Polygon effect
The so-called polygon effect occurs when a traction mechanism ( chain and toothed belt are traction mechanism drives ) drives a machine through a drive wheel in a form-fitting manner (ie by meshing).
This traction device cannot run up and down in a circular manner on the drive wheel, so that this traction device bends. This creates a polygon (polygon) from the circular drive wheel with a different number of chords according to the diameter of the drive wheel.
Definition and occurrence of polygon effect
If the drive wheel now rotates at a constant angular speed , the polygon support of the traction mechanism results in different effective radii. The speed of the traction device then fluctuates periodically around an average speed. Furthermore, this results in unpleasant excitations in the longitudinal and transverse direction of the traction device, which can lead to vibrations , which in the extreme lead to a so-called resonance catastrophe and thus mostly to material breakage.
Due to the oscillation phenomenon caused by the polygon effect and the inaccuracy of transmission, there are simplified calculations in all areas of mechanical engineering in which traction means, chains and toothed belts are used. In engine construction in particular, an exact transmission behavior is required for the camshaft control (with chain or toothed belt), which can be calculated in advance in complex calculations. For positioning tasks with timing belt-driven vehicles, failure to take the polygon effect into account can lead to inaccuracies in approaching exact positions.
Round steel chain drive in the chain hoist
The polygon effect in steel link chains z. B. in the chain transmission is different from that for round steel chains because round steel chains consist of a sequence of 90 ° to one another twisted chain links. These twisted chain links lie differently in the chain sprocket and thereby cause changed geometric relationships. A distinction is made between so-called standing and lying chain links. The power from the hanging chain to the sprocket is only transmitted via the horizontal links.
In the case of round steel chains, the drive wheels have low numbers of teeth (corners) and thus the polygons only have a few sides. This has the advantage that the drive torques for the chain wheel can be kept small and the chain wheel with drive does not require a lot of installation space. The smaller this number of polygon sides is, the greater the effects of the polygon effect.
Kinematic conditions on round steel chain drives
If a round steel chain wheel (see figure) rotates at a constant angular speed, the following kinematic conditions arise:
You can see that the kinematics repeats itself after 90 °, i.e. is periodic, because the chain wheel has 4 pockets (360 ° / 4 = 90 °!). The two acceleration jumps during a period excite the loads hanging on the chain to oscillate in the longitudinal direction of the chain, since the round steel chain (elastic) forms a single-mass oscillator with the hanging load. This forced oscillation leads to undesirable operating conditions.
Vibration through polygon effect
If a load of 1,600 kg is raised with a 2.3 kW chain hoist at an average lifting speed of 8 m / min and then lowered, the accelerations and corresponding dynamic forces shown in the picture on the right are generated.
It can be seen that in addition to the lifting load of 15696 N (= 1600 kg • 9.81 m / s²) an additional force of 5280 N (= 1600 kg • 3.3 m / s²) loads the chain when lowering. This occurs here with a chain length of 10.3 m. After starting up, resonances of up to the 4th order are passed through, the frequencies are below 10 Hz. These low-frequency vibrations can be observed with the naked eye and sometimes cause an amplitude of more than 40 mm.
Simulation of the dynamic overall situation
If you describe the physical relationships mathematically precisely and still know the properties of the chain and the chain hoist very precisely - this can be determined experimentally - you can solve all these descriptive equations using numerical solution methods and calculate the behavior of the load and the chain hoist in advance .
This requires countless computing steps of the simulation or solution program with a correspondingly high computing time requirement of up to a few hours. The result should then, with sufficiently accurate modeling, agree well with the measured reality.
The picture shows good agreement between measurement and calculation (simulation) for a polygon effect-excited lifting process. It also shows the measurement setup with chain hoist , chain , load cell and load.
literature
- Christian Landschuetzer: Analysis of vibrations on single-strand electric chain hoists . Diss. TU Graz, 2004.
Web links
- Theo Korse, Martin Sopouch: A new timing chain without polygon effect (theoretically), published in MTZ worldwide 5/2004, p. 382.