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.
 Supported end conditions  Make use of end block with single self aligning bearings.
 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/cm^{2} 2.060 x 10^{6}

E.I.g
F = k x 
W.L.^{4}
^{ END CONDITION}

^{ }
^{ VALUE OF K}
 
^{ } 1^{ST }Mode

2^{nd} Mode
 
Fixed , Supported
Fixed , Fixed

1.47
1.57

^{ }2.56
2.46

DATA :
SHAFT DIA

I = cm^{4}

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 10^{6}
S.NO.

SPEED RPM
1^{ST} MODE

VALUE OF K

I=(πd^{4})/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 10^{6}
S.NO.

SPEED RPM
2^{ND} MODE

VALUE OF K

I=(πd^{4})/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 10^{6 }
S.NO.

SPEED RPM
1^{ST} MODE

SPEED RPM
2^{ND} MODE

VALUE OF K

VALUE OF K

I=(πd^{4})/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 10^{6 }
S.NO.

SPEED RPM
1^{ST} MODE

SPEED RPM
2^{ND} MODE

VALUE OF K

VALUE OF K

I=(πd^{4})/64

^{WT.}
^{IN grams}

^{Fth =}
^{K.(EIG)/WL4}

^{Fth =}
^{K.(EIG)/WL4}

^{Fact=}
^{RPM/TIME}

^{Fact=}
^{RPM/TIME}

1.
 
2.

I'm really excited in your design. I can't wait to build it.
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