Traction sheave

Fig. 1 Traction sheave of a hoisting machine at the Zollern colliery

The drive pulley ( also called Koepe pulley after its inventor Carl Friedrich Koepe ) is the name given to the cable carrier of a drive machine, in which the drive energy of the motor is transmitted to the hoisting cable by means of frictional engagement . Traction sheaves are used, among other things, in shaft hoisting systems , elevators and lift systems.

construction

Fig. 2 Side view of a traction sheave

Fig. 3 Traction sheave with an electric tower hoisting machine from 1923 in Oelsnitz / Erzgebirge

Traction sheaves are mostly manufactured as cast steel or gray cast iron constructions , sometimes also as welded constructions. They consist of a solid wall or a spoke disk. Depending on the intended use, both hardened and unhardened discs are used. The diameter of the traction sheaves depends on the nominal diameter of the hoisting rope used. Depending on the type of rope used, it is 40–120 times the nominal rope diameter. In shaft hoisting machines the traction sheave diameter can be 6–8 meters, in small passenger elevators the traction sheave diameter is less than half a meter. The diameter of the traction sheave has a major influence on the required engine torque. The larger the traction sheave diameter, the greater the required engine torque must be. There are traction sheaves in which the drive motor is integrated; these combined sheaves have weights of up to 70 tons, depending on the power of the hoisting machine motor. The traction sheave is equipped with grooves to increase the contact surface and thus the friction; the different groove shapes depend on the required traction capacity of the pulley. The grooves must have sufficient hardness so that the groove contact surface cannot plastically deform. The pairing of the hoisting rope / traction sheave must be coordinated to ensure the best possible power transmission. This applies to traction sheave diameter, groove shape and nominal diameter of the hoisting rope.

Groove shapes

There are four groove shapes in traction sheaves:

• Round groove without undercut (also semicircular groove )
• Round groove with undercut (also seat groove)
• Keyway
• V-groove with undercut

Depending on the groove shape used, the rope is guided well (round groove) or pressed into the groove (wedge groove). The guidance and the pressure are two factors that have a significant influence on the one hand on the driving ability and on the other hand on the service life. The round groove offers the worst power transmission. With the V-groove there is enormous transverse pressure on the rope cross-section, which is why the V-groove places the greatest strain on the rope. However, the V-groove offers the greatest driving ability. The round groove with undercut is the most common groove shape.

Undercut

If a rectangular groove is pierced under the round or rope groove, it is referred to as an undercut. The stronger the undercut, the greater the contact pressure and the greater the wear on the rope and the rope groove. The undercut angle, which is designated with α (not to be confused with the wrap angle given with the same symbol, see below), is the angle between the rope center point and the two transition points from the groove and is between a minimum of 70 ° and a maximum of 106 °.

Driving ability

Fig. 4 Wrap angle α

A crucial component for a traction sheave is its ability to drive. The driving ability is the increase in the transferable circumferential force depending on the pretensioning force , the coefficient of friction and the wrap angle (see Fig. 4 and 5). In order to ensure sufficient traction between the suspension ropes of the traction sheave, the traction must be proven both mathematically and by driving tests. The driving ability depends on the coefficient of friction (also called the coefficient of friction) and the wrap angle of the hoisting rope. ${\displaystyle F_{2}}$ ${\displaystyle \mu }$ ${\displaystyle \alpha =\alpha _{2}-\alpha _{1}}$

Frictional engagement

Since power is transmitted by means of frictional engagement, a high coefficient of friction, also known as the coefficient of friction or coefficient of friction, is required. For this reason, steel grooves are only used in smaller elevator systems with conveyor ropes made of high-strength fiber ropes. Since steel cables are generally used in larger conveyor systems, it is necessary to use a traction sheave chuck. Materials that are wear-resistant and have a high coefficient of friction of 0.4–0.7 are used as traction sheave chucks in the traction sheave groove. This ensures sufficient frictional engagement. When installing the traction sheave chuck, the groove depth should correspond to ½ times the nominal rope diameter. Both the grooves and the traction sheave chuck are subject to a certain amount of wear, which becomes noticeable through abrasion of the grooves or the traction sheave chuck. Depending on the operating condition or wear of the traction sheave chuck, the coefficient of friction, which significantly influences the wraparound friction on the traction sheave, can be worsened.

Wrap angle

Fig. 5 Cable forces at the traction sheave a) and infinitesimal section b)

The wrap angle is between 135 ° and 210 °, depending on the guidance of the hoisting rope. A larger angle of wrap reduces the risk of zipline because the rope has more contact surface. It can be achieved by positioning the traction sheave in relation to the rope deflection sheave. By increasing the horizontal distance between the traction sheave and the deflecting sheaves, the wrap angle also increases in floor conveyor systems. The wrap angle is essentially due to the type of construction and is an unchangeable quantity after the completion of the conveyor system.

Derivation of the driving ability

In the following, the derivation of the ratios according to the Eytelwein equation is shown (cf.).

With the assumption that the rope force is greater than the force , the model is shown in Figure 5 a). The traction sheave is mounted in its center and the rope runs on the circumference. For the equilibrium of forces in the x- and y-direction, with the infinitesimal free section from Figure 5 b), the angles of the rope support points and the tangential and normal force as well as the respective differential quantities result: ${\displaystyle F_{1}}$ ${\displaystyle F_{2}}$ ${\displaystyle \alpha _{1}}$ ${\displaystyle \alpha _{2}}$ ${\displaystyle F_{\text{t}}}$ ${\displaystyle F_{\text{n}}}$

${\displaystyle {\begin{aligned}\sum ^{\rightarrow }F_{x}=0:\quad &\left(F+dF\right)\cos {\frac {d\alpha }{2}}-F\cos {\frac {d\alpha }{2}}-dF_{\text{t}}=0\\&dF\cos {\frac {d\alpha }{2}}-dF_{\text{t}}=0\\\sum ^{\rightarrow }F_{y}=0:\quad &\left(F+dF\right)\sin {\frac {d\alpha }{2}}+F\sin {\frac {d\alpha }{2}}-dF_{\textrm {n}}=0\\&\left(2F+dF\right)\sin {\frac {d\alpha }{2}}-dF_{\text{n}}=0.\end{aligned}}}$

Both equilibrium conditions are based on Amonton's law ,

${\displaystyle dF_{\text{t}}=\mu dF_{\text{n}}}$

associated with the coefficient of friction and, when inserted, result in: ${\displaystyle \mu }$

${\displaystyle dF\cos {\frac {d\alpha }{2}}-\mu (2F+dF)\sin {\frac {d\alpha }{2}}=0.}$

Under the conditions that the angles are small and higher order differentials are viewed as small, the equation can be simplified:

${\displaystyle {\begin{aligned}dF-\mu Fd\alpha &=0\\{\frac {dF}{F}}&=\mu d\alpha .\end{aligned}}}$

The integration over the rope section results in : ${\displaystyle \alpha =\alpha _{2}-\alpha _{1}}$

${\displaystyle {\begin{aligned}\int \limits _{F_{2}}^{F_{1}}{\frac {dF}{F}}&=\mu \int \limits _{\alpha _{1}}^{\alpha _{2}}d\alpha \\\ln |F_{1}|-\ln |F_{2}|=\ln \left|{\frac {F_{1}}{F_{2}}}\right|&=\mu (\alpha _{2}-\alpha _{1})=\mu \alpha \\{\frac {F_{1}}{F_{2}}}&=e^{\mu \alpha }.\end{aligned}}}$

The rope forces and are greater than or equal to zero, as ropes can only transmit tensile forces. This determines the maximum possible balance of forces. Since it can be smaller than , the condition that no slipping occurs can be formulated as follows: ${\displaystyle F_{1}}$ ${\displaystyle F_{2}}$ ${\displaystyle F_{1}}$ ${\displaystyle F_{2}}$

${\displaystyle F_{2}\cdot e^{-\mu \alpha }\leq F_{1}\leq F_{2}\cdot e^{\mu \alpha }.}$

If the maximum possible ratio between and is not used , there is a division into a useful and a safety angle. ${\displaystyle F_{1}}$ ${\displaystyle F_{2}}$ ${\displaystyle \alpha }$

For greater than , the traction capacity of the traction sheave is: ${\displaystyle F_{1}}$ ${\displaystyle F_{2}}$

${\displaystyle {\frac {F_{1}}{F_{2}}}=e^{\mu \alpha }}$

defined. (cf.)

Surface pressure

Due to the wear and tear of the drive pulley chuck, special attention must be paid to the surface pressure.

The surface pressure should not be greater than: ${\displaystyle 200\,\mathrm {\frac {N}{cm^{2}}} }$

The surface pressure can be roughly determined from: ${\displaystyle p}$

• Traction sheave diameter ${\displaystyle D}$
• Nominal rope diameter ${\displaystyle d}$
• Kraft Trum 1 ${\displaystyle F_{1}}$
• Power Trum 2 ${\displaystyle F_{2}}$

according to the formula:

${\displaystyle p={\frac {F_{1}+F_{2}}{D\cdot d}}}$

development

The focus of development is particularly on increasing the propulsive capacity. Various approaches are being pursued to increase the driving ability. One approach is to increase the friction by using new types of plastic ropes. Another, in connection with steel ropes, tries to increase the traction capacity by inserting permanent magnets in the so-called magnetic friction disc. Both approaches aim to reduce the moving masses in the conveyor system while at the same time reducing wear.

literature

• Heinz M. Hiersig : Lexicon of mechanical engineering. VDI-Verlag, Düsseldorf 1997, ISBN 3-540-62133-4 .
• Markus Michael, Thomas Risch, Klaus Nendel: Investigation of the traction capability of high-strength fiber ropes on traction sheaves. In: 4th specialist colloquium of the Scientific Society for Technical Logistics at the Technical University of Chemnitz. October 9 and 10, 2008. sn, Chemnitz 2008, ISBN 978-3-9812554-0-9 , pp. 73 ff., ( Digital version (PDF; 31.35 KB) ).

Individual evidence

1. ↑ Technical requirements for shaft and inclined conveyor systems (TAS), sheet 11/1. Chapter Definitions. (last accessed October 30, 2012).
2. ^ Walter Bischoff , Heinz Bramann, Westfälische Berggewerkschaftskasse Bochum: The small mining dictionary. 7th edition. Verlag Glückauf GmbH, Essen 1988, ISBN 3-7739-0501-7 .
3. ^ F. Hymans, AV Hellborn: The modern elevator with traction drive. Published by Julius Springer, Berlin 1927, pp. 24–29.
4. ↑ Bruno Grösel: stage technology: mechanical devices. 4th edition. Oldenbourg Verlag in Veritas Bildungsverlag, Vienna 2007, ISBN 978-3-7029-0555-2 , p. 283.
5. ↑ ^{a b c d} Martin Scheffler (ed.), Klaus Feyrer, Karl Matthias: conveyors, hoists, elevators, industrial trucks. Friedrich Vieweg & Sohn Verlagsgesellschaft mbH, Wiesbaden 1998, ISBN 3-663-16319-9 , p. 273.
6. ↑ Technical requirements for shaft and inclined conveyor systems (TAS). Chapter 3.3. Rope carrier.
7. ↑ BOSCH REXROTH AG Patent WO / 2002/004081 PROSPECTUS CONTACT. (last accessed October 30, 2012).
8. ↑ The 70-ton colossus hovers on the hook. In: k + S Information. 4/2005.
9. ^ ^{A b} Thomas Gärtner: News from the elevator. In: TG Consult (Ed.), Edition September 7, 2003.
10. ↑ ^{a b} Elevator, traction sheave grooves (p . 8), as well as: The rope lifespan (p. 9) In: Gustav Wolf Seil- und Drahtwerke (Ed.): Elevator ropes . Edition 07/03. Online ( Memento of March 16, 2007 in the Internet Archive ), (accessed via Archive Org. On March 26, 2015.)
11. ^ Thomas Barthel, Wolfgang Scheunemann, Wolfram Vogel: Ropes and rope constructions. ( Memento of the original from March 5, 2016 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. Chapter traction sheaves. In: Lift Report. 6/2008. Retrieved July 21, 2011. 
12. ^ Olaf Döring: Elevators I. Technology and function. Slide 8 .: Traction sheave drive. Training material, publisher: Freiwillige Feuerwehr Telgte. ( ppt , accessed July 21, 2011.).
13. ↑ Jürgen Mayer (Ed.): Fördertechnik. Traction sheave shapes. In: Exam preparation 2007, online ( Memento from March 23, 2015 in the Internet Archive ) (accessed via Archive Org on January 14, 2016)
14. ↑ TRa 1100 construction hoists with passenger transport. Chapter: 1122 traction sheaves. (last accessed October 30, 2012).
15. ↑ Michael Pyper: Two are better than one. In: Technical article, publisher: Wittur AG System Antriebstechnik Dresden.
16. ↑ M. Kaufhold: About main shaft promotion with Koepe disk. In: Polytechnisches Journal . 322, 1907, pp. 753-756.
17. ^ ^{A b} Paul Burgwinkel: Specialist article shaft conveyor technology. In: Lehrmaterial, Ed .: RWTH Achen.
18. ↑ J. Maerks: A new type of traction sheave. In: Glückauf, Berg- und Hüttenmännische magazine. Association for mining interests in the Oberbergamtsiertel Dortmund (ed.), No. 50, 67th year, December 12, 1931, pp. 1541–1544.
19. ↑ Dynamic determination of the traction capability in traction sheave-driven elevator systems. In: Patent DE 102006042909A1. October 11, 2007, TSG Technical Services Service Gesellschaft mbH, Erfurt.
20. ↑ ^{a b} Oliver Berner: Service life of wire ropes in traction sheave elevators when combining grooved profiles. Edited by the Institute for Materials Handling and Logistics.
21. ↑ ^{a b} Hans Bansen (Ed.): The mining machines . Third volume: The shaft hoisting machines. Published by Julius Springer, Berlin 1913, pp. 90–95.
22. ↑ ^{a b} W. H. Müller, F. Ferber: Technical mechanics for engineers. 3. Edition. Berlin, Paderborn, Fachbuchverlag Leipzig in Carl-Hanser-Verlag 2008.
23. ↑ ^{a b c} U. Gabbert, I. Raecke: Technical mechanics for industrial engineers. 5th edition. Hanser, Munich / Vienna 2010.
24. ↑ H. Martin, P. Römisch, A. Weidlich: Material foot technology selection and calculation of elements and assemblies of the conveyor technology. 9th edition. Vieweg, Wiesbaden 2008.
25. ↑ DIN EN 81 - 1: Safety rules for the construction and installation of lifts Part 1: Electrically operated passenger and freight lifts. 2010 Appendix M
26. ↑ G. Thumm: Use of textile-reinforced plastics in lightweight lift cages. In: ThyssenKrupp techforum 2004. Volume 6, ThyssenKrupp, Stuttgart-Vaihingen 2004, pp. 60–63.
27. ↑ R. Herhold, T. Leonhardt: Use of magnetic friction disks to increase the driving ability. In: From innovative crane technology to virtual reality. Volume 16, Magdeburg International Crane Conference 2008, pp. 109–121.
28. ^ T. Schmidt, T. Leonhardt, M. Anders: Multiple-Grooved Magnetic Traction Sheaves. In: International Material Handling Research Colloquium. Volume 11, Milwaukee: Material Handling Industry of America. Pp. 391-405. 2010

Web links

• Groove shapes in traction sheaves. In: Kasper Aufzüge company information (PDF file; 437 kB). (last accessed on October 30, 2012)
• Technical rules for elevators TRa 003 - calculation of traction sheaves , accessed on May 29, 2014