Appunti Industrial Measurements + Domande Scritto, Prof. Palermo

Introduction

The measurement of a physical quantity is composed by a number, an uncertainty range and a measurement unit

X = (x ± μ) g

• x = best value
• μ = uncertainty range
• g = measurement unit

The element that provides in measuring the physical quantity is the transducer

Passive Transducers: The energy necessary to do the conversion is provided by the measurand

Active Transducers: ... an external power source

Static Characteristics of Measurement Systems

Measurement Range

Is the range of measured values, the instrument can measure holding the other metrological characteristics (Sensibility, Stiffness, Rapidity, Precision)

The measurement range is limited by the upper limit and the lower limit

Nominal load: is the name of the upper limit if the lower limit is 0

Limit load: is the upper limit admitted to avoid permanent damages in the transducer

Sensibility (Sensitivity)

Is the attitude of the transducer to detect "small" variations of the measurand

Sensitivity S' is the derivative of the graduation curve

S = dσ/di

i ⟶ transducer ⟶ σ

Introduction

The measurement of a physical quantity is composed by a number, an uncertainty range and a measurement unit

X = (x ± u) θ

The element that provides in measuring the physical quantity is the transducer

• Passive
• Active

The energy necessary to do the conversion is provided by the measurand or an external power source

Static Characteristics of Measurement Systems

Measurement Range

Is the range of measurand values, the instrument can measure holding the other metrological characteristics (Sensibility, Stiffness, Rapidity, Precision)

The measurement range is limited by the upper limit and the lower limit

Nominal load: is the name of the upper limit if the lower limit is 0

Limit load: is the upper limit admitted to avoid permanent damages in the transducer

Sensibility

Is the attitude of the transducer to detect "small" variations of the measurand

Sensitivity S' is the derivative of the graduation curve

S = dσ/di

Accuracy and Precision

Accuracy

Is the function of systematic errors; it quantifies the closeness of the measure to the true value of the measurand (x_t)

Inaccuracy: ε_a = ^{(x̄ - x_t)}⁄_xt · 100

Precision

Is the function of random errors. A high precision means to obtain the same result doing many measures of the same quantity (under unchanged conditions)

• Highly Precise

  Poorly Accurate

  Systematic errors → Non Negligible

  Random errors → Negligible

• Poorly Precise

  Highly Accurate

  Systematic errors → Negligible

  Random errors → Non Negligible

• Highly Precise

  Highly Accurate

  Systematic errors → Negligible

  Random errors → Negligible

Hysteresis

Hysteresis error is defined as the maximum difference between the outputs of the same measure, when the load is increasing and decreasing.

If the input does not reach the full-scale value, hysteresis error is lower.

Repeatability

Is the aptitude of the instrument in giving the same outputs for the same inputs, under equal measurement conditions in short-time intervals.

It's quantified through the Repeatability Coefficient, which represents the value below which (with a probability of 95%) we may expect the difference between two successive measures.

Reproducibility

Is the aptitude of the instrument in giving the same output under changes of measurement conditions.

If the Reproducibility > Repeatability we must train operators in using instruments.

If the Repeatability > Reproducibility we must enhance maintenance of the instruments.

Stability

Stability is the attitude of the instrument in holding constants its metrological characteristics in time.

It can be quantified in several ways:

• In terms of the duration of a time interval over which a metrological characteristic changes by a stated amount.
• In terms of the change of a property over a stated time interval.

Resolution

The resolution represents the smallest change in a quantity that causes a perceptible change in the indication.

Noise

Noise is defined as the set of random variations of the transducer output caused by the transducer itself and/or by random combinations of influence on the measured.

• To reject noise it's possible to use filters.
• Filtering not always can make the signal free from noise; it depends on the distance between signal and noise band in the frequency domain.
• Minimum detectable signal: Under the hypothesis of a noise-free signal, i