experiment ii-1a study of pressure distributions in lubricating oil...

STUDY OF PRESSURE DISTRIBUTIONS IN LUBRICATING OIL FILMS

USING MICHELL TILTING PAD APPARATUS

OBJECTIVE

To study generation of pressure profile along and across the thick fluid film (converging,

diverging and uniform) in Michell Pad

THEORY

Slider thrust bearing as shown in Fig.1 is used to sustain axial thrust in mechanical systems. A

hydrodynamic lubricated slider bearing develops load carrying capacity by virtue of the relative

motion of the two surfaces separated b

of pressure development in the presence of relative velocity, physical wedge, and a medium

having viscosity at the interface of mating solids.

Fig.1 Thrust slider bearing geometry

(a) Couette flow (b) Poiseuille flow

Fig.2 Mechanism of pressure development in slider

Physical insight in pressure development in the film can be gained by examination of governing

equations and their solutions. For this purpose, following analytical relations are provided.

EXPERIMENT II-1A


USING MICHELL TILTING PAD APPARATUS


diverging and uniform) in Michell Pad Thrust Bearing.



motion of the two surfaces separated by a fluid film. Figure 2(a) – (c) demonstrated mechanism


having viscosity at the interface of mating solids.

Fig.1 Thrust slider bearing geometry

(a) Couette flow (b) Poiseuille flow

(c) Resulting velocity profile

Fig.2 Mechanism of pressure development in slider bearing



h1 = Separation at leading edge

h2 = Separation at trailing edge





(c) demonstrated mechanism




= Separation at leading edge

= Separation at trailing edge

A. Pressure distribution in film for infinitely long bearing (L>>B):

2

2b 2

L 3

3 u h (n 1) Bp y

2L h

η − = −

(1)

B. Pressure distribution in film for short bearing (L<<B):

b 1 2

S 2 2 2

2

6 u L (h h )(h h )p

h (n 1) h

η − −=

− (2)

C. Film thickness relation

1 2

1

h hh h x

L

− = −

D. Approximate pressure distribution in film for finite bearing (L=B):

F L S

1 1 1

p p p= +

(4)

DESCRIPTION OF SETUP

The apparatus consists essentially of a plane M.S. Slider, which may be accurately

positioned relative to moving belt, which carries a thick oil film. The main body of machine

consists of bearing blocks; two steel drums in turn are carrying a plastic P.V.C. belt. One

drum is driven by variable speed D.C motor. The apparatus is contained in a M.S tank,

which is filled with the oil to such a level that the lower part of the belt is submerged.

The oil pressure developed between the slider and moving belt is indicated by tubes secured

to the slider. These tubes are equally spaced along the axis of the slider in the direction of

motion, while a further set is located transversely.

PROCEDURE 1. Measure the length and width of the pad.

2. Record the value of viscosity of lubricating oil.

3. The gap between tilting pad and the belt is adjusted by using four knobs provided on the

pad holder.

4. The motor is started and the speed is gradually increased till we get required speed of

shaft, which is connected to motor by a V-belt drive.

5. The readings for the pressure heads in all the tubes are measured only after the

equilibrium condition has been reached. Temperature of the oil should be noted at this

time.

6. Keeping the h1 and h2 same, pressure head reading for different speeds are taken.

7. The h1 and h2 are changed and then the same procedure above is repeated (For

converging and diverging films).

(3)

STUDY OF PRESSURE

OIL FILM IN JOURNAL BEARING

OBEJECTIVE

To study the pressure distributions in lubricating oil film

and loads.

THEORY

A journal bearing consists of a cylindrical body around a rotating

either for supporting a radial load or simply as a guide for smooth transmission of torque. It

involves a stationary sleeve (or bush) in a housing structure as shown in following Fig.1. It

shows the cross section of a journal be

inner surface of sleeve/bush. When motion is initiated (refer Fig.1 (b)), the shaft first rolls up

the wall of the sleeve in the direction opposite to rotation due to metal

the steel shaft and bearing. With an adequate lubricant supply, a supporting wedge shaped film

of lubricant is almost immediately formed to lift the journal into steady

Once the shaft is in steady state, it assumes a position i

coordinates are eccentricity ‘e’ and attitude angle ‘

displacement of the journal centre ‘

between the load line and the line between these centres. Eccentricity decreases and attitude

angle commonly increases with more vigorous oil pumping action by the journal at higher

speeds and with increased lubricant viscosity.

Fig.1 Sequence of journal motion from start

EXPERIMENT II-1B

STUDY OF PRESSURE DISTRIBUTIONS IN LUBRICATING

OIL FILM IN JOURNAL BEARING

the pressure distributions in lubricating oil films in journal bearing at different speeds

A journal bearing consists of a cylindrical body around a rotating shaft. This system is used



shows the cross section of a journal bearing at rest with the journal surface in contact with the


the wall of the sleeve in the direction opposite to rotation due to metal-to-metal friction betwee


of lubricant is almost immediately formed to lift the journal into steady-state position (Fig.1(c)).

Once the shaft is in steady state, it assumes a position in the bearing clearance circle whose

’ and attitude angle ‘φ’(refer Fig. 2). Eccentricity is simply the

displacement of the journal centre ‘Oj’ from the bush centre ‘Ob’. Attitude angle is the angle

the line between these centres. Eccentricity decreases and attitude


speeds and with increased lubricant viscosity.

Fig.1 Sequence of journal motion from start-up to steady state

DISTRIBUTIONS IN LUBRICATING

s in journal bearing at different speeds

shaft. This system is used



aring at rest with the journal surface in contact with the


metal friction between


state position (Fig.1(c)).

n the bearing clearance circle whose

’(refer Fig. 2). Eccentricity is simply the

’. Attitude angle is the angle

the line between these centres. Eccentricity decreases and attitude


Fig.2 Cross section of a journal bearing with nomenclature

Physical insight in pressure development in the film can be gained by examination of

governing equations and their solutions. For this purpose, following analytical relations ar

provided.

D. Pressure distribution in film for infinitely long bearing (L>>D):

(

(L

b

2 22

2 cos ( sin )6 u Rp

c 2 1 cos

+ ε θ ε θη = + ε + ε θ

Value of ‘ε’ can be calculated using the following

(2

s

RW 12 N LR

C

ε π − ε π − = πη

E. Pressure distribution in film for short bearing (L<<D):

( )

( )b

S 2 3

sin3 up z

Rc 1 cos

ε θη = − + ε θ

Value of ‘ε’ can be calculated using the following

(

2

s

R 16W 2 N LR 1 1

C 4 1

= πη − ε +

Fig.2 Cross section of a journal bearing with nomenclature


governing equations and their solutions. For this purpose, following analytical relations ar

Pressure distribution in film for infinitely long bearing (L>>D):

)

)( )2 22

2 cos ( sin )

2 1 cos

+ ε θ ε θ

+ ε + ε θ

’ can be calculated using the following equation (2):

( )( )( ) ( )

0.52 2 2

2 2

4

1 2

ε π − ε π − − ε + ε

Pressure distribution in film for short bearing (L<<D):

2

2

2 3

Lp z

2

= −

’ can be calculated using the following equation (4):

)2

2 22

R 16W 2 N LR 1 1

4 1

πε = πη − ε + π − ε


governing equations and their solutions. For this purpose, following analytical relations are

(1)

(2)

(3)

(4)

F. Approximate pressure distribution in film for finite bearing (L=D):

F L S

1 1 1

p p p= +

(5)

PROCEDURE

Measure the length of bearing and diameters of the bearing and journal. Record the value of

viscosity of lubricating oil. Insure the supply of the lubricant in bearing from the overhead

reservoir by appropriately turning the knob. Slowly run the journal and reach to the desired

journal speed. Load the bearing to the desired value by keeping the loads in the hanger. Record

the pressures indicated by mechanical gauges.

EXPERIMENT II-2A

PORTER AND PROELL GOVERNORS

OBJECTIVE

To study the performance characteristics of Porter and Proell governors

Porter governor

Proell governor

GOVERNOR PARAMETERS

l =0.13 m, c=0.051m, θ0=290

Mass of sleeve (M) = 3.1 kg

Each additional mass = 0.5 kg

Mass of each ball (m) = 0.835 kg

F= controlling force

GOVERNOR PARAMETERS

l =0.13 m, a=0.75 m

c=0.51 m, θ0=290

Mass of sleeve (M) = 3.1 kg

Each additional mass = 0.5 kg

Mass of each ball (m) = 0.835 kg

F= controlling force

PRINCIPLE OF PORTER GOVERNOR

Consider the ball of weight w kg and the sleeve with weight of W kg attached to the links

shown in Figure 1 rotating about an axis ZZ with an angular velocity ω rad/sec.

Taking moment about I,

Then BD×F= [w×ID+(W/2) ×2ID’]

F= (W+w) tanθ

Also H=2 [ l2-(r-c)

2]

1/2 (1)

F=[(W+w)(r-c)] / [ l2-(r-c)

2]

1/2 (2)

Speed of rotation changes, so also r, causing the height of sleeve, H to vary. This movement of

sleeve is used in controlling steam supply or fuel supply to engine to govern the speed of the

system. If the speed increases, the lift H is used to close the inlet fuel supply valve by a

corresponding amount, which decreases the speed. If the speed of the engine decreases, the drop

in height H of sleeve is used to open the valve further thus increasing the inlet supply and

increasing the speed, such a movement of the sleeve governs the engine speed.

Characteristics curves

PRINCIPLE OF PROELL GOVERNOR (Ref to Figure 2)

Taking moment about I

F=w (ID/BD) + W/2 (IC/BD)

ID= ID’-DD’= sin sinl aθ δ−

IC= 2ID’=2 sinl θ

BD= cos cosl aθ δ+

0δ θ θ= −

0 0[ { sin sin( )} ( / 2){2 sin }]/[ cos cos( )]F w l a W l l aθ θ θ θ θ θ θ= − − + + −

0sin sin sin sin( )r c l a c l aθ δ θ θ θ= + + = + + −

2 cosH l θ=

Speed-control device

The above figure shows a proposed speed-control device that could be mounted on an

automobile engine and would serve a two fold purpose.

1. To function as a constant-speed governor for cold mornings so that the engine will race

until the choke is reset. This speed control would enable the engine speed to be

regulated, thus maintaining a preset idle speed. The idle speed would be selected on the

dash- mounted speed –control level.

2. To function as an automatic cruise control for freeway driving. The desired cruising

speed could be selected by moving the indicator lever on the dashboard to the desired

speed.

[Note: the above diagram is for better understanding of any governor system, in general.]

EXPERIMENT II-2B

CORIOLIS FORCE DEMONSTRATOR

OBJECTIVE To demonstrate Coriolis component of acceleration

APPARATUS

Coriolis acceleration demonstrator from GUNT, Germany

Apparatus for Demonstration of Coriolis acceleration

THEORY

The task of this handy table unit is to demonstrate the Coriolis force on bodies in a rotating

reference system. A water tank is attached to a rotating boom; this can be placed in motion by a

motor. With the aid of a pump, a thin jet of water is generated in the tank; this is sprayed

radially from the outside in the direction of the centre of rotation of the rotating boom.

Depending on the speed of the setup and the outlet speed of the jet, the jet is deflected by an

apparent force, the Coriolis force. The speed of the motor is electronically controlled and

displayed digitally. The unit stands on rubber feet and requires, apart for filling with water, only

a mains supply.

Demonstration

Coriolis force on a water jet in circular motion

· As a function of the rotational speed

· As a function of the direction of rotation

MASS MOMENT OF INERTIA OF

OBJCTIVE

To study gyroscopic principle and determine mass moment of inertia of the rotor.

THEORY

Consider a disc rotating at high speed with angular velocity

Disc with spin axis OX and precision axis OY

Angular momentum of the disc=

rI =mass moment of the inertia about OX

Let the above disc now rotate (precess) about vertical axis i.e. OY

angular velocity ωp rad/sec.

The change in angular momentum of the disc in time t, covering an angle

AB= Ir ωs∆θ = ∆H, where H= Ir

Disc rotating about its spin axis as well as around the precision axis.

EXPERIMENT II-3A

MASS MOMENT OF INERTIA OF THE ROTOR


Consider a disc rotating at high speed with angular velocity ωs rad /sec about the spin axis OX.

Disc with spin axis OX and precision axis OY

Angular momentum of the disc=r sI ω

moment of the inertia about OX kg-m2

Let the above disc now rotate (precess) about vertical axis i.e. OY (precession axis) with

change in angular momentum of the disc in time t, covering an angle ∆θ is

ωs, angular momentum.



about the spin axis OX.

axis) with


The rate of change of angular momentum is dH

Tdt

=

0lim r st r s p

dH II

dt t

ω θω ω→

∆∴ = =

∆�

Where ,

p

t

θω

∆=

∆

r s pT I ω ω∴ =

Therefore a couple T must act on the disc in a plane perpendicular to OB

(OB is now Torque axis) called as gyroscopic couple (horizontal axis).

r s pT I ω ω∴ = Nm

A gyroscopic torque is developed due to the precession of a spinning rotor.

To understand the procedure to find out the orientation of gyroscopic couple.

EXPERIMENT II-3B

BALANCING OF ROTATING MASSES

OBJECTIVE

To study the effect of rotating unbalance and balancing of rotating masses.

APPARATUS

Weights and clamping bolts.

THEORY

If the center of mass of rotating machine (such as alternator, pump impeller, compressor

impeller etc) does not lie on the axis of rotation, the inertia forces are given by 2

i

WeF

g

ω=

Where

e= eccentricity, i.e. the distance from the center of mass to the axis of rotation.

W=unbalance weight

ω=angular velocity of rotation of unbalance weight.

I. Balancing of single revolving mass.

There are two different cases to consider, viz.,

(a)Those in which the balance weight may be arranged to revolve in the same plane as

unbalance weight.

(b)Both the plane of balancing weights are on one side of the plane of unbalances.

(c)One plane of balancing weight is on either side of the plane of unbalance.

For complete balancing in rotating system, the following two conditions must be fulfilled.

The center of mass of mass of the system should lie on the axis of rotation when resultant of all

the inertia forces during the rotation will be zero.

The resultant couple due to all the inertial forces during rotation must be zero.

Therefore, resultant equations are:

1 1 2 2

We w e w e= +

And

1 1 1 2 2 2

Wea w e a w e a= +

Or

1 1 1 2 2 2

Web w e b w e b= +

Where e1 and e2 are the eccentricity of balancing weights w1 and w2 respectively and a1 and

a2 (or b1 and b2) are their distances from one of the bearings. (Under dynamics balance bearing

reaction due to inertia forces are zero.)

II. Balancing of multiple rotating masses on a rotor:

1. Two balancing masses in two planes are sufficient to produce complete dynamic

balance of general rotating system. The resulting equation may be written as 1

0

0n

i i i

n

W e Cosφ=−

=

=∑

1

0

0n

i i i

n

W e Sinφ=−

=

=∑

1

0

0n

i i i i

n

W e a Cosφ=−

=

=∑

1

0

0n

i i i i

n

W e a Sinφ=−

=

=∑

Where unbalance W1 is present in n different planes, and their orientation is measured

w.r.t any reference line as shown in Fig. 2

Fig. 2

EXPERIMENT II-4

MECHANISM SIMULATION USING WORKING MODEL

OBJECTIVE

To understand how to study the behavior of a mechanismwithout fabricating it.

APARATUS

Working Model Software and a PC

THEORY

Working model software simulates any mechanism drawn in its environment. Such simulation

software is based on the equations of motion of any mechanism, followed by numerical

integration.

TASK

1. Do Kinematic (get rocker velocity and acceleration graph for 1 rad/sec rotation of crank)

analysis of the following four-bar mechanism.

2. Do Kinematic and Dynamic Analysis (get velocity, acceleration and force plots for

piston and crank) of a single cylinder I C engine with following parameters, using

Working Model.

Crank radius = 250 mm, Crank weight = 35 kg,

Connecting rod height = 500mm, Connecting rod width = 100mm,

Connecting rod weight = 2 kg,

Piston height = 200mm, Piston width = 200mm,

Piston weight = 1 kg,

Gas Force = 100 N, it should only be acting during downward stroke

Gravity = 9810 mm/sec2

Note: Combustion should get cutoff for crank velocity greater than 35 rad/sec (Hint: write logic

for to be acting only when crank velocity is less than 35 rad/sec and piston velocity less than

zero).

All dimensions in meter

and degree

EXPERIMENT II-5A

BALANCING OF FOUR CYLINDER INLINE ENGINE MODEL

OBJECTIVE

To study the resonance conditions in a 4-cylender in-line Variable Crank Angle apparatus.

DESCRIPTION OF SETUP

The four identical inline cylinders are placed in a housing, which in turn is mounted on a

cantilever beam. The crank angles of the three cylinders are adjustable with respect to the fourth

one. A variable speed motor whose speed can be controlled drives the cranks.

The unbalance primary or secondary forces excite vertical (up and down) vibrations which get

amplified under resonance condition.

Components of an IC engine unit

THEORY

i) Four-cylinder, symmetrical, 180° crank offset

F1 = 0 F2 = 4 .λ .m.r.w

2

M1= 0 M2 = 0

ii) Four-cylinder, asymmetrical, 90° crank offset

F1 = 0 F2 = 0

M1 = 1.414 m.r.w2.a M2 = 4.λ.m.r.w

2.a

iii) Two-cylinder, 180° crank offset

F1= 0 F2 = 4 λ.m.r.w2

M1= 4.m.r.w2.a M2 = 0

iv) Single-cylinder

F1 = 4.m.r.w

2 F2 = 4.λ.m.r.w

2

M1 = 0 M2 = 0

where F1 and F2 are the primary and secondary forces respectively.

M1 and M2 are the primary and secondary moments respectively.

M - oscillating mass = 47.8 g; r - crank radius = 15mm

w - speed in rad/s; λ= r/l = 0.214 l-length of connecting rod

a-distance between cylinders(centre to centre) = 35 mm

EXPERIMENT II-5B

EPICYCLIC GEAR TRAIN MECHANISM

OBJECTIVE

To study epicyclic gear train and determine experimentally the input torque, holding torque and

output torque.

EPICYCLIC GEAR TRAIN

Any combination of gear wheels by means of which motion is transmitted from one shaft to

another is called a gear train. In an epicyclic gear train, a planetary wheel rotates about its own

axis as well as about another gear known as the sun gear. The “bodily” rotation of the planet

around the sun is generally carried by an arm which may transmit rotation to other gears.

Following formulae hold true for the given set up.

Gear ratio =speed of driver shaft/ speed of driven shaft ………………… (1)

Input torque, Ti =(V x I x η x4500)/(746 x2π N) kg-m ………………… (2)

Holding torque = (T1-T2) x R1 kg-m ………………… (3)

Output torque = (T3-T4) x R2 kg-m ………………… (4)

Where

T1-T2 = spring balance tensions of holding arrangement in kg.

T3-T4= spring balance tensions of output torque measurement arrangement in kg.

R1 = radius of holding drum in meter.

R2 = radius of output brake drum in meter.

η=efficiency of the motor.

N= motor RPM

UNIVERSAL VIBRATION

OBJECTIVE

Study damped, undamped, free and forced vibration

EXPERIMENT

The system consists of a rectangular section bar supported at one end by a trunnion fitted in

ball bearing and at the other end by a helical spring (see Fig.1). The beam is

vertical plane by a motor driving a shaft carrying two discs with unbalanced masses. The

amplitude and frequency may be

to the beam tracing a record

speed of 3 RPM. To determine the phase between beam

pencil stylus is pivoted from the member of the frame and races a record on a paper attached

to the disc carrying out of balance weights.

METHOD-1

To study the free vibrations of the system for different

and determine the log decrement factor.

EXPERIMENT II-6

UNIVERSAL VIBRATION MACHINE

Study damped, undamped, free and forced vibration.


ball bearing and at the other end by a helical spring (see Fig.1). The beam is


amplitude and frequency may be recorded by an electrically actuated pencil stylus

record on to a paper. The drum (d=9.38cm) is driven

o determine the phase between beam displacement and exciting


to the disc carrying out of balance weights.

Experimental set up

study the free vibrations of the system for different damper settings. Draw the

the log decrement factor. Also find the natural frequency.


ball bearing and at the other end by a helical spring (see Fig.1). The beam is excited in a


by an electrically actuated pencil stylus attached

driven at a constant

exciting force, the


the decay curve

FREE VIBRATIONS

Response of an

Let Z= distance on the paper drum

V= surface velocity of the drum

Time , t=Z/V and V=( π

Logarithmic decrement

1 2 0 1

log( / ) (1/ ) log( / )x x n x xδ = =

Damping coefficient

/ 2ξ δ π= , if

or ξ = 2 2/ 4δ π δ+

Natural frequencies (ωn)

2

2 / 1n dω π τ ξ= −

(d

τ =measured from response curve)

Damped natural frequency (ωd)

d aω ω ξ= −

FORCED VIBRATIONS

The equation of motion of the system is given by

1 2 3 1 2Ml x t Cl x t Kl x t me l l t

Where, x(t) is the spring displacement.

The above equation may be written as

( ) ( ) ( ) sin( )eq eq eq eqM x t C x t K x t m e t+ + =

Response of an under damped spring mass system

Let Z= distance on the paper drum

V= surface velocity of the drum

π d N)/60 where N=3r.p.m

d=9.38cm

1 2 0 1log( / ) (1/ ) log( / )x x n x x= = (1)

, if ξ <<1 (2)

2 2δ π δ+ if ξ is not small

(3)

=measured from response curve)

21ω ω ξ= −

The equation of motion of the system is given by 2 2 2 2

1 2 3 1 2( ) ( ) ( ) sin( )Ml x t Cl x t Kl x t me l l tω ω+ + =

Where, x(t) is the spring displacement.

The above equation may be written as 2

( ) ( ) ( ) sin( )eq eq eq eqM x t C x t K x t m e tω ω+ + = (4)

Where,

2

1eqM Ml= , 2

2eqC Cl=

The natural frequency is given by,

/n eq eq

K Mω = (5)

The response x(t) =x0 sin(ωt-φ ) can be written in dimensional form as

0

1/ 222 2 2

1( )

{1 ( / ) } {2 / }

eq

eqn n

x KH

m eω

ω ω ω ξω ω= = − +

(6)

2tan 2 /{1 ( / ) }n nφ ξω ω ω= − (7)

The damping may be determined from the amplitude-frequency curves by the half-power

method (see fig.3). Draw a horizontal line parallel to /n

ω ω axis at a height of / 2px to cut

the response curve at 1

/n

ω ω and2

/n

ω ω . Then the damping ratio, ξ is

ξ =1/2 ×intercept= ½[(ω2-ω1)/ωn]

Amplitude-frequency curve

Frequency Response and Phase Relationship of a single Frequency Response and Phase Relationship of a single degree of freedom

of freedom System.

experiment ii-1a study of pressure distributions in lubricating oil...

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