Location and size of the crossover section

Owing to the fact that the winding should be mostly positioned parallel to the winding flange, meeting an orthogonality condition, it is necessary to adjust the winding width to the number of turns per layer of the winding. In particular for non-circular shaped coil cross-sectional areas, it is desired to locate the crossover area to the small side of the coil body, also called winding head. This is due to the fact, that non-circular coils are being mounted on a sheet metal package or in a circular arrangement. The coils should be rather small, in order to avoid a contact with the neighboring coil or the sheet metal package. For orthocyclic round coils three winding geometries can be defined:

a) Equal number of turns per layer

b) Unequal number of turns per layer, starting with shortened layer

c) Unequal number of turns per layer, starting with longer layer

The choice of the winding structure to be used basically depends on the design of the coil or the coil body. Among others, the available space conditions for winding width and winding height must be considered. Moreover, it is possible to influence the location and the end of the last winding by selecting a clever winding pattern. The winding height of an orthocyclic coil winding results from the following equation:

${\displaystyle h=[1+(n-1)\cdot \sin 60^{\circ }]\cdot d}$

${\displaystyle h}$ -Winding height

${\displaystyle n}$ - Number of layers

${\displaystyle d}$ - max. wire gauge above the varnish (CuL)

Since an orthocyclically wound coil with at least 300° of the circumference of winding layers has the tightest circle package of the wire cross-sections. This winding method reaches the highest fill factor and is the best way to fill the available winding cross-section with round wires. Square coils are seen as orthocyclically wound when the winding and layer jump occur only on one of the sides of the winding cross-section. In theory, a geometric fill factor of 0.91 will be reached. In practice, however, the value cannot be reached because there exists a winding jump and layer jump area and the wire insulation is not taken into account.

Orthocyclic winding

${\displaystyle A\Delta ={\frac {d^{2}}{4}}\cdot {\sqrt {3}}}$

${\displaystyle \Sigma A\Delta ={\frac {d^{2}\cdot \pi }{4}}\cdot {\frac {60}{360}}\cdot 3={\frac {d^{2}\cdot \pi }{8}}}$

fill factor = ${\displaystyle {\frac {\Sigma A\Delta }{A\Delta }}}$ = ${\displaystyle {\frac {\frac {d^{2}\cdot \pi }{8}}{{\frac {d^{2}}{4}}\cdot {\sqrt {3}}}}}$ = ${\displaystyle {\frac {d^{2}\cdot \pi }{8}}\ {\frac {1}{{\frac {d^{2}}{4}}\cdot {\sqrt {3}}}}}$

${\displaystyle ={\frac {\pi }{2\cdot {\sqrt {3}}}}}$ = 0,907

In general, it can be stated that the requirements that need to be fulfilled for orthocyclic windings are very high. The summation of all tolerances has to be kept at a very low value. Consequently, the following values can be named as indicatory values: a) Tolerance of the winding space width

${\displaystyle \Delta b=0,2\cdot d}$

${\displaystyle \Delta b}$ - tolerance of winding space

${\displaystyle d}$ - max. wire gauge including the varnish coat (CuL)

b) Tolerance of the wire Max. wire diameter tolerance should not be larger than

${\displaystyle \Delta d=0,4\cdot {\frac {d}{n}}}$

${\displaystyle \Delta d}$ - gauge – wire tolerance

${\displaystyle n}$ - number of turns per layer

${\displaystyle d}$ - nominal wire gauge including the varnish coat (CuL)

This corresponds to about half the wire tolerance according to the specification of the German standard DIN46435.

Manufacturing orthocyclic windings

Even if the demands for low tolerances of the wire and the winding space had to be observed with correspondingly high technical effort, there would still remain the problem that the wire guiding on the machine side has to follow the previously described winding design also at high winding speeds. In practice, this is hardly possible at high winding speeds since, e.g., at 18.000 windings per minute, the wire guide for a wire with a thickness of 0.3 mm would need to perform a winding pitch in only 0.7 ms. The problem is amplified by the fact that in practice the ideal wire is never absolutely straight. These unevennesses and bends resulting from the winding of the wire on delivery rolls have the effect that the wires are never completely close together according to their actual diameter but at a distance according to their unevenness.

This gap formation is additionally influenced during the winding-up of the wire by the surface quality of its coating, e.g. the sliding behavior as well as by the expansion behavior or stiffness of the copper. The wire elongation may be between 6% and 3% depending on the wire diameter and the supplier. Practice has shown that an orthocyclic winding can only be manufactured in an acceptable way when choosing a very high wire elongation level (stretching leads to a straight or even wire) at the beginning. For the reasons described above, it is therefore in practice impossible for the wire guide to determine a precise gradient according to the wire diameter.

These unpredictable circumstances may be prevented or counteracted at the beginning of the winding by forcing the wire, meaning, every single winding of the first layer on the inner coil diameter, into a predefined position. The wire places itself into a prefabricated groove geometry of the coil body and the wire guide does not need to follow it exactly but only approximately. Since the wire always loses in cross-sectional area due to the wire drawing to be used and the necessary deflections (mechanical stresses under tensile load) during winding, the distance between the grooves is designed only for the max. possible wire diameter. Effects of bends and tolerances of the wire and the coil body as well as changing surface qualities can be avoided that way. Especially wire bends that develop due to wire deflections caused by, e.g., pulleys, wire eyelets or even the wire guiding nozzle itself within the wire feeder of a winding machine can lead to deformations that remain on the winding of a coil. Applying grooves to the winding basis supports the layer-accurate position of the wire during the winding process. This behavior is particularly beneficial for the winding processes where a plastic deformation of the wire is unavoidable immediately before the depositing of the wire onto the winding basis. This behavior can be observed especially in the needle winding technology. Owing to physical reasons, it is unavoidable that the wire leaves the wire guiding nozzle at an angle of approx. 90°. Therefore, mechanical tensions remain inside the wire that are visible in the form of a bent winding on the winding basis. As a result, the following windings, or also the following layers, can change in their desired position.

Starting from the second layer, the relocation is facilitated, since the wire is guided through the inter-spaces of the preceding layer. In case of deflections that are not too excessive as far as the process is concerned, the wire leads itself and with a constant number of windings per layer. It means for the wire guiding movement that the smaller the distance of the wire guiding nozzle towards the coil, the more precise the tracking must be. In certain circumstances it can be completely performed without a relocating movement, if the distance from the nozzle to the coil is that long that the force component against the guiding behavior of the wire itself has no longer an effect. Owing to the self-guiding behavior of the wire, it is therefore possible that also during orthocyclic winding the wire guide can run continually and does not need to follow gradually.

Design of an orthocyclic winding

The design or interpretation of the required space of an orthocyclic winding is usually realized by applying an iterative approach. At first, the specified parameters of the required number of windings, the required wire cross section and the maximum space available for an insulated coil are used for the calculation basis.

Calculation example

An orthocyclic winding design for a round coil with 150 windings, a wire diameter of 0.3 mm and a maximum winding width of 9 mm shall be calculated. The winding diameter at the winding base measures 8 mm.

Structure of a coil with an even number of turns per

Given:

Wire-Ø Cu 0,3 mm → CU1L=0,334 mm (According to the table)

Coil width: should be 9 mm // 150 turns, coil inner diameter 8mm.

a) Calculation of the winding width In the first iteration step, a winding with the same number of windings per layer is assumed or taken as a basis.

9/0,334 → 26,9 turns/layer → chosen 26 turns per layer

${\displaystyle Windingwidth=26\cdot 0.334+0.5\cdot 0.334=8.85mm}$

b) Calculation of the number of layers

Number of layers = 150/26 = 5,76 → 6 layers

c) Calculation of the winding height

${\displaystyle {\text{Winding height h}}=[1+(h-1)\cdot \sin 60^{\circ }]\cdot d}$

${\displaystyle {\text{ Winding height h}}=[1+(6-1)\cdot \sin 60^{\circ }]\cdot 0.334=1.78mm}$

d) Calculation of the winding height in the layer cross section area

${\displaystyle h_{\text{Lagensprung}}=1.78+5\%=1.86mm}$

b=8,85 mm; e=1,78 mm; c=1,86 mm; d=0,334 mm; winding structure calculation example for an orthocyclic area. 150 turns in 6 layers with 26 turns per layer and an equal number of turns per layer

e) Calculation of the outer diameter of the coil

${\displaystyle {\text{Outer diameter }}:D=2\cdot h+innerdiameterofwinding}$

${\displaystyle D=1.78\cdot 2+8=11.56mm}$

f) Calculation of the outer dimensions of the coil in the cross section area

${\displaystyle {\text{ Outer diameter }}:D_{\text{max}}=2\cdot h_{\text{layer step}}+innerdiameterofwinding</}$

${\displaystyle D_{\text{max}}=1.86\cdot 2+8=11.72mm}$

Summary of results: The calculation showed that the space needed for the purely orthocyclic winding with enameled wire fills a rectangular area that measures 1.86 mm x 8.85 mm. Taking into account the assumption that it is a round coil with an inner diameter of 8 mm, then, the outer diameter is 11.72 mm. The winding space constraints (flanges of a coil body) of a winding support must have a diameter of at least D_min=11,72mm considering the layer jump area.

Calculation of the fill factor

The fill factor measures the ratio between the volume of a winding package and the volume needed to house the winding pack. For this purpose, it is necessary to take the required space for the rotation diameter of the coil in the "cross over section" into consideration.

Scheme for the needed volume of a winding; D1=1,78mm D=8mm D2=1,86mm

a) Calculation of the mechanical fill factor

The imaginary space with the dimensions of 8,85 mm x 1,86 mm contains an area of 16.461 mm². The sum of all partial spaces of the insulated turns equals

${\displaystyle A={\frac {\pi \cdot D^{2}}{4}}\cdot n}$

A = Amount of partial spaces of the insulated wires D_L= wire gauge above the varnish n= number of turns

${\displaystyle A={\frac {\pi \cdot 0.334^{2}}{4}}\cdot 150=13.14mm^{2}}$

${\displaystyle F_{\text{mech}}=A_{\text{wire}}/A_{\text{Winding space}}\cdot 100\%}$

${\displaystyle F_{\text{mech}}=13.14mm^{2}/16.461mm^{2}\cdot 100\%}$

${\displaystyle F_{\text{mech}}=79.8\%}$

b) Calculation of the electrical fill factor

The imaginary space with the dimensions of 8,85 mm x 1,86 mm contains an area of 16.461 mm². The sum of all partial spaces of the not insulated turns equals

${\displaystyle A={\frac {\pi \cdot D^{2}}{4}}\cdot n}$

A= Amount of partial spaces of the not insulated wires

D_Cu= pure copper wire gauge

n= number of turns

${\displaystyle A={\frac {\pi \cdot 0.3^{2}}{4}}\cdot 150=10.59mm^{2}}$

${\displaystyle F_{\text{electr}}=A_{\text{ wire }}/A_{\text{ Winding space }}\cdot 100\%}$

${\displaystyle F_{\text{electr}}=10.59mm^{2}/16.461mm^{2}\cdot 100\%}$

${\displaystyle F_{\text{electr}}=64.3\%}$

Characterization of distributed winding

In case of stator windings that are electrically commutated or supplied by an m-phase net, these phase windings are often banked (distributed windings). The number of holes q constitutes a characteristic dimension of the winding setup. It states how many slots q per phase m and pole (provided by pole number 2p) are available.

${\displaystyle q={\frac {N}{2p\cdot m}}}$

q = Number of holes

N = Number of slots

2p = Number of poles

m = Number of phases

In the case of distributed windings, q ≥ 1, and if q is integer, it is an integral slot winding. If q = zq/nq is a fractional rational number, it is referred to as fractional slot winding. When it comes to single tooth winding, q < 1 and thus always a fractional rational number.

Example for a distributed winding topology

The winding scheme shows the execution of three-phase winding with 30 groups of coils at a winding pitch of 1:6 with the same width at a star connection. The combination of the star connections is depicted in form of a circle on the yellow contact bar. Each coil needs two slots. Consequently, 30 slots (coil groups) x 2 slots / group = 60 slots are required in order to achieve a consistent occupancy of the slots. The number of poles amounts to 10. The respective number of holes is:

${\displaystyle q={\frac {60}{2\cdot 5\cdot 3}}=2}$

Inside slotted stator laminations

The needle-winding technique basically represents the only feasible winding process for inside slotted stator laminations. The stator mainly consists of a steel package, two end plates and slot insulation. The particular benefit of this process technology lies in the fact that the winding machine produces a completely winded assembly group when adequate electrical slot fill factors are employed. If, however, the use of single teeth requires joining and interconnecting operations, all interconnecting measures of the coil sections of one phase may be executed by the winding machine for the stator laminations. In this case, the electric slot fill factor may amount up to 45%. Since manufacturing a functioning stator merely requires a small effort, the negative impact on the electric fill factor is gladly accepted. In order to be able to use various additional functions of the winding machine, the end plates are often designed in a way which allows e.g. the taking on of cutting terminal contacts. In addition, winding space restrictions and laying ducts for the connecting wires of a phase may be integrated.

Example for a lead from for a full sheet metal package stator displaying several design characteristics

The material costs are also low due to the small number of individual components. In combination with the modest costs of the means of production, stator laminations constitute a practical solution. Three essential basic concepts frequently come to the fore when dealing with the design of stator laminations. Stator laminations for concentrated winding are divided into the following main groups.

Paper-insulated stator laminations

Paper-insulated stator

Insulation paper or insulation foil is usually attached to the slots of the stator package before the insulated end plates are installed. The insulation material, e.g. Nomex or Mylar or Kapton, is taken from the endless strip. It is pre-hemmed, cut to the length of the stator and inserted. The insulation strip must be slightly longer than the stator package to ensure complete insulation of the winding. Thin insulation takes up little of the slot area, which improves the fill factor of the winding.

Insulated stator laminations at end plates

Concept of an end plated insulated stator

When using this type of stator design, lining the slot with insulation paper is not required. The plastic end plates are designed in a way that the sides of the injected shafts insulate half of the stator slot. It is also beneficial, that costs for paper as well as costs for the production process for the mounting of the paper do not arise. Under consideration of a certain wall thickness of these injected shafts, z-shaped overlapping of the shafts in the area of the stator nut center may be achieved in order to increase the creepage distance and clearance to avoid dielectric breakdowns. However, a disadvantage constitutes in the fact that the depth of the shot of the injection process is limited depending on the stator lengths and the plastic material used. When e.g. using PA with a solid material content (e.g. glass fibers) of approx. 25% and a shot of approx. 25 mm depth, a wall thickness of at least 0.5 mm may be achieved. However, it has negative repercussions on the fill factor compared to the use of insulation paper which e.g. is only 0.1 mm thick.

Molded stator laminations

Concept for a coated stator

An extended form of the stator's end insulation with injected slot shafts constitutes in the moulded stator. In the last few years, injection moulding has progressively been developed. It now allows to place the stator package into the injection mould and to facilitate the moulding process. In doing so, the wall thickness reached is similar to the one of the end plates with injected slot shafts. A particular benefit of this process lies in the fact that a pre-assembly of the end bells and the insulation paper can be avoided which prevents the danger of insulation gaps that could lead to short circuits. However, due to the very costly complex injection mould, costs are only covered at a batch size of approx. 50.000 stators per year, compared to single component insulation. In addition, the diversity in types is only conditionally lucrative since a new injection mould needs to be produced whenever the length of the package or the laminations changes.

Outside slotted stator laminations

Schematics for flyer winding of an outer-grooved stator

Outside slotted stator laminations may be processed with the needle-winding technique, the flyer-winding technique and the linear-winding technique. The selection of the process depends on the desired number of turns in the winding and the intended fill factors. Consequently, flyer-winding is particularly used if a thin wire and thus high numbers of windings are expected in combination with a medium and high voltage application. Therefore, it is typically used with “white goods”, such as e.g. household applications, or in general domestic engineering with an operating voltage of 230 V. In the case of stators with less windings and a lower mass, it is common to process outside slotted stator laminations using the needle-winding technique or the linear winding technique.

• 
  Linearwinding application used for an outer grooved stator
• 
  Needle winding application for an outer grooved stator

Basically, there is also a variety of different ways of insulation for outside slotted stator laminations as it is for inside slotted stator laminations:

Verschieden isolierte Vollblechschnitte

Segmented stator coils

Polechain consisting of segments

Segmented stator coils are used, for example, if a high winding number is required in addition to the demanded high fill factor and the corresponding orthocyclic winding. They are preferably processed with the flyer-winding technique as well as with the linear-winding technique. For this type of stator construction, it is particularly beneficial to produce accurately layered windings with extremely high fill factors because of the freely accessible winding space. However, the design of the segmented stator coils has negative repercussions on the material and production costs. Often, complex processes need to be applied in order to form the single teeth to a round stator. Another disadvantage constitutes in the large number of contact points, except when the pole-chain winding technique is used.

For segmented stator coils, a distinction is made between T-segments and plugged engine coils. The latter may be bodiless or winded onto a coil body and subsequently be transferred to a T-segment or directly to the stator laminations, depending on the application. Contingent on the expected contact points, there are three different options for the production of T-segments. For one, there is the classic single T-segment with the disadvantage of having a high number of contact points. In addition, there is the phase winded T-segment with a reduced number of contact points. Finally, there is also the winding of pole chains with a drastically reduced number of contact points.

T-segments

Winding tool for the fixation of a T-segment in a linear winding process

T-segments are preferably processed with the linear winding technique or the flyer-winding technique. For this, the winding supports are designed in a way that a mounting at the tooth back can be carried out. It is in particular the outer geometry that will serve as the contact surface of the adjacent tooth later on, which is used for securing the tooth in the winding device. It is also quite common to place a dovetail slot in the outer part of the back of the tooth which is axially arranged to the tooth and serves the purpose of securing the tooth in the winding device. Insulation of the winding of the T-segment may be performed the same way as for inside and outside stator laminations which is either by paper insulation, end bell insulation or as a moulded tooth.

Phase-wise wound T-segments

Winding tool for the fixation of a T-segment chain in a linear winding process

In combination with a series connection, T-segments are often produced as a phase compound in the form of a toothed chain. As is the case of single T-segments, the linear-winding technique as well as the flyer-winding technique are also applied in this context. When it comes to the winding of the teeth, the final wire of the first tooth is guided to the next tooth and then serves as the starting wire for the second tooth. This process continues, depending on the number of a phase's sub-segments. The design of the components does not show any substantial difference compared to the one of classic single teeth. The main reason for the processing of T-segments into one tooth chain lies in the reduced of number of contact points. Six contact points are required for three wound single tooth poles. However, only two contact points are needed if the just mentioned arrangement inside the winding machine is adopted. When using high current with low operating power, this type of manufacture is especially beneficial since it reduces contact resistances and potential errors. However, it is a very complex endeavor to form the tooth chains to a complete stator which is of disadvantage. It must be ensured, for example, that the end wires of each tooth are equipped with tension relief to ensure that the winding does not open during handling. Usually, it is taken care of with adhesive tape or pole or bag-type forming of the tooth's frontal insulation where the wire may be attached after the winding process. Single teeth are easy to handle, whereas tooth chains must be built in carefully, taking into account the risk of damaging the connecting wires.

Plugged tooth coils

Stator design with plugged tooth coils

Plugged tooth coils are frequently used in a star-shaped stator design where a final ring or yoke is mounted after the assembly of the coils. Inside slotted stator laminations can also be fitted with plugged tooth coils. But in that case, fill factor losses can be registered due to the plug-in direction from the inside to the outside. Conical windings are only possible and beneficial, if the plug-in direction is from the outside to the inside. As for the type of insulation, it is possible – as with the classical single teeth – to work with paper insulations or insulating end plates. If insert moulding is applied with a star-shaped package, it is not referred to as plugged tooth coils anymore because of the necessary direct winding with a needle winding system, flyer winding technique or linear winding technique. Plugged tooth coils eventually require at least two contact points per coil, just as the single teeth. Toothed chains of a phase connected in series are rarely produced since, compared with the already difficult assembly of phase-wise wound T-segments, they will be followed by further assembly movements (pushing onto the stator pack) and the changing length ratios of the connecting wires between the coil sections of a phase. Therefore, two cut-and-clamp contacts per coil are frequently used for plugged tooth coils which finally reach into a control card or a lead frame via pin-like forms of the contacts.

Chains on poles (chained poles)

With this kind of stator design they try to combine the benefits of the needle-wound laminations. A minimum number of contact points – with the advantages of the linear wound single tooth creates a maximum fill factor.

For this, the chained poles winding technique is used that provides a very high fill factor due to the fact that the structure of the stator is opened up into a linear arrangement of the single teeth and besides, in contrast to the otherwise common single teeth, generates only a few contact points. The connecting wires of the coil sections of a phase connected in series do not need to be separated.

Schematics of an open winding space using a needle winding process for chained pools

When winding toothed chains, the flyer winding technique, also a type of needle winding and chain winding can be used.

Schematics of an open winding space using a flyer winding process for chained pools

A disadvantage when using the flyer winding technique is the fact that only one tooth at a time can be wound. So, toothed chains are developing as a result but due to the wiring topology most of the stators have to be undone again. A simultaneous winding of multiple stator phases usually is not possible. If, however, the flyer winding technique for toothed chains requires auxiliary tools for placing the wire into the winding space or the linear arrangement needs to be given up when the winding of a single tooth takes place, the wire can be directly deposited with the needle winding technique. A special benefit when using the needle winding technique is provided by the possibility to wind all three phases at the same time depending on the type of stator circuitry. Especially advantageous is the behavior of the connecting wires between the coils of the individual phases at the rounding of the teeth if the linear arrangement of the teeth for the winding does not need to be given up. Therefore, it is opportune to make sure that the connecting wires pass through the center of the rounding radius.

Three workpiece carrier with each one pole chain and a wire guide for a parallel winding of the phases U,V and W

Owing to this smart arrangement of the wires, it is possible to avoid changes in the wire length during rounding. When using the needle winding technique, it is quite common to wind multiple toothed chains simultaneously. This happens mainly on carrier tools or workpiece carriers that are positioned inside the needle winding machine. Owing to the fact that the phases U, V and W as well as multiple stators can be wound at the same time, the needle winding technique has a high performance density in connection with the use of toothed chains.

Example for calculating the fill factor of a stator lamination

An orthocyclic winding design for a stator with 40 windings per tooth at a wire diameter of 0.5 mm shall be calculated. The available insulated winding space is geometrically defined and has a surface of 35 mm². An insulation paper with a thickness of 0.25 mm is used.

• Determination of the mechanical fill factor

Given: Wire-Ø Cu 0,5mm → CU1L=0,548mm (Value according to norm) 40 turns, insulated winding space = 35mm^2, insulation paper 0,25mm

Geometry aspects for determining the mechanical fill factor; A= insulated winding space

When looking at the insulated winding space graphically and the required number of windings at a given wire diameter, it can be said that considering the space requirements for the winding nozzle (required groove width: about 3*0.548=1.6 mm) only 38 windings can be introduced into the winding space of the stator slot.

${\displaystyle A={\frac {\pi \cdot D^{2}}{4}}\cdot n\cdot 2}$

${\displaystyle A={\frac {\pi \cdot 0.548^{2}}{4}}\cdot 38\cdot 2=17.9mm^{2}}$

A= Accumulated partial spaces of the insulated wires

D_L= wire gauge including the varnish coat

n= Number of turns per tooth

${\displaystyle F_{\text{mech}}=A_{\text{wire}}/A_{\text{winding space}}\cdot 100\%}$

${\displaystyle F_{\text{mech}}=17.9mm^{2}/35mm^{2}\cdot 100\%}$

${\displaystyle F_{\text{mech}}=51.1\%}$

• Determination of the electrical fill factor The theoretical consideration takes place by assuming that the uninsulated wire is to be found in the uninsulated groove.

Given: Wire-Ø Cu 0,5mm 38 turns, non-insulated winding space = 41mm^2

Geometry aspects for determining the electrical fill factor; A= non insulated winding space

${\displaystyle A={\frac {\pi \cdot D^{2}}{4}}\cdot n\cdot 2}$

A= Accumulated partial spaces of the non insulated wires

D_Cu= wire gauge excluding the varnish coat

n= Number of turns per tooth

${\displaystyle A={\frac {\pi \cdot 0.5^{2}}{4}}\cdot 38\cdot 2=14.9mm^{2}}$

${\displaystyle F_{\text{electr}}=A_{\text{ wire }}/A_{\text{winding space}}\cdot 100\%}$

${\displaystyle F_{\text{electr}}=14.9mm^{2}/41mm^{2}\cdot 100\%}$

${\displaystyle F_{\text{electr}}=36.3\%}$