5. Content
Page 2 9001A_002-032e-07.13
Content
1. Introduction ................................................................................................................................... 4
2. Important Instructions.................................................................................................................... 5
2.1 For Your Safety .................................................................................................................... 5
2.2 Unpacking............................................................................................................................ 6
2.3 Load Washer Handling......................................................................................................... 6
2.4 Tips on Use of Manual ......................................................................................................... 7
3. General Description ....................................................................................................................... 8
3.1 Applications ......................................................................................................................... 8
3.2 Design and Principle of Operation........................................................................................ 9
4. Mounting..................................................................................................................................... 11
4.1 General Aspects of Mounting............................................................................................. 11
4.1.1 Mounting with Mounting Set Type 9422A............................................................ 12
4.1.2 Mounting with Pretensioning Elements Type 9420A............................................. 14
4.1.3 Mounting with Pretensioning Elements Types 9455/56 ........................................ 14
4.1.4 Force Distributing Rings......................................................................................... 15
4.1.5 Connecting Quartz Sensors in Parallel ................................................................... 15
4.2 Force Contact..................................................................................................................... 16
4.2.1 Examples ............................................................................................................... 16
4.2.2 Calculations Related to Engagement of Force........................................................ 19
4.2.3 Examples ............................................................................................................... 21
4.3 Effect of Elasticity Conditions on the Measurements .......................................................... 24
4.4 Mounting Example............................................................................................................. 26
5. Measurement............................................................................................................................... 27
5.1 Basic Arrangement of a Measuring System......................................................................... 27
5.2 Range Selection and Threshold .......................................................................................... 28
5.3 Measuring High-Frequency Phenomena ............................................................................ 29
5.4 Measuring Quasistatic Phenomena .................................................................................... 29
5.5 Instructions and Safety Precautions.................................................................................... 30
6. Calibration and Maintenance....................................................................................................... 31
6.1 In-Situ Calibration of Force Sensors.................................................................................... 31
6.1.1 Working Point Calibration by Peak Value Comparison .......................................... 31
6.1.1.1 Test System Requirements ..................................................................... 32
6.1.1.2 Reference Sensor Installation ................................................................. 32
6.1.1.3 Load Application.................................................................................... 33
6.1.1.4 Calibration Process Worksheet............................................................... 34
6.1.2 Kistler Calibration Service ...................................................................................... 37
6. Content
9001A_002-032e-07.13 Page 3
7. Technical Data..............................................................................................................................38
7.1 Quartz Load Washers Type 9001A ... 9071A......................................................................38
7.2 Quartz Load Washers Type 9081B and 9091B....................................................................40
7.3 Included Accessories for Type 9001A … 9071A/9081B/9091B ..........................................41
7.4 Optional Accessories...........................................................................................................41
8. Appendix ......................................................................................................................................43
8.1 Glossary..............................................................................................................................43
8.2 Measurement Uncertainty ..................................................................................................47
8.3 Linearity..............................................................................................................................48
8.4 Frequency Range ................................................................................................................50
8.5 Influence of Temperature....................................................................................................51
Total Pages: 52
7. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 4 9001A_002-032e-07.13
1. Introduction
Please take the time to thoroughly read this instruction
manual. It will help you with the installation, maintenance,
and use of this product.
To the extent permitted by law Kistler does not accept any
liability if this instruction manual is not followed or prod-
ucts other than those listed under Accessories are used.
Kistler offers a wide range of products for use in measuring
technology:
Piezoelectric sensors for measuring force, torque, strain,
pressure, acceleration, shock, vibration and acoustic-
emission
Strain gage sensor systems for measuring force and
moment
Piezoresistive pressure sensors and transmitters
Signal conditioners, indicators and calibrators
Electronic control and monitoring systems as well as
software for specific measurement applications
Data transmission modules (telemetry)
Kistler also develops and produces measuring solutions for
the application fields of engines, vehicles, manufacturing,
plastics and biomechanics sectors.
Our product and application brochures will provide you
with an overview of our product range. Detailed data
sheets are available for almost all products.
If you need additional help beyond what can be found ei-
ther on-line or in this manual, please contact Kistler's ex-
tensive support organization.
8. Important Instructions
9001A_002-032e-07.13 Page 5
2. Important Instructions
It is absolutely essential to follow the instructions below,
which are intended to ensure your safety when working
with the equipment and guarantee a long, trouble-free
service life.
2.1 For Your Safety
Kistler load washers have been thoroughly tested and
left the factory in perfectly safe condition. To maintain
this condition and ensure safe operation the user must
follow the instructions and warnings in this manual
Load washers may only be mounted, used and main-
tained by persons familiar with the equipment and suit-
ably qualified for their particular work
If it has to be assumed that safe operation is no longer
possible, switch the equipment off and ensure it cannot
be switched on again inadvertently
It must be assumed that safe operation is no longer
possible:
if the equipment is visibly damaged
if it has been overloaded
if it no longer works
after prolonged storage under adverse conditions
after being severely stressed in transit
Mount the quartz crystal load washers as specified. See
section 4 "Mounting" for details.
Secure all of the parts mounted on the load washers
against the anticipated forces.
9. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 6 9001A_002-032e-07.13
2.2 Unpacking
Check all of the packaging for any damage in transit,
which must be reported to the freight forwarder and the
responsible Kistler distributor.
Please also check the included accessories (section 0).
Please report any missing parts to the responsible Kistler
distributor.
2.3 Load Washer Handling
The specified environmental and operating require-
ments must be met when working with the quartz crys-
tal load washer
The insulation resistance of piezoelectric sensors is of
critical importance; it must be about 1014 Ω (or at least
1013 Ω). To achieve this value all plug connections must
be kept scrupulously clean and dry. The insulation re-
sistance can be measured with Insulation tester Type
5493
Protect the connector of the load washer against dirt
and in particular make absolutely sure you never touch
the front of the connector with your fingers. Put the in-
cluded cover on if a connection is not being used
The cable for connecting the sensor to a charge amplifi-
er is a high-insulation type. Only use suitable connect-
ing cables specified by Kistler
10. Important Instructions
9001A_002-032e-07.13 Page 7
2.4 Tips on Use of Manual
We recommend that you read through the entire manual
thoroughly. However, if you cannot spare the time and are
already familiar with Kistler quartz crystal load washers,
you may skip to the sections with the information currently
required.
We have tried to organize this manual clearly so that the
required information is easily accessible.
Keep this manual in a safe place where it is readily accessi-
ble at all times.
If you lose your manual please contact your Kistler distribu-
tor for prompt replacement.
11. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 8 9001A_002-032e-07.13
3. General Description
Quartz crystal load washers are piezoelectric sensors. The
force to be measured is transferred to the quartz sensor el-
ements via the cover plate and base plate of the tightly
welded steel housing. The quartz elements produce an
electric charge proportional to the mechanical load. A
charge amplifier generates an electric voltage from this
charge. These signals are displayed, recorded or processed
in the familiar way.
Thanks to the extremely high resolution of quartz it is pos-
sible to measure a change in force of the order of 1 N un-
der a pretension of several tons.
The shape (load washer) and the relatively small dimen-
sions allow flexible application and easy mounting. Stand-
ard accessories (data sheets 9505_000-193 and
9420A_000-192) are available for special applications.
Sensitivity (charge per unit force) is a constant of quartz as
a material. The associated threshold is virtually the same
for all the load washers of different sizes.
This has three unique advantages:
High level of overload protection, very small forces can
be measured with one sensor with a large measuring
range
High rigidity; a sensor with a larger measuring range
undergoes less deformation
Several sensors can be electrically connected in parallel
to a single charge amplifier. The output signal is then
the sum of all of acting forces
3.1 Applications
Kistler load washers are very rigid and ideal for measuring
dynamic forces. This very high rigidity has extremely little
effect on the dynamic characteristics of the object being
measured, in which they are mounted.
Depending on the size of the force, quasistatic measure-
ment can be performed over several minutes or even hours
(the signal drift is only about ±50 mN/s). However, truly
static measurements over any length of time are not possi-
ble.
On the other hand, after a pause of any length a sensor
under continuous static load (for example, mounted in a
threaded connection) can be reconnected to a charge am-
plifier and the changes in load then measured accurately.
12. General Description
9001A_002-032e-07.13 Page 9
Measurements of dynamic forces (AC mode) are also pos-
sible over any length of time. Kistler load washers have a
virtually unlimited life and are not subject to sensitivity drift
caused by aging.
The force to be measured is transferred to the quartz sen-
sor elements via the cover plate and base plate of the
tightly welded steel housing. The quartz elements produce
an electrical charge proportional to the mechanical load.
The sensitivity (charge per unit force, a constant of quartz
as a material) and hence the threshold is virtually the same
for all of the different sized load washers.
The most important typical applications are
Forces involved in spot welding
Forces in presses
Changes in force in threaded connections under high
static pretension
Impact and forming forces
Cutting and forming forces
Braking forces in rail cars
Crash forces
3.2 Design and Principle of Operation
A quartz crystal load washer consists of one or two crystal
ring washers, an electrode and a housing with connector
(see Fig. 1).
The force to be measured must be evenly distributed over
the ring surface. The mechanical compressive stress results
in an electric charge being generated in the quartz crystal.
This charge is proportional to the applied force and does
not depend on the dimensions of the quartz washers (lon-
gitudinal piezoelectric effect).
13. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 10 9001A_002-032e-07.13
Q E
S
G
Q = Quartz washers
E = Electrode
G = Housing
S = Connector
F = Force acting on the load washer
Fig. 1: Schematic section through a quartz crystal load
washer
The generated charge is conducted from the electrode and
supplied to the plug connection. The polarity is chosen so
that a compression force generates a negative charge,
which is then converted into a positive voltage in the
charge amplifier. The housing serves as ground connection.
Unloading of the load washer produces a positive charge if
the negative charge generated beforehand by the load is
reset to zero by the charge amplifier being reset.
Connecting several load washers in parallel adds the charg-
es of the individual washers and the charge amplifier
measures the total force.
To ensure the forces to be measured are distributed evenly
over the ring surfaces, the contact surfaces on the object
being measured must be as flat, rigid and finely machined
as possible.
The housing of a load washer is tightly welded, however
the Fluoropolymer connector normally used is not abso-
lutely tight.
F
F
14. Mounting
9001A_002-032e-07.13 Page 11
4. Mounting
If something is not clear or difficulties are encountered
when mounting load washers, please contact the re-
sponsible Kistler distributor or, if appropriate, the manu-
facturer, for advice. To enable the query to be handled
effectively it is important to describe the measurement
problem and provide drawings or sketches that make
the type of load, engagement and point of application
of the force evident.
4.1 General Aspects of Mounting
Kistler load washers must be mounted between two finely
machined (preferably ground), rigid, parallel surfaces. This
allows force measurement over a wide frequency range.
The recommended surface roughness is Ra = 1,6 μm.
Load washers must always be mounted under pretension.
Reasons for this:
The sensor is fixed
Allows measurement of both compression and tension
forces
Presses the contact surfaces together so that the high ri-
gidity of the sensor can be fully exploited
When pretensioning, the force must be measured with
the sensor itself, and the charge amplifier set to the sen-
sitivity specified in the technical data. As the pretension-
ing bolt forms a force shunt, after being mounted the
sensor must be recalibrated to determine the sensitivity
of the complete measurement setup.
Depending on the application, the sensor is pretensioned
with 10 ... 20 % of the measuring range. This is achieved
by laying a steel shim (few microns thick) on the measuring
surface of the sensor (Fig. 2) or by pretensioning with a
special nut (Fig. 3).
15. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 12 9001A_002-032e-07.13
Fig. 2: Pretensioning with the aid of a steel shim; surface
finish and parallelism requirements
Fig. 3: Pretensioning with a special nut; surface finish and
parallelism requirements
4.1.1 Mounting with Mounting Set Type 9422A...
This set is included with each sensor of Types 9001A ...
9051A. It allows the sensor to be pretensioned up to 30 % of
its measuring range. The centering clip is used to center the
sensor with the bolt (Figure 4 and table).
The pretensioning bolt makes a force shunt, that is part of
the force acting on the sensor is taken by the bolt. The
sensitivity is then about 7 ... 9 % lower. The exact value is
to be found on the calibration sheet of the sensor.
17. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 14 9001A_002-032e-07.13
4.1.2 Mounting with Pretensioning Elements Type 9420A...
For sensors Types 9001A ... 9071A sets of specially manu-
factured pretensioning elements are available (Figure 5).
With these pretensioning bolts made of high-strength steel
the sensor can be pretensioned up to 50 % of its measur-
ing range. They also ensure ideal force engagement.
Fig. 5: Load washer pretensioned with the pretensioning
set Types 9420A01 ... 9420A71 (see data sheet
9420A_000-192) available as accessory
4.1.3 Mounting with Pretensioning Elements Types 9455/56
With pretensioning elements Types 9455 and 9455 (avail-
able as accessory) sensor Types 9081B and 9091B can be
pretensioned with a force of up to 400 kN/600 kN. The
pretensioning as well as the calibration of the pretensioning
element can be performed as a service at Kistler's main fac-
tory in Winterthur, Switzerland.
Fig. 6: Load washer pretensioned with the pretensioning
set Type 9455/9456 (see data sheet
9420A_000-195) available as accessory
18. Mounting
9001A_002-032e-07.13 Page 15
4.1.4 Force Distributing Rings
The bearing surfaces must be flat and rigid. If they cannot
be finely machined, localized overloads and damage to the
surface of the sensor must be avoided by using a force dis-
tributing ring (Fig. 6).
Fig. 7: Mounting with a force distributing ring
Types 9505 ... 9575 (see data sheet
9505_000-193)
4.1.5 Connecting Quartz Sensors in Parallel
As all load washers nominally have the same sensitivity,
several sensors can be connected in parallel to a single
charge amplifier. The output signal then corresponds to the
sum of all of the forces acting on the connected sensors.
19. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 16 9001A_002-032e-07.13
4.2 Force Contact
The full measuring range can only be exploited if the force
is evenly distributed. The mounting surfaces should prefer-
ably be ground. Accessories like spherical washers, force
distributing rings, insulating rings and force distributing
caps make mounting easier in many cases (see data sheet
9420A_000-192). At the maximum allowed load of the
particular load washer of whatever size a surface pressure
Gmax of approximately 150 N/mm2
arises.
If the force is applied eccentrically or the object being
measured deforms, bending moments arise. The resultant
bending stress is superimposed on the direct stress. In these
cases the measuring range specified in the table of tech-
nical data no longer applies. The maximum allowed surface
pressure σmax must not be exceeded. The maximum al-
lowed bending moments specified in the technical data can
be used to determine the total load (see section 4.2.2)
As a load washer cannot take tensile stresses, the direct
stress must always be greater than the bending stress. The
direct stress is produced by the sum of measured force and
pretension force.
4.2.1 Examples
The ideal mode of force engagement produces an even
surface pressure on the load washer and is free from shear
forces and moments. Several examples of how force can be
applied most effectively with various accessories (data
sheet 9420A_000-192) are listed below.
Measurement of a screw force
When measuring a screw force it is essential to avoid load
case a), as it causes an overload at the inside edge. To en-
sure accurate measurement and exploitation of the full
measuring range, a matching element for introducing the
force must be manufactured.
20. Mounting
9001A_002-032e-07.13 Page 17
The bearing surfaces on the load washer must be finished
by grinding. A good grease (such as Kistler Type 1063)
must be used to reduce the friction.
a) b)
Fig. 8: Measurement of force in a screw connection;
a) ineffective introduction of force, b) with con-
structional element
Measurement of force between roughly machined and/or
oblique surfaces
Measurement between rough and/or oblique surfaces
should be avoided if possible (Fig. 9, Case a)). Machine the
mounting surfaces, preferably by grinding. A force distrib-
uting ring or a spherical washer should only be used as a
temporary solution (Fig. 9, Case b). However, under load a
spherical washer will no longer allow compensation for
misalignment.
Fig. 9: Force measurement between roughly machined
and oblique surfaces, a) ineffective introduction of
force, b) with force distributing ring and spherical
washer
Measurement of a point force
A force distributing cap prevents introduction of force at a
point. If the plate is too thin it is deformed into a dish
shape and overloads the inside edge of the load washer
(Fig. 10, Case a)) in a similar way to the first example de-
scribed (Fig. 8, Case a)). As shown in Case b), the force
distributing cap provides a remedy.
a) b)
21. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 18 9001A_002-032e-07.13
Fig. 10: Measurement of a point force; a) ineffective intro-
duction of point force, b) with force distributing
cap
Measurement of force on a beam with two load washers
The deflection of a beam supported on two load washers
can result in local deformation of the washers (Fig. 11,
Case a)). A simple truss arrangement as shown in Fig. 11,
Case b) provides a remedy.
Fig. 11: Measurement of force on a beam with two load
washers; a) ineffective application of force, b) with
simple truss arrangement
a) b)
a) b)
22. Mounting
9001A_002-032e-07.13 Page 19
4.2.2 Calculations Related to Engagement of Force
Fig. 12 shows the general load case for a load washer, with
the pretension force FV, the axial force F and a side force FS
acting simultaneously.
Fig. 12: Combined load of force and bending moment
If the side force Fs is unavoidable, the following situation
happens:
Relative to the center of gravity of the load washer, the
side force Fs produces a bending moment Fs · h. This results
in the bending stress σB, which is counteracted by the neg-
ative component of the measured force. On this diagram
the measured force F produces a relatively small direct
stress σF (σF < σB). As a load washer cannot take any tensile
stress, an additional force Fv must be produced by means
of a pretensioning bolt.
To prevent any tensile stresses forming, the maximum
bending stress σBmax. must remain under 50 % of the max-
imum allowed direct stress σmax.. This means that, in the
presence of the maximum allowed bending stress, the
measuring range of a load washer is reduced to 50 %. If
the measured force F is less than 50 % of the measuring
range, with a bending stress acting at the same time the
missing force Fv must be applied by means of a pretension-
ing bolt.
F
FS σtotal = σB + σF + σFv
σB
σFFVh
σFv
23. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 20 9001A_002-032e-07.13
It is also necessary to be aware of the requirement that the
side force Fs must not exceed 10 % of the direct force (F +
Fv) (based on a coefficient of friction μ = 0,1). For most
applications this assumption includes a factor of safety
against sliding of approximately 50 %.
From the information in the technical data (section 6.1)
(range = Fmax and max. MB), if the pretension force FV and
the measured force F are known it is possible to make a
simplified calculation of the allowed bending moment:
Fig. 13: Load diagram
Case A: Rising range of load diagram
F+Fv < ½ · Fmax
Bending moment MB:
( )V
max
max
B FF
F
M2
M +⋅
⋅
≤
Case B: Falling range of load diagram
F+Fv < ½ · Fmax
( )Vmax
max
max
B FFF
F
M2
M −−⋅
⋅
≤
2·Mmax
Mmax
Fmax
½·Fmax F+FV
M
Case A Case B
24. Mounting
9001A_002-032e-07.13 Page 21
If the bending moment is known the maximum allowed
force is determined by the pretension force and the meas-
ured force.
Case A:
B
max
max
V M
M2
F
FF ⋅
⋅
≥+
Case B:
B
max
max
maxV M
M2
F
FFF ⋅
⋅
−≤+
4.2.3 Examples
Example 1:
A load washer Type 9061A is mounted in the structure of a
machine in order to measure the forces generated, the
configuration is similar to that shown in Fig. 11.
The following values are obtained from the technical data
(section 6.1):
Fmax = 200 kN
Mmax = 800 N⋅m
The load washer was pretensioned with 100 kN, the max-
imum allowed measured force is given as 20 kN. Case B
therefore applies. The side force acts at a lever arm of ap-
proximately 0,25 m. With these figures the following are
obtained for the maximum allowed side force:
( ) mN640kN100kN20kN200
kN200
mN8002
MB ⋅=−−⋅
⋅⋅
≤
and:
kN2,560
m0,25
mN640
h
M
F B
s =
⋅
=≤
In this example, as the measured force was substantially
less than the pretension force the maximum allowed values
of the bending moment or lateral friction force (see Exam-
ple 2) are not exceeded.
F
FS
FVh
25. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 22 9001A_002-032e-07.13
Example 2:
In the next example a measured force considerably higher
than the pretension force is assumed. The side force FS that
produces a bending moment is also acting in this case.
The technical data gives the following values for the sensor
Type 9041A:
Fmax = 90 kN
Mmax = 240 N⋅m
The measured force F is assumed to be 0 ... 60 kN, the pre-
tension force FV is 10 kN. The lever arm of the side force FS
is given as h = 0,1 m.
As FS acts continuously and independently of F, the worst
case is F = 0, and case A applies
F+ FV < ½ · Fmax (Case A)
( ) mN53,3kN10
kN90
mN2402
MB ⋅=⋅
⋅⋅
≤
and
kN0,53
m0,1
mN53,3
h
M
F B
s =
⋅
=≤
To calculate the no-sliding condition the coefficient of
friction of μ = 0,1 is used with the smallest measured force
F = 0:
kN1,0kN)10kN(0)F(FF V =⋅+=⋅+= μμμ
The no-sliding condition is satisfied, as FS < Fμ
26. Mounting
9001A_002-032e-07.13 Page 23
Example 3:
The next example shows the case of a measured force that
acts eccentrically. The bending moment results from the
lever arm b. The sensor Type 9041A is considered again,
with the following values:
Fmax = 90 kN
Mmax = 240 N⋅m
The pretension in this case is given as FV = 20 kN, and the
measured force F is limited to the range 0 ... 50 kN. As the
side force FS is dependent on the measured force F, Case B
applies. As the moment is produced by the measured force,
the formula can be modified to calculate the allowed dis-
tance b.
( ) FbFFF
F
M2
M Vmax
max
max
B ⋅=−−⋅
⋅
≤ or
( ) 1)
F
FF
(
F
M2
FFF
FF
M2
b Vmax
max
max
Vmax
max
max
−
−
⋅
⋅
=−−⋅
⋅
⋅
≤
mm2,121)
kN50
kN20kN90
(
kN90
mN2402
bzul =−
−
⋅
⋅⋅
≤
If the full measuring range of the sensor is to be exploited
by the measured force, it must therefore be certain that the
force acts at the center of gravity of the sensor.
b
F
FV
27. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 24 9001A_002-032e-07.13
4.3 Effect of Elasticity Conditions on the Measurements
With pretensioned connections, attention must be given to
the diversion of force without fail.
Fig. 13 shows its influence as a function of the elasticity
conditions, by means of stress-strain diagrams.
In the ideal case the force shunt via the pretensioning ele-
ments is very small, so that almost all of the measured
force is transferred and thus measured by the load washer.
If the force shunt is large, it is still basically possible to per-
form measurements, provided the setup is calibrated.
However, there is a risk of the size of the force shunt
changing during operation (for example as material com-
pression, together with changes in temperature or defor-
mations), and falsifying the measurement result despite
calibration.
In all cases in accordance with Fig. 14 recalibration with the
washer mounted and pretensioned is necessary.
Examples
a) The bolt used for pretensioning has approximately the
same rigidity as the load washer (with surrounding ele-
ments). Each of the two parts takes half of the external
force F. The load washer only measures 50 % of the
acting force F (F u = 0,5 F).
b) If the load washer (with surrounding elements) is con-
siderably more flexible than the bolt, only a small pro-
portion of the external force is measured (Fu <<F). This
solution should be avoided if possible.
c) If the load washer (with surrounding elements) is con-
siderably more rigid than the bolt (ideal case), almost
the entire force is measured (F u ≈F). The exact value of
the force shunt is determined by the calibration.
28. Mounting
9001A_002-032e-07.13 Page 25
F: External force
FB: Force of the pretensioning bolt
FU: Force of the load washer
f: Elongation
Fig. 14: Effect of the elasticity conditions on the
measured result
F F
FFF
FF
F
F
U U UB B B
f f f
FB
FB
FB
FU
FU
FU
a) b) c)
29. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 26 9001A_002-032e-07.13
4.4 Mounting Example
An example of mounting a bearing shows the effect of the
way the force is applied and the load path.
In Fig. 14 the load washer has been mounted between
flange and foundation, or alternatively between flange and
bolt head. If a force acts on the bearing, in the case on the
right the greater part of the force is measured with the
load washer. The proportion involved in the force shunt
approximately corresponds to the ratio of the rigidity of the
load washer on the one hand, to the rigidity of the shank
of the bolt between its head and the foundation on the
other.
The situation is much worse with the alternative mounting
configuration on the left. If, for example, a force acts on
the bearing in the direction of the foundation, the bearing
flange takes almost all of it. Estimation of the ratio of the
rigidity of the bearing flange on the foundation on the one
hand, and the rigidity of the bolt with load washer on the
other, quickly makes it evident that the force shunt for the
load washer is very small. The more rigid the flange the
lower the proportion of the force that can be measured by
the load washer.
Fig. 15: Example of bearing force measurement
force F
wrong right
flange
flange
30. Measurement
9001A_002-032e-07.13 Page 27
5. Measurement
5.1 Basic Arrangement of a Measuring System
A measuring system is assembled from a quartz crystal load
washer, a highly-insulated low-noise connecting cable and
charge amplifier, a display and/or data acquisition and pro-
cessing unit.
Fig. 16: Measuring system configuration
In the charge amplifier the electrical charge generated by
the sensor is converted into a proportional voltage, which
may be displayed, recorded or further processed. The con-
necting cable for the transducer must be highly insulating
and low-noise. The effect of the cable length (>15 m) can
be obtained from the instruction manual for the charge
amplifier employed.
From the charge amplifier to the display or recorder, ordi-
nary coaxial cables may be used.
31. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 28 9001A_002-032e-07.13
5.2 Range Selection and Threshold
A distinction must be made between the measuring range
of the load washer and that of the charge amplifier. Load
washers are calibrated in two ranges: 100 % and 10 %. It
is possible to select an even narrower measuring range,
such as 1 % of FS.
In the calibrated part measuring range (10 %) load wash-
ers have roughly the same linearity as in the nominal range
(100 %).
The measuring range desired for performing a measure-
ment can be selected freely on the charge amplifier (for
example Kistler Type 5015A…). Charge amplifier Type
5015A… provides continuous measuring setting ranges.
Together with load washers the following forces ranges in
N results: 1 … 50 000 N/V or 10 N to 500 kN for 10 V
output voltage. Of course the maximum admissible force
for the load washer in use must not be exceeded. For
ranges above 50 kN there is the charge divider 10 : 1 (for
example Kistler Type 5361).
It is for example possible to select a measuring range of
10 N and measure small force fluctuations superimposed
on a static pretension of, say, 10 kN. Briefly overloading
small measuring ranges by a factor of 50 does not normally
harm the charge amplifier. With bigger overloads it de-
pends on the capacitance of the input cable whether the
amplifier is damaged or not.
The operating instructions for the particular charge amplifi-
er used will provide information regarding is overload ca-
pacity.
For practical purposes at least, the threshold of a load wash-
er may be regarded as infinitely low. Together with a stand-
ard charge amplifier the practical limit is around 0,01 N
(signal-to-noise ratio about 50 %).
32. Measurement
9001A_002-032e-07.13 Page 29
5.3 Measuring High-Frequency Phenomena
Thanks to their high rigidity, quartz load washers are emi-
nently suited for measuring rapidly changing processes. As
the mounting situation has a decisive effect, the natural
frequencies specified in the table of technical data are more
of theoretical importance.
If a load washer is installed into a cylinder of the same di-
ameter for measuring axial force, it can be said without
contradiction that the dynamic properties of the measuring
object are not affected by installing the load washer. There
is no need whatever to take the natural frequency of the
load washer into consideration.
If on the other hand a large mass has to be supported on
three or four load washers, this assembly constitutes a
spring-mass oscillator. Obviously the natural frequency of
this system depends on the rigidity and not on the natural
frequency of the load washers and the magnitude of the
mounted mass. The natural frequency becomes higher as
the load washers used become larger (that is more rigid).
The fact that the natural frequency of a larger load washer
is itself smaller is not important as far as the natural fre-
quency of the system is concerned. Thus dynamometers
with natural frequencies of several kHz can readily be
manufactured.
Force links assembled from load washers (see data sheet
9301B_000-107), have natural frequencies from 22 to
85 kHz, depending on size and weight.
5.4 Measuring Quasistatic Phenomena
Purely static measurements over any length of time are not
possible with the piezoelectric measuring principle.
The time interval during which so-called quasistatic meas-
urements can be performed depends on the insulation re-
sistance of the sensor and connecting cable on the proper-
ties of the charge amplifier employed.
With an insulation resistance of >1013 Ω and <0,04 pC/s
amplifier drift current, a time-dependent error of about
±0,5 N/min results using a load washer. Assuming a measur-
ing range of 5 000 N, this value implies an error of 0,1 % if
the measurement lasts 10 minutes.
33. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 30 9001A_002-032e-07.13
If the temperature of the transducer changes during the
measurement, a similar error signal must be expected; this
is often called the "temperature drift". It is caused by me-
chanical stresses acting on the quartz washers as a result of
thermal expansion. Changes in the temperature in the
structure in which the sensor is mounted also often have
an effect. Different coefficients of thermal expansion can
lead to deformation of the structure.
In principle a quartz load washer measures not the absolute
amount of a force but only changes of force. Normally the
force change is measured between the unloaded and load-
ed states. With pretensioned force links the unloaded state
may be defined at an effective pretension of several tons.
The quasi-static properties of a charge amplifier are de-
scribed in the relevant operating instructions.
5.5 Instructions and Safety Precautions
The supporting surfaces for a load washer must be fine-
ly machined (Ra = 1,6), flat and rigid
The maximum measuring range (100 %) may be ex-
ploited only if the force is distributed uniformly over the
entire supporting surface
With uneven surface loading, due to superimposed
flexure for example, the maximum measuring range is
limited not by the range given in the table of technical
data but by the highest local surface pressure (see
chapter 4.2.2)
If a load washer is used to measure screw force, the
friction surface should be lubricated well (special grease
Type 1063). With high surface pressure a thin washer
of beryllium copper will prevent pitting
To maintain the high insulation resistance the connect-
ing plug must be kept clean. The same applies to the
plug of the connecting cable. If necessary they should
be cleaned with Freon or rectified benzene. If the cable
is disconnected from the sensor, the protective cover
Type 1891 should be screwed on in its place
If trouble is encountered due to ground loops, the load
washer can be insulated from the object mass with so-
called insulating washers (see data sheet 9420A_000-
192)
34. Calibration and Maintenance
9001A_002-032e-07.13 Page 31
6. Calibration and Maintenance
6.1 In-Situ Calibration of Force Sensors
Absolute measurement results can only be made if the
complete measurement assembly, e.g. the pretensioned
load washer and its mounting fixtures, has been calibrated.
If it is possible to remove the force measurement assembly,
without influencing the pretension and load distributing of
the force sensor, the assembly can be sent to a Kistler Cali-
bration Centre for recalibration. If, however, the sensor is
integrated into the machine structure, it normally is not
possible to remove the force measurement assembly for re-
calibration. In this case an in-situ calibration must be per-
formed.
6.1.1 Working Point Calibration by Peak Value Comparison
The test system is calibrated by comparing its output with
that of a reference measurement chain at loads around a
specific working point. An average sensitivity is calculated
from the peak values of both the reference and test sys-
tems recorded over multiple load cycles.
It is important to note the calculated sensitivity, S*, is valid
for a specific measurement chain, i.e. sensor, charge ampli-
fier and display unit. Exchanging sensors or amplifiers will
make the calibration invalid.
Furthermore, the sensitivity S* is calculated around a spe-
cific working point and will invariably differ slightly from
any works calibration results, which would have been de-
rived using a standard continuous calibration procedure. It
is generally also recommended to check the distribution of
the average sensitivity by calculating the standard devia-
tion of the sensitivity S*.
35. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 32 9001A_002-032e-07.13
KISTLER
Fz
6.1.1.1 Test System Requirements
Reference measurement chain:
The reference measurement chain consists of a cali-
brated pre-loaded force sensor and charge amplifier.
Signal conditioning:
The signal readout devices for both the reference
and test systems must be equipped with peak-hold
functionality.
Load application:
The calibration force must be ramped from zero to
the required working point and back. An external
actuator, e.g. a hydraulic cylinder, should be used if
the calibration loads can not be applied with the test
system's internal actuation mechanism.
6.1.1.2 Reference Sensor Installation
Place the reference sensor directly in the force path of the
test system as shown in 17. Always make use of force dis-
tribution caps or spherical washers and ensure that the test
force is applied centrically through the reference sensor.
Fig. 17: Typical in-situ calibration setup
test system sensor
force distributing cap
reference sensor
base plate
36. Calibration and Maintenance
9001A_002-032e-07.13 Page 33
6.1.1.3 Load Application
A typical load cycle is shown in Figure 18.
1. The system must be in an unloaded condition to define
the zero force bias;
2. Reset the charge amplifiers and, if necessary, the peak
hold functions for both the reference and test system
measurement channels.
3. Apply the load to the required working point and then
back to the unloaded condition.
4. Record the peak values from the reference as well as
the test-system read-outs.
Reference system
F [MU] Force signal
FFS [MU] Measurement range (Full Scale) for reference
system charge amplifier
FREFi [MU] Reference system output for load cycle i
[MU] Peak value measured by the reference meas-
urement chain (for cycle i)
Test system
Q [pC] Charge signal
QFS [pC] Measurement range (Full Scale) for test sys-
tem charge amplifier
QUUTi [pC] Test system output for load cycle i
iUUTQˆ [pC] Peak value displayed on the test system
readout (for cycle i)
M
Reset charge amplifiers, start of measurement
Fig. 18: Load cycle definition
Detailed Steps for the in-situ calibration of a typical test
system is shown in Fig. 19 and the Calibration Process
Worksheet on the following page.
iREFFˆ
37. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 34 9001A_002-032e-07.13
6.1.1.4 Calibration Process Worksheet
1. Set up the charge amplifier fort he maximum range of the reference sensor and the corresponding
sensitivity as shown on the calibration certificate.
Range: Fnom
[MU]
Sensitivity: Cal. Cert. )REF(Fnom
S [pC/MU]
2. Set up the test system amplifier to approximately determine the charge output of the test sensor.
For the first iteration, use the maximum range of the charge amplifier. If the charge signal is very
small and can not be measured properly, reduce the amplifier's charge range.
Range: Qmax
[pC]
Sensitivity: SUUT
1 [pC/pC]
3. Pre-load the system at least three times.
4. Calculate and set the range of the reference channel. If required, change the sensitivity from the
reference sensor's calibration certificate to closely match this range.
Range: FFS
= 1,25 ·
0REFFˆ Fnom
[MU]
Sensitivity: Cal. Cert. )REF(FFS
S [pC/MU]
5. Calculate and set the range of the test system charge amplifier.
Range: QFS
= 1,25 ·
0UUTQˆ QFS
[MU]
Sensitivity: Cal. Cert. SUUT
1 [pC/MU]
38. Calibration and Maintenance
9001A_002-032e-07.13 Page 35
6. Apply load at the working point at least 5 times, note the peak values from both the reference and
test systems for each cycle.
i 1 2 3 4 5
iREFFˆ [MU]
iUUTQˆ [pC]
7. Calculate the peak sensitivity for each cycle.
i
i
REF
UUT
i
Fˆ
Qˆ
*S =
i 1 2 3 4 5
Si
* [pC/MU]
8. Calculate the average sensitivity:
5
*S
*S
i
5
1i=
=
S* [pC/…..MU
]
9. Enter the new sensitivity S* into the test system charge amplifier.
10. Apply load at the working point to confirm results..
REFFˆ [MU]
UUTFˆ [MU]
40. Calibration and Maintenance
9001A_002-032e-07.13 Page 37
6.1.2 Kistler Calibration Service
To maintain their position on the world market products
have to meet extremely stringent quality requirements. ISO
9001 requires test equipment to stand in a known and val-
id relationship to nationally recognized standards. Tracea-
bility must be ensured. Kistler offers the following calibra-
tion services:
Swiss Calibration Service (SCS)
Kistler is accredited as SCS Calibration Center No. 049 for
equipment measuring pressure, force, acceleration and
electrical charge. To ensure traceability and specified
measurement uncertainties, calibration equipment and
methods are regularly monitored and audited.
In-Situ Calibration
Kistler offers an in-situ calibration services for cases in
which the instruments and equipment to be calibrated
cannot be transported.
Calibration in One of the Calibration Centers
In addition to in-situ calibration Kistler offers a service that
allows customers to have transportable instruments and
equipment calibrated in one of the calibration centers.
41. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 38 9001A_002-032e-07.13
7. Technical Data
Please note that all technical data and information is sub-
ject to change at any time without prior notification.
7.1 Quartz Load Washers Type 9001A ... 9071A
42. Technical Data
9001A_002-032e-07.13 Page 39
Fig. 20: Dimensions of quartz load washers Type 9001A …
9031A
Fig. 21: Dimensions of quartz load washers Type 9041A …
9071A
43. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 40 9001A_002-032e-07.13
7.2 Quartz Load Washers Type 9081B and 9091B
Fig. 22: Dimensions quartz load washers,
Type 9081B and 9091B
44. Technical Data
9001A_002-032e-07.13 Page 41
7.3 Included Accessories for Type 9001A … 9071A/9081B/9091B
Type/Art. No.
Special grease 1063
Mounting set 9422A…
(metric threads for
Types 9001A ... 9051A)
Connector protector 3.414.366
(Type 9081B/9091B)
7.4 Optional Accessories
Type
Set of pretensioning elements 9420A...
for load washers (see data sheet
9420A_000-192) and
(data sheet 9451A_000-869) 9455...
9456...
Mounting Accessories
Force measurement with load washers
(see data sheet 9001A_000-182)
Force distribution ring for load washers 95x5
(see data sheet 9505_000-193)
Spherical washer for load washers 95x3
(see data sheet 9505_000-193)
Insulating washer for load washers 95x7
(see data sheet 9505_000-193)
Force distribution cap for load washers 95x9
(see data sheet 9505_000-193)
Cables
Connecting and extension cables:
Data sheet cables for force, torque and
strain sensors (1631C_000-346)
45. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 42 9001A_002-032e-07.13
Connecting cable for sensors with KIAG 10-32 neg.
connection, Type 1631C…
Connecting cable for sensors with KIAG 10-32 neg. con-
nection, Type 1941A
Connecting cable for sensors with KIAG 10-32 neg. con-
nection, Type 1983AD
Please see data sheet 1631C_000-346 for more infor-
mation about the cables.
Examples for measuring chains
Sensor Connecting cable maXYmos TL
Type 90x1A Type 1631C... Type 5877A...
Sensor Connecting cable Charge amplifier
Type 90x1A Type 1631C… Type 5015A…
Sensor Connecting cable Charge amplifier
Type 90x1A Type 1983AD Type 5073A111
cable PFA
cable PFA
cable fluoropolymer
IP65
IP65
IP67 connector welded
BNC
TNC
BNC
46. Appendix
9001A_002-032e-07.13 Page 43
8. Appendix
8.1 Glossary
Best straight line see Appendix 8.3.
Cable capacitance The capacitance, and thus the length of the connecting
cable, has no influence on the measuring result when
Kistler special cables and Kistler charge amplifiers are used.
Calibrated measuring range Measuring range or part of the measuring range for which
the sensor has been calibrated. Because of the high lineari-
ty of quartz crystal sensors, the sensitivity of a measuring
range can usually also be used for smaller measuring rang-
es. Calibration in the mounted condition is advisable in the
case of unusual measuring arrangements and/or if the
measurement must meet very high requirements for accu-
racy. For applications in shunt mode, calibration in the
mounted condition is essential.
Calibration certificate Document for sensors and devices stating the results of the
factory calibration.
Charge amplifier Part of a measuring chain which converts the charge signal
from the sensor into a proportional voltage signal.
Charge signal Output signal in picocoulomb (pC) of a piezoelectric sensor
without integral charge amplifier.
Coulomb Unit of electric charge.
1 coulomb corresponds to 1 ampere-second (1 C = 1 As).
Crosstalk Signal at the output of a sensor, produced by a measurand
acting on the sensor, which is different from the measur-
and assigned to this output. For example, when a load in
the Fy direction produces an Fz signal in a three-component
sensor.
Degree of protection Protection of electrical equipment by suitable enclosures,
covers etc. according to EN60529. The degree of protec-
tion is stated by IP (International Protection) followed by
two digits. The first digit stands for the level of protection
against touching and the entry of solid bodies, the second
for the level of protection against the entry of water. IP65
indicates, for example, complete protection against touch-
ing, as well as against the entry of dust and water spray
from all directions.
47. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 44 9001A_002-032e-07.13
Disturbance Forces, moments and environmental influences acting on
the sensor such as the temperature, which the sensor does
not measure as a measurand and which produce an output
signal (error). Example: when an additional bending mo-
ment acts on a force sensor.
Drift Unwanted changes in the output signal independent of the
measurand as a function of time.
Frequency range see Appendix 8.4.
FSO Full Scale Output. Difference in output signal between the
zero and end points of the measuring range
Ground insulation Electrical resistance of a sensor between signal line and
ground, or of a charge amplifier between connector shield-
ed and ground.
Hysteresis see Appendix 8.3.
Insulation resistance Electrical resistance of a sensor, cable or the input of a
charge amplifier, measured between signal line and ground
connection.
Linearity see Appendix 8.3.
Measurand Physical quantity, state or characteristic which is measured,
e.g. force, torque etc.
Measuring chain Interconnection of several individual components to meet
measuring requirements. Measuring chains usually consist
of sensors and amplifiers in conjunction with data acquisi-
tion, display, evaluation and recording equipment such as
PC or printer.
Measuring range, charge amplifier Charge, voltage or current range of the signal input. Entry
in units of the measurand is also possible depending on the
type of charge amplifier.
Measuring range, sensor Range in which the quality of the measurement within the
stated tolerances is guaranteed. This range must be re-
garded as a binding maximum range.
Natural frequency Frequency of free (not forced) oscillations of the entire
sensor. In practice the (usually lower) natural frequency of
the entire mounting structure governs the frequency
behavior, see also Annex 8.4.
Operating temperature Range of ambient temperatures in which the sensor is to
be operated. The temperature-dependent tolerances stat-
ed apply only within this range. Higher temperatures can
cause irreversible damage to the sensor.
Output signal see "Charge signal"
48. Appendix
9001A_002-032e-07.13 Page 45
Overload Maximum value of the measurand with which a sensor can
be loaded without sustaining damage. This refers to a safe-
ty margin and is not an extended measuring range. The
characteristics specified in the calibration certificate are no
longer guaranteed in the event of an overload. Neverthe-
less, measurements made during an overload in most cases
provide useful results.
pC (picocoulomb) 1 picocoulomb = 10-12
coulomb. See "Coulomb".
piezoelectric The characteristic of quartz crystals in which mechanical
loading produces a proportional electric charge.
Pretension Continuous force loading of a measuring element resulting
from the application of tension sleeves or tension bolts so
that an applied force (force or pressure sensors) is acting
on the measuring element as well as on the tension ele-
ment (force shunt).
Preload Loading of a calibration object prior to the calibration cy-
cles for realization of a well-defined load at the beginning
and end of the calibration cycles.
Prestress Repeated loading (1 … 3 times) of a calibration object prior
to the calibration cycles applied for eliminating stresses
within the object and/or for ensuring a rigid force applica-
tion.
quasistatic Describes the ability of Kistler sensors and charge amplifiers
to undertake short-term measurements or DC-similar
measurements.
Range see "Measuring range"
Scaling Output voltage per unit of the measurand at the analog or
monitor output of a charge amplifier.
Sensitivity Nominal value or calibrated value stated in the calibration
certificate of the change in signal produced by the sensor
per change in measurand.
Sensor System which produces a definite change in the output
signal as a function of the change of the measurand acting
on it.
Temperature influence see Appendix 8.5.
49. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 46 9001A_002-032e-07.13
Threshold Smallest change in the measurand, which produces a
measurable change in the sensor signal. In practice, the
rule of thumb applies that the threshold is about two to
three times as large as the typical noise signal of a charge
amplifier. This value can, however, only be achieved in
dynamic measurements, whereas with quasistatic meas-
urements, drift and environmental influences are limiting
factors.
Time constant The time constant describes the behavior of a high-pass filter
(RC element), and represents the time after which the signal
has fallen to 1/e of the output value. The time constant de-
pends on the measuring range selected on the charge ampli-
fier. Possible values vary from approx. 0,01 s in the most
sensitive range to approx. 100 000 s in the least sensitive
range. The largest possible time constant must be selected
for quasistatic measurements. The time constant enables the
measuring error to be estimated in relation to the measuring
duration. You will find detailed information on time con-
stants and sensitivity ranges in the operating instructions for
your charge amplifier.
50. Appendix
9001A_002-032e-07.13 Page 47
8.2 Measurement Uncertainty
Systematic errors, accuracy
Accuracy is the extent of the conformity between a meas-
ured value and a true value of the measurand. In a piezoe-
lectric measuring chain it is determined by many systematic
errors, such as
Sensor linearity
Sensor hysteresis
Crosstalk from other measurands
Charge amplifier linearity
Disturbance (forces, moments)
Disturbance (environmental influences, like temperature)
Duration of the measurement
etc.
Experience with a measuring chain consisting of sensor,
cable and charge amplifier shows that an accuracy in the
range of 1 ... 2 % of the measuring range is achieved. This
value does not include errors due to influences from exter-
nal sources acting on the measuring chain, due to mechan-
ical adaptation of the sensor and environmental influences.
For the highest accuracy requirements, we recommend cal-
ibration of measuring ranges specific to the application.
Measurement uncertainty of charge amplifiers
When random and systematic errors together are quanti-
fied as variance, measurement uncertainty can be derived.
With charge amplifiers, this mainly depends on type. The
following typical values apply:
Laboratory charge amplifier ±0,2 ... 0,5 % FSO
Industrial charge amplifier ±1 % FSO
Higher accuracy can be achieved with the following proce-
dures:
Calibration in the Kistler factory
Calibration with charge amplifier Type 5395A
Restriction of the temperature range
Random errors, precision, reproducibility
Precision or reproducibility is the extent of conformity
between independent data measured under specified con-
ditions.
Repeatability
Repeatability is understood as "serial precision" for exam-
ple conformity between several measurements in sequence
under largely unchanged conditions.
51. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 48 9001A_002-032e-07.13
This requirement is found mainly in repetitive measure-
ments in production processes, where good repeatability is
usually sufficient for process monitoring. Accuracy primarily
plays only a subordinate role, when measurements can be
directly related to conforming/nonconforming parts.
For good repeatability, piezoelectric measuring technology
offers the particular advantage that the charge can be dis-
charged with <Reset> before every measurement, enabling
the zero point to be re-determined. Errors due to zero drift
caused by influences changing with time, such as the tem-
perature, are thus basically excluded.
With Kistler piezoelectric measuring chains, a typical repeata-
bility within 0,1 % FSO can be assumed.
8.3 Linearity
Sensor linearity
The quartz crystal produces an electric charge, which is ex-
actly proportional to the load. However, certain unavoida-
ble deviations occur due to the mechanical construction of
the sensor. Linearity represents the maximum deviation be-
tween ideal and actual output signal characteristics in rela-
tion to the measurand in a specific measuring range. It is
expressed in percentage of the particular measuring range
limit and is defined according to ANSI/ISA-S37.1 as the
closeness of the calibration curve to a "best straight line"
passing through the zero point:
"Best Straight Line“ – A line midway between the two
parallel straight lines closest together and enclosing all
Output vs. Measurand values on a Calibration Curve.
The best straight line can be determined as follows:
Best straight line – geometric definition
Two parallel straight lines must be located which are as
close as possible to one another and enclose the entire cal-
ibration curve. In addition, the center parallel must pass
through the zero point (no force, no output signal). The
slope of this center parallel corresponds to the sensitivity of
the sensor. Half the distance between the two parallels
(measured in the ordinate direction) is the linearity.
52. Appendix
9001A_002-032e-07.13 Page 49
Best straight line – mathematical definition
The minimization of maximum deviation is known as Che-
byshev’s approximation. The best straight line is deter-
mined as follows:
x = measurand (reference)
Q = sensor charge signal or output signal from the
charge amplifier
Q (x) = calibration curve, rising and falling
s = slope of the best straight lines
Best straight line: yi = s xi (with starting value for slope s)
Form residues: resi = Qi - yi
Σres = resmax + resmin sum min. + max. deviation
Recursive minimization of Σres = f (s) by changing s un-
til Σres = 0
Linearity a = resmax = |resmin|
Fig. 23: Best straight line, linearity and hysteresis
Hysteresis
Quartz itself has a scarcely measurable hysteresis. Howev-
er, the mechanical construction of the sensor can result in
slight hysteresis, but this is below the specified value (%
FSO) in every measuring range. If a greater hysteresis oc-
curs, then the sensor has not been correctly installed.
Hysteresis (b%) is included in the linearity (±a%) and does
not have to be additionally taken into account in estimat-
ing the measurement uncertainty.
Charge amplifier linearity
The linearity of charge amplifiers is typically within the
range of ±0,05 % of the measuring range selected. For the
accuracy of the measurement, this is usually negligible
compared with other influences.
53. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 50 9001A_002-032e-07.13
0.01
0.1
1
10
100
0.01 0.1 1 10
8.4 Frequency Range
Because of their mechanical quality, piezoelectric sensors
have very low damping. The useful frequency range is lim-
ited in the upwards direction by the increasing resonance
rise.
Key: f = Measuring frequency
fn = Natural frequency
A/A0 = Amplitude ratio
The following approximate values apply to the amplitude
error or achievable accuracy as a function of frequency:
Accuracy 10 % fmax
≈ 0,3 · natural frequency
5 % fmax
≈ 0,2 · natural frequency
1 % fmax
≈ 0,1 · natural frequency
Fig. 24: Schematic representation of frequency response
and phase response
1.0
1.1
1.2
0.1 0.2 0.3 0.4
0A
A
Phase response
nf
f
ϕ
-180
-90
0
0.01 0.1 1 10
nf
f
54. Appendix
9001A_002-032e-07.13 Page 51
In their dynamic behavior, piezoelectric sensors are superior
to all other measuring methods. Their high rigidity results
in the highest possible natural frequencies. Piezoelectric
sensors are thus ideal for measuring measurands which
change rapidly over time. Their dynamic behavior is there-
by largely determined by the surrounding structure. There-
fore the frequency response of the entire measuring ar-
rangement must be investigated for the largest possible,
useful measuring range.
There are two possibilities here:
Frequency analysis
The measuring arrangement is stimulated with a pulse
hammer and the sensor output signal then subjected to a
frequency analysis.
FEM
In the finite-element method, a homogeneous body is
substituted for the sensor closely approximating to the
dimensions and average density of the sensor. The average
modulus of elasticity of this equivalent body is then contin-
uously varied until its natural frequency coincides with that
of the actual sensor (Technical data). An equivalent body
defined in this way is usually a good approximation of the
sensor. The equivalent substitute body is inserted into the
structure to be simulated, and by this means the natural
frequency of the structure is calculated. Using this proce-
dure, the FEM can be used to determine the frequency be-
havior of a measuring arrangement with good approxima-
tion.
8.5 Influence of Temperature
Temperature changes during a measurement result in an
error signal in the form of a zero drift. In critical applica-
tions, we recommend that protection be provided for the
sensor as far as possible against changes in temperature.
Temperature error of the zero point (static error)
Temperature error [unit of the measurand/°C] is the great-
est change to the output signal in a specified measuring
range after a specific sensor temperature change, following
which the sensor is again in thermal equilibrium with its
environment. Temperature errors are caused by changes in
stress in the sensor, which in turn are influenced by the
pretension or installation conditions.
55. Quartz Load Washers Types 9001A … 9071A,
9081B, 9091B
Page 52 9001A_002-032e-07.13
Temperature gradient error (dynamic error)
A temporary change in the output signal is denoted as
temperature gradient error, when the temperature of the
environment or surrounding medium changes with a cer-
tain rate. In this case, the sensor is not in thermal equilibri-
um with the environment.
The temperature gradient error is primarily determined by
the installation conditions and the application, and cannot
be generally specified. However, the temperature gradient
error can be significant, particularly in the case of sensitive
measurements and small measured values. It is therefore
extremely important to keep the sensor temperature con-
stant during the actual measuring time.
Fig. 25: Example of a temperature error of the output
signal zero for a temperature rise from 150 °C to
200 °C (immersion bath).
Temperature coefficient of sensitivity
Change in the sensitivity, i.e. the slope of the best straight
line, as a function of temperature. The temperature distri-
bution in the sensor is assumed to be homogeneous, and
in thermal equilibrium with the environment. The tempera-
ture coefficient of the sensitivity is typically only approx.
0,02 %/°C, and is thus mostly negligible compared with
other influences.
Sensor
Temperature
Temperature[°C]
Tauchbadfehler 150....200°C
0 2 4 6 8Zeit [Min.]
Ausgangssignal
50
100
150
200
Temperatur[°C]
Sensor
Temperatur
Immersion Bath Error 150 ... 200 °C
Outputsignal
Temperature[°C]
Time [Min.]
Sensor
Temperature
Temperature error of the
zero point (static error)
Temperature gradient error
(dynamic error)
