EFFICIENT
SETUP OF THE BELT CONVEYOR SPEED THROUGH OF TEMPLATES
Daniel Corrêa da
Silva
IFRJ, Brazil
E-mail: danielsilvanilo@gmail.com
Carlos Eduardo
Soares Maia
IFRJ, Brazil
E-mail:
carloseduardosoares2001@gmail.com
Letícia Ali
Figueiredo Ferreira
CEFET/RJ, Brazil
E-mail: leticialifig@gmail.com
Ana Carla de
Souza Gomes dos Santos
IFRJ
and CEFET/RJ, Brazil
E-mail: ana.carla@ifrj.edu.br
Genildo Nonato
Santos
IFRJ, Brazil
E-mail: genildo.santos@ifrj.edu.br
Submission: 2/25/2020
Revision: 3/3/2020
Accept: 3/6/2020
ABSTRACT
It is not obvious to adjust the speed of a conveyor
belt so that it is possible to optimize the transport for each piece conveyed
even with various studies presented in this area. The complex methodologies
that are shown and the many adaptations indicated in these studies may
contribute to the low adoption of these configurations. A study made, in this
work, from videos of advertisements showing belt conveyor in operating on the
factory floor which presented only 44% efficiency. In this work, it was shown,
through theoretical studies, a mathematical model that presents the
relationship between the speed and the transport capacity of conveyor belts.
Based on a model, a graphical method (using templates) has been proposed that
helps in choosing the conveyor belt speed for most efficient configurations
that can be identified and adopted simply and without many adaptations to the
system as a whole.
Keywords: belt conveyor speed; belt conveyor load; belt conveyor energy
consumption; graph method for efficient solutions
1.
INTRODUCTION
The conveyor belt is the most
versatile and widespread to move the production inside industries (DIAS; LIMA;
TOSTES, 2008) because it is very trustable and it stands out by its higher
level of productivity and lowers the cost of maintenance (NOGUEIRA, 2004). The
efficiency of a production line would be compromised if a perfect functioning
of the processes of transportation of raw material, semi-finished and finished
products was not ensured, in all stages of its manufacture, from the beginning
to the finished product (NOGUEIRA, 2004). Due to the mentioned characteristics,
the conveyor belt is a fundamental equipment inside an industry. In that way,
the study and the implementation of management techniques that aim for the
energetic efficiency of these devices are highly relevant in the industry
sector (DIAS; RAMALHO, 2009).
Efficiency studies applied to
conveyor belt are often found in the technical literature. Tsai and Lee (1996)
presented a belt position control using a robust controller in a fixed
operation point. In Dias, Lima, and Tostes (2008), a
strategy type LQG-LTR is used to control the conveyor belt speed where a
neural-net estimates the most efficient speed of the conveyor device. In Shiton (2010), is discussed a mathematical model that
optimizes the electric power consumed in a conveyor belt.
However, all those methods, that
depend on complicated adaptations of the controlling equipment, are rarely
implemented on the nation’s industries factory floors.
This work presents a study made on
the efficiency related to the speed of conveyor belts, based on in national
advertisements videos, published by companies that sell this type of equipment.
The result of this study can be used as an indication that optimal methods of
adjusting the speed of the belts are not usually adopted in Brazilian
industries. As a major contribution of this work, it is suggested an efficient
method of adjusting the belt speed, based on simple templates, that do not
require any adaptation about the installation of new equipment to be adopted on
the factory floor.
To that end, the paper presents the
main theoretical foundations in chapter 2, the work methodology in chapter 3,
the results and discussions in chapter 4, and, finally, the final
considerations in chapter 5.
2.
THEORETICAL FOUNDATION
To allow a superficial survey of the
relationship between the efficiency and speed of conveyor belts in the national
industrial park, a study of advertising videos published by suppliers of this
type of equipment in the country was done. Many videos with advertisements for
conveyor belts, in operation, installed in industries can be found on the
internet. When analyzing several of these videos, it was noticed that the belts
were operating much below their maximum transport capacity - the ratio between
the visible area of the belt being used to transport products and the total
area of the conveyor belt (ŠTATKIĆ
et al., 2015).
That is, based on the assumption
that on the conveyor belt, in the space between two products being transported
in sequence, there is no room for anything else, it can be considered that this
conveyor is operating at its maximum transport capacity. The transport capacity
of a conveyor belt is a function of several parameters, including the conveyor
belt speed (ŠTATKIĆ et al.,
2015). For this conclusion, imagine a tram that always runs at a constant speed
and possible passengers that depart from random points to meet the tram.
If the speed with which passengers
move to board the tram is considered equal, the faster the tram travels, the
fewer passengers can board. Similarly, a very fast belt conveyor tends to have
less area occupied by-products transported than a slower belt conveyor. However,
it is not so obvious to answer whether the fastest moving tram, at the end of
the same period, carries more or fewer passengers than the slowest tram.
Just
as it is not obvious to say at what speed the belt conveyor, at the end of the
same time, will transport more products. As there is a direct relationship
between reducing speed and reducing electricity consumption on moving belts
(SHIRON, 2010), the question to be asked at this point is whether it is
possible to reduce the speed of the treadmill, keeping the same amount of
products transported in the same period, thus reducing energy consumption.
For the answer to this question, it
is necessary to understand how the speed of the conveyor is related to the
capacity to transport products of the belt conveyor. Thus, this relationship
will be deduced from the information obtained in generic works that talk about
the modeling of transport or that talk about efficiency measures in conveyor
belts (HILTERMANN et al., 2011).
2.1.
Relation
between the speed and the transport capacity
In different models, the terms usual
speed () and usual capacity (
) are the speed and the transport
capacity that is initially adjusted for the operation of the treadmill.
However, it is not possible to adjust these two parameters separately. The
reduction in speed of the conveyor will cause a change in the transport
capacity, as well as the example of the tram that was given previously, as long
as the properties of the lines that feed the conveyor do not change. That is,
the number of products per unit of the time they reach the treadmill does not
change.
The terms and
are the percentages of belt speed reduction
and the change in transport capacity. Thus, reducing the speed by a percentage
of
will cause a change in the effective transport
capacity in
. The best assumption to make is
that the relationship between
and
is non-linear,
. However, for small speed
reductions, this non-linear relationship can be approximated to a linear
relationship using the Taylor series (CHAPRA; CANALE, 2016), Equation (1),
truncated in its second term. Taylor's series is a mathematical tool that
allows expanding any function in a polynomial series of infinite terms whose
coefficients are calculated from operations of derivatives of degree (i).
|
|
(1) |
The
operations of derivatives of degree i is a function
related to , and,
is the approximation error when the series is
truncated in its second term.
The
literature recommends that approximations are made to the surroundings of the
initial point of operation of the model because the errors related to this
approximation are directly proportional to that distance. And in this case, is the starting point. The term
that appear when expanding the Equation (1),
, is interpreted as being an
inclination factor of a linear function that was calculated as a result of the
Taylor expansion. Equation (2) is the result of the substitution of the term
in Equation (1) by the term
, commonly used in the literature.
In the deduction of Equation (2), it is common to consider that
is equal to zero when
is equal to zero. That is, at this point,
there is no change in parameters
and
the belt works as it was initially adjusted.
The
approximation sign that appears in Equation (2) is because the truncation error
was removed from the original expression,
Equation (1). In Taylor's series, the truncation error
is always greater than or equal to the term
. Thus, it is expected that
, a factor that helps in the
development of the expression
. Thus, the truncation error
always remains less than or equal to the value
that is the result of the calculation of
, that is, less than or equal to the
value of
. The value of
also reflects the value of the error in the
approximations. Errors greater than 30% are considered high in the literature
in general. Thus, in this work, this pattern will be considered.
2.2.
The
product transport
The
number of products transported by a conveyor in a given period, , can be described according to the
parameters as shown in Equation (3) (HILTERMANN et al., 2011).
(3)
In
Equation (3) the number of parts transported by the belt is the product between
the belt speed, the carrying capacity, and , which is a scale conversion
constant (HILTERMANN et al., 2011).
is used to convert the time unit of the speed
between days, hours, minutes and seconds, if necessary.
and
represent the percentage of speed reduction
and the percentage of change in effective transport capacity. However,
and
are related by Equation (2) which forms a
system of equations with Equation (3).
3.
METHODOLOGY
Something
around 20 videos related to conveyor belts, which was identified operating on
the factory floor, was analyzed. The transport capacity was measured in the
videos, and through this measurement, it was possible to conclude that belt
conveyors were operating, on average, with something around 44% of their
transport capacity. For this procedure, the passage of each product on the belt
conveyor is marked, the video is paused, areas occupied by-products, and free
on the belt conveyor are estimated, and then the ratio between these areas is
calculated. Afterward, the video is
advanced until the last marked product disappears from the screen, the video is
paused again, and the whole procedure is repeated. An average was applied to
the set of values, and that resulted in a value of 44% for the transport
capacity.
An example of this type
of mechanism can be seen in the video of the Piraquê's
factory in Rio de Janeiro (DEMATIC LATIN AMERICA. Youtube: Dematic Reference Piraque, Rio de Janeiro - Portuguese,
c2016. Available at:
<https://www.youtube.com/watch?v = lFEAZm-Oul0>. Accessed on: Sept. 6,
2019.) showing a conveyor belt operating on the factory floor of a national
industry. This initial study serves as a strong indication that efficient
configurations related to operations with conveyor belts (speed adjustments)
are not usually adopted in many national industries. The system of Equations
(2) and (3) models the relationship between the reduction in speed and the
effect that this reduction has on transport capacity and also the number of
products transported in a period. Figure (1) shows the complete model used.
Figure
1: The model used for the calculation of the speed reduction impact in the
number of products transported.
3.1.
Using
the equations system
To
demonstrate the use of Equations (2) and (3) a case study of one of the
analyzed videos will be presented. As defined in Equation (2), is the ratio between
and
. It is assumed here that different
belt conveyors have different parameters. This is due to the different
construction characteristics of each of these devices. Thus, different belt
conveyors respond differently to the same reduction in speed. In the analyzed
video, parameter
was measured - the estimate of this parameter
depends on measurements made on a running belt.
To
do this, you must maintain the number of parts that arrive at the belt per unit
of constant time, vary the belt speed gradually and for each of these
variations measure the number of parts transported by that belt at that same
time.
Using
Equation (3) it is possible to calculate the value of for each applied
. The linear adjustment of points
and
results in a line whose slope value is the
value of parameter
. The measurement resulted in a
equal to 0.9. In the case study, we will
consider four more tracks whose
values are values
around the calculated for the video. The
parameters are equal to 0.7, 0.8, 0.9, 1.0 and
1.1 for the set of 5 tracks. When measuring the transport speed of the products
by the conveyor (displacement by time) the video concluded that this speed is
2.25 products per second. For the case study, it will be assumed that all five
belt conveyors have a
speed of 2.25 products per second (same as the
treadmill analyzed in the video).
An initial transport capacity () of 44% will also be adopted, a
value achieved by analysis already presented. Thus, when Equation (3) is
applied, it can be concluded that all five conveyors carry a quantity of 85536
products per day (
) in the initial configuration.
Simulating the model, Equation (3), it was possible to obtain the data shown in
the Figure (2). The simulation
was adjusted to convert the time unity from
seconds to days, having a value defined in 86400 seconds per day. The speed
of all five belt conveyor is reduced graduated
from 0 to 25%, it is calculated for each reduction
(Equation (2)) and the amount of
products(parts) transported per day (Equation (3)). The Figure (2) shows the
calculated values by the Equations (2) and (3).
Simulating
the model, Equation (3), it was possible to produce the data presented in
Figure (2). In the simulation was adjusted to convert the speed time unit
from seconds to days, having its value set at 86400 seconds per day. The
speed of all five belts is reduced gradually
from 0 to 25%, it is calculated for each reduction
(using Equation (2)) and the number of
products (pieces) transported per day (using Equation (3)). Figure (2) shows
the values calculated by Equations (2) and (3).
Figure
2: Five different belt conveyors are imagined with each one using different parameters. Equations (2) and (3)
are used to simulate the behavior of transporting parts per day due to the
reduction in speed for each of the belt conveyors. It was considered that all
the belt conveyors initially had the same parameters of speed and effective
transport capacity.
As
expected, the behavior of the belt conveyor concerning the total transport of
products is greatly altered when speed reductions occur. Looking at Figure (2)
it is possible to observe that for the curve where is 0.9, a 10% reduction in speed does not
affect the total quantity of parts transported per day. As in this case,
although there was a reduction in speed, there was also an increase in the
transport capacity and thus the total quantity of parts transported per day was
maintained. This increase in the effective transport capacity offset the
decrease in speed. It is possible to observe that when
is 1.0 the total quantity of products
transported per day does not increase or is maintained with the reduction of
speed.
3.2.
Establishing
boundaries for the problem
As
has been seen, in some of the curves shown the reduction in speed also reduces
the transport capacity. Thus, it is necessary to answer questions such as: -
what is the maximum value that allows speed reductions without
reducing transport capacity? For the answer to this question, we will have to
solve the optimization problem presented in Equation (4).
(4)
Subject to the following restrictions:
|
|
(5) |
As a solution to the problem, it was obtained that must be less than 1 so that all restrictions
of the problem are met, which is the fundamental characteristic of the conveyor
belt.
4.
RESULTS
Using
the model defined by the system of Equations (2) and (3) it is possible to draw
a general solution model (a template) for the problem. This template shows
several possible situations where different parameter settings can be compared.
The results of the model simulations will be centered at the limit point of K since
this limit is our reference and also for the reason that there may be
situations where the total quantity of products transported per day by the belt
conveyor falls so insignificantly with the reduction of the speed that it is
possible to assume that point as being an acceptable point. In the simulations,
a value of 85000, a
value of 2.25 products per second and a
value of 44% will be used. Only speed
reductions (
) that result in
values below 0.3 (30%) will be used.
A
template containing several solutions that start from the initial belt setup
point (,
, and
) is shown in Figure (3). These
solutions include those solutions for belt conveyor that have the value of
parameter
ranging from 0.7 to 1.1. The interpretation of
the graph presented in Figure (3), although it seems complicated, is simple to
understand. An example case will be used with a belt conveyor that has a
parameter defined for a more accessible
explanation.
Figure 3:
Five different belts conveyor are imagined with each one using different
parameters and all starting from an initial configuration
(
,
and
). As there
is a reduction in the initial speed of the belts, each belt takes a different
trajectory over the level curves that define the quantities of parts
transported per day given a specific configuration.
You
can imagine that the belt conveyor you want to adjust to is the one with a of 0.8. It is possible to see that it
transports 85000 parts in its initial configuration with
,
, and
. With a reduction in speed of
almost 20% it still maintains that same amount of parts transported. In the
graph, the dashed line 0.8 remains within the same level curve, 8.5E4. However,
in this case, the estimate has a maximum error of 25% (21250 pieces) for that
point. With a 10% reduction in speed, the same number of products transported
is maintained, however, now the maximum error of the estimate is around 12.5%
(10620 pieces).
The error related to the estimates
is still high and a more accurate study on real situations of conveyors in
operation could provide elements that would allow improving these estimates.
Despite this, the feedback presented allows for a very clear view of the impact
on the number of products transported when the belt speed is changed.
Reductions in belt speed that do not cause changes in the number of products
transported can be adopted as adjustment points that increase the energy
efficiency of the set.
5.
CONSIDERATIONS
In
this work, the study of the relationship between the product transport capacity
and speed on a conveyor belt was approached theoretically. A mathematical model
(Equations (2) and (3)) for this relationship was developed and through this
model, it was possible to demonstrate that in some situations it is possible to
reduce the belt speed without changing one of the main functionalities within an
industrial production line, the number of products transported by a belt
conveyor within a certain period of time. This reduction in speed allows a
reduction in the energy cost by operating the belt conveyor. Using the
mathematical model, it was possible to design a graphical solution (the
template in Figure (3)) that allows easily adjusting the belt conveyor speed.
This simplicity that the graphic tool offers for adjustments on the belt
conveyor transport velocity is the main differential of this work when compared
to the others already published.
This
was a theoretical study, but it shows evidence that this behavior of belt
conveyors can occur in real situations. That is why it is proposed, as future
work, a practical study that proves this theoretical study. It is proposed also
a theoretical study that investigates how the relationship between the
percentage of speed reduction and the percentage of increased transport
capacity is influenced by the quantity and distribution of secondary feeding
lines (other conveyor belts that feed the main conveyor). This theoretical
study is important, as it can show new ways to configure belt conveyors more
efficiently.
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