Radar sensor for continuous level
measurement of bulk solids
VEGAPULS SR 68
Probus PA
Document ID: 38296
Quick start
Mounting
Electrical connection
Quick start
The quick start procedure enables a quick setup with many applications. You can nd further information in the respective chapters of the
operating instructions manual.
1. Distance from the vessel wall > 200 mm, the antenna should
protrude > 10 mm into the vessel
200 mm
(7.87
")
Fig. 1: Distance of the antenna to the vessel wall/vessel ceiling
2. Note min. socket diameter depending on the socket length
3. Note the instructions for sealing
For further information see chapter "Mounting".
1. Make sure that the power supply corresponds to the specications on the type label.
2. Connect the instrument according to the following illustration
00
0
1
1
9
9
2
2
1
8
8
3
3
1
7
7
4
4
6
6
5
5
0
Bus
ca. 10 mm
2
3
4
Set parameters
2
+
( )
(-)
1
2
5
678
5
1
Fig. 2: Electronics and connection compartment, single chamber housing
1 Voltage supply, signal output
2 For display and adjustment module or interface adapter
3 Selection switch for bus address
4 For external display and adjustment unit
5 Ground terminal for connection of the cable screen
For further information see chapter "Connecting to power supply".
1. Go via the display and adjustment module to the menu "Setup".
2. Select in the menu item "Medium" the medium of your application, for example "Powder/Dust".
VEGAPULS SR 68 • Probus PA
38296-EN-130624
Quick start
3. Select in the menu item "Application" the vessel, the application
and the vessel form, for example, silo.
4. Carry out the adjustment in the menu items "Min. adjustment" and
"Max. adjustment".
Parameterization example
F
ther steps
ur
The radar sensor as a distance measuring instrument measures the
distance from the sensor to the product surface. For indication of the
real level, an allocation of the measured distance to the percentage
height must be carried out.
")
1 m
(39.37
100%
2
")
35 m
(1378
0%
1
Fig. 3: Parameterization example
1 Min. level ≙ max. meas. distance
2 Max. level ≙ min. meas. distance
For this adjustment, the distance is entered for min. and max. level.
If these values are not known, an adjustment with distances, for
example, of 10 % and 90 % is also possible. Starting point for these
distance specications is always the seal surface of the thread or
ange.
1. In the menu "Additional settings", menu item "Damping" you can
adjust the requested damping of the output signal.
2. Select the output characteristics in the menu item "Current out-put".
The quick start is then nished. For further information see chapter
"Parameter adjustment".
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VEGAPULS SR 68 • Probus PA
3
Contents
Contents
1 About this document
1.1 Function ........................................................................................................................... 6
1.2 Target group ..................................................................................................................... 6
1.3 Symbolism used ............................................................................................................... 6
Please note the Ex-specic safety information for installation and operation in Ex areas. These safety instructions are part of the operating
instructions manual and come with the Ex-approved instruments.
Editing status: 2013-05-16
5
1 About this document
1 About this document
1.1 Function
This operating instructions manual provides all the information you
need for mounting, connection and setup as well as important instructions for maintenance and fault rectication. Please read this information before putting the instrument into operation and keep this manual
accessible in the immediate vicinity of the device.
1.2 Target group
This operating instructions manual is directed to trained specialist
personnel. The contents of this manual should be made available to
these personnel and put into practice by them.
1.3 Symbolism used
Information, tip, note
This symbol indicates helpful additional information.
Caution: If this warning is ignored, faults or malfunctions can result.
Warning: If this warning is ignored, injury to persons and/or serious
damage to the instrument can result.
Danger: If this warning is ignored, serious injury to persons and/or
destruction of the instrument can result.
Ex applications
This symbol indicates special instructions for Ex applications.
List
•
The dot set in front indicates a list with no implied sequence.
Action
→
This arrow indicates a single action.
1 Sequence of actions
Numbers set in front indicate successive steps in a procedure.
Battery disposal
This symbol indicates special information about the disposal of batteries and accumulators.
38296-EN-130624
6
VEGAPULS SR 68 • Probus PA
2 For your safety
2 For your safety
2.1 Authorised personnel
All operations described in this operating instructions manual must
be carried out only by trained specialist personnel authorised by the
plant operator.
During work on and with the device the required personal protective
equipment must always be worn.
2.2 Appropriate use
VEGAPULS SR 68 is a sensor for continuous level measurement.
You can nd detailed information on the application range in chapter
"Product description".
Operational reliability is ensured only if the instrument is properly
used according to the specications in the operating instructions
manual as well as possible supplementary instructions.
2.3 Warning about incorrect use
Inappropriate or incorrect use of the instrument can give rise to
application-specic hazards, e.g. vessel overll or damage to system
components through incorrect mounting or adjustment.
2.4 General safety instructions
This is a state-of-the-art instrument complying with all prevailing
regulations and guidelines. The instrument must only be operated in a
technically awless and reliable condition. The operator is responsible
for the trouble-free operation of the instrument.
During the entire duration of use, the user is obliged to determine the
compliance of the necessary occupational safety measures with the
current valid rules and regulations and also take note of new regula-
tions.
The safety instructions in this operating instructions manual, the national installation standards as well as the valid safety regulations and
accident prevention rules must be observed by the user.
For safety and warranty reasons, any invasive work on the device
beyond that described in the operating instructions manual may be
carried out only by personnel authorised by the manufacturer. Arbitrary conversions or modications are explicitly forbidden.
The safety approval markings and safety tips on the device must also
be observed.
Depending on the instrument version, the emitting frequencies are in
the C or K band range. The low emitting frequencies are far below the
internationally approved limit values. When used correctly, there is no
danger to health.
38296-EN-130624
VEGAPULS SR 68 • Probus PA
7
2 For your safety
2.5 CE conformity
The device fullls the legal requirements of the applicable EC guidelines. By axing the CE marking, we conrm successful testing of the
product.
You can nd the CE Certicate of Conformity in the download section
of our homepage.
Electromagnetic compatibility
Instruments with plastic housing as well as in four-wire or Ex-d-ia
version are designed for use in an industrial environment. Nevertheless, electromagnetic interference from electrical conductors and
radiated emissions must be taken into account, as is usual with a
class A instrument according to EN 61326-1. If the instrument is used
in a dierent environment, the electromagnetic compatibility to other
instruments must be ensured by suitable measures.
2.6 NAMUR recommendations
NAMUR is the automation technology user association in the process
industry in Germany. The published NAMUR recommendations are
accepted as the standard in eld instrumentation.
The device fullls the requirements of the following NAMUR recom-
mendations:
NE 21 – Electromagnetic compatibility of equipment
•
NE 43 – Signal level for malfunction information from measuring
•
transducers
NE 53 – Compatibility of eld devices and display/adjustment
•
components
NE 107 – Self-monitoring and diagnosis of eld devices
•
For further information see www.namur.de.
2.7 Radio license for Europe
The instrument is approved according to EN 302372-1/2 (2006-04)
for use in closed vessels.
2.8 Radio license for USA/Canada
The instrument is in conformity with part 15 of the FCC regulations.
Take note of the following two regulations:
The instrument must not cause any interfering emissions
•
The device must be insensitive to interfering immissions, including
•
those that may cause undesirable operating conditions
Modications not expressly approved by the manufacturer will lead to
expiry of the operating licence according to FCC/IC.
The instrument is in conformity with RSS-210 of the IC regulations.
The instrument may only be used in closed vessels made of metal,
concrete, or bre-reinforced plastic.
8
VEGAPULS SR 68 • Probus PA
38296-EN-130624
2 For your safety
2.9 Environmental instructions
Protection of the environment is one of our most important duties.
That is why we have introduced an environment management system
with the goal of continuously improving company environmental protection. The environment management system is certied according
to DIN EN ISO 14001.
Please help us fulll this obligation by observing the environmental
instructions in this manual:
Chapter "Packaging, transport and storage"
•
Chapter "Disposal"
•
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VEGAPULS SR 68 • Probus PA
9
3 Product description
Type plate
3 Product description
3.1 Conguration
The nameplate contains the most important data for identication and
use of the instrument:
1
2
3
4
5
6
7
8
9
10
Fig. 4: Layout of the type label (example)
1 Instrument type
2 Product code
3 Approvals
4 Power supply and signal output, electronics
5 Protection rating
6 Measuring range
7 Process and ambient temperature, process pressure
8 Material, wetted parts
9 Hardware and software version
10 Order number
11 Serial number of the instrument
12 Symbol of the device protection class
13 ID numbers, instrument documentation
14 Reminder to observe the instrument documentation
15 NotiedauthorityforCEmarking
16 Approval directive
16
15
14
13
12
11
Serial number
10
With the serial number of the instrument on the type label you can nd
the following data on our homepage:
Article number of the instrument (HTML)
•
Delivery date (HTML)
•
Order-specic instrument features (HTML)
•
Operating instructions at the time of shipment (PDF)
•
Order-specic sensor data for an electronics exchange (XML)
•
Test certicate pressure transmitters (PDF)
•
Go to www.vega.com, "VEGA Tools" and "Serial number search".
As an alternative, you can nd the data via your Smartphone:
Download the smartphone app "VEGA Tools" from the "Apple App
•
Store " or the "Google Play Store"
Scan the Data Matrix code on the type label of the instrument or
•
Enter the serial number manually in the app
•
VEGAPULS SR 68 • Probus PA
38296-EN-130624
3 Product description
Scope of this operating
instructions manual
Scope of deliver
Application area
Functional principle
y
This operating instructions manual applies to the following instrument
versions:
Hardware from 2.1.1
•
Software from 4.5.0
•
The scope of delivery encompasses:
Radar sensor
•
Documentation
•
– this operating instructions manual
– Test certicate Measurement accuracy, depending on the
instrument VEGAPULS SR 68 (optional)
– Operating instructions manual "DIsplay and adjustment module
PLICSCOM" (optional)
– Supplementary instructions "GSM/GPRS radio module"
(optional)
– Supplementary instructions manual "Heating for display and
adjustment module" (optional)
– Supplementary instructions manual "Plug connector for con-
tinuously measuring sensors" (optional)
– Ex-specic "Safety instructions" (with Ex versions)
– if necessary, further certicates
3.2 Principle of operation
The VEGAPULS SR 68 is a radar sensor for continuous measurement
of bulk solids also under dicult process conditions. It is particularly
suitable for level measurement in high silos and large bunkers.
The instrument is also suitable for applications in liquids.
The antenna of the radar sensor emits short radar pulses with a
duration of approx. 1 ns. These pulses are reected by the product
and received by the antenna as echoes. The transit time of the radar
pulses from emission to reception is proportional to the distance and
hence to the level. The determined level is converted into an appropriate output signal and outputted as measured value.
Packaging
Transport
38296-EN-130624
VEGAPULS SR 68 • Probus PA
3.3 Packaging, transport and storage
Your instrument was protected by packaging during transport. Its
capacity to handle normal loads during transport is assured by a test
based on ISO 4180.
The packaging of standard instruments consists of environmentfriendly, recyclable cardboard. For special versions, PE foam or PE
foil is also used. Dispose of the packaging material via specialised
recycling companies.
Transport must be carried out under consideration of the notes on the
transport packaging. Nonobservance of these instructions can cause
damage to the device.
11
3 Product description
Transport inspection
Stor
age
age and transport
Stor
temperature
PLICSCOM
VEGACONNECT
The delivery must be checked for completeness and possible transit
damage immediately at receipt. Ascertained transit damage or concealed defects must be appropriately dealt with.
Up to the time of installation, the packages must be left closed and
stored according to the orientation and storage markings on the
outside.
Unless otherwise indicated, the packages must be stored only under
the following conditions:
Not in the open
•
Dry and dust free
•
Not exposed to corrosive media
•
Protected against solar radiation
•
Avoiding mechanical shock and vibration
•
Storage and transport temperature see chapter "Supplement -
The display and adjustment module PLICSCOM is used for measured
value indication, adjustment and diagnosis. It can be inserted into the
sensor or the external display and adjustment unit and removed at
any time.
You can nd further information in the operating instructions "Display and adjustment module PLICSCOM" (Document-ID 27835).
The interface adapter VEGACONNECT enables the connection of
communication-capable instruments to the USB interface of a PC. For
parameter adjustment of these instruments, the adjustment software
PACTware with VEGA-DTM is required.
You can nd further information in the operating instructions "Interface adapter VEGACONNECT" (Document-ID 32628).
VEGADIS 81
PLICSMOBILE T61
Protective cap
12
The VEGADIS 81 is an external display and adjustment unit for VEGA
®
plics
sensors.
For sensors with double chamber housing the interface adapter
"DISADAPT" is also required for VEGADIS 81.
You can nd further information in the operating instructions "VE-GADIS 81" (Document-ID 43814).
The PLICSMOBILE T61 is an external GSM/GPRS radio unit for
transmission of measured values and for remote parameter adjustment of plics
DTM by using the integrated USB connection.
You can nd further information in the supplementary instructions
"PLICSMOBILE T61" (Document-ID 37700).
The protective cover protects the sensor housing against soiling and
intense heat from solar radiation.
®
sensors. The adjustment is carried out via PACTware/
VEGAPULS SR 68 • Probus PA
38296-EN-130624
3 Product description
You will nd additional information in the supplementary instructions
manual "Protective cover" (Document-ID 34296).
Flanges
Electr
onics module
Antenna impedance cone
Screwed anges are available in dierent versions according to the
following standards: DIN 2501, EN 1092-1, BS 10, ANSI B 16.5,
JIS B 2210-1984, GOST 12821-80.
You can nd additional information in the supplementary instructions
manual "Flanges according to DIN-EN-ASME-JIS" (Document-ID
31088).
The electronics module VEGAPULS series 60 is a replacement part
for radar sensors of VEGAPULS series 60. There is a dierent version
available for each type of signal output.
You can nd further information in the operating instructions "Elec-tronics module VEGAPULS series 60" (Document-ID 36801).
The antenna impedance cone is used for optimum transmission of
microwaves and for sealing against the process.
You nd further information in the operating instructions "Antenna impedance cone VEGAPULS 62 and 68" (Document-ID 31381).
38296-EN-130624
VEGAPULS SR 68 • Probus PA
13
4 Mounting
Screwing in
4 Mounting
4.1 General instructions
On instruments with process tting thread, the hexagon must be tightened with a suitable screwdriver. Wrench size see chapter "Dimen-sions".
Warning:
The housing must not be used to screw the instrument in! Applying
tightening force can damage internal parts of the housing.
Protection against moisture
Suitability for the process
conditions
Protect your instrument further through the following measures
against moisture penetration:
Use the recommended cable (see chapter "Connecting to power
•
supply")
Tighten the cable gland
•
Loop the connection cable downward in front of the cable gland
•
This applies particularly to:
Outdoor mounting
•
Installations in areas where high humidity is expected (e.g. through
•
cleaning processes)
Installations on cooled or heated vessels
•
Make sure that all parts of the instrument exposed to the process are
suitable for the existing process conditions.
These are mainly:
Active measuring component
•
Process tting
•
Process seal
•
Process conditions are particularly:
Process pressure
•
Process temperature
•
Chemical properties of the medium
•
Abrasion and mechanical inuences
•
You can nd the specications of the process conditions in chapter
"Technical data" as well as on the nameplate.
4.2 Mounting preparations - Horn antenna
The instrument is also available in versions with an antenna whose
diameter is larger than the process tting (thread, ange). In such
cases the antenna must be disconnected from the process tting
before mounting. Proceed as follows:
1. Loosen the hexagon socket screws (3) on the antenna socket
with an Allen wrench (size 3)
2. Remove the antenna (4)
Note:
The plastic cone may not be pulled out of the antenna socket.
38296-EN-130624
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VEGAPULS SR 68 • Probus PA
4 Mounting
3. Insert the antenna from below into the vessel socket and secure it
against falling o
4. Retighten the antenna with hexagon screws to the antenna
socket; torque max. 2.5 Nm (1.8 lbf ft)
Note:
The radar sensor with rinsing air connection or antenna extension
is provided with a notch on the antenna socket. This notch must be
aligned with the marking on the process tting (the marking species
the position of the polarisation of the radar signal).
1
2
3
4
Fig. 5: Dismounting of the horn antenna
1 Marking for the polarisation
2 Marking at the antenna socket
3 Hexagon screws on the antenna socket
4 Antenna
38296-EN-130624
VEGAPULS SR 68 • Probus PA
4.3 Mounting preparations - Parabolic antenna
The instrument is also available in versions where the antenna has
a diameter larger than the process tting (thread, ange). With such
versions the antenna must be disconnected from the process tting
before mounting. Proceed as follows:
1. Clamp VEGAPULS SR 68 with the ange, e.g. in a bench vice
2. Hold the connection piece (3) with a wrench on the at surfaces
(width across ats 22 mm)
3. Loosen counter nut (2) completely with a wrench (width across
ats 36 mm) in the direction of the antenna
4. Loosen compression nut (1) completely with a wrench (width
across ats 41 mm) in the direction of the antenna
5. Remove the parabolic antenna (4) axially
6. Mount sensor ange on the adapter ange and fasten it tightly
7. Check if the O-ring seal is present on the connection piece and
make sure it is not damaged.
15
4 Mounting
Note:
A damaged O-ring seal must be replaced: FKM (SHS FPM 70C3
GLT), FFKM (Kalrez 6375)
8. Remount the parabolic antenna (4)
9. Fasten compression nut (1) with a wrench (width across ats 41),
torque max. 50 Nm
10. Fasten counter nut (2) with a wrench (width across ats 36),
torque max. 40 Nm
Note:
On the version with rinsing air connection, make sure that the holes
in the antenna and in the process tting coincide. This ensures a sufcient air ow (the air is led through the holes to the feed system. A
rinsing of the whole parabolic antenna is not intended).
The emitted radar impulses of the radar sensor are electromagnetic
waves. The polarisation is the direction of the electrical wave component. By turning the instrument in the connection ange or mounting
boss, the polarisation can be used to reduce the eects of false
echoes.
The position of the polarisation is marked on the process tting of the
instrument.
38296-EN-130624
VEGAPULS SR 68 • Probus PA
4 Mounting
Installation position
1
Fig. 7: Position of the polarisation
1 Marking with screwed version
2 Markingwithangeversion
2
Mount the sensor at least 200 mm (7.874 in) away from the vessel
wall.
200 mm
")
(7.87
Fig. 8: Mounting of the radar sensor on the vessel top
If you cannot maintain this distance, you should carry out a false
signal storage during setup. This applies particularly if buildup on the
vessel wall is expected. In such a case, it is recommended to repeat
the false signal storage at a later date with existing buildup.
Inowingmedium
38296-EN-130624
VEGAPULS SR 68 • Probus PA
Mounting should not be too close to the inowing material as the
microwave signal will be interferred. The optimum mounting position is
on the opposite of the lling. To avoid strong pollution, the distance to
the lter or dust extraction must be as big as possible.
With bulk solids silos with lateral pneumatic lling, mounting should
not be in the lling stream as the microwave signal will be interferred.
The optimum mounting position is next to the lling. To avoid strong
pollution, the distance to the lter or dust extraction must be as big as
possible.
The socket piece should be dimensioned in such a way that the
antenna end protrudes slightly out of the socket.
19
4 Mounting
ca. 10 mm
Fig. 11: Recommended socket mounting with horn antenna
20
(0.39")
> 10 mm
Fig. 12: Recommended socket mounting with parabolic antenna
When using a swivelling holder, keep in mind that the distance
between antenna and socket gets smaller as the inclination of the
sensor increases. Additional false reections may be generated which
can inuence the measuring result at close range.
VEGAPULS SR 68 • Probus PA
38296-EN-130624
Fig. 13: Distance between antenna and socket with horn antenna
4 Mounting
38296-EN-130624
VEGAPULS SR 68 • Probus PA
Fig. 14: Distance between antenna and socket with parabolic antenna
If the medium has good reective properties, VEGAPULS SR 68
with horn antenna can also be mounted on a longer socket piece.
Recommended values for socket heights are specied in the following
illustration. You must carry out a false echo storage afterwards.
The instrument is also optionally available with an antenna extension.
The antenna length can be selected (either ex works or later) to allow
the antenna to protrude slightly out of the end of the mounting socket.
Due to the antenna extension however, disturbing reections are
generated in the close-up range. This can lead to an increase in the
required minimum distance, especially with poorly reecting media
such as plastic powder. In practice, a cleanly constructed mounting
socket, if necessary with rounded edges, introduces fewer disturbing
inuences than an antenna extension.
To measure as much of the vessel volume as possible, the sensor
should be aligned so that the measuring beam reaches the lowest
level in the vessel. In a cylindrical silo with conical outlet mounting is
carried out on a socket. It should be positioned on one third up to the
half of the vessel radius.
22
38296-EN-130624
VEGAPULS SR 68 • Probus PA
4 Mounting
r
1
1
rr...
3
2
/
/
Fig. 16: Orientation
If mounting in the centre of the silo is not possible, the sensor can be
directed to the vessel center by using the optional swivelling holder.
The following description shows a simple way to determine the
required angle of inclination.
38296-EN-130624
VEGAPULS SR 68 • Probus PA
23
4 Mounting
α
d
a
Fig. 17: Proposal for installation after orientation VEGAPULS SR 68
The angle of inclination depends on the vessel dimensions. It can be
easily checked with a suitable level or water leve on the sensor.
The following chart species the distance "a" between installation
position and vessel centre dependent on the measuring distance for
inclination angles of 2° … 10°.
Distance d
(m)
20.10.10.20.30.4
40.10.30.40.60.7
60.20.40.60.81.1
80.30.60.81.11.4
100.30.71.11.41.8
150.51.01.62.12.6
200.71.42.12.83.5
250.91.72.63.54.4
301.02.13.24.25.3
2°4°6°8°10°
Example:
In a vessel 20 m high, the installation position of the sensor is 1.4 m
from the vessel centre.
The necessary angle of inclination of 4° can be read out from this
chart.
38296-EN-130624
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VEGAPULS SR 68 • Probus PA
4 Mounting
Proceed as follows to adjust the angle of inclination with the swivelling
holder:
1. Loosen terminal screw of the swivelling holder with a fork spanner
SW 13
2. Direct the sensor, check angle of inclination
Information:
The max. angle of inclination of the swivelling holder is approx. 15°
3. Tighten the terminal screw, torque max. 20 Nm.
Information:
The hexagon screws must not be loosened.
Vessel installations
Agitators
The mounting location of the radar sensor should be a place where no
other equipment or xtures cross the path of the microwave signals.
Vessel installations, such as e.g. ladders, limit switches, heating spirals, struts, etc., can cause false echoes and impair the useful echo.
Make sure when planning your measuring site that the radar sensor
has a "clear view" to the measured product.
In case of existing vessel installations, a false echo storage should be
carried out during setup.
If large vessel installations such as struts or supports cause false
echoes, these can be attenuated through supplementary measures.
Small, inclined sheet metal baes above the installations scatter the
radar signals and prevent direct interfering reections.
Fig.18:Coversmoothproleswithdeectors
If there are agitators in the vessel, a false signal suppression should
be carried out with the agitators in motion. This ensures that the
interfering reections from the agitators are saved with the blades in
dierent positions.
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VEGAPULS SR 68 • Probus PA
25
4 Mounting
Fig. 19: Agitators
Material heaps
Mounting in the vessel
insulation
Large material heaps are detected with several sensors, which can be
mounted on e.g. traverse cranes. For this type of application, it is best
to orient the sensor toward the solid surface. A mutual infuence of the
sensors is not possible.
Fig. 20: Radar sensors on traverse crane
Information:
Keep in mind that for these applications, the sensors are designed
for relatively slow level changes. When using VEGAPULS SR 68 on
a movable bracket, the max. measuring rate must be observed (see
chapter "Technical data").
Instruments for a temperature range up to 250 °C or up to 450 °C
have a distance piece between process tting and electronics housing. Ths distance piece is used for thermal decoupling of the electron-
ics against high process temperatures.
Information:
The distance piece must only be incorporated up to max. 50 mm in
the vessel isolation. Only then, a reliable temperature decoupling is
guaranteed.
38296-EN-130624
26
VEGAPULS SR 68 • Probus PA
(1.97")
max. 50 mm
Fig. 21: Mounting of the instrument on insulated vessels.
For level measurements in concrete silos, the sensors are often
mounted in protective boxes. These boxes can be for example metallic, closed subsurface enclosures.
12
Fig. 22: Mounting of the instrument in an subsurface enclosure
1 Subsurface enclosure
2 Concrete bottom
For this application, the minimal amounts of stray radiation from the
sensor can be reected and strengthened by the walls of the subsurface enclosures. In the case of sensors with plastic housings, this can
lead to coupling disturbances. This can be avoided by using a sensor
with aluminium or stainless steel housing.
The silo walls of multiple chamber silos are often made of prole
walls, such as e.g. prole sheeting, to ensure the required stability. If
the radar sensor is mounted very close to a heavily structured vessel
wall, considerable false reections can be generated. Hence the sen-
27
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