................................................................................................... 3

3.1 Sample Calculation ........................................................................................ 3

3.1.1 Performance Analysis ............................................................................ 4

3.1.2 Calculation of Temperature.................................................................... 6

3.1.3 Calculation of Minimum Film Thickness .............................................. 9

3.1.4 Further Design Considerations ............................................................. 10

3.2 Calculation for Changing of Lubricating Oil .............................................. 11

3.2.1 Performance Analysis .......................................................................... 11

3.2.2 Calculation of Temperature.................................................................. 14

3.2.3 Calculation of Minimum Film Thickness ............................................ 16

3.2.4 Further Design Considerations ............................................................. 17

4.0 RESULT AND DISCUSSION ....................................................................... 18

4.1 Lubricating Oil ISO VG 32 ......................................................................... 20

4.2 Lubricating Oil ISO VG 68 ......................................................................... 22

5.0 CONCLUSION ............................................................................................... 24

2

1.0 INTRODUCTION

A possible by-product in the aluminium smelting process is fluorine and adequate

ventilation of plant is most important from a health hazard point of view.

Centrifugal fans are commonly employed to discharge ventilation air to a chimney

stack.

In the particular plant, the fan motors have liquid film journal bearings with specific

specification. The plant operators find that some bearings operate adequately whilst

others fail due to wiping of the white metal bearing lining. The failure might due to

many reasons, thus, calculations and proving are needed to be done in order to

determine the causes and to determine which specifications are needed to be

configured.

2.0 PROBLEM ANALYSIS

The journal bearings specification given might have problems due to

misalignment and is not safe. Calculations on performance, temperature and film

thickness must be determined so that the specifications given can be changed in

order for the bearing to be safe to operate.

3

3.0 ANALYSIS

The specifications for the journal bearing are as follow:

All the method of calculations is done by referring Calculation Methods for

Steadily Loaded Axial Groove Hydrodynamic Journal Bearings. The code for this

book is ESDU Data Item No 84031.

3.1 Sample Calculation

This calculation show the step-step in order to solve this problem which is contain

performance analysis, calculation of temperature, calculation of minimum film

thickness and further design.

4

3.1.1 Performance Analysis

Firstly the designer must assume for the value of temperature of the lubricant in the

film, Te and temperature in the groove, Tg.

Te = 50 °C and Tg = 42 °C

Refer to the Figure 1,

ηe = 0.0258 Ns/m2 and ηg = 0.0356 Ns/m

2

=

= 24.22

Refer to Figure 2,

For ratio b/d = 0.06/0.1 = 0.6 and W’ = 24.22

Epsilon, ԑ = 0.87

Refer Figure 3,

For epsilon, ԑ = 0.87

Ratio b/d = 0.6

H’ = 116

=

= 269.3 W

5

Refer Figure 4,

For epsilon, ԑ = 0.87

F = 2.31

Refer Figure 5,

For epsilon, ԑ = 0.87

b/d = 0.6

Q’s = 0.46

The angular extent each groove, = 22.92

For a/b = 0.8,

= 2.31 x 0.026 x

= 0.1604

Hence,

=

= 1.52 x 10-6

m3/s

Qs = Q’s.Cd3 N.b.d

= 0.46 x 0.000153 x 15 x 0.06 x 0.1

= 6.21 x 10-6

m3/s

6

Q = Qp +

Qs

= 1.52 x 10-6

+ (0.8)( 6.21 x 10-6

)

= 6.49 x 10-6

m3/s

Q’r = 0.8 (1 – epsilon, ԑ)

= 0.8 (1 – 0.87)

= 0.104

Qr = Q’r . Cd. N. b. d

= 0.104 x 0.00015 x 15 x 0.06 x 0.1

= 1.404 x 10-6

m3/s

3.1.2 Calculation of Temperature

The Peclet number is,

=

= 4.218

Z =

=

= 5.31

7

= 1 + (2.75) (

)

= 1.18

= (

)

= 0.4427

= (

)

= 0.955

Using the equation for Q > Qs

C = 1.7 x 106

Te – Tf =

=

( )

= 11.67

8

Therefore,

Te = 11.67 + Tf

= 51.67

Tg – Tf =

(Te – Tf)

=

(50 - 42)

= 2.02

Tg = 2.02 + Tf

= 42.02

The agreement between the assumed and calculated value is acceptable because the

temperature difference is within 2K.

Tmax – Tg = (Te – Tg )

= 1.18 (50 – 42)

= 9.44

Therefore,

Tmax = 9.44 + 42

= 51.44 (acceptable)

Tout – Tf =

=

= 10.81

Tout = 10.81 + 40

= 50.81 (acceptable because not higher than 80 °C)

9

3.1.3 Calculation of Minimum Film Thickness

Calculate nominal minimum film thickness,

h =

(1- )

=

= 9.75 x 10-6

m

= 2 x 10-4

x 0.06

= 1.2 x 10-5

Hence,

=

= 0.08

Refer Figure 6,

hedge = 0.025 x 0.00015

= 3.75 x 10-6

m

Refer Figure 7,

The minimum film thickness, hs

hs = 6.26 x 10-6

m

Therefore, film thickness at the edge is not safe because hedge is less than hs.

10

3.1.4 Further Design Considerations

Checking the laminar operation,

Re =

=

= 11.97

Re√

= 11.97 √

= 0.4634

From Sketch 1, the value is still inside laminar region.

Checking for stability of the bearing and whirl problem,

=

= 3.44 x 10-3

The value is less than 0.2 and will not encounter whirl problem.

11

3.2 Calculation for Changing of Lubricating Oil

These calculations are specified for changing of lubricating oil from ISO VG 46 to

ISO VG 32. Any requirement of changing of lubricating oil in the future can be

done by using the same method.

3.2.1 Performance Analysis

Te = 50 °C and Tg = 40 °C

Refer to Figure 1,

ηe = 0.018 Ns/m2 and ηg = 0.027 Ns/m

2

=

= 34.72

Refer to Figure 2,

For ratio b/d = 0.06/0.1 = 0.6 and W’ = 34.72

Epsilon, ԑ = 0.895

Refer Figure 3,

For epsilon, ԑ = 0.895

Ratio b/d = 0.6

H’ = 131

12

=

= 212.22 W

Refer Figure 4,

For ԑ = 0.895

F = 2.23

Refer Figure 5,

For ԑ = 0.895

b/d = 0.6

Q’s = 0.45

The angular extent each groove, = 22.92

For the a/b = 0.8,

= 2.23 x 0.026 x

= 0.1548

13

Hence,

=

= 1.935 x 10-6

m3/s

Qs = Q’s.Cd3 N.b.d

= 0.45 x 0.000153 x 15 x 0.06 x 0.1

= 6.075 x 10-6

m3/s

Q = Qp +

Qs

= 1.935 x 10-6

+ (0.8)( 6.075 x 10-6

)

= 6.795 x 10-6

m3/s

Q’r = 0.8 (1 – epsilon, ԑ)

= 0.8 (1 – 0.895)

= 0.084

Qr = Q’r . Cd. N. b. d

= 0.084 x 0.00015 x 15 x 0.06 x 0.1

= 1.134 x 10-6

m3/s

14

3.2.2 Calculation of Temperature

The Peclet number is,

=

= 4.218

Z =

=

= 5.43

= 1 + (2.75) (

)

= 1.19

= (

)

= 0.4372

= (

)

= 0.9525

15

Using the equation for Q > Qs

C = 1.7 x 106

Te – Tf =

=

( )

= 9.16

Therefore,

Te = 9.16 + 40 = 49.16

Tg – Tf =

(Te – Tf)

=

(50-40) = 1.67

Tg = 1.67 + 40 = 41.67

The agreement between the assumed and calculated value is acceptable because the

temperature difference is within 2K.

Tmax – Tg = (Te – Tg)

= 1.19 (50 – 40) = 11.9

Therefore,

Tmax = 11.9 + 40 = 51.9 (acceptable)

Tout – Tf =

=

= 8.03

Tout = 8.03 + 40 = 48.03 (acceptable because not higher than 80 °C)

16

3.2.3 Calculation of Minimum Film Thickness

Calculate nominal minimum film thickness,

h =

(1- )

=

= 7.87 x 10-6

m

= 2 x 10-4

x 0.06

= 1.2 x 10-5

Hence,

=

= 0.08

Refer Figure 6,

hedge = 0.025 x 0.00015

= 3.75 x 10-6

m

Refer Figure 7,

The minimum film thickness, hs

hs = 6.26 x 10-6

m

Therefore, film thickness at the edge is not safe because hedge is less than hs.

17

3.2.4 Further Design Considerations

Checking the laminar operation,

Re =

=

= 17.18

Re√

= 17.18 √

= 0.6654

From Sketch 1 the value is still inside laminar region.

Checking for stability of the bearing and whirl problem,

=

= 3.44 x 10-3

The value less than 0.2 and will not encounter whirl problem.

18

4.0 RESULT AND DISCUSSION

At this section there will be a summary about the result of the problem and

discussion about the problem.

Parameters 1st iteration 2

nd iteration 3

rd iteration

Te 47 55 50

Tg 42 41 42

Ηe 0.03 0.021 0.0258

Ηg 0.036 0.039 0.036

W’ 20.83 29.76 24.22

0.85 0.882 0.87

H’ 107 123 116

F 2.35 2.28 2.31

1.175 1.17 1.18

Qp 1.53 x 10-6

1.37 x 10-6

1.52 x 10-6

Qs 6.35 x 10-6

6.07 x 10-6

6.21 x 10-6

Qr 1.62 x 10-6

1.27 x 10-6

1.404 x 10-6

Q 6.61 x 10-6

6.23 x 10-6

6.49 x 10-6

H 288.9 232.47 269.3

New Te 51.83 50.22 51.67

New Tg 41.79 42.06 42.02

The iterations are made to find the suitable value of effective temperature of

lubricant in the film, Te, and temperature in the groove, Tg. Both of this value must

be within 2K range from the assumed value to be acceptable to be used.

From the table above we obtained the adequate temperature for Te and Tg which is

51.67 and 42.02. Therefore, we can proceed with this value to calculate its

minimum film thickness and further design.

19

From the value of Te and Tg, we can calculate the maximum temperature, outlet

temperature, minimum film thickness and further design. The maximum

temperature is important because if the bearing temperature is too high, plastic

deformation of bearing material might occur in some operating conditions.

Therefore, it is needed to set the limit for maximum temperature of the bearing. The

outlet temperature is also needed to be determined to avoid deterioration.

Table above shows the calculated value. We can see that, the maximum and

outlet of the temperature for the bearing is 53.4 and 50.81. The maximum

temperature was determined by the material selected because the maximum

allowable bearing temperature depends on the lining material used. For this project

the maximum allowable temperature is 53.4 °C and this value is considered

appropriate. While for the outlet temperature is 50.81 °C and it is acceptable

because for the hydrocarbon oil contact with the atmosphere the recommend

temperature is below 80 °C for normal lubricant life.

From the table also we can see that the minimum safe thickness is 6.26µm. the

nominal minimum film thickness, h and hedge should be more than this value for it

to be safe. But from the analysis that has been done, the nominal minimum film

thickness is safe which is 9.75µm but not the hedge. The hedge not considered safe

because it not exceed the minimum film thickness which is 3.75µm. Therefore, the

existing design is not safe for the operating conditions.

Tmax 53.4

Tout 50.81

h 9.75 x 10-6

1.2 x 10-5

0.08

0.025

hedge 3.75 x 10-6

hs 6.26 x 10-6

20

4.1 Lubricating Oil ISO VG 32

The calculation is the same with all the previous calculation and shown in table

below for the result.

Parameters 1st iteration 2

nd iteration

Te 40 50

Tg 45 40

Ηe 0.0271 0.018

Ηg 0.022 0.027

W’ 23.06 34.72

0.86 0.895

H’ 112 131

F 2.32 2.23

1.19 1.192

Qp 2.47 x 10-6

1.935 x 10-6

Qs 6.11 x 10-6

6.075 x 10-6

Qr 1.51 x 10-6

1.134 x 10-6

Q 7.36 x 10-6

6.795 x 10-6

H 273.2 212.2

New Te 51.68 49.16

New Tg 41.97 41.67

The assumed value shows difference in temperature that less than 2K. Therefore,

we can proceed to calculations to know whether the ISO VG 32 can be used or not.

21

The calculations are the same with the previous calculation and the result is shown

in the table below:

Table above shows the result after calculations of the same method. We can

see that the nominal minimum film thickness, h is above the minimum safe film

thickness, hs. So, the film thickness is safe but not for hedge. We can see that the

value of hedge is lower than hs. So, the oil ISO VG 32 cannot be used for this

condition. Therefore, we need to change the oil to ISO VG 68.

Tmax 50.6

Tout 48.03

h 7.87 x 10-6

1.2 x 10-5

0.08

0.015

hedge 2.25 x 10-6

hs 6.26 x 10-6

22

4.2 Lubricating Oil ISO VG 68

The calculation is the same with all the previous calculation and shown in table

below for the result.

Parameters 1st iteration 2

nd iteration

Te 55 54

Tg 40 43

Ηe 0.029 0.031

Ηg 0.058 0.051

W’ 21.55 20.16

0.85 0.849

H’ 108 107

F 2.34 2.36

1.19 1.192

Qp 9.45 x 10-6

1.08 x 10-6

Qs 6.48 x 10-6

6.41 x 10-6

Qr 1.62 x 10-6

1.63 x 10-6

Q 6.13 x 10-6

6.21 x 10-6

H 281.9 298.5

New Te 52.62 53.12

New Tg 43.35 43.33

The assumed value shows difference in temperature that less than 2K. Therefore,

we can proceed to calculations to know whether the ISO VG 68 can be used or not.

23

The calculations are the same with the previous calculation and the result is shown

in the table below:

As we can see from the table above the value of Tmax and Tout can be

accepted. The value for the nominal minimum film thickness, h and hedge of the

bearing are higher than the value of the minimum film thickness, hs. Therefore, the

bearing with lubricating oil ISO VG 68 can be used with the operating condition.

Now, we can proceed to calculation to determine its stability and the whirl

problem. The results are as shown in the table below:

Reynold number, Re 9.976

Laminar condition, Re√

0.37

Whirl problems,

3.44 x 10-3

The Reynold number is calculated and by referring Sketch 1, we can know

the location of the condition to be laminar or turbulence region. Then, as the

bearing is purely gravitational, stability have to be checked whether it will

encounter whirl problem or not. From the result above, we can see that the bearing

is located at the laminar region. The value of whirl problem has not exceeded 0.2

which means the bearing will not encounter whirl problem.

Tmax 50.6

Tout 48.03

H 1.13 x 10-6

1.2 x 10-5

0.08

0.045

hedge 6.75 x 10-6

hs 6.26 x 10-6

24

5.0 CONCLUSION

First of all, the calculations started with the determination of the temperature

to be assumed for the outlet. The specifications are fixed to what is given.

Lubricating oil ISO VG 46 (default) is used. Then, the assumed value determined is

proven to be correct if the value of temperature difference is less than 2K.

When the temperatures are correct, the calculations can be proceeded to

calculate the film thickness. By using ISO VG 32 as the first choice, it is proven

that the lubricating oil is not suitable as the film thickness at the hedge is lower than

the minimum film thickness, making it not safe. Therefore, the lubricating oil is

needed to be changed.

By using ISO VG 68 as the second choice, the film thickness is more reliable

and is safe as the film thickness at the edge is higher than the minimum film

thickness. Therefore, advanced calculations on Reynold number and the whirl

problem are conducted. By referring Sketch 1, the Reynold number determined is at

laminar region and by more calculation, the bearing is proven to be not encounter

with whirl problem.

In conclusion, the appropriate lubricating oil to be used with the given

specifications is lubricating oil ISO VG 68.