Velocity is a variable derived from the distance or angle. It can be obtained either by direct measurement or by differentiating the position.
- Differentiation of analogue signals
If the position is available as an analogue voltage, the velocity can be determined by means of analogue differentiation using a differentiating circuit. The disadvantage of this process is that the disturbance element in the position signal is differentiated as well and as a consequence there are mostly very large disturbance elements in the velocity signal.
- Differentiation with digital measuring systems
On incrementally operating measuring systems the number of the pulses added together in a counter in a defined unit of time represents a measure for the average velocity in this unit of time. If these measuring systems are used in a computer system for position and velocity control, the pulses counted after a unit of time must be read and added to the position, i.e. the increments moved within the unit of time are measured.
On absolute measuring systems the difference is formed from two sequential values that in turn again produces the average velocity within the unit of time.
This method of determining the velocity is largely immune to interference and is often used these days in control circuits with digital signal processing.
- DC generator
To measure angular velocities, essentially DC generators have been used up to now (Figure G 9 a). Even at low rotation speed these devices provide a DC signal that can be evaluated without problems. This voltage is proportional to the rotation speed over a wide tacho rotation speed range. A disadvantage for these generators is the collector with brushes necessary for commutation; collectors require regular maintenance. The voltage tapped on the collector is dependent on the position of the rotor in the magnetic field. To achieve a high level of uniformity in the output voltage, the rotor must have as many poles as possible.
- AC generator
AC generators (Figure G 9 b) are maintenance-free as they do not require commutation. A sinusoidal output voltage is induced in the stator windings; this amplitude of this voltage is proportional to the rotation speed. The number of poles on the rotor and the rotation speed define the frequency of the measurement voltage. For measurement purposes the aim is therefore as many poles as possible. After rectification the measurement voltage provides a measure of the velocity. The direction of movement is defined via the phase offset on the two voltages. Problems can arise with the uniformity of the measured signal at very low rotation speeds.
- Angular velocity transducer
A very simple rotation speed measurement is provided by using an inductive sensor. It comprises a coil around which there are rod magnets (Figure G 9 c). If magnetic material is moved past a pole on the magnet, there is a change in the magnetic flux in the coil and therefore a voltage is induced. For a very simple application a gearwheel can be used to change the field directly. The frequency of the output voltage is then defined by the rotation speed and the number of teeth. An analysis circuit can convert the pulse frequency into an analogue voltage or a digital value.
- Velocity transducer
These transducers often operate based on the generator principle and are called electrodynamic sensors. As (Figure G 9 d) shows, the transducer comprises a tubular shape double coil in which
a permanent magnet moves. A relative displacement on the magnet in relation to the coil generates, according the generator principle
U = N · l · B · v N = number of conductors
I = length of the conductor in the magnetic field
B = magnetic induction
v = velocity of the conductor
a voltage on the output of the coils.
During this process it is irrelevant whether the coil is moving in a magnetic field or a magnet is moving in a coil. In both cases the term active sensor is used; these sensors measure a distance change per unit time, that is the velocity. The transducers are in practice used for measuring lengths of up to 1 m.
If the distance is measured, it is also possible to obtain the velocity from the differentiation of the distance signal. However, this action often results in signals with interference (noise). Nevertheless this method is often used for feedback controls.
Figure G 9: Methods for velocity measurement; a) DC generator (tacho), b) AC generator, c) Inductive DC transducer for angular velocities, d) Inductive velocity transducer for translatory movements