dynamic analysis of machine foundation by gary yung

HKIE-IEM-CIE Tripartite Seminar Recent Developments in Limit State Design for Geotechnical Works

HKIE-IEM-CIE Tripartite Seminar on Recent Developments in Limit State Design for Geotechnical Works

Copyright ©2014 by Geotechnical Division, The Hong Kong Institution of Engineers All right reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher Published by: Geotechnical Division, The Hong Kong Institution of Engineers Printed in Hong Kong


FOREWORD

The Tripartite Seminar aims to create a platform for interactive discussions and sharing of experiences in geotechnical related aspects amongst the Hong Kong Institution of Engineers (HKIE), the Institution of Engineers, Malaysia (IEM) and the Chinese Institute of Engineers (CIE, Taiwan). The Seminar is hosted in turns among the three professional institutions after the first collaboration in 2009 at Taiwan. While structural designs have moved to limit state design for many years, it is still a norm to design the geotechnical works using a working stress approach with lumped factors of safety in many places around the world. With emergence of Eurocode 7 “Geotechnical Design” in 2004, reviews on applicability of limit state to geotechnical designs have taken place in various countries. Some countries such as Malaysia have already migrated into limit state design several years ago. Eurocodes will also be adopted in infrastructure projects in Hong Kong starting next year. With this initiative, the HKIE Geotechnical Division and the Hong Kong Geotechnical Society have organized and supported a series of activities including this Tripartite Seminar in raising the awareness and interests of industrial practitioners on limit state geotechnical designs. Speakers from Malaysia, Taiwan and Hong Kong are invited to exchange experience and keep abreast on the application of limit state design and possible impacts onto geotechnical works, in particular related to foundation, excavation and tunneling works. Reviews on design methodology, case studies will also be covered in the Seminar. A total of eleven papers from the three institutions will be presented. On behalf of the HKIE Geotechnical Division, the Hong Kong Geotechnical Society and the Seminar Organizing Committee, we would like to express our sincere thanks to Mr YU Ter Chyuan, Executive Secretary of the Chinese Institute of Engineers and Ir Jack PAN Kok Loong of the Institution of Engineers, Malaysia for helping us in organizing their delegations to participate in the Seminar. We would also like to thank the delegates’ input in preparing the technical papers and presentations. Finally, we would like to thank the work of the Organizing Committee of the Seminar for their dedicated efforts. Ir. Rupert LEUNG Ir. Professor Charles NG Chairman President HKIE Geotechnical Division Hong Kong Geotechnical Society Ir. James SZE Chairman Organizing Committee


CONTENTS Foreword Recent Development in Local Geotechnical Standards for Migration to Eurocodes: A Hong Kong Perspective

1

Florence W Y Ko Eurocode 7 Implementation in Hong Kong – A Designer’s Perspective 19

Sean D. Arnold Development of Limit State Partial Factor Method for Design of Excavation and Lateral Support Works in Hong Kong

31

Thomas Hui, Raymond Yim & P L R Pang Dynamic Analysis of Machine Foundation: When a Static Force cannot Give the Full Picture

45

Gary Yung Design and Construction Considerations for Steel Struts in Excavation of KVMRT Project in Malaysia

59

Yee-Eng Loh, Shaw-Shong Liew, Yean-Chin Tan & Han-Seng Tong Comparison Study of Pile Design between Conventional Working Stress and EC7 Limit State Design Approaches

71

EG Balakrishnan, Kai-Ming Lee & Yew-Lun Allan Chwee Assessment of External Stability of Reinforced Soil Wall using British Standard BS 8006 and Eurocode 7

91

Swee-Huat Chan, Yi-Heng Yoo, Chee-Siong Lim, Kim-Chuan Yap & Lee-Ching Hiew

Case Studies of Tunnel Lining Adopting Limit State Design 109

Yi-Chang Eric Chai & Min-Yi Jackie Tsai Geotechnical Challenges of the National Freeway No. 1 Widening Project, Wugu-Yangmei Section

117

Jiunn-Ding Chen & Chiao-Ann Hsiao


Limit State Design and Construction Control for Deep Excavation and Protection of Adjacent MRT Running Tunnels

131

Hsiao-Chou Chao & Chien-Chung Huang The Influence of Existing Structures Based on Shield Tunnel Passing through under the MRT Station

153

Fish Gao & Hsiuan Lin


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Dynamic Analysis of Machine Foundation: When a Static Force cannot Give the full picture

Gary Yung

AECOM, Hong Kong E-mail : [email protected]

ABSTRACT Machine foundations provide a robust platform for machinery to operate in a smooth manner with minimal maintenance requirements. An unexpected vibration can be detrimental to the machine components, ground settlement, structural integrity of foundation, and other machines or working personnel adjacent to it. If vibrations become excessive and uncontrollable, a machine can be forced to shut down or a catastrophic failure can result from fatigue failures of machine components. To avoid this, the serviceability limit state design takes into account of vibration control. Machine vendors usually specify different levels of foundation performance and serviceability vibration limits depending on the machine types for engineers to design the machine foundation. However, in design office, dynamic design is often considered as a secondary check or sometime even omitted due to the lack of time and budget allocated to the project. This paper will present various design approaches from a rule of thumb static design to a comprehensive dynamic analysis and discuss their limitations. A case study of large machine foundation with stringent vibration limits will be presented to demonstrate the necessity and complexity of a full dynamic analysis. This study aims to deliver the message that a static force does not always give the full picture. Project managers and engineers can achieve a better insight into dynamic analysis for those machine foundations that are sensitive to vibration, and then be upfront with the clients about the design time and budget required for the dynamic analysis and evaluation. 1. INTRODUCTION Machine foundations provides a robust platform for machinery to operate efficiently and reliably. Vendors continuously improve the productivity and efficiency of their machine by increasing the machine size and operating speed. On the other hand, the requirements of vibration control can become more stringent due to higher machinery specifications. Consequently, modern machine foundations are required to resist larger dynamic forces at higher operating speeds while controlling vibrations. Unexpected vibrations can be detrimental to the machine components, foundation settlement, structural integrity of foundation, and other machines or working personnel adjacent to it. If vibration becomes excessive and uncontrollable, the machine may be forced to shut down, and even lead to fatigue failure in the machine components resulting in a catastrophic incident. Dynamic analysis of machine foundation is a crucial justification step to ensure the performance and safety of the machine. The vibration of foundation subjected to machine load can be assessed by different approaches including the pseudo-static approach with rules of thumb, natural frequency analysis, modal analysis, time history analysis and frequency domain analysis. To study the dynamic soil-structure interaction, an impedance function method is commonly used to study the dynamic behaviours between soil and


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structure. Dynamic soil stiffness and damping coefficients are frequency dependent, and will be briefly discussed in this paper. Site specific geotechnical data and machine dynamic forces are important design parameters for a success machine foundation design. However, this information is not always available at the time of design. The difficulty of undertaking the machine foundation design without these parameters will be highlighted. Since the interface of soil-structure is often assumed to be rigid, the dynamic effect of flexible behaviour of machine foundation can be underestimated. A case study of high-speed machinery supported on shallow foundation will be presented to demonstrate the importance of considering the higher-order dynamic responses. 2. DYNAMIC EFFECT DUE TO HARMONIC FORCE The dynamic response of a single degree of freedom system subjected to a harmonic force can be represented in Figure 1. A dynamic amplification factor (DAF) is given by:

Fig. 1 - Dynamic Amplification Factor of SOF System

frequency of dynamic force natural frequency of system ( )

k system stiffness m system mass If DAF is greater than 1, the machine foundation system is under the influence of resonance. Machine vendor often requires a frequency separation between the natural frequency of foundation system and the excitation frequency (e.g. . Under-tuning or over-tuning the foundation system can be achieved by changing the system stiffness and mass. However, the machine foundation is a system with multi-degrees of freedom which contains more than one natural frequency. The case study at the end of this paper will discuss the difficulty of avoiding all the primary resonances.


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3. DIFFERENT DESIGN APPROACHES Machine vendors often specify different vibration requirements based on the nature of machine. Machine such as mobile generators can tolerate the vibrations induced by its own unbalance forces. A simple rule-of-thumb is sufficient for the type of these machine foundations. In contrast, a critical machine such as high speed gas turbine in the production line cannot be operated with excessive vibrations. A dynamic analysis with the consideration of dynamic soil-structure interaction becomes necessary. Design of machine foundations can be categorised into three approaches:: 3.1 Category 1- Static Analysis with Rule of Thumb Machine vendor sometime is confident that the induced unbalance force of machine is insignificant to cause any vibration issue based on the empirical results (e.g. mobile generators or small pump stations). The design can be simplified to rule-of-thumb approach by providing sufficient mass into the foundation system to control the vibration. ACI 351 recommends the weight of foundation system at least three times the weight of a rotating machine and at least five times the weight of a reciprocating machine. The considered machine weight includes both moving and stationary machine parts. No rigorous dynamic analysis is needed. 3.2 Category 2 – Natural Frequency Analysis Vendors may require the machine foundation system to be designed such that no system resonance is occurred during the normal operation. Natural frequency analysis can be used to demonstrate sufficient frequency separation between the system resonance and the excitation frequency. A sufficient frequency separation is achieved when any primary natural resonance of the foundation system is less than 0.5 or greater than 1.5 times the excitation frequency. Unfortunately, in many cases, the frequency separation cannot be achieved and a vigorous dynamic analysis (Category 3) would then be recommended. 3.3 Category 3 – Forced Vibration Analysis Vendor or the client may identify that the machine is crucial and sensitive to vibration. In this case, a forced vibration response analysis such as a harmonic analysis or time-history dynamic analysis is required to evaluate the foundation dynamic response. If the soil radiation damping and the dynamic soil-structure interaction are to be considered in the machine foundation design, a frequency domain dynamic analysis together with impedance functions would then be recommended. This paper will focus on Category 3 case. A case study of a large machine foundation subjected to steady-state harmonic loads will be presented at the end to demonstrate the benefits of this approach. It should be noted that some key design parameters are considered unnecessary or not provided by the vendor for the dynamic design, which can limit the analysis options.

4. IMPORTANT DESIGN PARAMETERS When vibration control is identified as the crucial to the machinery, the design team including mechanical, geotechnical, and structural engineers will work closely together to provide a foundation


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solution which satisfies all economic, performance and safety aspects. The design parameters necessary to perform a detail dynamic analysis include geotechnical investigation, machine weight and centre of gravity, operating frequency ranges, rotating component weight and balance quality, machine unbalanced actions and machine vibration tolerances. Amongst these, the geotechnical parameters and unbalance actions are often the unavailable or unknown at the time of design. 4.1 Dynamic Soil or Rock Properties Gunter Klein and Dietrich Klein (2003) present typical natural frequencies of machine foundation system (Figure 2). When the machine such as turbo-generator operates at 30Hz and is supported on a shallow rock foundation, the foundation system may be difficult to avoid resonance. The dynamic shear modulus of foundation material is an important parameter to determine the machine dynamic behaviours. The client and project managers sometime underestimate the importance of in-situ geotechnical data such as dynamic shear modulus which may require additional site access or expenditure to obtain.

Fig. 2 - Natural Frequency of Support System {Source from Gunter Klein and Dietrich Klein (2003)}

The dynamic shear modulus is commonly obtained by measuring shear wave velocity in the field (e.g. cross-hole method, down-hole method, up-hole method and seismic reflection). The relationship between dynamic shear modulus and measured-in-field shear wave velocity are as follows:

where

dynamic shear modulus of sub-grade (Pa) soil density (kg/m3) shear wave velocity (m/s)

The case study at the end of this paper demonstrates the difficulty of avoiding resonance without in-situ dynamic geotechnical data.


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4.2 Unbalanced Forces Unbalanced forces are essential design parameters to perform the forced dynamic analysis. However, another common unknown design parameter is the dynamic forces induced by the machine components. Machine foundation can be excited by dynamic forces due to reciprocating, rotating and impulsive actions. Reciprocating and rotating machines, such as diesel generators, gas turbines, centrifugal compressors and electrical motors are subjected to steady-state harmonic dynamic actions. Whereas, impulsive machines, such as forging hammers and metal forming presses, are subjected to sudden impulsive force. Discussions in this paper will be limited to the reciprocating and rotating machines. Salesmen always describe their machines as perfectly balanced and with no significant dynamic force. The vendor often does not explicitly provide the unbalanced force for the client or designers. In these cases, the unbalanced force can be estimated by ISO 1940/1 and ACI 351 when the rotating mass and balance quality grade are given by the manufacturer:

where

dynamic force (zero to peak) (kN) rotating mass (kg) mass eccentricity based on the balance quality grade in ISO 1940/1 (mm) circular operating frequency of the machine (rad/s)

service factor allow for increased unbalance during the machine service life generally at least equal to 2 or stated by the manufacturer 5 DYNAMIC SOIL-STRUCTURE INTERACTION The design of machine foundation is complex dynamic soil-structure interaction problem. Academia has been investigated the soil-structure interaction problem since early 1920s. However, very few design standards or guidelines have addressed the dynamic soil-structure interaction.

5.1 Review of Dynamic Soil-Structure Interaction Research activities on the effect of soil-structure interaction in the seismic application had been considerably increased in the 60s and 70s due to the extensive developments of Nuclear Power Plants (Roesset 2013). In the early development, linear and frequency independent springs were used to simulate the stiffness of the foundation. By 70s, the effect of soil-structure interaction was generally considered as more important for relatively stiff and massive structures such as Nuclear Power Plants. The radiation damping has been considered as an important factor in the soil-structure interaction problem. Soil radiation or geometric damping dissipates energy by propagating waves away from the foundation to the soil mass, increasing the effective damping. However, in soil-structure interaction, the radiation damping is frequency dependent and is difficult to determine in the time domain. Veletsos and Wei (1971) and Luco and Wstmann (1971) represented the soil dynamic stiffness and damping characteristics as frequency dependent, which also called complex valued impedance function. Kausel (1974) realized that the application of impedance function in seismic engineering can be extend to the dynamic design of machine foundation. Dynamic response of pile-supported foundation depends on the dynamic stiffness and damping written by Novak in 1970s. El Naggar and Novak present a model to


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allow for nonlinear soil behaviours in pile foundation with the energy dissipation through radiation damping and soil hysteresis. Wolf and Deeks (2004) publish a machine foundation textbook to explain the application of impedance functions together with work examples.

5.2 Impedance Stiffness Approach for Dynamic Soil-structure Interaction To study the dynamic soil-structure interaction for machine foundation, the soil-foundation interface is assumed to be rigid. The unbounded soil performs as an energy damper to dissipate energy through propagating wave energy towards the soil mass, which is called radiation damping or geometric damping. The impedance stiffness approach has been used to represent the dynamic soil-foundation behaviours. Practicing engineers often are not familiar with impedance functions involved in dynamic soil-structure interaction. Indeed, many design standards and regulations are only qualitatively to describe the general effects and significance of dynamic soil-structure interaction such as in EN 1998-5:2004. Only few design references such as ACI 351 and Canadian Foundation Engineering Manual provide guidelines to evaluate the dynamic behaviours of machine foundation by the impedance stiffness approach. To help understanding of the basic concept of dynamic impedance stiffness, the equations of motion in time domain and frequency domain are discussed. The typical equation of motion in the time domain ( is

(1) where M mass constant C damping constant

static spring constant dynamic action

Frequency domain representation for the harmonic force

(2) Frequency domain representation for displacement, velocity and acceleration

(3)

(4)

(5) where imaginary number,

Euler’s formula, By substituting (2) to (5) into (1) and cancelling in both sides, an alternative equation of motion represented in the frequency domain ( ) is:


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Dynamic stiffness is defined as as a function of frequency ( )

thus

At the low frequency, the real part of dynamic stiffness ) is a positive value, the displacement response is in phase with the driven dynamic force. In contrast, at the high frequency, the real part of dynamic stiffness becomes a negative value which represents the displacement response is 180 out of phase to the dynamic force. At the resonance frequency ( , the real part of dynamic stiffness becomes zero, and only imaginary part ) is remained. Interestingly, the dynamic response at resonance is only controlled by damping, and the displacement response is 90 out of phase to the dynamic force. In dynamic design of machine foundation (Wolf and Deeks 2004), a dimensionless frequency ( is commonly used instead of frequency . The dynamic stiffness is rewritten in terms of spring coefficient and damping coefficient as a function of dimensionless frequency

where characteristic length of the foundation shear wave velocity of the first soil layer

Manual computation of the impedance response functions and dynamic responses can be tedious. Computer programs such as Matlab and DYNA6 can be used to determine the impedance stiffness and damping coefficients. DYNA6 has been developed in University of Western Ontario, Canada by El Naggar and adopted in Canadian Foundation Manual for the machine foundation design.

5.3 Limitations of Impedance Stiffness Approach The impedance stiffness approach, which assumes the interface of soil-foundation to be rigid, is only capable of evaluating the dynamic response of a rigid machine foundation with six degrees of freedom. In practice, however, not all machine foundation can be assumed to be rigid, especially for the high speed machinery. In terms of dynamic analysis, rigid and flexible machine foundations can be classified by the natural frequency of the foundation system and the machine operating frequency. ISO-10816-3 recommends that the support system can be considered as rigid foundation when the first natural frequency of foundation system is higher than the operational frequency by at least 25%, otherwise the foundation system is considered to be flexible.


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For flexible foundations with the consideration of soil-structure interaction, the dynamic response can be studied using a finite element (FE) model coupling with the frequency dependent soil stiffness and damping coefficients, determined by the impedance functions with the assumptions of a non-flexible foundation and a rigid soil-foundation interface (by computer programme such as DYNA6 or Matlab). 6. CASE STUDY OF HIGH SPEED MACHINE FOUNDATION A foundation with one or more high speed machines can be a complex dynamic soil-structure interaction problem. While this case can be analysed by assuming the interface of soil-foundation to be rigid with no flexural deformation of foundation, the effects of flexural deformation can be detrimental to the vibration control. Some advanced finite element analysis (FEA) packages, such as SAP2000, are capable of modelling a flexible machine foundation with the dynamic soil stiffness and damping coefficients in the form of impedance functions.. 6.1 Problem Definition Multiple high speed machines supported on a single block foundation is not uncommon for gas compression station. As the case study, two high speed centrifugal compressors driven by an electric motor (E-motor) were supported on a monolithic foundation shown in Figure 3.

Fig. 3 - General Arrangement of Gas Compression Unit

This gas compression station was identified as the crucial facility along the production line. The E-motor was rated as 25MW with an operational speed of 1800 rpm. High pressure compressor operated at a speed of 11867 rpm with a gear ratio of 6.59, whereas, low pressure compressor operated at a speed of 10045 rpm with a gear ratio of 5.58. The total weight of the equipment package including the steel skids was 126,600 kg. This equipment package was supported on a concrete block foundation. The weight of concrete foundation without piles was 552,600kg, which provided the foundation to equipment weight ratio of 4.36. Shallow sandstone was found at the location of the gas compression station. Shear velocity of sandstone ranging from 600 m/s to 1000 m/s were obtained by geotechnical field tests. Table 1 specifies a range of allowable peak-to-peak vibration displacements and the maximum vibration velocity in relative to different operational frequencies.


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Table 1 –Vibration Limits of Machine Foundation

6.2 Machine Foundation Resonated with Shallow Rock DYNA6 with the consideration of dynamic soil-structure interaction was used to evaluate the natural frequency of the foundation system. Although the machine foundation was supported on relatively good shallow sandstone, the vibration response still could not meet the stringent vibration limit given by the vendor due to the fact that the machine foundation system could not avoid the resonances at the machine operational speed. In the early development of the design solution, a concrete block foundation supported directly on the shallow rock was considered. The natural frequency of this type of foundation, however, appeared to be fairly closed to the machine operational frequency. Figure 4 illustrates the primary foundation natural resonances in relative to the machine operational frequencies. Primary natural resonances of the machine foundation were horizontal (Y), vertical (Z) and rocking (RX) modes. The E-motor operated at low frequency (24Hz to 32Hz) whereas the compressors operated at high frequency (134Hz to 208Hz). Horizontal natural frequency (Y) appeared to be at the machine operational frequency in this case. The maximum velocity response thus exceeded the vibration limit of 0.75mm/s shown in Figure 5. A number of attempts were used to provide sufficient frequency separation between the foundation natural frequencies and the machine operational frequency, however very little success was achieved. By enlarging or reducing the foundation footprint, and by increasing or decreasing the mass of foundation, the horizontal and vertical natural frequencies shifted together in the same manner. Since the horizontal and vertical natural frequencies were fairly closed to each other, it always one of them fell within the machine operational frequency. As a result, it was concluded that the block foundation, in this case, was not a practical solution to avoid resonance.

Fig. 4 - DYNA6 - Primary Natural Frequency (Block Foundation)

Peak-Peak vibration Disp. ( m) Max vibration speed (mm/s)rpm Hz

Low Pressure Compressor Low Freq 1800 30 8 0.75High Freq 10045 167 1.4 0.75

High Pressure Compressor Low Freq 1800 30 8 0.75High Freq 11867 198 1.2 0.75

Operational Freq


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Fig. 5 - DYNA6 - Dynamic Response (Block Foundation)

In terms of adjusting individual natural frequency and providing frequency separation, the pile foundation was a better solution. The concept of pile foundation (Figure 6) is similar to table-top foundation, which consists of large diameter of piles with sleeves to isolate the machine foundation from the surrounding rock. The sleeved pile (Figure 7) reduces the horizontal stiffness (reduces horizontal natural frequency). The large diameter of pile increases the vertical stiffness (increase vertical and rocking natural frequencies).

Fig. 6 - Pile Foundation isolated from Surrounding Rock

Fig. 7 - Pile Sleeve Detail

Figure 8 presents the dynamic response of pile foundation with the appropriate pile sleeve length to avoid resonance. The sleeved pile foundation successfully established natural frequency separation. The primary horizontal resonance occurred before the low machine operational frequency, while the vertical and rocking natural frequencies occurred in between the low and high machine operational frequencies.


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The vibration response was controlled under 0.75mm/s within the operational frequency shown in Figure 9.

Fig. 8 - DYNA6 - Primary Natural Frequency (Pile Foundation)

Fig. 9 - DYNA6 - Dynamic Response (Pile Foundation)

It is noted that DYNA6 did not indicate any vibration response at high operational frequencies. The flexure behaviour of foundation was not considered in DYNA6, hence, a finite element model coupling with the frequency dependent pile stiffness and damping coefficient was established to ensure that any vibrations due to flexure of the foundation were acceptable. 6.3 Finite Element Model with Frequency Dependent Pile Stiffness A mass foundation with a total number of 12 piles was simulated by using a finite element package (Strand7) together with frequency dependent pile springs from DYNA6 (Figure 10). The concrete foundation was modelled using brick elements. Compressor skids were modelled using steel beams. Masses of compressors, motor and associated components were modelled as translational node masses. The frequency dependent pile springs were modelled at the bottom of concrete foundation. Frequency dependent damping ratios were considered as individual modal damping ratios.


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Fig. 10 - Finite Element Model

6.4 Unexpected Vibration due to Flexural Deformation In general, the primary natural frequencies by Strand7 agreed with DYNA6 results (Table 2). No primary resonances fell within the machine operational frequency. However, flexural deformation of foundation appeared to be triggered by the unbalanced force of E-motor shown in Figure 11.

Table 2 – Natural Frequency with Mass Participation Ratio

Force vibration analysis was undertaken separately to evaluate the vibration response due to the E-motor and compressors. Figure 12 presents the dynamic response of the machine foundation subjected to the unbalance force due to E-motor or compressors. A clear frequency separation was achieved for the dynamic response triggered by the unbalanced forces of compressors. The sleeved piles under-tuned the horizontal resonance; and the relatively large diameter piles over-tuned the vertical resonance.


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Fig. 11 - Flexural Deformation of Foundation at 39Hz

In contrast, the flexural natural frequency at 39Hz (Mode 4) was triggered by the unbalanced force of E-motor, which was fairly closed to the machine operational frequency. Fortunately, with a further adjustment of pile sleeve length, the flexural resonance due to E-motor was shifted towards the higher frequency, and the total dynamic response satisfied the vendor vibration requirement shown in Figure 13.

Fig. 12 - Dynamic Responses due to E-motor and Compressors

Fig. 13 - Dynamic Responses with Flexible Behaviours of Foundation

0

1

2

3

4

5

6

0 20 40 60 80 100

Velocity

(mm/s)

Frequency (Hz)

E motor Compressors

0

1

2

3

4

5

0 20 40 60 80 100 120 140 160 180 200 220 240

Max

Velocity(m

m/s)

Frequency (Hz)

0.75mm/s limit


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7. CONCLUSIONS Different design approaches for vibration control of machine foundations have been presented. Forced vibration analysis is recommended for all critical machine foundation. Dynamic soil or rock properties and unbalanced forces induced by the machine components are the important design parameters. Dynamic soil-foundation interaction written in the form of impedance functions considers the soil radiation damping and dynamic soil stiffness, however, the soil-foundation interface is assumed to be rigid, and the dynamic effect of flexible structure might be underestimated. A case study of using finite element model with dynamic soil stiffness and damping coefficient has been presented. A sleeved pile foundation was adopted to avoid foundation resonances coincided with the machine operational frequency. The dynamic effect of flexible machine foundation has been found that it can be detrimental to the vibration control. Consequently, a finite element model is recommended to consider the dynamic soil-foundation interaction for the vibration-sensitive machine foundation. REFERENCES ACI 351.1R-99 – Grouting between Foundations and Bases for Support of Equipment and Machinery. Canadian Foundation Engineering Manual 4th Edition – Canadian Geotechnical Society 2006.

Poulos, Harry G. "Behavior of laterally loaded piles: I-single piles." Journal of the Soil Mechanics and Foundations Division 97.5 (1971): 711-731.

Günter Klein and Dietrich Klein (2003). Geotechnical Engineering Handbook, Procedures Vol.3 . Ernst & Sohn.

Wolf John P. (1994) Foundation Vibration Analysis Using Simple Physical Models, PTR Prentice Hall.

Wolf John P. and Deeks Andrew J. (2004) Foundation Vibration Analysis: A Strength-of-materials Approach, Elsevier.

Roesset Jose M. (2013) Soil Structure Interaction The Early Stages, Journal of Applied Science and Engineering, Vol. 16, No. 1, pp. 1-8

Veletsos, A. S., & Wei, Y. T. (1971). Lateral and rocking vibration of footings. Journal of Soil Mechanics & Foundations Div.

Kausel, E.(1974) “Forced Vibration of Circular Foundations on Layered Media” Sc. D. Thesis, Massachusetts Institute of Technology.

Novak, M. (1974). Dynamic stiffness and damping of piles. Canadian Geotechnical Journal, 11(4), 574-598.

Luco, J. E., & Westmann, R. A. (1971). Dynamic response of circular footings. Journal of the engineering mechanics division, 97(5), 1381-1395.

Luco, J. E. (1975). Impedance functions for a rigid foundation on a layered medium. Nuclear Engineering and Design, 31(2), 204-217.

El Naggar, M. H., & Novak, M. (1994). Non-linear model for dynamic axial pile response. Journal of geotechnical engineering, 120(2), 308-329.

dynamic analysis of machine foundation by gary yung

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