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.