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A behavior model for Digital Twins of vacuum suction cups
Valentin Stegmaiera,b,c,*, Tobias Eberhardtc, Walter Schaafc, Nasser Jazdib, Michael Weyrichb
aGraduate School of Excellence advanced Manufacturing Engineering (GSaME), University of Stuttgart, Nobelstraße 12, 70569 Stuttgart, Germany
bInstitute of Industrial Automation and Software Engineering, University of Stuttgart, Pfaffenwaldring 47, 70569 Stuttgart, Germany
cJ. Schmalz GmbH, JohannesSchmalzStraße 1, 72293 Glatten, Germany
* Corresponding author. Tel.: +49 7443 2403 7443; Email address: valentin.stegmaier@gsame.unistuttgart.de
Abstract
Vacuum handling systems are widely used in production systems. Most of the systems key performance indicators (KPIs) relevant for industry 4.0
use cases can be derived from its vacuum level characteristics. Vacuum suction cups are key components of vacuum gripping systems and have
a significant influence on the system behavior. For modelling suction cups, mainly constant volume chambers are currently used. However, these
do not represent the suction cups dynamic behavior exactly enough. Therefore, a novel model is presented allowing the vacuum curve simulation
mainly based on the forcedisplacement characteristic curve. The presented model is validated in an industrially relevant scenario.
Keywords: Vacuum suction cups, Vacuum gripping systems, Digital Twin, Behavior model
1. Introduction
Vacuum gripping systems are widely used in industry due
to their robustness and easy implementation compared to
competing technologies [1]. Through gripping the handling
objects from just one side, an easy adaption to different sizes,
forms and weight of objects is possible with only little or no
modification [2]. As a result, vacuum gripping systems hold
great potential for future flexible production systems. In
general, such systems consist of components from six major
categories: Vacuum generators, fluidic connections, fastening
elements, switches and system monitoring elements, valves and
of course vacuum suction cups [3]. Most key performance
indicators (KPIs) in vacuum gripping systems such as the
evacuation time, the energy consumption or the gripping force
retrieve from the vacuum level in the system [2]. One of the
most influencing parts on this vacuum level are vacuum suction
cups [4]. These are currently mainly modeled using constant
volumes due to the lack of indepth investigations. However,
this leads to considerable deviations with regard to the vacuum
curve. Therefore, this article presents a novel approach to
model the dynamic behavior of suction cups with a significant
increase in modeling accuracy.
In the following existing approaches for behavior models of
vacuum suction cups are presented (section 2), followed by a
presentation of a variety of industry relevant suction cups used
in the modeling and validation (section 3). Afterwards, a new
approach is deducted from general thermodynamic equations
(section 4) and finally validated using a test setup (section 5).
The paper closes with a conclusion and an outlook (section 6).
2. State of the art
There has been some work related to the behavior modeling
of vacuum suction cups except those based on constant
volumes. One is the work of Fritz [4], who used simulated and
measured curves of the inner volume over the differential
pressure applied to the suctions cups. From this data, models
based on lookuptables were built. These models are generally
able to describe the behavior of the vacuum level, but do not
link it to the force applied to the suction cup an require high
experimental effort.
Griebel [6] focuses in his work on the development and
characterization of fluidmechanical compliant actuators. Most
relevant for the behavioral modeling of vacuum suction cups is
the consideration of force versus displacement characteristics.
However, the focus is on the development and characterization
of actuators, but not on the modeling of the behavior of vacuum
suction cups.
The work of Liu et al. [5] deals with the modeling of suction
cups used for windowcleaning robots. The focus is on the
modeling of the holding force as a function of the vacuum and
the contact area. However, the behavior of a suction cup during
its evacuation is not modeled.
Novotny and Horak [6] focus in their paper on the modeling
of suction cups for gripping of glass. The focus is on the
modeling of radial and axial force application in order to design
gripping processes on glass. Different vacuum levels are
considered, but not the actual evacuation process.
Conclusion of the state of the art: In general, there are
studies and approaches to model suction cups during the
handling process. Only Griebel [7] and Fritz [4] concentrate on
the process of evacuation, but Griebel [7] focuses on the
development and characterization of suction cups. Fritz [4]
comes closest to model the evacuation process, but is based on
the inner volume of suction cups depending on the vacuum
level, which must be determined at great expense. In the
following, an approach will be presented that enables
behavioral modeling similar to Fritz [4], but with significantly
less preliminary work required and direct consideration of the
applied forces.
3. Examined suction cups
In the field of industrial automation, there is a wide variety
Please cite this article as: V. Stegmaier, T. Eberhardt, W. Schaaf, N. Jazdi, M. Weyrich, “A behavior model for Digital Twins of vacuum suction cups”, 2022,
submitted
of suction cups for different applications. In order to enable a
modeling that is highly generally applicable, the model has to
be built and validated on a broad spectrum of industrially used
suction cups. For this purpose, the suction cup portfolio of a
wellknown component manufacturer in vacuum handling
technology is used [8]. The suction cups and their
characteristics are shown in Table 1.
Table 1: Examined suction cups with their properties
Suction cup designation Shape Number
of folds
Material Size
[mm]
SAB 60 NBR60 G1/4IG Round
1.5 NBR60 60
SAB 60 HT160 G1/4IG Round
1.5 HT160 60
SAXB 60 ED85 G1/4IG Round
1.5 ED85 60
SPB1 60 ED65 G1/4IG Round
1.5 ED65 60
SAF 60 NBR60 G1/4IG Round
0 NBR60 60
SUF 60 SI55 G1/4IG Round
0 SI55 60
SAXM 60 ED85 G1/4IG Round
0 ED85 60
SPB2 50 ED65 G1/4IG Round
2.5 ED65 50
FSGB 25 NBR55 G1/4IG Round
3.5 NBR55 25
SPB4 50 SI55 G1/4IG Round
4.5 SI55 50
SAOF 60x23 NBR60 G1/4IG Oval 0 NBR60 60
4. Modeling
Current system simulation tools mostly use differential
equations to describe the behavior of components. Therefore,
we present a set of differential equations to describe the
behavior of vacuum suction cups.
4.1. Behavior modeling
The dynamic behavior of a suction cup can be described
with the help of the mass and energy balance. These balances
can be used to determine all relevant parameters for the system
simulation. The required variables with their unit and
description are listed in Table 2.
Table 2: Nomenclature of used variables
Symbol
Unit Description Symbol
Unit Description
cp,m
J
kg
⋅
K
Isobaric heat capacity Q J Heat
E
kin
J
Kinematic energy
m
kg
Mass
Epot J Potential energy T
K
Temperature
Q
H
J
s
Heat flow rate
U
J
Inner energy
Rs
J
kg
⋅
K
Universal gas constant
V m3 Volume
n
mol
Amount of substance
W
J
Work
p
N
m²
Pressure t s Time
Z  Compressibility factor
ρ
kg
m
³
Density
Φ J
s
Energy flow rate H J Enthalpy
4.1.1. Mass balance
The mass balance considers the mass flow entering and
leaving the suction cup through the system boundary. It can be
described as follows (1) [9].
dm
dt
=
m
i (1)
With the real gas law (2), the mass of the gas in the suction
cup can be related to the temperature and the pressure [10].
p
⋅
V
=
m
⋅
Z
⋅
R
s
⋅
T
(2)
Finally, the mass flow rate results from the change in mass
over time as a function of temperature and pressure. In addition,
in the following the suction cup is considered to be ideally
terminated with the surface. This means that the inflow and
outflow of mass is only possible through the hose connection,
not considering leakage. Using the time derivative of (2) and
this simplification, equation (1) results in (3).
m
=
V
⋅
ρ
p
dp
dt
+
(
ρ
)
dV
dt

V
⋅
ρ
T
dT
dt
(3)
4.1.2. Energy balance
The evacuation of the suction cup is a transient process. The
energy balance can be set up according to the first
thermodynamic law (4) [9].
Q + W +
( H + Epot + Ekin ) = U2
 U1 (4)
The left side of equation (4) describes the change in energy
due to the transport of heat across the system boundary, the
work done on the system and the inflow and outflow of mass.
The righthand side of equation (4) describes the change in
energy by subtracting the internal energy before the change
from the internal energy after the change. For an infinitesimally
small time step, this difference of the internal energies can be
described with the help of the total differential of the caloric
equation of state for the internal energy as follows (5).
dU =
∂U
∂T
p,n
dT +
∂U
∂p
T,n
dp +
∂U
∂n
T,p,nj≠i
k
i=1
dni (5)
The partial differential equation can be solved under
consideration of a constant isochoric heat capacity and with the
help of the relationship between the heat capacities as well as
the real gas law and transformed leads to (6).
dU
= ρ
⋅
V
⋅
cp,m

h
T
dT
+
V
⋅
h
Z
⋅
R
s
⋅
T

1
dp +
(
h
∙
ρ
)
dV

(p)
dV
(6)
Furthermore, a volume work must be applied to compress
the suction cup during evacuation (7) [9].
dW
=

(
p
)
dV
(7)
With equations (6) and (7) and the neglect of kinetic and
potential energies, equation (5) finally results in (8).
Please cite this article as: V. Stegmaier, T. Eberhardt, W. Schaaf, N. Jazdi, M. Weyrich, “A behavior model for Digital Twins of vacuum suction cups”, 2022,
submitted
ρ
⋅
V
⋅
cp,m 
h
T
dT
dt + V
⋅
h
Z
⋅
Rs
⋅
T  1
dp
dt +
(
h
⋅
ρ
)
dV
dt
= Q
H + Φ
(8)
The equations resulting from the balancing of mass (3) and
energy (8) can be used to represent the suction cup in a system
simulation environment. A module exactly mapping these
equations is the translational mechanical converter module of
the MATLAB extension Simscape [11].
4.2. Inner volume
The internal volume of such a suction cup is required for the
depiction of the behavior of vacuum suction cups. In order to
examine this inner volume closer, the industrially used suction
cups from section 3 are examined. For this purpose, finite
element method (FEM) simulations are carried out using the
software COMSOL Multiphysics.
Since the translational mechanical converter module
describes the internal volume of the component as a function
of a displacement along an axis, the volume of the suction cup
is determined via its displacement. For the simulation, the
suction cup is placed on a plate. The divergence theorem is used
to evaluate the internal volume via the displacement. A closed
surface is required for this. Therefore, the suction cup is closed
with an extruded cap. To reduce the computational effort of the
simulation, only a circular section of the suction cup is
simulated. The initial model and the sliced circular section of
the SAB 60 NBR60 G1/4IG are presented in Figure 1.
Figure 1: Initial model of the suction cup (left) and the sliced model for the
FEM simulation (right)
The differential pressure required to compress the suction
cup is approximated with the help of a surface load. The surface
load is controlled by the displacement due to better
convergence. Three example pictures of the simulation of the
SAB 60 NBR60 G1/4IG are shown in Figure 2. The left
image represents the initial situation without displacement, the
middle one, a state at about half of the displacement, and the
right one the state of the suction cup when the simulation is
finished. The graphical evaluation of these states shows good
concordance of the simulation with the real behavior of the
suction cups when vacuum is applied.
Figure 2: Suction cup at 0 mm (left), 7.2 mm (middle) and 14.28 mm (right)
displacement
The volume over displacement curves resulting from these
simulations are shown in Figure 3.
Figure 3: Volume over displacement for the different suction cups
The evaluation of the different curves show an almost linear
behavior between volume and displacement for all suction
cups. Therefore, the volume reduction over the displacement is
approximated using a linear function for the behavior model.
The material properties have a negligible effect on the internal
volume of the suction cup for the considered suction cups.
Therefore, SAB 60 NBR60 G1/4IG and SAB 60 HT160
G1/4IG have an identical volumedisplacement characteristic.
5. Validation
5.1. Simulation setup
We validate the behavioral model for vacuum suction cups
using the commonly used system simulation software
MATLAB Simscape. To realize the desired functionality the
translational mechanical converter besides further function
blocks are used. This results in a subsystem shown in Figure 4.
Figure 4: Implementation of the behavioral model for the suction cup
The core functionality of the model includes the
translational mechanical converter, the position sensor, the
force source, the hard stop and the lookup table. The cylinder
retracts during the evacuation process. In the process, a force
from the force source counteracts it. This force source is
controlled by the lookup table, which outputs the
corresponding force value from the forcedisplacement
characteristic curve according to the current position detected
Please cite this article as: V. Stegmaier, T. Eberhardt, W. Schaaf, N. Jazdi, M. Weyrich, “A behavior model for Digital Twins of vacuum suction cups”, 2022,
submitted
by the position sensor. The hard stop limits the travel distance,
which is set according to the stroke of the suction cup.
However, since this system can easily swing open, we add an
additional friction source to counteract the swinging of the
cylinder movement. The green connections between the
elements represent mechanical connections. The brown ones
represent physical signals and the orange ones represent heat
exchange. Since the processes under consideration takes place
very quickly, the insulation capacity of the suction cup can be
assumed to be ideal in order to simplify the model. For this
reason, we connect the orange port of the cylinder to an ideal
thermal insulator. In addition to the building blocks, the inputs
and outputs of the implemented model are also shown. Firstly
the fluidic connection, which corresponds to the connection of
the suction cup to the vacuum system. In addition, the upper
and lower force connection are shown, which represent the
force introduction to the handling object as well as to the
gripping system. Figure 4 also shows the required input
parameters for the model on the left. The forcedisplacement
characteristic is used in the lookup table. Stroke, dead volume
and effective crosssectional area mainly used in the cylinder.
The stroke is also used in the hard stop to limit the working
distance of the cylinder according to the stroke of the suction
cup. We use this model with its parameters for all experiments.
To validate the functionality of the equations shown, we
present two different results in the following. Firstly, the
simulated and measured pressure over time are compared to
show the match over the entire pressure range in a qualitative
way. Secondly, typical vacuum levels between 200 mbar,rel
and 800 mbar,rel are used to present the quantifiable
concordance for different suction cups.
5.2. Test setup
To validate the model, first the required parameters for the
model need to be determined. The parameters stroke, dead
volume and effective cross sectional area can be derived from
the results of the conducted FEM simulations. The stroke and
dead volume are direct output variables, whereas the effective
cross sectional area is calculated from the output volume, dead
volume and stroke. The forcedisplacement characteristic, on
the other hand, is determined on a material testing machine. For
this purpose, the suction cups are clamped and loaded up to a
force limit, which is shown in Figure 5.
Figure 5: Test setup to acquire the forcedisplacement characteristic of a
suction cup
After clamping the suction cup, a starting position is
manually set so that the suction cup is just above the steel plate
on the base. We have placed a white plastic plate on this steel
plate, afterwards also used for the evacuation tests. In this way,
any influence of the substrate on which the suction cup rests on
the results can be ruled out. After the start of the measurement,
the red bar descends at a defined speed of 0.5 mm/s. The lateral
displacement is recorded with the aid of a displacement
measuring system. The counterforce of the suction cup at a
given position is recorded by means of a load cell. As soon as
a limit force of 300 N is reached, the measurement stops and
the machine moves back to the defined start position. This
measurement is repeated ten times for each suction cup. Force
and displacement pairs are recorded and stored in a table, which
can then be feed into the model. An example of such a force
displacement characteristic is shown in Figure 6.
Figure 6: Forcedisplacement characteristic of the SAB 60 NBR60 G1/4IG
On the one hand, the four recognizable sections of the graph
are recognizable. In the area up to about 7 mm, the half fold of
the 1.5 fold suction cup is compressed, in the area up to about
12 mm the one entire fold. Between 12 mm and shortly before
14 mm, the one entire fold rests on the half fold, which results
in an additional increase in the force gradient. From just before
14 mm, the suction cup is fully seated, which means the end of
the stroke. The further displacement results in an elastic
deformation of the footprint in the suction base. On the other
hand, the scatter of the measurements with increasing
displacement is considerable. Due to dynamic effects during
compression and relaxation of the suction cup, its size is
variable to a certain degree. Since the length is zeroed with the
first change in force, the length changes slightly until locking
leading to the visible scatter. The magnitude of this scatter is
different for the different suction cups. With the help of the
parameters from the FEM simulation and the measurement, the
behavior model from Figure 4 is executable. To demonstrate its
functionality, we use a simplified test setup consisting of the
different suction cups, fluidic connections, a pressure sensor
and a pneumatic ejector, as shown in Figure 7. We realized the
control of the measurements and the recording of the temporal
pressure curves with a Beckhoff PLC and a cycle time of 1 ms.
Please cite this article as: V. Stegmaier, T. Eberhardt, W. Schaaf, N. Jazdi, M. Weyrich, “A behavior model for Digital Twins of vacuum suction cups”, 2022,
submitted
Figure 7: Simplified test setup
5.3. Qualitative evaluation
For the qualitative evaluation of the presented behavior
model for suction cups, we plot the measured and simulated
pressure characteristics over time, as shown in Figure 8. The
measurement curve shown in blue contains the mean, minimum
and maximum values of ten measurement repetitions with the
area in between in light blue. However, since the scatter of the
measurements with a maximum of 42 mbar is very small, a
difference between the minimum and maximum curves is
hardly visible.
Figure 8: Comparison of measurement and simulation for SAB 60 NBR60
G1/4IG
Comparing the measurements with the simulation shown in
red, a deviation can be detected below 400 mbar,rel. This is
mainly due to the dynamic processes of the collapse of the
suction cup. However, there is a basic concordance between
measurement and simulation especially if one considers the
dynamic of the process. Above 400 mbar,rel there is a very
good qualitative agreement. To better classify the general
concordance, a quantified comparison of measurement and
simulation is presented in the section below.
5.4. Quantitative evaluation
To quantify the deviation between simulation and
measurement, the industrially relevant vacuum levels between
200 mbar,rel and 800 mbar,rel in steps of 100 mbar are
considered [12]. At the corresponding vacuum levels, the
absolute time deviation between measurement and simulation
is determined, shown in Figure 9 for the considered suction
cups. In it is clearly visible that the absolute time deviation for
all suction cups is always smaller than 30 ms, which is
considerably low. Four of the eleven suction cups provide a
significant increase in deviation. If these are neglected, the
maximum deviation can even be reduced to less than 10 ms for
the entire vacuum range presented. In addition, the particularly
large deviation of the SPB4 50 SI55 G1/4IG is noticeable. For
a better classification of the deviations, their values are related
to the total time needed for the vacuum level under
consideration, resulting in Figure 10. This clearly shows that
the percentage deviation between measurement and simulation
is always less than 25%. With the exception of SPB4 50 SI55
G1/4IG, the percentage deviation decreases with increasing
vacuum level.
Figure 9: Absolute deviation over levels of vacuum for all suction cups
For the range from 500 mbar,rel upwards, the deviation is
always less than or equal to 10%. There are even suction cups
such as the SAB60 NBR60 G1/4IG or SAXB 60 ED85 G1/4
IG whose deviation over the entire vacuum range is less than
5%. Preliminary tests showed the strong influence of the
suction cups’ inner volume on the concordance. Particularly in
the case of suction cups with a large number of folds, the inner
volume can only be simulated with a certain deviation due to
the current structure of the executed FEM simulations. Main
reason are the folds moving outwards during compression in
the FEM simulation leading to a larger inner volume than in the
real evacuation process. If we now consider an entire vacuum
gripping system instead of just one suction cup without
significant tubing, as done in the simplified test setup, the total
volume to be evacuated increases significantly.
Figure 10: Percentage deviation over levels of vacuum for all suction cups
Please cite this article as: V. Stegmaier, T. Eberhardt, W. Schaaf, N. Jazdi, M. Weyrich, “A behavior model for Digital Twins of vacuum suction cups”, 2022,
submitted
This reduces the influence of the error caused by the suction
cups, which should promise even better results for the
simulation of entire gripping systems using the presented
behavior model for suction cups. With the help of the presented
model, common vacuum suction cups can be modeled mainly
based on the forcedisplacement characteristic. This enables
highly accurate modeling with little effort and direct linkage to
the displacements and forces applied to the suction cup, both
relevant for different applications.
6. Conclusion and outlook
In this paper, we present a novel behavioral model for the
behavior of vacuum suction cups during evacuation. For this
purpose, we derive differential equations from the mass and
energy balance. The correlation of displacement and internal
volume of commercially available suction cups is investigated
using FEM simulations. It reveals an approximately linear
relation. The model created based on this finding and the
derived differential equations enables behavioral modeling
with a very good correlation solely based on the parameters
stroke, dead volume, effective cross sectional area and the
forcedisplacement characteristic. The required parameters can
be determined using the results of the conducted FEM
simulations. Alternatively, these parameters can also be
determined with measurements on material testing machines
and calculations in CAD programs.
Future work may address the blow off behavior of vacuum
suction cups.
Acknowledgements
This work was supported by the Ministry of Science,
Research and the Arts of the State of BadenWurttemberg
within the sustainability support of the projects of the
Excellence Initiative II.
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