How the Tesla Model X motor works

 Today is a bit of a special episode. Why? It's because I want to describe, in succinct detail, how the Tesla model 3's motor works.

When developing the Tesla model 3, new motors are replaced, new motors that use new induction motors, the IPMSynRM, and make use of both magnetic and reluctance action. How do these motors work?

To get a clear answer, the electric motor of a model S is an induction motor. The induction motor has both a stator and rotor.  

Alternating currents from the battery pack flow into the motor's outer windings, creating a rotating magnetic field. This generates Electromotive forces, which in turn generates forces on the rotor bars. This makes the rotor to spin. These motors are efficient, but not up to the mark. 3-4% is lost in the rotor bar. The most crucial component is starting torque, but there is a motor technology based on permeant magnets that is even better. 

Let's first go over the relationship between current, magnetic field, and electromotive force, which is Faraday's law of electromagnetic induction, seen here.

Imagine we have a wire with a voltmeter and a battery and a resistor to prevent the overflow of current.

If there is a steady current in the first coil, then no current (emf) is induced in the second coil. Or, we'll have a switch and we get an induced current when we close the switch. When the current is steady it induces no current in the second coil, but there is an induced emf in the second coil. A changing magnetic field will give rise to an induced current.

The induced emf is -N multiplied by the flux change divided by the change in time. The faster the magnetic flux changes, the greater the induced emf will be in the second coil. A change in magnetic field will change the flux. The flux is the field multiplied by the area by cosine of theta.

In order to require a change in flux, you can change the flux, area, or angle with respect to coil normal line. Emf is like the voltage, measuring the total flux over time. B is the Magnetic field. Tθheta is the angle with respect to coil normal line.

ℰ = -N∆ΦB/∆t

ΦB = BAcosθ. 

We can change the flux by moving the magnet into or out of the coil. Therefore putting a magnet between some coils would create an induced emf.

Let's say we have a circular wire and magnetic field going into the page. Say the magnetic field is constant. If we get the area to go up, the magnetic flux will increase, leading to an induced emf to the circuit.

Let's say we have a square coil of wire, and let's say the magnetic field B is directed into the page. If we rotate the coil, then the angle will change. Because the angle changes there will be an induced emf where the magnetic flux will decrease whenever the angle is not 0. 

N also represents the number of loops. The current is the induced emf divided by circuit, or ℰ/R, and the power we just calculate through I^2 R which means the power  can be generated by the change in magnetic field or the change in flux. 

For an automobile, the most crucial
performance parameter is its starting torque, and there is a more efficient motor technology using permeant magnets. An efficient rotor,, placed permanent magnets in a solid iron cylinder. With a little intuition, we need to analyze the interaction between the RMF and the combined magnetic field, and observe how the south and north poles interact with each other.

The RMF (rotating magnetic field) definately rotates here, and experiences maximum torque at 45 degrees. This is because the attractive and repulsive forces are passing tangentially. This this is the perfect angle to start your electric car.

The rotor has no induced current, which reduces the input energy requires, which leads to higher efficiencies than induction motors, and the PM motor runs on synchronous speeds.

However permanent magnets have terrible performance when cruising at high speeds, because of the back emf, the magnetic field lines link with the stator windings and generate an emf, which is called back emf, which reverses. This is why permanent motors perform terribly in high-speed applications, and generates eddy currents, increasing the heat of a machine, since the current will change and result in a magnetic fueld that increases and reverses more as speed increases. How do we solve this problem?

And now, we want to take a quick look at Eddy currents. The eddy current is basically small pools of swirling electrons to resist a magnet from falling on an object. 

This video gives a good demonstration of eddy current.

Eddy currents is a result of electromagnetic induction. Suppose a metal disk is rotating about an axis of rotation. We apply an external magnetic field B to a small circular region, where B points to the board.

We apply an external magnetic field which is uniform and it points into the field. A disc rotates through the following region which is an external magnetic field. The magnetic flux at position 1 is zero since the magnetic field at position 1 is zero. See above to see the relationship between flux and field. As position 1 moves to position 2, the flux increases and by Lenz's law the induced current in the disk will create a magnetic field that opposes the change in Φ.

At position A, there is no magnetic flux, but when the point moves to position B, there is a magnetic flux since we have an area and a uniform magnetic field B, increasing the magnetic flux. From Farady's law, a change in magnetic flux will induce and emf. As our disk rotates, there is an emf, and the emf will in turn induce an electric current that will flow through that region, these are known as eddy currents. By Lenz's law we can determine the direction of these electric currents. As position 1 moves to position 2, magnetic flux increases. By Lenz's law the induce current will create a magnetic field that will oppose the change in Flux. Thus, the induced magnetic field will point out of the board. 

By right hand rule, the induced current will point in a counterclockwise direction. This induced electric current will produce a force in the opposite direction of the field. By right hand rule, the force will point to the left. So up clockwise, down counterclockwise.

The magnetic force will create a torque, which creates a certain rotation, that points in the clockwise direction, which will in turn slow down. The force points in the opposite direction of the pendulum. When there is a no magnetic field, we go clockwise when there is a decrease in magnetic flux, thus making the direction of the Eddy current in the clockwise direction.

We need to model this design so it will work at all speeds.

Reluctance is a medium's ability to oppose magnetic fields. For high-speed applications, Tesla's engineers utilized iron's reluctance property. For example, a nail sticks to a permanent magnet due to the reluctance force. Air is not good at resisting the reluctance force.

When cutting the iron, it makes the rotor at a high reluctance state. However, turning the rotor by just 45 degrees will subsequently result in a low reluctance state.  The rotor tries to tend to obtain a low reluctance state.

If magnetic field rotates the rotor will rotate with it. The rotor produced is the RMF speed and the torque produced by this force is the reluctance torque, and such motors are called synchronous reluctance motors. I'm not entirely sure how to rotor rotates with the magnetic field, though. SynRMs are highly efficient and have no reluctance issues which make them good with high speed applications. Permanent magnets are both good for low and high speeds, and integrate them. We achieve this design integration by placing the permanent magnets into the slotted cuts of the motor within the iron core, reducing the magnet's effect on stator winding and this reduced the back emf, or the counter electromotive force. 

We call this design the permanent magnet synchronous reluctance motor. The relative permeability of the magnets is around the same as the air, so they will oppose the field to pass through it. This generates the reluctance torque. Let's discuss relative permeability. 

Permeability is measured in Newtons per ampere squared. In electromagnetism, permeability is the measure of magnetization that a material obtains in response to an applied magnetic field. How easy is an element magnetized when a field is introduced to it? Air has lower permeability than iron, so the magnetic fields won't change too much when the field is introduced, and the field will move along with the magnet.

Scientist performed a magnetic finite element analysis on these. 

Using a resultant field, we can perform further analysis, which the permanent magnet and reluctance has completely different behavior in regards to the position of the RMF.

The permanent magnets don't experience torque since there is no tangential component for these forces and the torques that the remaining forces produce cancel each other out.

Rotating a magnet 45 degrees has produced maximum torque out of permenant magnets. The torque the rotor produces goes to 0 again when rotating a magnet 90 degrees. 

This allows us to obtain the permanent magnet's torque curve. The iron, at the initial the torque will be 0, but as we offset the motor experiences a maximum torque, and the torque becomes 0 when rotated 45 degrees. 

We get the maximum torque from the motor if the RMF angle is around 50 degrees. 

This gets 50 degrees for obtaining the maximum torque from the motor. Tesla engineers make sure that the RMF is around 50 degrees, guarantee a maximum torque.

The permanent magnets produced a back emf force.

Tesla Motors aligned the rotating magnetic field opposite to the permenant magnetic field. This way, even at high speed, motors won't produce too much back emf, and the torque production will mostly come from the reluctance effect, this is IPNSynRM motor technology. Each magnet in model 3 motors is segmented, reducing the eddy currents and preventing overheating. 

Notice the 2 magnetic fields are opposite directions to each other.

This motor has efficiencies of up to 96% compared to 94% of other motors. IPM-SynRMs have definately become promising in the new forefront of motor technology.