Jtam.dvi


JOURNAL OF THEORETICAL

AND APPLIED MECHANICS

50, 1, pp. 47-59, Warsaw 2012

50th anniversary of JTAM

STATIC AND DYNAMIC ANALYSIS OF TELESCOPIC BOOM

OF SELF-PROPELLED TUNNELLING MACHINE

Damian Derlukiewicz

Jacek Karliński

Wrocław University of Technology, Institute of Machines Design and Operation, Wrocław, Poland

e-mail: damian.derlukiewicz@pwr.wroc.pl; jacek.karlinski@pwr.wroc.pl

The paper presents selected aspects of the strength analysis of the self-
propelled tunnelling machine boom. The principles of creating calcu-
lation models for numerical simulations with use of the finite element
method are given. The study also presents two ways of conducting nu-
merical calculations in both the static and dynamic range. A detailed
example of numerical FEM tests of the telescopic boom is provided.

Key words: finite element method, strength calculations, static and dy-
namic analysis, self-propelledmining machines

1. Introduction

Difficult geological conditions andmore intense tunnelling andmining proces-
ses taking place today in many building sites lead to a high mechanisation
level of building works. Because of this, specialised self-propelled tunnelling
machines are constructed, which enable a sufficient progress in the tunnelling
works. Among the machines most frequently used in the tunnelling and buil-
ding sites, there are those directly used in the preliminary works. These are
the vehicles used for slabbing, drill rigs and bolt setters. The common feature
of those machines is the fact that the working tools are placed on a boom.
The boommounted on self-propelled tunnellingmachines should have a suffi-
cient number of degrees of freedom to minimise the time related to changing
the location of the machines. Most frequently, this is a straight-line structure
ended (in the case of drill rigs and bolt setters) with a rotating head (turnover
fixture). An example of this kind of machine is presented in Fig.1.
In the case of drill rigs, this part allows one to position the drill rig mast

so as to ensure stable perpendicularity of the drill rig axis to the surface of



48 D. Derlukiewicz, J. Karliński

Fig. 1. Drilling machine FaceMaster with two booms (www.minemaster.eu [13])

the walls or ceiling. The size of the machine and its working range are, in
this case, determined by the size of the excavation tunnel and the size of the
drillingmastmountedon theboom.Themast length rangesbetween4and7m
dependingon theneeds, determining the size of theboommounted on the self-
propelled tunnelling machines. In order to reduce the costs of manufacturing
the entire machine, it is important to standardise particular parts and units
and to design a universal boom which could be mounted on various types
of machines. Because the boom with the mast is a significant load for the
structure, itsmass should be as smallest as possible. This brings about serious
engineeringproblemsstemming fromtheoperation,manufacturing technology,
material limitations, etc. Today, this problem is solved bymeans of a straight-
line feedingmechanismwhich guarantees a sufficient working range and, after
moving, reduced distance between the centre of gravity of the working part
(boom with the drilling mast) in relation to the front axis of the machine.
Another important feature, besides the limitations related to the preliminary
works, are loads related tomotion of self-propelled tunnellingmachines.Many
years of experience gained while operating the booms in mines suggest that
most failures take place in the transport position (with the boomprotruding).
There are several reasons for that. The operational loads in the course of
preliminary works (e.g. drilling) may be closely determined both with respect
to the direction and value. When a self-propelled tunnelling machine moves
from one place to another, the loads affecting the structure and boom are
of dynamic character which is hard to specify. In such circumstances, it is
necessary to carryout experimental researchor computer simulation basede.g.
on the finite-elementmethod.The computer simulation, in this case, shouldbe
givenpriority over the research sincewithoutpreparinganexpensiveprototype
weare able todetermineboth the temporaryvalues of forces and thedirections
of their action, and the effort value for a given spot of the structure. It should
bekept inmind that any change of the boomstructure geometrywill influence
both its strength and load (change of mass).



Static and dynamic analysis of telescopic boom... 49

This paper is aimed at strength analysis of the boom structure using the
finite-element method (Rusiński, 1994; Rusiński et al., 2000) in the dynamic
and static scope, taking into consideration thematerial and geometrical nonli-
nearity (Kleiber andWoźniak, 1991;Woźniak andKleiber, 1982). Theanalysis
comprised the simulation of the strength test connected with the vehicle front
wheels going over a barrier 150mmhighwith themaximum speed of 12km/h,
and the analysis of the influence exerted by thedrillmast positionwith respect
to the boomwhile drilling on the effort of the boom structure.

2. Computational model

Based on the technical documentation of the boom structure (prepared in
CAD/FEM system, Fig.2) the geometrical (shell) model has been created
(Fig.3). Then based on the geometrical model the discretemodel of the boom
were created. The boom structure is supported on twomotor operators (rising
and rotating ones) and connected by means of joints with the platform. Its
frontal part is loadedwith a feedingmechanism or amastwhich can rotate on
two planes (horizontal and vertical) in relation to the boom. All connections
and additional masses are taken into consideration in the discrete model, and
are presented in Fig.4.

Fig. 2. The working unit with a separate boom



50 D. Derlukiewicz, J. Karliński

Fig. 3. Shell model of the mining machine boom

Fig. 4. Discrete model prepared for static analysis

The strength calculations were prepared using the finite-element method.
They were divided into the following stages:

• static linear strength calculations carried out using FEM (Karliński and
Wach, 2006; Kleiber and Woźniak, 1991; Rusiński, 1994) of the boom
structure; determination of shifts and strains in particular points of the
structure;

• analogous dynamic calculations.

In the case of dynamicanalysis, theywere carried out taking into consideration
the geometrical and material nonlinearity, using the explicite type algorithm
(Jones andWierzbicki, 1993; Karliński andWach, 2008; Pam-CrashUserMa-
nual, 1989; Wierzbicki and Abramowicz, 1983) for solving the equations of
motion. The static analysis was carried out within the linear range using the
implicite type algorithm included in themodule of one of computer-aided de-
sign packages.



Static and dynamic analysis of telescopic boom... 51

Theboom structurewasmade of steel S355 andWELDOX700. The static
material properties ofWELDOX 700 are as follows:
plasticity limit – (Re)min =700MPa

tensile strength – (Rm)min =780-930MPa

extension – A5 =14%

for E350 steel, the material properties are as follows:
plasticity limit – (Re)min =355MPa

tensile strength – (Rm)min =490-630MPa

extension – A5 =20-22%

The dynamic linear analysis of the unit reaction to external excitation was
carried out using CAD/FEM system (Rusiński et al., 2000; ,18]. To achieve
that, the TRANSIENTRESPONSE analysis was used. It can serve to deter-
mine adynamic response of the unit (shifts, speeds, acceleration, deformations
and strains) to the task changing in time, such as shift, speed, acceleration or
force (Karliński and Iluk, 2000; Karliński et al., 2006).
The dynamic linear analysis using the finite-elementmethod is carried out

in compliance with the following equation of motion

KU(t)+CU̇+MÜ(t)=F(t) (2.1)

where K,Mand Carematrices of rigidity,mass anddamping, U(t), U̇(t) and
Ü(t) are displacements, velocities and accelerations, respectively and F(t) is
a time function of force.
It is assumed that thematrices of rigidity,massanddampingdonot change

in time.
Equation (2.1) was solved using the method of direct integration of the

equations of motion using the β Newmark algorithm (Rusiński et al., 2000).
The β Newmarkmethod is amore precise linear acceleration method and

uses the following equations to calculate the speed and acceleration

U̇t+∆t = Ü+(1−γ)∆tÜt+γ∆tÜt+∆t (2.2)

and

Ut+∆t =Ut+ U̇t∆t+
(1

2
−β
)

∆t2Üt+β∆t
2
Üt+∆t (2.3)

When we extend Eq. (2.3) so as to express Üt+∆t using Ut, U̇t, Üt and
Ut+∆t components

Üt+∆t =
1

β∆t2
(Ut+∆t−Ut)−

1

β∆t
U̇t−

( 1

2β
−1
)

Üt (2.4)



52 D. Derlukiewicz, J. Karliński

Using Eq. (2.4), equation (2.1) may take the following form

U̇t+∆t =
γ

β∆t
(Ut+∆t−Ut+∆t)+

(

1−
γ

β

)

U̇t+
(

1−
γ

2β

)

∆tÜt (2.5)

and henceforth

KUt+∆t+C
[ γ

β∆t
(Ut+∆t−Ut+∆t)+

(

1−
γ

β

)

Ut+
(

1−
γ

2β

)

∆tÜt

]

+M
[ 1

β∆t2
(Ut+∆t−Ut)−

1

β∆t
U̇t−

( 1

2β
−1
)

Üt

]

=Rt+∆t

(2.6)

When we take all the coefficients to the left-hand side and then abridge, we
get

(

K+
1

β∆t2
M+

γ

β∆t
C

)

Ut+∆t =Rt+∆t

+M
[ 1

β∆t2
Ut+

1

β∆t
U̇t+

( 1

2β
−1
)

Üt

]

+C
[ 1

β∆t2
Ut+

(γ

β
−1
)

U̇t+
∆t

2

(γ

β
−2
)

Üt

]

(2.7)

With known displacements, velocities and accelerations for time t we can
determine the displacements for time t+∆t, and then find the velocities and
accelerations for t+∆t, using Eqs. (2.2) and (2.4).
For the modelled dynamic system, the algorithm takes the following form

in this method:

1. Assumption of the initial conditions

U0, U̇0, Ü0

2. Calculation of the integration constants for the chosen time ∆t

a0 =
1

β∆t
, a1 =

γ

β∆t
, a2 =

γ

β∆t
, a3 =

1

2β
−1, a4 =

1

β
−1,

a5 =
∆t

2

(γ

β
−2
)

3. Assumption of the effective rigidity matrix K∗ in the form

K
∗ =K+a0M+a1C

4. Abridging of the rigidity matrix K∗

5. Calculation of the effective force vector for time t+∆t

R
∗

t+∆t =Rt+∆t+M(a0Ut+a2U̇t+a3Üt)+C(a1Ut+a4U̇t+a5Üt)



Static and dynamic analysis of telescopic boom... 53

6. Calculation of displacements for t+∆t

K
∗
Ut+∆t =R

∗

t+∆t

7. Calculation of acccelerations for t+∆t

Üt+∆t = a0(Ut+∆t−Ut)−a2U̇t−a3Üt

8. Calculation of velocities for t+∆t

U̇t+∆t = U̇t+(1−γ)∆tU̇t+γ∆tÜt+∆t

9. Steps 5-8 should be repeated for each time period.

The analysis was carried out integrating the equation ofmotionwith chan-
ging the time period equal to:

• for the time from 0 to 0.03s – 480 integration steps with the duration
value of 0.0000625s

• from 0.03 to 0.21s – 140 integration steps of 0.001285s

• from 0.21 to 0.27s – 40 integration steps of 0.0015s

• from 0.27 to 1.00s – 100 integration steps of 0.0073s.

The analysis takes also into consideration damping amounting to 3% of the
critical damping for the first formof natural vibrations of the entire structure.
The value is based on research carried out on similar objects (the first form of
free vibrations of the telescopic booms used in undergroundmining inmobile
anchor machines) (Karliński et al., 2007)

3. FEM strength calculation

The boomdiscretemodel was developed with three- and four-joint shell finite
elements, based on the thick shell theory.The average size of the finite element
was ca. 30mm. Because during the strength test the material may become
partiallyplastic (material nonlinearity) andthe configurationmaysignificantly
change as a result of large deflections (geometrical nonlinearity), all the finite
elements used were adopted for calculations with both types of nonlinearity.

The discrete boom models for static and dynamic analysis (Pam-Crash
User Manual, 1989) are presented in Figs.4 and 5, where all necessary con-
nections to the machine platform are included and shown. Different thickness
of the metal plates are indicated by colours of finite elements.



54 D. Derlukiewicz, J. Karliński

Fig. 5. Discrete model prepared for dynamic analysis

The strength calculations were conducted for the assumed boundary con-
ditions for both static anddynamic cases.Thepreviouslymentioned boundary
conditions assumed the following (Karliński et al., 2004):

• non-linear strength calculations of the boom structure in the dynamic
range: simulation of the machine passing through the rectangular ob-
stacle of height of 150mmwith speed 12km/h

• linear strength calculations of the boom structure in the static range:
simulation of the work of the boom the most adverse configuration –
maximum turningmoment working on the boom) loaded by the feeding
force 15000N.

The static analysis takes into consideration the load of the structuremass
and forces connected with the drill advance for the most adverse drill mast
position in relation to the boom (drilling with the boom perpendicular to
the wall, the boom protruding to the maximum length) (Derlukiewicz and
Karliński, 2004).
The dynamic load affecting the boom, in the case of the dynamic analysis,

stems from themachine frontwheels going over an obstacle 150mmhighwith
themaximum speed available for the machine, which is a kinematic coercion,
Fig.6.Toachieve theadequate analysis conditions, the entirekinematic system
of the boomwasmodelled (Karliński, 2001). Themodel of dynamic load taken
into consideration in thedynamiccalculation isbasedon theexperience related
to this type of machines operating in KGHM Polish Cooper mine, where all
machines designed by leading producerMineMaster Ltd. are analysed during
the designing process according to such a extreme condition.



Static and dynamic analysis of telescopic boom... 55

Fig. 6. Characteristics of the kinematic coercion

Exemplary results in the form of contour lines of maximum stresses ac-
cording to Huber-Misses hypothesis were presented in Figs.7 and 8 for static
analysis. Results for the dynamic analysis in a selected step of time (where
Huber-Misses stresses were the highest in the area of the contact of external
and internal pipes) are presented in Fig.9.

Fig. 7. Stress contour lines according to Huber-Misses hypothesis in the internal
tube of the boom – static analysis



56 D. Derlukiewicz, J. Karliński

Fig. 8. Stress contour lines according to Huber-Misses hypothesis in the external
tube of the boom – static analysis

Fig. 9. Maximum stress contour lines according to Huber-Misses hypothesis for a
dynamic test in the selected time step t=0.153s

4. Conclusions

The advanced CAD/FEM techniques enable to conduct not only the basic
but also sophisticated strength analyses of any structure. Inmost cases, expe-
rimental tests are used to verify the fulfillment of standard requirements for



Static and dynamic analysis of telescopic boom... 57

the approval of implementation the machine into practise. With the use of
FEM and computer simulations, these structures which do not meet the re-
quirements are eliminated already at the design stage. Sometimes, numerical
simulations are the only tests which are done to approve the machine.
Results of FEM calculations are always on the safe side, providing a suffi-

ciently accurate answer to the set loading states and boundary conditions. In
virtual models of protective structures, the simplification is limited tomodels
of the material and its behaviour under impact loads and to the quality of
manufacturing technology.
The study of the boom stress resulted in the development of a boomwith

a sufficient number of degrees of freedom (Fig.10). The boom strength requ-
irements were met thanks to use of a computer-aided design combined with
advanced strength analysis carried out using the finite-element method.

Fig. 10. Mining machine FaceMaster 2.5 with two booms installed
(www.minemaster.eu [13])

This problemwas solved thanks to the cooperation between the designers
and the entity preparing calculations. Simultaneous designing and strength
analysis enabled obtaining of the optimum shape of the structure taking into
consideration the costs and technologies ofmanufacturing in a short period of
time.Thanks to that itwas possible to avoid the costs related to constructinga
failed product,which in this case, is the boom(Karliński et al., 2008;Karliński
and Wach, 2006; Koziolek et al., 2010). The calculations made confirm the
usefulness of numericalmethods, including the finite-elementmethod for both
the dynamic and static analysis of complex issues of the structure mechanics
(physical, geometrical nonlinearities and contact).



58 D. Derlukiewicz, J. Karliński

In such circumstances, the most important part is to establish the design
guidelines (kinematic requirements, choice of materials and the power trans-
mission method, etc.) and to define appropriately and adequately boundary
conditions for the structuremodel. It is also necessary to take into considera-
tion the geometrical and physical nonlinearity, and to choose an appropriate
model describingmaterial properties specifying the type of material characte-
ristics and the phenomena taking place such as isotropic hardening, hardening
proportional to the speed of deformation etc.

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Statyczna i dynamiczna analiza wysięgnika teleskopowego samojezdnej

maszyny górniczej

Streszczenie

Wartykule zaprezentowanowybrane zagadnienia dotyczącemetodykiwykonywa-
nia analiz wytrzymałościowych wysięgników samojezdnych maszyn górniczych przy
pomocy metody elementów skończonych. Przedstawiono zasady budowania modeli
obliczeniowych.Wpracy zaprezentowano przykłady liczbowe obejmujące analizywy-
trzymałościowewykonane dla obciążeń statycznych i dynamicznych.

Manuscript received October 4, 2010; accepted for print April 6, 2011