Suitable Airgap

Suitable Airgap

There is not a definite answer

Suitable Airgap

There is not a definite answer

$\delta = 0.2 + 0.01 P^{0.4}$mm when p=1

P: power

Suitable Airgap

There is not a definite answer

$\delta = 0.2 + 0.01 P^{0.4}$mm when p=1

P: power

$\delta = 0.18 + 0.006 P^{0.4}$mm when p > 1

Suitable Airgap

There is not a definite answer

$\delta = 0.2 + 0.01 P^{0.4}$mm when p=1

P: power

$\delta = 0.18 + 0.006 P^{0.4}$mm when p > 1

Smallest airgap is 0.2 mm

Suitable Airgap

For heavy duty motors the gap may be increased by 60 %.

Suitable Airgap

For heavy duty motors the gap may be increased by 60 %.

For converter driven motors airgap can be increased by 60 % to reduce rotor surface losses.

Suitable Airgap

For heavy duty motors the gap may be increased by 60 %.

For converter driven motors airgap can be increased by 60 % to reduce rotor surface losses.

For high speed machines increase airgap (eqn. 6.25 of the textbook)

Suitable Airgap

For heavy duty motors the gap may be increased by 60 %.

For converter driven motors airgap can be increased by 60 % to reduce rotor surface losses.

For high speed machines increase airgap (eqn. 6.25 of the textbook)

For very large diameter machines airgap is approximate to D/1000.

Ex:

What should be the suitable airgap if the motor in the previous example (30 kW) is a heavy-duty motor?

Ex:

What should be the suitable airgap if the motor in the previous example (30 kW) is a heavy-duty motor?

$\delta= 1.6 \; 0.8 \; 0.006 (30k)^{0.4}=0.88 \approx 0.9mm$

Mechanical Constraints

Tip Speed

What is the rotational speed of a machine with 0.5m diameter rotor, to reach the tip speed reach to the speed of sound (1 Mach)?

Mechanical Constraints

Tip Speed

What is the rotational speed of a machine with 0.5m diameter rotor, to reach the tip speed reach to the speed of sound (1 Mach)?

Max allowable tip speed: 75m/s for high-strength non-magnetic alloy sleeves, and 100 m/s for carbon-fiber sleeves

Reading: Section 6.1 of textbook

Mechanical Loadability

Mechanical Loadability

Rotor material should withstand centrifugal forces (especially at high speeds).

Mechanical Loadability

Rotor material should withstand centrifugal forces (especially at high speeds).

Centrifugal Stress:

$\sigma_{mech} = C' \rho r_r^2 \Omega^2$

$\Omega$: Mechanical speed in rad/s

$\rho$: Density of the material

Centrifugal Stress:

$\sigma_{mech} = C' \rho r_r^2 \Omega^2$

Centrifugal Stress:

$\sigma_{mech} = C' \rho r_r^2 \Omega^2$

$C'= 1$ for a thin cylinder

Centrifugal Stress:

$\sigma_{mech} = C' \rho r_r^2 \Omega^2$

$C'= 1$ for a thin cylinder

$C'= (3+v)/8$ for a smooth homogenous cylinder

Centrifugal Stress:

$\sigma_{mech} = C' \rho r_r^2 \Omega^2$

$C'= 1$ for a thin cylinder

$C'= (3+v)/8$ for a smooth homogenous cylinder

$C'= (3+v)/4$ for a cylinder with a small bore

Centrifugal Stress:

$\sigma_{mech} = C' \rho r_r^2 \Omega^2$

$C'= 1$ for a thin cylinder

$C'= (3+v)/8$ for a smooth homogenous cylinder

$C'= (3+v)/4$ for a cylinder with a small bore

$v$: Poisson's ratio

Centrifugal Stress:

$\sigma_{mech} = C' \rho r_r^2 \Omega^2$

$C'= 1$ for a thin cylinder

$C'= (3+v)/8$ for a smooth homogenous cylinder

$C'= (3+v)/4$ for a cylinder with a small bore

$v$: Poisson's ratio

Poisson's ratio, deflection of a golf ball, deflection of a face, 2:15

Centrifugal Stress:

$\sigma_{mech} = C' \rho r_r^2 \Omega^2$

$C'= 1$ for a thin cylinder

$C'= (3+v)/8$ for a smooth homogenous cylinder

$C'= (3+v)/4$ for a cylinder with a small bore

$v$: Poisson's ratio

Poisson's ratio, deflection of a golf ball, deflection of a face, 2:15

Poisson Ratios of metals: Aluminium=0.34, Steel=0.29, Copper=0.34

Ex. 6.3:

Calculate the maximum diameter for a smooth steel sylinder having a small bore. The speed is 15.000 rpm. Yield strength is 300 MPa. The density of the material is 7860 kg/m³.

Other Mechanical Constraints

Bending Modes

Dynamics of Mechanical Systems: Resonance

Transfer function and mathematical modelling

Dynamics of Mechanical Systems: Resonance

Transfer function and mathematical modelling

Tacoma Bridge

Forced vibration-1, Resonant Freq.

Torsional Resonance

Resonant Modes

Cantilever Vibration

Resonant Modes

Modal Shapes

Modal Shapes

Critical Speeds

The rotational speed should be below the critical speed (preferably with a safety factor)

Critical Speeds

The rotational speed should be below the critical speed (preferably with a safety factor)

Usually the limiting factor for very high-speed machines:

Critical Speeds

The rotational speed should be below the critical speed (preferably with a safety factor)

Usually the limiting factor for very high-speed machines:

Ex 6.5

Calculate the max. length with a safety factor k=1.5 for a smooth solid rotor when the rotor diameter is 0.15 m and the rotor speed is 20.000 rpm.

Review: Aspect Ratio

Review: Aspect Ratio

$\chi = \dfrac{L'}{D}$

Typical Aspect Ratios

Typical Aspect Ratios

Asynchronous Machines:

$\chi \approx \dfrac{\pi}{2p} \sqrt[3]{p}$

Typical Aspect Ratios

Asynchronous Machines:

$\chi \approx \dfrac{\pi}{2p} \sqrt[3]{p}$

Synchronous Machines:

$\chi \approx \dfrac{\pi}{4p} \sqrt{p}$

Typical Aspect Ratios

Asynchronous Machines:

$\chi \approx \dfrac{\pi}{2p} \sqrt[3]{p}$

Synchronous Machines:

$\chi \approx \dfrac{\pi}{4p} \sqrt{p}$

Define $D_i$ and $L$

Define $D_i$ and $L$

Usually $0.5 < D_i/L < 2.5$

Define $D_i$ and $L$

Usually $0.5 < D_i/L < 2.5$

Small diameter for high-speed or servo-type motors, why?

Define $D_i$ and $L$

Usually $0.5 < D_i/L < 2.5$

Small diameter for high-speed or servo-type motors, why?

Small inertia,

Define $D_i$ and $L$

Usually $0.5 < D_i/L < 2.5$

Small diameter for high-speed or servo-type motors, why?

Small inertia,

Low tip speed!

Define $D_i$ and $L$

Usually $0.5 < D_i/L < 2.5$

Small diameter for high-speed or servo-type motors, why?

Small inertia,

Low tip speed!

Bending Modes

How to define Outer Diameter $D_o$?

How to define Outer Diameter $D_o$?

How to define $D_o$?

How to define $D_o$?

Source: T.Miller - Electric Machine Design Course, Lecture-5, Slide4

How to choose height of the slots?

How to choose height of the slots?

Slot Ratio (d): Ratio of the inner stator slot diameter to outer stator slot diameter

How to choose height of the slots?

Slot Ratio (d): Ratio of the inner stator slot diameter to outer stator slot diameter

Reading Assignment: The Rediscovery of Synchronous Reluctance and Ferrite Permanent Magnet Motors

How to choose height of the slots?

For the same outer diameter:

How to choose height of the slots?

For the same outer diameter:

As the slot ratio increases (i.e. higher slots):

How to choose height of the slots?

For the same outer diameter:

As the slot ratio increases (i.e. higher slots):

• Electric loading increases (more copper can be fit)

How to choose height of the slots?

For the same outer diameter:

As the slot ratio increases (i.e. higher slots):

• Electric loading increases (more copper can be fit)

• Diameter for the rotor gets smaller (less surface area & less torque)

How to choose height of the slots?

For the same outer diameter:

As the slot ratio decreases (i.e. shorter slots):

How to choose height of the slots?

For the same outer diameter:

As the slot ratio decreases (i.e. shorter slots):

• Electric loading decreases (less area for copper)

How to choose height of the slots?

For the same outer diameter:

As the slot ratio decreases (i.e. shorter slots):

• Electric loading decreases (less area for copper)

• Diameter (&rotor volume) gets larger

There should be an optimum point!

How to choose height of the slots?

Assume parallel (rectangular) slots: copper area is proportional to slot height:

How to choose height of the slots?

Assume parallel (rectangular) slots: copper area is proportional to slot height:

$I \propto (1-d)$

How to choose height of the slots?

Assume parallel (rectangular) slots: copper area is proportional to slot height:

$I \propto (1-d)$

Electrical Loading is current per circumference

How to choose height of the slots?

Assume parallel (rectangular) slots: copper area is proportional to slot height:

$I \propto (1-d)$

Electrical Loading is current per circumference

$K_s \propto (1-d)/d$

How to choose height of the slots?

Assume parallel (rectangular) slots: copper area is proportional to slot height:

$I \propto (1-d)$

Electrical Loading is current per circumference

$K_s \propto (1-d)/d$

Torque can be expressed as:

$T \propto \sigma . Vol_R$

How to choose height of the slots?

Assume parallel (rectangular) slots: copper area is proportional to slot height:

$I \propto (1-d)$

Electrical Loading is current per circumference

$K_s \propto (1-d)/d$

Torque can be expressed as:

$T \propto \sigma . Vol_R$$\propto [(1-d)/d].d² \propto (1-d).d$

How to choose height of the slots?

Assume parallel (rectangular) slots: copper area is proportional to slot height:

Torque can be expressed as:

$T \propto \sigma . Vol_R$

How to choose height of the slots?

Assume parallel (rectangular) slots: copper area is proportional to slot height:

Torque can be expressed as:

$T \propto \sigma . Vol_R$$\propto [(1-d)/d].d² \propto (1-d).d$

Optimum point=?

How to choose height of the slots?

Assume parallel (rectangular) slots: copper area is proportional to slot height:

Torque can be expressed as:

$T \propto \sigma . Vol_R$$\propto [(1-d)/d].d² \propto (1-d).d$

Optimum point=?

d=0.5

How to choose height of the slots?

But parallel teeth are more common: Slots gets wider with diameter

$I \propto (1-d²)$

How to choose height of the slots?

But parallel teeth are more common: Slots gets wider with diameter

$I \propto (1-d²)$

Electrical Loading is current per circumference

How to choose height of the slots?

But parallel teeth are more common: Slots gets wider with diameter

$I \propto (1-d²)$

Electrical Loading is current per circumference

$K_s \propto (1-d²)/d$

Torque can be expressed as:

$T \propto \sigma . Vol_R \; \propto [(1-d²)/d].d² \propto (1-d²).d$

Optimum point= $d= 1/\sqrt{3} = 0.58$

How to choose height of the slots?

Stator Slot Types:

Stator Slot Types:

Stator Slot Types:

Most Common Types:

• Open Slots: Constant width, easy repair and assembly

Stator Slot Types:

Most Common Types:

• Open Slots: Constant width, easy repair and assembly

• Semi-closed Slots: Difficult to assembly but better magnetic characteristics

Stator Slot Types:

Most Common Types:

• Open Slots: Constant width, easy repair and assembly

• Semi-closed Slots: Difficult to assembly but better magnetic characteristics

• Tapered Slots: Varying width (constant tooth width)

Stator Slot Types:

There are several other options. Depending on operating conditions, manufacturing constraints etc.

Stator Slot Types:

There are several other options. Depending on operating conditions, manufacturing constraints etc.

Stator Slot Types:

There are several other options. Depending on operating conditions, manufacturing constraints etc.

Production of Electric Machines

TES Generators and Motors

Induction Motors: Overhauling a Motor

Rewinding a Large Motor

Automatic Coil Insertion

E-propulsion System

BMW i-8

Case Study: Ferrite vs. NdFeB

Case Study: Ferrite vs. NdFeB

Base Design

• Di=100mm

• L =100mm

• Slot Ratio=0.7

• Airgap = 1.5mm

• Magnet (NdFeB)= 4mm, Brem=1.1T

Reading Assignment: The Rediscovery of Synchronous Reluctance and Ferrite Permanent Magnet Motors

Case Study: Ferrite vs. NdFeB

Base Design

• Current Density = 6.7 A/mm2

• Electrical Loading = 30kA/m

• Shear Stress = 18 kPa

• Output Torque = 28 Nm

• Magnet (NdFeB)= 4mm, Brem=1.1T

Reading Assignment: The Rediscovery of Synchronous Reluctance and Ferrite Permanent Magnet Motors

Base Design with NdFeB

Magnets replaced with Ferrite (Brem=0.4 T)

Double Ferrite Thickness (4mm -> 8mm)

Reduce teeth width until saturation

Electric loading is 157% of the base design

Reduce back-core (yoke) until saturation

Total volume reduces to 83%.

Comparison of Electrical and Magnetic Loadings

Selection of number of stator slots

Selection of number of stator slots

Advantages of Low number of slots:

• Reduced manufacturing cost

• Less space lost due to insulation and slot opening

Selection of number of stator slots

Advantages of Low number of slots:

• Reduced manufacturing cost

• Less space lost due to insulation and slot opening

Disadvantages of low number of slots

• Increased leakage inductance

• Reduced breakdown torque

• Larger MMF harmonics

Selection of number of stator slots

Advantages of High number of slots:

• Reduced tooth pulsation

• Higher overload capacity

• Better Cooling

Selection of number of stator slots

Advantages of High number of slots:

• Reduced tooth pulsation

• Higher overload capacity

• Better Cooling

  Disadvantages of high number of slots

• Increased magnetizing current

• Poor Cooling

• Difficult manufacturing

Number of Slots vs Winding Factor

Further Reading

Selection of Phases - Poles

T.Miller Electric Machine Design Course, Lecture 10-12

Ref

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