FORCE

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MECHANICAL MEASUREMENTS
Prof. Dr. Ing. Andrei Szuder Tel.
40.2.1.4112604 Fax. [phone] www.labsmn.pub.
ro szuder_at_labsmn.pub.ro
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FORCE TORQUE MEASUREMENT
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Force vs. Mass measurements

• Balance systems compare weight of the known
  etalon with the force applied to the measuring
  arm

F
Fe

• If the measured force, F is the weight of a
  stationary object, then we balance the mass of
  the object with the mass of the etalon.

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Force MeasurementBy An ElasticElement

• Elastic elements are often employed for force
  measurements via stress/strain Hookes law

Where K is the deflection constant and y is the
deflection at some characteristic point. Table
13.1 in the textbook lists some characteristic
cases
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Important note Do not confuse the deflection
constant K with the Bridge Constant, also
labeled by K!
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Torque Measurements

• Most often, torque sensors are used in measuring
  the power of rotary machines, hence their other
  name, dynamometers. In this use, we measure
  dissipated energy by applying brake load to the
  shaft of a rotary engine, and measuring the
  angular velocity and torque.

where T is torque, F is force at displacement R
from the axis of rotation and ? is an angular
velocity (rad/s)
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Dynamometer types

• The main challenges in dynamomemeter design and
  use are controlled energy dissipation and signal
  transmission from the rotary member to the
  stationary equipment (using some kind of
  brushes). Today wireless transmission systems are
  often used.
• Based on the medium which dissipates energy
  (heat), dynamometers are classified as mecanical,
  hydraulic, electrical and transmission.
• Transmission dynamometers are passive elements
  inserted into the system - they do not dissipate
  energy.

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Torque Measurement By Different Strain
Gauge Configurations
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Dynamic response Second Order Systems

• Given the spring stiffness k, the damping
  coefficient c and the mass m, the spring/mass
  system with the damping element will follow

c
k
y
m
Fapplied
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2nd Ord. System Response To A Step Function
If the system is excitedby a step function
The general solution can be expressed as
where
is the undamped natural frequency (in radians)
is the damped natural frequency (in radians)
is the critical damping ratio,
is the critical damping coefficient,
is the static displacement as time goes to
infinity and
is the response phase lag
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The displacement due to an impulse signal will
depend essentially on two parameters the
critical damping ratio, ?, and the undamped
natural frequency, ?n.
Underdamped systems will swing above the
equilibrium few times before they settle at the
final level, while overdamped systems approach
the steady state from one side only!
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2nd Ord. System Response To A Harmonic Excitation
If the system is excitedby a harmonic function
it will pass through a transient stage and settle
into a stationary oscillation, with a certain
amplification ratio, yd /ys, and a phase lag, ? .
where
is the excitation cyclic frequency (rev/s) and
is the system undamped natural cyclic frequency.
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Notice that undamped system excited at natural
frequency will reach infinite amplification
ratio, i.e. it will come into resonance with the
excitation force. In practice, we try to limit
the useful frequency range to 20-40 of the
natural frequency, and have the damping ratio of
around 70.
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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.

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Torque measurement

• 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

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Torque measurement
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Torque measurement
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Torque measurement
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Torque measurement
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Torque measurement
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Torque measurement

• The excitation voltage for the strain gage is
  inductively coupled, and the strain gage output
  is converted to a modulated pulse frequency
• Maximum speed of such an arrangement is 15,000
  pm.

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Load cells
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Load cells

• Load cells became are the method of choice for
  industrial weighing applications

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Load cells

• Strain-gage load cells convert the load acting on
  them into electrical signals. The gauges
  themselves are bonded onto a beam or structural
  applied. In most cases, four strain gages are
  used to obtain maximum sensitivity and
  temperature compensation. Two of the gauges are
  usually in tension, and two in compression, and
  are wired with compensation adjustments
• Piezoresistive Similar in operation to strain
  gages, piezoresistive sensors generate a high
  level output signal, making them ideal for simple
  weighing systems because they can be connected
  directly to a readout meter.

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Load cells

• Inductive and reluctance Both of these devices
  respond to the weight-proportional displacement
  of a ferromagnetic core. One changes the
  inductance of a solenoid coil due to the movement
  of its iron core the other changes the
  reluctance of a very small air gap.
• Magnetostrictive The operation of this sensor is
  based on the change in permeability of
  ferromagnetic materials under applied stress. It
  is built from a stack of laminations forming a
  load-bearing column around a set of primary and
  secondary transformer windings. When a load is
  applied, the stresses cause distortions in the
  flux pattern, generating an output signal
  proportional to the applied load. This is a
  rugged sensor and continues to be used for force
  and weight measurement in rolling mills and strip
  mills.

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Load cells

• New Sensor Developments
• Fiber optic load cells are gaining attention
  because of their immunity to electromagnetic and
  radio frequency interference (EMI/RFI),
  suitability for use at elevated temperatures, and
  intrinsically safe nature. Work continues on the
  development of optical load sensors.
• Two techniques are showing promise
• measuring the micro-bending loss effect of
  single-mode optical fiber
• measuring forces using the Fiber Bragg Grating
  (FBG) effect.

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Load cells