=Paper=
{{Paper
|id=Vol-1852/p02
|storemode=property
|title=Hardware and software implementation of a parallel-plates rotational rheometer
|pdfUrl=https://ceur-ws.org/Vol-1852/p02.pdf
|volume=Vol-1852
|authors=Guendalina Nicoletti
}}
==Hardware and software implementation of a parallel-plates rotational rheometer==
https://ceur-ws.org/Vol-1852/p02.pdf
Hardware and software implementation of a
parallel-plates rotational rheometer
Guendalina Nicoletti
Department of Civil Engineering and Architecture
University of Catania (Italy)
email: nicoletti.guendalina@studium.unict.it
Abstract—A rotational strain controlled rheometer with For instance, the polymeric materials are characterized by
parallel-plate was designed and realized in SMT configura- complex rheological properties, in particular for flow condi-
tion, which allows exhaustively to characterize materials having tions in real applications. For this reason in the laboratory
highly viscoelastic properties. In this particular case, composite
materials, reinforced by dispersed particles, were tested: they are created simple kinematically flow situations and easily
are constituted by the elastomer polydimethylsiloxane (PDMS), controllable.
with addition of different filler concentrations, in particular Operational protocols definition and processing of experi-
carbon black, electrically conductive elastomers useful in elec- mental results are fondamental for execution of rheological
tronic devices.The study of rheological material properties can tests. Usually the rheological properties of polymers such as
contribute to the better realization and manufacturing process
of the product. Since the dynamic properties evaluation has been elastic, viscous and viscoelastic are typically determined using
done through oscillatory testing at fixed range of frequencies, in equipment operating in sweep frequencies, including the DSR
order to measure the complex modulus G* of the material. Dyanamic Shear Rheometer. An independent variable, called
Index Terms—Rheometer, Complex modulus G*, Viscoelastic, forcing, varies over the time, and in general is considered a
Carbon black stress, deformation or deformation gradient.
II. H ARDWARE I MPLEMENTATION
I. I NTRODUCTION
The strain controlled rotational rheometer are constituted by
The linear viscoelasticity theory is a prerequisite for the un- two parallel plates, the bottom plate is moved by a stepper-
derstanding of the rheological characteristic of many materials motor, which allows to apply a predetermined rotation speed,
[1]. Defining a viscoelastic system by properties intermediate which thus determines a sliding flow inside the fluid interposed
between solid and a fluid. A dissipation of internal energy between the two plates. This motor can apply a torque in both
and hence the stress - deformation deviation usually are directions, generating the oscillatory stresses; in this case the
verified in two phases interaction of solid - liquid and elastic device can control both the intensity of the deformation that
- viscose, respect to a perfectly elastic state. In fact, a perfect its frequency [8], [9].
elastic response requires a potential energy acquired during The phase shift between the deformation and stress is
deformation phase,restoring it totally in order to observe the determined by the transducer to measure the torque keeping
transformation reversibility [2], [3], [4]. the plate in motion, obtaining the stress undergone by fluid.
The major or lesser influence of the solid matrix on liquid The measurement of viscoelastic properties have been anal-
phase causes an infinite variety of viscoelastic responses, ized at different frequencies using the rotational rheometer
whose extreme limits are the solid pure elastic and viscous made in laboratory.
fluid. Afterwards the main viscoelastic mathematical relations
are explained widely in rheological analysis. In the physical
phenomena, the real materials are identified with a continuous
homogeneous and isotropic model [5].
The study of the rheological properties and viscosity mea-
surement arise for exploration of materials dynamic behav-
ior; a special equipment called rheometers are used to this
purporse, which generally allow to measure dynamics (forces
and torques) and kinematics (displacement, velocity and time)
variables [6], [7]. Rheological quantity is obtained by mathe-
matical equation solutions and experimental test, considering Fig. 1. 3D CAD model Solidworks of rheometer and its realization
also some geometric parameters of the used instrument and
physical parameters of tested material. The undercarriage of the testing machine is structured on
one central axis, constituted by beams made of metal, with the
Copyright c 2017 held by the authors. L shape , fixed on a wooden base, which had been carried out
8
to integrate to the test bench so as in order to reduce vibrations the specimen has been knurled, in order to ensure a greater
and oscillations during the testing. adherence and avoid slippage of its during the test (Fig. 3).
The lower part of the rheometer machine is composed of a
component, attributable to the cup shape, made up of a bushing
for the connection with the stepper motor shaft, fixed by a
screw. The upper part of the cup acts as a container in which
it is located the specimen to be tested, and used for biological
materials it allows to contain their physiological solution. This
component was derivated by aluminum cylinder in the Heavy
Equipment Mechanics Laboratory of the University of Catania,
realized with the lathe and milling machine, dimensioning
the component taking in account the available space presents Fig. 3. 3D CAD model Solidworks of upper disk and sheet of styrene
between the two horizontal rails.
By means a transducer, the phase difference is calculated
A motor Phidgets 3321-0 - 28STH32 NEMA-11 Bipolar
between the angular deformation and the tangential stress. In
Stepper, with integrated planetary gearbox Gearbox 27: 1 and
this regard, specifically another type of load cell was made to
stepper function, characterized by a maximum speed of 120
measure the deformations undergone by the specimen during
rpm and a rated torque of 1.4 Nm has been implemented [10],
the test. In this case, the tested specimen can be compared to a
[11]. All system was designed as sine wave generator to apply
band pass filter, having a similar frequency response. This load
the desired shear strain to the specimen.
cell consists of a flexible styrene sheet (Plasticard with 1 mm
Aluminum was chosen as the optimal solution to solve the
thickness), containing a strain gauge configured in Wheatstone
problems, such as the excessive weight of the cup that could
quarter-bridge, placed on the middle line of the foil to provide
stress the lower stepper, and the oxidation caused by the saline
a measure without mistakes.
solution for in-vitro tests on biological materials. Moreover, it
A lateral slot has been formed on the top plate, which allows
has been provided the realization of a hole in the container,
the insertion of the foil, and the other side is stuck to the
threaded to be able to connect a flexible rubber tube (Fig. 2).
undercarriage by corner plates and the bolts.
The two motors have the same electrical characteristics, for
this reason a single control device of Phidgets Controllers 1067
was chosen, with a sensitivity of 1/16 step, required for precise
positioning, using a switch of activation of stepper-motor.
For the acquisition of the signals supplied by the load cell
and strain gauge, a PXI platform of the National Instrument
is used. It is able to offer solutions for high - performance
measurement and automation systems. But the most important
thing is the ability to perfectly synchronize the signals from
the various sensors. In this project, the system implemented is
Fig. 2. 3D CAD model Solidworks of lower disk and its realization
as follows:
An another stepper motor, on upper part of rheometer, • Chassis NI PXIe - 1073
equipped with a worm screw in order to convert its rotary • NI PXIe - 6341 PXI Multifunction I/O Module for DAQ
motion into linear, and thus assume the function of the linear • NI PXIe - 6341 PXI Multifunction I/O Module for DAQ
actuator to apply an appropriate compression to the specimen. • Front-Mounting Terminal Block NI TB -4330 8Ch Bridge
A load cell was tied to actuator, with a capacity of 150N, Input, necessary for the acquisition of the strain gauge.
necessary for the detection of the compression force. In The signal of the load cell is acquired by NI SCB - 68A and
addition, the appropriate metal guides have been fixed to the subsequently processed in the control system. Furthermore,
upper beam, by bolts, in order to maintain in axis the load all the above mentioned modules have a double insulation
cell during the ascent and descent of the upper plate. The between each channel and the ground, for safety purposes and
load cell is connected to a signal amplifier of Transducer barrier against any noises during the testing.
Tecniques TMO-01 able to modify the voltage output of the
load cell [mV], supplied with the correct voltage (12 VDC) III. S OFTWARE I MPLEMENTATION
by generator. The rheometer is controlled by the CS control software
The other plate made of aluminum has the shape of a developed in environment N I LabV IEW tm , to activate the
cylindrical punch. In its upper side the bearing housing has system and to analyze the results. The block diagram contained
been obtained with mechanical interference. Using a bolt, all the codes for the machine automation and algorithms to
inside of all system, enables to make it integral with the perform the required measures. To facilitate the debugging,
load cell and free rotation of upper plate in function of the the entire block diagram is divided into several sections, each
viscoelastic response. The end of the punch in contact with designed to perform a specific function.
9
The first step of the measure process consists to apply loss factor tanδ. Finally all required data will be saved in an
compression of the sample until reaching the desired value, Excel file.
by driving the actuator. This compression is expressed by the
percentage of the sample thickness, and already the upper plate IV. T ESTED M ATERIAL
touches the sample, the percentage of fixed displacement is The rheological tests were performed on samples of com-
applied. posite polymeric material. The aim is to demonstrate that the
The actuator is moved with a gradual descent up until to composite material has superior properties to those of each one
touch the sample, checking that the signal of the load cell is component, as the reinforcing phase has significantly better
around zero, displaying the graph on front panel. When the mechanical properties, both in terms of resistance and rigidity.
top plate starts to compress the sample, a slight increase of The composite materials generally are classified according
the signal is verified. The value represented the regulation of to the physical structure of the reinforcement and not for its
the actuator movement depending on the desired compression composition. In this activity were tested samples of composite
rate is called threshold, in this is set at - 0.016. In this way material in dispersed particles, constituted by the elastomer
the contact position is defined with extreme precision. The polydimethylsiloxane (PDMS), Sylgard 184, with various car-
control logic of this mechanism is controlled by the While bon black concentrations [13], [14].
loop shown in Fig. 4. Within this loop a comparison between
the signal of the load cell and the above-mentioned threshold
value has been done, which is managed by the Flip - Flop SR
custom-made in LabVIEW:
• If the signal of the load cell is below the threshold, the
actuator will drop quickly with a continuous movement
• If this threshold value is exceeded, the actuator has
touched the sample, resulting in a slowing it down,
performing a controlled displacement and applying the
Fig. 5. Tested samples: pure PDMS and PDMS with a % of CB
percentage of compression.
Sylgard 184 belongs to the ”silicones family.” They are
seeds of thermoplastic materials - highly crosslinked crys-
talline. It is characterized by a low glass transition temperature,
−125◦ C, which gives it a good thermal stability compared to
other polymers.
The fully crosslinked polydimethylsiloxane is a very trans-
parent and brittle material, which crumbles at low stresses and
deformations. It presents other properties, including a high
permeability, good dielectric properties, weather resistance,
lubrication properties, good biocompatibility, and visual clar-
ity. PDMS is the most important polixanes, and used in the
scientific and commercial areas. The mechanical strength of
the pure polydimethylsiloxane products plays a subordinate
role, for instance silicon gel for encapsulation of electronic
parts, prosthesis, absorption of vibrations.
To obtain an improvement of the properties of the fracture,
like tensile strength, tear strength and abrasion, and also a
consequent increase in the elastic modulus, the use reinforc-
ing fillers is necessary, usually addeding them in the non-
Fig. 4. Flip - Flop SR custom-made in LabV IEW tm crosslinked silicon at the production stage of compounding.
The main reinforcing filler is carbon black [15], [16].
The particular materials, as biological cartilage, require a The reinforcement phase, dispersed within the matrix,
certain waiting time after compression for the achievement of presents basic physical and geometric characteristics to im-
the equilibrium state. prove the mechanical and rheological properties of the final
The second step of the measure process is the heart of the composite. To synthesize these composites was used the
CS, imposing the oscillations to the sample, by stepper - motor method of solution blending. This method provides initially to
[12]. identify an appropriate solvent (chloroform, acetone, toluene),
In the last step, the acquired data are processed to extract in which the polymer is treated in solution. The chosen solvent
the necessary rheological quantities, for the characterization is used to mix with the polymer, so the suspension of the
of the materials, including the complex modulus G∗ and the additive is dispersed in the same solvent. In the mixing phase,
10
the surface of the additive is coated by the polymer and, after
the removal of the solvent, is favored interconnection between
M (t) = M sin ( ω t + δ ) ⇒ τ = τ0 sin ( ω t + δ ) (3)
the additive and the polymer. The carbon black was added
before the beginning of the crosslinking, previously dispersed Phase angle δ represents the delay between the application
in chloroform and then added to the silicon. of the deformation and the stress. The shear stress is repre-
The carbon black is presented as finely carbon powder, black sented by the sum elastic and viscous components:
in color, formed by particles of almost spherical shape. The
carbon black particles generate the aggregates agglomerate in τ = τ0 cos δ sin ( ω t ) + τ0 sin δ cos ( ω t ) (4)
cluster. The particles size is a fundamental property, which
dividing τ for the maximum deformation is obtained the
does not change when carbon black is mixed in any other
so-called complex modulus G∗ :
polymeric material. Finer particles provide a more effective
reinforcement and a higher viscosity, resulting in an increase τ0
G∗ = = G0 sin ( ω t ) + G00 cos ( ω t ) (5)
in the coagulation force, with the necessity of more energy to γ0
make possible their dispersion in a composite material. It is possible to define G∗ as the measure of the total
The increase of the amount of carbon black improves the resistance relative to the deformation of material, when it is
hardness and the resistance to traction of the rubber, which repeatedly subjected to a shear stress. It can be estimated as
becomes more rigid with a remarkable wear resistance. This the vector sum of the storage module G0 and the loss module
filler provides different physical characteristics, ultraviolet G00 .
absorption and electrical conductivity, used in equipment and
high-performance electronic devices. For the realization of G0 = γτ00 cos δ G00 = γτ00 sin δ (6)
samples, it has been designed an aluminum mold, in order to
obtain the same thickness, diameter, regular and homogeneous The ratio between the storage modulus and the loss mod-
shape. This mold allows to solidify the polymer melt by ulus measures the relation between dissipated energy and the
curing, even at high temperatures. In fact, the samples tested potential energy stored during a cycle, knowned as loss factor:
in this activity have undergone a hardening process at a
G00
temperature of 100◦ C. tan δ = (7)
G0
V. E XPERIMENTAL T ESTS Referring to the rheometer used in lab, the styrene sheet
The creep and relaxation tests in the linear regime are with the strain gauge acts as a transducer, through which it
important for the determination of the viscoelastic behavior is possible to determine the response of the tested sample in
of a material. More frequently, however, the viscoelasticity terms of torque, and therefore shear stress. Considering the
of a fluid is measured through mechanical - dynamic tests, scheme shown in Fig. 6, in which is shown the top view of the
commonly referred to as frequency response [17], [18], [19], set constituted by the upper plate and the sheet, it is possible
[20], [21]. In this project the strain controlled rheometer works to derive the appropriate mathematical relationships between
in SMT configuration, ie separate motor and transducer. The the physical quantities.
tests in oscillatory regime consist in subjecting the sample, By equilibrium of moments in the insertion point of the
placed between the two parallel plates, at a compression, sheet into the notch of the top plate, it is possibile to derive the
depending on the percentage of the thickness specimen, and relationship between the bending moment to which is subject
at a shear strain defining by an harmonic equation, so as to the plate and transmitted torque by the sample to the upper
measure the resulting stress. The equation that describe the plate:
sinusoidal displacement by stepper-motor, is given by:
Mf = F · b r
⇒ Mt = Mf (8)
Mt = F · r b
θs = θs0 sin ( ω t ) (1)
Therefore the corresponding deformation of the sample is
expressed by:
θs (t) θs0
γ = r = r sin (ω t) = γ0 sin (ω t) (2)
h h
with r radius of sample, h its thickness, ω oscillation
frequency and γ0 maximum angular strain amplitude.
It is necessary that the sample has the same diameter of the Fig. 6. Top view of the set constituted by the upper plate and the sheet
upper plate, for a better distribution of the load, to minimize
the mistakes during the measurement. The sample provides b is the distance from the center of the strain gauge at the
a tangential stress obtained by a transducer, measuring the point of application of the tangential force F, and r the radius
torque transmitted to the upper plate by the sample: of the sample, which coincides with the radius of the top plate.
11
The bending moment is represented by the equation of the percentage of carbon black CB causes a consequent increase
calibration curve of sheet. of G∗ , as found in the literature.
It is possible to determine the shear stress τ : Moreover, the dynamic modulus is independent by applied
compression. By experimental data analisys, the values of
Mt Mt 2 Mt complex modulus G∗ is acquired at a specific frequency,
τ = = r = (9)
Wt Ip π r3 (0.1 Hz and 1.95 Hz), varying the shear strain. In the short
VI. A NALYSIS OF R ESULTS linear viscoelastic range (LVE) at low strain G∗ is manteined
constant; in correspondence of a certain shear strain value,
The rheological tests were performed on specimens com-
the linear viscoelastic region end and the modulus decrease
posite polymeric material specimens having different concen-
slightly. Furthermore this critical value of deformation as-
tration of carbon black. The samples have problems inherent
sumes values lower than the decreasing of the concentration of
repeatability of execution tests on the same specimen, due to
carbon black. With the addition of carbon black, the composite
the dependence of filler agglomerations by state deformation
material become more rigid and viscous, with a consequent
undergone [22], [23]. It was decided to adopt a standard test
increasing of the module G∗ , with also the probability of
procedure, in the following way:
deterioration at low deformations, causing a reduction of the
1) By stepper - motor, an angular deformation is fixed on LVE region.
the sample, with three different amplitudes: 5◦ , 10◦ and Some scientists have observed that for elastomers enriched
15◦ . with carbon black, there was no presence of agglomerations
2) Three different percentages of compression have been induced by deformation [25], [26]. However, if this phe-
defined, in function of the sample thickness: 25%, 50% nomenon is verified, the curve of the complex modulus G∗
and 75%, each of which is applied for strain amplitude presents a maximum point at the low deformation region,
specified at point 1. rather than a plateau. In order to form this plateau, it is
The protocol of each test requires that the stepper - motor necessary that create the filler agglomerates in the microscopic
takes 5 oscillations at the same frequency, for a number of structure of the sample. Since the reinforcing phase is dis-
times equal to 10. Furthermore, after the desired compression, persed randomly, it can form a single agglomeration due to
a waiting time is set equal to 60 seconds, for the redistribution the low filler concentrations. This phenomenon could occur in
of the tensions into the polymer. All samples were tested at a short average distances between the aggregates, since their
a constant ambient temperature (T = 24◦ C). The obtained densification result in the formation of a crosslinked structure.
experimental data are rapresented according to the angular The heterogeneity of the material is also due to the size of the
deformation applied to the sample or at different frequencies agglomerates, which increases with the applied load.
[24]. By amplitude strain sweep is also possible to observe
By frequency response of the tested sample, it is possible to a frequency dependence, with an increase of the complex
extract one of the rheological variables, the complex modulus modulus, for each concentration of filler.
G∗ . In Fig. (7) is shown parameterized curves according to
the filler concentrations and the percentage of compression
applied, at a given angular deformation / frequencies, in
logarithmic scal.
Fig. 8. Dynamic modulus G∗ vs shear strain
To analyze the variation of viscoelastic response for the
tested material is represented in terms of shear stress, plotted
vs. time and applied to different amplitudes of angular defor-
mation.
In Fig. (9), at fixed frequency (1Hz), the increasing am-
plitude of deformation is observed and also a proportional
increasing of the stress undergone by the tested specimen. The
Fig. 7. Dynamic modulus G∗ vs frequency curves are shifted, showing the viscoelastic behavior of the
PDMS samples were tested and considered as reference VII. C ONCLUSION
for comparison with other composite materials, in order to The aim of this paper was to verify the accuracy and
highlight the reinforcing effect of the filler. Increasing the reliability of a rotational rheometer with parallel plates, made
12
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