Whirling Speed OF Shaft manual PDF

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WHIRLING OF SHAFT APPARATUS Instruction Manual

INSTRUCTION MANUAL FOR WHIRLING OF SHAFT OBJECTIVE: To find out critical speed experimentally and to compare the whirling Speed of a shaft with Theoretical values.

AIM: 1. To study the effect of whirling of the shaft. a. Both ends fixed. b. Both ends supported. c. One end fixed other end supported.

2. To study the modes of vibration and to measure the frequency of each case.

Detail of shaft: Shaft no. 01 02 03

Diameter in (mm) 4mm 5mm 6mm

L = length of shaft E = young's modulus of elasticity D = Density of material G = acceleration due to gravity

Diameter (m) 4*10-3 5*10-3 6*10-3 = = = =

in

Length in mm 1000mm 1000mm 1000mm

1000 mm 2 x 106 kg/cm2 0.0078kg/cm3 9.81 m/sec2

INTRODUCTION When the natural frequency of a system coincides with the external forcing system frequency the phenomenon is called resonance. The speed at which resonance occurs is known as critical speeds. These speeds are also called whirling speeds or whipping.

At these speeds the amplitude of vibration of rotors is excessively large and large amount of force is transmitted to the foundation. In the region of critical speeds, the system may fail, due to excessive vibration in transverse direction

therefore, it is very important to find jut natural frequency of the shaft to avoid the occurrence of resonance, which may result in failure of the shaft. The excessive vibration in the system is due to eccentric loading, non-Uniform distribution of material voids, cavities in the material & bending of shaft etc.

Let us consider a shaft, the ends of which are fixed in ball bearings under following end fixing conditions at motor end as well as tail end.

EQUIPMENT DETAILS The whirling of shaft apparatus is developed for the demonstration of whirling phenomenon. 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 bearings of motor spindle from these testing shafts. The special features of this equipment are as follows:-

(A)

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

(B)

Ball bearing fixing ends:- The ends fix the shaft while it rotates. The shaft & the end-fixing device 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.

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 blocks with single selfaligning bearing. (2) Fixed end conditions: -Make use of end blocks with double bearing. The guards D1 & D2 can be fixed at any position on the supporting bar frame, which fits on side support F. Rotating shafts are to be fitted in blocks in A &B stands. .

SPEED CONTROL OF DRIVING MOTOR The driving motor is 230V DC 1/16H.P; 6500 RPM. A dimmer state of 240v, 2amp, and 50 cycles is used to control speed of the rotating shaft.

PROCEDURE 1. Fix the flexible shaft at the ball bearing ends M & N . for different End condition i.e. supported end & fixing end conditions. 2. Measure the critical speed of the shaft with the help of a tachometer at resonance. 3. Take the shaft to maximum first & then slowly reduce the speed to avoid excessive amplitude of vibrations at resonance. . 4. Higher mode is observed first & corresponding speed is noted & then speed is further reduced to observe next mode of lower frequency.

OBSERVATION TABLE CASE-1 SUPPORTED END CONDITION: (A) Supported, Supported Sr. no.

L (cm)

D (cm)

N (rpm)

1 2

CASE-2 FIXED END CONDITIONS: (B) Fixed, Fixed Sr. no.

L (cm)

D (cm)

N (rpm)

1 2

CASE-3 FIXED & SUPPORTED END CONDITIONS:

(C) Fixed, Supported Sr. no.

L (cm)

D (cm)

N (rpm)

1 2

When N = rpm of the shaft D, L = Diameter & length of shaft respectively

CALCULATION: 1. Moment of inertion of shaft, I 2. Mass of shaft 3. Area of shaft

= = =

( / 64) * D 4

m4

Area*length*density ( / 4) * D 2

m2

When both end are fixed: Static deflection of shaft due to mass of the shaft 

=

WL4 383EI

Frequency of transverse vibration, fn

meter

0.571 Hz 

Critical of whirling of speed of the shaft (in r.p.s) is equal to the frequency of transverse vibration in Hz Nc (r.p.s)

=

fn (Hz)

When both end are supported: Static deflection of shaft due to mass of the shaft 

=

5WL4 383EI

Frequency of transverse vibration, fn

meter

0.5615 Hz 

Critical of whirling of speed of the shaft (in r.p.s) is equal to the frequency of transverse vibration in Hz Nc (r.p.s)

=

fn (Hz)

When one end is fixed and other is supported: Static deflection of shaft due to mass of the shaft 

=

WL4 185 EI

Frequency of transverse vibration, fn

meter 0.564 s

Hz

Critical of whirling of speed of the shaft (in r.p.s) is equal to the frequency of transverse vibration in Hz Nc (r.p.s)

=

fn (Hz)

PRECAUTION TO BE OBSERVED

(1) If the revolutions of an unloaded shaft are gradually increased it will be found that a certain speed is reached at which violent instability will occur, the shaft deflecting into a single bow. But if this speed is quickly run through, the shaft will become straight again and 11:11 uniformly until at another higher speed, the same phenomenon will occur, deflection now being in double bow & so on.

(2) The speed of shaft should be increased rapidly and jump over the 1stcritical speed rather than observing it because it will increase the speed of rotation & amplitude bringing the failure of shaft. If however, the shaft is taken to higher mode first and corresponding critical speed noted and then by reducing the speed furthers the next mode of lower frequency can be observed without any danger of increase in amplitude.

(3) It is destructive test and fresh test pieces may be used every time.

(4) Fix the apparatus firmly on suitable foundation.

RESULT CASE-1 SUPPORTED END CONDITION: Mode

Calculated value of critical speed

Measured value of Critical speed

% Error

Measured value of Critical speed

% Error

1st 2nd

CASE-2 FIXED END CONDITIONS: Mode

Calculated value of critical speed

1st 2nd

CASE-3 FIXED & SUPPORTED END CONDITIONS: Mode

Calculated value of critical speed

Measured value of Critical speed

% Error

1st 2nd

COMMENTS:There is a different between theoretical speed of whirl'& actual speed observed due to following reasons:

(1) The end conditions are not as exact as assumed in theory.

(2) Pressure of damping at the end bearing.

(3) Assumption made in theoretical predictions

(4) Lack of knowledge of exact properties of shaft material

(5) A uniformly loaded shaft has theoretical infinite number of natural frequencies of transverse vibrations for fundamental mode. Observation of the first mode of whirling is, therefore, not so defined and thus difficult. 2ndmode can be easily observed.

(6) The sample rod is being used again & again resulting in error due to its bending in every

Series of tests conducted on it.

EXPERIMENTS With elastic rods EXPT. NO. 1

END FIXINGS

MODE OF WHIRL

Supported fixed 1st Mode

2

Supported fixed 2nd Mode

3 4

Supported Supported

1st Mode

Supported Supported

2nd Mode...