Acta Polytechnica


https://doi.org/10.14311/AP.2021.61.0292
Acta Polytechnica 61(1):292–306, 2021 © 2021 The Author(s). Licensed under a CC-BY 4.0 licence

Published by the Czech Technical University in Prague

STRESS ANALYSIS AND TOPOLOGY OPTIMIZATION OF A
CHAIN BUCKET ELEVATOR USING ANSYS

Edward Yin∗, Emmanuel M. Seckley, Evans Kesse Asiedu,
Stephen Cobbinah

University of Mines and Technology, Faculty of Engineering, Department of Mechanical Engineering, P.O.
Box 237, Tarkwa, Ghana

∗ corresponding author: eyin@umat.edu.gh

Abstract. A failure of conveyor chain links in a production process can cause unscheduled shutdowns,
which increase the throughput time coupled with damaged buckets and chain links, which increase
maintenance and repair costs. Since failures of conveyor chains are inevitable, this research aims to
modify the design of the chain bucket elevator by incorporating a ratchet mechanism, which will prevent
the chain bucket assembly from dropping to the bottom of the chain bucket elevator whenever there is
a chain-link failure and also avoid the jamming of the bucket chain assembly against one another when
dropping to the bottom of the elevator during failure. The number of damaged buckets and chains will
be minimal, thereby reducing the maintenance and repair costs. Also, the time required for replacing
the failed chain link will be reduced, which in turn, will reduce the down-time, thereby increasing the
production rate. The ratchet mechanism, which can withstand a maximum load of 38.10 kN, comprises
a toothed wheel, a pawl, and a spring. An analytical method was employed for the initial analysis and
the results were verified using the FEM. Topology Optimization was carried out on the beam and lever
with results showing a 20% and 26% weight reduction from the original, respectively. The stresses
induced in the beam and lever increased significantly by 36% and 47%, respectively, because of the
optimization, however, they remained within the acceptable limits.

Keywords: Stress analysis, bucket elevator, conveyor chain links, optimization, finite element method.

1. Introduction
The FE based design optimization (DO) is a well-
developed and established method for determining
design parameters that lead to the best measurable
performance (optimal solution) of a mechanical struc-
ture, device, or system under given constraints. As
a result, there is a rising demand for lower produc-
tion cost, more efficient, less expensive and innovative
methods to improve the performance of the existing
systems. Optimization can be used to solve different
engineering problems, including design of aircraft and
aerospace structures aiming for minimum weight, vi-
bration and noise optimization of automobiles for ride
comfort, optimal design of electrical networks, analy-
sis of statistical data and building empirical models
from experimental results to obtain the most accu-
rate representation of the physical phenomenon as
well as optimal production planning, controlling and
scheduling.

Depending on the type of design variables, the finite
element-based optimization may be classified as a
parameter or size, shape and topology optimization.
While shape and size optimizations are quite well
known, the topology optimization is beginning to gain
its importance in commercial optimization codes. The
topology optimization generates the optimal shape of
a mechanical structure as shown in Fig. 1. In this
study, the topology optimization will be employed

to optimize the components of the modified bucket
elevator.

In the topological optimization, the objective func-
tion (f) is a subject that is minimized or maximized
to the defined constraints (gj). The density of each
finite element (i) is treated as a design variable (ηi)
in the topological problem. The pseudo density for
each element varies from 0 to 1; where ηi ≈ 0 repre-
sents material to be removed; and ηi ≈ 1 represents
material that should be kept. Mathematically, the
optimization problem is expressed as:

F = minimize or maximize w.r. to ηi (1)

Subjected to ≤ ηi ≤ 1 where i = 1, 2, 3 . . . N (2)
gjl < gj < gju where j = 1, 2, 3 . . .M (3)

Where
N = number of finite elements
M = number of constraints
gj = computed jth constraint value
gjl = lower bound for jth constraint
gju = upper bound for jth constraint
Central chain bucket elevators are basically designed

to move granular materials vertically through a height.
The elevators use an endless chain with a series of
buckets attached to it. The bulk material is spread
into an inlet hopper where the buckets dig into the
material and convey it up over the head sprocket.
Thereafter, the buckets throw the material out via

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https://doi.org/10.14311/AP.2021.61.0292
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vol. 61 no. 1/2021 Stress analysis and topology optimization of a chain bucket elevator. . .

Figure 1. Topology Optimization Process [1].

Figure 2. Parts of a Bucket Elevator [3].

a discharge spout. The buckets are returned down
to the tail sprocket at the bottom and the cycle is
repeated..
The bucket elevator consists of buckets to contain

the material, chain/belt drive to carry the buckets and
transmit the pull. In addition, it also has an electrical
motor to drive the chain or belt, loading and discharge
spout for loading the buckets at the boot and receiving
the discharged material at the head, respectively. A
tensioning device is also installed for maintaining the
chain/belt tension. All these accessories are enclosed
and protected in a casing [2]. Fig 2 shows the various
parts of the bucket elevator.

The buckets are designed to stay upright after scoop-
ing the material to prevent spillage. The head is one
of the major structural elements of the overall elevator.
It supports the weight of the buckets and belt and
accommodates the drive and anti-run back device [4].

Bucket elevators are the most efficient means of ele-
vating free-flowing granular materials and even some
sticky materials. Bucket elevators offer a practical,

efficient, and economical means of elevating a wide
variety of dry, free-flowing bulk materials vertically [5].
The bucket elevators are employed in various appli-
cations and are the ideal solution where products
need to be elevated and only consume a small ground
area [6]. They are employed in the lime, cement,
and grain industry for conveying fertilizers, powders,
grains, minerals, salt, potash and in the building in-
dustry for conveying stones and mortar. They are
also suitable for transporting hot materials (up to
1000 °C). For free-flowing bulk materials, which need
to be conveyed vertically, bucket elevators are the best
option. Conveyed products are mostly granular solids,
which range from powders to rocks. Limitations de-
pend on how easily a product can be loaded into and
discharged from the bucket. Large granular products
are difficult to load while sticky products are difficult
to discharge. For products that are fragile and easily
crushed, slower conveyance speeds must be used [6].

There are mainly two types of bucket elevators; the
belt and chain bucket elevators. The main difference
between the two is that the former uses an endless
belt with pulley whilst the latter uses an endless chain
with a sprocket as shown in Fig 3 a) and b).

Whenever the chain links of the bucket elevator fail,
it takes the technicians a minimum of three (3) days to
fix it. This is because when one of the chain links fails,
all the chains together with the buckets drop to the
bottom of the bucket elevator. A chain block is then
used to pull the chain link up through a height of be-
tween 15 to 25 m depending on where it failed to join
them. In addition to this, some of the links and buck-
ets get damaged and they need to be replaced with
new ones. This results in an increased down-time and
severely affect the production time. Moreover, since
the damaged buckets and links need to be replaced
with new ones, the maintenance cost is increased. In
view of this; the research aims to address this problem
by introducing a ratchet mechanism, which will hold
the chain links and buckets in position when there is a
failure in order to prevent them from being damaged

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E. Yin, E. M. Seckley, E. K. Asiedu, S. Cobbinah Acta Polytechnica

Figure 3. Chain and Belt Bucket Elevator.

Figure 4. Failed Chain Links [7].

and also address the difficulty in joining the chain
links together again.
Bucket elevators are very important to the extent

that the whole production process halts whenever the
elevator is not in operational condition and this is
mostly caused by failure of chain links as shown in
Fig. 4. Although other parts such as the bearing,
shaft, and gears can also fail, the failure of chain
links is much more frequent. Failure of chain links
does not only reduce productivity but also the cost of
maintenance because of damaged buckets and links
associated with the failure. The specifications of the
investigated bucket elevator are shown in Table 1.
The above data were obtained from East African

Portland Cement Company (EAPC), Kenya. On the
average, the downtown is three (3) days, which in
terms of hours is 72 hrs. Therefore, the amount
of cement lost during the downtime is 5760 tons
(5,760,000 kg), which in terms of bags of cement, is
115,200 bags of cement. It is therefore imperative to
analyse and come up with a design that will reduce
down-time, which in turn, will increase productivity.
Down-time is the number of hours during which the
bucket elevator is not in operation. An analytical
method was employed in designing the various compo-
nents of the ratchet mechanism and these results were

verified using the FEA. Subsequently, a topology opti-
mization was carried out to obtain an optimal shape
of each component. A stress analysis was performed
for the stress levels induced in the optimal shape.

2. Literature review
A thorough literature analysis has been carried out
to comprehend the subject matter. The literature
review mainly focused on various studies on bucket
elevators to improve its performance and the failure
of the chain links. Various methods of analysing the
bucket elevator and obtained results are discussed.
Also, failure modes and causes of failure of the chain
links are presented.
In their study, Patel et.al. [8] improved the design

of a belt bucket elevator by changing the material
of the pulley shaft from EN-8 to EN-24. EN-24 had
a better fretting corrosion resistance than EN-8. A
static structural analysis was performed on the shaft
using ANSYS simulation software under standard
operating conditions. The performance of the two
materials under deformation, safety factor and von
Mises stress were compared as shown in Table 2.

It was concluded that the belt bucket elevator failed
mainly due to breaking occurring at the inner edge

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vol. 61 no. 1/2021 Stress analysis and topology optimization of a chain bucket elevator. . .

SN Item Quantity
1. Capacity 80 t/hr
2. Power Rating 57 kW
3. Speed 1.62 m/s
4. Diameter of Sprocket 0.762 m
5. Weight of Chain per Unit Length 57 kg/m
6. Height 30 m
7. Width 1.5 m
8. Average Temperature 75 °C

Table 1. Specification of Bucket Elevator.

Deformation/mm Von Mises stress/MPa Safety Factor
Existing material EN-8 2.2381 199.11 2.3
New material EN-24 1.9412 1 82.02 3.0

Table 2. Simulation Results.

of the pulley, which is considered as fretting corro-
sion. From the analysis shown in Table 2, EN-24 was
suggested for the shaft as it showed better results for
deformation, von Mises stress and safety factor than
the existing material, i.e., EN-8.

Using the Finite Element Analysis, Yashaswini et.al.
[6] designed and optimized a bucket elevator with a
capacity range of 10− 20 tons/hr. The modelling of
the bucket elevator was done using CAD software and,
subsequently, the bucket and gear shaft assembly was
simulated using ANSYS simulation software under
various capacities of 10, 15 and 20 tons/hr. The de-
formation, maximum deflection and factor of safety
of the bucket together with that of the gear shaft
assembly was determined as shown in Table 3 and
Table 4. A modal analysis was also used to determine
vibration characteristics of the components.

It was concluded from the simulation results that
the static stresses developed in the Bucket Elevator
are within the permissible limits. From the Modal
analysis, it was observed that the bucket may vibrate
violently at a frequency of 170Hz during a speed of
1m/sec on the chain drive with a frequency range
between 0− 300Hz whereas the gear shaft undergoes
vibrations at a frequency of 1117Hz. In conclusion,
the capacity of the bucket elevator was increased to
20 tones/hr.

In their paper, Taher et.al. [9] designed a combi-
nation of a belt conveyor and chain bucket elevator,
which is controlled automatically by a micro controller
with a weight sensor attached to it for packaging.
Prototypes of the belt conveyor and chain conveyor
were produced by employing various workshop pro-
cesses such as metal cutting, soldering, welding, bor-
ing, drilling, grinding, facing and turning. The belt
conveyor and bucket elevator were then synchronized
to perform the function for which they were designed
i.e. to automate the handling of bulk material and its
packaging. It was concluded that the control system

helps packaging the right amount of material in sev-
eral packets. Once set, the required skill for operating
the system is also reduced, as compared to a manual
system.
In their paper, Barshi et. al. [10] modelled and

analysed a belt bucket elevator using SOLIDWORKS
to optimize the weight and discharge capacities of the
bucket elevator. The weight reduction was carried out
on both the bucket and shaft by changing the bucket
material from structural steel to aluminium and shaft
material from structural steel to EN-8. The weight
of the bucket was reduced from 3.2 to 2 kg, which
resulted in a 38.27% decrement since aluminium is
lighter than structural steel, whereas the diameter of
the shaft reduced from 187mm to 168mm since EN-8
material is a stronger material than steel.
In their studies, Deoka et. al. [11] used the FEA

and Topology optimization techniques to carry out a
weight reduction of the buckets of a bucket elevator.
The maximum stress value of the existing buckets was
very low, as compared to the allowable stress, and
therefore the need for optimization. The topology
optimization was used to find the best design concept
that meets the design requirements. Three iterations
were performed by reducing the thickness of the orig-
inal buckets, which was 2.96mm. The thickness of
buckets used for iterations I, II and III were 1.5, 1.2
and 1.2mm, respectively, and they were all in the safe
region. The corresponding weights were 2.34, 1.88
and 1.88, respectively. The authors concluded that
using a bucket thickness of 1.2mm showed positive
results with the stress and deflection in a permissible
range and this resulted in a weight reduction of 36%.
In their paper, Shinde et. al. [12] performed a

material optimization and modal analyses using the
FEA. The main goal of this paper was to obtain a new
material that meets the strength requirements of a
bucket of a bucket elevator and to predict the response
of the buckets to a resonance under any external force.

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E. Yin, E. M. Seckley, E. K. Asiedu, S. Cobbinah Acta Polytechnica

Output Capacity/t/hr Max. Deflection/mm Max. Stress/MPa Factor of safety
10 0.08 226 1.16
15 0.07 233.9 1.068
20 0.08 247.9 1.008

Table 3. Gear Shaft Assembly Simulation Result.

Output Capacity/t/hr Max. Deflection/mm Max. Stress/MPa Factor of safety
10 3.104 230.444 1.084
15 4.541 116.583 2.14
20 5.906 153.251 1.6

Table 4. Gear Shaft Assembly Simulation Result.

The bucket was modelled using CAD, meshing was
done using HYPERMESH and, finally, ANSYS was
used to perform the static and modal analyses. It was
concluded that the design was safe since the stress
and deformation values were below the critical values.
In their study, Pérez-Aparicio et. al [13] employed

the Discontinuous Deformation Analysis (DDA) to
analyse the bucket elevator discharge of granular ma-
terials for several velocities, bulk materials and bucket
shapes. The results were in good agreement with
existing analytical and experimental results. The be-
haviour of granular materials inside and outside of
the most common bucket types was determined us-
ing a parametric analysis. It was concluded that the
most efficient shape of the bucket for any specific
working conditions can be designed using the analyses
presented.
In their paper, Chavhan et. al. [14] modelled and

subsequently performed the Finite Element Analy-
sis of an elevator bucket. The authors considered
two buckets, one made of steel and the other one
of epoxy. Static structural analyses were performed
using ANSYS and validated experimentally using uni-
versal testing machine (UTM). The weights of steel
and epoxy buckets were 624 g and 147 g, respectively,
and resulted in a 76.4% decrement. Also, the maxi-
mum load carrying capacity of steel and epoxy buckets
were 10 kg and 6 kg, respectively, hence, the designed
bucket was safe.
Rademacher [15] studied the non-spill discharge

characteristics of bucket elevators and developed a
non-spill theory for a simplified two-pulley model of a
vertical bucket elevator with cylindrical buckets con-
veying a (very) cohesive material. The theory allows
for an interrelated analysis and optimization of wheel
radius, bucket height, bucket width, bucket spacing,
wall friction coefficient inside the buckets, pulley speed,
capacity, boundaries of the discharging flow of con-
veyed material, optimum - position of the chute and
dimensioning of the casing head. In conclusion, a
spill-free combination of the relevant parameters was
found.

Haris [16] investigated the causes of a failure of a
chain system through a characterization of the failed
component. The analysis revealed that the weld de-
fects such as craters lead to a crack propagation and
a cyclic loading causes the fatigue failure. The fatigue
failure occurred due to this inherited crack at the outer
circumference of the weld within the chain attachment
and outer chain link plate. This type of defect can also
be categorized as a manufacturing defect. The fatigue
crack propagation was evident by progressive beach
marks, and the scanning electron microscopy (SEM)
analysis revealed the types of microstructures that
resulted at the heat affected zone (HAZ). Hardness
testing using the Rockwell Tester found the different
hardness profiles at the three areas, i.e., weld metal,
base metal and heat affected zone. The maximum
hardness values were found at the heat affected zone
and the weld metal. Cracks generated at the outer
circumference of the weld within the chain attachment
and outer chain links’ plate within the material led to
the fatigue failure. Haris proposed that the thickness
of the outer link should be increased, but did not
study how this increase will impact the weld strength
or weld defects (craters) within the chain link.
In their study, using a visual examination, Sujata

et. al [17] found a shallow crack on the surface of
the chain link under a stereo-binocular microscope.
The authors found that the fracture surface showed
coarse crystalline features. The sample containing the
crack was cut, mounted, metallographically prepared
and observed under an optical microscope. The visual
examination revealed a crack-like surface defect and
the optical micrograph showed an oxide entrapment
in the material near the surface. The authors used
Energy Dispersive X-Ray (EDX) analysis in the SEM
for the investigation and found that the non-metallic
inclusions between the crack surfaces, were mainly iron
oxide. The authors concluded that the conveyor chain
links had failed due to the presence of manufacturing-
in defects. The defects were identified as forging laps
or folds and can be summarized as inherent defects.
The investigation also showed that surface defects were
present in the billet itself. They then recommended

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vol. 61 no. 1/2021 Stress analysis and topology optimization of a chain bucket elevator. . .

that the billet should be properly dressed, and the
surface defects should be removed prior to the forging
operations. The significance of the coarse crystalline
features and the iron oxide inclusions were not stated
in this paper.
Bošnjak et. al. [18] carried out a failure investi-

gation of the bucket wheel excavator crawler chain
link to diagnose the cause of the damage. To identify
the reasons behind the chain link failures, stress state
calculations were performed as well as experimental in-
vestigations, which included visual and metallographic
examinations, chemical composition analysis and tests
of mechanical properties. The sulphur content ob-
tained from the chemical analysis of both samples
was higher, as compared with the specifications. This
resulted in a decreased impact toughness, particularly
under impact conditions. The significant decrease of
elongation compared with the specified values con-
firmed the presumptions based on the results of the
chemical composition. The obtained low values of
elongation and contraction meant that the samples
had a very low resistance to crack initiation and crack
propagation. Based on the results of the numeri-
cal–experimental analyses, it was concluded that the
chain link breakdowns are caused by ‘manufacturing-
in’ defects. The carbon content obtained from the
chemical analysis was lower than that of the required
standard, but the paper never considered this obser-
vation.

Yin et. al. [7] carried out a failure analysis of bucket
elevator conveyor chain links using a visual examina-
tion, chemical analysis, and metallographic analysis.
These processes were performed on both failed and
functioning conveyor chain link samples. The carried
out visual examination revealed that the failure was
brittle fracture, because there was no necking. In ad-
dition, the researchers observed an offset between the
sprockets evidenced by indentations on the outer link
of the chain link as well as vibrations within the bucket
elevator system. A chemical analysis performed on
5 samples established that Silicon (Si), Phosphorus
(P), Sulphur (S), Manganese (Mn), Chromium (Cr)
and Molybdenum (Mo) all met the British standard
EN 10293 requirements for steel casting for engineer-
ing use but Carbon (C) did not. It was concluded that
the failure was brittle fracture induced by inclusions,
which were the root cause of failure of the conveyor
chain links.

2.1. Summary
From the reviewed papers, it can be seen that an ex-
tensive amount of work has been done on optimization
of the bucket elevator by focusing on weight reduction
of various components of the bucket elevator. The
FEM is seen as an important tool in the optimization
process and is less expensive, compared to an exper-
imental approach. The failure of a bucket elevator
chain link is inevitable as shown in literature pub-
lished by [7, 16–18]. The main cause of the failure was

all determined to be manufacturing defects (holes and
inclusions), which generate micro-cracks. These micro-
cracks propagate until a fracture occurs. Although
other parts such as bearing, shaft, and gears can also
fail, they do not fail as frequently as chain links. The
failure of chain links does not reduce only productivity
but also increases the cost of maintenance because of
damaged buckets and links associated with the failure.
This paper mainly delves into how the design can
be improved to minimize down-time and eliminate
damaging the bucket and chain links during a failure
of a chain link.

3. Design optimization and
operation

The proposed design incorporates a ratchet mech-
anism, which restricts the chains with the buckets
mounted on it to move only in the clockwise direction.
The chains never fail when the buckets are empty, but
fail when they are filled with cement. When the chain
fails, it descends to the bottom because of the force
of gravity. While descending to the bottom, the mo-
tion of the chain tends to be in the counter clockwise
direction, thus, the incorporated ratchet mechanism
restricts the chain to move only in the clockwise direc-
tion and the chain is held in position and is prevented
from dropping to the bottom of the elevator. The
proposed design is shown in Fig. 5.

3.1. Components of the ratchet
mechanism

The main function of the ratchet mechanism is to
ensure that the chain is prevented from dropping to
the bottom when there is a failure. The ratchet is
made up of toothed wheel (sprocket), a pawl/lever,
and a spring. A break out section of the ratchet
mechanism is shown in Fig. 6.
The toothed wheel in this case is a spur gear and

it is the rotating member of the mechanism. The
prime mover, which is the motor, drives the chain and
because the chain is in contact with the toothed wheel
(spur gear), it rotates along with the chain. A lever
is hinged/pivoted at one end and the other end is
shaped to fit into a notch of the ratchet wheel to allow
for clockwise motion and prevent counter-clockwise
motion. A spring is incorporated to hold the pawl
against the teeth to ensure that the pawl is in position
all the time to perform its function effectively. Since
the ratchet mechanism is going to be incorporated
into an existing bucket elevator, the sprocket, chain
and shaft will be the same as that of the existing
bucket elevator.

4. Methodology
In this study, an analytical method was employed
to determine the dimensions of each component of
the incorporated ratchet mechanism and verified with
the FEM (ANSYS). An analytical method was used

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E. Yin, E. M. Seckley, E. K. Asiedu, S. Cobbinah Acta Polytechnica

Figure 5. Designed bucket elevator.

Figure 6. Ratchet mechanism.

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vol. 61 no. 1/2021 Stress analysis and topology optimization of a chain bucket elevator. . .

38.10 kN

1.5 m

0.75 m

Figure 7. Free body diagram of beam.

to obtain the maximum force and, subsequently, the
diameter of the beam. The spring as well as the
pawl/lever were also designed according to the force
and the results were validated using ANSYS simula-
tion software. Table 6 shows the various dimensions
of the various parts of the ratchet mechanism.

4.1. Design calculation
The design calculations involve calculations on the
design of the beam, pawl and spring.

4.1.1. Design of the beam
The beam is the horizontal member on which the pawl
will be mounted. It has a fixed support as shown in
Fig. 7.
The data collected from the plant on the existing

bucket elevator.
• The length of the bucket elevator = 1.5m
• The weight of a bucket fully loaded with cement

= 36 kg
• The mass of a chain link per unit length = 88 kg/m
• The height of the bucket elevator = 30m
• For structural steel, the yield strength is 250MPa
• The length of the elevator should be equal to the
length of the bucket elevator for an easy assembly.

• The length of the beam is also = 1.5m
• One bucket, fully loaded with cement, weighs 36 kg
• The chains always fail within the range of 15m to
25m, the average between these two heights is 20m

• The number of buckets at a height of 20m = 59
buckets

• For 59 buckets, the Mass = 36 kg × 59 = 2124 kg
• The mass per unit length of chain = 88 kg/m
• Since the average height is 20m, Mass of chain

= 88× 20 = 1760 kg
• The total mass = mass of chain + mass of buckets

= 1760 + 2124 = 3884 kg
• Total weight, WT = mg = 3864× 9.81 = 38.10 kN
The free body diagram of the beam is shown in

Fig. 8.
The Shear Force and Bending Moment diagram are

shown in Fig. 9.
From Fig. 9, it can be seen that the maximum Shear

Force (V ) and Bending Moment (M) are 18.95 kN and
7.14 kN, respectively.

Figure 8. Free body diagram.

Figure 9. Shear force and bending moment diagram.

The beam is subjected to two main types of stresses:
• Bending stress
• Shear stress
From [18], the maximum bending and shear stress of
a cylindrical beam is given in equations (4) and (5),

σb = 32M
πd3 = 32 · 7.14

πd3 = 72727.443
d3 (4)

The maximum shear stress is also given by:

τmax = 16V
3πd2 = 16 · 18.95

3πd2 = 32170.519
d2 (5)

Using the distortion energy theory [18], the Von
Mises Stress, ∇ is given by;

∇ =
Å
Sy

n

ã
(6)

where Sy = Yield strength, n = Factor of safety.
Also, the Von Mises Stress [18], ∇ is given by;

∇ = {σ2
b + 3τ2

max}0.5 (7)

Equating equations (6) and (7) gives,Å
Sy

n

ã
= {(72727.443/d3)2 + 3(32170.519/d2)2}0.5Å
Sy

n

ã
= 5289280965/d6 + 3104826878/d4

Dividing through by 3104826878d6 gives,

d6

3.105× 109

Å
Sy

n

ã2
= 1.704 + d2

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E. Yin, E. M. Seckley, E. K. Asiedu, S. Cobbinah Acta Polytechnica

30°

BC

A

500 mm

Figure 10. FBD for ratchet mechanism.

3.221× 10−10d6
Å
Sy

n

ã2
= 1.704 + d2

d2{3.221× 10−10d4
Å
Sy

n

ã2
− 1} = 1.704

Either d2 = 1.704 or {3.221× 10−10d4
Ä

Sy

n

ä2
− 1} =

1.704. When,
d2 = 1.704

=⇒ d = ±1.305 m

When,

{3.221× 10−10d4
Å
Sy

n

ã2
− 1} = 1.704

using Structural steel, Sy = 250MPa, and a factor of
safety of 5,

d = ± 4

Ã
2.704

3.221× 10−10
Ä

250×106

5

ä2 = ±42.81 mm

From the two diameters calculated, the diameter of
the beam is 43mm, because 1.305m is too large.

4.1.2. Design of pawl
• The pawl is the member that fits into the notch of
the sprocket to lock it.

• The pawl is of a rectangular shape and, from the
collected data:

• The face width of the sprocket = 65mm
• The tooth thickness of the sprocket = 60mm
• Since the pawl is to fit into the notch of the sprocket,

the width of pawl should be equal to the face width
of the sprocket teeth. The width of the pawl =
65mm

• Also, the height of the pawl should be equal to the
tooth thickness of the sprocket teeth. The height
of the pawl = 60mm

From the proposed design, Fig. 10 can be deduced,
and therefore the length of the pawl, AC, can be
calculated.
From Fig. 10: The length of the pawl AC =

500 sin 30° = 577mm. Since the force acting on the

pawl is 38.10 kN and it is a compressive force, the
compressive stress is given by

∇c = −F
A

= − 38.1
0.577× 0.065 = −1.015 MPa (8)

From the Euler formula, the critical load for a member
fixed at one end and free at the other end is given by

Pc = π2EI

4L2 = π2 · 210 · 109 · 0.05 · 0.063

4 · 12 · 0.5772 =

= −40.07 kN (9)
Therefore, the critical compressive stress is given by

∇cr = 140.07
0.577 · 0.05 = −4.855 MPa

Since ∇c < ∇cr, the pawl will not fail when it is
being compressed by 38.10 kN force. Therefore, the
dimensions for the pawl are, L = 577mm,W = 50mm
and H = 60mm.

4.1.3. Design of spring
In the design of the spring, because of space consid-
erations, the total number of turns and the overall
length of the spring are specified. The total number
of turns Nt and overall length Lo are 10 turns and
537mm, respectively. Also, the type of the end of the
spring is squared and ground because it has a good
transfer of loads [18]. The diameter of the spring wire
is set to 25mm so that the spring can withstand the
load acting on it.

From Table 5,
Nt = Na + 2 (10)

Number of active turns,
Na = Nt − 2 = 8 turns

From Table 5, Solid Length,
Ls = dNt = 25 · 10 = 250 mm (11)

From Table 5, Pitch

P = Lo − 2d
Na

= 537− 2 · 25
8 = 60.87 (12)

From [18], the deflection of the spring is calculated
using equation (13),

Lo = deflection(y) + Ls

=⇒ y = 537− 250 = 287 mm (13)
For the stability of the spring,

Lo =≤ 5.26D
=⇒ Lo ≤ 5.26 · 110 ≤ 578.86 mm (14)

Since Lo(537) < 578.86mm, it implies that the spring
is stable

Outside diameter, OD = D + d =
= 110 + 25 = 135 mm (15)

Inside diameter, ID = D − d =
= 110− 25 = 85 mm (16)

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Type of spring ends
Term Plain Plain and ground Squared or closed Squared and ground
End coils Ne 0 1 2 2
Total coils Nt Na Na + 1 Na + 2 Na + 2
Free length Lo pNa + d p(Na + 1) pNa + 3d pNa + 2d
Solid length Ls d(Nt + 1) dNt d(Nt + 1) dNt

Pitch P (Lo − d)/Na Lo/(Na + 1) (Lo − 3d)/Na (Lo − 2d)/Na

Table 5. Formulas for the Dimensional Characteristics of Compression Spring (Na = Number of active coil) [18].

Part Dimensions

Beam Length – 1.5 m
Diameter – 43 mm

Pawl/Lever
Length – 577 mm
Width – 50 mm
Height – 60 mm

Spring

Total number of turns Nt = 10 turns
Overall length, Lo = 537mm
Diameter of spring wire, D = 25mm
Number of active turns, Na = 8 turns
Solid Length, Ls = 250mm
Pitch P = 60.87
Outside diameter, OD = 135mm
Inside diameter, ID = 85mm
K = 132.75 kN/m

Table 6. Design parameters.

4.2. Force analysis of ratchet mechanism

Figure 11. Force analysis of ratchet mechanism.

Member AB is the Beam on which the lever is
mounted. Member DE is the spring that keeps the
pawl in position, i.e., in the flute of the sprocket. FS

is the force in the spring. FP is the force acting on
the pawl. FAX and FAY are the forces acting at the
fixed end A of the beam in the X and Y direction,
respectively. FBX and FBY are the forces acting at
the fixed end B of the beam in the X and Y direction,
respectively. MA and MB are the moments acting at
points A and B of the beam. The force that will act
on the pawl is 38.10 kN, since this is the weight that

the pawl must withstand when there is a failure of
any of the chain links. The force that will act on the
spring will be the torque transmitted by the sprocket
onto the pawl during the operation. This force was
calculated as:

P = Fsvs (17)

where
P – Motor Power
Fs – Force on the Spring
Vs – Linear velocity of the Sprocket

Also,

Fs = P

vs
= 57

1.62 = 35.18 kW (18)

CAD models were designed using the Autodesk In-
ventor student software, and the simulation was done
using the ANSYS academic software. Fig. 12 is a flow
chart showing the procedure for the stress analysis
and topology optimization.

4.3. Kinematic analysis of ratchet
mechanism

The kinematic diagram of the ratchet mechanism is
shown in Fig 13.

From the kinematic diagram shown in Fig. 13, the
displacement of the Pawl/Lever X is given by:

X = L · sin� 0 ≤ � ≤ 30° (19)

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E. Yin, E. M. Seckley, E. K. Asiedu, S. Cobbinah Acta Polytechnica

Figure 12. Flow chart for FEM analysis.

Figure 13. Kinematic diagram.

where
X is the Displacement
L is the length of pawl/lever
� is the angle subtended by the pawl and the x-axis

The velocity of the Pawl/Lever is given by:

Ẋ = dX

dt
= dX

d�
× d�

dt
(20)

but
d�

dt
= ω (21)

Putting eqn (21) into eqn (20) gives,

Ẋ = ω
dX

d�
(22)

From eqn (19),

dX

d�
= L cos� (23)

Putting eqn (23) into eqn (22) gives,

Ẋ = ωL cos� 0 ≤ � ≤ 30° (24)

The acceleration of the pawl/lever is given by:

Ẍ = dẊ

dt
= dẊ

d�
× d�

dt
(25)

From eqn (21), d�
dt = ω

Ẍ = ω
Ẋ

d�
(26)

From eqn (24),

dẊ

d�
= −ωL sin� (27)

Putting eqn (27) into eqn (26) gives,

Ẍ = −ω2L sin� 0 ≤ � ≤ 30° (28)

5. Results and discussion
5.1. Kinematic analysis
The kinematic analysis was carried out on the ratchet
mechanism to determine the maximum displacement,
velocity and acceleration. From equations (19), (24)
and (28), the following graphs were plotted as shown
in Fig. 14. The displacement was a function of the
length and the angle subtended by the pawl whereas
the velocity and acceleration were a function of length
and the angle subtended by the pawl as well as the
angular speed of the sprocket. These parameters
influenced their respective maximum values occurring
at different angular positions.

The maximum displacement was determined to be
0.2885m as shown in Fig. 14a and occurred when the
angle subtended between the pawl and the beam was
30° or 0.5236 rad. From equation (1), it was deduced

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vol. 61 no. 1/2021 Stress analysis and topology optimization of a chain bucket elevator. . .

(a).

(b).

(c).

Figure 14. Force analysis of ratchet mechanism.

that the maximum displacement was equal to the
half-length of the pawl since sin 30° equals to 1/2.
The velocity reached a maximum when the angle

subtended between the pawl and the beam was zero.
The obtained value was 2.453m/s as shown in Fig. 14b,
which was equal to the product of the angular velocity
and the length of the pawl since cos 0° is unity.

The acceleration of the pawl was equal to half of the
product of the length of the pawl and the square of the
angular velocity since the sin of 30° equals to 1/2. The
value obtained was 5.216 m/s2 as shown in Fig. 14c.

5.2. Finite element analysis
The sizing of the pawl, spring and beam was done
using analytical formulas to determine the dimensions
of the parts. Subsequently, a static structural analysis
of the parts was carried out to validate the results
obtained analytically, using ANSYS academic. These
results are presented in Fig. 15.

The maximum von Mises stress acting on the beam,
as shown in Fig. 15a, was 70.87MPa and occurred at
the midspan of the beam where the force was applied.
The material used was structural steel with a yield
strength of 250MPa, and therefore the design was
safe since the maximum stress was less than the yield
strength of the material. As a result, the maximum
deformation will also be at the midspan with the factor
of safety being more than unity (1).
For the pawl, the maximum von Mises stress, as

shown in Fig. 15b, occurred at the tip as the force
was applied at that point. The obtained value of
the stress was 82.75MPa, which was lower that the
yield strength of the structural steel (250MPa). As a
result, the maximum deformation will also be at the
tip with the factor of safety being more than unity (1).
Case hardening of the tip of the pawl is, therefore,
recommended to prevent an excessive wear as the tip
will be in a direct contact with the sprocket.

The maximum von Mises stress acting on the spring,
as shown in Fig. 15c, was 132.54MPa and it occurred
at the inner fibre of the spring. The material used
was structural steel with a yield strength of 250MPa,
and therefore the design was within the safe region. It
was also noted that the spring had the highest stress
acting on it, and therefore is the most critical part
of the ratchet mechanism so it must be monitored
regularly during a regular maintenance. As the spring
would be subjected to pull-release cycles repeatedly, a
fatigue analysis was performed to estimate the fatigue
life of the spring. The fatigue life of the spring was
estimated to be 1.16e05 as shown in Fig. 15d.

5.3. Topology optimization analysis
The stress profile from the simulation of the beam
and lever showed that there is a room for a topology
optimization, so it was carried out using ANSYS aca-
demic simulation software and the results are shown
in Fig. 16 and Fig. 17.

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E. Yin, E. M. Seckley, E. K. Asiedu, S. Cobbinah Acta Polytechnica

(a). (b).

(c). (d).

Figure 15. Static structural analysis.

(a). (b).

(c). (d).

Figure 16. Lever topology optimization.

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vol. 61 no. 1/2021 Stress analysis and topology optimization of a chain bucket elevator. . .

(a). (b).

(c). (d).

Figure 17. Beam topology optimization.

The topology optimization was carried out to ob-
tain the best possible shape to reduce weight, thereby
saving material. The original mass of the lever was
reduced from 19.949 kg to 14.777 kg and the volume
was reduced from 2.5413m3 to 1.8824m3. This re-
sulted in a 26% reduction in mass and volume. Due to
the mass and volume reduction, the von-Mises stress
increased from 82.75MPa to 156.28MPa which was
a 47% increment from the original stress value, but
still being within the permissible limits.

The topology optimization was also carried out for
the beam as well to obtain the best possible shape at
the lowest cost. The original mass of the beam was
reduced from 13.024 kg to 10.401 kg and the volume
from 1.6592m3 to 1.325m3. This resulted in a 20%
reduction in mass and volume. Due to the mass
and volume reduction, the von-Mises stress increased
from 70.869MPa to 111.13ṀPa, which was a 36%
increment from the original stress value, but still being
within the permissible limits.

The maximum stresses from the simulation occurred
at the tip of the beam and at the midspan of the
beam where the force was applied, and therefore a
heat treatment should be carried out in that region
to increase its strength.

6. Conclusion
The bucket elevator was modified by incorporating a
ratchet mechanism for the purpose of preventing the
bucket chain assembly from dropping to the bottom
of the elevator when there is a chain failure, which
is inevitable. An analytical method was used for the
design and, subsequently, a static structural analysis
of the various members of the mechanism was carried
out using ANSYS with the stresses being within the
permissible limits. The maximum von Mises stress

acting on the beam was 70.87MPa and, after an opti-
mization, it increased to 111.13MPa. For the lever,
the maximum von Mises stress was 82.75MPa and
this value increased to 156.28MPa after an optimiza-
tion. The maximum von Mises stress acting on the
spring was 132.54MPa. Although the stresses in-
creased after the optimizations, it resulted in a 20%
and 26% reduction in mass and volume of the beam
and lever, respectively. A kinematic analysis of the
mechanism was also performed and the displacement,
velocity, and acceleration of the pawl were 0.2885m,
2.453m/s and 5.216m/s2, respectively. In conclusion,
this mechanism will aid in reducing the down-time
and maintenance costs, thereby increasing produc-
tivity. The adoption of this new design in the lime,
cement, and grain industry as well as in the building
industry will improve productivity.

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	Acta Polytechnica 61(1):292–306, 2021
	1 Introduction
	2 Literature review
	2.1 Summary

	3 Design optimization and operation
	3.1 Components of the ratchet mechanism

	4 Methodology
	4.1 Design calculation
	4.1.1 Design of the beam
	4.1.2 Design of pawl
	4.1.3 Design of spring

	4.2 Force analysis of ratchet mechanism
	4.3 Kinematic analysis of ratchet mechanism

	5 Results and discussion
	5.1 Kinematic analysis
	5.2 Finite element analysis
	5.3 Topology optimization analysis

	6 Conclusion
	References