# chapter5

```Chapter 5: Tool Dynamometers
LEARNING OBJECTIVES
] Different types of transducers used in Dynamometers
] Design Requirements
] Types of Dynamometers
--------------------------------------------------------------------------------------------------------------------Introduction:
Dynamometers are devices used to measure cutting forces in machining operation. The
cutting force cannot be detected or quantified directly but their effect can be sensed
using Transducer. For example, a force which can neither be seen nor be gripped but
can be detected and also quantified respectively by its effect and the amount of those
effects (on some material) like elastic deflection, deformation, pressure, strain etc.
These effects, called signals, often need proper conditioning for easy, accurate and
reliable detection and measurement. In other words, Measurement involves three
stages
Conversion into another suitable variable (deflection, expansion etc)
Amplification, filtration and stabilization
Measurement of cutting force(s) is based on three basic principles:
] measurement of elastic deflection of a body subjected to the cutting force
] measurement of elastic deformation, i.e. strain induced by the force
] measurement of pressure developed in a medium by the force.
Measuring deflection caused by the cutting force(s)
Under the action of the cutting force, say FC in turning, the tool or tool holder elastically
deflects as indicated in Fig.1 Such tool deflection, δ is proportional to the magnitude of
the cutting force, FC, simply as,
Treating the tool as a cantilever beam, we can write the deflection of the tool as
Since for a given cutting tool and its holder, E and I are fixed, we can write, δ F
C
Compiled by: Jagadeesha T, Assistant Professor, MED, National Institute of Technology, Calicut
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Fig.1: Deflection of the cutting tool.
The deflection, δ, can be measured
mechanically by dial gauge (mechanical transducer)
electrically by using several transducers like; ⎯ potentiometer; linear or circular ⎯
capacitive pickup ⎯ inductive pickup
LVDT ( Linear Variable Differential Tranformer)
Figure 2: Electrical transducers working based on deflection measurement
(a) linear pot (b) circular pot (c) capacitive pick up (d) LVDT type
Compiled by: Jagadeesha T, Assistant Professor, MED, National Institute of Technology, Calicut
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Under the action of the cutting force, say FC in turning, the tool or tool holder elastically
deflects as indicated
In case of mechanical measurement of
the tool deflection by dial gauge,
calibration is done by employing known
loads, W and the corresponding tool
deflections, δ are noted and then
plotted as shown in Fig. 3. Here the
slope of the curve represents the
constant, k of the equation
δ = k (constant) F
C
The capacitative pick up consists of two
plates with an intervening air gap. The
mechanical deformation causes a
change in air gap, thus changing the
capacitative effect.
Fig. 4 Capacitative pick up dynamometer
Measuring cutting force by monitoring elastic strain caused by the force.
Increasing deflection, δ enhances sensitivity of the dynamometer but may affect
machining accuracy where large value of δ is restricted, the cutting forces are suitably
measured by using the change in strain caused by the force. Fig. 4 shows the principle
of force measurement by measuring strain, ε, which would be proportional with the
magnitude of the force, F (say F ) as,
c
Compiled by: Jagadeesha T, Assistant Professor, MED, National Institute of Technology, Calicut
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Figure 4: Measurement of cutting force by strain gauges
M = Bending moment
Z = Sectional modulus of the tool section
I = plane moment of inertia of the plane section
y= distance of straining surface from the neutral plane of the beam
The strain, ε induced by the force changes the electrical resistance, R, of the strain
gauges which are firmly fixed/pasted on the surface of the tool-holding beam as
G = gauge factor (around 2.0 for conductive gauges) . The change in resistance of the
gauges connected in a wheatstone bridge produces voltage output ∆V, through a strain
measuring bridge (SMB) as indicated in Figure 5.
Figure 5: Force measurement by strain gauge based transducer.
Out of the four gauges, R , R , R and R , two are put in tension and two in compression
1
2
3
4
as shown in Fig. 4. The output voltage, ∆V, depends upon the constant, G and the
summation of strains as,
Compiled by: Jagadeesha T, Assistant Professor, MED, National Institute of Technology, Calicut
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Measuring cutting forces by pressure caused by the force
This type of transducer functions in two ways :
the force creates hydraulic or pneumatic pressure (through a diaphragm
or piston) which is monitored directly by pressure gauge as indicated in
Figure 6.
the force causes pressure on a piezoelectric crystal and produces an emf
proportional to the force or pressure as indicated in Figure 7.
emf = λtp where λ = voltage sensitivity of the crystal
t = thickness of the crystal
p = pressure
Figure 6: Force measurement by strain gauge based transducer
Figure 7 : Force measurement by strain gauge based transducer
Compiled by: Jagadeesha T, Assistant Professor, MED, National Institute of Technology, Calicut
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Requirement of a cutting force dynamometer
The dynamometer should have sufficient mechanical rigidity to avoid excessive
deformation of the cutting edge under the action of cutting forces
It should have sufficient sensitivity to enable measurement of cutting forces with
sufficient accuracy
It should have high stiffness and low mass, ensuring 100 percent transmissibility
of force by its very high natural frequency. This feature will also enable the
recorded force to be unaffected by the exciting vibration due to machining
process itself. Example : milling , grinding and shaping
It should be capable of indicating individual force components without any cross
effect, while measuring such forces simultaneously
The measuring system should be stable with reference to time, temperature and
humidity, requiring only occasional checking after calibration.
Compiled by: Jagadeesha T, Assistant Professor, MED, National Institute of Technology, Calicut
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