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Necessary Calculations of Ultra-Light Overhead
Conveyor Systems for In-House Transportation
Batin Latif Aylak1, Cyril Alias1, Hermias C.N. Hendrikse2, Bernd Noche1
1 Department of Transport Systems and Logistics, University of Duisburg-Essen, Duisburg, Germany
{batin.aylak, cyril.alias, bernd.noche}@uni-due.de
2 ESTEQ Engineering (Pty) Ltd, Pretoria, South Africa
h.hendrikse@esteq.com
Abstract – Due to the ever-increasing level of global competition,
logistics companies face difficult challenges on a daily basis. In
order to survive this competition, they need to develop new
technologies. The term ultra-light overhead conveyor system is
relatively novel to the logistics industry. It is a rope-based
conveying system in which the vehicles can move automatically
on the rope using a specific mechanism which drives the vehicle.
The concept and design of an ultra-light overhead conveyor
system are explained by using Computer-Aided Design (CAD)
software. The operating time of the vehicles and recharge time of
batteries are calculated, a number of assumptions as well as
some rope sag calculations are made according to different
scenarios. A discrete event simulation model is built using
Tecnomatix Plant Simulation in order to test the impact of
certain variables on the performance of the system.
I. INTRODUCTION
The classical overhead conveyor system is usually
composed of overhead transportation systems bound to rails
with individually controllable vehicles, the whole coming
together as a complex material flow system [1]. The rail-
based systems are installed according to the desired
transportation paths and performance. The vehicles are
individually maneuverable along the rails and wired places
within the rails manage the electrical supply of the motors [2].
It should be noted here that the majority of publications
discuss the sector of internal transportation and within this
especially take into account the basic implementation of the
overhead conveyor systems [3]. This paper, on the other hand,
focuses on the necessary calculations behind ultra-light
overhead conveyor systems.
These systems are principally used in mid-range and large-
scale batch production – especially in the car industry [4].
They are usually implemented as individually maneuverable
vehicles which undertake the transportation of goods between
warehouses and production areas [5], connect physically
divided rooms with one another in [6] and [7], function as
assembly-shuttles in [8] or as mobile workplaces in [9].
When taking into account the different years of publication,
one recognizes the – at times pronounced – differences in
content published. Articles from the seventies mostly depict
the advantages and disadvantages of the opposing Power &
Free Conveyor system in [10] and [11], as well as the
development of accompanying turnouts, transfer stations and
elevators [12]. Later publications, however, focus on special
designs for the overhead conveyor system vehicle with regard
to load suspension devices in [9], [13] and [14], other
conveyor systems in [15] or improvements in performance –
for example, climbing power [16].
Simulation has been defined as the imitation of the real-
world process or system over time. Simulation tools are
specifically designed to limit transient effects on
measurements, which can be used in estimating a set of
efficiency measures in production systems, inventory
systems, manufacturing processes, material handling and
logistics operations [17].
Two papers on this concept and simulation scenarios have
already been published, namely [19] and [20]. The aim of the
paper at hand is to add necessary technical calculations and
different simulation scenarios. After explaining the vehicle
concept, this article will exemplify these calculations, present
the pertaining simulation model and conclude with
considerations as to the transition from models to real life.
II. CONCEPTUAL DESIGN
This section deals with the conceptual design of the ultra-
light overhead conveyor system. The vehicle concept is a
simpler system technology, as it implements centrifugal force
in order to change the direction as desired. This concept is
based on a one-rope track system, consisting of a polyester
rope. In this concept, no second levels are required for
steering. In addition, no lane change is performed. The
complete system is a closed ropeway network with a single
level.
The vehicle is a lifting unit equipped with an electric motor
Fig. 1. Main components of the concept
complete with bevel gear and hooks similar to those of a
crane mechanism. A slide-mounted wheel and a counter
wheel position the vehicle on the polyester rope.
This concept features a lithium battery supplying the
power. The vehicle is equipped with two actuators, which are
laterally moved out in order to change direction.
Fig. 1 illustrates the main components of the concept at
hand. It also shows how a proposed ropeway network must be
designed to move the vehicle, including a winch with a raised
package, through a steering mechanism using centrifugal
force.
Fig. 2 illustrates the steering profiles. The direction
changing mechanism, i.e. three polyester ropes meeting
through an H-profile, creates a junction, which in turn
establishes a focal point for the vehicle. This point of contact
allows for the division of the track in two directions. The
vehicle can change direction through a linear actuator with T-
tails extending outward. Using this actuator, the vehicle can
be moved linearly to the left or right. This movement on the
x-axis is crucial for steering. Hence, in a sense the vehicle is
guided into the proper direction using the asymmetric steering
profile installed on both sides, which uses the T-tail of the
actuators with the T-opening inwards. As the vehicle
approaches the changing mechanism, the actuator extends
either to the left or to the right according to the required
direction and fits into the steering profile. This tangential
clamping generates a centrifugal force and ultimately
provides the force for the steering on an H-guide profile.
Fig. 3 illustrates the individual components of the vehicle.
A specially designed slide-mounted wheel ensures that it can
move independently along the track system. A spring-loaded
pressure counter wheel ensures the necessary stability and
positioning. The vehicle is independent of the utility grid and
is driven by an electric motor with an angular gear and built-
in lithium battery. Battery recharge is only necessary at
certain time intervals. The linear shaped actuator, enabling
direction changes of the vehicle, is shown in Fig. 3.
In order to change direction, the vehicle must receive the
information to change course before it comes to the track
changing position. This signal is required in order to control
the linear actuators. If instructions are received, the linear
actuator moves out to the left or right and the insertion can
begin.
Due to the one-rope construction, the vehicle can become
unstable and start to swing, since the stabilization effect of the
basic concept is missing in this system. Consequently, a
conical opening must be present to ensure safe insertion. This
assures a secure insertion of the actuator into the T-opening of
the steering section.
III. TECHNICAL CALCULATIONS OF AN ULTRA-LIGHT
OVERHEAD CONVEYOR SYSTEM
In order to choose a suitable rope and to be able to procure
it afterwards, basic observations and calculations are required
in advance for the rope to fully meet its requirements.
Ropes can only absorb traction forces and transmit them to
supporting points. With an ultra-light construction the ratio of
the rope’s net weight (i.e. linear load [N/m]) to the load (i.e.
net weight of vehicle + payload [N]) is so small that it is
rendered technically insignificant for the calculations. The
resulting parallelogram of forces is shown in Fig. 4.
The rope transmits the traction forces Fz to the pillars.
Horizontal and vertical forces emerge on the rope anchorage.
The derivative of vertical force on the hall floor is problem-
free, since the support pillars on the hall floor are to be
anchored for the absorption of the horizontal force.
The horizontal forces decrease with the rising sag and
increase with the dropping sag. In terms of permissible sag
the optimum has to be chosen in order to attain the objective
of an ultra-light construction. Therefore, an overview of the
relation between sag of the rope and force reactions on the
pillars is shown in Fig. 5.
Fig. 2. Steering profiles
Fig. 4. D
raft of parallelogram of forces
Fig. 3. Components of the vehicle
The permissible sag is to be chosen according to conditions
present in the hall where the system will be implemented and
used. Attention should be paid that the horizontal and vertical
forces while choosing the pillar. Selecting a slightly higher
sag can minimize net weight, with the side effect of also
reducing the horizontal force.
A suitable rope acquired on the market must have a
breaking load larger than or the same as 150 000 Newton (i.e.
25 000 N × 6).
After selecting the suitable rope type, additional
calculations will be carried out in order to determine turning
moment, speed and engine capacity. Subsequently a suitable
engine can be chosen for the vehicle. In total, twelve
calculations are necessary and all shall be performed in detail
here.
In order to evaluate the turning moment on a wheel MR, the
traction resistance must be determined, using the following
formula:
MR = FFW × r (1)
The radius is 0.04 meter (r = 0.04m), while FFW stands for
the tractional (or driving) resistance. The latter is the sum
from the air resistance FLuft, the rolling resistance FRoll, the
increase resistance FSteig, as well as the acceleration resistance
FBe, which are presented one by one hereafter.
FFW = FLuft + FRoll + FSteig + FBe (2)
A. Air resistance
To determine the air resistance FLuft, the following formula
can be used:
FLuft = A2 × CW × D × v2 (3)
D stands for the front surface of the vehicle. In the same vein
it concerns the projection surface of the vehicle’s front on a
vertical surface. A maximum value of 1 m² is assumed as a
front surface. Thus, the vehicle is not expected to be larger
than D = 1 m2.
Another parameter of the formula is the drag coefficient CW,
which concerns a dimensionless value that depends on the
vehicle’s form. A human has a drag coefficient of CW = 0.78.
This value was used for the calculation, given the vehicle’s
smaller drag coefficient and the resulting margin of tolerance.
The air density is referred to by A. It changes depending on
the temperature. For the calculation a constant value A = 1.2
kg/m³ will be used.
The driving speed is expressed with v, for which the value v
= 1 m/s is assumed.
When calculating the starting formula (3) with the actual
values, the air resistance amounts to 0.468 Newton.
FLuft = A2 × CW × D × v2
FLuft = (1.2 kg/m³)2 × 0.78 × 1 m² × (1 m/s)2 = 0.468 N
B. Rolling resistance
In order to calculate the driving resistance, the rolling
resistance must be established as well. The following
arithmetic expression serves this purpose:
FRoll = μr × m × g × cos α (4)
In order to avoid sliding, a rubber strap is glued to the rope
pulley, thus developing an adhesive force between the rope
and the pulley.
The rolling resistance coefficient μr depends on the type of
tyres used. A resistance coefficient of 0.015, which also
applies to car tyres on asphalt, is assumed since it can be
regarded as the maximum value. This creates a safety buffer,
seeing as the assumed resistance coefficient μr = 0.015 is
guaranteed to be lower in the context of a real-world
construction. This is justified by the choice of construction
materials, namely a rubber of synthetic fibre. Yet,
recommendations for the combination of the mentioned
materials lack in specialist literature.
The angle α is assumed with a slope of α = 5°.
A maximum value of 40 kg is adopted for the mass,
composed of 20 kg of maximum weight for the load that is
able to move the vehicle, and 20 kg of maximum weight of
the vehicle itself. Hence, m has the value m = 40.
When calculating the formula (4) with the actual values (m
= 40 kg; g = 9.81 m/s²; μr = 0.015; α = 5°), the rolling
resistance amounts to 5.68 Newton.
FRoll = μr × m × g × cos α
FRoll = 0.015 × 40 kg × 9.81 m/s² × cos5° = 5.68 N
C. Increase resistance
The next quantity to be determined is the increase
resistance FSteig. It is the product of mass and acceleration due
to gravity by Sinus Alpha.
FSteig = m × g × sin α (5)
Computing the actual values with (5), the increase
resistance amounts to 34.2 N.
FSteig = m × g × sin α
FSteig = 40 kg × 9.81 m/s² × sin 5° = 34.2 N
Fig. 5. Relation between sag of the rope and force reactions on the pillars
D. Acceleration resistance
The acceleration resistance FBe can be determined by means
of the following formula:
FBe = (ei × mV + mP) × a (6)
The parameter ei corresponds to rotational inertia, which
must be evaluated in advance. The mass of the vehicle is
known as mV, the vehicle load capacity as mP, which are
assumed with their maximum weight of 20 kg each. The
measured acceleration of the vehicle a is known as 0.5 m/s².
For the calculation of the rotational inertia ei, the quantities
displayed in Fig. 6 also need to be considered.
While JRolle is defined as the mass moment of inertia of
wheels, JWelle is defined as mass moment of inertia of the
shaft. The mass moment of inertia refers to the upper wheel,
since it is the one connected to the engine.
A further parameter to determine the rotational inertia ei is
the dynamic radius (without deformation) rdyn. The entire
formula to calculate the rotational inertia ei reads as follows:
ei = [(JRolle + JWelle)/(m × rdyn²)] + 1 (7)
First, the yet unknown quantity of mass moment of inertia
of the wheels JRolle must be determined as follows:
JRolle = [mR × (r1² + r2²)] / 2 (8)
The illustration featured in Fig. 6 will help with the
calculation of this formula by yielding the following values:
r1 = (15 mm) / 2 = 7.5 mm = 0.0075 m
r2 = (90 mm) / 2 = 45 mm = 0.045 m
rdyn = middle radius
mR = 0.6 kg
By means of quantity insertion the formula (8) delivers the
following sum:
JRolle = [0.6 kg × ((0.0075 m)² + (0.045 m)²)] / 2
JRolle = 6.25 × 10−5 kg×m²
The mass moment inertia of the shaft JWelle can be
calculated in such a way that the product of the mass and
squared shaft radius is divided by two.
JWelle = (m × rW²) / 2 (9)
By calculating the formula (9) with the actual computation
values (m = 0.118 kg and rW = 0.010 m), JWelle is determined.
JWelle = (m × rW²) / 2
JWelle = [0.118 kg × (0.010 m)²] / 2 = 0.59 × 10−5 kg×m²
Since two quantities of the mass moment inertia, JRolle and
JWelle, are available, they can be integrated into the formula (7)
in order to determine the rotational inertia ei.
ei = [(JRolle + JWelle)/(m × rdyn²)] + 1
ei = [(6.25 × 10−5 kg×m² + 0.59 × 10−5 kg×m²) / (40 kg ×
(0.045 m)²)] + 1 = 1.00084 ≈ 1
Now that all quantities needed to establish the acceleration
resistance FBe are known, they can be included in its
calculation of the formula (6) in order to gain the acceleration
resistance of 20 Newton.
FBe = (ei × mV + mP) × a
FBe = (1 × 20 kg + 20 kg) × 0.5 m/s² = (20 kg + 20 kg) × 0.5
m/s² = 40 kg × 0.5 m/s² = 20 N
E. Tractional resistance
All quantities necessary for the determination of the
tractional (or driving) resistance FFW have been used for the
computation of formula (2). The driving resistance equals
60.528 Newton.
FFW = FLuft + FRoll + FSteig + FBe
FFW = 0.468 N + 5.86 N + 34.2 N + 20 N = 60.528 N
F. Turning moment on a wheel
On the basis of this completed step, it is now possible to
undertake the originally targeted calculation of the turning
moment of the wheel MR. The turning moment can be
asserted as 2.4212 Newton meter.
MR = FFW × r
MR = 60.528 N × 0.004 m = 2.4212 Nm
G. Turning moment
Based on the turning moment of the wheel, the calculation
of the turning moment n is enabled. It must be taken into
account that the angular speed ω is determined from the
quotients of speed v and radius r.
n = (ω × 60) / (2 × π) (10)
n = (v × 60) / (r × 2 × π) (11)
After converting the formula (11) accordingly and inserting
the known values, the turning moment is 238.73 rotations per
minute.
n = (v × 60) / (r × 2 × π)
n = (1m/s × 60) / (0.04 m × 2 × π) = 238.73 rotations/min
Fig. 6.
Graphic to determine the mass moment of inertia of the wheels
Fig. 7. Exemplary distance
to calculate the driving time of the vehicle
H. Engine capacity
The engine capacity P forms another physical quantity that
is to be determined. It can be calculated from the product of
force and speed. Another possibility is to derive it from the
product of turning moment and angular speed.
P = F × v (12)
P = M × ω = (M × v) / r (13)
Using the actual values in the formulae (12) and (13), the
engine capacity of 60.52 W is ascertained.
P = F × v
P = 60.52 N × 1 m/s = 60.52 W
P = (M × v) / r
P = (2.4212 Nm × 1m/s) / 0.04 m = 60.52 W
I. Driving time of vehicle
It is also essential how much driving time the vehicle needs
for one distance. Since this depends on the length of each
required distance, only exemplary calculations are possible. It
refers to the exemplary distance presented in Fig. 7.
The general formula to calculate time results from the
quotients of the route length and speed:
t = s / v (14)
While the speed is already known to be v = 1 m/s, the
overall length of the route consists of individual sections
marked in Fig. 7 amounts to 50 meters for this example.
s = 18.75 m + 12.5 m + 12.5 m + 6.25 m = 50 m
The time here amounts to 50 seconds, as a consequence of
the values of the parameters entered into the formula (14).
t = s / v
t = (50 m) / (1 m/s) = 50 s
In order to determine the driving time of the vehicle, its
need to decelerate shortly before each point has to be taken
into consideration. Therefore, the time is multiplied with a
factor of 1.5, so that the driving time of the vehicle would
amount to 75 seconds for the example route.
tf = t × 1.5 = (50 s) × 1.5 = 75 s
The same procedure allows for the calculation of the
driving time for all other possible distances.
J. Energy supply
The energy supply of the vehicle is ensured by means of an
integrated lithium battery. It can be charged in a specially
provided charging station. It is advisable to avoid a total
discharge and to ascertain that the vehicle comes to the
charging station before only 20% of battery capacity remains.
By charging from around 80 % battery capacity, the charging
current could only be powered up in reduced form, which
would impede the battery charge to 100%.
In case of longer-term and regular use of the vehicle and to
foster long durability, it is advisable to keep the battery at a
capacity between 20 and 80% during use. This also results in
the respective percentage values of the calculation displayed
in Table I.
TABLE I
OVERVIEW OF THE POWER-CONSUMING DEVICES AS WELL AS THEIR USAGE
Device
Usage (in W)
SPS Device
7
LED Light (warning light)
7
Cylinder Lifting Magnet
8
Electrical Engine
93
Inductive Sensor
2.4
Reflex Switch 1
4.8
Reflex Switch 2
4.8
Total
127
The following parameters are known:
Battery voltage: UAkk = 24 V
Battery capacity: CAkk = 40 Ah
Energy consumption: Pges = 120 W
Battery remaining energy: 20%
Charging current: I = 6 A
K. Operating time of vehicle
In order to calculate the operating time of the vehicle the
following formula is used.
Toperating time = [(CAkk × UAkk) / Pges] × 80% (15)
The operating time of the vehicle for the predefined
charging level equals 6.05 hours.
Toperating time = [(CAkk × UAkk) / Pges] × 80%
Toperating time = [(40 Ah × 24 V) / 127 W] × 80 % = 6.05 h
L. Charging time of vehicle
The charging time is derived from the following
calculation.
Tcharging time = (CAkk / I) × 80% × 1.3 (16)
The charging time amounts to 6.93 hours.
Tcharging time = (CAkk / I) × 80% × 1.3
Tcharging time = (40 Ah / 6 A) × 80% × 1.3 = 6.93 h
IV. SIMULATION MODEL EXPLANATION
This model focuses on the analysis of the one ultra-light
overhead conveyor system in one application area. This
application area could be a warehouse, a depot, a production
area or an assembly department. The hypothetical application
area in the simulated model serves daily from 8 am to 4 pm.
Packages must be delivered between the four stations. Each
station has a loading and an unloading station. Fig. 8
illustrates the layout of the application area. Setup and
dismantling are given priority. General functions and
Fig. 8. Layout of the application area
regularly recurring processes, such as the charging of the
lithium battery and lane changes at intersections or in curves,
are clarified. The system is located and connected on the
same level, thus constituting a closed rail network.
Furthermore, all work and transfer places, in which people
are deployed as assistants, are connected within one network
segment with one another. Corner or mizzen masts support
the polyester rails.
Similar to a crane, the vehicle is a hoisting unit equipped
with an EC motor, bevel gears and a lifting hook. Using a
pulley, the vehicle is positioned on the polyester rope.
Lithium batteries provide the energy supply.
The vehicle is equipped with two actuators extendable from
the side, which are indispensable for direction changes, and
thus take advantage of centrifugal force. A change in
direction does not require the vehicle to stop but can take
place whilst the system is moving. Furthermore, the entire
system is equipped with inertial sensors, which are installed at
regular intervals in order to measure velocity and positioning.
The installed system is thus able to determine how fast each
vehicle is moving and where it is located. Congestion and
collisions can also be avoided in this manner.
Another very important component is the accumulator
charging station, directly attached to the conveyor. The
vehicle does not have to leave the installation but instead
drives directly to the charging station, running parallelly to
the transport lane. An equally significant aspect is the way in
which the charging process takes place since this can
contribute to the battery’s lifespan, idle times and, above all,
to the system efficiency as a whole, including velocity. These
and other recurring processes, such as stations designed for
lane changes, are expanded on in the model.
Plant Simulation is a discrete-event-simulation tool that
creates digital models of logistics systems. Thus, the
characteristics of a system are explored and its performance
optimized. These digital models allow running experiments
and examining what-if scenarios without disturbing existing
production systems or – when used in the planning process –
long before production systems are actually installed [18].
Fig. 9 shows a simulation model in design edition.
TABLE II
OVERVIEW OF SCENARIOS
Scenario
Scen. 1
Scen. 2
Scen. 3
Scen. 4
Failures
YES
YES
YES
NO
Vehicle Speed
0.8 m/s
0.9 m/s
1 m/s
1 m/s
Loading Time
20 s
20 s
20 s
20 s
Battery Reserve
20
20
20
20
Station 1
745
751
753
752
Station 2
794
797
799
798
Station 3
807
836
807
839
Station 4
823
830
829
826
Total
3,001
3,188
3,289
3,308
The exact dimensions of the application area are defined in
the model, which are assumed to equal 625 m2. Moreover, the
vehicle speed is also defined, as well as loading and
unloading times for each station, including the battery
recharge station.
ShiftCalendar defines the eight-hour shift lasting seven
days a week. The model is set up with the EventController to
start at eight o’clock in the morning and end after seven days.
When a vehicle fails, it turns red and awaits repair. The model
is set up to charge the battery up to a value of 50 (assumed as
80% of full capacity) and to recharge it automatically when it
reaches a threshold value of 10 (20%). The new battery
charge indicators are added in the model. They will not show
a battery recharge, which takes seven hours with batteries
enduring for six hours. Table II shows the parameter and
assumptions of the different scenarios examined.
Fig. 10 is a complete summary of all the simulation runs
showing the results after having taken into consideration
failures as well as vehicle speed, loading time, battery reserve
and throughput values for each station. As can be seen when
comparing scenarios 1, 2 and 3, increasing the speed
increases throughput for all stations. Scenario 4 shows the
increase in throughput when failures are ignored but the
increase is minimal, indicating that a technical availability
value of 95% does not have a significant impact on the model.
Fig. 9. Simulation model in design edition
Fig. 10. Scenario throughput
V. CONCLUSION
This paper aims to illustrate necessary calculations of ultra-
light overhead conveyor systems used for in-house
transportation purposes. There are a lot of applications of
overhead conveyor systems in the industry already. However,
these applications are only eligible for heavier loads. In this
case, the system was designed for light and ultra-light loads.
Moreover, using ropes instead of rail makes it possible to
rearrange the complete configuration of the system easily and
swiftly, which would be impossible with rail-based conveyor
systems. Thus, this proposed conceptual model is fairly more
flexible than previous overhead conveyor systems.
VI. OUTLOOK
In order to gain more precious results, it is necessary to
construct a real application of the ultra-light overhead
conveyor system. Once this has occurred, a simulation model
will show concrete results. Using these results, the ultra-light
overhead conveyor system can be compared with other
transport systems. This comparison will show whether or not
ultra-light overhead conveyor systems are profitable for firms.
According to these results, necessary changes should be
applied to the real system. After all, results of simulation runs
do not show the optimal solution – they just show the real
performance of the system.
Another aspect is the connection of such innovative
transport systems to logistics control towers in order to
provide decision-makers with opportunities of real-time
process monitoring and control on superior levels [21].
ACKNOWLEDGMENT
The authors cordially thank those colleagues at the
Department of Transport Systems and Logistics of the
University of Duisburg-Essen, Germany, that have supported
this work actively by means of inspiring discussions and
fruitful collaboration.
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