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{{Language_sel|LANG=ger|ARTIKEL=Elektro-Mechanischer Kraftaufnehmer}}
{{PSM_Infobox}}
Electro-mechanical force transducers (load cell)
__FORCETOC__

==Physical measuring principle==

The physical measuring principle of the electro-mechanical force transducer, also known as a spring-loaded force transducer, is based on the [[Deformation#Elastic deformation|linear-elastic deformation]] of a suitable deformation body. When a tensile or compressive force is applied, elastic elongation or compression occurs and the [[Strain Gauge|strain gauges]] applied to the spring body elongate accordingly. This elongation corresponds to the ratio of the applied force to the spring constant of the deformation body ('''Fig. 1''').

[[File:Electro-mechanical_Force_Transducer-Fig1.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 1''':
|width="600px" |Scheme and operating principle of the electro-mechanical load cell
|}

In the case of solid materials, the spring constant corresponds to the [[Elastic Modulus|modulus of elasticity]] of the spring material ('''Eq. 1''').

{|
|-
|width="20px"|
|width="500px" | <math> \Delta L_{mech} = \frac{F\ L}{E\ A_{0}}</math>
|(1)
|}

By changing the geometry (cross-section ''A''0), force transducers for different force measurement ranges (e.g. 0.5 N to 1,000 kN) can be realised via the [[Stiffness#Tensile stiffness|tensile]] or [[Stiffness#Compressive and buckling stiffness|compressive stiffness]] ''E''⋅''A''0 of the spring body. The deformation causes a change in resistance of the strain gauges connected as a Wheatstone bridge, which in turn leads to a change in voltage ('''Eq. 2''').

{|
|-
|width="20px"|
|width="500px" | <math> \frac{dR}{R_{0}}=\epsilon \ (1+2\mu)+\frac{d\rho }{\rho_{0}}</math>
|(2)
|}

with
{|
|-
|''R''
|width="15px" |
|electrical resistance 
|-
|''μ''
|
|[[Poisson's Ratio|Poisson's ratio]] 
|-
|''ρ''
|
|specific resistance 
|-
|''ε''
|
|strain of the [[Strain Gauge|strain gauge]] 
|}

The proportionality of electrical voltage and strain in the load cell allows [[Calibration|calibration]] in the force unit to be carried out in the case of elastic reversible [[Deformation|deformation]]. When using such load cells in temperature control chambers, compensation for thermal expansion Δ''L''ther must be carried out ('''Eq. 3''').

{|
|-
|width="20px"|
|width="500px" | <math> \Delta L_{ther} = \Delta T L_{0} \ \alpha_{ther}</math>
|(3)
|}

with
{|
|-
|''L''0
|width="15px" |
|length of the deformation element 
|-
|''α''ther
|
|[[Thermal Expansion Coefficient|thermal expansion coefficient]] 
|}

==Design variants of force measuring systems==

Under load, this type of load cell always undergoes [[Deformation|deformation]] that is significantly greater than that of the [[Piezoelectric Force Transducer|piezoelectric force transducer]] and can no longer be neglected in terms of [[Machine Compliance|machine compliance]]. Modern testing systems therefore allow correction curves to be recorded that can compensate for such [[Measurement Deviation|measurement deviations]] in compliance. Sensors based on [[Strain Gauge|strain gauges]] operate largely drift-free and are therefore particularly well suited for [[Quasi-static Test Methods|quasi-static and static testing]] tasks. So-called [[Creep Plastics|creep]], i.e. the time-dependent but reversible change in the output signal under constant applied force, is extremely low, as it can be minimised by selecting the layout and arrangement of the [[Strain Gauge|strain gauges]]. Strain gauge-based force measurement systems always achieve higher limit frequencies when the nominal load of the transducers is high. Force transducers for small forces generally have soft spring elements with large deformations and a correspondingly low resonance frequency of the transducer. Various versions of these electromechanical force transducers are available in testing technology. These include, for example, bending beam transducers with [[Stiffness#Bending stiffness|bending stiffness]] ''E''⋅''I''y ('''Fig. 2a''') and S-shaped force transducers ('''Fig. 2b'''), whereby overload generally leads to detachment of the strain gauge or to [[Deformation#Plastic deformation|plastic deformation]] of the deformation element ('''Fig. 2c''') and thus to destruction of the force measuring cell [1].

[[File:Electro-mechanical_Force_Transducer-Fig2.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 2''':
|width="600px" |Design variants of electro-mechanical force transducers a) Bending cantilever, S-type transducer b) and overload of force transducers c)
|}

==See also==

* [[Strain Gauge|Strain gauge]]
* [[Material Testing Machine|Material testing machine]]
* [[Tensile Test#Tensile Test, Force Measurement Technique|Tensile test, force measurement technique]]
* [[Piezoelectric Ceramic|Piezoelectric ceramic]]
* [[Piezoelectric Force Transducer#Types of Load Cells|Piezoelectric force transducer – Types of load cells]]

==References==

{|
|-valign="top"
|[1]
|Laible, M., Müller, R. K., Bill, B., Gehrke, K.: Mechanische Größen elektrisch gemessen – Grundlagen und Beispiele zur technischen Ausführung. Expert Verlag, Renningen (2009) 7th Edition (ISBN 978-3-8169-2892-8)
|}

[[Category:Tensile Test]]
[[Category:Stiffness Compliance]]

Electro-mechanical Force Transducer - Revision history