Machine Foundation

ISET GOLDEN JUBILEE SYMPOSIUMIndian Society of Earthquake Technology Department of Earthquake Engineering Building IIT Roorkee, Roorkee October 20-21, 2012 Paper No. C018 ANALYSIS OF RECIPROCATING MACHINE FOUNDATIONS RESTING ON PILES M. Bharathi 1 , Dr. Swami Saran 2 and Dr. Shyamal Mukerjee 3 1 M.Tech. Student, Indian Institute of Technology Roorkee, [email protected] 2 Professor Emeritus, Indian Institute of Technology Roorkee, [email protected] 3 Assistant Professor, Indian Institute of Technology Roorkee, [email protected] ABSTRACT Machine foundations are generally classified as special foundations. They require a detailed analysis of the foundation response to the dynamic load resulting fromthe anticipated operation of the machine. Reciprocating type machines produce periodic unbalanced forces. The basic operating mechanismof a reciprocating machine consists of a piston crank system and the operating speeds of such machines are usually less than 1000 rpm. Dynamic forces developed in reciprocating machines are much larger when compared to those generated in rotary machines. Reciprocating machines are normally founded on block foundations. Under unavoidable situations reciprocating machines have also been founded on piles. Reciprocating machines resting on piles are analyzed with the help of solutions developed for dynamic behavior of pile groups. This paper describes the behavior of reciprocating machines resting on piles. An attempt has been made to study the behavior of the reciprocating machine foundation system subjected to dynamic loads. A reciprocating machine resting on a pile group was selected such that the soil, pile and machine parameters resemble actual field conditions and it was analyzed for the dynamic conditions. MATLAB programs were developed for different modes of vibration i.e. (vertical, sliding, rocking and coupled) and the machine foundation systemwas analyzed for different soil, pile and machine parameters and the variation in the natural frequency and amplitude of the systemwas studied. Results of the analysis have been presented in the formof charts for vertical and coupled modes of vibration. Keywords: Reciprocating Machines, Pile groups, Coupled Vibration, Frequency, Amplitude 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 its accessories [8]. 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 the machine foundation soil system[3]. Reciprocating machines produce periodic unbalanced forces. Engines, Compressors and Pumps belong to this category. The basic mechanismconsists of a piston that moves within a cylinder, a connecting rod, a piston rod and a crank. The operating speed of these machines is less than 1000rpm, but the dynamic forces developed are more than that of rotary machines [13]. Fig. 1 Parts of a reciprocating machine Reciprocating machines are very frequently encountered in practice. They are rested on a concrete block or a hollow concrete block. In the latter case, the mass of the system is less and hence the natural frequency will be greater than the former case. The depth of embedment plays a vital role in the stiffness and damping values of the system [14]. The foundation for the machines thus formed rests either on soil or pile groups. When the foundation rests on the pile group the block formed serves the purpose of the pile cap [12]. Fig. 2 Foundation on soil Fig. 3 Foundation on piles CODAL PROVISIONS Codes suggest guidelines and limitations in the design of a structure. For machine foundations ACI 351 -3R -04 [1], SAES – Q – 007[11], DIN 4024[5], IS 2974- Part 1[6], CP 2012[4] and 1S0 10816 [7] were some of the codes given by different nations. But none of the codes suggested the limitations or guidelines for the design of machine foundations resting on piles. Among all the codes the most common emphasis was on the eccentricity of the machine foundation soil system. Finally, from the Indian Code IS 2974 - Part 1 the limit for permissible value of amplitude was adopted for the design process. This, amplitude was decided based on the type of the machine. For reciprocating type of machines the value was 0.2 mm[6]. DYNAMIC ANALYSIS OF PILE GROUP FOR MACHINE FOUNDATION The machine foundation system vibrates in all six degrees of freedom. Of the six modes, translation along vertical axis and rotation around vertical axis can occur independently of any other motion and are called decoupled modes. But the translation along the longitudinal or lateral and the corresponding rotations always occur together and are called coupled modes [13]. In field conditions the machine foundation system is subjected to coupled sliding and rocking vibration. Hence the dynamic analysis of the machine foundations subjected to coupled sliding and rocking motion passing through the common centre of gravity of machine and foundation becomes must. Fig.4 Reciprocating machine on pile group METHODS FOR ANALYSIS There are two types of analysis of the dynamic behavior of pile group and they are adopted to analyze and design the reciprocating machine supported on the pile group. Pseudo-Static Analysis In this approach, approximate values of horizontal and vertical seismic co-efficient, are adopted and equivalent seismic forces are calculated to design the pile foundation for structures located in seismic regions. When these equivalent seismic forces are added to the static forces, the pile foundation is subjected to eccentric inclined load [13]. Dynamic Analysis In this method, the pile is subjected to sinusoidally varying dynamic force which is modeled as a single degree of freedomsystem. Here, the soil was assumed to be composed of independent infinitesimally thin horizontal layers of infinite extent which could be considered as a generalized Winkler material possessing inertia and dissipates energy [13]. METHOD ADOPTED Analysis of pile groups supporting machine is done with the help of relations developed by Novak and others based on the dynamic analysis for different modes of vibration. The stiffness and damping of a pile depends on soil properties, pile properties and type of pile support. When the stiffness and damping of a pile is calculated then applying the interaction factor to it the group stiffness and damping is determined. Thus the amplitude and frequency variation of a pile group for varying pile, machine and soil parameters are calculated. PARAMETERS SELECTED A 3x3 pile group is selected and the variation in the frequency and amplitude for vertical, sliding, rocking and coupled modes of vibration are studied varying the parameters. The soil, machine and pile parameters are selected in such a way that they represent the actual field conditions. Soil The soil parameter is represented by the Shear modulus of the soil. For the multiple soil layer the shear modulus of the soil increases with depth. This is represented by the parabolic variation of soil profile. Pile Group For the Machine foundation the pile group is selected according to the plan area of the Machine. Usually the plan area of the machine is not symmetrical. But in our problem the pile group arrangement is assumed to be symmetrical to simplify the analysis. The spacing between the piles is varied from 2d to 4d [2] and the variation of natural frequency and the amplitude of the system are studied. The piles in a pile group may be arranged in any of the following pattern. Machine The operating frequency and the weight of the reciprocating machine are selected such that the parameters suite the values of the machines that are used in the industries. The operating frequency of the reciprocating machines used in the industries varies between 300 to 1000 rpm usually. The weight of the reciprocating machine varies from300kN to 1700 kN. ANALYSIS RESULTS FROM MATLAB The MATLAB [9, 10] programs were written for different modes of vibration and the results obtained were checked manually and the program was verified. Based, on the results obtained from MATLAB programs conclusions were drawn. The following charts were prepared with the results obtained from the MATLAB programs varying the parameters. Case (i) The machine parameters i.e. the machine weight and the operating frequency are kept constant and the spacing between the piles are varied. Wm = 400 kN (ω = 41.88 rad/sec) & OS = 400 rpm When the weight of the machine & the operating frequency are kept constant and the spacing between the piles are increased i. The weight of the pile cap increases ii. The distance fromthe c.g of the pile systemincreases When the spacing is increased from2d to 4d the total mass increases from 253kg to 608kg whereas the stiffness in vertical direction increases from 2.7x10 5 to 3.35x10 5 . Thus the increase in stiffness is less when compared to the increase in total mass. Hence, the natural frequency decreases. Case (ii) The machine weight and the spacing between the piles are kept constant and the operating frequency are varied. Wm = 400kN (ω = 41.88 rad/sec) and S = 3d 0 10 20 30 40 50 1.5 2.5 3.5 4.5 N a t u r a l f r e q u e n c y i n r a d / s S/d wnz (rad/s) wn1 (rad/s) wn2 (rad/s) Fig.5 Natural frequency variation with S/d 0.0001 0.001 1.5 2.5 3.5 4.5 A m p l i t u d e i n m S/d Az (m) Fig. 6 Vertical Amplitude variation with S/d 1.00E-05 1.00E-04 1.5 2.5 3.5 4.5 A m p l i t u d e i n m S/d AX (m) Fig. 7 Horizontal amplitude variation with S/d 1.00E-06 1.00E-04 1.5 2.5 3.5 4.5 A m p l i t u d e i n m S/d AR (rad) Fig. 8 Rotational amplitude variation with S/d When the machine weight & spacing between the piles are kept constant and the operating frequency is increased the amplitude decreases as the natural frequency moves away fromthe operating frequency. Case (iii) The operating frequency of the machine and the spacing are kept constant and the weight of the machine is varied. OS = 400rpm (ω = 41.88 rad/sec) & S = 3d 0.00001 0.0001 0.001 200 400 600 800 1000 1200 A m p l i t u d e i n m OSin rpm Az Fig.9 Vertical Amplitude variation with operating speed 1.00E-06 1.00E-05 1.00E-04 200 400 600 800 1000 1200 A m p l i t u d e i n m OS in rpm Axc Fig.10 Horizontal Amplitude variation with operating speed 1.00E-06 1.00E-05 1.00E-04 200 400 600 800 1000 1200 A m p l i t u d e i n m OSin rpm Arc Fig.11 Rotational Amplitude variation with operating speed When the operating frequency and the spacing between the piles are kept constant and the weight of the machine is increased the natural frequency of the systemdecreases with nominal change since the mass of the system increases. The amplitude also decreases as the natural frequency moves away fromthe operating frequency of the system. Case (iv) The operating frequency of the machine, the weight of the machine and the spacing are kept constant and the pile parameters i.e. the length and the diameter of the pile are varied. OS = 400rpm (ω = 41.88 rad/sec), Wm=400kN & S =3d 0 5 10 15 20 25 30 35 40 200 400 600 800 1000 1200 N a t u r a l f r e q u e n c y i n r a d / s Weight in kN wnz (rad/s) wn1 (rad/s) wn2 (rad/s) Fig.12 Natural frequency variation with Machine weight 0.0001 0.001 200 400 600 800 1000 1200 A m p l i t u d e i n m Weight inkN Az (m) Fig.13 Vertical Amplitude variation with Machine weight 1.00E-05 1.00E-04 200 400 600 800 1000 1200 A m p l i t u d e i n m Weight inkN AX (m) Fig.14 Horizontal Amplitude variation with Machine weight 1.00E-06 1.00E-05 1.00E-04 200 400 600 800 1000 1200 A m p l i t u d e i n m Weight inkN AR (rad) Fig.15 Rotational Amplitude variation with Machine weight Thus, when the operating frequency of the machine, the weight of the machine and the spacing are kept constant and the L/d ratio of the pile is varied the amplitude attains a maximumvalue when the natural frequency is far away from the operating frequency. Case (v) The operating frequency of the machine is kept constant and the weight of the machine is varied along with the spacing. OS = 400rpm (ω = 41.88 rad/sec) 0 10 20 30 40 50 60 70 80 90 10 15 20 25 30 35 40 45 50 55 F r e q u e n c y L/d wnz(rad/s) wn1(rad/s) wn2(rad/s) Fig.16 Natural frequency variation with L/d 1.0E-04 1.0E-03 1.0E-02 10 20 30 40 50 60 A m p l i t u d e i n m L/d Az(m) Fig.17 Vertical Amplitude variation with L/d 1.0E-05 1.0E-04 1.0E-03 10 20 30 40 50 60 A m p l i t u d e i n m L/d AX(m) Fig.18 Horizontal Amplitude with L/d 1.0E-06 1.0E-05 1.0E-04 10 20 30 40 50 60 A m p l i t u d e ( i n r a d ) L/d AR(rad) Fig.19 Rotational Amplitude with L/d 10 30 50 70 90 110 300 450 600 750 900 2 2.5 3 3.5 4 F r e q u e n c y Weight in kN and S/d wnz (rad/s) wn1 (rad/ s) wn2 (rad/ s) Fig.20 Frequency variation with varying machine weight and spacing 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 0.001 300 450 600 750 900 2 2.5 3 3.5 4 A m p l i t u d e Weight in kN and S/d Az (m) Fig.21 Vertical amplitude variation with varying machine weight and spacing 0.00001 0.00002 0.00003 0.00004 0.00005 0.00006 0.00007 300 450 600 750 900 2 2.5 3 3.5 4 A m p l i t u d e Weight in kN and S/d AX (m) Fig.22 Horizontal amplitude variation with varying machine weight and spacing 0.000006 0.000008 0.00001 0.000012 0.000014 0.000016 0.000018 0.00002 300 450 600 750 900 2 2.5 3 3.5 4 A m p l i t u d e Weight in kN and S/d AR (rad) Fig.23 Rotational amplitude variation with varying machine weight and spacing As the spacing between the piles increases the weight of the pile cap increases which possibly may intend the increase in the machine weight. In this case the operating frequency is kept constant and as the natural frequency of the systemmoves away fromit the amplitude gets reduced. CONCLUSIONS When the spacing between the piles is increased, the increase in the stiffness is less when compared to the increase in the mass of the systemand hence the natural frequency decreases. As the difference between the natural frequency and operating frequency increases the amplitude decreases. The increase in machine weight contributes a nominal change in the natural frequency, hence, the reduction in amplitude is also very less. When L/d ratio of the pile is increased the natural frequency attains a maximumvalue when it moves far away fromthe operating frequency. Varying both the spacing between the piles and the machine weight the natural frequency of the system moves far apart from the operating frequency for coupled mode of vibration. 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