DOM MANUALS

AIM: To Find out Critical Speed Experimentally And To Compare The Whirling Speed Of a Shaft.

EQUIPMENTS: Tachometer, Shaft, End fixing arrangement etc.

THEORY: This apparatus is developed for the demonstration of a whirling phenomenon.

The shaft can be tested for different end conditions.

The apparatus consists of a frame to support its driving motor, end fixing and sliding blocks etc.

A special design is provided to clear out the testing of bearing of motor spindle from these testing shafts. The special design features of this equipment are as follow:

A. COUPLING

A flexible shaft is used to drive the test shaft from motor.

B. BALL BEARING FIXING ENDS.

The end fixes the shaft while it rotates. This can be replaced within a short time with the help of this unit. The fixing ends provide change of end fixing condition of the rotating shaft as per the requirement.

SHAFT SUPPLIED WITH THE EQUIPMENT

Polished steel shaft are supplied with the machine. The dimensions being as under :

SHAFT NO.	DIAMETER (APPROX)	LENGTH(APPROX)
1.	4.0 MM	900 MM
2.	4.7 MM	900 MM

END FIXING ARRANGEMENT

At motor end as well as tail end different end conditions can be developed by making use of different fixing blocks.

1. Supported end conditions - Make use of end block with single self aligning bearings.
2. Fixed end condition - Make use of end block with double bearing.

GUARDS D1 AND D2 :

The guards D1 and D2 can be fixed at any position on the supporting bar frame which fits on side supports F. Rotating shafts are to be fitted in blocks in A and B stands.

SPEED CONTROL OF DRIVING MOTOR :

The driving motor is 230V , DC 1/6 HP, 3000 RPM, universal motor and speed control unit is a dimmer state of 240V, 2 Amps, 50 C/S.

MEASUREMENT OF SPEED :

To measure the speed of the rotating shaft a simple tachometer may be used on the opposite side of the shaft extension of the motor.

WHIRLING OF ELASTIC SHAFTS :

If L = Length of the shaft in cms.

E = young’s module kg/cm² 2.060 x 10⁶

I = 2nd moment of inertia of the shaft cm4 W = Weight of the shaft per unit length kg/cm. g = Acceleration due to gravity of cms/sec2 = 981 Then the frequency of vibration for the various modes is given by the equation :

E.I.g

F = k x --------

W.L.⁴

END CONDITION	VALUE OF K
	1ST Mode	2nd Mode
Fixed , Supported Fixed , Fixed	1.47 1.57	2.56 2.46

DATA :

SHAFT DIA	I = cm4	W = kg/cm
3.8 mm 5.0 mm	X 10-4 x 10-4	0.15 x 10-2 0.28 x 10-2

CALCULATIONS :

a) Both ends of shafts free (supported) 1^st and 2^nd mode of vibration can be observed of shafts with 3/16” dia and ¼” dia.

b) One end of shaft fixed and the other free; 1^st and 2^nd mode of vibration can be observed on shaft with 3/16” dia.

c) Both ends of shaft fixed- 2^nd mode of vibration cannot be observed on any of the shafts as the speeds are very high and hence beyond the range of the apparatus.

FIXED – FIXED

DIAMETER OF BRASS ROD = 0.4 CM

WEIGHT = 150 GRM = KG/CM = 0.0015

YOUNG MODULUS E = 2.06 X 10⁶

S.NO.	SPEED RPM 1ST MODE	VALUE OF K	I=(πd4)/64	WEIGHT in grams	Fth = K.(EIG)/W	Fact = RPM/TIME
1
2

DIAMETER OF BRASS ROD = 0.47 cm

WEIGHT = 190 gram = KG/CM = 0.0019

YOUNG MODULUS E = 2.06 X 10⁶

S.NO.

SPEED RPM 2ND MODE

VALUE OF K

I=(πd4)/64

WEIGHT in grams

Fth = K.(EIG)/W

1
2

SUPPORTED – FIXED

DIAMETER OF BRASS ROD = 0.4 cm

WEIGHT = 190 gram = KG/CM = 0.0019

YOUNG MODULUS E = 2.06 X 10⁶

S.NO.	SPEED RPM 1ST MODE	SPEED RPM 2ND MODE	VALUE OF K	VALUE OF K	I=(πd4)/64	WEIGHT IN grams	Fth = K.(EIG)/WL4	Fth = K.(EIG)/WL4	Fact= RPM/TIME	Fact= RPM/TIME
1.
2.

DIAMETER OF BRASS ROD = 0.47 cm

WEIGHT = 140 gram = KG/CM = 0.0014

YOUNG MODULUS E = 2.06 X 10⁶

S.NO.	SPEED RPM 1ST MODE	SPEED RPM 2ND MODE	VALUE OF K	VALUE OF K	I=(πd4)/64	WT. IN grams	Fth = K.(EIG)/WL4	Fth = K.(EIG)/WL4	Fact= RPM/TIME	Fact= RPM/TIME
1.
2.