# Tachogenerator

Sunday, April 29th, 2018 -

The tachogenerator is a direct-type velocity transducer. It is essentially the opposite of an electric motor since its input is a rotating shaft and its output is a voltage Vo proportional to the input angular velocity ωs: The constant of proportionality Kt is generally linear within a large dynamic range but does vary in relation to: load current, maximum input velocity and temperature. These variations are usually amply documented in the manufacturer data sheets and do not present a problem. Figure 1 shows a typical relationship between Vo and ωs for different load resistors.

## Characteristic of Tachogenerator

The principle of operation of a tachogenerator, being the dual of an electric motor, is also based on Faraday’s law of electromagnetic induction which states, as shown by eqn (2), that: the magnitude of a voltage induced in a single loop conductor is proportional to the rate of change of lines of forces passing through (or linked with) that loop.

Where B is the magnetic flux density, ‘I’ the length of the active portion of the conductor linking the flux, w is the relative velocity between the conductor and the magnetic field and 10+8 is the number of lines a single loop must link per second in order to induce a voltage of 1 V. In the tachogenerator case the magnetic flux density B and the loop length l are constants, so the output voltage Vo is proportional to the shaft angular velocity W, as required and a shown previously in eqn (1).

This phenomena is therefore the same which gives rise to the back electromotive force (b.e.m.f.) in electric motors. The equivalent circuit of a tachogenerator is also the dual of an electric motor and is shown in Figure 2:

where Tin is the torque input whereas Fa, Ma, La and Ra are all armature parameters, respectively friction, mass, winding self inductance and winding resistance. RL represents the electric load connected to the tachometer. Ignoring any transients, and therefore the effects of all reactive com­ ponents, we can show that the output voltage is given by eqn (3): which, once again, can be simplified back to eqn (1) by lumping Ka and the resistances in the total constant Kt. The output voltage Vo can be in direct current form in the case of the dynamo (a d.c. tachogenerator) or alternating current form in the case of the alternator (an a.c. tachogenerator).

Compared to other velocity transducers the main advantage of a tachogen­erator is that it provides an output without the need for a power supply. Its main drawbacks, on the other hand, are that it has an analogue output (which requires AID conversion when interfaced to a computer); the output can suffer from large fluctuations, and it has a shorter operational life.

Both of the latter two drawbacks are caused by the presence of the commutator in the d.c. type tachogenerator and can therefore be reduced if an a.c. type tachogenerator is used since this one employs slip rings to extract the power from the armature windings. The a.c. output would however require rectification and smoothing before interfacing to the AID or the use of a peak detector.