**4. Different configurations of magnetic speed multiplier systems**

by currents, with less efficiency than with permanent magnets, as is the case in the speed

0 0,2 0,4 0,6 0,8 1 **beta**

Figure 9 shows, on the same basis, the evolution of the normal force density, Fsn = F/Se, ver‐

The force F is perpendicular to the surfaces of the air gap; it produces no motive force but tends to introduce constraints on the bearings, as we shall see later. The normal force densi‐ ty is calculated for the low speed rotor and for the high speed rotor. It is much higher on the

The normal force density level, which comes from the following relationship for flux density

2

m

0 2 .2 <sup>m</sup> <sup>=</sup> <sup>B</sup> Fsn

0 0,2 0,4 0,6 0,8 1 **beta**

2

1'

permanent magne

high speed airgap

<sup>0</sup> <sup>2</sup> *sn <sup>B</sup> <sup>F</sup>*

low speed airgap

1

2' 3' 3

2' 3 3' 1

1'

Figure 10. Vernier permanent magnet synchronous generator

2

low speed rotor side, making it impossible to balance the force on the stator.

B, is, in most cases, still well above the level of tangential force density.

polyphase winding

**Fsn (N/m²)**

Figure 9. Normal force density (kv = 10)

**Figure 9.** Normal force density (kv = 10)

power ratio is unrivalled in this kind of application [8].

4.

The

in figure 5, is thus the following:

kv = 5 kv = 10

0,5 1 1,5 2 2,5 3 

magnetic slot

 

low speed rotor

Nrs permanent magnets

stator

low speed rotor

kv =20

<sup>=</sup> <sup>×</sup> (10)

(10)

stator

high speed rotor

: length of the rotor

Lf

permanent magnet

Lf

high speed rotor

: length of the rotor

Nrh permanent magnets

multiplier. This is a general principle observed in all converters using magnets.

0

0,05

**ks**

Figure 4. Variation of the coupling coefficient in terms of α and Λ

Figure 5. Magnetic gear: operating principle

Figure 6. Position at maximum force

τ1.Lf.

254 Advances in Wind Power

It is

la

Figure 8. Tangential force density for different values of kv (Bar = 1.2 T)

sus , for a value of kv equal to 10.

**Figure 8.** Tangential force density for different values of kv (Bar = 1.2 T)

**Fst (N/m²)**

l

0,1

0,15

The device described above can be applied in numerous ways within a wind conversion chain.

It must be noted that Vernier-type interaction, of the magnetic teeth with small permanent magnets, can be achieved directly in an electric motor [1,8], which has the double advantage of being of a relatively simple design, with high performance at low speeds, for the given reasons (electromechanical conversion at high frequency). This shows its potential for direct drive use, without multiplier.

Figure 10 shows the design of such a machine, with Ns = 12, Nr = 10, p = 2, kv = 5. This config‐ uration will be a base to compare performance, in the next paragraph, for sizing at 10kW, corresponding to a medium power wind turbine/conversion system.

Despite its main problem, which is that it operates naturally with a low power factor (typi‐ cally 0.4 to 0.7), this configuration lends itself admirably to wind turbine generator design because its mass power ratio is unrivalled in this kind of application [8]. The kind of application [8].

**Figure 10.** Vernier permanent magnet synchronous generator

Figure 11. Magnetic speed multiplier with cylinder design

Figure 12. Arrangement of the bearings in cylindrical structure

stator: small permanent magnets slow rotor (magnetic teeth)

> high speed rotor: large permanent magnets

The :

This

is still problematic.

low speed rotor The design of the magnetic speed multiplier conversion chain has the major advantage of allowing de-coupling between the electric problems (overheating, power factor …) and the problems arising from the Vernier effect in speed conversion.

high speed rotor We will also show that, given the high level of tangential force density attained in the multi‐ plier, this solution may be more efficient in terms of weight and size than the more direct solution shown in Fig. 10.

The design generally adopted for the multiplier, based entirely on the principle described in figure 5, is thus the following:

(a) External stator (b) External rotor

It should also be noted that the assembly consisting of alternating magnetic and nonmagnetic teeth is not easy to achieve because the magnetic teeth should be laminated or made with SMC material. The achievement of this complex, highly heterogeneous, structure,

stator

slow rotor: small permanent magnets stator (magnetic teeth)

> high speed rotor: large permanent magnets

kind of application [8].

The

The :

This

This

kind of application [8].

The

The :

2

permanent magne

2

1'

1'

permanent magne

1

2' 3' 3

2' 3' 3

2' 3 3' 1

1

1'

polyphase winding

1'

2

2

polyphase winding

Figure 11. Magnetic speed multiplier with cylinder design **Figure 11.** Magnetic speed multiplier with cylinder design

high speed rotor: large

stator: small permanent magnets slow rotor (magnetic teeth) slow rotor: small permanent magnets stator (magnetic teeth) This figure immediately brings out a major difficulty in designing this type of device. This architecture is based on the overlap of three concentric cylinders, the two rotors and the sta‐ tor, all rotating in relation to each other, the rotational guidance of the two rotors is necessa‐ rily delicate [3]. Figure 11. Magnetic speed multiplier with cylinder design

> high speed rotor: large

stator

Figure 12. Arrangement of the bearings in cylindrical structure **Figure 12.** Arrangement of the bearings in cylindrical structure

magnetic teeth should be laminated or made with SMC material. The achievement of this complex, highly heterogeneous, structure, is still problematic. The figure 12 shows two examples of bearing arrangement to solve the problem mentioned, but in all cases the additional constraints on by the bearings will be a source of accelerated aging of the structure.

It should also be noted that the assembly consisting of alternating magnetic and nonmagnetic teeth is not easy to achieve because the

In the first alternative arrangement (a), it is the magnetic teeth which act as low speed rotor. The small permanent magnets are on the stator. In the second arrangement (b), the magnetic teeth are fixed; the small permanent magnets are on the low speed rotor, which is external.

It should also be noted that the assembly consisting of alternating magnetic and nonmagnetic teeth is not easy to achieve because the magnetic teeth should be laminated or made with SMC material. The achievement of this complex, highly heterogeneous, structure, is still problematic.

The following photographs show an example of such a design. The magnetic teeth are secured using epoxy resin, the resulting assembly is reinforced by threaded rods visible in Figure 13(c).

The following photographs show an example of such a design. The magnetic teeth are secured using epoxy resin, the resulting

(a) Virtual photography

assembly is reinforced by threaded rods visible in Figure 13(c).

assembly is reinforced by threaded rods visible in Figure 13(c).

The

The :

This

is still problematic.

is still problematic.

aging of the structure.

This

rily delicate [3].

kind of application [8].

The

The :

kind of application [8].

256 Advances in Wind Power

1

2' 3' 3

2' 3' 3

(a) External stator (b) External rotor

This figure immediately brings out a major difficulty in designing this type of device. This architecture is based on the overlap of three concentric cylinders, the two rotors and the sta‐ tor, all rotating in relation to each other, the rotational guidance of the two rotors is necessa‐

It should also be noted that the assembly consisting of alternating magnetic and nonmagnetic teeth is not easy to achieve because the magnetic teeth should be laminated or made with SMC material. The achievement of this complex, highly heterogeneous, structure,

(a) External stator (b) External rotor

It should also be noted that the assembly consisting of alternating magnetic and nonmagnetic teeth is not easy to achieve because the magnetic teeth should be laminated or made with SMC material. The achievement of this complex, highly heterogeneous, structure,

The figure 12 shows two examples of bearing arrangement to solve the problem mentioned, but in all cases the additional constraints on by the bearings will be a source of accelerated

In the first alternative arrangement (a), it is the magnetic teeth which act as low speed rotor. The small permanent magnets are on the stator. In the second arrangement (b), the magnetic teeth are fixed; the small permanent magnets are on the low speed rotor, which is external. It should also be noted that the assembly consisting of alternating magnetic and nonmagnetic teeth is not easy to achieve because the magnetic teeth should be laminated or made with SMC material. The achievement of this complex, highly heterogeneous, structure, is still problematic. The following photographs show an example of such a design. The magnetic teeth are secured using epoxy resin, the resulting assembly is reinforced by threaded rods visible in Figure 13(c).

2' 3 3' 1

1

2' 3 3' 1

2

2

1'

1'

permanent magne

high speed rotor

stator

high speed rotor

stator

low speed rotor

slow rotor: small permanent magnets stator (magnetic teeth) high speed rotor: large permanent magnets

slow rotor: small permanent magnets stator (magnetic teeth) high speed rotor: large permanent magnets

low speed rotor

permanent magne

1'

polyphase winding

1'

2

Figure 10. Vernier permanent magnet synchronous generator

Figure 10. Vernier permanent magnet synchronous generator

Figure 11. Magnetic speed multiplier with cylinder design

Figure 12. Arrangement of the bearings in cylindrical structure

Figure 12. Arrangement of the bearings in cylindrical structure

**Figure 12.** Arrangement of the bearings in cylindrical structure

stator: small permanent magnets slow rotor (magnetic teeth) high speed rotor: large permanent magnets

stator: small permanent magnets slow rotor (magnetic teeth) high speed rotor: large permanent magnets

**Figure 11.** Magnetic speed multiplier with cylinder design

Figure 11. Magnetic speed multiplier with cylinder design

2

polyphase winding

(b) Stator (c) Low speed rotor (magnetic teeth) (d) High speed rotor

Figure 13. Prototype of a magnetic gear **Figure 13.** Prototype of a magnetic gear

An

An

Figure 13. Prototype of a magnetic gear

performing one or more multiplier stages.

high speed rotor slow speed rotor 1 2' An alternative solution to figures 10 and 11, described in [5,7], consists of combining the high-speed generator and the speed multiplier within the same structure, by inserting a pol‐ yphase winding between the magnetic teeth, in accordance with the following figure: (b) Stator (c) Low speed rotor (magnetic teeth) (d) High speed rotor

3

2 1'

3'

This solution is attractive, but the technological design difficulties lead to sub-optimization (e.g. increase of air gap ...), so it is highly

The principle we have just described can be advantageously implemented in discoid structures, such as that in the figure 15,

Figure 14. Combining the high-speed generator and the speed multiplier **Figure 14.** Combining the high-speed generator and the speed multiplier

unlikely that the result would be better than with the simplified solution seen in Figure 10.

This solution is attractive, but the technological design difficulties lead to sub-optimization (e.g. increase of air gap...), so it is highly unlikely that the result would be better than with the simplified solution seen in Figure 10.

The principle we have just described can be advantageously implemented in discoid struc‐ tures, such as that in the figure 15, performing one or more multiplier stages.

Figure 15. Magnetic speed multiplier: one stage discoid structure **Figure 15.** Magnetic speed multiplier: one stage discoid structure

This Rmax l1 l2 l3 This magnetic gear design has the advantage of being more compact than the cylindrical de‐ sign for a higher level of torque, because it allows better use of the maximum radius. Above all, it has the advantage of being mechanically simpler; the rotors can be maintained by a simple bearing on each side of the stator.

low speed rotorhigh speed rotorstator Rmin On the other hand, in the structure shown in Figure 15, the rotors are subjected to huge axial forces that we will quantify, which will also constrain the bearings. This is typical of discoid structures and can be tricky to control. It is the main design problem.

low speed shaft high speed shaft

#### Figure 16. Main dimensions of the speed multiplier **5. Design of a magnetic gear**

The

Figure 19. Normal forces

Figure 19. F1 = 130 kN F2 = 54 kN In order to clarify the potential uses of magnetic multipliers in the design of a wind conver‐ sion chain, we will size the electro mechanic device for an electric output power of 10 kW. This power output corresponds to an average power installation, for example for a small farm or a small group of isolated houses. This type of turbine has grown significantly.

low speed rotorhigh speed rotorstatorlow speed shaft high speed shaft To quantify the level of performance, we will compare the combination of multiplier and high-speed generator to a direct drive, low speed generator: a Vernier configuration like that in Figure 10. A study carried out in [1,8] shows that the power density of this configuration is significantly better than that obtained using a more conventional configuration with a large number of poles.

The nominal speed, Nlow, of the wind turbine used for this study, is 150 RPM.

The following table presents the principal characteristics obtained with a Vernier generator operating in association with an active rectifier.


**Table 1.** Electrical characteristics of a 10 kW Vernier generator

This solution is attractive, but the technological design difficulties lead to sub-optimization (e.g. increase of air gap...), so it is highly unlikely that the result would be better than with

The principle we have just described can be advantageously implemented in discoid struc‐

low speed rotor

low speed rotor

structures and can be tricky to control. It is the main design problem.

low speed rotor

The nominal speed, Nlow, of the wind turbine used for this study, is 150 RPM.

stator

To quantify the level of performance, we will compare the combination of multiplier and high-speed generator to a direct drive, low speed generator: a Vernier configuration like that in Figure 10. A study carried out in [1,8] shows that the power density of this configuration is significantly better than that obtained using a more conventional configuration with a

F1 = 130 kN F2 = 54 kN

In order to clarify the potential uses of magnetic multipliers in the design of a wind conver‐ sion chain, we will size the electro mechanic device for an electric output power of 10 kW. This power output corresponds to an average power installation, for example for a small farm or a small group of isolated houses. This type of turbine has grown significantly.

low speed shaft high speed shaft

The following table presents the principal characteristics obtained with a Vernier generator

stator

On the other hand, in the structure shown in Figure 15, the rotors are subjected to huge axial forces that we will quantify, which will also constrain the bearings. This is typical of discoid

l1 l2 l3

This magnetic gear design has the advantage of being more compact than the cylindrical de‐ sign for a higher level of torque, because it allows better use of the maximum radius. Above all, it has the advantage of being mechanically simpler; the rotors can be maintained by a

low speed shaft high speed shaft

stator

low speed shaft high speed shaft

high speed rotor

high speed rotor

high speed rotor

Rmax

Rmin

tures, such as that in the figure 15, performing one or more multiplier stages.

the simplified solution seen in Figure 10.

258 Advances in Wind Power

Figure 15. Magnetic speed multiplier: one stage discoid structure

simple bearing on each side of the stator.

**Figure 15.** Magnetic speed multiplier: one stage discoid structure

Figure 16. Main dimensions of the speed multiplier

**5. Design of a magnetic gear**

This

The Figure 19.

Figure 19. Normal forces

large number of poles.

operating in association with an active rectifier.

The main dimensions of this generator are shown in Table 2.


**Table 2.** Principal dimensions of the Vernier generator

We observe that the high operating frequency, 225Hz, at low speed, 150 RPM, leads to a mass-power ratio of about 400 W/kg, taking into account only the weight of the active parts. The mass-power ratio of a conventional machine, with a large number of poles, would be in the order of 200W/kg. The efficiency of the Vernier machine is comparable to a conventional machine, under the same operating conditions, with more iron losses, but with less Joule loss. This is also a direct consequence of increased frequency.

The speed multiplier, which will be linked to a high speed machine, will be sized in operat‐ ing conditions similar to that of the Vernier machine, in particular for the operating frequen‐ cy of the low speed rotor, frs, which will be of the order of 225 Hz.

The low-speed rotor has Nrs permanent magnet pairs, the operating frequency, frs, is then equal to:

This

The

Figure 19. Normal forces

$$f\_{rs} = \frac{N\_{rs} \cdot N\_{slov}}{60} \tag{11}$$

With frs = 225 Hz, we obtain Nrs = 90 pairs of permanent magnets for the entire low-speed rotor.

The choice of the multiplication ratio is an important parameter for optimizing the system; the higher the ratio the lower the size of the generator. On the other hand, in accordance with the results of Figure 8, the higher the ratio the lower the tangential force density within the multiplier, resulting in an increase of the size of the multiplier.

It is not within the scope of this chapter to optimize this system; we find simply that beyond kv = 10, according to the results shown in Figure 8, the tangential force density decreases rapidly, so we will take kv = 10 as the multiplication ratio, which leads to a nominal speed rotation of the generator, Nhigh, of 1500 RPM.

From this value we deduce the number of pole pairs, p: 

$$\begin{aligned} \text{For of pole pairs, } & \mathbf{p} \mathbf{:} \\\\ & \mathbf{p} = \frac{N\_{rs}}{k\_v} = \mathbf{9} \end{aligned} $$

These selected values of p and Nrs will allow us to calculate the main dimensions of the mul‐ tiplier as defined in the figure 16: low speed shaft high speed shaft Figure 15. Magnetic speed multiplier: one stage discoid structure

Figure 16. Main dimensions of the speed multiplier **Figure 16.** Main dimensions of the speed multiplier

Figure 19. The torque on the low-speed rotor is calculated from the discoid air gap surface and the tan‐ gential force density, Fst, as follows:

low speed shaft high speed shaft

$$T\_{low} = \frac{2}{3} \cdot \pi \le \cdot (R\_{\text{max}}^3 - R\_{\text{min}}^3) \cdot F\_{st} \tag{13}$$

The generator should deliver an electrical power of 10 kW with 90% efficiency. The genera‐ tor input power, Pm, is then equal to 11.1 kW. Ignoring the efficiency of the speed multiplier, we get a torque, Tlow, equal to:

$$T\_{low} = \frac{60 \cdot P\_m}{2 \cdot \pi \cdot N\_{low}} \approx 700 \text{ Nm} \tag{14}$$

The tangential force density, Fst, being fixed to an average value of 40.103 N/m² in accord‐ ance with the results of Figure 8, the radius Rmax and Rmin can be deduced from the above formulae. Taking a value for Rmax that is slightly lower than the outer radius of the Vernier machine, Rmax = 210 mm, the radius, Rmin, is equal to 100 mm.

The thicknesses of the speed multiplier discs, l1, l2, l3, can be deduced from the dimensions of the small permanent magnets in the elementary domain defined in Figure 3, by adopting the fol‐ lowing values for the adimensional parameters: Λ = 1, α = 0.2, ε = 0.05. The calculation is lengthy but not difficult. The following table summarizes the dimensions of the (speed) multiplier:


**Table 3.** Dimensions of the magnetic speed multiplier

· 60 *rs slow*

With frs = 225 Hz, we obtain Nrs = 90 pairs of permanent magnets for the entire low-speed

The choice of the multiplication ratio is an important parameter for optimizing the system; the higher the ratio the lower the size of the generator. On the other hand, in accordance with the results of Figure 8, the higher the ratio the lower the tangential force density within

It is not within the scope of this chapter to optimize this system; we find simply that beyond kv = 10, according to the results shown in Figure 8, the tangential force density decreases rapidly, so we will take kv = 10 as the multiplication ratio, which leads to a nominal speed

> 9 *rs v N*

stator

high speed rotor

high speed rotor

high speed rotor

Rmax

Rmin

(13)

low speed rotor

low speed rotor

low speed rotor

<sup>2</sup> ( ) <sup>3</sup> *low st T R RF* = × £× - ×

p

stator

F1 = 130 kN F2 = 54 kN

3 3 max min

The torque on the low-speed rotor is calculated from the discoid air gap surface and the tan‐

low speed shaft high speed shaft

stator

low speed shaft high speed shaft

These selected values of p and Nrs will allow us to calculate the main dimensions of the mul‐

l1 l2 l3

low speed shaft high speed shaft

*N N <sup>f</sup>* <sup>=</sup> (11)

*<sup>p</sup> <sup>k</sup>* = = (12)

*rs*

the multiplier, resulting in an increase of the size of the multiplier.

rotation of the generator, Nhigh, of 1500 RPM.

tiplier as defined in the figure 16:

Figure 16. Main dimensions of the speed multiplier

**Figure 16.** Main dimensions of the speed multiplier

gential force density, Fst, as follows:

Figure 15. Magnetic speed multiplier: one stage discoid structure

From this value we deduce the number of pole pairs, p:

rotor.

260 Advances in Wind Power

This

The Figure 19.

Figure 19. Normal forces

The obtained result shows that the mass of the magnetic gear is substantially greater than that of the Vernier machine, counting only the active parts. The structure of the Vernier ma‐ chine being hollow, unlike that of the speed multiplier, the addition of structural elements gives us the same result, i.e. about 50 kg (for the entire device). The technologies used being similar, this result is to be expected.

On the other hand, the extremely compact structure of the discoid multiplier gives a smaller size than the direct drive Vernier machine, the external diameter being slightly smaller, the length is reduced by almost a third.

The associated generator works at a nominal speed of 1500 RPM. It is driven with a torque equal to one tenth of the low-speed torque, i.e. 70 Nm. Designed on the principle of a per‐ manent magnet synchronous machine, for which a torque per unit mass of 2 Nm/kg is possi‐ ble [10], the mass of the associated generator would be about 30 to 40 kg. This leads to a total mass of less than 100 kg for the multiplier and generator combined.

The specific power of the system is then equal to 100 W/kg.

The efficiency of the magnetic gear is essentially related to losses in the small permanent magnets from the low-speed rotor, and to losses in the magnetic teeth, which are subject to a highly variable magnetic field. So efficiency will be calculated on the basis of these losses, ignoring the iron losses in the magnetic yokes.

The figure 17 shows the spatial evolution of the magnetic flux density in the permanent magnets of the low-speed rotor (configuration of Figure 7).

In a Vernier structure, the temporal evolution of the magnetic field is similar to the spatial evolution, therefore, we note from the figure that the amplitude, ΔB, of the temporal compo‐ nent, is approximately equal to 0.4 T, with a magnetic field of 1.2 T when the permanent magnets are polarized in the forward direction, and 0.4 T when they are polarized in the op‐ posite direction.

**Figure 17.** Flux density in the low-speed permanent magnets.

The permanent magnets are parallelepipeds 3 mm thick (in the direction of magnetization), 110 mm high and 5.4 mm wide on average; the volume, Va, is equal to 1782 mm3. The fol‐ lowing equation then allows the calculation of losses in a permanent magnet:

$$P\_f = \frac{\pi^2 \cdot f^2 \cdot \Delta B^2 \cdot t\_a^2}{6 \cdot \rho} \cdot V\_a \tag{15}$$

Total losses in the permanent magnets are equal to 2 Nrs Pf = 156 W.

The associated generator works at a nominal speed of 1500 RPM. It is driven with a torque equal to one tenth of the low-speed torque, i.e. 70 Nm. Designed on the principle of a per‐ manent magnet synchronous machine, for which a torque per unit mass of 2 Nm/kg is possi‐ ble [10], the mass of the associated generator would be about 30 to 40 kg. This leads to a total

The efficiency of the magnetic gear is essentially related to losses in the small permanent magnets from the low-speed rotor, and to losses in the magnetic teeth, which are subject to a highly variable magnetic field. So efficiency will be calculated on the basis of these losses,

The figure 17 shows the spatial evolution of the magnetic flux density in the permanent

In a Vernier structure, the temporal evolution of the magnetic field is similar to the spatial evolution, therefore, we note from the figure that the amplitude, ΔB, of the temporal compo‐ nent, is approximately equal to 0.4 T, with a magnetic field of 1.2 T when the permanent magnets are polarized in the forward direction, and 0.4 T when they are polarized in the op‐

The permanent magnets are parallelepipeds 3 mm thick (in the direction of magnetization), 110 mm high and 5.4 mm wide on average; the volume, Va, is equal to 1782 mm3. The fol‐

2 2 22

*f a f Bt P V*

r

*a*

× ×D × <sup>=</sup> <sup>×</sup> <sup>×</sup> (15)

6

lowing equation then allows the calculation of losses in a permanent magnet:

p

mass of less than 100 kg for the multiplier and generator combined.

The specific power of the system is then equal to 100 W/kg.

magnets of the low-speed rotor (configuration of Figure 7).

ignoring the iron losses in the magnetic yokes.

**Figure 17.** Flux density in the low-speed permanent magnets.

posite direction.

262 Advances in Wind Power

The figure 18 shows the spatial evolution of the magnetic field in the magnetic teeth (config‐ uration of Figure 7).

The amplitude of variation of the magnetic field in the teeth is 1 T. The calculation of losses depends on the nature of the material used to make the teeth, and on the thickness of the lamination, if these teeth are made of stacked plates, so it is not possible to quantify the level of loss. However, taking an average value of specific loss, at 225 Hz and 1T, i.e. 15W/kg for a common material, with 2.75 kg of magnetic teeth, the losses are in the order of 40 W.

The efficiency of the magnetic gear, which follows from the previous calculation of losses, is close to 98%. Taking into account the additional iron losses and mechanical losses induced by stress on the bearings, efficiency remains well above 90%. 

**Figure 18.** Flux density in the magnetic teeth

This

Figure 19.

The final problem to consider in the design of the device lies in taking into account normal forces, F1 and F2, which act on the discs. These forces are calculated from the air gap surface and from the results of Figure 9. They are shown in Figure 19. low speed shaft high speed shaft Figure 16. Main dimensions of the speed multiplier The

Rmin

Figure 19. Normal forces **Figure 19.** Normal forces

These forces are very high and are a major problem in bearing design. The axial force on the bearings is equal to the resultant force exerted on the stator, i.e. 76 kN. This problem exists in most discoid machines and hampers their development.
