# Force sensor vs Strain Sensor

Newton's first law of inertia states that "Every body persists in its state of rest or of uniform motion in a straight line unless it is compelled to change that state by forces impressed on it". The other words it means that "if no net force applied on a body, its acceleration(a) will be equal to zero".

To understand force sensor, let us understand force first. As mentioned when force is applied to a free body, it gives the body an acceleration in the direction of force. From Newton's research acceleration is proportional to acting force 'F' and inversely proportional to the property of a body called mass 'm'.

a = F/m
Where a is acceleration ,
F is the Force and is vector quantity
m is the mass and it is scalar value

The force unit is "the force which will accelerate 1 kg mass to acceleration of value 1 m/s2". The unit of this force is also referred by Newton.

Newton's third law provides relation between two bodies. It states that "To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal and directed to contrary parts".

In engineering density of medium refers to amount of matter per unit volume. The measurement of force is very important in the branch of civil and mechanical engineering for various measurements. Whenever pressure is measured; it requires measurement of force. Usually force is measured when dealing with solids; whereas pressure is measured when dealing with fluids such as liquids and gases. In other words, force is considered when action is applied to the spot while pressure is measured when force is distributed over large area.

Force sensors are categorized into two broad classes viz. quantitative and qualitative.

A quantitive sensor actually measures the force and represents its value in terms of an electrical signal. For example strain gauge and load cell.

The qualitative sensors are the threshold devices. Their function is that output signal will be available when magnitude of force exceeds a predetermined threshold level. This is subject to strong force. The computer keyboard is the example of such type of force sensor. This type of qualitative force sensors are used in motion and position detectors. The qualitative pressure sensors are pressure sensitive floor mat and piezoelectric cable.

Following methods are employed in force sensor to sense the force.

1.)By balancing the unknown force against the gravitational force of a standard mass.

2.)By measuring the acceleration of a known mass to which the force is applied.

3.)By balancing the force against an electromagnetically developed force.

4.)By converting the force to a fluid pressure and measuring that pressure.

5.)By measuring the strain produced in a elastic member by the unknown force.

Methods 3, 4 and 5 are most commonly used in modern sensors.

In most of the sensor designs, force does not get convert directly into electrical signal. some intermediate steps are taken. For example, force sensor can be developed by combining force to displacement converter and position sensor.

Former can be designed using simple coil spring whose compression displacement x is defined using spring coefficient k and force F such that
x = k* F

Figure-1(a) depicts force sensor consisting of spring and LVDT displacement sensor . LVDT sensor produces voltage proportional to applied force. The other type of sensor constructed is shown in fig-2.b) using spring and pressure sensor. The pressure sensor is combined with a fluid filled bellows which is subjected to force. The fluid filled bellows functions as a force to pressure converter by distributing a localized force at its input over the sensing membrane of a pressure sensor.

## Strain Gauge

One of the popular example of strain sensor is strain gauge. It is a resistive elastic sensor whose resistance is function of applied strain. As all the materials require some force to deform and hence resistance can be proportional to the applied force. This is referred as piezoresistice effect. The effect is expressed using gauge factor(Se) as mentioned in the table for few of the materials.

Material Strain gauge factor Resistance Temperature coefficient of resistance
57% Cu and 43% Ni 2 100 10.8
Platinum Alloys 4 to 6 50 2160
Silicon -100 to +150 200 90000

For small variations in resistance below about 2% , resistance of wire depends on gauge factor as follows:
R = R0 * (1 + x), where R0 is the resistance with no stress applied and x proportional to gauge factor. Resistance increase with tension and decrease with compression.

The semiconductor strain gauges are quite sensitive to temperature variations and hence temperature compensating networks are incorporated in the design of strain gauges.