Force Measurement

Force MeasurementWhere is it required?

• Weighing of an object• Dynamics of vehicles• Control applications such as deployment of air bag in a vehicle• Study of behaviour of materials under different types of loads• Vibration studies• Seismology or monitoring of earthquakes

Force Measurement

1.The forces acting within and between parts of a mechanism are fundamental to the safety, assembly, and use of any piece of equipment, whether that equipment be freely acting or an integral part of a process.

2. Force measurement is needed in many industries, and though the precision required may vary from a few percent to a few parts per million.

Force MeasurementThe SI system of units

Force and other Physical Quantities

1.Mass

Mass is a measure of the amount of material in an object, being directly related to the number and type of atoms present in the object. Mass does not change with position, movement, or alteration of the body’s shape unless material is added or removed.

The unit of mass in the SI system is the kilogram (kg)

Force Measurement

Force and other Physical quantities 2. Force •Force is a measure of the interaction between bodies. •Force takes a number of forms including short-range atomic forces, electromagnetic and gravitational forces.•Force is a vector quantity, with both direction and magnitude.•If the forces acting on a body in equilibrium are summed around the periphery of the body then they add to zero.

Force Measurement

Force and other Physical quantities

2. Force • If there is any resultant force acting then the body is not in equilibrium and it will accelerate such that the rate of change of the body’s momentum (velocity times mass) is equal to the force

• If the body is held stationary in some way, then there will be a reaction acting on the body from the support structure that is equal in magnitude and opposite in direction to the force imposed

Force Measurement

Force and other Physical Quantities 2. Force

With any vector quantity, the force and reaction may be projected onto three orthogonal axes, and the equilibrium may be considered independently parallel to each of those axes.

Frequently a force measurement system will react properly only to forces along its principal axis, and if this should not coincide exactly with the direction of the total applied force to be measured then an erroneous result may be generated.

Force Measurement


2. Force The SI unit of force is the Newton (N)

defined as the unit of force which would give to a mass of one kilogram is moved to an acceleration of 1 metre per second, per second.

It is not convenient, in practice, to produce an acceleration of 1 metre per second, per second acting on a mass of one kilogram in order to realise a standard of force of 1 Newton.

Force Measurement


1.Force Instead the practical realisation of the unit of force

makes use of known masses which, when subjected to the effect of local gravitational force, exert a known force on an earth located support.

The mechanical structure to handle and control such masses is known as a deadweight machine.

Force Measurement


3. Weight • weight is taken to mean the same as mass, and is measured in kilograms

• weighing as a process for determining the mass of an object

Force Measurement


4. Load• Load is a term frequently used in engineering to mean the force exerted on a surface or body

Force MeasurementForce Measurement Methods Direct method: This involves a direct comparison with a known gravitational force on a standard mass.Indirect method: This involves the measurement of the effect of force on a body. For example.1. Measurement of acceleration of a body of known mass

which is subjected to force.2.Measurement of resultant effect (deformation) when the force is applied to an elastic member.3.Transducing the unknown force to a fluid pressure and then measuring the fluid pressure. 4. Balancing the unknown force against a magnetic force

developed on account of interaction of a current carrying coil and a magnet.

Force MeasurementForce Measurement Methods

Direct method:1.Mechanical Weighing systems

i. Equal Arm Balance ii. Unequal Arm Balance

E.g The analytical balance

Multiple – lever systems

The pendulum Force-Measuring Mechanism


The analytical balance


Electromagnetic Balance:


Electromagnetic Balance :Advantages:

1.Easy to Use

2.Less sensitive to changes in environment

3.Smaller in size

4.Faster response

5.Produces electrical output

6.Easy to use with electronic automatic systems


Hydraulic Load Cell:


Hydraulic load cell :Advantages:

1.Good Dynamic Response

2.High load capacity up to 500 kN

3.Special units may measure up to 50 MN

4.Accuracy is about to 0.1% and resolution up to 0.02%

Disadvantages:

1.Friction between cylinder and piston

2.Maintenance

3.Sensitive to temperature


Pneumatic Load Cell:


Pneumatic load cell :Advantages:

1.Good dynamic Response

2.Load capacity up to 350 kN for single unit

3.Error 0.1% on full scale

Disadvantages:

1.Non linearity- so Care should be taken in the design

2.Dynamically unstable – so viscous damper is used

3.Sensitive to temperature

Force MeasurementForce Measurement MethodsElastic Sensing Elements :

Earlier methods discussed all are for measuring loads at static or slow varying conditions.

Many Force measuring systems employ some mechanical elastic member or a combination of members for measurement of both static as well as dynamic loads which may vary at frequencies upto many Khz.

Force MeasurementForce Measurement MethodsDiaphragm:

Force MeasurementForce Measurement MethodsDiaphragm:


Diaphragm:

Force MeasurementForce Measurement MethodsBellows:



Force MeasurementForce Measurement MethodsBourdon tubes:

Force MeasurementForce Measurement MethodsBourdon tubes:

Force MeasurementForce Measurement MethodsElastic devices commonly used for direct or indirect measurement of Force:

1.Coil Springs in tension

2.Proving rings in tension or compression

3.Load cells in tension or compression

Force MeasurementForce Measurement MethodsSpring Balances:

When force is applied

X= 8 D3n F/ Gd4

•The deflection of spring which is a linear function of force

• The displacement is indicated by a pointer and scale arrangement

• Reading accuracy may be improved by using mechanical magnifying systems.

Force MeasurementForce Measurement MethodsElastic devices commonly used for direct measurement of Force:

Coil Springs in compression

Force MeasurementForce Measurement MethodsElastic devices commonly used for direct measurement of Force:

Coil Springs in tension

Force MeasurementForce Measurement MethodsRing:• Steel rings, specially used for material testing where dead-weight gauges impractical to use because of material size

X= (π/2 – 4/ π)d3 F/ 16 EI• A displacement transducer is attached to the top and bottom of the proving ring• LVDT is normally used for measurement of deflection in the order of 1 mm• Strain gauge also can be used to measure the strain caused by the applied force• supporting 2kN to 2 MN

Force MeasurementForce Measurement MethodsRing:

Force MeasurementForce Measurement MethodsLoad Cells• Utilize an elastic member as the primary transducer and strain gauges as secondary transducer

• Strain gauge load cells

• Peizoelectric load cells

Force MeasurementStrain gauge :• Let us consider a long straight metallic wire of length l circular cross section with diameter d

• When this wire is subjected to a force applied at the end, a strain will be generated and as a result, the dimension will change (l changing to l+Δl, d changing to d+Δd and A changing to A+ΔA). For the time being, we are considering that all the changes are in positive direction

Force MeasurementStrain gauge :Now the resistance of the wire:

Force MeasurementStrain gauge :



• The change in resistivity of the material due to applied strain that occurs due to the piezo-resistance property of the material

• All the elements in the equation are independent of the geometry of the wire, subjected to strain, but rather depend on the material property of the wire

• Due to this reason, a term Gage Factor is used to characterize the performance of a strain gage

• The Gage Factor of metallic strain gages varies in the range 1.8 to 2.6

Force MeasurementStrain gauge :• The semiconductor type strain gages have a very large Gage Factor, in the range of 100-150 • The commercially available strain gages have certain fixed resistance values, such as, 120Ω, 350 Ω, 1000 Ω, etc. The manufacturer also specifies the Gage Factor and the maximum gage current to avoid self-heating (normally in the range 15 mA to 100 mA) • The choice of material for a metallic strain gage should depend on several factors. The material should have low temperature coefficient of resistance • It should also have low coefficient for thermal expansion


•Few alloys qualify for a commercial metallic strain gage areAdvance (55% Cu, 45% Ni): Gage Factor between 2.0 to 2.2

Nichrome (80% Ni, 20% Co): Gage Factor between 2.2 to 2.5

• Isoelastic another trademarked alloy with Gage Factor around 3.5 is also in use

• Semiconductor type strain gages, though having large Gage Factor, find limited use, because of their high sensitivity and nonlinear characteristics

Force MeasurementMetallic Strain gauge :

• They can be of two types: unbonded and bonded

• Capacity 300 MN

• The unbonded strain gage is normally used for measuring strain (or displacement) between a fixed and a moving structure by fixing four metallic wires in such a way, so that two are in compression and two are in tension

• The bonded strain gage, the element is fixed on a backing material, which is permanently fixed over a structure, whose strain has to be measured, with adhesive

• Most commonly used bonded strain gages are metal foil type

Force MeasurementMetallic Strain gauge :• The metal foil type strain gage is manufactured by photo-etching technique• The thin strips of the foil are the active elements of the strain gage, while the thick ones are for providing electrical connections• Because of large area of the thick portion, their resistance is small and they do not contribute to any change in resistance due to strain, but increase the heat dissipation area• It is easier to connect the lead wires with the strain gage• The strain gage in can measure strain in one direction only. But if we want to measure the strain in two or more directions at the same point, strain gage rosette, which is manufactured by stacking multiple strain gages in different directions, is used.


Un-Bonded type:


Bonded type:


Three element strain gage rosette 45 :

Force MeasurementForce Measurement MethodsSemiconductor type strain gauge• Semiconductor type strain gage is made of a thin wire of silicon, typically 0.005 inch to 0.0005 inch, and length 0.05 inch to 0.5 inch

• They can be of two types: p-type and n-type

• In p-type the resistance increases with positive strain

• In n-type the resistance decreases with positive strain

• MEMS pressure sensors is now a days becoming increasingly popular for measurement of pressure

Force MeasurementForce Measurement MethodsSemiconductor type strain gauge

Force MeasurementForce Measurement MethodsSemiconductor type strain gauge

Force MeasurementForce Measurement MethodsFactors considered in the design of load Cell

1. Stiffness of elastic element

2. Optimum positioning of gauges on the element

3. Provision for temperature compensation

Force MeasurementForce Measurement MethodsStrain gauge Load Cell

Force MeasurementForce Measurement MethodsStrain gauge Load Cell• Normal strain experienced by a strain gage is in the range of micro strain (typical value: 100 x 10-6)

• The change in resistance associated with it is small ΔR/R=Gε

• If a single strain gage is connected to a wheatstone bridge, with three fixed resistances, the bridge output voltage is going to be linear

• A single strain gage is normally never used in a wheatstone bridge. This is not because of improving linearity, but for obtaining perfect temperature compensation

Force MeasurementForce Measurement MethodsStrain gauge Load Cell• Load cells are extensively used for measurement of force; weigh bridge is one of the most common applications of load cell

• Here two strain gages are fixed so as to measure the longitudinal strain, while two other measuring the transverse strain

Force MeasurementForce Measurement MethodsStrain gauge Load Cell• The strain gages, measuring the similar strain (say, tensile) are placed in the opposite arms, while the adjacent arms in the bridge should measure opposite strains (one tensile, the other compressional

• The longitudinal strain developed in the load cell would be compressional in nature, and is given by:

ε=− F/AE

where F is the force applied, A is the cross sectional area and Y is the Young’s modulus of elasticity

Force MeasurementForce Measurement MethodsStrain gauge Load Cell• Tensile strain:

ε= νF/AE

where F is the force applied, A is the cross sectional area and Y is the Young’s modulus of elasticity ; ν- Poisson’s ratio

Force MeasurementForce Measurement MethodsStrain gauge Load Cell• Tensile- Compressive load cell:

Using two strain gauges with 90 deg

E0= (1+ ν)Gf εei/4

Where E0- Out voltage of the Bridge

Ei – Input voltage

Using Four strain gauges with 90 deg

E0= (1+ ν)Gf εei/2

Force Measurement

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