Force measurement

The force acting between two bodies is determined by measuring the force . The devices or technical facilities for this are called scales or general force gauges , force transducers or force sensors if they are weight forces . The term dynamometer (from Greek: dynamis - force), which is still used occasionally in the English-speaking world, dates back to the 19th century .

This article provides an overview of the operating principles of the measurement of forces between two bodies. Individual sensor types are linked. For the basics of sensor technology, see measuring device .

The force that is exerted on a body by a force field can be determined by the acceleration caused by a distance-time measurement .

Spring dynamometer

Arrangements

The force is a vector quantity that can act in all three directions of space. Therefore one differentiates:

One-component force measurement

Most force sensors only measure force in one direction. The direction of force flow and measurement direction of the sensor must match so that tension or pressure is measured.

Multi-component force measurement

The force is measured in two or three spatial directions.

Depending on the installation, one differentiates:

Direct force measurement

The sensor connects two components and takes over the entire flow of forces. It must therefore meet the requirements for the strength and rigidity of the connection. The measuring range of the sensor must be larger than the force to be measured.

Indirect force measurement

The sensor is integrated into a component and only records part of the force to be measured (force shunt measurement). The advantage is that there are fewer demands on the sensor in terms of strength. The disadvantage is that calibration is necessary when installed.

Torque measurement

If the lever arm is known , a torque can be recorded as a force.

acceleration

If one of the two bodies is a test mass integrated into the measuring device, one speaks of an acceleration sensor .

Elastic deformation with displacement measurement

A modern 6-axis force / moment sensor that records both forces and torques in all three spatial directions.
The sensor is equipped with six or more strain gauges that detect deformations in the micrometer range. These deformations are converted into three force and torque components using a calibration matrix.

Most sensors use the elastic deformation of metal and convert the force linearly into a path. The Hooke's law describes the relationship; simplified:

${\displaystyle F=D\cdot \Delta l}$

( Spring force, spring constant , path difference after application of force) ${\displaystyle F}$ ${\displaystyle D}$ ${\displaystyle \Delta l}$

In the idle state (static force measurement) the spring force is equal to the force to be measured. The distance difference is determined with the methods of distance measurement for very small distances and displayed as a force. This includes:

• Spring dynamometers often used in school lessons, ring dynamometers , rotary scales , gravimeters
• inductive sensor : distance measurement with plunger
• capacitive sensor : the deformation changes the distance between two capacitor plates . The capacity does not change linearly with the force. These sensors are suitable for temperatures up to 700 ° C and especially for long-term measurements over several years.
• optical scanning in the atomic force microscope
• optical interference force sensors : a laser interferometer measures the distance to the deformation body. No electronics are required at the measuring point, no glue required, optical quantization without an A / D converter. The TU Ilmenau developed such sensors in 1984.
• Waveguide force microscopy : It is a method for measuring mechanical forces in biological systems on a small area. Waveguide resonance modes are excited in a flat, elastic layer system . If the system is locally deformed on the surface, for example by cell adhesion forces, the magnitude of the forces acting can now be determined using the resonance shift of the modes. Resolution up to 20 nN.

outdated:

• Mirror precision extensometer according to Martens : The deformation body moves a mirror via levers. A light pointer shows the measured value.
• Measure the path difference with a precision microscope on a line scale.
• Proving Ring : A ring converts the force into a change in length. Inside the ring there is a leaf spring which is made to vibrate manually. With a micrometer it is dampened again once without and once with force. The force is read on the micrometer as the difference between the two settings.

Elastic deformation with resistance measurement

• Strain gauges (DMS) increase their electrical resistance when stretched. They are glued onto deformation bodies or directly onto the measuring object and evaluated electrically. Frequencies up to 8 MHz are possible, they require temperature compensation, the long-term behavior is not so good because of the creep . A distinction is made between:
  • Metal strain gauges: The elongation and transverse contraction increase the electrical resistance.
  • Semiconductor strain gauges: The specific electrical resistance increases with expansion due to internal forces ( piezoresistive effect ). This effect results in a much greater sensitivity to metallic strain gauges.
• Thin-film sensors (DFS) are based on the same functional principle as strain gauges in that the electrical resistance changes with expansion or compression. Now, however, no strain gauges are glued to the deformation body, instead the strain-sensitive resistors are deposited directly on the sensor body and connected atomically. The DFS are then positioned directly in the power flow. Due to the double design of the Wheatstone measuring bridge , redundancy is included and the long-term behavior is significantly better because the viscoelastic processes of the adhesive layer are eliminated. The temperature behavior is also very good.
• Force Sensing Resistor (FSR) reduce their electrical resistance when force is applied. They consist of two insulated glued foils, one is coated with resistance material, the other with contact strips. You will e.g. B. used in touchpads .

outdated:

• Tasimeter : Change in resistance of coal due to pressure.

Magnetoelastic effect

The influence of the force changes the magnetic permeability µ (inverse magnetostriction ). This changes the magnetic flux transmitted from the primary coil to the secondary coil.

${\displaystyle F=f(\mu )}$

The advantages of this operating principle are high robustness against overloads and high sensitivity. The ABB company markets this measuring principle, which has been patented since 1954 , under the name Pressductor ^® .

Piezoelectricity

Main article: Piezoelectricity

In a piezoceramic element, the action of force creates a charge distribution Q that is proportional to the force.

${\displaystyle F\thicksim Q}$

Piezoelectric force transducers can be designed to be very rigid and also measure highly dynamic (up to over 100 kHz) forces. Due to the discharge of the charge, good results are not achieved with static and quasi-static loads. By stacking 3 discs with different measuring directions, multi-component force transducers are also possible.

Electromagnetic compensation

They work like an electrodynamic loudspeaker. A moving coil is located in a magnetic field. The current through the coil is proportional to the force on the coil when the deflection is compensated. A position control with a distance sensor keeps the coil in a fixed position. The general formula of the Lorentz force results in:

${\displaystyle F=B\cdot I\cdot l\quad \mid {\text{wenn}}\ B\perp l}$

( magnetic flux density, current, effective conductor length) ${\displaystyle B}$ ${\displaystyle I}$ ${\displaystyle l}$

Such force sensors can only measure very small forces (max. 20 ... 30 N) and are therefore used in precision scales, among other things.

Vibrating string principle

The period of a tensioned string or belt depends on the tension.

${\displaystyle F=4\cdot m_{\mathrm {b} }\cdot l^{2}\cdot f^{2}}$

( static tension force (strand force), related belt mass in kg / m, free strand length, natural frequency) ${\displaystyle F}$ ${\displaystyle m_{\mathrm {b} }}$ ${\displaystyle l}$ ${\displaystyle f}$

• general vibrating string transducers
• The belt tension of drive belts can be adjusted by optical frequency measurement of the vibration.

literature

• Wolfgang Weiler: Handbook of physical-technical force measurement. Vieweg Verlag, 1993, ISBN 3-528-08945-8
• Moritz Rühlmann: General mechanical engineering , Schwetschke Verlag, 1862 ( Google Books )

swell

1. ↑ Giebel, Karl-Friedrich: Waveguide microscopy: a new method for measuring force in biological systems. Doctoral thesis University Library Konstanz, July 17, 2003
2. ↑ Pressductor ^® ( Memento of the original dated September 8, 2014 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. 
3. ↑ Measure the belt tension

Web links

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