National Physical Laboratory

How many different types of force transducer are there? (FAQ - Force)

There are many types of force transducer and they are used with instrumentation of varying complexity. In designing or specifying a force measurement system for an application, it is useful to understand the basic operation of the transducer to be used and also their broad operating characteristics.

Details of different types of force transducers are given below under the following headings:

Strain gauge load cells

These are the most common type of force transducer, and a clear example of an elastic device. Each cell is based on an elastic element to which a number of electrical resistance strain gauges are bonded. The geometric shape and modulus of elasticity of the element determine the magnitude of the strain field produced by the action of the force. Each strain gauge responds to the local strain at its location, and the measurement of force is determined from the integration of these individual measurements of strain.

The rated capacities of strain gauge load cells range from 5 N to more than 50 MN. They have become the most widespread of all force measurement systems and can be used with high resolution digital indicators as force transfer standards.

The elastic element

The shape of the elastic element used in load cells depends on a number of factors including the range of force to be measured, dimensional limits, final performance and production costs.

Typical Strain Elements

The diagram shows a selection of different elastic elements and gives their typical rated capacities. Each element is designed to measure the forces acting along its principal axis, and not to be affected by other forces such as side loads. The arrows in the figure indicate the principal axis of each element.

a) compression cylinder 50 kN to 50 MN
b) compression cylinder (hollow) 10 kN to 50 MN
c) toroidal ring 1 kN to 5 MN
d) ring 1 kN to 1 MN
e) S-beam (bending or shear) 200 N to 50 kN
f) double-ended shear beam 20 kN to 2 MN
g) double-bending beam (simplified) 500 N to 50 kN
h) shear beam 1 kN to 500 kN
i) double-bending beam 100 N to 10 kN
j) tension cylinder 50 kN to 50 MN

The material used for the elastic element is usually tool steel, stainless steel, aluminium or beryllium copper, the aim being a material which exhibits a linear relationship between the stress (force applied) and strain (output) with low hysteresis and low creep in the working range. There also has to be high level of repeatability between force cycles to ensure that the load cell is a reliable measuring device. To achieve these characteristics it is usual to subject the material to a special heat treatment. This may include a sub-zero heat treatment cycle to achieve maximum stability.

The electrical resistance strain gauge

In electrical terms, all electrical resistance strain gauges may be considered as a length of conducting material, like a wire. When a length of wire is subjected to a tension within its elastic limit, its length increases with corresponding decrease in its diameter and change of its electrical resistance. If the conducting material is bonded to an elastic element under strain then the change in resistance may be measured, and used to calculate the force from the calibration of the device.

The most common materials used for the manufacture of strain gauges are copper-nickel, nickel-chromium, nickel-chromium-molybdenum and platinum-tungsten alloys and these are generally referred to by their trade names. There are a variety of resistance strain gauges available for various applications, some of which are described below. Each strain gauge is designed to measure the strain along a clearly defined axis so that it can be properly aligned with the strain field.

Foil strain gauges

The foil strain gauge is the most widely used type and several examples are shown in the diagram.  It has significant advantages over all other types of strain gauge and is employed in the majority of precision load cells. It consists of a metal foil pattern mounted on an insulating backing or carrier, constructed by bonding a sheet of thin rolled metal foil, 2 µm - 5 µm thick, on a backing sheet of 10 µm - 30 µm thick. The measuring grid pattern including the terminal tabs is produced by photo-etching.

Metal Foil Strain Gauges

The production techniques used are similar to those used in the integrated circuit manufacturing industry and lend themselves to automation and thus low unit cost. Typical backing materials are epoxy, polyimide and glass-reinforced epoxy phenolic resin. The backing provides electrical insulation between the foil and the elastic element, facilitates handling and presents a readily bondable surface. Sometimes the gauge is manufactured backed with an adhesive layer, reducing the amount of handling needed and time consumed. The epoxy or epoxy-derived backing material is difficult to handle due to its brittle nature, but it is preferred for use in high-precision load cells because of its superior performance especially in creep and low level of moisture absorption compared to polyimide type plastic.

A large variety of foil gauges are now commercially available to the transducer designer and general user.

Semiconductor strain gauges

These are manufactured from strips of semi-conducting silicon in either the ‘n’ or ‘p’ form. The output from a semiconductor gauge is very high compared to a wire or foil gauge. The gauge factor is a measure of the output for a given strain, and is typically 100 - 150 for a semiconductor and 2 - 4 for wire and foil. The output from semiconductor gauges is non-linear with strain, but they exhibit essentially no creep or hysteresis and have an extremely long fatigue life. High temperature sensitivity of the gauges means that careful matching of the gauges is required on any given load cell, and they are usually computer matched into sets on manufacture, but a high level of temperature compensation may still be required on the completed transducer. This type of gauge is widely used on ‘small’ transducers such as force transducers, accelerometers and pressure sensors whose sensing element may be micro-machined out of a single piece of silicon.

Thin-film strain gauges

Thin-film strain gauges are produced by sputtering or evaporating thin films of metals or alloys onto the elastic element. The manufacture of a thin film strain gauge system will go through several stages of evaporation and sputtering and may have up to eight layers of material. There are a number of thin-film strain gauge force transducers available covering a range of 0.1 N to 100 N in the form of a single- or double-bending beam configuration. These devices are highly cost effective when produced in large quantities due to the manufacturing techniques involved. This makes them ideally suited for use in large-volume products such as shop scales and pressure transducers.

Wire strain gauge

The wire strain gauge was the original type of resistance strain gauge, though now widely replaced by cheaper foil or thin film types. However the wire strain gauge is still used extensively for high temperature transducers and stress analysis, and is available made from a wide range of materials. The wire is typically 20 µm - 30 µm in diameter and may be bonded to the substrate using ceramic materials. It is less commonly used in the free form where the wire is looped around insulated pins which are mounted on the elastic member.

The nominal resistance of the strain gauge varies with the type and application. Wire gauges have resistances in the range of 60 ohms to 350 ohms, foil and semiconductor gauges from 120 ohms to 5 k ohms and thin film types around 10 k ohms. Selection criteria may include size, self-heating and power requirements. If several load cells are to be connected together then matched resistance may be important.

Piezoelectric crystal force transducers

When a force is exerted on certain crystalline materials, electric charges are formed on the crystal surface in proportion to the rate of change of that force.  To make use of the device, a charge amplifieris required to integrate the electric charges to give a signal that is proportional to the applied force and big enough to measure. The first transducers to apply the piezoelectric effect for measurement used naturally grown quartz but today mostly artificial quartz is used. Because of this these devices are often known as quartz force transducers,  though here more the general term piezoelectric crystalwill be used.

Piezoelectric Load Washers

These piezoelectric crystal sensors are different from most other sensing techniques in that they are active sensing elements. No power supply is needed and the deformation to generate a signal is very small which has the advantage of a high frequency response of the measuring system without introducing geometric changes to the force measuring path.

When packaged as a load washer, as in the photograph, and compressed under a force of 10 kN a typical piezoelectric transducer deflects only 0.001 mm. The high frequency response (up to 100 kHz) enabled by this stiffness and the other inherent qualities of the piezoelectric effect makes piezoelectric crystal sensors very suitable for dynamic measurements.

Extremely fast events such as shock waves in solids, or impact printer and punch press forces can be measured with these devices when otherwise such measurements might not be achievable. Piezoelectric sensors operate with small electric charge and require high impedance cable for the electrical interface.  It is important to use the matched cabling supplied with a transducer.

Mounting of a Load Washer

Piezoelectric crystal sensors are primarily designed for applications using a pre-tensioned bolt which allows the measurement of forces in both tension and compression. Mounting of a load washer in this way is illustrated in the diagram. The pre-loading is important to ensure optimum linearity and the sensor must be calibrated after mounting.  An extension of this principal is the use of force measuring pins which are placed within the structure of a machine and respond to the forces within the structure.

There is a small leakage of charge inherent in the charge amplifier, which is called drift of the signal. So while piezoelectric force transducers are ideally suited for dynamic measurements they cannot perform truly static measurements. Measurements can be made over a period of  minutes or even hours and  piezoelectric transducers are said  to take 'quasi-static' measurements.

Piezoelectric crystal sensors are suitable for measurements in laboratories as well as in industrial settings. The measuring range is very wide and the transducers survive high overload (typically > 100 % of  full-scale output). The sensors' small dimensions, large measuring range and rugged packaging makes them very easy to use. They can operate over a wide temperature range and survive temperatures of up to 350 °C.

Multi-Component Crystal Force Sensor

Multi-component piezoelectric force transducers

Multi-component piezoelectric force transducers measure the forces in three orthogonal axes and the diagram shows the operating principle of such a transducer.

Force F acts upon the transducer and is transmitted to each of three discs with the same magnitude and direction. Each piezoelectric crystal ring (shown ‘exploded’ in the figure) has been cut along a specific axis and the orientation of the sensitive axis coincides with the axis of the force component to be measured. Each then produces a charge proportional to the force component specific to that disc. The charge is collected via the electrodes inserted into the stack.

Measuring force through pressure

Hydraulic load cell

The hydraulic load cellis a device filled with a liquid (usually oil) which has a pre-load pressure. Application of the force to the loading member increases the fluid pressure which is measured by a pressure transducer or displayed on a pressure gauge dial via a Bourdon tube.

Hydraulic Load Cell

When used with a pressure transducer, hydraulic load cells are inherently very stiff, deflecting only about 0.05 mm under full force conditions. Although capacities of up to 5 MN are available, most devices fall in to the range of 500 N to 200 kN. The pressure gauge used to monitor the force can be located several metres away from the device by the use of a special fluid-filled hose. In systems where more than one load cell is used a specially designed totaliser unit has to be employed.

Hydraulic load cells are self-contained and need no external power. They are inherently suitable for use in potentially explosive atmospheres and can be tension or compression devices. Measurement uncertainties of around 0.25 % can be achieved with careful design and favourable application conditions. Uncertainties for total systems are more realistically 0.5 % to 1 %. The cells are sensitive to temperature changes and usually have facilities to adjust the zero output reading, the temperature coefficients are of the order of 0.02 % to 0.1 % per °C.

Pneumatic load cell

The operating principles of the pneumatic load cell are similar to those of the hydraulic load cell (above). The force is applied to one side of a piston or a diaphragm of flexible material and balanced by pneumatic pressure on the other side.  This counteracting pressure is proportional to the force and is displayed on a pressure dial.

The sensing device consists of a chamber with a close-fitting cap. The air pressure is applied to the chamber and builds up until it is equal to the force on the cap. Any further increase in pressure will lift up the cap allowing the air to bleed around the edge until pressure equilibrium is achieved. At this equilibrium position the pressure in the chamber is an indication of the force on the cap and can be read by the pneumatic pressure dial gauge.

Other types of force measurement system

Elastic devices

The loading column is probably the simplest elastic device, being simply a metal cylinder subjected to a force along its axis. In this case the length of the cylinder is measured directly by a dial gauge or other technique, and an estimate of the force can be made by interpolating between the lengths measured for previously applied known forces.  The proving ring is functionally very similar except that the element is a circular ring, and the deformation is usually measured across the inside diameter. These transducers have the advantage of being simple and robust, but the main disadvantage is the strong effect of temperature on the output.  Such methods find use in monitoring the forces in building foundations and other similar applications.

The linear variable differential transducer (LVDT) may be used within a load cell to measure the displacement of an elastic element instead of using strain gauges. The LVDT is essentially a transformer which provides an alternating current (AC) output voltage as a function of the displacement of a separate movable magnetic core. The lack of friction and the low mass of the core results in high resolution and low hysteresis, making this device ideal for dynamic measurement applications.

Capacitive load cells use a capacitance sensor to sense the displacement of an elastic element. In most cases the sensor consists of two parallel plates standing opposite each other. The changing length of a spring member produces a change in the gap between two plates, and hence a change in electrical capacitance. In the case of small weighing instruments such as domestic scales, the spring also provides parallel guidance of the scale's platform.

An optical strain gauge can be formed in a manner similar to a wire strain gauge by the use of optical fibres. The deflection of the elastic  force-bearing member with the optical strain gauge bonded to it will result in length changes in the optical fibres. If monochromatic light is used to feed two optical strain gauges experiencing different strain levels then the phase difference between the two beams emerging from the gauges, in number of half wavelengths, is a measure of the applied force.

The interference-optical load cell uses a high-resolution displacement measuring method. A fork-shaped spring is deformed by the force, the deformation being in the region of 40 µm, and the change of the aperture of the fork is measured by a Michelson interferometer. For the same resolution, the maximum elastic deformation and with it the strain of the material need not be as large as in the case of the strain gauge load cell. The deformation element is made of quartz (silica glass) with very small temperature dependence. Any residual error may be corrected by the use of a temperature sensor and computer. These systems have a limited temperature range from 5 °C to 40 °C for an overall performance better than 0.01%, and the hysteresis and creep are both particularly small. Optical systems based on Moiré fringe measurements are also manufactured.

Vibrating elements

In the case of the tuning-fork load cell, the force transducer consists of two parallel band splines which are connected at their ends and vibrate in opposite directions in resonance. The mode of vibration is like that of a tuning fork and the resonant frequency changes if the element is subjected to a tensile or compression force. The excitation of the vibration and the reciprocal reception of the vibration signals are carried out by two piezoelectric elements (see piezoelectric crystal force tranducers) close to the vibration node of the tuning fork. The tuning fork is typically about 25 mm long and made of Elinvar (Nickel steel with 13 % Chromium), with a rated capacity of 8 N, a resonant frequency of 6 kHz to 7 kHz and a linearity performance of between 0.01 % and 0.02 %

The vibrating-wire transducer consists of a taut ferromagnetic wire that is excited into transverse vibrations by a drive coil. These vibrations are detected using a pick-up coil. Both coils have permanent magnet cores and once the wire has been excited to its resonant frequency for a given tension, it is maintained at this frequency by connecting the two coils through an amplifier to form a self-oscillating system. Each resonant frequency is a measure of the wire’s tension and hence, applied force at that instant. The advantage of the vibrating wire transducer is its direct frequency output which can be handled by digital circuitry eliminating the need for an analogue-to-digital converter. The vibrating wire principle is used to measure force in pressure transducers and strain levels in civil engineering applications.

In the surface-wave resonator load cell, an ultrasonic transmitter which is actuated  by alternating voltage and consists of comb-shaped electrodes on a quartz substrate, emits surface sound waves directed according to the inverse piezoelectric effect.  A second system which is arranged in the same way converts these sound waves back into an alternating voltage, according to the piezoelectric effect.  The amplifier is so arranged that the system vibrates in natural frequency.  The deformation of a spring, which depends on force, changes the resonator frequency.

Magneto-elastic devices

The magneto-elastic force transducer is based on the effect that when a ferromagnetic material is subjected to mechanical stress, the magnetic properties of the material are altered and the change is proportional to the applied stress. Due to the sturdy construction, high signal level and small internal resistance, the magneto-elastic load cell can be used in rough and electrically disturbed environments such as in rolling mills.  The rated capacities of these devices is in the range from 2 kN to 5 MN.

Dynamic balance devices

Gyroscopic load cells exploit the force sensitive property of a gyroscope mounted in a gimbal or frame system. A commercially available gyroscopic load cell incorporates a dynamically balanced heavy rotor on a spindle, itself mounted in the inner frame of a two-gimbal system. The arrangement has three axes of rotational freedom mutually at right angles and has the axis of origin on the centre of gravity of the rotor. The force to be measured by the transducer is applied through the lower swivel and a couple is produced on the inner frame causing the gimbals to precess. The time taken for the outer gimbal to complete one revolution is then a measure of the applied force. The gyroscopic load cell is essentially a fast responding digital transducer and is inherently free of hysteresis and drift.

The force balance uses a feedback circuit to compare the electrical output to the force input. A typical system has attached to the force input member an electrical coil which operates in the flux gap of a permanent magnet.  An electric current passed through the coil generates a restoring force in opposition to the applied force. A displacement transducer is used to sense the displacement of the force input member, its output being amplified and used to control the current in the coil until the restoring force exactly balances the applied force and restores the force input member to its original position. The coil current to achieve this balance is proportional to the applied force and is measured as a voltage sensed across a resistor in series with the coil. This type of device has good dynamic performance, small deflection and relative insensitivity to environmental conditions. They are inherently stable and accurate and as a result are often considered for the use as secondary standards. This type of device is mainly a competitor for the mechanical analytical balance in mass determination.

Plastic deformation

Plastic deformation may be used as a method of permanently recording an applied force. The force is applied to a small (usually metal) element which suffers permanent deformation beyond the elastic limit of the material.  The deformation for a particular size, shape and material properties may be calibrated by testing of similar elements.

Last Updated: 25 Mar 2010
Created: 8 Oct 2007