Parameters of the Motor

Common strengths of motors for electric vehicles are high efficiency, optimal controllability and a very small environmental impact [90]. Further important aspects of electric machines for an immediate in-wheel application are as follows:

- the maximum efficiency level for continuous operation, - high efficiency ratio over the entire speed range, - a limited value of unsprung masses,

- a torque overload ability in accordance with the power supply capacity (current, voltage and power limitations) and significant torque reserve for improved driveability and gradeability,

- low noise level (including magnetic origin), - absence of contacts, simplicity of maintenance.

Graphic representation of the load characteristics of an electric motor for achievable driving performance can be displayed in a torque-speed diagram as in Figure 3.23. This diagram provides information that the motor is able to be operated backwards and forwards, as well as that the motor can be driven and braked (see e.g. [40]

and [76]), which is a significant aspect for an application in an electric vehicle. The main focus of this diagram is the area in which the vehicle moves forward, as this is the main function of the vehicle. The forward braking area corresponds to the operation of the motor as generator to recuperate the kinetic energy of the vehicle.

Furthermore, there are two ranges that are distinguished: the constant torque range (basic speed range) and the field weakening range. In the first range, the continuous torque (nominal torque) or the peak torque for a short time (e.g. acceleration or climbing a curb) can be specified and is already available for starting. In case that speed is increased at nominal torque, the mechanical power also increases until the nominal power is reached.

39 That is why for the possibility of rotational speeds by nominal power the torque must be reduced with increasing speed. By these conditions a range of constant power is realized. Therefore, the electric motor has to be able to demand higher power to deliver the discussed range of specified motor performance scenarios.

Figure 3.23 – Torque-speed diagram for permanent magnet synchronous motor

From the diagram it is possible to calculate the current, voltage and electrical power limits of the motor. A torque-speed diagram can be influenced by relatively simple parameter variations, for example by varying the number of pole pairs, what allows to define any operating point of the motor in a relatively simple way. It is also necessary to consider the fact, that an in-wheel motor is a system that is operated under conditions of limited power supply. These are limitations e.g. of maximum current of supply cables, battery current and voltage, etc. This circumstance inevitably develops an electric motor to ensure the operation of the motor in two control ranges: left and right from of the nominal speed. It should be noted that the control downwards of nominal speed can be provided by the torque constancy mode and control upwards can be provided by the power constancy mode.

The fulfillment of in-wheel motor requirements leads to the implementation of new non-traditional motor designs with increased active volume level. The last mentioned is possible due to the application of the synchronous motor with permanent magnets or so-called PMSM by using a special combined winding.

The torque generating in a PMSM motor takes place in the magnetically active air gap between stator and rotor.

To generate a sufficiently high torque in the installation space limited by the wheel, the motor must have a specific force density related to the air gap to be as high as possible. The actual torque generation is based on the main effect of the force effect in the magnetic field. One part of the meandering copper winding is the air gap winding and another part is the slot winding. The air gap winding is glued onto a thin foil directly onto the stator back iron and the slot winding is inserted into the slots of the back iron. The cross-section view of the winding phases is shown schematically in Figure 3.24. The meander-shaped structure and changing orientation of the permanent magnets corresponds to the alternating current flows in the respective phases. Since all three phases together are as wide as a permanent magnet, each magnetic pole can be used at the same time for torque generation by using the Lorentz force. This results in an evenly variation of torque over the total circumference of the in-wheel motor.

40 Back iron

Laminated core Stator

Rotor

Magnet Magnet

Air gap winding

Slot winding

Figure 3.24 – Schematic diagram of combined winding [17]

Interactions that are responsible for energy conversion can be explained on the basis of the physical appearance of the Lorentz force. The Lorentz force is a force which acts on a current carrying conductor (combined windings) in a magnetic field. The general Equation for the Lorentz force according to [20] is:

𝐹_𝐿= 𝑙_𝑐𝑐∙ 𝐼 ∙ 𝐵_𝐻 (3.13)

with the current 𝐼, the length 𝑙_𝑐𝑐 interspersed by the magnetic field, the magnetic field 𝐵_𝐻. For a common torque, it must be ensured that each individually formed force acts in the same direction. For this purpose, the current flow directions must be the same. The generated motor torque for combined winding can be approximately calculated as a torque that is proportional to the number of pole pairs, the magnetic flux of the permanent magnets and the air gap radius, as Equation (3.14) describes:

𝑀_𝑒𝑙= 2 ∙ 𝑝_𝑝∙ 𝑟_𝑎𝑔∙ 𝐹_𝐿= 𝑝_𝑝∙ 𝑟_𝑎𝑔∙ 𝑙_𝑐𝑐∙ 𝐼 ∙ 𝐵_𝐻 (3.14) Thus, the motor torque is at first depending on the variable string current, the final proportional relation between torque and current is expressed by the motor constant 𝑘𝑀:

𝑀𝑒𝑙= 𝑘𝑀∙ 𝐼 ∙ 𝐵𝐻 (3.15)

𝑘𝑀 can be expressed as:

𝑘_𝑀= 2 ∙ 𝑝_𝑝∙ 𝑟_𝑎𝑔∙ 𝑙_𝑐𝑐∙ 𝐵_𝐻 (3.16) The same motor constant 𝑘_𝑀 can be used for the proportional relationship between induced counter-voltage 𝑈_𝑀 and angular frequency of the motor 𝜔𝑀:

𝑈_𝑀 = 𝜔_𝑀∙ 𝑘_𝑀 (3.17)

An electric quantity flowing through the cross-section of a circuit is an amount of current in the circuit.

Consequently, the electrical power is directly proportional to the potential difference and the current in the circuit (see Equation (3.18)):

𝑃_𝑒𝑙 = 𝑈_𝑀∙ 𝐼 (3.18)

Thus, from the calculation of the required torque of the electric motor for an in-wheel motor, it can be seen that the motor constant 𝑘_𝑀 and the value of the magnetic field 𝐵_𝐻 have a leading influence. It is worth mentioning that 𝑘_𝑀 depends on the motor parameters, which are essentially geometric. And the influence on the value of the magnetic field can be achieved only by two options: Either the selection of the magnetic assembly or application of different materials. Furthermore, advanced parameters of the motor with air gap and slot winding can be determined according to the approaches highlighted in [90][19] [20][91].

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