UDC 62-218.2 :62-13 :001.4

DEUTSCHE NORM

April 1988

Machine foundations ~-

DI IVFlexible structures that support

4024machines with rotating elementsPart 1

Maschinenfundamente ; elastische Stützkonstruktionen für Maschinen mit rotierenden Massen Supersedes DIN 4024 ,January 1955 edition .

c

In keeping with current practice in standards published by the International Organization for Standardization (ISO), a comm ahas been used throughout as the decimal marker.

The DIN 4024 series of standards currently comprises the following Parts :

DIN 4024 Part 1 Machine foundations ; flexible structures that support machines with rotating element s

DIN 4024 Part 2 (at present at the stage of draft) Machine foundations ; rigid structures that support machines wit hperiodic excitatio n

In this standard, the term'load' is used for forces acting on a system from the outside ; this applies equally to compoun dterms that include the component 'load' (cf . DIN 10rß,0 Part 1) .

ContentsPag e

1 Scope and field of application 2

2 Concepts 22 .1 Vibration 22 .2 Types of vibration 22 .3 Damping 22 .4 Action-effects 32 .5 Model 32 .6 Machinery 32 .7 Types of foundation 3

3 Materials and ground3 .1 Reinforced concrete3 .2 Steel3 .3 Ground

4 Loads4 .1 Machinery4 .1 .1 General4 .1 .2 Static loads4 .1 .3 Dynamic loads4 .2 Foundation4 .2.1 Permanent loads4 .2.2 Imposed loads4.2.3 Creep and shrinkage of reinforced concrete4 .2 .4 Effects of temperature, wind and earthquakes

5 Design5 .1 General5 .1 .1 Objectives5.1 .2 Static analysis5 .1 .3 Dynamic analysis5 .2 Model study5 .2 .1 Principles5 .2.2 Requirements

Pag e

5 .2 .3 Simplified representation 55.3 Natural vibration 65 .3 .1 Natural frequencies and modes of vibration 65 .3 .2 Assessment of vibration behaviour on the basis o f

natural vibration

65 .4 Analysis of vibration due to unbalance 75 .4 .1 General 75 .4 .2 Foiced vibration 75 .4 .3 Natural modes of vibration 75 .4 .4 Equivalent-load method 75.5 Analysis of transient vibration 75.5 .1 General 75 .5 .2 Short-circuit 85.6 Loads on the foundation and ground 8

6 Further design criteria 86.1 Design action-effects 86.2 Reinforced concrete foundations 86.3 Steel foundations 86.4 Ground 8

7 Detailing 97 .1 Reinforced concrete foundations 97 .1 .1 Table foundations 97 .1 .2 Spring foundations 97 .1 .3 Slab foundations 97 .1 .4 Platform foundations 97.2 Steel foundations 97 .2 .1 Table foundations 97 .2 .2 Spring foundations 1 07 .2 .3 Platform foundations 1 07 .2 .4 Corrosion protection 1 0

Standards and other documents referred to 1 0

-5 >= oy a= dy

y ~0y

vN. :=

_=C o2 b

ďm . _f9= m

a m roV

.~ y `

N m m ~a~ LL 2

QotC7 T7,0 a?r~ d

m = ..m

1=LL2 m

Continued on pages 2 to 1 0

Vervielffi ltigung It, DIN-Merkblatt j

Beuth Verlag GmbH, Berlin, has the exclusive right of sate for German Standards (DIN-Normen) .

DIN 4024 Part 1 Engl, Price group 812 .90

Sales No . 0108

Page 2 DIN 4024 Part 1

1 Scope and field of applicatio nThis standard specifies requirements for steel or reinforce dconcrete structures that support mechanical system s('machine foundations', for short) . Such mechanical sys-tems are understood to be machinery with mainly rotatin gelements, the foundations of which are capable of generat -ing flexural vibration in at least one plane . For the purpose sof this standard, a distinction is made among the followingtypes of machine foundation :

a) table foundations ;

b) spring foundations ;

c) slab foundations ;

d) platform foundations .

The requirements specified here are intended to preven tthe static and dynamic loads from transmitting unaccept-able vibration to the environment or causing damage to th emachinery and its foundation . This standard establishescriteria for determining vibration behaviour, deals wit hdesign action-effects, and covers principles of constructio nbased on experience to date with machine foundations .

2 Concept s2.1 Vibratio nFor the purposes of this standard, vibration is a process i nwhich a mechanical quantity,q,varies as a function of tim e(see figure 1), alternating at least once between a minimu mnegative and a maximum positive (peak) value .

Figure 1 . Vibratio n

The mechanical vibration quantities of concern are :

a) displacement (e .g . deflection, deformation) ;b) vibration velocity ;

C) vibration acceleration ;

d) restoring forces and moments (associated with dis -placement) ;

e) damping forces and moments (usually associated wit hvibration velocity) ;

f) inertia forces and moments (in proportion to the vibra-tion acceleration) ;

g) external forces and moments ('excitation') .

2 .2 Types of vibration

2 .2 .1 Periodic vibratio n

Periodic vibration is a process in which the magnitude o fa quantity, q, periodically varies with time (see figure 2) ,this being expressed by the following formula :

q(t) = q(t+nT)

(i )

where n is a whole number and T is an increment of tim e

The reciprocal of T, in s, is the frequency, f, in Hz .

Figure 2 . Periodic vibratio n

2 .2 .2 Harmonic vibratio nHarmonic vibration is a periodic vibration process in whic ha quantity, q, is a sinusoidal function of time (see figure 3) ,this being expressed by the following formula :

q( t ) = 4 sin (wt + (po)

(2 )

,wherer1 is the amplitude ;

w is the angular frequency based on the equatio n

2 nw=-, = 2nf ;

ro o is the zero phase angle .

Figure 3 . Harmonic vibratio n

2 .2 .3 Transient vibratio nTransient vibration is a temporary state during which th epeak values or the duration of vibration are not stead y(e .g .when the machine is turned on or off,when a vibratio nprocess starts or ends, or during short-circuit) .

2 .2 .4 Free vibratio nFree vibration is that which results when a linear system i sexcited once, i .e . any loads varying with time cease to act onthe system . This process involves system-related natura lmodes of vibration and the associated natural frequencies ,the lowest of which being referred to as the fundamenta lnatural frequency.

2 .2 .5 Forced vibratio nForced vibration is a state of vibration caused by externa lforces that vary with time .

2.3 Damping

Damping is a system characteristic by which kinetic energ yis dissipated and either irreversibly converted to othe rforms of energy, particularly heat, or conducted away to th eenvironment .

The forms of damping of concern are :

a) material damping,where the damping force is given by :

o = ~ ~ xP

(3)

DIN 4024 Part 1 Page 3

or, when allowing for stiffness :

FD = kB c • x

(4)

b) viscous damping,where the damping force is given by :

FD =dv•z

(5 )

or, when allowing for stiffness :

j'u = kv•c•,z

(6 )

The quantities used to characterize the damping are :

a) damping factor (Lehr damping factor), D 1 )

d BD= (7 )

2•Sl

c• m

k13

CD (8 )2 ~

m

dvD= (9 )2 c• m

D = 2 m (10)

b) logarithmic decremen t

2rL• DA =

(11 )1•-D 2

where, in equations (3) to (11) ,

S2

is the excitation frequency,

dß, dv'), kn t) and kv are damping characteristics (quan-tities with different units) ,

c

is the elastic (spring) constant (of asingle-degree-of-freedom system) ,

in

is the mass (of a single-degree-of -freedom system) ,

z

is the vibration velocity .

2.4 Action-effect sForthe purposes of this standard, action-effects are forces ,moments and quantities of displacement that occur as aresult of static or dynamic loading .

2.5 ModelFor the purposes of this standard, a model is a represen-tation of the actual mechanical system, used for the calcu -lation of essential system characteristics . Each possibl eindependent displacement of a material point or a modelelement, within a spatial configuration, is defined as adegree of freedom . Where vibration in any one coordinat einfluences vibration in other coordinates, the system maybe represented by several, mutually independent model s('decoupling') .

2.6 Machinery2 .6 .1 Service frequency (rotational speed )The service frequency is the rotational speed under servic econditions, expressed in s -1 (or in min-1 ) .

2.6.2 Service frequency rangeThe service frequency range is the range of rotationalspeeds under service conditions .

2 .6 .3 Excitation frequency

Excitation frequency is the frequency at which dynami cloads act on the system . It is often the same as the servic efrequency.

2 .6 .4 Balanced qualityThe balanced quality of a system is a measure, Q, of the roto runbalance, expressed as Q = e • Q,where a is the eccentric -ity of the rotor (cf.VDI 2060) .

2 .6 .5 Driving momen t

The driving moment is the torque at the input of a drive nmachine (e .g . a turbine) .

2 .6 .6 Output momen tThe output moment is the torque at the output of a drivin gmachine (e .g . a generator) .

2 .6 .7 Vacuum forc e

Vacuum forces are static loads that result when vacuum i nthe condensor of a steam turbine is produced .

2 .6 .8 Terminal short circuit and loss of synchronisatio n

Terminal short circuit and loss of synchronisation ar etransient malfunctions that occur as a result of a rapidchange in the magnetic forces in the air gap of an electri cmachine .

2.7 Types of foundation2 .7.1 Machine supportA machine support is a flexible structure in the form o fa slab or a configuration of beams on which the machin esystems rests and is anchored .

2 .7.2 Table foundatio nA table foundation consists of a slab placed on props tha tare usually arranged in pairs. The props usually rest on areinforced concrete base, the latter resting on the ground .

2 .7.3 Spring foundatio nA spring foundation is made up of spring elements, usuall yconsisting of several prefabricated springs having definedspring constants, and the supporting structure, which i sdefined as the structure beneath the spring elements ,including the ground .

2 .7.4 Slab foundatio nA slab foundation is made from reinforced concrete an drests directly on the ground .

2 .7.5 Platform foundationA platform foundation is a construction that is made o fslabs or beams,on which the machine system directly rests ,and that is integral with a multi-storey structure .

3 Materials and .groun d

3.1 Reinforced concreteConcrete of at least strength class B25 as specified i nDIN 1045 shall be used .

For the dynamic analysis, the static moduli of elasticity a sgiven in DIN 1045 maybe assumed . Where precise informa-tion about the damping characteristics is not known, th edamping factor, D, of the entire system (machine plu sfoundation) may be assumed to be 0,02. Where stiffness -related viscous damping is a factor, kv should be selecte dso that D is less than or equal to 0,02 at the highest calcu-lated natural frequency, f . (see subclause 5 .3) . For loa dcases that involve significantly higher loading than tha tduring normal service, a higher damping factor may beassumed .

t ) in the relevant literature, the symbol0 is used forD,k or bfor dv, and V for kB .

Page 4 DIN 4024 Part 1

Reinforcing steel, suitable for loads that are not predomi-nantly static, shall be used formembers subject to dynami cloads ; the reinforcement of such members shall not b emade from smooth reinforcing steel .

3 .2 Steel

Steel of at least grade St 37-2 as specified in DIN 17 100 shal lbe used .

For the dynamic analysis, the static moduli of elasticity a sgiven in DIN 18800 Part 1 may be assumed . Where preciseinformation about the damping characteristics is not avail -able, stiffness-related material damping may be assumed ,as well as a damping characteristic, hß, equal to 0,02 .For load cases that involve loading significantly higher tha nthat during normal service, a higher damping factor may b eassumed .

3.3 Groun d

For the dynamic analysis, the resiliency of the ground nee donly be considered in special cases (cf. subclause 5 .2) ,except for slab foundations, where the resiliency must b econsidered . It may, however, be advantageous to conside rthe damping of the ground .

The dynamic characteristics of the ground (e .g . shea rmodulus and Poisson's ratio) can only be determined b yfield or laboratory measurements. Since measured value stend to be widely dispersed, calculation of the dynami cloading should be based on limit values forthese quantities ,which can be found in the relevant literature, [1] to [3] ,

4 Loads4.1 Machinery4 .1 .1 Genera l

The machine manufacturer shall provide the following infor -mation :a) erection loads ;b) loads during normal service ;C) loads during malfunction ;d) service frequency and service frequency range ;e) any thermal effects of the machine or the ancillary

equipment on the foundation .

The static and dynamic loads in each of the above case sshall be given separately .

If the machine manufacturer requires the foundation to b eof a particular stiffness, the above load information shall bestated in the form of displacement values which are not t obe exceeded .If vibration is to be restricted (to prevent damage to th emachine .and its ancillary equipment), even in the case o fmalfunction, the manufacturer shall provide relevant limi tvalues .

4 .1 .2 Static loads

The following are static loads during normal service :a) the mass of the rotors and the machine casing ;b) the mass ofthe condensers, depending on howtheyar e

erected and the amount of water they contain ;C) the vacuum force in a turbine whose condensors ar e

connected to the turbine casing via compensator s(both vertical and horizontal) ;

d) the machine's driving and output moments that act o nthe foundation via the casing (vertical pairs of forces) ;

e) friction loads on the bearing faces (predominantly hori-zontal), caused by the thermal expansion of the casing :

f) loads due to the mass of the ancillary equipment an dthe effective forces and moments (that act both verti-cally and horizontally), e .g . thermal expansion, flo wforces and vapour pressure ;

g) thermal effects from the machine and its ancillaryequipment.

In the case of turbines, a difference in temperature o f20K across the foundation cross section may b eassumed, unless otherwise specified by the machinemanufacturer.

Erection loads are generally transient mass loads that d onot occur during normal servive, and include the load sresulting from erection equipment and lifting gear.

4.1 .3 Dynamic load s

The following are dynamic loads during normal service :a) bearing forces (both vertical and horizontal), resulting

from rotor unbalance, depending on the rotationa lspeed ;

b) periodic operating loads, resulting from the particula rmachine performance, that act on the foundation vi athe casing orthe bearings, e .g. forces at twice orsevera ltimes the rotational frequency of single-phase a .c .machines or biowers,forces from the casing at twice th emains frequency of a three-phase machine, or slip -frequency magnetic forces from an induction machine ;

C) forces and moments that result from turning th emachine on or off, or other transient situations (e .g .those associated with the operation of shock convert-ers or occurring during synchronization) .

The major dynamic loads that result from malfunction are :a) an increase in the periodic bearing loads in the case o f

exceptionally high rotor unbalance caused, for example ,by blade breakage or rotor distortion ;

b) terminal short circuit or loss of synchronization in th egenerator or motor ;

C) shock to pipes or fittings upon emergency shut-down .

4.2 Foundatio n

4 .2.1 Permanent load s

The design values of the self-weight of the structure shall bedetermined in accordance with DIN 1055 Part 1 .

4.2 .2 Imposed load s

Imposed loads need not be considered for the structure a sa whole, but the individual members shall be designed t ocarry particular imposed loads, these being the subjec tof agreement among the machine manufacturer, the foun-dation designer and the client . Unless otherwise specified ,an imposed load of 5 kN/m 2 shall be assumed .

4 .2 .3 Creep and shrinkage of reinforced concreteShrinkage of reinforced concrete shall be considered, a sset out in DIN 1045, and no allowance shall be made fo rcreep (cf . subclause 7.1) .

4.2 .4 Effects of temperature, wind and earthquake sWhere the effects of temperature, wind and earthquake sneed to be considered, refer to the relevant standards (e .g .DIN 1045, DIN 1055 Part 4 and DIN 4149 Part 1) .

5 Design5.1 Genera l

5 .1 .1 Objective s

Machine foundations are intended to accommodate th estatic and dynamic loads from the machine .They should bedesigned on the basis of machine movement during normal

DIN 4024 Part 1 Pag

service (i .e . the minimum performance requirements to besatisfied), and to prevent unacceptable vibration fro mbeing transmitted to the environment.This can be assesse don the basis of the vibration amplitudes of rotors, especiall yat the bearings, and the associated vibration and forces .

Any effect that malfunction has on the foundation shall no timpair subsequent machine performance under servic econditions .

To verify compliance with these general requirements, astatic and dynamic analysis shall be made, instead of calcu -lations .

5 .1 .2 Static analysi s

The static analysis of machine foundations, i .e . analysis o fthe action-effects of the system under static loading, shal lbe based on specified load cases (cf .subclause 6 .1) for th emachinery (cf. subclause 4 .2.1) and for the foundatio n(cf. subclause 4 .2) . Since such an analysis is the same a sthat made for similar structures, it is not dealt with here .

Compliance with any limit displacement values specified bythe machine manufacturer under defined load condition s(cf. subclause 4 .1 .1) shall be verified .

In the case of machine foundations made from reinforce dconcrete, deformation due to creep may be limited b ymeans of a suitable structural design (cf . subclause 7.1) .

Where thermal effects are to be considered in the analysisof reinforced concrete foundations, the 2nd moment o feffective cross-sectional area may be assumed to be equa lto 0,3 1 .

The static analysis of steel machine foundations ma ygenerally be limited to a determination of the suppor treaction, as the vibration load on such foundations is low.

5 .1 .3 Dynamic analysisDynamic analysis of machine foundations serves to asses svibration behaviour and to determine the action-effect sof the system under dynamic loading. It is to be based o na model of the entire system that has largely linear charac -teristics and several degrees of freedom. The metho dof assessment of the vibration behaviour (displacement)and of determining dynamic forces will depend on whethe rdynamic excitation forces are to be considered or not .

Where excitation forces are not considered, predicting th evibration behaviour may be based on a comparison o fthe calculated natural frequencies of the machine with it sexcitation frequencies, and then assessing the excitatio npotential of these natural modes . The action-effects ca nthen be determined by assuming analogous maximum dis -placement values based on the natural modes established .

Where excitation forces declared by the machine manufac -turer are used in the calculation, or where such ar eassumed, predicting the vibration behaviour and determin -ing the action-effects may be based on an analysis o fforced vibration, in which case natural vibration is also to b edetermined .

Dynamic analysis and consideration of the dynamic com-ponent in subsequent calculations may generally b edispensed with if the mass of the rotating elements .is lessthan one one-hundredth of the mass of the entire syste m(machine plus foundation) . (Note that for platform founda-tions, the foundation is understood to comprise only thos emembers which are directly loaded .) Otherwise, in the cas eof systems whose elements run at different rotationalspeeds,theirexcitation unbalance at any one speed mayb eneglected if the sum of the masses of the individual ele-ments is less than one one-hundredth of the mass of th eentire system .

5.2 Model stud y

5 .2 .1 Principle s

A model is intended to facilitate analysis of the vibrat ibehaviour of the entire system (machine plus foundati cThe system is represented by a linear-elastic model hav idistributed or concentrated masses on spring supports .Texcitation source,as well as system characteristics suc hmass, stiffness and damping, are to be included so aspermit a sufficiently accurate assessment .

5 .2 .2 Requirement sThe model usually consists of beam elements in whi pshear and torsion deformation have been accounted fRotation inertia maybe neglected . In the case of reinforceconcrete, the 2nd moments of area of the cross-sectio nareas may be determined for the cross section exhibiti rno cracks (state 1) . The distribution of mass may eit hbe represented realistically, or the mass assumed to tdistributed at different points . It should be noted, howeV Ethat if calculation is based on distributed masses, t hrequired accuracy can be achieved with substantially few (degrees of freedom than with concentrated masses . Ithe case of reinforced concrete foundations, the machi nshaft and casing may usually be seen as static ; for ste (and steel/concrete composite foundations, a more preci sanalysis should be made .

Each model point (node) has up to six degrees of freedo ni .e. three translational and three rotational . The number odegrees of freedom that need to be considered in a parti cular case cannot be specified here .

The numberof nodes required and the numberof degrees ofreedom 'to be assigned to them depends on severafactors, including :

a) the geometry of the entire system ;b) the type of vibration to be investigated (vertical, hor i

zontal or torsional) ;

c) the relevant frequency range ;d) the calculation method selected .

If the system is symmetrical with respect to the verticalcentre plane in the longitudinal direction, it will have sym •metric and antimetric natural modes of vibration that ca nbe calculated using models that represent each half o fthe system . The relevant frequency range, .i .e. the range ofnatural frequencies that approaches the service frequency ,will affect the minimum number of translational degrees o ffreedom that need not be considered .This number shouldbe greater than twice the order of the highest natural fre-quency in the relevant frequency range .

Damping maybe neglected when calculating natural vibra-tion, but should be considered when calculating force dvibration .

Where it is necessary to consider the resiliency of th eground (cf. subclause 3.3), the continuous resiliency maybe represented by a number of springs .

5 .2 .3 Simplified representatio n

The foundation usualiydoes not need to be represented in aspatial configuration . Rather, it may be represented b ymodels of the individual components, one each for trans-lation and rotation in the two vertical planes and in the hori -zontal plane, The rotational component may often b edispensed with .

For consideration of horizontal vibration, the foundatio nmay generally be assumed to be decoupled from the sup -port and to be laterally retained by springs .

For table foundations, the natural flexural vibration of th eprops maybe calculated separately from the entire system .

Page 6 DIN 4024 Part 1

b)

C)

The following simplifications are permitted for the calcula-tion of vertical vibration .

a) Where the flexural strength of the spring-supporte dsystem is high relative to the stiffness of the spring sup -ports, i .e . where

13 . 1 ct

E -

i1

(12 )

is less than or equal to 50 (see figure 4), the n- it maybe assumed that the flexural system is rigid fo r

calculation of the natural frequencies generated b ythe spring supports, o r

- the spring supports maybe neglected forcalculatio nof higher natural frequencies .

In the case ofspring foundations,where the stiffness, cu ,of the supporting slabs, beams or other supports is a tleast ten times the stiffness, cF, of the spring elements ,i .e. where CUICF is not less than 10, then the foundatio nmay be assumed to be separate from the support and t oconsist of a configuration of beams resting on springelements .For calculation purposes, this means that the resiliency ,cu, of the foundation, as well as the effect of its mass ,can be neglected .

The effect of the ground and that of the mass of th efoundation may usually be neglected, provided one o fthe three following conditions is met (see figure 5) .c t : The lowest natural frequency, f t , of the foundatio n

plus machine (mass rrrn) on the spring support ,where the foundation (mass nij is assumed to b erigid, is at least 20% lower than the lowest servic efrequency, fn, .

C2:The lowest natural frequency, f,, of the entire sys-tem,assumed to be a rigid bodyvibrating on flexibl eground,is at least 20%lowerthan the lowestservic efrequency, f,,, .

,

C3:The lowest natural frequency, f t , of the foundation a ssuch,assumed to be rigid, is at least 25%lowertha nthe lowest natural frequency, fB , of the foundatio nas such, assumed to be rigid and on flexible ground .

l

E•ICt

C2

C3

r.

i

.

ft--------------- -

When calculating ft and

f2, E • I shall be assume dto approach infinity.

mo

Co

Modelm„

C B

- ~Ct )

ft =t

2~nV I . f

fm

f>02fm

t

CBC2) fj= 2-n m,•m

ft

fm~

fZ02fm

~,

1

CeC3) fj = 2-I-~ m,

fB= 2;n m

+---

f?0,25 fB

Figure 5. Simplification c)

ft

fB

5.3 Natural vibratio n

5 .3 .1 Natural frequencies and modes of vibratio nThe natural frequencies ft to & and the modes associate dwith them shall be calculated in ascending order.The number of natural frequencies and modes to b eestablished shall be selected so that the highest natura lfrequency calculated is at least 10%higherthan the servic efrequency. This requirement may be dispensed with in th ecase of foundations for machines with high service frequen -cies (i.e . where fn, > 75Hz) ; however, depending on th eanalysis model, the number of natural frequencies to b ecalculated, n, shall comply with the following :a) n =10 for two-dimensional models in which onlyvertica l

displacements are considered and in which symmetri cand antimetric vibration are not decoupled ;

b) n = 6 for two-dimensional, symmetrical models in whic honlyvertical displacements are considered and in whic hsymmetric and antimetric vibration are decoupled.

5 .3 .2 Assessment of vibration behaviouron the basis of natural vibratio n

An assessment of the vibration behaviour of a machin efoundation, in respect of the objectives given in sub -clause 5 .1 .1, may, as a simplification, be based on the rela -tionship of the natural frequencies, fn, to the servic efrequencies, fm .If both conditions land 2below are met for each decouple dmodel, subsequent analysis may be dispensed with ,

1. First order natural frequency

ft z 1,25•fm

(13 )o r

ft s 0 1 8 • fn,

(14 )

2. Higher order natural frequencies

a) Higher order natural frequencies that approach th eservice frequency :

A S 0 . 9 -/mand

(15 )

fn + 1 Z 1,1 • f m

Mode l

.~

~.

\

r~'

f3

`'~---~

f4

Figure 4 . Simplification a)

When calculating fn,withlarger than 2, c ; shall beassumed to be zero .

DIN 4024 Part 1 Page 7

b) if condition 2a is not met,it shall suffice that fn is lessthan f,,, where n is equal to 10 or 6 (cf. sub -clause 5.3 .1) .

Where conditions 1 and 2 are not met, a more preciseassessment of vibration behaviour can nonetheless b eattained by analyzing the excitation potential of the natura lmodes of vibration . For this purpose, the highest natura lmodes, assuming they lie within the frequency rang edefined by conditions 1 and 2 above, may be analyzed fo rthe magnitude of the relative displacement, xi , ,, at th ebearings, i, of the machine shaft . Each natural mode ofvibra -tion shall be checked separately for each bearing, i, for ful-filment of the following condition :

I

2

xin •

1

2fn

2<3

(16)fn - f m

If this condition is not met, then forced vibration shall b eanalyzed in accordance with subclause 5.4 .Note that analysis as specified in subclause 5 .4 is recom-mended for steel/concrete composite foundations fo rmachines whose service frequency, f m, is less than 75 Hz o rwhere fm is greater than f,, (where n is equal to 10 or 6 a sgiven in subclause 5 .3 .1) .

5.4 Analysis of vibration due to unbalanc e5.4.1 Genera lIf the vibration behaviour cannot be adequately assessedusing the methods given in subclause 5 .3, an analysi sof forced displacement as set out in subclause 5 .4.2 i srequired on the basis of the excitation forces declared bythe machine manufacturer. In the absence of such informa-tion, the forces as determined in accordance with sub -clause 5.4 .2 may be introduced in the calculation .The dis -placement values thus obtained may then be compare dwith the data given by the manufacturer, if any, or with th evalues obtained in accordance with subclause 5 .4 .3, takin gthe operative state and, If necessary, the malfunctionin gstate, into account.The forces due to unbalance, in both the operative and mal -functioning states, may be determined in accordance withsubclause 5.4 .2, 5 .4.3 or 5 .4 .4 .

5 .4 .2 Forced vibratio n

If information on forces due to unbalance (in the operativeand malfunctioning states) has been provided by th emachine manufacturer, they may be used to establis hdisplacements and forces using the model formed to deter -mine natural frequencies, following the principles set outbelow.In the absence of such information, the forces may be cal -culated in accordance with VDI 2060, on the basis o fbalanced quality, as follows .

a) Operative stat eThe balanced quality shall be assumed to be one grad elower than that for the relevant machine group as speci -fied in VDI 2060 .

b) Malfunctioning stat eThe forces due to unbalance shall be assumed to be si xtimes the value established for the operative state .

The excitation forces shall be analyzed for each bearing ,taking into account the balanced quality selected, th eservice frequency as the excitation frequency, and th erotary mass component .As a simplif!cation,since the phasepattern of the excitation forces is unknown, the forces atthe bearings may first be assumed to be unidirectional ,and then to act in opposite directions. If the natura lfrequencies lie within the range of 0,95 to 1,05 fm ,the exci-tation frequency may be assumed to be shifted to either of

the two adjacent natural frequencies, provided that they li ewithin the specified range and that the magnitude of th eexcitation force is kept constant .

5.4 .3 Natural modes of vibration

if calculating the displacement can be dispensed with, th eforces may be determined on the basis of the natura lmodes of vibration adjacent to the service frequency, thi sbeing intended to simplify the analysis that would be re-quired for forced vibration . On the basis of the natura lmodes and the associated action-effects, for each membe rthat incorporates a bearing, maximum amplitudes an dforces for the operative and malfunctioning states shall b eassumed, and the forces obtained by conversion . Fo rmembers that do not incorporate bearings, the action -effects shall be determined by superimposing load dis -placement curves .The following amplitudes, effective at the bearings, may b eassumed for the particular machine. group in accordanc ewith VDI 2056 .

a) Operative stat eThe value associated with the operating frequency fo rthe assessment criterion given in VDI 2056which is on egrade higher than that guaranteed by the manufacture rshall be taken as the amplitude under service condi-tions at the particular bearing .

b) Malfunctioning stat eThe amplitude in the case of malfunctioning shall b eassumed to be six times that values used for the opera -tive state .

5.4.4 Equivalent-load metho din the case of slab- or beam-type foundations of simpl egeometry, the dynamic analysis may be simplified b yassuming equivalent static loads, based on the unbalanc eduring the malfunctioning state, so that results err on th esafe side for the operative state .Starting with a balanced quality, e • Q, equal to 2,5 mm/s fo rthe relevant machine group (see VDI 2060) in the operativestate, a balanced quality equal to 38 mm/s is assumed ,which is six times that of the next highest grade. The un-balance force, K, is then a function of the rotor weight force ,L, and the operating frequency, fm, so that

K-1,2 L 50

(17)

The static equivalent load, F, is a function of the frequenc yratio,

n

fn

(18 )

where f n is the nearest natural frequency in the plane bein gconsidered, so tha t

1F=

I1__

I •K,

(19 )

with F a maximum of 15 K .

F shall then be assumed to act at the bearings according t othe rotary mass component.To determine the action-effects ,an equivalent system should be used that has fixed bearing sat the nodes of the natural modes of vibration being Investi -gated .The signs (+or-) of the equivalent-load componentof the bearings should be selected to produce the maxi -mum possible amount of deformation within the system .

5.5 Analysis of transient vibration5.5.1 GeneralTransient vibration that can affect the balanced quality o fthe system may occurwhen the machine is turned on or off,or during certain other transient operative states . It may be

Page 8 DIN 4024 Part 1

assumed that the action-effects determined for the mal -functioning state in accordance with subclause 5 .4 alsoaccount for the loads that occur during transient vibration ,i .e. these need not be analyzed separately .In the case of electric machines, however, there are certai nrare malfunction states (e .g. terminal short-circuit, main sshort-circuit followed by shut-down, or loss of synchronisa-tion) that can result in very large antimetric loads on th esystem which are transmitted to the foundation via th emachine casing . A two-pole terminal short-circuit in a nelectric machine running at a high speed of rotation is to b econsidered representative for such loads . Analysis of th eresulting action-effects is described In subclause 5,5 .2.

5 .5 .2 Short-circui t

The short-circuit moment affects the foundation via th egenerator or motor casing in the form of opposite pairs o fvertical forces, the moment vector being parallel to th eshaft axis . The resulting displacements and loads can becalculated as a function of the excitation/time relationshi por by using the equivalent-load method .Where the machine manufacturer has not specified th eshort-circuit moment, Mk, as a function of time, analysi smay be based on the following equation for three-phas emachines :

1Mk (t) 10 MO (e-vo,4 • sin O N • t

-

etro,4 -sin 2QN • t

Mo (f -etuo,15)

2

(20)

wher e

M O is the resulting nominal torque from the actual powe rgenerated ;

ON is the mains frequency (not always the same as th eoperating mains frequency) ;

t

is time, in s .

For determining forced vibration, the natural frequenciesshall be taken to be at least 1,2 times the mains frequency .Where the natural frequencies of antimetric natural mode sof vibration lie within the range of 0,95 to 1,05 O N , the exci -tation frequency (i .e . mains frequency) shall be shifted tothese natural frequencies for calculation purposes .Loads from short-circuit may also be determined in a simpli -fied manner by the equivalent-load method, for which a valu ethat is 1,7 times the maximum short-circuit moment i sassumed . If the machine manufacturer has not specified th elatter,the maximum value of Mk may be assumed to be 12 Mo.

5.6 Loads on the foundation and groun dThe effects of dynamic loads during normal operation anddue to malfunction shall be considered when designing th efoundation and for the analysis of earth pressure .If the equivalent-load method is used for analyzing the sup -port reaction, it may be assumed that counteracting mas sforces contribute to maintaining equilibrium .If the foundation has been assumed to be decoupled fromthe ground in one ormore planes forthe purpose ofdynam-ic analysis (cf. subclause 5 .2), then the maximum desig nvalues of the dynamic support reaction in the relevant plan emay be taken as the equivalent loads . For analysis of eart hpressure, the loads due to malfunction may be neglected .

In the case of spring foundations, the isolating function o fthe spring elements is usually so great that the dynami cloads on the foundation during both normal operation an dmalfunction can be neglected .

6 Further design criteria6.1 Design action-effect sBy superimposing the peak values obtained from static an ddynamic analysis, the following loading conditions shall b econsidered .

1: Static loads during erection .2: Static loads during normal operation .3: Dynamic loads during normal operation .4: Loads resulting from malfunction or short-circuit .

Load cases M, B and S below shall be established, fro mwhich the loads relevant to design can be derived ;

M : load condition 1 ;B : load conditions 2 and 3 ;S: load conditions 2 and 4 .

Note that the action-effects from dynamic loads in vertica land horizontal directions need not be taken as actin gsimultaneously ,

The resonance of those members for which, in the analysis ,no dynamic loads could be established because of an in -adequate model, shall be accounted for by assuming a nequivalent vertical load equal to 100% of the permanen tload for load case S .

6 .2 Reinforced concrete foundationsThe design of reinforced concrete foundations shall be i naccordance with DIN 1045 .

Load cases M and S

Loads shall be assumed to be predominantly static, a yiel dstrength of up to 420MN/m 2 of the reinforced concret ebeing used in the calculation .

Load case BThe specifications relating to loads that are not pre -dominantly static shall be taken into account. It shall b everified that the amplitude of concrete compressiv estresses due to coexistent flexure and longitudinal force sdoes not exceed 0,33 ßR and that the shear stresses do notlie in shear range 3 .If, however, the dynamic loads during normal operatio n(loading condition 3) are multiplied by a coefficient allow-ing forfatigue of 3 or more,analysis may be based on load swhich are predominantly static, in which case the restric -tions stated above foramplitude and shearstresses may b eignored .

Load case SWhere the loads due to unbalance as a result of malfunc-tion are multiplied by a factor of at least six times thos eduring normal operation, analysis of load case B may bedispensed with .

6.3 Steel foundationsVerifying the strength of steel foundations may usually b edispensed with .

In exceptional cases, a general stress analysis as specifie din DIN 18 800 Part 1 as well as a stability analysis as speci -fied in DIN 4114 Parts 1 and 2 shall be made for load cases M ,B and S .Such is required in any case forprops .ln this regard,the permissible loads specified for load case H shall b etaken for cases M and B, and those specified for load cas eHZ, for case . S. Furthermore, analysis of load case B shal linclude a service strength analysis using load group 86 a sspecified in subclause 4.4 of DIN 4132, February 198 1edition .

Where .the loads due to unbalance as a result of malfunc -tion are multiplied by a factor of at least six times thos eduring normal operation, analysis of load case 8 may b edispensed with .

6.4 GroundDetermination of the permissible loading of the groun dshall be in accordance with DIN 1054 .

DIN 4024 Part 1 Page t

7 Detailing7.1 Reinforced concrete foundation s7.1 .1 Table foundation s7.1 .1 .1 Machine support (slab )The machine support shall not be joined to the rest of th ebuilding in which the foundation is to be erected .In orderto achieve the most uniform creep behaviourat th ebearings, cross sections shall be selected so that nearl yidentical displacements occur at the bearings directly sub -jected to concentrated loads under the self-weight of th emachine and slab .This same principle shall also be applie dto ensure equal displacements at the rotor bearings rela-tive to the machine casing .All structural members shall be reinforced throughout,eve nif this is not required by the design . Links shall preferably b eused as shear reinforcement .

Anchorages and recesses shall be arranged so that th ereinforcement, in its main loading direction, is not adverselyaffected .

The slab shall be cast in concrete without constructio njoints, the concreting operation being carefully prepared ,for example ,a) by using retarding agents for placing the concrete i n

layers ;

b) by providing foradequate quantities of concrete mixin gcomponents and transport capacity ;

C) by using well-supported formwork when the concrete i snot placed centrally ;

d) by keeping the joints between props and slab thor-oughly clean .

If the base or other supporting structures are to be con-creted later, the connecting joints shall be cleaned an dprepared to ensure an adequate bond, this also applyin gfor the concrete topping . Concrete toppings about 20 cm i nthickness shall be reinforced and be joined with the founda -tion by means of projecting reinforcements .

7.1 .1 .2 PropsProps shall not be joined to the rest of the building in whic hthe foundation is to be erected, except for lightweight ele -ments, which may be fastened directly to the props b ymeans of flexible intermediate layers to prevent vibrator yeffects . Reinforced concrete intermediate platforms shal lbe erected on the base with their own props .

The cross section of the props shall be selected so that ,under permanent load, roughly the same compressiv estresses are induced in all props . For longitudinal reinforce-ment of props, the percentage of reinforcement shall be a tleast equal to 0,8.The reinforcing bars shall have a diamete rof at least 10 mm .

The props shall be concreted without joints .

71 .1 .3 Base

The base should be separated by a joint from other parts o fthe building in which the foundation is to be erected . It sthickness should be about one-tenth of its length .The self-weight of the base, including the loads from inter -mediate platforms and concrete toppings, should b eselected to be about the same as the loads from th emachine support with the machine, the loads from con-densor and props being disregarded here .To prevent differ-ences in settlement, all permanent loads (excludin gvacuum forces) should act on the centre of gravity of th ebase area .The mass of reinforcement by base volume should be a tleast equal to 30 kg/m 3 part of the reinforcement shall b earranged in a spatial configuration .When placing the concrete, vertical joints shall be avoided .

7.1 .2 Spring foundations

7.1 .2 .1 Machine suppor tSubclause 7.1 .1 .1 shall apply for the machine support ospring foundations .Steel plates should be fitted to the underside of the su pport, above the spring elements .

7.1 .2 .2 Spring elements

Spring elements usually consist of a number of individua lsprings which have defined stiffness in both the vertical an dhorizontal directions .The spring travel shall be higher than that calculated an dshould be half as large as the deflection due to the self •weight of the system .

The spring element shall be prestressabie to permit itsremoval during operation without the machine suppor tbeing lifted .

Dampers,which are capable of acting in all directions and o faccommodating thermal expansion, may be connected i nparallel to the spring elements in order to prevent move-ment of the machin e ,support under accidental loading con -ditions .

7.1 .2 .3 Supporting structure

Regardless of the material used for the machine support ,the supporting structure may be made from either rein -forced concrete or steel . It maybe a part of the building i nwhich the machine foundation is to be erected .The spring elements may be concentrated (e .g . on props )ordistributed (e .g . on beams) .The zone in which they are t obe erected, particularly in the case of props, should bedesigned so that further elements can be added later .

7.1 .3 Slab foundation sSubclause 7.1 .1 .1 shall apply for the machine support of sla bfoundations.

7.1 .4 Platform foundation sIt is rarely possible to predict the dynamic behaviour of aplatform foundation, owing to the interaction between i tand the building in which it is installed,this interaction bein gvery difficult to measure . Therefore, platform foundation sare generally used only for small machine systems . In cas eof doubt, it should be possible to separate the foundatio nfrom the surrounding structure, should it prove inappropri-ate.

7.2 Steel foundations7.2 .1 Table foundation s

7.2 .1 .1 Machine support (slab)The machine support shall not be joined to the rest of th ebuilding in which the foundation is to be erected .Steel foundations shall only be made from fully welde dmembers or those having slip-resistant joints with high -strength bolts, such as GV or GVP joints as specified i nDIN 18 800 Part 1 .Where the machine manufacturer has not specified partic -ularstiffness requirements for the foundation,the followin gminimum requirements should be maintained .

E• 1a) The average relative stiffness

Gof the machine sup -

port in the longitudinal direction should be about twic eas large as the average relative stiffness of the shaftassembly.ln the above formula,G is the permanent loadon the machine support due to its self-weight, that ofthe machine, and that of the shaft, respectively .

b) The stiffness of the girders, E • 1, which are subject t odirect loading from the machine, should be as large a spossible, and be at least one-fifth of the stiffness of th emachine support in the longitudinal direction .

Page 10 DIN 4024 Part I

The points at which forces are introduced, particularly thos eat the prop connections and the bearing faces, shall b ecarefully designed . When prestressed bolts are used fo rmachine attachment, It shall be ensured that they ca naccommodate the loads resulting from prestressing .In general,the cross sections used need only be resonance -free at the machine bearings or pipework connections . It is ,however, recommended that the cross section of upperbo xgirders be highly tuned, this being a requirement fo rmachines having an operating frequency of less than 75 Hz ,

7.2 .1 .2 Prop s

Props shall not be joined to the rest of the building in whic hthe foundation is to be erected, except for lightweight ele-ments, which may be fastened directly to the props b ymeans of flexible intermediate layers to prevent vibratoryeffects . Heavy intermediate platforms shall be erected o nthe base with their own props.

Since the vibration behaviour of props varies according t othe type of connection orjoint used,this shall be allowed fo rin the design .

7.2 .1 .3 Bas eSubclause 7.1 .1 .3 shall apply for the base of steel fou ltions .

7.2.2 Spring foundation sSubclause 7.2 .1 .1 shall apply for the machine suppo rspring foundations, subclauses 7.1 .2 .2 and 7.12 .3 applyfqr the spring elements and the supporting structure .

7.2 .3 Platform foundationsSubclause 7.1 .4 shall apply for steel platform foundati c

7.2 .4 Corrosion protectionFor steel foundations installed in closed, well-heated b LIngs, It is generally not required to provide internal c oslon protection (e .g . for hollow cross sections) .Where corrosion protection is necessary, thespecificatl (given in the DIN 55928 series shall apply .

Standards and other documents referred t oDIN

1045 Structural use of concrete ; design and constructio n

DIN

1054 Permissible loading of subsoi l

DIN

1055 Part 1 Design loads for structures ; materials to be stocked, construction materials and structural memb eself-weight and angle of frictio n

DIN

1055 Part 4 Design loads for structures ; imposed loads ; wind loads on structures not susceptible to vibratio n

DIN

4114 Part 1 Structural steelwork ; safety against buckling, overturning and bulging ; design principles

DIN

4114 Part 2 Structural steelwork ; safety against buckling, overturning and bulging ; constructio n

DIN

4132 Structural steelwork ; design and construction of craneway s

DIN

4149 Part I Buildings in German earthquake zones ; design loads ; design and construction of conventional buildi n

DIN 17 100 Steels for general structural purposes ; quality standardDIN 18800 Part 1 Steel structures ; design and constructio n

DIN 55928 series Corrosion protection of steel structures by organic and metallic coating s

VDI 2056 Evaluating the mechanical vibration of machines 2 )

VDI 2060 Evaluating the balanced condition of rotating rigid bodies 2)

[1] Grundbautaschenbuch (Foundation Engineering Handbook), 3rd ed., Part 1, section 1 .14 : Lorenz/Klei n : Bodendynamik uErdbeben (Soil dynamics and earthquakes), Berlin : Ernst & Sohn, 1980.

[2] Haupt, W. Bodendynamik (Soil dynamics), Braunschweig, Wiesbaden : Vleweg, 1986.

(3]

Studer, J . ; Ziegler, A . Bodendynamik (Soil dynamics), Berlin : Springer, 1986.

Previous editionDIN 4024 : 01 .55 .

AmendmentsIn comparison with the January 1955 edition of DIN 4024, the following amendments have been made .a) Title and DIN number have been changed .b) The standard has been completely revised to bring it into line with the state of the art .

International Patent Classificatio nE 02 D 27/44

E 02 D 31/08

F 16 M 1/'0 0

F16M5/00

F16M9/00

F 16 M 13/0 0

F16F15/0O

2) Issued by the Verein Deutscher Ingenieure (Society of German Engineers), D-4000 Düsseldorf 1 ;obtainable from Beuth Verlag GmbH, Burggrafenstra9e 6, D-1000 Berlin 30 .