# Machine Foundation

Topics: Rotation matrix, Euclidean geometry, Vibration Pages: 14 (2789 words) Published: April 8, 2013
Machine Foundations
Sinchan Roy Chowdhury

CIVIL ENGG DEPT SEC: AY

ID NO: 110409040
SESSION-2012-13 7th SEM UG

Sinchan Roy Chowdhury

CIVIL ENGG DEPT SEC: AY

ID NO: 110409040
SESSION-2012-13 7th SEM UG

BENGAL ENGINEERING AND SCIENCE UNIVERSITY
SHIBPUR

[Pick the date]

BENGAL ENGINEERING AND SCIENCE UNIVERSITY
SHIBPUR

[Pick the date]
A Project under the guidance of Dr Kalyan Kumar Chattopadhya

ACKNOWLEDGEMENT
I am grateful to Prof Kalyan Kumar Chattopadhay for giving me the opportunity to carry out this project thus helping me to enhance my knowledge regarding this particular topic.

INDEX
CONTENT| PAGE NO|
INTRODUCTION| 1|
TYPES OF MACHINES| 1|
TYPES OF FOUNDATIONS| 2|
SOLUTIONS FOR SDOF SYSTEMS| 2|
DEGREES OF FREEDOM| 6|
METHODS OF ANALYSIS(BARKAN)| 7|
BLOCK VIBRATION TEST| 10|
ANALYSIS OF FOUNDATION (BARKAN’S METHOD)| 12|
ELASTIC HALF SPACE METHOD| 16|
REFERENCE| 23|

INTRODUCTION

Machine foundations require a special consideration because they transmit dynamic loads to soil in addition to static loads due to weight of foundation, machine and accessories
In a machine foundation the dynamic load is applied repetitively over a very long period of time but its magnitude is small and therefore the soil behaviour is essentially elastic, or else deformation will increase with each cycle of loading and may become unacceptable.

The amplitude of vibration of a machine at its operating frequency is the most important parameter to be determined in designing a machine foundation, in addition to the natural frequency of a machine foundation soil system.

Types of Machines
There are many types of machines that generate different periodic forces. The most important categories are:
1. Reciprocating machines: The machines that produce periodic unbalanced forces (such as steam engines) belong to this category. The operating speeds of such machines are usually less than 600r/min. For analysis of their foundations, the unbalanced forces can be considered to vary sinusoidally. 2. Impact machines: These machines produce impact loads, for instance, forging hammers. Their dynamic loads attain a peak in a very short interval and then practically die out. 3. Rotary machines: High-speed machines like turbo-generators or rotary compressors may have speeds of more than 3,000r/min and up to 12,000r/min

Types of foundations

Solutions for vibrations of SDOF systems
* Free Undamped Vibration
mu+ku=0
Ut=U02+iU02ωne-iωnt+U02-iU02ωneiωnt

* Free Damped Vibration

mu+cu+ku=0

Ut=e-ωnβt[U02+iU02ωn1+β2e-iωn1+β2t +U02-iU02ωn1+β2eiωn1+β2t]

C2m=ωnβ

1) β = 1 {Critically Damped Condition}

2) β > 1 {Over Damped Condition}

3) β < 1 {Under Damped Condition}

* Forced Vibrations

mu+cu+ku=PeiΩt

u(t)= e-ωnβtAe-iωn1+β2t +Beiωn1+β2t+Pk1(1-Ω2ωn2+2iβΩωn)eiΩt

A=(iωnβ+ωn1+β2)u02ωn1+β2+iu02ωn1+β2+(-iωnβ-ωn1+β2+Ω)2ωn1-β2Pk11-Ω2ωn2+2iβΩωn

B=(-iωnβ+ωn1+β2)u02ωn1+β2+-iu02ωn1+β2+(iωnβ-ωn1+β2+Ω)2ωn1-β2Pk11-Ω2ωn2+2iβΩωn

DEGREES OF FREEDOMS
A typical concrete block is regarded as rigid as compared to the soil over which it rests. Therefore, it may be assumed that it undergoes only rigid-body displacements and rotations. Under the action of unbalanced forces, the rigid block may thus undergo displacements and oscillations as follows

1. translation along Z axis
2. translation along X axis
3. translation along Y axis

METHODS OF ANALYSIS

* LINEAR ELASTIC SPRING METHOD (BARKAN 1962)

Barkan , using the concept of subgrade reactions developed the following elastic constants

1) Coefficient of elastic uniform...