din-4024-1-1988-04-01machine-foundations-flexible-structures-that-support-machines-with-rotating-elements

UDC 62-218 .2 :62-13 :001 .4
April 198 8
DEUTSCHE NORM
Machine foundations
~-
DI IV
Flexible structures that support
machines with rotating elements
402 4
Part 1
Maschinenfundamente ; elastische Stützkonstruktionen für Maschinen mit rotierenden Massen
Supersedes DIN 4024 ,
January 1955 edition .
In keeping with current practice in standards published by the International Organization for Standardization (ISO), a comm a
has 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 h
periodic excitatio n
In this standard, the term'load' is used for forces acting on a system from the outside ; this applies equally to compoun d
terms that include the component 'load' (cf . DIN 10rß,0 Part 1) .
c
Contents
Pag e
Pag e
1 Scope and field of application
2
2 Concepts
2 .1 Vibration
2 .2 Types of vibration
2 .3 Damping
2 .4 Action-effects
2 .5 Model
2 .6 Machinery
2 .7 Types of foundation
2
2
2
2
3
3
3
3
3 Materials and ground
3 .1 Reinforced concrete
3 .2 Steel
3 .3 Ground
4 Loads
4 .1 Machinery
4 .1 .1 General
4 .1 .2 Static loads
4 .1 .3 Dynamic loads
4 .2 Foundation
4 .2.1 Permanent loads
4 .2.2 Imposed loads
4.2.3 Creep and shrinkage of reinforced concrete
4 .2 .4 Effects of temperature, wind and earthquakes
5 Design
5 .1 General
5 .1 .1 Objectives
5.1 .2 Static analysis
5 .1 .3 Dynamic analysis
5 .2 Model study
5 .2 .1 Principles
5 .2.2 Requirements
5 .2 .3 Simplified representation
5.3 Natural vibration
5 .3 .1 Natural frequencies and modes of vibration
5 .3 .2 Assessment of vibration behaviour on the basis o f
natural vibration
5 .4 Analysis of vibration due to unbalance
5 .4 .1 General
5 .4 .2 Foiced vibration
5 .4 .3 Natural modes of vibration
5 .4 .4 Equivalent-load method
5.5 Analysis of transient vibration
5.5 .1 General
5 .5 .2 Short-circuit
5.6 Loads on the foundation and ground
5
6
6
6 Further design criteria
6.1 Design action-effects
6.2 Reinforced concrete foundations
6.3 Steel foundations
6.4 Ground
8
8
8
8
8
7 Detailing
7 .1 Reinforced concrete foundations
7 .1 .1 Table foundations
7 .1 .2 Spring foundations
7 .1 .3 Slab foundations
7 .1 .4 Platform foundations
7.2 Steel foundations
7 .2 .1 Table foundations
7 .2 .2 Spring foundations
7 .2 .3 Platform foundations
7 .2 .4 Corrosion protection
9
9
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9
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10
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10
Standards and other documents referred to
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DIN 4024 Part 1
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Page 2 DIN 4024 Part 1
1 Scope and field of applicatio n
This standard specifies requirements for steel or reinforce d
concrete structures that support mechanical system s
('machine foundations', for short) . Such mechanical systems are understood to be machinery with mainly rotatin g
elements, the foundations of which are capable of generat ing flexural vibration in at least one plane . For the purpose s
of this standard, a distinction is made among the followin g
types of machine foundation :
a)
b)
c)
d)
table foundations ;
spring foundations ;
slab foundations ;
platform foundations .
Figure 2 . Periodic vibratio n
The requirements specified here are intended to preven t
the static and dynamic loads from transmitting unacceptable vibration to the environment or causing damage to th e
machinery and its foundation . This standard establishes
criteria for determining vibration behaviour, deals wit h
design action-effects, and covers principles of constructio n
based on experience to date with machine foundations .
2 .2 .2 Harmonic vibratio n
Harmonic vibration is a periodic vibration process in whic h
a quantity, q, is a sinusoidal function of time (see figure 3) ,
this being expressed by the following formula :
t
q( ) = 4 sin (wt + (po)
2n
2 Concept s
w=,
2 .1 Vibratio n
For the purposes of this standard, vibration is a process i n
which a mechanical quantity,q,varies as a function of tim e
(see figure 1), alternating at least once between a minimu m
negative and a maximum positive (peak) value .
(2 )
,where
r1 is the amplitude ;
w is the angular frequency based on the equatio n
=
2nf ;
ro o is the zero phase angle .
Figure 3 . Harmonic vibratio n
2 .2 .3 Transient vibratio n
Transient vibration is a temporary state during which th e
peak values or the duration of vibration are not stead y
(e .g .when the machine is turned on or off,when a vibratio n
process starts or ends, or during short-circuit) .
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 h
vibration velocity) ;
f) inertia forces and moments (in proportion to the vibration acceleration) ;
g) external forces and moments ('excitation') .
2 .2 Types of vibratio n
2 .2 .1 Periodic vibratio n
Periodic vibration is a process in which the magnitude o f
a 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 .
2 .2 .4 Free vibratio n
Free vibration is that which results when a linear system i s
excited once, i .e . any loads varying with time cease to act on
the system . This process involves system-related natura l
modes of vibration and the associated natural frequencies ,
the lowest of which being referred to as the fundamenta l
natural frequency.
2 .2 .5 Forced vibratio n
Forced vibration is a state of vibration caused by externa l
forces that vary with time .
2 .3 Dampin g
Damping is a system characteristic by which kinetic energ y
is dissipated and either irreversibly converted to othe r
forms of energy, particularly heat, or conducted away to th e
environment .
The forms of damping of concern are :
a) material damping,where the damping force is given by :
Po =
~~x
(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 )
dB
D=
(7 )
2•Sl c• m
k13
D
C
2 ~
m
D=
dv
2 c• m
D=
2
m
(8 )
(9 )
(10)
b) logarithmic decremen t
A=
2rL• D
(11 )
1•-D 2
where, in equations (3) to (11) ,
is the excitation frequency,
S2
dß, dv'), kn t) and kv are damping characteristics (quantities with different units) ,
c
is the elastic (spring) constant (of a
single-degree-of-freedom system) ,
in
is the mass (of a single-degree-of freedom system) ,
is the vibration velocity.
z
2.4 Action-effect s
2 .6 .4 Balanced quality
The balanced quality of a system is a measure, Q, of the roto r
unbalance, 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 n
machine (e .g . a turbine) .
2 .6 .6 Output momen t
The output moment is the torque at the output of a drivin g
machine (e .g . a generator) .
2 .6 .7 Vacuum forc e
Vacuum forces are static loads that result when vacuum i n
the 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 e
transient malfunctions that occur as a result of a rapi d
change in the magnetic forces in the air gap of an electri c
machine .
2.7 Types of foundation
2 .7.1 Machine support
A machine support is a flexible structure in the form o f
a slab or a configuration of beams on which the machin e
systems rests and is anchored .
2 .7.2 Table foundatio n
A table foundation consists of a slab placed on props tha t
are usually arranged in pairs. The props usually rest on a
reinforced concrete base, the latter resting on the ground .
2 .7.3 Spring foundatio n
A spring foundation is made up of spring elements, usuall y
consisting of several prefabricated springs having defined
spring constants, and the supporting structure, which i s
defined as the structure beneath the spring elements ,
including the ground .
Forthe purposes of this standard, action-effects are forces ,
moments and quantities of displacement that occur as a
result of static or dynamic loading .
2 .7.4 Slab foundatio n
A slab foundation is made from reinforced concrete an d
rests directly on the ground .
2.5 Mode l
2 .7.5 Platform foundation
A platform foundation is a construction that is made o f
slabs or beams,on which the machine system directly rests ,
and that is integral with a multi-storey structure .
For the purposes of this standard, a model is a representation of the actual mechanical system, used for the calcu lation of essential system characteristics . Each possibl e
independent displacement of a material point or a model
element, within a spatial configuration, is defined as a
degree of freedom . Where vibration in any one coordinat e
influences vibration in other coordinates, the system may
be represented by several, mutually independent model s
('decoupling') .
2 .6 Machinery
2 .6 .1 Service frequency (rotational speed )
The service frequency is the rotational speed under servic e
conditions, expressed in s -1 (or in min-1 ) .
2.6.2 Service frequency rang e
The service frequency range is the range of rotational
speeds under service conditions .
2 .6 .3 Excitation frequency
Excitation frequency is the frequency at which dynami c
loads act on the system . It is often the same as the servic e
frequency.
3 Materials and .groun d
3 .1 Reinforced concrete
Concrete of at least strength class B25 as specified i n
DIN 1045 shall be used .
For the dynamic analysis, the static moduli of elasticity a s
given in DIN 1045 maybe assumed . Where precise information about the damping characteristics is not known, th e
damping factor, D, of the entire system (machine plu s
foundation) may be assumed to be 0,02. Where stiffness related viscous damping is a factor, kv should be selecte d
so that D is less than or equal to 0,02 at the highest calculated natural frequency, f . (see subclause 5 .3) . For loa d
cases that involve significantly higher loading than tha t
during normal service, a higher damping factor may b e
assumed .
t ) in the relevant literature, the symbol0 is used forD,k or b
for dv, and V for kB .
Page 4 DIN 4024 Part 1
Reinforcing steel, suitable for loads that are not predominantly static, shall be used formembers subject to dynami c
loads ; the reinforcement of such members shall not b e
made from smooth reinforcing steel .
3 .2 Stee l
Steel of at least grade St 37-2 as specified in DIN 17 100 shal l
be used .
For the dynamic analysis, the static moduli of elasticity a s
given in DIN 18800 Part 1 may be assumed . Where precise
information 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 n
that during normal service, a higher damping factor may b e
assumed .
3.3 Groun d
For the dynamic analysis, the resiliency of the ground nee d
only be considered in special cases (cf . subclause 5 .2) ,
except for slab foundations, where the resiliency must b e
considered . It may, however, be advantageous to conside r
the damping of the ground .
The dynamic characteristics of the ground (e .g . shea r
modulus and Poisson's ratio) can only be determined b y
field or laboratory measurements . Since measured value s
tend to be widely dispersed, calculation of the dynami c
loading should be based on limit values forthese quantities ,
which can be found in the relevant literature, [1] to [3] ,
4
Loads
4 .1 Machinery
4 .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 ancillar y
equipment on the foundation .
The static and dynamic loads in each of the above case s
shall be given separately .
If the machine manufacturer requires the foundation to b e
of a particular stiffness, the above load information shall b e
stated in the form of displacement values which are not t o
be exceeded .
If vibration is to be restricted (to prevent damage to th e
machine .and its ancillary equipment), even in the case o f
malfunction, the manufacturer shall provide relevant limi t
values .
4 .1 .2 Static load s
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 n
the foundation via the casing (vertical pairs of forces) ;
e) friction loads on the bearing faces (predominantly horizontal), caused by the thermal expansion of the casing :
f)
loads due to the mass of the ancillary equipment an d
the effective forces and moments (that act both vertically and horizontally), e .g . thermal expansion, flo w
forces and vapour pressure ;
g) thermal effects from the machine and its ancillary
equipment.
In the case of turbines, a difference in temperature o f
20K across the foundation cross section may b e
assumed, unless otherwise specified by the machin e
manufacturer.
Erection loads are generally transient mass loads that d o
not occur during normal servive, and include the load s
resulting 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), resultin g
from rotor unbalance, depending on the rotationa l
speed ;
b) periodic operating loads, resulting from the particula r
machine performance, that act on the foundation vi a
the casing orthe bearings, e .g. forces at twice orsevera l
times the rotational frequency of single-phase a .c .
machines or biowers,forces from the casing at twice th e
mains frequency of a three-phase machine, or slip frequency magnetic forces from an induction machine ;
C) forces and moments that result from turning th e
machine on or off, or other transient situations (e .g .
those associated with the operation of shock converters 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 e
generator 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 b e
determined in accordance with DIN 1055 Part 1 .
4.2 .2 Imposed load s
Imposed loads need not be considered for the structure a s
a whole, but the individual members shall be designed t o
carry particular imposed loads, these being the subjec t
of agreement among the machine manufacturer, the foundation 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 concret e
Shrinkage of reinforced concrete shall be considered, a s
set out in DIN 1045, and no allowance shall be made fo r
creep (cf . subclause 7.1) .
4 .2 .4 Effects of temperature, wind and earthquake s
Where the effects of temperature, wind and earthquake s
need to be considered, refer to the relevant standards (e .g .
DIN 1045, DIN 1055 Part 4 and DIN 4149 Part 1) .
5 Desig n
5 .1 Genera l
5 .1 .1 Objective s
Machine foundations are intended to accommodate th e
static and dynamic loads from the machine .They should b e
designed on the basis of machine movement during normal
DIN 4024 Part 1 Pag
service (i .e . the minimum performance requirements to b e
satisfied), and to prevent unacceptable vibration fro m
being transmitted to the environment.This can be assesse d
on the basis of the vibration amplitudes of rotors, especiall y
at the bearings, and the associated vibration and forces .
Any effect that malfunction has on the foundation shall no t
impair subsequent machine performance under servic e
conditions .
To verify compliance with these general requirements, a
static 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 f
the action-effects of the system under static loading, shal l
be based on specified load cases (cf .subclause 6 .1) for th e
machinery (cf. subclause 4 .2.1) and for the foundatio n
(cf. subclause 4 .2) . Since such an analysis is the same a s
that made for similar structures, it is not dealt with here .
Compliance with any limit displacement values specified by
the machine manufacturer under defined load condition s
(cf. subclause 4 .1 .1) shall be verified .
In the case of machine foundations made from reinforce d
concrete, deformation due to creep may be limited b y
means of a suitable structural design (cf . subclause 7.1) .
Where thermal effects are to be considered in the analysis
of reinforced concrete foundations, the 2nd moment o f
effective cross-sectional area may be assumed to be equa l
to 0,3 1 .
The static analysis of steel machine foundations ma y
generally be limited to a determination of the suppor t
reaction, as the vibration load on such foundations is low.
5 .1 .3 Dynamic analysis
Dynamic analysis of machine foundations serves to asses s
vibration behaviour and to determine the action-effect s
of the system under dynamic loading. It is to be based o n
a model of the entire system that has largely linear charac teristics and several degrees of freedom . The metho d
of assessment of the vibration behaviour (displacement)
and of determining dynamic forces will depend on whethe r
dynamic excitation forces are to be considered or not .
Where excitation forces are not considered, predicting th e
vibration behaviour may be based on a comparison o f
the calculated natural frequencies of the machine with it s
excitation frequencies, and then assessing the excitatio n
potential of these natural modes . The action-effects ca n
then 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 e
assumed, predicting the vibration behaviour and determin ing the action-effects may be based on an analysis o f
forced vibration, in which case natural vibration is also to b e
determined .
Dynamic analysis and consideration of the dynamic component in subsequent calculations may generally b e
dispensed with if the mass of the rotating elements .is les s
than one one-hundredth of the mass of the entire syste m
(machine plus foundation) . (Note that for platform foundations, the foundation is understood to comprise only thos e
members which are directly loaded .) Otherwise, in the cas e
of systems whose elements run at different rotational
speeds,theirexcitation unbalance at any one speed mayb e
neglected if the sum of the masses of the individual elements is less than one one-hundredth of the mass of th e
entire system .
5 .2 Model stud y
5 .2 .1 Principle s
A model is intended to facilitate analysis of the vibrat i
behaviour of the entire system (machine plus foundati c
The system is represented by a linear-elastic model hav i
distributed or concentrated masses on spring supports .T
excitation source,as well as system characteristics suc h
mass, stiffness and damping, are to be included so as
permit a sufficiently accurate assessment .
5 .2 .2 Requirement s
The model usually consists of beam elements in whi p
shear and torsion deformation have been accounted f
Rotation inertia maybe neglected . In the case of reinforce
concrete, the 2nd moments of area of the cross-sectio n
areas may be determined for the cross section exhibiti r
no cracks (state 1) . The distribution of mass may eit h
be represented realistically, or the mass assumed to t
distributed at different points . It should be noted, howeV E
that if calculation is based on distributed masses, t h
required accuracy can be achieved with substantially few (
degrees of freedom than with concentrated masses . I
the case of reinforced concrete foundations, the machi n
shaft and casing may usually be seen as static ; for ste (
and steel/concrete composite foundations, a more preci s
analysis should be made .
Each model point (node) has up to six degrees of freedo n
i .e. three translational and three rotational . The number o
degrees of freedom that need to be considered in a parti c
ular case cannot be specified here .
The numberof nodes required and the numberof degrees o
freedom 'to be assigned to them depends on sever a
factors, 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 vertical
centre plane in the longitudinal direction, it will have sym •
metric and antimetric natural modes of vibration that ca n
be calculated using models that represent each half o f
the system . The relevant frequency range, .i .e. the range of
natural frequencies that approaches the service frequency ,
will affect the minimum number of translational degrees o f
freedom that need not be considered .This number should
be greater than twice the order of the highest natural frequency in the relevant frequency range .
Damping maybe neglected when calculating natural vibration, but should be considered when calculating force d
vibration .
Where it is necessary to consider the resiliency of th e
ground (cf. subclause 3.3), the continuous resiliency ma y
be represented by a number of springs .
5 .2 .3 Simplified representatio n
The foundation usualiydoes not need to be represented in a
spatial configuration . Rather, it may be represented b y
models of the individual components, one each for translation and rotation in the two vertical planes and in the hori zontal plane, The rotational component may often b e
dispensed with .
For consideration of horizontal vibration, the foundatio n
may 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 e
props maybe calculated separately from the entire system .
Page 6 DIN 4024 Part 1
The following simplifications are permitted for the calculation of vertical vibration .
a) Where the flexural strength of the spring-supporte d
system is high relative to the stiffness of the spring sup ports, i .e . where
13 .
1
mo
Co
Model
m„
CB
ct
i
(12 )
E -1
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 y
the spring supports, o r
- the spring supports maybe neglected forcalculatio n
of higher natural frequencies .
b) In the case ofspring foundations,where the stiffness, cu ,
of the supporting slabs, beams or other supports is a t
least ten times the stiffness, cF, of the spring elements ,
i .e. where CUICF is not less than 10, then the foundatio n
may be assumed to be separate from the support and t o
consist of a configuration of beams resting on sprin g
elements .
For calculation purposes, this means that the resiliency ,
cu, of the foundation, as well as the effect of its mass ,
can be neglected .
C) The effect of the ground and that of the mass of th e
foundation may usually be neglected, provided one o f
the 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 e
rigid, is at least 20% lower than the lowest servic e
frequency, fn, .
C2: The lowest natural frequency, f,, of the entire system,assumed to be a rigid bodyvibrating on flexibl e
ground,is at least 20%lowerthan the lowestservic e
frequency, f,,, .
,
C3: The lowest natural frequency, f t , of the foundation a s
such,assumed to be rigid, is at least 25%lowertha n
the lowest natural frequency, fB , of the foundatio n
as such, assumed to be rigid and on flexible ground .
l
Mode l
E• I
Ct
r.
C2
C3
i
.
f
t
---------- --- - - -
.~
When calculating ft and
f2, E • I shall be assume d
to approach infinity.
~.
\
r~'
f3
When calculating fn,with
larger than 2, c ; shall be
assumed to be zero .
`'~ - - -~
f4
Ct )
f
t
=
t -~
V I.
2~n
f
f
m
f
>02fm
C2)
t
fj= 2n
CB
m,•m
fm
ft
f
~
Z02fm
C3)
j
= 2-I-~
f
~,
m,
1
fB= 2;
n
Ce
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 n
The natural frequencies ft to & and the modes associate d
with them shall be calculated in ascending order.
The number of natural frequencies and modes to b e
established shall be selected so that the highest natura l
frequency calculated is at least 10%higherthan the servic e
frequency. This requirement may be dispensed with in th e
case of foundations for machines with high service frequen cies (i.e . where fn, > 75Hz) ; however, depending on th e
analysis model, the number of natural frequencies to b e
calculated, n, shall comply with the following :
a) n =10 for two-dimensional models in which onlyvertica l
displacements are considered and in which symmetri c
and antimetric vibration are not decoupled ;
b) n = 6 for two-dimensional, symmetrical models in whic h
onlyvertical displacements are considered and in whic h
symmetric and antimetric vibration are decoupled.
5 .3 .2 Assessment of vibration behaviour
on the basis of natural vibratio n
An assessment of the vibration behaviour of a machin e
foundation, 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 e
frequencies, fm .
If both conditions land 2below are met for each decouple d
model, subsequent analysis may be dispensed with ,
1. First order natural frequency
ft z 1,25•fm
(13 )
or
(14 )
ft s 0 8 • fn,
2. Higher order natural frequencies
a) Higher order natural frequencies that approach th e
service frequency :
1
A
S 0 . 9 -/m
and
Figure 4 . Simplification a)
fn + 1 Z 1,1 • f m
(15 )
DIN 4024 Part 1 Page 7
b) if condition 2a is not met,it shall suffice that fn is less
than f,,, where n is equal to 10 or 6 (cf. sub clause 5.3 .1) .
the two adjacent natural frequencies, provided that they li e
within the specified range and that the magnitude of th e
excitation force is kept constant .
Where conditions 1 and 2 are not met, a more precis e
assessment of vibration behaviour can nonetheless b e
attained by analyzing the excitation potential of the natura l
modes of vibration . For this purpose, the highest natura l
modes, assuming they lie within the frequency rang e
defined by conditions 1 and 2 above, may be analyzed fo r
the magnitude of the relative displacement, xi , ,, at th e
bearings, i, of the machine shaft . Each natural mode ofvibra tion shall be checked separately for each bearing, i, for fulfilment of the following condition :
5.4 .3 Natural modes of vibratio n
if calculating the displacement can be dispensed with, th e
forces may be determined on the basis of the natura l
modes of vibration adjacent to the service frequency, thi s
being intended to simplify the analysis that would be required for forced vibration . On the basis of the natura l
modes and the associated action-effects, for each membe r
that incorporates a bearing, maximum amplitudes an d
forces for the operative and malfunctioning states shall b e
assumed, and the forces obtained by conversion . Fo r
members 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 e
assumed for the particular machine. group in accordanc e
with VDI 2056 .
a) Operative stat e
The value associated with the operating frequency fo r
the assessment criterion given in VDI 2056which is on e
grade higher than that guaranteed by the manufacture r
shall be taken as the amplitude under service conditions at the particular bearing .
b) Malfunctioning stat e
The amplitude in the case of malfunctioning shall b e
assumed to be six times that values used for the opera tive state .
I
xin •
2
fn
2
1
2
<3
(16)
fn - f m
If this condition is not met, then forced vibration shall b e
analyzed in accordance with subclause 5.4 .
Note that analysis as specified in subclause 5 .4 is recommended for steel/concrete composite foundations fo r
machines whose service frequency, f m, is less than 75 Hz o r
where fm is greater than f,, (where n is equal to 10 or 6 a s
given in subclause 5 .3 .1) .
5 .4 Analysis of vibration due to unbalanc e
5.4.1 Genera l
If the vibration behaviour cannot be adequately assesse d
using the methods given in subclause 5 .3, an analysi s
of forced displacement as set out in subclause 5 .4.2 i s
required on the basis of the excitation forces declared by
the machine manufacturer . In the absence of such information, 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 d
with the data given by the manufacturer, if any, or with th e
values obtained in accordance with subclause 5 .4 .3, takin g
the operative state and, If necessary, the malfunctionin g
state, into account.
The forces due to unbalance, in both the operative and mal functioning states, may be determined in accordance wit h
subclause 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 operativ e
and malfunctioning states) has been provided by th e
machine manufacturer, they may be used to establis h
displacements and forces using the model formed to deter mine natural frequencies, following the principles set out
below.
In the absence of such information, the forces may be cal culated in accordance with VDI 2060, on the basis o f
balanced quality, as follows .
a) Operative stat e
The balanced quality shall be assumed to be one grad e
lower than that for the relevant machine group as speci fied in VDI 2060 .
b) Malfunctioning stat e
The forces due to unbalance shall be assumed to be si x
times the value established for the operative state .
The excitation forces shall be analyzed for each bearing ,
taking into account the balanced quality selected, th e
service frequency as the excitation frequency, and th e
rotary mass component .As a simplif!cation,since the phase
pattern of the excitation forces is unknown, the forces at
the bearings may first be assumed to be unidirectional ,
and then to act in opposite directions . If the natura l
frequencies lie within the range of 0,95 to 1,05 f m ,the excitation frequency may be assumed to be shifted to either of
5.4.4 Equivalent-load metho d
in the case of slab- or beam-type foundations of simpl e
geometry, the dynamic analysis may be simplified b y
assuming equivalent static loads, based on the unbalanc e
during the malfunctioning state, so that results err on th e
safe side for the operative state .
Starting with a balanced quality, e • Q, equal to 2,5 mm/s fo r
the relevant machine group (see VDI 2060) in the operative
state, a balanced quality equal to 38 mm/s is assumed ,
which is six times that of the next highest grade . The unbalance 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 y
ratio,
n
(18 )
fn
where f n is the nearest natural frequency in the plane bein g
considered, so tha t
F=
1
I1__
I •K,
(19 )
with F a maximum of 15 K .
F shall then be assumed to act at the bearings according t o
the rotary mass component.To determine the action-effects ,
an equivalent system should be used that has fixed bearing s
at the nodes of the natural modes of vibration being Investi gated .The signs (+or-) of the equivalent-load componen t
of the bearings should be selected to produce the maxi mum possible amount of deformation within the system .
5 .5 Analysis of transient vibration
5.5.1 General
Transient vibration that can affect the balanced quality o f
the 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 als o
account 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 n
rare malfunction states (e .g. terminal short-circuit, main s
short-circuit followed by shut-down, or loss of synchronisation) that can result in very large antimetric loads on th e
system which are transmitted to the foundation via th e
machine casing . A two-pole terminal short-circuit in a n
electric machine running at a high speed of rotation is to b e
considered representative for such loads . Analysis of th e
resulting action-effects is described In subclause 5,5 .2.
5 .5 .2 Short-circui t
The short-circuit moment affects the foundation via th e
generator or motor casing in the form of opposite pairs o f
vertical forces, the moment vector being parallel to th e
shaft axis . The resulting displacements and loads can b e
calculated as a function of the excitation/time relationshi p
or by using the equivalent-load method .
Where the machine manufacturer has not specified th e
short-circuit moment, Mk, as a function of time, analysi s
may be based on the following equation for three-phas e
machines :
1
Mk (t) 10 MO (e-vo,4 • sin O N • t
etro,4 -sin 2Q N • t
2
-etuo,15)
(20)
- Mo (f
wher e
M O is the resulting nominal torque from the actual powe r
generated ;
O N is the mains frequency (not always the same as th e
operating mains frequency) ;
t
is time, in s .
For determining forced vibration, the natural frequencies
shall be taken to be at least 1,2 times the mains frequency .
Where the natural frequencies of antimetric natural mode s
of vibration lie within the range of 0,95 to 1,05 O N , the exci tation frequency (i .e . mains frequency) shall be shifted t o
these 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 e
that is 1,7 times the maximum short-circuit moment i s
assumed . If the machine manufacturer has not specified th e
latter,the maximum value of Mk may be assumed to be 12 Mo.
5 .6 Loads on the foundation and groun d
The effects of dynamic loads during normal operation an d
due to malfunction shall be considered when designing th e
foundation 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 s
forces contribute to maintaining equilibrium .
If the foundation has been assumed to be decoupled from
the ground in one ormore planes forthe purpose ofdynamic analysis (cf. subclause 5 .2), then the maximum desig n
values of the dynamic support reaction in the relevant plan e
may be taken as the equivalent loads . For analysis of eart h
pressure, the loads due to malfunction may be neglected .
In the case of spring foundations, the isolating function o f
the spring elements is usually so great that the dynami c
loads on the foundation during both normal operation an d
malfunction can be neglected .
6 Further design criteri a
6 .1 Design action-effect s
By superimposing the peak values obtained from static an d
dynamic analysis, the following loading conditions shall b e
considered .
1:
2:
3:
4:
Static loads during erection .
Static loads during normal operation .
Dynamic loads during normal operation .
Loads resulting from malfunction or short-circuit .
Load cases M, B and S below shall be established, fro m
which 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 l
and horizontal directions need not be taken as actin g
simultaneously ,
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 n
equivalent vertical load equal to 100% of the permanen t
load for load case S .
6.2 Reinforced concrete foundations
The design of reinforced concrete foundations shall be i n
accordance with DIN 1045 .
Load cases M and S
Loads shall be assumed to be predominantly static, a yiel d
strength of up to 420MN/m 2 of the reinforced concret e
being used in the calculation .
Load case B
The specifications relating to loads that are not pre dominantly static shall be taken into account. It shall b e
verified that the amplitude of concrete compressiv e
stresses due to coexistent flexure and longitudinal force s
does not exceed 0,33 ßR and that the shear stresses do no t
lie in shear range 3 .
If, however, the dynamic loads during normal operatio n
(loading condition 3) are multiplied by a coefficient allowing forfatigue of 3 or more,analysis may be based on load s
which are predominantly static, in which case the restric tions stated above foramplitude and shearstresses may b e
ignored .
Load case S
Where the loads due to unbalance as a result of malfunction are multiplied by a factor of at least six times thos e
during normal operation, analysis of load case B may be
dispensed with .
6.3 Steel foundations
Verifying the strength of steel foundations may usually b e
dispensed with .
In exceptional cases, a general stress analysis as specifie d
in 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 e
taken for cases M and B, and those specified for load cas e
HZ, for case . S. Furthermore, analysis of load case B shal l
include a service strength analysis using load group 86 a s
specified in subclause 4 .4 of DIN 4132, February 198 1
edition .
Where .the loads due to unbalance as a result of malfunc tion are multiplied by a factor of at least six times thos e
during normal operation, analysis of load case 8 may b e
dispensed with .
6 .4 Ground
Determination of the permissible loading of the groun d
shall be in accordance with DIN 1054 .
DIN 4024 Part 1 Page t
7 Detailin g
7.1 Reinforced concrete foundation s
7.1 .1 Table foundation s
7.1 .1 .1 Machine support (slab )
The machine support shall not be joined to the rest of th e
building in which the foundation is to be erected .
In orderto achieve the most uniform creep behaviourat th e
bearings, cross sections shall be selected so that nearl y
identical displacements occur at the bearings directly sub jected to concentrated loads under the self-weight of th e
machine and slab .This same principle shall also be applie d
to ensure equal displacements at the rotor bearings relative to the machine casing .
All structural members shall be reinforced throughout,eve n
if this is not required by the design . Links shall preferably b e
used as shear reinforcement .
Anchorages and recesses shall be arranged so that th e
reinforcement, in its main loading direction, is not adversely
affected .
The slab shall be cast in concrete without constructio n
joints, 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 g
components and transport capacity ;
C) by using well-supported formwork when the concrete i s
not placed centrally ;
d) by keeping the joints between props and slab thoroughly clean .
If the base or other supporting structures are to be concreted later, the connecting joints shall be cleaned an d
prepared to ensure an adequate bond, this also applyin g
for the concrete topping . Concrete toppings about 20 cm i n
thickness shall be reinforced and be joined with the founda tion by means of projecting reinforcements .
7.1 .1 .2 Props
Props shall not be joined to the rest of the building in whic h
the foundation is to be erected, except for lightweight ele ments, which may be fastened directly to the props b y
means of flexible intermediate layers to prevent vibrator y
effects . Reinforced concrete intermediate platforms shal l
be 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 e
stresses are induced in all props . For longitudinal reinforcement of props, the percentage of reinforcement shall be a t
least equal to 0,8.The reinforcing bars shall have a diamete r
of at least 10 mm .
The props shall be concreted without joints .
71 .1 .3 Bas e
The base should be separated by a joint from other parts o f
the building in which the foundation is to be erected . It s
thickness 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 e
selected to be about the same as the loads from th e
machine support with the machine, the loads from condensor and props being disregarded here .To prevent differences in settlement, all permanent loads (excludin g
vacuum forces) should act on the centre of gravity of th e
base area .
The mass of reinforcement by base volume should be a t
least equal to 30 kg/ m 3 part of the reinforcement shall b e
arranged in a spatial configuration .
When placing the concrete, vertical joints shall be avoided .
7.1 .2 Spring foundations
7.1 .2 .1 Machine suppor t
Subclause 7.1 .1 .1 shall apply for the machine support o
spring foundations .
Steel plates should be fitted to the underside of the su p
port, above the spring elements .
7.1 .2 .2 Spring elements
Spring elements usually consist of a number of individua l
springs which have defined stiffness in both the vertical an d
horizontal directions .
The spring travel shall be higher than that calculated an d
should be half as large as the deflection due to the self •
weight of the system .
The spring element shall be prestressabie to permit its
removal during operation without the machine suppor t
being lifted .
Dampers,which are capable of acting in all directions and o f
accommodating thermal expansion, may be connected i n
parallel to the spring elements in order to prevent movement 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 n
which 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 o
be erected, particularly in the case of props, should be
designed so that further elements can be added later .
7.1 .3 Slab foundation s
Subclause 7.1 .1 .1 shall apply for the machine support of sla b
foundations.
7.1 .4 Platform foundation s
It is rarely possible to predict the dynamic behaviour of a
platform foundation, owing to the interaction between i t
and the building in which it is installed,this interaction bein g
very difficult to measure . Therefore, platform foundation s
are generally used only for small machine systems . In cas e
of doubt, it should be possible to separate the foundatio n
from the surrounding structure, should it prove inappropri ate.
7.2 Steel foundation s
7.2 .1 Table foundation s
7.2 .1 .1 Machine support (slab)
The machine support shall not be joined to the rest of th e
building in which the foundation is to be erected .
Steel foundations shall only be made from fully welde d
members or those having slip-resistant joints with high strength bolts, such as GV or GVP joints as specified i n
DIN 18 800 Part 1 .
Where the machine manufacturer has not specified partic ularstiffness requirements for the foundation,the followin g
minimum requirements should be maintained .
E• 1
of the machine sup G
port in the longitudinal direction should be about twic e
as large as the average relative stiffness of the shaf t
assembly.ln the above formula,G is the permanent loa d
on the machine support due to its self-weight, that of
the machine, and that of the shaft, respectively .
b) The stiffness of the girders, E • 1, which are subject t o
direct loading from the machine, should be as large a s
possible, and be at least one-fifth of the stiffness of th e
machine support in the longitudinal direction .
a) The average relative stiffness
Page 10 DIN 4024 Part I
The points at which forces are introduced, particularly thos e
at the prop connections and the bearing faces, shall b e
carefully designed . When prestressed bolts are used fo r
machine attachment, It shall be ensured that they ca n
accommodate 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 x
girders be highly tuned, this being a requirement fo r
machines having an operating frequency of less than 75 Hz ,
7.2 .1 .3 Bas e
Subclause 7.1 .1 .3 shall apply for the base of steel fou l
tions .
7.2 .1 .2 Prop s
Props shall not be joined to the rest of the building in whic h
the foundation is to be erected, except for lightweight elements, which may be fastened directly to the props b y
means of flexible intermediate layers to prevent vibratory
effects . Heavy intermediate platforms shall be erected o n
the base with their own props.
Since the vibration behaviour of props varies according t o
the type of connection orjoint used,this shall be allowed fo r
in the design .
7.2 .3 Platform foundations
Subclause 7.1 .4 shall apply for steel platform foundati c
7.2.2 Spring foundation s
Subclause 7.2 .1 .1 shall apply for the machine suppo r
spring foundations, subclauses 7.1 .2 .2 and 7.12 .3 apply
fqr the spring elements and the supporting structure .
7.2 .4 Corrosion protection
For steel foundations installed in closed, well-heated b L
Ings, It is generally not required to provide internal c o
slon 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 o
DIN
DIN
DIN
1045
1054
1055 Part 1
DIN
DIN
1055 Part 4
4114 Part 1
DIN 4114 Part 2
DIN 4132
DIN 4149 Part I
DIN 17 100
DIN 18800 Part 1
DIN 55928 series
VDI 2056
VDI 2060
Structural use of concrete ; design and constructio n
Permissible loading of subsoi l
Design loads for structures ; materials to be stocked, construction materials and structural memb e
self-weight and angle of frictio n
Design loads for structures ; imposed loads ; wind loads on structures not susceptible to vibratio n
Structural steelwork ; safety against buckling, overturning and bulging ; design principles
Structural steelwork ; safety against buckling, overturning and bulging ; constructio n
Structural steelwork ; design and construction of craneway s
Buildings in German earthquake zones ; design loads ; design and construction of conventional buildi n
Steels for general structural purposes ; quality standard
Steel structures ; design and constructio n
Corrosion protection of steel structures by organic and metallic coating s
Evaluating the mechanical vibration of machines 2 )
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 u
Erdbeben (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 editio n
DIN 4024 : 01 .55 .
Amendments
In 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 n
E 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 .