# Mod10 Dynamometers

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Module
2
Mechanics of
Machining
Lesson
10
Dynamometers for
measuring cutting
forces
Instructional objectives
At the end of this lesson, the students would be able to
(i) show the general principle of measurement
(ii) classify and apply different transducers for converting cutting forces
into suitable signals
(iii) state the design requirements of tool-force dynamometers
(iv) develop and use strain gauge type dynamometer for
turning
drilling
milling
grinding
(i) General principle of measurement.
The existence of some physical variables like force, temperature etc and its
magnitude or strength cannot be detected or quantified directly but can be so
through their effect(s) only. For example, a force which can neither be seen
nor be gripped but can be detected and also quantified respectively by its
effect(s) 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. The basic principle and general method of measurement is
schematically shown in Fig. 10.1.
The measurement process is comprised of three stages:
Stage – 1 : The target physical variable (say force) is converted proportionally
into another suitable variable (say voltage) called signal, by using
appropriate sensor or transducer.
Stage – 2 : The feeble and noisy signal is amplified, filtered,
rectified (if necessary) and stabilized for convenience
and accuracy of measurement.
Stage – 3 : where the conditioned signal (say voltage) is quantitatively
determined and recorded by using some read out unit like
galvanometer, oscilloscope, recorder or computer.
Physical variable
(cutting force, temp. etc.)
Conversion into another
suitable variable
(deflection, expansion etc)
Amplification, filtration and
stabilization
Transducing stage (1)
Signal
Conditioning stage (2)
Conditioned signal
Fig. 10.1 General principle of measurement.
(ii) Different types of transducers used in dynamometers for
measuring machining forces.
Measurement of cutting force(s) is based on three basic principles :
(a) measurement of elastic deflection of a body subjected to the
cutting force
(b) measurement of elastic deformation, i.e. strain induced by the
force
(c) measurement of pressure developed in a medium by the force.
The type of the transducer depends upon how that deflection, strain or
pressure is detected and quantified.
(a) Measuring deflection caused by the cutting force(s)
Under the action of the cutting force, say P
Z
in turning, the tool or tool holder
elastically deflects as indicated in Fig. 10.2. Such tool deflection, δ is
proportional to the magnitude of the cutting force, P
Z
, simply as,
=
EI
L
P
Z
3
3
δ
(10.1)
where, L = overhang or equivalent projected length of the cantilever
type tool (holder)
E = physical property (Young’s modulus of elasticity of the
beam)
I = size (plane moment of inertia) of the beam section.
Since for a given cutting tool and its holder, E and I are fixed and the equation
10.1 becomes,
δ α P
Z
or, δ = kP
Z
(10.2)
where, k is a constant of proportionality.
P
Z
L
δ
Fig. 10.2 Cutting tool undergoing deflection,
δ
due to cutting force, P
Z
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
as schematically shown in Fig. 10.3.
opto-electronically by photocell where the length of the slit through
which light passes to the photocell changes proportionally with the
tool – deflection
All such transducers need proper calibration before use.
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. 10.4. Here the slope
of the curve represents the constant, k of the equation (10.2). Then while
actual measurement of the cutting force, P
Z
, the δ* is noted and the
corresponding force is assessed from the plot as shown.
In capacitive pick up type dynamometer, the cutting force causes proportional
tool deflection, δ , which causes change in the gap (d) and hence
capacitance, C as
d6.3
A.
C
π
ε
=
(10.3)