Electro-mechanical Force Transducer

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Electro-mechanical force transducers (load cell)

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 linear-elastic deformation of a suitable deformation body. When a tensile or compressive force is applied, elastic elongation or compression occurs and the 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).

Fig. 1:

Scheme and operating principle of the electro-mechanical load cell

In the case of solid materials, the spring constant corresponds to the modulus of elasticity of the spring material (Eq. 1).

$\Delta L_{mech}={\frac {F\ L}{E\ A_{0}}}$

(1)

By changing the geometry (cross-section A₀), force transducers for different force measurement ranges (e.g. 0.5 N to 1,000 kN) can be realised via the tensile or compressive stiffness E⋅A₀ 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).

${\frac {dR}{R_{0}}}=\epsilon \ (1+2\mu )+{\frac {d\rho }{\rho _{0}}}$

(2)

with

R		electrical resistance
μ		Poisson's ratio
ρ		specific resistance
ε		strain of the strain gauge

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

$\Delta L_{ther}=\Delta TL_{0}\ \alpha _{ther}$

(3)

with

L0		length of the deformation element
αther		thermal expansion coefficient

Design variants of force measuring systems

Under load, this type of load cell always undergoes deformation that is significantly greater than that of the piezoelectric force transducer and can no longer be neglected in terms of machine compliance. Modern testing systems therefore allow correction curves to be recorded that can compensate for such measurement deviations in compliance. Sensors based on strain gauges operate largely drift-free and are therefore particularly well suited for quasi-static and static testing tasks. So-called 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 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 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 plastic deformation of the deformation element (Fig. 2c) and thus to destruction of the force measuring cell [1].

Fig. 2:

Design variants of electro-mechanical force transducers a) Bending cantilever, S-type transducer b) and overload of force transducers c)

See also

• Strain gauge
• Material testing machine
• Tensile test, force measurement technique
• Piezoelectric ceramic
• Piezoelectric force transducer – Types of load cells

References

[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)