sem.org imac xix 194301 dynamic analysis cranes

8/10/2019 Sem.org IMAC XIX 194301 Dynamic Analysis Cranes

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Dynamic Analysis of Cranes

M. A. NASSER

Associate Prof

(Visiting Researcher, Mechanical Engineering Department, The University of Dundee, Dundee, DDl 4HN, Scot land, UK.)

Production Engineering & Mechanical Design Dept., Faculty of Engineering, Menoutia University, Shebin El Kom, Egypt

ABSTRACT:

The objective of this paper is to analyze the crane

structures as a step to study their effects on the

structures working integrally with them. The interaction

between cranes and those structures has dominant

effects on the global system behavior. Crane structures

may have many forms of space structures. It is not

logical or economical to perform experimental modal

analysis to al l of them to investigate the structural

behavior of such structures and carry out the in-site tests

of measuring their effects on the structures integral with

them. In this paper a tria l is made to estimate the crane

structures eigenpairs numerically on the basis of fini te

element methods, The finite element method was

applied firstly on a small space structure. Small space

slightly complicated structure is designed, manufactured

and dynamically analyzed experimentally

and

analytically to validate the model. The results indicate

good agreement between theoretical and experimental

eigepairs. An in-site crane is analyzed on the basis of

the refmed model. The results of the analy tical study

and measured frequencies indicated that there is some

coincidence between exciting frequencies and system

natural frequencies. Crane/barrage interaction was

analyzed and the deflections in the barrage structure

were theoret ically predicted by using the m-site crane

eigenpairs and reactions between the crane and the

barrage structure in a tria l to reduce their hazards on the

masonry structures. The results indicated that high

inning speeds cause less deflection but they still

serious because they cause dynamic fluctuation along

their track. Running speeds of cranes on such structores

are recommended.

NOMONCLATURE:

N : number of modes.

[ a [cl w4~1 :

mass, damping, stiffness and

modal shape matrices.

r;

: force vector.

R

: reaction forces.

X,Y,Z > : coordinates.

iLCXG] :?

vertical acceleration, velocity and

displacement vectors

ww> :

vectors of acceleration, velocity and

displacement.

Q>

: resulting wheel loads applied to the

barrage.

$1

: modal shape vector.

1

: modal participation factor.

0

: natural frequency

sub-script:

: mode number.

B : part of barrage and arch structure.

c :crane

w : wheel.

NW : wheel number.

INTRODUCTION:

Cranes as a mechanical system are the conventional

way to move the steel water gates, which control the

water flow according to irrigation and marine needs.

Some cranes have large steel structure and others

have small steel structures. Large and small cranes

running over railway fixed over the top of the steel

structure. The steel structure carrying the crane is

running along the barrage masonry structure on a

railway fixed at the top of the barrage. The railroad of

small size cranes is always in the upstream side, while

it is in the upstream and downstream edges of the

barrage in the case of large cranes. Large running

cranes use diesel engines, and some fured cranes use

electric

motors. The diesel engine, power

transmission system and the

running

of the crane over

the barrages generate serious vibrations, [l-Z]. Some

types of cranes are now out of service in some

important infrastructure places, representing a vital

problem despite their storage over the structure. The

traffic over the reservoir generates vibration, which

move the crane vertical ly to play as a vibrating

system,

instigating regenerative vibrations on the

reservoir structure. It is recommended to keep this

crane away from the structure. Electromechanical

systems are now used to control steel water gates, [I].

Studying cranes dynamics can helps in their v ibration

reduction 13-41. An experimental modal parameters

verification of container crane structure was

numerically obtained using finite element method.

Forced vibration tests as well as ambient v ibration

due to wind load ing were performed. The validation

between numerical and experimental results was

obtained, [3]. An experimental and numerical

identification of a container crane (55OOkN) structure

natural frequencies, mode shapes and modal

parameters are presented. A numerical dynamic

model using finite element methods was applied. The

beams are modelled as line-beam elements. Service

transient behaviour of the structure has been obtained

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and used for stress analysis and structural parameters

identifications. Wind and crane motion forces are used

for ambient vibration testing and their results are briefly

included, [4]. An application of modal analysis as a

basis for remode lling of Iarge structure crane was

performed. The results of the analyt ical study and

measured frequencies indicated that there are some

coincidence between exciting frequencies and system

natural frequencies, Careful investigation and diagnosis

of vibration problems should be firstly done and

followed by the structure remodelling using fini te

element method to overcome some dynamic problems,

[5]. This study may be used as a cornerstone of the

dynamic analysis of large scale complicated structures.

Firstly, diagnosis process should be done to detect the

fault or faults that generate high levels of vibrations.

These faults must be corrected to reduce energetically

exciting force. Remodelling process can be done after

this to make structural modif ication options using

computers equipped with fini te element structural

analysis software. Some other works, [6-S] have app lied

the modal analysis technique to other types of cranes.

Modal analysis was used for the ultimate purpose of

crane safety by reducing the swinging. Swinging of the

payload during and after transit poses a major safety and

site efficiency problem. The objective of this research is

to design implementable stabilizing controllers for a

distributed model of the crane system. An exact moda l

analysis of the closed loop system is performed

assuming constant tension and no damping. An

approach has been used to incorporate spatially varying

tension and damping. Design of the control gains is

demonstrated using a root locus approach. The theory is

successfully tested on a gantry crane system. The

controller significantly reduces the time required for the

payload oscillations to damp out, [6]. Motion-induced

vibrations have been reduced in flex ible systems in a

feed forward way using a time-varying impulse

sequence. The decoupled moda l responses for a general

linear time-varying system are firstly approximated.

Upon this approximation, the time-varying impulse

sequences to suppress the vibrational modes are found.

The performance of this method was demonstrated with

two practical examples: a moving overhead crane and a

two-link robot manipu lator. Consequently, this study

has provided an input shaping technique applicable to

the vibration suppression of broader classes of flex ible

systems, 171. The transient response of the truck crane

structure due to winch operation when the loading beam

is operated in the vertical direction from the crane frame

axis has been examined by modal analysis. The transient

vibration strains in the lower beam were observed in an

actual track crane and numerical simulations were

carried out. Then, relationships between the winch

operation and transient vibration strain levels were

presented for the various operation patterns of the

winch, [S]. Vibration and moda l analysis of the moving

mechanical systems are very complicated processes.

The modelhng of different parts of such systems and the

interactions between these parts is difficult to be

obtained. The crane/barrage is very similar to

vehicle/bridge or train/rail 19-121 interaction, which

should be considered. Some models of assessing

vehicle/bridge interactions have been investigated and

some case studies are given [9]. The bridge-vehicle

interaction in curved box Girder Bridge was

investigated [lo]. Train-bridge, which is very similar

to crane ructure under time-varying system mode

synthesis technique, has been investigated

[ll].

Another analysis of coupled vibration between

railway vehicle wheels and rail for the case of an

infinite number of vehicles in vertical and horizontal

directions by using of an approximate model was

predicted 1121. In the case of cranes there is an

interaction between the crane structure and the

structure integral with them. Another wheel-rail

interface is due to the interaction between the steel

structure carrying the crane and the barrage. The

modelling of such arge-scale ranesover the barrages

is a complicated process due to many complicated

crane/rail/steel structure/ rail/bridge interactions. In

this paper the top part of the crane will treated as a

perturbed mass n order to reduce the complications

of interactions between the top part and the crane

structure. The available instrumentation will be used

for testing the small-scalemodel for the comparison

with the analytical findings from finite element

methods. The updated finite element method should

be used or the eigen analysis of an m-site crane. The

analytical should be compared with earlier

experimental results. The modal reactions as well as

the modal parametersof the crane and the integrated

structure should be used to determine the deflection

causedby crane running over the integrated structures

with the crane o define their safe unning velocities.

ANALYSIS:

The natural frequenciesand mode shapes f the crane

spacestructure were evaluated analytically by using

the finite elementanalysis. A lesscomplicated model

was designed,built, analysed and tested to update the

finite element model. The updated the finite element

model is then applied to the m-site crane. The

structure was modelled by beam elements.The model

shown in Fig. (2) is made up of 49 nodes and 129

elementswhile the in-site crane structure is divided

into 96 nodesand 188 elements.The top trolley of the

crane was treated as a perturbed mass.The Equation

of motion of the svstemcan be written as:

To estimate he natural frequenciesand mode shapes,

the damping in the system assumed o be neglected

then the equation (1) takes the following:

l..ctic>+[~c cl=~~c~ - (2)

The damping neglecting assumption makes the

system under analysis seems to be linear, so the

systemmotion can be consideredas harmonic motion

as ollowing:

6, >= bc bowt

(3)

From equation (3) substituting nto equation (2)

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Solving equation (4) considering @]# 0 then:

(5)

The static analysis of the system is special case of the

dynamic analysis, so the equation (2) takes the

followinrr form:

(6)

(7)

For the integrating structure on which the crane is

running over, the equation of motion in the vertical

direct ion (z), is as the following:

The analysis is concentrated on the dynamics of only 6

spans of the integrated structure. The 6 spans are

divided into thee equal parts, two under the crane, two

frontal and two backward the crane. To determine the

crane/barrage response, the mathematical model of the

crane described is solved every time step and by using

the eigenpairs obtained from the modal analysis of the

bridge to solve the system modal. Modal forces

corresponding to the different barrage modes are

computed using the cranes static wheel loads. The

crane wheels NW =8 wheels and the equation and

then;

.WW=I

Numerical integrations are used to solve the integrating

structures modal equations by estimating the modal

participation factors h, ,...h,v and their time derivation

k,(t) h,Jg. The Newmark-Beta method is used for

the numerical integration.

d%,(i)

dt2

+C du?)

, T+w&@>= F,,,@,i) (10)

fori=l+ N

The barrage displacements at wheels positions are

computed from;

I = ,

Whd

The crane was considered as 2-dimensional by only

considering the vertical and traverse motions along the

barrage. The computed wheel displacements are used as

restraints. This process is repeated for each crane

moving on the barrage and the displacements were

estimated for one arch of the barrage. The first 5 modes

are sufficient to obtain accurate displacements at the

barrage arch, centres. The first longitudinal mode

combined with different transverse modes is sufficient

to obtain mid-span displacements at eccentric location.

The analysis time is increased by one time step and new

crane positions are estimated by repeating this

procedure.

EXPERIMENTAL WORK:

The instrumentation that has been used to collect and

process vibrat ion data for the crane space structure

model described later in this section is shown in Fig.

(1). The principal components are a PCB model

J353B65 accelerometers and PCB 086CO2 impact

hammer their corresponding line-drive supply

amplifiers PCB 48OCO2, which allow low-level

vibration data to be transmitted to the dual dynamic

signal analyser HP 3567019 dual channel signal

analyser connected by a Pentium PC allows data to be

collected easily and transferred directly ME Scope

Modal analysis software. The model of 35x35~72 cm

is symmetric around two axis as shown in Figure (2)

is made of 18.35m steel bars of 5x5mm square cross

section. A total of 129 element and 49 nodal points

were the measurement stations, for 147

measurements. To excite al l vibrationa l modes with a

specific frequency range, careful consideration must

be given to choice the common reference degree of

freedom. The driving point degree of freedom would

be a vibra tional node number 20. The test model was

hanged up to a fixed structure by using soft rubber

strings and impacted by using the impact hammer.

The vibrat ion signals were measured by the

piezoelectric accelerometer. The signals from the

impact hammer and the accelerometer were

conditioned through the two conditioning amplifiers.

The analogue signals of the exciting force and

resulting vibration are then passed onto the dual

channel signal analyser, which analyses and stores

those signals. The processed signals are then passed

onto computer equipped with the modal analysis

software package. ME Scope modal Plus, VT520

Vibrant Technology is used for experimental modal

analysis. The same procedure was repeated for the

model after perturbing by adding a mass of 24.525 N

onto the top surface mesh to simulate the top trolley

of the in-site crane.

(a) Instrumentation.

(b) Photo.

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he Experimental Set-Up.

(a) Outer Surface Meshing

(6) Configuration.

Fig. (2) The Model.

RESULTS& DISCUSSION:

The natural frequencies obtained by finite element and

impulse excitation methods for the crane space structure

model and the model perturbed by adding mass are very

closely as shown in (Table-l) and figure (3). The natural

frequencies obtained from the modal test matches very

closely, less than 2.2 % with fmite element results for

the model and 2.7 % for the perturbed model. The

percentage-damping factors for different modes from

modal tests of the model and perturbed model clearly

show that the percentage damping factor values

decrease with higher modes as shown in figure (4). The

results indicated that the added mass to the system has

great effects on the frequency and damping of the

system. Figure (5) shows some frequency response

functions obtained during the modal test of the model.

The first eight modes are given in figure (6). Those

modes are thoroughly examined by animation and

reprints to know the nature or the type of each mode.

Figure 7 (a and b) shows some in-site gate cranes.

The crane under the study Fig. (7-a) is more or

complete ly different than cranes shown in tigure (7-

b). The integrating structures with them are also

different in dimensions and geometry. The

dimensions of the crane structure (9416952N) under

the study are given in figure (7-c) and the top trolley

carrying the crane is 195219N in weight. The top

trol ley is treated as a perturbed mass.

The specifications of the integrated structnre are

given in reference [2]. Table (2) and Fig. (8) present

the natural frequencies of the m-site crane in both

analytical and experimental conditions, The analytical

and experimental results matches very closely, less

than 4.2 %. Figure (9) and (10) illustrate the

deflection of the mid-span barrage and arch due to the

running of the crane for the crane running speeds of

10, 15 and 20 km/h. The analysed crane is integrated

with a barrage of 110 arches each arch span is 5.4 m.

Four wheels of the crane wheels are running over the

spandrel wall of the barrage in the downstream

direction and the other four wheels are running over a

wall of 110 arches of the same span. The deflection

values of the arch are generally less than those of the

barrage spandrel wall, this because of the larger width

of the arch. The width of the arch is 205 cm while the

width of the spandrel wall is 68 cm. The reaction

forces play with the mode shape the vital ro le in this

relationship. The fast mode was considered because

its dominant effect in this condit ion. The results

indicated that the lower velocities cause higher

deflections. Despite the higher speeds cause lower

deflections, they are not recommended because they

cause large fluctuations in the deflect ion with distance

for higher speeds. These fluctuations are severe

dynamic loading to the structures integral with those

cranes.

The work in this paper presents an analysis of the

dynamics of crane, as typical ly used for barrages

gates handling operations, for the ultimate purposes of

research into infrastructure safety. Dynamical models

are proposed for the crane based on a simplif ication

of the structure into a space structure frame of the

below trolley and the overhead tro lley. Full three-

dimensional motion is encompassed in the dynamical

equations of motion, and various movement scenarios

are examined. The crane/barrage dynamics was

studied. The phenomenon is explained and

investigated using pure geometry and a numerical

method to assess its effect in practise. This paper is

concerned with the investigation of non-destructive

methods of structural testing using fin ite element

models. Non-destructive methods of structural testing

have growing popularity in their appl ication to the

quality control of our strategic infrastructure such as

barrages and reservoirs structures. In this research, the

finite element models are used as a tool to investigate

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theoretically the dynamic behaviour of large-scale

barrage structure regarding the crane dynamic load, it

structures. Thus, test data Corn a site may be interpreted

is important to know which is the most critica l natural

in frequency domain to assess the integr ity of a

frequency of the structure The most critical natural

structural dynamics. A real situation during crane

frequency is likely to be that which is closest to the

working, it is necessary, however, to keep a record of

dominant excitation tiequency in the crane motion

the vibrat ion responses of the barrage structure during

input. This would be known by analysing vibration

the crane motion to be able to make any

spectra of a typica l loca l in-site crane motions and the

recommendation for the design and operation of a real

modal analysis of the crane structure.

Made Crane model Structure.

I

Perturbed Crane model.

Frequency (Hz) Dam ping Frequency (Hz)

Damping

7-h w, Th

11 2.07E3 2.050E3 1.582 4.663E3 4.612E3

12 2 5E3 2.466E3 938.836E-3 5.128E3 5 116E3

13 2.63E3 2.603E3 3.873 5.659E3 5.618E3

14 3.2983 3.085E3 1.177 6.lE3 6.139E3

Table (1) The Frequencies and Damping of the Models.

. . , _ I

594.061E-3

593.491E-3

764.467&3

551.042E-3

0 -: i

0 2 4 6 b 10 12 14 16

Fig. (3) Mode Frequency of the Models.

I * stru. . stru.+mass I

0 5

Mode 10

Fig. (4) Mode Damping of the Models.

Fig. (5) Some FRFs of the Model .

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Fig. (6) Some Mode Shapes of the Model.

A

d-

--

l -

(b) Photo.


7/8

(c) Outer Dimensions.

Fig. (7) In-Site Crane.

Table (2) Mode Frequency of the In-Site Crane.

30 ,

. Th. XExp.

I

25 _

3 A

E. 20. .x

E 15. Y

s

10. *xx=

2

IL

5.

xxx..

xx=

0 (

0 5 IO 15 20

Mode

Fig. (8) Mode Frequency of the In-Site Crane.

0

-0.05

4

-0.1

2-0.15

E

5

-0.2

5 -0.25

al

2 -0.3

-0.35

-0.4

-0.45

Pos ition of Front Axle (m.)

Fig. (9) Barrage Deflection.

0

-0.05

a -0.1

s

go.15

P

T$ -0.2

cl

-0 25

-0.3 J

Position of Front Axle (m.)

Fig. (10) Arch Deflection.

CONCLUSIONNS:

1, The modal analysis results carried out on the model

and perturbed model are agree very closely with

experimental fmdings. The study gave a good

confidence that modal analysis could used to verify

and update

crane dynamics during their

qualification testing.

2. Finite e lement analysis is capable to anticipate the

dynamic characteristics and behaviour of crane

structures during

their operation to avoid the

coincidence

between forced

and

natural

frequencies of the crane system.

3.Experimental modal analysis of other cranes are

only required when the accuracy and reliability of

such systems are required.

4. It is recommended that the running velocities of the

cranes should kept as min imum as possible.

Despite the higher speeds cause lower deflections.

The higher

running velocities are not

recommended

because they cause large

fluctuations in the deflection with distance for

higher speeds. These fluctuations are severe

dynamic loading to the struchues integra1 with

those cranes.

REFERENCES:

111. Helal M., Nasser M., Abdel-Rahman S., Younis M.

6% Zanoon S., Vibration Measurements and

L)ynamic Analysis of Aswan Reservoir Structure due

to Traffic loads, National Water Research Center,

Mech. & Elect. Research Institute, Tech. Report (In

Arabic), Delta Barrage, Egypt, 1996.

[2]. Helal M., Nasser M., Abdel-Rahman S. & Attia

M., Dynamic Analysis of Reservoir and Barrages:

Assuit Barrage Nat ional Water Research Center,

Mech. & Elect. Research Institute, Tech. Report (In

Arabic), Delta Barrage, Egypt, 1997.

[3]. Dinevski D., Oblak M. & Novak A., Experimental

Verification of the Container Crane Natural

Frequencies, Proc. of the 8 Int. Conf.

Computational

Methods

and Experimental

Measurements, Rohodes, Greece. 1997, PP 245 -

254.

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[4]. Dinevski D. & Oblak M., Experimenta l and

Numerical Dynamic Analysis of a Container Crane

structure, Stablbau, Vol. 66, 1997, PP 70-77.

[S]. Ahmed K. & El-Khatib A., Applied Modal

Analysis as a Basis for Remodeling of Large

Structure, Proc. of the 13 IMAC, Nashville,

Tennessee, USA, 1995, PP 1100 - 1105.

[6]. Josbi-SandeepBr Rahn Christopher D., Position

Control of a Flexib le Cable Gantry Crane: Theory

and Experiment, Proc. of the American Control

Conf. Vo1.4, Part 4, Seattle, WA, USA, June, 21-23,

1995. PP 2820-2824

[7]. Cho Jung Keun& Park Youn Sik, Vibration

Reduction in Flexib le Systems Using a Time-Vaving

Impulse Sequence, Robotica, Vol. 13, No. , Part 3,

May-Jun 1995, PP 305-313.

[S]. Nobukawa Hisashi, Kunikata Mamoru& Manabe

Yoshitugu, Transient Response of a Truck Crane

due to Winch Operation, Nippon-Kikai-Gakkai-

Ronbunshu-C-Hen. Vol. 56, No. 526, June 1990, PP

1371-1376.

[9]. Bat a M., Bily V. and Polak M., Models to Assess

Vehicle/Bridge Interaction, J. of Heavy vehicle

System, V.3, No 1- 4, 1996, PP 1 - 9.

[lo]. Senthilvasan J., Brameld G. and Thambiratnam

D.,

Bridge-Vehicle Interaction in Curved Box

Girder Bridge, J. of Microcomputers in Civil

Engineering, V.l2,No.3, 1997, PP 171 - 181.

[ll]. Young Y. & Zhen Q., Train-Bridge Time-

Vaying System Mode Synthesis Technique, Proc. of

the 5 IMAC, London, England, 1987, PP 1692 -

1698.

1121. Sueoka A., AYABE T. & Iizuka Y., Analysis of

Coupled Vibration Between Railwq Vehic le Wheels

and Rail in Both Vertical and Horizontal Directions

Using an Approximate Mode l with an Infin ite

Number of Vehicles, Int. J. of JSME, Series C, V.37,

NO. 4, 1994. PP 65 I-660.

ACKNOWLEDGEMENTS:

The author would like to thank the support of M&ERI,

NWRC, Egyptian Ministry of Irrigation and Water

Resources for the experimental facilities they have offered

me to conduct this work, in particular to Prof. Helal and Dr.

Abdel Rabman. Also the author would like to thank the

support of the Mechanical Engineering Department, the

University of Dundee, in particular to Prof. J im Hewit the

Professor of Mechanical Engineering for the computing

and other facilities he has offered me to conduct this paper.

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