Accuracy
In metrology, accuracy is defined as the degree of agreement between the displayed (measured) and the “correct” value.
Sensors: Accuracy
In the International Dictionary of Metrology (VIM), accuracy is defined as:
“Extent of approximation of a measured value to a true value of a measured quantity”
A measuring device (a sensor, a display device) is considered accurate if it has high measurement precision and high measurement accuracy .
“Measurement accuracy” is not a fixed quantity and is not expressed quantitatively. A measurement is “more accurate” if it has a smaller measurement deviation.
” Measurement accuracy ” is also not a quantity. With a high degree of measurement accuracy, systematic errors and absolute deviations are small.
” Measurement precision ” describes the “degree of agreement between indications or
measurements obtained by repeated measurements on the same or similar objects under specified conditions” (VIM, Dictionary of Metrology).
Measurement Uncertainty
Measurement uncertainty describes the dispersion of measured values. It can be characterized, for example, by a standard deviation (or by multiples of the standard deviation). However, it generally also includes systematic errors, such as deviations from standards. Method A for determining measurement uncertainty uses statistical methods performed on values
All (statistical) components not attributable to determination method A are assigned to determination method B. These are based on information, e.g., experience, technical data from a calibration certificate, the accuracy class of a tested measuring instrument, drift, etc.
The “standard measurement uncertainty” is a measurement uncertainty that is determined as the standard deviation.
The relative standard measurement uncertainty describes the standard deviation divided by the absolute value of the measured value and is usually expressed as a percentage.
Accuracy class
according to VIM, Dictionary of Metrology:
“Class of measuring instruments or measuring systems that meet specified metrological requirements, which are intended to ensure that measurement deviations or instrument measurement uncertainties remain within specified limits under defined operating conditions.”
The accuracy class is generally indicated by a (positive) number, or by a sign or symbol.
The accuracy class thus serves to compare similar sensors, as a summarizing (and highly simplifying) selection criterion.
The following properties are used to classify force and torque sensors into an accuracy class:
- Relative standard measurement uncertainty
- Relative linearity deviation and hysteresis
- Temperature-related drift of the zero signal
- Temperature-related drift of the slope of the characteristic curve
Example Load Cell
The load cell is specified in the data sheet with an accuracy class of 0.5%.
The relative standard measurement uncertainty is determined, for example, by the standard deviation, especially when more than 10 measurements have been carried out.
When calibrating a sensor, three series of measurements are usually carried out, whereby the force is increased, for example, in 5 or 10 steps, in order to determine the repeatability and the linearity deviation.
The repeatability or “range” brv is determined as the maximum difference in output signals at the same force in the same installation positions, relative to the mean output signal reduced by the zero signal in the installed state. brv is a measure of comparability.
Fig. 1: Result of the calibration of a 5 kN load cell
The datasheet for the 5kN load cell specifies an accuracy class of 0.5. In the present (representative) example, the range at 25% of the rated load is 0.16% of 1.25 kN (of the actual value). Since the standard deviation cannot be calculated due to the small number of measurements, the calibration report calculates the difference between the maximum and minimum values
Due to its range of 0.16% at a load level of 25%, the 5kN force sensor can be classified in accuracy class 0.2.
Another criterion for classification is the relative linearity deviation. At 0.04%, this is also significantly smaller than the accuracy class of 0.2%. The relative linearity deviation describes the maximum deviation of a force transducer’s characteristic curve, determined under increasing force, from the reference line, relative to the full-scale value used.
To determine the hysteresis, calibration under increasing and decreasing loads would be necessary. A special case of hysteresis is the zero-point return error (at 0% load). This is shown in the present calibration certificate and is less than 0.00% (beginning and end of the measurement series). Since the force sensor is made of high-strength spring steel, a systematic error is usually responsible for the hysteresis, e.g., the use of linear guides, insufficiently flat ground contact surfaces for the force sensor, storage of spring energy in accessories for force application, etc.
The temperature-related drift of the slope depends on the properties of the spring steel (decrease in the modulus of elasticity with increasing temperature) and on the properties of the strain gauge (increase or decrease in the k-factor with increasing temperature). These properties are known as systematic influences and are compensated for well below 0.2%/10°C. Therefore, they only need to be measured as part of type approval or can even be derived from the strain gauge’s technical data.
For the force sensor to be classified in accuracy class 0.5, the temperature-related drift of the characteristic value (the slope) should be less than 0.5%/10°C.
The temperature-related drift of the zero signal must be measured and compensated for individually for each sensor.
Figure 2 shows the temperature-related drift of the zero signal for a 5kN sensor:
Fig. 2: Temperature-related drift of the 5kN between 20°C and 80°C.
Fig. 3: Measurement of the temperature-induced drift of the zero point of the 5kN load cell.
For a force sensor to be classified in accuracy class 0.5, the temperature-related drift of the zero signal over a temperature range of 10°C should be less than 0.5% of the sensor’s characteristic value.
With a characteristic value of 1 mV/V (FS, “Full Scale”), this means a maximum drift of 0.005 mV/V / 10°C.
Figures 2 and 3 show the drift per 60°C. For the given force sensor, the drift is therefore 0.00838 mV/V/60°C = 0.0014 mV/V/10K = 0.14% FS/10K
