Me K6D Series Manuel utilisateur
Multicomponent Sensor K6D / F6D / K3R
Instruction manual
Version: 07.10.2019
ME-Meßsysteme GmbH
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Inhaltsverzeichnis
Multicomponent Sensor K6D / F6D / K3R.........................................................................................1
Function of the K6D Multicomponent Sensors............................................................................4
Calibration matrix..........................................................................................................................4
Example of a calibration matrix (K6D, F6D).............................................................................5
Matrix Plus for K6D / F6D sensors............................................................................................6
Example of a calibration matrix "B"............................................................................................6
Example of Fx...........................................................................................................................6
Example of Fz...........................................................................................................................6
Offset of the origin.............................................................................................................................7
Scaling of the calibration matrix.....................................................................................................7
Example of Fx...........................................................................................................................7
Matrix 6x12 for K6D sensors...........................................................................................................7
Stiffness Matrix..................................................................................................................................9
Example of a stiffness matrix.....................................................................................................9
Calibration Matrix for K3R Sensors..............................................................................................10
Commissioning of the sensor.......................................................................................................10
Commissioning of the 6x12 sensor ............................................................................................11
Screenshots......................................................................................................................................12
A ing a force / moment sensor ............................................................................................12
Configuration as Master / Slave..............................................................................................13
Changelog.........................................................................................................................................14
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Function of the K6D Multicomponent Sensors
The set of K6D Multicomponent Sensors comprises six in epen ent force sensors
equippe with strain gauges.
Using the six sensor signals, a calculation rule is applie to calculate the forces within three
spatial axes an the three moments aroun them.
The measurement range of the multicomponent sensor is etermine :
•by the measurement ranges of the six in epen ent force sensors, an
•by the geometrical arrangement of the six force sensors or via the iameter of the
sensor.
The in ivi ual signals from the six force sensors cannot be irectly associate with a
specific force or moment by multiplying with a scaling factor.
The calculation rule can be precisely escribe in mathematical terms by the cross pro uct
from the calibration matrix with the vector of the six sensor signals.
This functional approach has the following a vantages:
•Particularly high rigi ity,
•Particularly effective separation of the six components (“low cross-talk”).
Calibration matrix
The calibration matrix A escribes the connection between the in icate output signals U of
the measurement amplifier on channels 1 to 6 (u1, u2, u3, u4, u5, u6) an components 1 to 6
(Fx, Fy, Fz, Mx, My, Mz) of the loa vector L.
Measure value: output signals u1, u2, ...u6 on
channels 1 to 6 output signal U
Calculate value: forces Fx, Fy, Fz;
moments Mx, My, Mz Loa vector L
Calculation rule: Cross pro uct L = A x U
The calibration matrix Aij inclu es 36 elements, arrange in 6 rows (i=1..6) an 6 columns
(j=1..6).
The unit of the matrix elements is N/(mV/V) in rows 1 to 3 of the matrix.
The unit of the matrix elements is Nm/(mV/V) in rows 4 to 6 of the matrix.
The calibration matrix epen s on the properties of the sensor an that of the measurement
amplifier.
It applies for the GSV-8 measurement amplifier an for all amplifiers, which in icate bri ge
output signals in mV/V.
The matrix elements may be rescale in other units by a common factor via multiplication
(using a “scalar pro uct”).
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The calibration matrix calculates the
moments around the origin of the
underlying coordinate system.
The origin of the coordinate system is
located at the point where the z-axis
intersects with the facing surface of the
sensor.1) The origin and orientations of the
axes are shown by an engraving on the
facing surface of the sensor.
1) The position of the origin may vary with
different K6 sensor types. The origin is
documented in the calibration sheet. E.G
the origin of K6 68 is in the center of the
sensor.
Example of a calibration matrix (K6D, F6D
u1
in mV/V
u2
in mV/V
u3
in mV/V
u4
in mV/V
u5
in mV/V
u6
in mV/V
Fx in N / mV/V -217.2 108.9 99.9 -217.8 109.2 103.3
Fy in N / mV/V -2.0 183.5 -186.3 -3.0 185.5 -190.7
Fz in N / mV/V -321.0 -320.0 -317.3 -321.1 -324.4 -323.9
Mx in Nm / mV/V 7.8 3.7 -3.8 -7.8 -4.1 4.1
My in Nm / mV/V -0.4 6.6 6.6 -0.4 -7.0 -7.0
Mz in Nm / mV/V -5.2 5.1 -5.1 5.1 -5.0 5.1
The force in the x- irection is calculate by multiplying an totalling up the matrix elements
of the first row a1j with the rows of the vector of the output signals uj.
Fx = -217.2 N/(mV/V) u1+ 108.9 N/(mV/V) u2 + 99.9 N/(mV/V) u3
-217.8 N/(mV/V) u4+ 109.2 N/(mV/V) u5 +103.3 N/(mV/V) u6
For example: on all 6 measurement channels is u1 = u2 = u3 = u4 = u5 =u6 = 1.00mV/V
isplaye . Then there is a force Fx of -13.7 N.
The force in the z irection is calculate accor ingly by multiplying an summing the thir
row of the matrix a3j with the vector of the in icate voltages uj:
Fz = -321.0 N/(mV/V) u1 -320.0 N/(mV/V) u2 -317.3 N/(mV/V) u3
-321.1 N/(mV/V) u4 -324.4 N/(mV/V) u5 -323.9 N/(mV/V) u6.
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Matrix Plus for K6D / F6D sensors
When using the "Matrix Plus" calibration proce ure, two cross pro ucts are calculate :
matrix A x U + matrix B x U *
Measure values: output signals u1, u2, ... u6 at
channels 1 to 6 output signals U
Measure values are output signals as mixe
pro ucts: u1u2, u1u3, u1u4, u1u5, u1u6, u2u3 of
channels 1 to 6
output signals U*
Calculate value: Forces Fx, Fy, Fz;
Moments Mx, My, Mz Loa vector L.
Calculation rule: Cross pro uct L = A x U + B x U *
Example: example-calculation-16101424-k6 68.p f
Example of a calibration matrix "B"
u1·u2
in (mV/V)²
u1·u3
in (mV/V)²
u1·u4
in (mV/V)²
u1·u5
in (mV/V)²
u1·u6
in (mV/V)²
u2·u3
in (mV/V)²
Fx in N / (mV/V)² -0.204 -0.628 0.774 -0.337 -3.520 2.345
Fy in N /(mV/V)² -0.251 1.701 -0.107 -2.133 -1.408 1.298
Fz in N / (mV/V)² 5.049 -0.990 1.453 3.924 19.55 -18.25
Mx in Nm /(mV/V)² -0.015 0.082 -0.055 -0.076 0.192 -0.054
My in Nm / (mV/V)² 0.050 0.016 0.223 0.036 0.023 -0.239
Mz in Nm / (mV/V)² -0.081 -0.101 0.027 -0.097 -0.747 0.616
The force in the x- irection is calculate by multiplying an summing the matrix elements A
of the first row a1j with the rows j of the vector of the output signals uj
plus matrix elements B of the first row a1j with the rows j of the vector of the mixe -
qua ratic output signals:
Example of Fx
Fx = -217.2 N/(mV/V) u1 + 108.9 N/(mV/V) u2 + 99.9 N/(mV/V) u3
-217.8 N/(mV/V) u4 + 109.2 N/(mV/V) u5 +103.3 N/(mV/V) u6
-0.204 N/(mV/V)² u1u2 – 0.628 N/(mV/V)² u1u3 + 0.774 N/(mV/V)² u1u4
-0.337 N/(mV/V)² u1u5 – 3.520 N/(mV/V)² u1u6 + 2.345 N/(mV/V)² u2u3
Example of Fz
Fz = -321.0 N/(mV/V) u1 -320.0 N/(mV/V) u2 -317.3 N/(mV/V) u3
-321.1 N/(mV/V) u4 -324.4 N/(mV/V) u5 -323.9 N/(mV/V) u6.
+5.049 N/(mV/V)² u1u2 -0.990 N/(mV/V)² u1u3 +1.453 N/(mV/V)² u1u4
+3.924 N/(mV/V)² u1u5 +19.55 N/(mV/V)² u1u6 -18.25 N/(mV/V)² u2u3
Attention: The composition of the mixe qua ratic terms may change epen ing on the
sensor.
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Offset of the origin
Forces which are not applie in the origin of the coor inate system are shown by an
in icator in the form of Mx, My an Mz moments base on the lever arm.
Generally speaking, the forces are applie at a istance z from the facing surface of the
sensor. The location of the force transmission may also be shifte in x- an z- irections as
require .
If the forces are applie at istance x, y or z from the origin of the coor inate system, an
the moments aroun the offset force transmission location nee to be shown, the following
corrections are require :
Correcte moments Mx1, My1, Mz1 following
a shift in force transmission (x, y, z) from the
origin
Mx1 = Mx + y*Fz - z*Fy
My1 = My + z*Fx - x*Fz
Mz1 = Mz + x*Fy - y*Fx
Note: The sensor is also exposed to the moments Mx, My and Mz, with moments Mx1,
My1 and Mz1 displayed. The permissible moments Mx, My and Mz must not be exceeded.
Scaling of the calibration matrix
By referring the matrix elements to the unit mV/V, the calibration matrix can be applie to all
available amplifiers.
The calibration matrix with the N/V an Nm/V matrix elements applies to the GSV-1A8USB
measuring amplifier with an input sensitivity of 2 mV / V an an output signal of 5V with a 2
mV/V input signal.
Multiplication of all matrix elements by a factor of 2/5 scales the matrix from N/(mV/V) an
Nm/(mV/V) for an output of 5V at an input sensitivity of 2 mV/V (GSV-1A8USB).
By multiplying all matrix elements by a factor of 3.5/10, the Matrix is scale from N/(mV/V)
an Nm/(mV/V) for an output signal of 10V at an input sensitivity of 3.5 mV/V (eg GSV-8DS)
The unit of the factor is (mV/V)/V
The unit of the elements of the loa vector (u1, u2, u3, u4, u5, u6) are voltages in V
Example of Fx
Analog output with GSV-8DS, input sensitivity 3.5 mV / V, output signal 10V:
Fx = 3.5/10 (mV/V)/V
(-217.2 N/(mV/V) u1 + 108.9 N/(mV/V) u2 + 99.9 N/(mV/V) u3
-217.8 N/(mV/V) u4 + 109.2 N/(mV/V) u5 +103.3 N/(mV/V) u6
) +
(3.5/10)² ( (mV/V)/V )²
(-0.204 N/(mV/V)² u1u2 – 0.628 N/(mV/V)² u1u3 + 0.774 N/(mV/V)² u1u4
-0.337 N/(mV/V)² u1u5 – 3.520 N/(mV/V)² u1u6 + 2.345 N/(mV/V)² u2u3
)
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Matrix 6x12 for K6D sensors
With the sensors K6D150, K6D175, K6D225, K6D300 it is possible to use a 6x12 matrix
instea of a 6x6 matrix for error compensation.
The 6x12 matrix offers the highest accuracy an the lowest crosstalk, an is recommen e
for sensors from 50kN force.
In this case, the sensors have a total of 12 measuring channels an two connectors. Each
connector contains an electrically in epen ent force-torque sensor with 6 sensor signals.
Each of these connectors is connecte to its own measuring amplifier GSV-8DS.
Instea of using a 6x12 matrix, the sensor can also be use exclusively with connector A, or
exclusively with connector B, or with both connectors for re un ant measurement. In this
case, a 6x6 matrix is supplie for connector A an for connector B. The 6x6 matrix is
supplie as a stan ar .
The synchronization of the measure ata can be e.g. with the help of a synchronization
cable. For amplifiers with EtherCat interface a synchronization via the BUS lines is possible.
The forces Fx, Fy, Fz an moments Mx, My, Mz are calculate in the software GSVmulti.
There the 12 input channels u1...u12 are multiplie by the 6x12 matrix A to get 6 output
channels of the loa vector L.
The channels of connector "A" are assigne to channels 1...6 in the GSVmulti software..
The channels of connector "B" are assigne to channels 7...12 in the GSVmulti software.
After loa ing an activating the matrix 6x12 in the GSVmulti software, the forces an
moments are isplaye on channels 1 to 6.
Channels 7...12 contain the raw ata of connector B an are not relevant for further
evaluation. These channels (with the esignation " ummy7") to " ummy12") can be hi en
from the isplay an the recor ing via the function "Channel"--> "Hi e".
When using the 6x12 matrix, the forces an moments are calculate exclusively by
software, since it is compose of ata from two separate measuring amplifiers.
Tip: When using the GSVmulti software, the configuration an linking to the 6x12 matrix can
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be one by "Save Session". an "Open Session" is presse . so that the sensor an channel
configuration only has to be carrie out once.
Stiffness Matrix
The stiffness matrix is efine by:
f=S∗u
With the loa vector f:
f=
[
Fx
Fy
Fz
Mx
My
Mz
]
, the shifts vector u:
u=
[
ux
uy
uz
x
y
z
]
an with the stiffness matrix S:
S=
[
c11 c12 c13 c14 c15 c16
c21 c22 c23 c24 c25 c26
c31 c32 c33 c34 c35 c36
c41 c42 c43 c44 c45 c46
c51 c52 c53 c54 c55 c56
c61 c62 c63 c64 c65 c66
]
The forces
Fi
have the unit N or kN
The moments
Mi
have the unit kNm, or Nm or Nmm
The shifts
ui
have the unit m or mm
The angle
i
are expresse in ra ians
The stiffness matrix is symmetric:
cij=cji
Example of a stiffness matrix
K6D130 5kN/500Nm
93,8 kN/mm 0,0 0,0 0,0 3750 kN 0,0
0,0 93,8 kN/mm 0,0 -3750 kN 0,0 0,0
0,0 0,0 387,9 kN/mm 0,0 0,0 0,0
0,0 -3750 kN 0,0 505,2 kNm 0,0 0,0
3750 kN 0,0 0,0 0,0 505,2 kNm 0,0
0,0 0,0 0,0 0,0 0,0 343,4 kNm
When loa e with 5kN in x- irection, a shift of 5 / 93.8 mm = 0.053 mm in the x irection,
an a twist of 5 kN / 3750 kN = 0.00133 ra results in the y- irection
When loa e with 15kN in z- irection, a shift of 15 / 387.9 mm = 0.039 mm in the z irection
(an no twist).
When Mx 500 Nm a twisting of 0,5kNm / 505,2kNm = 0.00099 ra results in the x-axis, an
a shift from 0,5kNm / -3750 kN = -0,000133m = -0,133mm.
When loa e with Mz 500Nm a twisting results of 0,5kNm / 343.4 kNm = 0.00146 ra about
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the z-axis (an no shift).
Calibration Matrix for K3R Sensors
The sensors of the type K3R allow the measurement of the force Fz an the moments Mx
an My.
The sensors K3R may be use for isplaying 3 orthogonal forces Fx, Fy, an Fz, when the
measure torques are ivi e by the lever arm z ( istance of force application Fx, Fy of the
origin of the coor inate system).
ch1 ch2 ch3 ch4
Fz in N / mV/V 100,00 100,00 100,00 100,00
Mx in Nm / mV/V 0,00 -1,30 0,00 1,30
My in Nm / mV/V 1,30 0,00 -1,30 0,00
H 0,00 0,00 0,00 0,00
The force in the z irection is calculate by multiplying an summing the matrix elements of
the first row A1J with the lines of the vector of the output signals uj
Fz = 100 N/mV/V u1 + 100 N/mV/V u2 + 100 N/mV/V u3 + 100 N/mV/V u4
Example: on all 6 measurement channels is u1 = u2 = u3 = u4 = 1.00 mV/V isplaye . Then
a force Fz results of 400 N.
The calibration matrix A of K3R sensor has the imensions 4 x. 4
The vector u of the output signals of the measuring amplifier has the imensions 4 x. 1
The result vector (Fz, Mx, My, H) has the imension of 4 x. 1
At the outputs of ch1, ch2 an ch3 after applying the calibration matrix, the force Fz an the
moments Mx an My are isplaye . On the Channel 4 output H is constantly isplaye 0V
by the fourth line.
Commissioning of the sensor
The “GSVmulti” software is use to show the measure forces an moments. The GSVmulti
software an relate manuals can be ownloa e from the website.
Schritt Beschreibung
1 Installation of the GSVmulti software
2 Connect the measuring amplifier GSV-8 via USB port;
Connect the sensor K6D to the measuring amplifier.
Switch on the measuring amplifier.
3 Copy irectory with calibration matrix (supplie USB stick) to suitable rive an path.
4 Start GSVmulti software
5 Main win ow: Button A Channel;
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Ce manuel convient aux modèles suivants
3
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