Article citation information:
Blatnický,
M., Dižo, J., Molnár,
D., Droździel, P. Design of a
manipulator of a conveyor for bulk materials – calculation of the center
of gravity of the conveyor. Scientific
Journal of Silesian University of Technology. Series Transport. 2022, 117, 43-56. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2022.117.3.
Miroslav BLATNICKÝ[1],
Ján DIŽO[2],
Denis MOLNÁR[3],
Paweł DROŹDZIEL[4]
DESIGN OF A MANIPULATOR OF A CONVEYOR FOR BULK MATERIALS –
CALCULATION OF THE CENTER OF GRAVITY OF THE CONVEYOR
Summary. The
predominant goal of the research presented in this paper is the design of a
manipulator for a conveyor of bulk materials based on the given requirements.
This issue is an emerging topical one mainly for the reasons of increasing
efficiency and speed, as well as the safety of maintenance of machines and
equipment. Especially, another essential aspect is the reduction of the
physical strain on operators during service operations on the conveyor of bulk
materials. The introductory part of this paper attends to the materials
used for the production of steel structures, their technological processing, as
well as different types of joining of their components. The practical part was
set out to ascertain the mass and position of the center
of gravity of the load itself – the conveyor. From the perspective
of acting, it loads the entire proposed structure, although in different
operating modes.
Keywords: steel
structure, analytical calculation, center of gravity,
technology, handling
1. INTRODUCTION
Today, steel
structures (Figure 1) are exploited in technical practice in an extremely wide
range of applications and represent a significant element not only in
contemporary mechanical engineering but also in civil engineering and
architecture. The area of construction of steel structures needs to be analyzed
for design, legal standards and regulations, type of loading, construction
material, and also from the perspective of the mechanical tests of the material
used and its mechanical, physical, technological and chemical properties.
Moreover, safety and reliability in long-term use in conjunction with the
economy of the given construction are other essential aspects for the engineers
of steel structures [1-4].
Today, an
enormously wide range of different steels is produced, intended primarily for
the manufacture of machinery, equipment, and construction engineering. Through
the right selection of materials, it is possible to achieve the ideal service
life of the structure under a given load, and at the same time, minimize costs.
Accordingly, the economy of the project can be maximized [5-7].
Fig.
1. The proposed steel structure – conveyor frame (orange) and trolley
(gray) together with conveyor of bulk materials
All steels
have their own specific properties, which result from their chemical
composition and technologies used in processing (steelmaking) in the course of
the actual production. Mechanical properties characterize how the material
withstands the action of applied external force. Steels used in the
construction of steel structures are commonly stressed in various ways. Thus,
their mechanical properties are substantial. The mechanical properties are
conclusively a decisive factor in selecting the appropriate material. Given the
mechanics, if we apply an external force to an element of the structure, a
deformation will occur. Moreover, if we reach the limit state, a fracture will
occur and expand. The final shape change is the result of the interaction
between the external and internal forces. The interaction acts against the
induced deformation. In the case of the component returning spontaneously to
its original shape after unloading, it is elastic deformation. Conversely, when
the component does not return to its original shape after unloading and remains
deformed in varying degrees, then it is a plastic deformation [8-12].
Steel
structures consist of various steel elements made chiefly from metallurgical
semi-finished products. For the sake of the simplification of transport,
production as well as assembly, various joints are exploited in the creation of
steel structures. The connections between the individual structural elements
are realized through the mentioned joints. Based on the possibility of
disassembling the structure after its assembly, we separate the joints into
detachable and non-detachable [13-15].
The connected
components interact with each other by action and reaction forces, which must
be transmitted smoothly through the joints. When designing the technical
parameters of metal structures, it is required to involve the condition of the
resulting rigidity of the unit in the design requirement. This rigidity is
ensured, moreover, through the connection of all the elements into one unit.
Each commonly used joint has its own characteristics associated with the
load-carrying capacity, stress distribution, and assembly procedure, in
addition to the impact on the structural properties of the joined components.
Every designer should be thoroughly acquainted with all the above-mentioned
facts at an early stage of the design. It is crucial to consider the level of
stress and the manner of the applied loads to determine what type of joint is
suitable for a given purpose. Therefore, the designer must have accurate
information about the cyclic stress and impact stress along with their impact
on the structures [16, 17].
2. REQUIREMENTS
IMPOSED FOR THE PROPOSED STEEL STRUCTURE
The
equipment is dedicated to being integrated into an existing production line for
packing milk powder into bags. The device is located on a supporting structure
above the milk powder filling machine. The structure must not interfere with
the operation of the filling line. For this reason, it must be anchored to the
ceiling at a height of 4.20 m above the floor. The design of the device needs
to be adapted to the requirement to be able to wash the tank. For the sake of
installation of the equipment in a food business, it is desirable to make the
supporting structure from stainless steel.
The
primary element of the device is a rotary feeder, which ensures the following
three requirements:
- to separate, using
pressure, the buffer hopper compartment, which is pressurized by a bag filler,
in which a required atmospheric pressure is,
- to prevent the transfer
of explosion and flame from the hopper compartment to the bag filler in case of
an explosion of milk powder in the buffer hopper. In this case, it concerns the
occupational safety of the workers operating the bag filler,
- to ensure the uniform
supply of milk powder into the bag filler, which has a great influence on the
accuracy of a bag filler weighing.
The rotary
feeder is required to be ATEX certified, which
guarantees the applicability of the rotary feeder for the separation of two
spaces in the event of an explosion. The materials used for the production of
all parts of the rotary feeder that come into contact with the material to be
conveyed need to be certified for direct contact with foodstuffs. In addition,
the electric gearbox of the rotary feeder shall be adapted for speed control
using a frequency converter to regulate the power as per the needs of the milk
powder filler to bags.
The
rotary feeder is connected to the intermediate hopper by a short stainless
steel pipe and a fabric compensator, which minimizes the transmission of
vibrations from the buffer hopper to the bag filler. For this reason, the
influence on the strain gauge weight sensors is minimized. The compensator is
rated for a reduced blast pressure to match the resistance of the buffer
hopper.
Based
on the above requirements, a manually operated manipulator of bulk material
conveyor will be designed along with a structure for its anchoring and travel.
The mentioned manipulator and its travel need to be installed for the sake of
service or maintenance interventions, moreover, for the reason of cleaning the
conveyor itself as well as the interconnecting pipe joining the hopper of the
product (milk powder) to the equipment employed for packaging the milk powder.
There is plenty of options for dealing with such servicing operations, for
example, handling with external manipulators, hoists, and mechanical or
electric forklifts. Nevertheless, through the food operation, the high demands
on cleanliness, the weight of the conveyor itself together with its drive of
approximately 230 kg, as well as the economy of the solution itself, it is
evidently the optimal solution. This is further elaborated in this paper.
Because of the acting of relatively small passive resistances during the
movement of the manipulator (trolley) on the travel, it will be manipulated
through pushing by the operator. The conveyor, in this case, is considered only
as a load acting on the structure, given the fact that it is supplied as a
whole by an external company.
Fig.
2. 2D model of a conveyor of bulk materials in a
retracted state with the individual components marked and the distances of
their centers of gravity considered
For
the solution, the first point of the issue is to deal with the load itself,
that is, the conveyor (Figure 2). It loads the whole structure. Individual
quantities and dimensions marked in Figure 2 are as follows: FGTR
– gravitational force of the lid, body and rotor of the conveyor, R1
– total reaction force sought in the arrangement when the rotor is
retracted, FGST
– gravitational force of the coupling of the drive with the guide rods, FGP
– gravitational force of the gearbox of the drive, FGM –
gravitational force of the electric motor of the drive, b1 – distance
between the center of gravity of the body with the rotor and the center of
gravity of the motor, b2
– distance between the center of gravity of the body with the rotor and
the center of gravity of the coupling, b3 –
distance between the center of gravity of the coupling and the center of
gravity of the gearbox, b4
– distance between the centers of gravity of the gearbox and the motor, l1
– searched distance between the center of gravity of the body with the
rotor and the center of gravity of the system, l2 – searched
distance between the center of gravity of the coupling with the rods and the
center of gravity of the system, T1 – the center of gravity of the system of
conveyor with the rotor retracted, T2 – the center of gravity of the coupling,
T3
– the center of gravity of the gearbox, T4 – the center
of gravity of the electric motor, T5 – the center of gravity of the body of
the conveyor with rotor.
It
is indispensable to determine the position of the center of gravity (dimensions
l1, l2 in Figure 2) of the
conveyor itself along its length (z-axis).
Additionally, to determine the position of the center of gravity within the
frame of the z-axis in different
operating modes of the device, or at the most unfavorable condition for
stresses on the trolley structure and the supporting structure. Furthermore, it
will be necessary to calculate the center of gravity of the trolley-conveyor
system, which will jointly load the proposed support structure. Due to the
rotational symmetry of the conveyor used, it is not required to attend to the
calculation of the center of gravity in the x-axis
and y-axis.
3. CALCULATION OF THE CENTER OF GRAVITY OF THE CONVEYOR
Because
it was not possible to obtain a functional CAD model of the conveyor used and
the manufacturer did not indicate the position of the center of gravity of this
device, it was essential to divide the device into several parts. Accordingly,
to ascertain the center of gravity of the whole system based on their masses
and positions of the centers of gravity (Figure 2). The system is made up of an
extension lid, a rotor, guide rods, a conveyor body, a coupling, a gearbox and
a drive electric motor. The centers of gravity of the individual parts were
determined in two ways. First is rough modeling in Autodesk Inventor and the
subsequent determination of the center of gravity through this program. While
the second is estimation regarding the known geometry and knowledge of the
internal arrangement of the components. The length dimensions were determined
from the measurements of the model, as supplied by the company, in the Autodesk
Inventor environment. As aforementioned, primarily, it is decisive to attend to
the position of the center of gravity of the conveyor within the frame of the
z-axis in the condition with the rotor and lid retracted, that is, in the
operating position.
First,
it is essential to determine the forces acting in the system from the known
values of the masses and the gravitational acceleration in line with equations
(1 - 4):
where
mTE
[kg] – mass of the conveyor body mTE = 130.2 kg, mR [kg] – mass
of the conveyor rotor mR
= 11 kg, mV [kg] –
mass of the conveyor lid mV
= 22.8 kg, mS
[kg] – mass of the coupling of the drive mS = 6 kg, mT
[kg] – mass of the two guide rods mT = 2.10 kg, mP [kg] – mass
of the gearbox of the drive mP = 26 kg, mm
[kg] – mass of the motor of the drive, g
[m∙s-2] – gravitational
acceleration g = 9.81 m∙s-2. Substituting the values into the
equations (1-4) and solving the equations, we obtain:
- FGTR = 1 608.84 N,
- FGST = 255.06 N,
- FGP = 255.06 N,
- FGM =
137.34 N.
Based
on the detected weights, it is possible to exploit the equilibrium condition
(5) to determine the value of the reaction at the center
of gravity of the whole system T1 (Figure 2):
By
virtue of the force and length parameters, we determine the position of the
center of gravity of the conveyor in the operating position. It can be seen from Figure 2 that the
sum of l1
+ l2
= 345.5 mm. Employing the moment equilibrium condition (6), we can determine
the dimension l1 sought:
Subsequently,
we can calculate the dimension l2 using the equation (7):
Substituting
the values into equations (5 - 7) in conjunction with solving the equations, we
obtain:
- R1 =
2 255.86 N,
- l1 =
144.31 mm,
- l2 =
201.19 mm.
Based on the
calculated center of gravity in the z-axis, it
emerges that there is no extreme change in the center
of gravity position despite the considerable distance of the overhang of the
conveyor drive. This phenomenon occurs because the drive with guide rods is
balanced through the ultra-heavy cast iron body of the conveyor.
Further, it
was required to calculate the position of the center of gravity of the conveyor
in the position with the rotor extended. This mode is applied in cases where
from the hygiene perspective, it is demanded to clean the inside of the
conveyor or to perform other types of maintenance. In this case, identical
masses as in the previous calculations have been certainly assumed. In
addition, the same position of the center of gravity of the
motor-gearbox-clutch system as in the previous case has been deemed because
there is no movement (Figure 3). Individual quantities and dimensions are as
follows: FGRV
– gravitational force of the conveyor lid and rotor, FGT –
gravitational force of the guide rod, FGO – gravitational force of the middle
part of the conveyor body, FGS – gravitational force of the coupling, FGP
– gravitational force of the drive gearbox, FGM –
gravitational force of the electric motor of the drive, c1 – distance
between the center of gravity of the lid with the rotor and the center of gravity
of the guide rods, c2
– distance between the center of gravity of the guide rods and the center
of gravity of the conveyor body, c3 – distance between the center of gravity
of the body and the center of gravity of the coupling, c4 – distance
between the centers of gravity of the coupling and the gearbox, c5
– distance between the center of gravity of gearbox and the center of
gravity of the motor, l3
– searched distance between the center of gravity of the guide rods and
the center of gravity of the system, l4 – searched distance between center of
gravity of the system and center of gravity of the body, T11 –
center of gravity of the conveyor lid with rotor, T12 – center of
gravity of the guide rods, T6 – center of gravity of the conveyor
system with the rotor extended, T7 – center of gravity of the conveyor
body, T8
– center of gravity of the coupling, T9 – center of
gravity of the gearbox, T10
– center of gravity of the electric motor, R2 – total
reaction sought in the system with the rotor extended.
Fig. 3. 2D model of a conveyor of bulk materials in an extended
state with the individual components marked and the distances of their centers of gravity considered
For
equations (8 - 11), we determine the forces acting in the system, whereby the
symbols from the previous calculation are retained:
Substituting the values into the given equations in
conjunction with solving the equations, we obtain:
- FGRV = 331.58 N,
- FGO = 1 277.26 N,
- FGT = 98.1 N,
- FGS =
58.86 N.
Because
the identical mass of the whole system as is in the previous case, the value of
the reaction R2
= R1
was considered following the equation (5). Based on the given knowledge, it is
feasible to determine the position of the center of gravity of the conveyor in
the operating position using the moment equilibrium condition (12), when we
determine the searched dimension l3 as:
Figure
3 shows that the sum of l3
+ l4
= 366.5 mm. Employing the acquired knowledge, we are able to determine the
distance between the center of gravity of the system and the center of gravity
of the body in the extended state. The calculation of the dimension l4 is
then given by equation (13):
Fig. 4. A 3D CAD model of the designed trolley with individual wheel
markings
Substituting the values into equations (12) and (13)
and solving the equations, we obtain:
- l3 =
327.97 mm,
- l4 =
38.53 mm.
Thus,
the position of the center of gravity of the conveyor
is ascertained. A conceptual design of the trolley (Figure 4) emerges from the
geometry of the conveyor. The trolley will be part of the proposed manipulator
and it will function as a conveyor carrier. After the preliminary design of the
shape of the trolley, it will be possible to determine the longitudinal and
transverse position of the center of gravity of the
entire conveyor trolley through further calculations. This assembly will load
the proposed supporting steel structure - a track of the manipulator. Because
the original design of the trolley is created in Autodesk Inventor, it was
possible to determine directly in this software the position of the center of gravity of the trolley itself in both the
transverse and longitudinal directions. The software determined the weight of
the trolley based on the model as mVO = 23 kg.
The
selected material for the trolley is steel EN X5CrNi18-10 with yield strength Re = 180 MPa. The total weight of the conveyor
including flanges, rubber seals and fasteners in the form of bolts, nuts and
washers (Figure 5) is mGTP
= 255.91 kg. Individual
components are listed in Table 1.
Fig. 5. Technical drawing of the conveyor
trolley
Tab. 1
A list of items of the conveyor trolley
|
Item |
Description |
Drawing - standard |
Material |
Qty |
Weight [kg] |
|
1 |
Trolley frame |
VT 213 132 |
DIN 1.4301 |
1 |
12.882 |
|
2 |
Wheel |
VT 313 116 |
DIN 1.4301 |
8 |
0.857 |
|
3 |
Axle pin |
VT 313 117 |
DIN 1.4301 |
8 |
0.257 |
|
4 |
Bolt M10x20 |
DIN 933 |
DIN 1.4301 |
8 |
0.024 |
|
5 |
Washer Ø10 |
DIN 128 |
DIN 1.4301 |
8 |
0.002 |
|
6 |
Washer Ø10 |
DIN 9021 |
DIN 1.4301 |
8 |
0.012 |
|
7 |
Bolt M16x28 |
DIN 933 |
DIN 1.4301 |
8 |
0.081 |
|
8 |
Washer Ø16 |
DIN 128 |
DIN 1.4301 |
8 |
0.008 |
|
9 |
Washer Ø16 |
DIN 125 |
DIN 1.4301 |
8 |
0.011 |
|
10 |
Bearing PTFE 25x35 |
– |
PTFE |
8 |
0.002 |
Based
on the known distance, we can assume that the sum of the values of distances of
the individual forces from the central center of
gravity is equal to the value of distance of 108 mm, that is, l5 = l6 + l7 =
108 mm. In the case of the longitudinal position of the center
of gravity, we consider the distance between the centers
of gravity of the conveyor with flanges and the trolley is l5 = 108 mm, based on
the model in Autodesk Inventor (Figure 6). Dimensions and quantities are as
follows: FGTP
– gravitational force of the conveyor with flanges and fasteners, FVO
– gravitational force of the trolley, l6 –
longitudinal distance between the center of gravity of the conveyor and the
center of gravity of the trolley-conveyor system, l7 – longitudinal
distance between the center of gravity of the system and the center of gravity
of the trolley, l5
– longitudinal distance between the center of gravity of the conveyor and
the center of gravity of the trolley, T13 – center of gravity of the
conveyor-trolley system in the longitudinal direction, T14 – center of
gravity of the conveyor with flanges and fasteners in the longitudinal
direction, T15
– center of gravity of the trolley in the longitudinal direction, R3
– total reaction sought in the center of gravity of the trolley-conveyor
system.
Fig. 6. A
longitudinal center of gravity of a system of the conveyor with trolley
First,
it is essential to determine the forces acting in the system from the known
values of the masses and the gravitational acceleration in line with formulas
(14) and (15):
where mGTP
[kg] - mass of the conveyor with flanges and fasteners mGTP = 255.91 kg, mVO
[kg] - mass of the trolley mVO = 23 kg, g [m∙s-2]
- gravitational acceleration g = 9.81
m∙s-2.
Substituting the values into the equations (14) and
(15) in conjunction with solving the equations, we obtain:
- FGTP =
2 510.477 N,
- FGVO =
225.06 N.
Second,
based on the detected weights, the longitudinal position (l6, l7) of
the center of gravity T13 can be determined
using both the equilibrium condition (16) and equation (17) (Figure 6):
Substituting
the values into equations (16), (17) and subsequently solving the equations, we
obtain:
- l6 =
8.91 mm,
- l7 =
99.1 mm.
A case of the transverse
center of gravity is deemed as the most negative case. In other words, it is
the case in which the center of gravity of the conveyor is the most distant
from the center of its body (Figure 7), that is, the transverse center of the
trolley. Quantities and dimensions marked in Figure 7 are as follows: FGTP
– gravitational force of the conveyor with flanges and fasteners, FVO
– gravitational force of the trolley, l8 – a
transverse distance between the center of gravity of the conveyor and the
center of gravity of the trolley-conveyor system, l9 – a
transverse distance between the center of gravity of the system and the center of
gravity of the, l1
– a transverse distance between the centers of gravity of the conveyor
and the trolley, T16
– center of gravity of the conveyor-trolley system in the transverse
direction, T17
– center of gravity of the conveyor with flanges and fasteners in the
transverse direction, T18
– center of gravity of the trolley in the transverse direction, R3
– the total reaction sought in the center of gravity of the
trolley-conveyor system. Such an instance occurs when the conveyor rotor is
retracted into the body. We consider the trolley as a transversely symmetrical
body.
Fig. 7. A
transverse center of gravity of the system of the conveyor with trolley
Based
on the weights (remain same as for the longitudinal direction), the
longitudinal position (l8, l9)
of the center of gravity T16 can be
determined using the equilibrium condition (18) and equation (19) (Figure 7):
Substituting
the values into equations (16) and (17) and solving the equations, we obtain:
- l8 =
11.88 mm,
- l9 =
132.4 mm.
4. CONCLUSION
This paper
focused on the analytical quantification of the masses and the center of gravity positions of the conveyor of bulk
materials. The conveyor will load the proposed structure in operation in
diverse operating modes. Because it was not feasible to obtain a functional CAD
model of the conveyor (supplied by an external company) and the manufacturer
did not even indicate the position of the center of
gravity of this device, it was necessary to divide the device into several
parts and determine the center of gravity of the
whole conveyor based on their masses and positions of the centers
of gravity. After considering the geometric and mass parameters of the
conveyor, a trolley was designed to move the conveyor in operation. Ultimately,
the determined sub-target can be regarded to have been met.
Future
research needs to be on calculations of reactions of the conveyor track from
the trolley transmitted through the prismatic wheels. Subsequently, it will be
attainable to determine the bending moments induced on the supporting structure
(track of the trolley) and to calculate the resistances acting against the
movement of the trolley. These will then be needed in the design of the
conveyor´s manipulator.
Source of
funding
This
research was supported by the Cultural and Educational Grant Agency of the
Ministry of Education of the Slovak Republic under project No.
KEGA 036ŽU-4/2021:
Implementation of modern methods of computer and experimental analysis of the
properties of vehicle components in the education of future vehicle designers.
Similarly, this work was also supported by the
Cultural and Educational Grant Agency of the Ministry of Education of the
Slovak Republic under project No. KEGA
023ŽU-4/2020: Development of advanced virtual
models for studying and investigation of transport means operation
characteristics.
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Received 07.07.2022; accepted in
revised form 15.09.2022
Scientific Journal of Silesian University of Technology. Series
Transport is licensed under a Creative Commons Attribution 4.0
International License
[1] University of Žilina,
Faculty of Mechanical Engineering, Department of Transport and Handling
Machines, Univerzitná 8215/1, 010 26 Žilina, Slovakia. Email:
miroslav.blatnicky@fstroj.uniza.sk. ORCID: https://orcid.org/0000-0003-3936-7507
[2] University of Žilina,
Faculty of Mechanical Engineering, Department of Transport and Handling
Machines, Univerzitná 8215/1, 010 26 Žilina, Slovakia. Email: jan.dizo@fstroj.uniza.sk. ORCID: https://orcid.org/0000-0001-9433-392X
[3] University of Žilina,
Faculty of Mechanical Engineering, Department of Transport and Handling
Machines, Univerzitná 8215/1, 010 26 Žilina, Slovakia. Email: denis.molnar@fstroj.uniza.sk.
ORCID: 0000-0002-9540-8636
[4] Faculty of Mechanical Engineering,
Lublin University of Technology, ul. Nadbystrzycka 36, 20-618 Lublin. Email:
p.drozdziel@pollub.pl. ORCID:
https://orcid.org/0000-0003-2187-1633