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No. 4-289
Bisheng Road
Zhangjiang High Tech park
Pudong New District
Shanghai 201204
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Company Description
Inclinometer is always used to measure the tilt angle refer to sea level. Since the traditional bubble level, to today’s electronic
inclinometer (Based on the principle of acceleration, or Electronic Liquid, or Liquid Capacitance), it has been over one hundred
years. During this period, the measurement technology developing rapidly, inclinometer’s specifications improved tremendously,
application becomes much broadly, as well as manufacturers comes more and more, however, for the definition & explanation on
inclinometer accuracy, it becomes more ambiguous, and the deviation comes larger.
Generally, related national & international measurement norms have specified accuracy in field, the definition and explanation
is universal and broad, but for the tilt measurement field, it is not very professional or proper.
In the market, there are many kinds of inclinometers, some of manufacturers consider the nonlinearity as the accuracy, but in actual
field, it is not correct . To define inclinometer accuracy, we need to know which factors affect accuracy firstly .
Take the Low-g MEMS inclinometer as an example, we get the angle data through measuring the sensing axis acceleration value
“a”, as we know a=g*sin Ø, this method has been stated on many paper and product datasheets. (Note: a means sensing axis
acceleration value, G means gravity value, Ø means tile angle).
In this point , we study to know that , to measure a tilt angel, it needs an accelerometer with DC response firstly. Also we can
understand in this way, inclinometer should have the same character of accelerometer. Therefore , to know the factors affect the
accuracy is actually to study what caused “a” error . From the existed documents and files, we know they are sensitivity error, offset,
nonlinearity, cross-axis sensitivity error, response frequency, input axis misalignment, repeatability, vertical axis misalignment, temperature
interference to zero and sensitivity (include temperature drift and repeatability ), noise and noise density.
It is not easy to make compensation on repeat measurement accuracy and temperature repeatability; they are depending on
the characters of the core sensing element. Also the sensitivity depends to characters of core sensing element , but it's related to
frequency response at the same time. For noise and noise density, we can reduce the interference through hardware & software
filtering. The frequency of inclinometer which based on accelerometer is about 30Hz, in the actual testing, it affects rarely to
sensitivity.
So, from all above, we may know that, cross-axis sensitivity, input axis misalignment, vertical axis misalignment and nonlinearity
should be considered into inclinometer which based on accelerometer. It's not proper to use the nonlinearity as the only method
to determine the accuracy of an inclinometer.
The cross-axis sensitivity means the angle that the tilt sensor may be banked to the normal tilt direction of sensor, and it shows
how much perpendicular acceleration or inclination is coupled to the inclinometer output signal. For example, for the single-axis
inclinometer with range±30°(assuming theX-axis as measured tilt direction), when there is a 0°tilt angle perpendicular to the Xaxis
direction(the actual measuring angle is no change, example as +8.505°), the output signal will generate additional error
occupied with 10° banking tilt angle , this error is called as cross-axis sensitivity error. SST300`s cross-axis sensitivity is ±0.1%FS,
the extra error is ±0.1%×30°=±0.03°(max), then real output angle should be( +8.505°±0.03°)roughly. So, under this situation, even
the linearity is up to 0.001°, it can be ignored compared with cross sensitivity error, if only consider linearity as accuracy, that will
cause serious error in actual measurement .
Allowed input-axis misalignment means that, during installation, allowed certain sensor horizontal (Z-axis) angle deviation , it
means sensing axis of inclinometer cannot be completely in line with theory X axis or Y axis of actual tilt direction, and user can
still install this unit and get accurate data. Usually, when install an inclinometer, we try to keep the unit tilting follow with we fixed
tilt direction or under allowed deviation angle. In the actual field measurement, an extra error will raise up while tilt angle comes
up, once the deviation angle between actual tilt direction and unit’s actual sensitivity axis is over 3°, for an inclinometer (±0.03°linearity
error and ±30° range), the extra error will reach ±0.3°~±0.5°, larger more than nonlinearity error.
Therefore, for inclinometer, the accuracy at room temperature should concern nonlinearity, repeatability, hysteresis, offset and
cross-axis sensitivity error, and should be calculated as below mathematical formula.
Δ=±
Other principled inclinometers should also redefine accuracy like this but not just linearity.
Regarding to the actual field installation, also need to consider more factor when calculating total error of an inclinometer :
1. There are a deviation between inclinometer’s sensitivity axis and unit’s housing, this deviation is not only live on x-y coordination,
it is alive in x-y-z coordination actually.
absolute linearity +repeatability +hysteresis +offset +cross-axis sensitivity 2 2 2 2 y e r r o r 2
Redefinition Accuracy of Inclinometer
Write by Mr. Stephan Zhan Shanghai Vigor technology Development Co. Ltd.
Email: [email protected] www.vigordigital.com
Picture 3 actual installation combined both cross-axis(banking tilt) and misalignment
As a really smart inclinometer, not only make correct error calculation method, also should eliminate the extra error which took by
actual installation deviation as well as actual object moving status.
2. When installing, the actual tilting axis can not completely parallel to the unit’s sensitivity axis or fixed housing edge. It is very difficult
to accurately align.
3. Most object’s actual tilting axis can not find easily. Also, the actual tilting axis is changed when object running or moving.because
of object’s mechanical deviation of assembly, installation, produce etc. errors itself and irregular movement.
So, a actual installation and measurement as picture 1, 2,3
cross-axis sensitivity error occupied actually desired installation without cross-axis sensitivity error
Picture1 Cross-axis sensitivity error occupied by actual installation and object’s mechanical errors itself & irregular movement.
Actual misalignment when installing Desired alignment
Picture 2 inclinometer’s sensitivity axis align to actual tilting direction/axis
Appendix I
Advanced Technology of Vigor SST Series Inclinometer
SST series inclinometer has a good performance in tilt measurement field, as Cross-axis sensitivity error and Offset are considered
as two important factors of sensor total accuracy. With the unique angle measurement technology, it solves the installation problem
for users, such as actual tilt input axis is not in line with natural tilt sensing axis of sensor. Also with the misalignment parameter, users
will know how to install and get the accurate angle data as well.
Vigor creatively combines with “cross-axis sensitivity error” and “input axis misalignment” data together, and makes possibiliy for
more accurate tilt measurement at any angle point:
1. In industrial field, the measured object doesn’t usually tilt according to theory X or Y axis, sometimes a little bearing gap of
mechanical component will not maketilt with theory X or Y axis, and also there are many similar factors to effect to accuracy. If the
cross-axis sensitivity error is large enough , Y axis output data of sensor will be affected while X axis tilts a lot, and it is the same for
X axis while Y axis tilting. Therefore, for an inclinometer with 3~5% cross-axis sensitivity, even linearity is high enough, the total accuracy
should be reduced to 3~5% of the labeled, but not only real linearity data.
2. I the inclinometer doesn't have the "Allowed input-axis misalignment" parameter, engineers cannot get the tilt angel data with
accuracy assurance when alignment by eyes in installation. A large deviation between sensing axis of sensor and the actual tilt
direction of object will make an extra "sinusoidal error", and this extra error will accumulate into the output of the sensor. The extra
error will rise up while the tilt angel comes up.
Vigor’s SST series inclinometer has perfectly solved above problem , and realized the real absolute combined accuracy .
Appendix II
Core Competence of Vigor in Tilt Measurement Field
1. Modal test have to be made on each housing of SST inclinometer, rather than simply fixing a PCBA board into it.
2. PCBA board made a complete model test independently, also made the same test for PCBA&housing together, as it solves resonance
interference by environment vibration when suppress by filter.
3. Inclinometer testing is strictly executed as per relevant Chinese and international standard implementation, including GB, GJB,
MIL, IEC, ISO, EN, etc...
4. Nearly 20 kinds of invention patents, utility model patents, patents of appearance and software copyrights in the field of tilt
measurement.
5. Each inclinometer adopts patented automatic testing technology, which will greatly reduce human interference on the quality,
and keep the same quality consistency.
6. Vigor provides most accurate inclinometer in the world. The absolute accuracy can reach ±5 arc-seconds @ -40~85℃and zero
stability is up to ±3.6 arc-seconds within 12 months. We are still making it better.
7. Vigor is the first one in the world to bring the philosophy of “reducing users application cost”. Over 100 kinds of accessories will
greatly save users' time and cost in the process of project.
8. With strong research and design ability, Vigor provides various inclinometers in the world to meet different application requirements ,
also customized products can be designed as special request. Over 30 different industrial signal interfaces are available (include
aerospace and aeronautic).
9. Vigor is the largest manufacturer specialized in inclinometer . Over 50 staffs can provide quick-to-answer service .
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