Download Force Measurement

Force Measurement
 Force
is a quantity capable of
changing the size, shape, or motion
of an object. It is a vector quantity
and, as such, it has both direction
and magnitude. In the SI system, the
magnitude of a force is measured in
units called Newton, and in pounds in
the British/American system.
Force Measurement
 If
a body is in motion, the energy of
that motion can be quantified as the
momentum of the object, the product
of its mass and its velocity. If a body
is free to move, the action of a force
will change the velocity of the body.
Force Measurement
There are four basic forces in nature:




gravitational,
magnetic,
strong nuclear, and
weak nuclear forces.
The weakest of the four is the gravitational force. It is also
the easiest to observe, because it acts on all matter and it
is always attractive, while having an infinite range. Its
attraction decreases with distance, but is always
measurable. Therefore, positional "equilibrium" of a body
can only be achieved when gravitational pull is balanced
by another force, such as the upward force exerted on our
feet by the earth's surface.
Force Measurement
Link-Type Load Cell
The diagram above
represents what might
happen if a strip of
metal were fitted with
four gauges.
An downward bend
stretches the gauges
on the top and
compresses those on
the bottom.
A load cell may
contain several similar
strain gauges
elements.
3
4
1
2
Shear Force Measurement
Beam-Type Load Cell
The strain gauges are bonded on
the flat upper and lower sections
of the load cell at points of
maximum strain. This load cell
type is used for low capacities
and performs with good linearity.
Its disadvantage is that it must be
loaded correctly to obtain
consistent results
http://www.rdpelectronics.com/ex/hiw-sglc.htm
Force Calculation
Where:
A is the cross-sectional area
E is the modulus of elasticity
P
ea =
AE
v is Poissin’s ratio of the material
Sg is a gauge factor
Vo =
vP
& et = AE
Sg P (1 + v )Vs
2 AE
Sg P
D R1 D R3
=
= Sg ea =
R1
R3
AE
VO
vSg P
D R2 D R4
=
= Sg et =
R2
R4
AE
VS
Force Measurement
Vo =
Sg P (1 + v )Vs
2 AE
VO
VO= k PVS
Therefore Force P is measured
in terms of Voltage out put as
VO
VS
Force Measurement
This Load incorporates ring as the elastic element. Ring-Type
The ring element can be designed to cover wide
range loads by:
SPR 3
• radius,
•The thickness, t,
•The depth w.
v o = 1.79
3
 = 1.79 PR3/(Ewt3) = K .P
Where E is modulus of Elasticity of material;
K for given ring is constant = 1.79 R3/(Ewt3)
Out put Volts = Vo = S  Vs and S is sensitivity of LVDT
P
vs
Ewt
Ewt 3
P = 0.56
vo
3
SR v s
Strain Gauge or LVDT could be employed to
measure displacement related to Force applied. In
case of LVDT compression of the ring , the
relationship between displacement  and Load P
and is given by:
Load Cell
R
LVDT
t
w
Ring-Type Load Cells

Industrial Ring-Type Load Cells
Torque:
Forces that cause extended objects to rotate
are associated with torques. Mathematically,
the torque on a particle is defined as
the cross-product:
Where
r
r is the particle's position vector relative
r to a pivot
F is the force acting on the particle.
Torque Measurement
A circular shaft with four strain gages
mounted on two perpendicular helices
that are diametrically opposite one
another as shown below. Gage 1 & 3
are mounted on right hand helix, sense
a positive; while 2 &4 are mounted on
left hand helix giving negative sense.
The shearing stress  in the circular
shaft is related to the applied torque T
by the equation:
TD 16T
t xz =
=
2J p D3
1
2
3
4
Torque Measurement
Where
TD 16T
t xz =
=
2J p D3
D is diameter of the shaft
J polar moment of inertia
xz is shearing stress
 is Stress as per Hooke’s Law
T is Torque applied
 is Poisson Ratio of Material
16T 1 + u
16T 1 + u
e1 =
(
) ; e2 = (
)
3
3
pD
E
pD
E
E is Modulus of Elasticity
Sg is sensitivity of Strain Gage
Vo is output voltage, and
Vs is supplied voltage to Bridge
VR1
VR2 VR3
VR4 16T 1 + u
==
==
(
)Sg
3
R1
R2
R3
R4
pD E
16T 1 + n
vo =
(
)Sg v S = kT
3
pD
E
Torque Measurement
Torque is measured by either sensing
the actual shaft deflection caused by
a twisting force, or by detecting the
effects of this deflection. The surface
of a shaft under torque will
experience compression and tension.
To measure torque, strain gage
elements usually are mounted in pairs
on the shaft, one gauge measuring
the increase in length (in the direction
in which the surface is under tension),
the other measuring the decrease in
length in the other direction.
Torque Measurement
A strain gage can be installed directly on a shaft. Because
the shaft is rotating, the torque sensor can be connected
to its power source and signal conditioning electronics via
a slip ring.
The strain gage also can be
connected via a transformer,
eliminating the need for high
maintenance slip rings.
The excitation voltage for the
strain gage is inductively
coupled, and the strain gage
output is converted to a
modulated pulse frequency.



t's a measure of the forces that
cause an object to rotate. Reaction
torque is the force acting on the
object that's not free to rotate. An
example is a screwdriver applying
torque to a rusted screw.
With rotational torque, the object is
free to rotate. Examples include
industrial motor drives and gear
reducers.
Torque and RPM determine
horsepower, and horsepower
determines system efficiencies.
Torque
Magnetostriction effect
Force or Torque Measurement
Vertical Foot Force

Abstract A capacitive transducer is developed which continuously
measures the vertical component of foot forces during walking. The
transducer is shaped like an insole and consists of two
subtransducer units, the front and rear. The outputs of the two units
are summed to give the total force exerted by the foot. Each unit has
a multilayered structure. The basic layer is a 2 mm Neoprene sponge
sheet sandwiched by two 50 μm copper foils. They as a whole form a
capacitor. The other two layers are a driving shield and static shield,
which minimise the effect of stray capacitance and power-line noise,
respectively. The transducer is thin (3·8 mm), light (90 g) and flexible
and so does not hinder the natural gait pattern. It can be attached to
the sale of the shoe easily by elastic bands and Velcro straps. The
accuracy of the transducer is well within ±10 per cent of the full
scale. An error analysis is made to clarify the change in sensitivity
owing to a localised foad. The results are used to compensate for the
inherent nonlinearity of the transducer units.