Hysteresis
Hysteresis , also hysteresis ("after-effect"; Greek hysteros (ὕστερος) "afterwards, later"), is a change in the effect that occurs with a delay compared to a change in the cause (e.g. the difference of on in the case of thermostat- controlled heating - and switch-off temperature). Hysteresis characterizes a - in relation to the input variable (for heating, the target temperature) - variant delayed behavior of the output variable (for heating, the actual temperature), which has reached its maximum or minimum.
In general terms, hysteresis is a system in which the output variable depends not only on the independently changeable input variable, but also on the previous state of the output variable. The system can therefore - depending on the previous history - adopt one of several possible states with the same input variable. This behavior is also called path dependency .
Hysteresis occurs in many natural and technical processes, especially in the magnetization of a magnet , in control engineering and cybernetics .
Typical for hysteresis behavior is the occurrence of a hysteresis loop, which is created by moving the causing variable back and forth between two different values. The best-known phenomenon is the hysteresis behavior of a ferromagnet in a magnetic field : If a non-magnetized ferromagnet is exposed to an external field and this is then switched off, the ferromagnet retains a positive or negative magnetization depending on the polarity (i.e. direction) of the external field. This residual magnetization is called remanence .
Hysteresis effects
technology
- Creep leads to relaxation processes (relaxation damping). Characteristic for such processes is the independence of the attenuation from the amplitude , but a dependence on the frequency .
- Hysteresis in ferromagnetic materials : The magnetization of such a material depends not only on the external field strength, but also on its history. A hysteresis loop is run through (hysteresis cycle).
- Pulp hysteresis
- Material technology : The elastic-plastic deformation behavior of a material is subject to hysteresis. A hysteresis loop is obtained when plotted in the stress-strain diagram .
- Cybernetics and control technology : two-position controllers have intrinsic hysteresis behavior.
- Logic circuits / interfaces: Schmitt triggers are threshold switches and generate precise logic signals from slow processes.
- Measurement technology : the reversal span of pointer instruments is also called hysteresis. It arises from mechanical inaccuracies such as play and / or friction, for example in the bearings of the measuring devices.
- Hysteresis in pacemaker regulators: pacemakers have a hysteresis-prone response behavior. Usually a certain lower frequency (“demand frequency”) is programmed, e.g. B. 60 beats per minute. The pacemaker normally intervenes as soon as the patient's pulse rate drops below the required rate and stimulates the heart muscle with 60 pulses per minute. If, on the other hand, the hysteresis function is programmed, the pacemaker only steps in at a lower frequency (e.g. 50 min −1 ), but then stimulates with the lower frequency (e.g. 60 min −1 ).
- Rheology : The flow behavior of non-Newtonian thixotropic fluids is also referred to as hysteresis. The change in viscosity , i.e. H. the decrease in the viscosity of such a fluid under the influence of a constant shear gradient, depending on the duration of the action. As the duration of the shear exposure increases, the hysteresis effect is increasingly irreversible.
- With liquid crystals , phase changes take the form of a hysteresis curve.
- Ferroelectrics have an electrical hysteresis behavior analogous to magnetic hysteresis
- In mobile communications , a hysteresis is used for handover between two base stations . A conversation that takes place when there is movement should only change the base station when the transmission signal of the current base station is 5 dB worse than that of the new one. This means that in the event of a disturbed (inhomogeneous) field profile, it is not necessary to transfer too often.
- Soil physics : In the saturation and drainage of soils, the relationship between pore water pressure ( suction tension ) and degree of saturation (or water content ) is hysterical. As a result, different suction tensions can arise for a water content and vice versa. In many cases, the water content is higher in a drainage process with the same suction tension than in the wetting process. The pore structure of natural soils with their wide pore size distribution provides an explanation. During the drainage process, large pores that are surrounded by smaller ones are only emptied when the suction tension is able to drain the small pores. Conversely, large pores prevent the wetting of adjacent small pores until the suction tension is reached, which can also wet the large pores. According to this model, hysteresis seems to occur mainly in sandy soil, while no significant effect could be found in clay.
Economics
In economics, such as economics , hysteresis describes the reaction of a market to external influences, after which a (price) system no longer returns to its original state after they have subsided.
mathematics
In dynamic systems , hysteresis refers to a reverse bifurcation phenomenon .
physiology
In physiology , a hysteresis is u. a. found in the lungs' resting elongation curve. This describes the fact that the volume of the lungs decreases more slowly when the intrapulmonary pressure decreases than it has increased when the pressure increases. The reason for this can be seen in the reorganization of the molecules of the surfactant factor during the breathing cycle.
Thermal hysteresis proteins (THP) lead to animals, e.g. B. fishing, to a protection against freezing : if they are increasingly present in the body fluid , there is a thermal or heat hysteresis in the ice formation . The body fluid then freezes at −5 ° C, for example, but thaws again at 0 ° C. This does not happen by increasing the molarity in the extracellular fluid, but by the fact that the binding of the THP to the ice crystals prevents further ice formation.
Hydrology
During the flood event of a river, with the same water level, the flow or the mean flow speed differs depending on whether the flood wave is coming or going:
- When the water level rises, the water level rises, so does the downhill force , the mean flow velocity and therefore the flow.
- When the flood wave runs down, however, this gradient is reduced, which is why the flow velocity and flow rate decrease accordingly.
The higher and shorter the flood wave, the more noticeable the hysteresis effect.
Examples to explain
Two-point controller
The two-position controller is a typical example. If the cause (input variable) is plotted on a horizontal axis and the effect (output variable) on the vertical axis, the curve has two horizontal levels. The transition from the upper to the lower level takes place at a lower x-axis point than the transition from bottom to top, which makes a hysteresis recognizable.
An example is the unfolding of the rear spoiler on a car: This "air flap" should be retracted at low speed and extended above 80 km / h in order to increase the contact pressure of the rear wheels. If the car drives in a convoy whose speed constantly fluctuates between 78 km / h and 83 km / h, the constant retraction and extension would put unnecessary stress on the spoiler mechanism. This is avoided by switching behavior with hysteresis:
- Above 80 km / h it extends, lower line on the hysteresis curve.
- Below 60 km / h the vehicle retracts, the upper line on the hysteresis curve.
The condition of the rear spoiler at the speeds between the switching points depends on the speed history:
- If the car was faster before, it remains extended until the car goes slower than 60 km / h.
- If the car was slower before, it stays in until the car goes faster than 80 km / h.
Hard and soft hysteresis curve
The hard and soft hysteresis are explained below using magnetism. The three pictures show hysteresis curves of a permanent magnet with a hard hysteresis curve, which has a high coercive field strength and high remanence , as well as two transformer iron cores (see also: dynamo sheet ), which have a small coercive field strength and different strong inclinations, magnetic shear and remanences; the latter two diagrams show a hard and a soft hysteresis curve which, unlike a permanent magnetic material, only have a small coercive field strength.
A single Weiss area of a ferromagnetic substance has a steep, almost vertical, hard hysteresis curve with bistable behavior - an effect that was used in the early years of computer technology to store bits in a core memory . In the case of ferromagnetism in a rectangular, punched-out transformer sheet , these Weiss areas are indeed in the rolling direction of the starting sheet , but in the case of an M-cut, for example, only in two legs favorable to the direction of the magnetic field. However, because the magnetic flux also has to run through legs in which the orientation of the Weis areas is not in the direction of the magnetic flux and which therefore have an inclined curve, there is a total of millions of "switches" (Weiss areas), which are oriented towards the Differentiate magnetic field direction from each other. The sum of all these almost vertical and inclined hysteresis curves is the "soft" and inclined hysteresis curve in the picture in the middle right. In the case of a toroidal transformer, on the other hand, the orientation of all Weiss areas is in the direction of the magnetic flux due to the rolling, which results in a steep, hard (overall) hysteresis curve. The remagnetization energy is the smallest here, which also corresponds to the smallest area within the hysteresis curve. This is why one speaks of hard rectangular cores with a steep hysteresis curve, which, like the soft curve, turns into an almost horizontal curve shortly before core saturation. There are special phenomena - depending on the number of Weiss districts oriented in the direction of the magnetic flux in relation to the ones lying across them:
- Only when the piece of iron has been demagnetized is the starting point at A. The blue piece of curve from A to B to C is also called a “virgin” curve or “new curve”.
- You can magnetize with an electromagnet up to point B in one direction and then - after reversing the polarity of the electromagnet - go on the red curve to point M. Then only a few Weiss districts were changed in their orientation. The vertical distance to the horizontal axis indicates how many districts were affected. It says something about the flux density.
- You can also go from A to C or to D or to E - it depends on how strong the electromagnet is. Between C and E all Weiss areas are oriented parallel, then one speaks of saturation . A further increase in the coil current only insignificantly increases the magnetic flux in the iron.
- When the electromagnet is switched off, you get back to F. Whether F is as high as C or a little or even much lower depends on the remanence . This is of the design, u. a. depends on the (remaining) air gap.
- If you reverse the polarity of the electromagnet and slowly increase the voltage-time area, you arrive at point G. The piece of iron has been demagnetized as long as the opposing field is present. To do this, the coercive field strength of the core in the electromagnet had to be overcome. After switching off the opposing field, the magnetization runs like an elastic spring back to the previous value F. The zero point A can only be reached if the modulation of the hysteresis curve is reduced in small steps or continuously by means of an opposing field that is constantly reversing and decreasing in polarity ( demagnetization ).
literature
- J. Möller , R. Völker: Wage formation and hysteresis: Empirical review of an insider-outsider model for the Federal Republic of Germany . In: Journal for Economics and Social Sciences . tape 111 , 1991, pp. 401-424 .
- A. Belke, M. Gocks: Strong hysteresis on the job market . In: ZWS magazine for economics and social sciences . tape 114 , 1994, pp. 345-377 .
Web links
Individual evidence
- ↑ www.haustechnikdialog.de: Hysteresis .