• 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 figure 10.2. such tool deflection, $\delta$ is proportional to the magnitude of the cutting force, Pz, simply as,

$\delta = P_z (\frac{L^3}{2EI})$

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,

$\delta \ \alpha \ P_z $ or, $\delta = kP_z$

Where, K is a constant of proportionality.

The deflection, $\delta$, 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 figure 10.3.

• Opto-electrically 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,

$\delta$ are noted and then plotted as shown in figure 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, Pz, the $\delta^*$ is noted and the corresponding force is assessed from the plot as shown.

In capacitive pick up type dynamo-meter, the cutting force causes proportional tool deflection, $\delta$, which causes change in the gap (d) and hence capacitance, C as $C = \frac{\epsilon.A}{3.6 \pi d}$

The change in C is then measured in term of voltage, $\triangle V$ which becomes proportional to the force. The final relation between Pz and $\triangle V$ is established by calibration.

In case of LVDT, the linear movement of the core, (coupled with the tool), inside the fixed coil produces proportional voltage across the secondary coil.

Figure 10.3 Electrical transducers working based on deflection measurement

(a) Linear pot.

(b) Circular pot.

(c) Capacitive pick up.

(d) LVDT type.

(b) Measuring cutting force by monitoring elastic strain caused by the force. Increasing deflection, $\delta$ enhances sensitivity of the dynamometer but may affect machining accuracy where large value of $\delta$ is restricted, the cutting forces are suitably measured by using the change in strain caused by the force. Figure 10.5 shows the principle of force measurement by measuring strain, $epsilon$ which would be proportional with the magnitude of the force F. (say $P_z$) as,

$\epsilon = \frac{\sigma}{E} = \frac{M / Z}{E} = \frac{P_z I}{Z.E} = k_1 P_z$

Where,

M = bending moment.

Z = sectional modulus (I/y) of the tool section.

I = plane moment of inertia of the plane section.

Y = distance of the straining surface from the neutral plane of the beam (tool0.

The strain, $\epsilon$ induced by the force changes the electrical resistance, R, of the strain gauges which are firmly pasted on the surface of the tool holding beam as $\frac{\triangle R}{R} = G\epsilon$

Where,

The change in resistance of the gauges connected in a wheatstone bridge produces voltage output $\triangle V$, through a strain measuring bridge (SMB) as indicated in Figure. 10.6. Out of the four gauges, $R_1, R_2, R_3 \ and R_4$, two are put in tension and two in compression as shown in figure. 10.6. the output voltage, $\triangle V$, depends upon the constant, G and the summation of strains as,

$\triangle V = \frac{GE}{4} [\epsilon_1 – (- \epsilon_2) + \epsilon_3 – (- \epsilon_4)]$,

Where, $\epsilon_1 \ and \epsilon_2$ are in tension and $\epsilon_{-3} \ and \epsilon_{-4}$ are in compression.

The gauge connections may be

1] Full bridge (all 4 gauges alive) – giving full sensitivity.

2] Half bridge (only 2 gauges alive)- half sensitive.

3] Quarter bridge (only 1 gauge alive) – 1/4 the sensitivity.

Measuring cutting forces by pressure caused by the force.

This type of transducer functions in two ways :

1] The force creates hydraulic pressure (through a diaphragm or piston) Which is monitored directly by pressure gauge.

2] The force causes pressure on a piezoelectric crystal and produces an emf proportional to the force or pressure as indicated in figure. 10.7.

Here, emf = $\lambda$ tp

Where

$\lambda$ = voltage sensitivity of the crystal.

T = thickness of the crystal.

P = pressure.