Introduction:

Dynamo-meters 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.

1] Conversion into another suitable variable (deflection, expansion etc)

2] Amplification, filtration and stabilization.

3] Reading or recording.

Measurement of cutting forces(s) is based on three basic principles:

1] Measurement of elastic deflection of a body subjected to the cutting force.

2] Measurement of elastic deformation, i.e. strain induced by the force.

3] 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 $F_c$ in turning, the tool cr tool elastically deflects as indicated in figure 1. Such tool deflection, $\delta$ is proportional to the magnitude of the cutting force $F_c$, simply as,

Treating the tool as a cantilever beam, we can write the deflection of the tool as

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

Since for a given cutting tool and its holder, E and I are fixed, we can write, $\delta \ a \ F_c$

The deflection, $\delta$ can be measured

1] Mechanically by dial gauge (mechanical transducer)

2] Electrically by using several transducers like : potentiometer, linear or circular capacitive pickup – inductive pickup.

3] LVDT (Linear Variable Differential Transformer)

Under the action of the cutting force, say $F_c$ 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, $\delta$ are noted and then plotted as shown in figure 3. Here the slope of the curve represents the constant, k of the equation.

$\delta \ = \ k \ (constant) \ F_c$

The capacititive pick up consists of two plates with an intervening air gap. The mechanical deformation causes a change in air gap, thus changing the capacitive effect.

Measuring cutting force by monitoring elastic strain caused by the force.

Increasing deflection, $\delta$ enhances sensitivity of the dynamo-meter 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 above shows the principle of force measurement by measuring strain, E, which would be proportional with the magnitude of the force, F (say $F_c$) as,

$\delta = \frac{\sigma}{E} = \frac{M/Z}{E}$

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, $\epsilon$ 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

$\frac{\triangle R}{R} = G_E$

G = Gauge factor (around 2.0 for conductive gauges). 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 below:

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 4. The output voltage $\triangle V$, depends upon the constant, G and the summation o strains as,

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

Measuring cutting forces by pressure caused by the force.

This type of transducer functions in two ways:

1] The force creates hydraulic or pneumatic pressure (through a diaphragm or piston) which is monitored directly by pressure gauge as indicated in figure 6.

2] The force causes pressure on a piezoelectric crystal and produces an emf proportional to the force or pressure as indicated in figure 7.

emf = $\lambda$ tp where, $\lambda$ = voltage sensitivity of the crystal.

t = thickness of the crystal

p = pressure.

Requirement of a cutting force dynamometer.

• The dynamometer should have sufficient 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 sue 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.

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 figure 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.

Different types of transducers used in dynamo-meters 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 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.