STRENGTH ANALYSIS OF THE FRAME OF THE
ESCALATOR USING THE FINITE ELEMENT
METHOD AND CALCULATION OF THE DRIVE
SYSTEM
by
Osman Altuğ AKYOL
September, 2004
İZMİR
ABSTRACT
Escalators are systems used for the transport of people between specific levels
and angles.
In this study, by doing stress analyses for static loading conditions of a frame of
escalators, determining the critical points of frame and optimization are aimed.
For the stress analysis, firstly, the loads effecting on the structure are calculated.
Then the frame is modeled. After introducing the material properties, loads effecting
on frame and the boundary conditions to the software (ANSYS), the stress analysis is
performed. The results obtained by the analyses are compared with the strain gauge
measurement values.
Keywords: Escalator, Frame, Stress Analysis, ANSYS
ÖZET
Yürüyen merdivenler, insanların belirli kotlar arasında belirli açılarda nakliyesini
sağlayan sistemlerdir.
Bu çalışmada, yürüyen merdivenin taşıyıcı sisteminin statik yükleme durumları
için gerilme analizinin yapılarak, taşıyıcı sistemin kritik noktalarını tespit etmek ve
optimizasyon çalışması yaparak iyileştirme amaçlanmıştır.
Gerilme analizi için; öncelikle yapı üzerine etki eden kuvvetler hesaplanmıştır.
Taşıyıcı sistemin modellenmesi yapılmıştır. Parçaların malzeme özellikleri, taşıyıcı
sisteme etki eden kuvvetler ve sınır şartları programa (ANSYS) tanıtıldıktan sonra
gerilme analizi yapılmıştır. Elde edilen analiz sonuçları strain gauge ölçüm değerleri
ile karşılaştırılmıştır.
Anahtar sözcükler: Yürüyen Merdiven, Taşıyıcı Sistem, Gerilme Analizi, ANSYS
1. Introduction Escalators are used for the transport of people between specific levels and angles.
They are designed to meet their transport capacity which is known as their most
important parameter.
The aim of this study is to give general information about escalators and to define
how the necessary design parameters are determined. In this study, in order to
determine whether the frame of escalators is safe or not, strenght analysis is
performed by using ANSYS software. To compute the engine power, all of the parts
of the drive system are examined.
2. Escalators and Determining General Dimensions
The main working principle of escalators is similar to those of conveyors. While
reverse station lies underside of the escalators, the drive station takes place on the
top. These two stations are connected by rails. By this way, a close loop is obtained
and steps move in this close loop.
The general dimensions of escalators are determined by using some dynamic
parameters. These dynamic parameters are climbing angel, height, step width and
velocity.
The angels are standardized as 27.3, 30 and 35 degrees. Height is the vertical
distance between the upper and bottom connection points of the escalators. Step
width is standardized as 600, 800 and 1000 mm. The velocity should not exceed 1
m/s.
3. Analysis of Frame Using the Finite Element Method
The finite element method is a numerical procedure that can be applied to obtain
solutions to a variety of problems in engineering Courant (1943) has been credited
with being the first person to develop the finite element method. It was not until 1960
that Clough (1960) made the term finite element popular. Zienkiewicz and Cheung
(1967) wrote the first book entirely devoted to the finite element method.
Firstly, the loads effecting the frame and the boundary conditions are determined
for each escalator. ANSYS is used for the analysis. In order to perform the analysis
correctly, the suitable element is selected from ANSYS. In this study, beam44
element is selected.
Figure 1. Beam44 element
(Moaveni, 2003)
4. Analysis of Frame (Height = 3000 mm, Climbing Angel = 30 degrees and Step
Width = 1000 mm)
Loads effecting the inclined sections of the escalator:
Passenger load Fy::
Fy= Gy×g= (m×B×Ny× φ)×g = (80×15×2×1)×9.81= 23544 N
Step load Fb:
Fb=NEB×mb×g=15.15.9.81=2207N
Total load effecting the upper station Füi:
Füi=0.5×g×(Güi+(NÜB+5)×mb.+ NÜB×m)=0.5×9.81×(550+(2+5)×15+2×80)
Füi=3997.55 N
Total load effecting the bottom station Fai:
Fai=0.5×g×(Gai+(NAB+5)×mb+ NAB×m)=0.5×9.81×(312+(2+5)+2×80)
Fai=2830.16 N
Total force Ft:
Ft=Fy+ Fb+ 2×Füi+2×Fai
Reaction forces at the connection points: Ra, Rb
Ra+Rb=Ft
Figure 2. H= 3000, A=300, Wb= 1000 mm
Figure 3. Frame profiles; 1) rectangular profile 80x60x5 mm 2) rectangular
profile 80x60x3 mm
The material of the rectangular profiles is St32.
Figure 4. Deformation of the frame
Figure 5. Displacement of the frame (Uy)
Figure 6. Illustration of the frame using nodes
Figure 7. Maximum stress
Figure 8. Minimum stress
Figure 9. Axial stress
Figure 10. Stress distribution of the upper connection point of the escalor
5. Strain-gauge Test
While locating the strain gauges, the sections that yield maximum stress are
selected. Strain gauge test is performed by Bias Engineering. (İpek, 2002)
Figure 11. Location of the strain-gauge
Figure 12. Output of gauge 1
Figure 13. Output of gauge 2
Figure 14. Output of gauge 3
Figure 15. Output of gauge 4
Figure 16. Output of gauge 5
Figure 17. Output of gauge 6
Figure 18. Output of gauge 7
6. Calculation of the Drive System
All the elements belonging to the drive system are modeled by using
SOLIDWORKS/2004 software and moment of inertia is calculated by the same
software.
In general, the working principle of escalators is based on the mechanism that
pulls the steps using chains. Chains are driven on the upper station by chain-wheels.
(Sabuncu, 2001)
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛××
+××××+++
+⎟⎟⎠
⎞⎜⎜⎝
⎛×++++++
+⎟⎟⎠
⎞⎜⎜⎝
⎛×++⎟⎟
⎠
⎞⎜⎜⎝
⎛×+×
=
∑
∑2
11
82
2
2
11
887911765
2
11
343
2
11
121
211
275.0
)332.0())((
.2().2(
)()(21
ww
m
NmNNNm
ww
IIIIIII
ww
IIwwIIw
KE
bant
yÜBABEBb
a
ϕ
(1)
VLNAmNwTQ bantyEB ×××−×××××−××= )503.0sin81.9(11 ϕη (2)
dtKEdQ )(
= olur.
dtdw11
11 =α (3)
T.w1: Engine power (Watt)
bantyEB LANmNwTQ ×−×××××−××= 5.7sin905.411 ϕη (4)
Total bant lenght:
28.2sin
×⎟⎠⎞
⎜⎝⎛ +×+×+= ÜBABbant NaNa
AHL (5)
Total bant weight
ρ×=∑ bantbant Lm (6)
FB=µ.FBY.LBant (7)
µ: Coefficient of friction (0.27-0.37)
µ= (0.27-0.37)
FBY: Load per meter (50 N/m)
ρ : 2.5 kg/m
η = 0.88
α11: 0.6 r/s2
Cycle: n1 = 960 d/d
n3=960/24.5=39.18 d/d
n11=39.18×23/65=13.865 d/d
w11=13.865× π/30 r/s
n8: 13.865×30/26~16 d/d
w8=16×π/30 r/s
)1000/()5.7sin8.784
)(00636.01.10068.005.312(11 ×⎥
⎦
⎤⎢⎣
⎡×+×××
+××+××+××+= η
ϕρϕ
bantEB
bantEBbB
LNALNmN
wT (8)
is obtained
7. Conclusions
The main aim of the strength analysis for the frame is to check whether the system
is safe or not. For the analysis, the strength analysis of the frames of the escalators
including different design parameters are done by using ANSYS software and stress
and displacement values are computed.
The escalators that are analysed are the ones that are frequently manufactured in
the factory. By choosing the step widths as 1000 mm, the load acting on the structure
is maximized.
From the analysis, it is seen that strain gauge test results are compatible with the
the finite element results which are performed using ANSYS software.
References
Clough, R.W. (1960). The Finite Element Method in Plane Stress Analysis.
Proceedings of American Society of Civil Engineers, 2nd Conference on Electronic
Computations, 23, 345-378.
Courant, R. (1943). Variational Methods for the Solution of Problems of Equilibrium
and Vibrations. Bulletin of the American Mathematical Society, 49, 1-23.
İpek, G. (2002). Yürüyen Merdiven Taşıyıcı Sisteminde Statik ve Dinamik Yükleme
Altında Strain Gauge Ölçümü. Bias Mühendislik.
Moaveni, S. (2003). Finite Element Analysis: Theory and Application with ANSYS.
(2nd ed.). New Jersey : Pearson Education, Inc.
Sabuncu, M. ( 2001). Yürüyen Merdiven Taşıyıcı Çelik Konstrüksiyonu Aksamı ve
Makina Motor Gücü Tespiti Projesi.
Zienkiewicz, O.C., & Cheung, Y.K.K. (1967). The Finite Element Method in
Structural and Continuum Mechanics. London: McGraw-Hill.