Magnetic friction disk

A magnetic drive pulley (MTS) is a drive pulley in which the drive capacity is increased by integrating permanent magnets into the groove construction.

construction

Fig. 1 Single module of the magnetic friction disc with pole discs 1, wire rope 2 running over it, magnets 3 and spacer disc 4

Magnetic friction disks, as shown in Figure 1, consist of ( ) pole disks, which are separated by ( ) spacer disks, and permanent magnets , which are distributed between the pole disks on the circumference of the traction disk. This arrangement creates a magnetic circuit that is closed by the wire rope in the groove of the MTS. In addition, the two pole disks define the shape of the drive pulley groove. The result is a magnetic force that increases the force transmission between the wire rope and the groove due to the resulting additional pressure. This means that there is an increased, load-dependent driving ability. As with the classic traction sheave (kTS) , the traction capacity is defined by the ratio of the two rope forces. B. in traction sheave elevator with counterweight application is possible. In conjunction with a round groove that is gentle on the rope, the magnetic traction sheave allows the wire ropes to have a longer service life while increasing their traction. With a higher traction capacity, the mass of the counterweight and the car can be reduced in an elevator system with a counterweight. This in turn enables the number of wire ropes to be reduced and the drive torque required for acceleration to be reduced. Other applications include electric hoists, shunting and emergency winches and crane hoists. ${\displaystyle 2n}$ ${\displaystyle n\in \mathbb {N} }$ ${\displaystyle 2n-1}$ ${\displaystyle n\in \mathbb {N} }$

functionality

The functional principle of the magnetic drive pulley is based on a magnetic circuit that is closed by the wire rope. As a result, the pole disks must have good magnetic conductivity, which is achieved by using ferromagnetic materials . The spacer, however, must be designed as a poor magnetic conductor or good resistance. Paramagnetic or diamagnetic substances are suitable for this .

Driving ability

Fig. 2 Cable forces on the magnetic friction pulley a) and infinitesimal section b)

The decisive property for a traction sheave is its ability to drive. The driving ability is the increase in the transferable circumferential force depending on the coefficient of friction (from the material combination and groove shape) and the wrap angle (see Fig. 2a). In the case of the magnetic traction sheave, the effect of the magnetic force, modeled in the line load , the traction sheave radius and the pretensioning force, are added. ${\displaystyle F_{1}/F_{2}}$ ${\displaystyle \mu }$ ${\displaystyle \alpha =\alpha _{2}-\alpha _{1}}$ ${\displaystyle q_{\text{m}}}$ ${\displaystyle r_{\text{TS}}}$ ${\displaystyle F_{2}}$

Derivation of the increased driving ability

In the following, analogous to the derivation of the Eytelwein equation, the relationships at the magnetic drive pulley are shown. With the assumption that the rope force is greater than the force , the model is shown in Figure 2 a). The traction sheave is mounted in its center and the rope runs on the circumference. The magnetic force is assumed to be the line load. For the equilibrium of forces in the x- and y-direction, with the infinitesimal free section from Figure 2 b), the angles of the rope support points and the tangential and normal force as well as the respective differential quantities result: ${\displaystyle F_{1}}$ ${\displaystyle F_{2}}$ ${\displaystyle q_{\text{m}}}$ ${\displaystyle \alpha _{1}}$ ${\displaystyle \alpha _{2}}$ ${\displaystyle F_{\text{t}}}$ ${\displaystyle F_{\text{n}}}$

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

Both equilibrium conditions are via Amonton's law , known as Coulomb's law,

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

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

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

Assuming small angles and neglecting higher order differentials, this can be summarized:

${\displaystyle {\begin{aligned}dF-\mu Fd\alpha -\mu q_{\text{m}}r_{\text{TS}}d\alpha &=0.\end{aligned}}}$

By separating the changeable and then integrating them, the following results:

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

The condition that no slipping occurs is for the MTS:

${\displaystyle {\begin{aligned}F_{\text{2}}\cdot e^{-\mu \alpha }+q_{\text{m}}r_{\text{TS}}(e^{-\mu \alpha }-1)&\leq F_{\text{1}}\leq F_{\text{2}}\cdot e^{\mu \alpha }+q_{\text{m}}r_{\text{TS}}(e^{\mu \alpha }-1).\end{aligned}}}$

It can be seen that the force amplification or reduction term is larger or smaller by a factor than with the kTS and thus a greater ratio of the two forces can be conveyed without slipping. For the propulsive ability (also ) it follows that this depends on the force itself as described above : ${\displaystyle q_{\text{m}}r_{\text{TS}}(e^{\mu \alpha }-1)}$ ${\displaystyle q_{\text{m}}r_{\text{TS}}(e^{-\mu \alpha }-1)}$ ${\displaystyle F_{\text{1}}\geq F_{\text{2}}}$ ${\displaystyle F_{\text{2}}}$

${\displaystyle {\begin{aligned}{\frac {F_{\text{1}}}{F_{\text{2}}}}&=e^{\mu \alpha }+{\frac {q_{\text{m}}r_{\text{TS}}(e^{\mu \alpha }-1)}{F_{\text{2}}}}.\end{aligned}}}$

Overall, the traction capacity of the magnetic traction sheave is greater than that of the conventional traction sheave for otherwise identical parameters . ${\displaystyle q_{\text{m}}>0}$

example

Fig. 3 Example of an elevator in 2: 1 suspension as a cut-out representation

For the example, an elevator in 2: 1 suspension with useful weight as shown in Figure 3 is used (cf.). The rope forces and are relevant for dimensioning . ${\displaystyle 2000\,{\text{kg}}}$ ${\displaystyle F_{1}}$ ${\displaystyle F_{2}}$

${\displaystyle {\begin{aligned}F_{\text{1}}&=\left(\underbrace {m_{\text{K}}} _{P+Q}+2m_{\text{sp}}(h-s_{\text{K}})\right)\left({\frac {g}{2}}+{\frac {{\ddot {s}}_{\text{K}}}{2}}\right)\\F_{\text{2}}&=(\underbrace {m_{\text{G}}} _{P+Q_{\text{max}}/2}+2m_{\text{sp}}s_{\text{K}})\left({\frac {g}{2}}-{\frac {{\ddot {s}}_{\text{K}}}{2}}\right)\end{aligned}}}$

In addition, the values ​​shown in the following table are used:

size	Value and unity
Acceleration due to gravity:	${\displaystyle g=9{,}81\,{\frac {\text{m}}{{\text{s}}^{2}}}}$
Cabin acceleration or deceleration:	${\displaystyle {\ddot {s}}_{\text{K}}=1\,{\frac {\text{m}}{{\text{s}}^{2}}}}$ or. ${\displaystyle {\ddot {s}}_{\text{K}}=-1\,{\frac {\text{m}}{{\text{s}}^{2}}}}$
Elevator head:	${\displaystyle h=30\,{\text{m}}}$
Suspension type:	${\displaystyle 2:1}$
Payload:	${\displaystyle Q_{\text{max}}=2000\,{\text{kg}}}$
Traction sheave wrap angle:	${\displaystyle \alpha =\pi }$
Traction sheave radius:	${\displaystyle r_{\text{TS}}=0{,}265\,{\text{m}}}$
Required security against rope breakage:	${\displaystyle 12}$
Wire rope diameter:	${\displaystyle 13\,{\text{mm}}}$
Minimum breaking force of the wire rope:	${\displaystyle 111{,}6\,{\text{kN}}}$
Specific wire rope dimensions:	${\displaystyle m_{\text{sp}}=0{,}723\,{\frac {\text{kg}}{\text{m}}}}$

In the systems with a classic traction sheave and magnetic traction sheave, the coefficient of friction of the groove and the added magnetic line load in the MTS differ. For the kTS a value of and for the MTS a value of which is more gentle on the rope is used. The value for the magnetic connector load is accordingly ${\displaystyle \mu =0{,}18}$ ${\displaystyle \mu =0{,}15}$ ${\displaystyle q_{\text{m}}=13\,{\frac {\text{kN}}{\text{m}}}=13{\frac {\text{N}}{\text{mm}}}.}$

size	classic traction sheave	Magnetic friction disk
Coefficient of friction (of the groove)	${\displaystyle \mu =0{,}18}$	${\displaystyle \mu =0{,}15}$
Magnetic line load	${\displaystyle q_{\text{m}}=0\,{\frac {\text{kN}}{\text{m}}}}$	${\displaystyle q_{\text{m}}=13\,{\frac {\text{kN}}{\text{m}}}}$

Result

Fig. 4 Visualization of the conditions at the traction sheave using the example.

The result can be shown in Figure 4. The rope force ratio (traction) is shown over the force per rope. The safety against the minimum breaking force (safety limit of the suspension ropes) is to be maintained by the actually occurring loads, represented by the respective work area . In the figure, this means that the work areas must be within the blue border. In addition, these must be within the respective driving ability range for correct dimensioning. In the figure it is also clear that the traction range of the magnetic drive pulley depends on the force , in contrast to the kTS where this is constant. The lower of the two rope forces is in the traction range and the lower traction limit shown above comes into play. ${\displaystyle F_{1}/F_{2}}$ ${\displaystyle F_{2}}$ ${\displaystyle F_{1}(Q;s_{\text{K}};{\ddot {s}}_{\text{K}})/F_{2}(s_{\text{K}};{\ddot {s}}_{\text{K}})}$ ${\displaystyle F_{2}}$ ${\displaystyle F_{1}/F_{2}\leq 1}$ ${\displaystyle F_{2}}$

As shown in the table below, this results in mass savings in the cabin and counterweight. In addition, the number of suspension ropes can be reduced from 4 to 3. ${\displaystyle 2290\,{\text{kg}}}$

size	classic traction sheave	Magnetic friction disk	difference
Cabin dimensions	${\displaystyle 2820\,{\text{kg}}}$	${\displaystyle 530\,{\text{kg}}}$	${\displaystyle -2290\,{\text{kg}}}$
Counterweight mass	${\displaystyle 3830\,{\text{kg}}}$	${\displaystyle 1540\,{\text{kg}}}$	${\displaystyle -2290\,{\text{kg}}}$
Number of ropes	${\displaystyle 4}$	${\displaystyle 3}$	${\displaystyle -1}$

In summary, the use of the magnetic friction disc enables significantly less material to be used in the cabin and counterweight. Gude and Hufenbach and Thumm provided an approach to realize this. In addition, a wire rope can be saved in the example, which reduces the workload when changing the rope. The change interval of the ropes can also be increased due to the rope-friendly groove design of the magnetic drive pulley. As a result, there are advantages in the manufacture and operation of an elevator system with a magnetic drive pulley.

Individual evidence

1. ↑ Patent WO03076324A1 : traction sheave for high-performance friction pairings . Registered on March 7, 2003 , published on September 18, 2003 , inventor: P. Gräbner. ‌
2. ↑ ^{a b} P. Gräbner: The magnetic friction disc as the basis of light constructions. In: Hoists, conveyors. Vol. 48, No. 5, 2008, pp. 356-359.
3. ^ ^{A b c} T. Schmidt, T. Leonhardt, M. Anders: Multiple-Grooved Magnetic Traction Sheaves. In: Proceedings of the 11th International Material Handling Research Colloquium (IMHRC), Milwaukee, WI, USA, June 21-25, 2010. pp. 391-405 ( PDF ).
4. ↑ ^{a b} 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.
5. ^ H. Ernst: Die Hebezeuge, Volume 1, Fundamentals and components. Friedrich Vieweg & Son, Braunschweig 1958.
6. ^ P. Gräbner: Elevators. In: discontinuous conveyor. Volume 1. 5th edition, Verlag Technik, Berlin 1989, ISBN 3-341-00647-8 .
7. ^ ^{A b} U. Gabbert, I. Raecke: Technical mechanics for industrial engineers. 5th edition, Hanser, Munich / Vienna 2010.
8. ↑ ^{a b} W. H. Müller, F. Ferber: Technical mechanics for engineers. 3rd edition, specialist book publ. Leipzig at Carl-Hanser-Verlag, Berlin / Paderborn 2008.
9. ^ Armin Siegel, Martin Anders, Thorsten Schmidt: Energy and weight reduction in hoisting systems with magnetic traction sheaves . In: Logistics Journal . tape 2013 , 2013, pp. 7–31 ( PDF [accessed November 3, 2013]).
10. ^ T. Schmidt, A. Siegel, M. Anders, T. Leonhardt: Advances in rope drives. In: Material Handling, Constructions and Logistics (MHCL). Volume 20, Belgrade 2012, pp. 7-12.
11. ↑ M. Gude, W. Hufenbach: Lightweight construction in elevator technology - the textile car. In: Proc. of 10th Dresden Lightweight Construction Symposium, Dresden, 22.-24.6. 2006. Volume 10, Dresden 2006, pp. 22.1-22.15.
12. ↑ G. Thumm: Use of textile-reinforced plastics in lightweight lift cages. In: ThyssenKrupp techforum 2004. Volume 6, ThyssenKrupp, Stuttgart-Vaihingen 2004, pp. 60–63.