How is the winding cross-induction of a 3 phases motor magnetically interact from one winding to the next?

Question

Considering a Squirrel Cage 3 phases motor. A multi-switch receive the 3 lines of the 3Ø power L1 L2 L3 and distribute the voltage to 6 wires. The multi-switch has 3 position, Speed 1 , OFF , Speed 2, or Low , OFF , Fast.
Schematically, there are 6 coils but each coil is built with 3 winding, hence a total of 18 physical winding . Each coil is calculated to be identical DC resistance of 30 ohms. Each coil are connected in series like in an hexagon (schematically speaking). The 6 coils are electrically accessible via 6 wires. After careful testing and analysis it is established that the multi-switch when positioned for Speed 2, will short 3 of the 6 wires such that the connection configuration becomes Star (see images below), if the switch is set to Speed 1 the configuration is Delta. Switch position OFF disconnect all wires from power.
In the case of Speed 1 (Slow), there are 3 coils (let’s call them Ua , Va , Wa) that are shorted together, which imply that when in Star configuration, the magnetic polarity of those 3 coils is reverse compare to the Delta configuration, while that 3 other coils ( Uv , Vb , Wb) remain with the same magnetic polarity.

Below is an image to represent the physical distribution of 6 of the 18 winding involved. It is clear that each coil will produce a magnetic field and that the sum of all 18 magnetic field will result in one magnetic field that will turn 360 degrees per cycle. That is the basic principle of an induction motor.

I have much difficulty wrapping my mind around the fact that reversing the polarity of 3 coils (9 winding) would not interact with the 3 other coils (again 9 winding) and produce a counter induction that would create heat just as it would happen if one was to connect in parallel the output of two transformer with wrong polarity and or phase. At one point some of the induced magnetic of each coil would induce a voltage in the next adjacent coil, creating some sort of counter-current, producing a loss of energy into heat.

Furthermore, how is it that by distributing the same voltage into 6 series connected coils would induce double the speed of the other case where now the 6 coils are turned into 3 coils ( 3 times two coils in parallel) . Such configuration would “pull” more current, intuitively resulting into an increase speed, instead the speed is lowered.

The Questions: 1- How are multiple winding energized with voltage of different phases and polarity not induce heat ? Basically I am trying to understand what exactly is magnetically happening in this Speed 1 configuration.

2- Why is it that when connecting in parallel two winding would result in a lower speed instead of a higher speed ? ( I guess if I would understand what’s happening from question 1, then question 2 would be answered).

Any WEB source of theoretical explanation is more than welcome. Cheers

Answer 1

The connection diagram seems like it may match the one shown below. With the star connection, the windings are connected in parallel forming a 4 poles with each winding receiving 231 volts. Withe the delta connection the windings are connected in series forming 2 poles with each winding receiving 200 volts.

A motor like this has a constant power rating, so the rated torque multiplied by the rated speed is constant. The rated torque for low speed operation is about twice the rated torque for high speed operation. The motor is designed to drive something like the spindle for a cutting tool. When a large cutting tool is mounted, it is driven at a lower speed and requires a higher torque compared to a smaller cutting tool driven at the higher speed.

Note that the lower voltage per coil for the high-speed connection reduces the torque capability for a given slip and the rated slip is 11.3% vs. 8% for the low-speed connection.

Image from Smeaton (Ed), Motor Application and Maintenance Handbook, Paul J. Dobbins, Ch 6, AC Three Phase Motors

This scheme is commonly called a Dahlander connection in recognition of US Patent 725415A granted on April 14, 1903 to Robert Dahlander and Karl Arvid Lindstroem. The diagram and explanation provided there may be of interest. However, I am having difficulty with both the diagrams in the question and those in the patent. I will try to find something that satisfies me, but I can't predict whether or not it might satisfy others.

The secret to this scheme is apparently that, for the usual winding scheme, poles are formed only in the center of each coil. Reversing the current direction in adjacent coils causes additional poles to be formed between the coils. The diagram below shows 8 poles in (a) with poles both in the centers of the coils and in the spaces between the coils. In (b) poles are formed only in the centers of the coils to provide just 4 poles. With winding shown for all three phases, the windings may be overlapped. At a given instant, the strength of the magnetic field of each phase would need to be considered. Apparently, the motor can be designed such that the same result as shown for one phase can be achieved.

Image from Puchstein, Lloyd, Conrad, Alternating Current Machines.

For the 3-phase, 2/4-pole, 18-coil motor in question, I would use just coils 1 and 2 from the diagram above, but say that represents one phase and that there are 3 coils and 3 phases per pole arranged as shown below. That represents Six groups of 3 coils each for a total of 18 coils. The diagram is for the connection with half of the six groups of coils connected with so that the current flows in the opposite direction to the other six groups providing magnetic poles both inside and between the coils. The pole markings assume that the magnetic poles exist in the location shown at the instant the phase producing that pole is dominant. The picture is more complex when the net effect of the three phases is considered.