Speed acquisition made simple
Speed acquisition is of central importance in the control and monitoring of motion processes. We cannot imagine our industrially powered modern world without it, whether in control and automation systems or in the regulation of traffic. The following article aims to provide a summary of the various ways in which these diverse tasks can be tackled simply and efficiently using magnetic sensors based on the Hall principle.
By Dr David Lin, iC-Haus GmbH -- EDN, September 11, 2008
One of the simplest examples of noncontact speed acquisition in everyday use can be found in the bicycle speedometer. This appliance shows the cyclist not only how fast he or she is moving but also the distance traveled, the total numfber of kilometers or miles cycled and the time needed to do so.
The speedometer operates on the following principle. The speed of the front wheel is logged and the traveling speed v deduced from the known diameter of the wheel. A small permanent magnet M mounted on one of the spokes passes a sensor S once with each turn of the wheel; in the simplest of cases this sensor is a reed relay which is fixed to the front wheel fork. This motion triggers an electrical counter pulse (Figure 1). The average speed is then calculated from the time T between each counter pulse.The advantage of noncontact speed acquisition with regard to lack of sensitivity to dirt and robustness is not only obvious in the bicycle example. Mechanical engineering, industrial and road traffic applications also profit from it.
Simple arrangements like the one illustrated in Figure 1 are, however, often not sophisticated enough, particularly when the speed significantly changes within one revolution. Here, subdividing the angle of rotation into small increments improves the accuracy of the logged current speed where more counter pulses are generated per revolution. Theoretically speaking, in the case of the bicycle speedometer we would have to fix a permanent magnet to each spoke of the wheel in order to increase the number of counter pulses per revolution. In practice pole wheels are used to this end; these can be described as a set of individual magnets arranged in a ring, where a large number of magnetic north and south poles are regularly spaced around the rim of the ring. On the sensor side integrated magnet-sensitive semiconductor elements are often used. These are based on Hall sensors which can be easily integrated into existing CMOS processes together with electronic amplification and evaluation units.
An integrated solution for pole wheel scanning exists, consisting of two Hall sensors which evaluate the local magnetic field difference along the circumference of the pole wheel and convert this into a digital signal which can be transmitted along long wires using the integrated line drivers (Figure 2). Differential scanning also has the advantage that homogenous magnetic disturbances fields from the two Hall sensors can be logged as common mode signals and effectively suppressed by the calculation of the difference.So that the electric output signals are also largely immune to outside interference the device includes complementary line drivers, enabling differential signal evaluation for the receiver and cables to be over one hundred meters in length.
The ever finer pole subdivisions along the circumference of the pole wheel increase the accuracy of speed and also the generated pulse repetition rate. With a magnetic input frequency of zero to 40 kHz a pole wheel with 120 poles (or 60 pole pairs) can log speeds from stationary to up to 40,000 rpm.
Design engineers often like to use existing construction elements for speed acquisition. Why affix an additional magnet to the bicycle spokes when the spokes can be directly logged magnetically? Gear wheels in drives are often easy to access and can provide information as to the speed either directly or by applying a known gear ratio. As long as the gear wheels are made of magnetizable steel, which in mechanical engineering is almost always the case, they can be mounted with a magnetic bias field, allowing the gear wheel circumference, thus magnetized, to be scanned.
Thanks to the geometric shape of the circumference with its teeth and gaps the bias field created by the bias magnet is modulated in its intensity. The magnetic fields lines are particularly concentrated around the teeth, resulting in a considerably higher field strength here than in the gaps. This difference in field strength between the teeth and gaps is logged by the iC and converted into the complementary pulse rate mentioned above. It becomes clear that differential signal conditioning is necessary in order to eliminate the common mode fraction of the magnetic bias field in the evaluation process.
So far we have only mentioned the possibility of increasing the speed acquisition accuracy by further subdividing the sensing wheel (pole or gear wheel). The simple differential sensor is also not able to recognize the direction of rotation; in other words, similar pulse repetition rates are generated regardless of whether the wheel turns backwards or forwards.
The field strength response along the wheel circumference can be expressed by a harmonic function according to:
Where x is the distance along the circumference, P the length of the magnetic period (distance from one pole to another of the same polarity) and B0 the amplitude of the magnetic field strength. The localized field strength displays extremes at the poles while disappearing completely at the pole boundaries. North and south poles differ in the signs of the magnetic field direction.
The temporal change in φ is identical to the circumference speed v of the pole wheel, resulting in the rpm being accrued from the overall number of pole pairs.
In the simplest of cases signal variables cos(φ) and sin(φ) can be converted into quadratic signals A and B by two back-end comparators to generate counter pulses. If the edges are used as time markers, the resolution of a magnetic period P can be improved by a factor of 2 compared to the simple method of differential scanning given in Figure 2. It is now also possible to differentiate between the directions of rotation using the change in edges between A and B.
A considerably higher resolution of angle φ is possible if we apply the interpolation process described in Figure 5. The graphic representation of sin(φ) versus cos(φ) produces a circle as a special Lissajous figure in which angle φ is immediately recognizable. The interpolator now compares the current angle value φ0 with predefined discrete angle positions and as a result generates the matching quadrature signals A and B.The device shown in Figure 4 has four Hall sensors plus an interpolator with an adjustable resolution of 6, 7 or 8 bits, enabling a magnetic period to be divided into 64, 128 or 256 increments. An angle increment (referenced to a 360° magnetic period P) thus measures 5.6°, 2.8° or just 1.4°. So that the absolute angle resolution can be referenced to the mechanical revolution of the pole wheel, this must be divided by the number of pole pairs. Using the pole wheel mentioned above with its 60 pairs of poles at a resolution of 8 bits, a total of 256 x 60 = 15,360 angle steps measuring 0.023° apiece are obtained (1.4 angular minutes).
A lower resolution is often sufficient, enabling the number of pole pairs to be kept small. Pole wheels with a very low number of poles and thus a small diameter have a large curvature at the circumference, however, and cannot be scanned by a linear Hall encoder. Here, solutions which have the Hall sensors arranged not in a line but in a circle can be implemented. A diametrical magnet is placed vertical to and at some distance above the center of the circle; this magnet can be treated as a specific pole wheel with only one pole pair.
As a magnetic period here is equal to a revolution of the magnet the mechanical angle resolution is identical to the resolution of the interpolator, thus resulting in 1.4° at 8 bits.
Besides quadrature signals solutions of this kind also provide the corresponding index signals (Z or zero pulses) at the beginning of each period. In the application given in Figure 6 a revolution counter can thus be realized with absolute position sensing.
As demonstrated in the above examples, speed can be logged in many different ways with a diverse range of applications. Integrated solutions which contain both Hall sensors and evaluation electronics are robust and compact. In the simplest case a speed acquisition system merely comprises a permanent magnet and a single IC, permitting speeds of up to 120,000 rpm.
