< class: center, middle # EE-568 Selected Topics in Electrical Machines ## Machine Design Basics ## Ozan Keysan [ozan.keysan.me](http://ozan.keysan.me) Office: C-113 <span class="meta">•</span> Tel: 210 7586 --- ### What do you need to know to design an electric machine? -- - ### Machine Type and type of construction -- - ### Rated Power (and power factor) -- - ### Rated Speed -- - ### Rated frequency/Number of Phases -- - ### Duty Cycle -- - ### Enclosure Class -- - ### Economics/Efficiency Requirement/Expected Life --- # Duty Cycle #### [Duty Cycle Operating Graphs](http://myelectrical.com/Portals/0/Images/PostImages/IEC60034DutyCycle.gif) -- ### S1: Continuous running duty -- ### S2: Short-time duty (e.g. S2 10-90 min) -- ### S3: Intermittent periodic duty (eg. S3 25%) -- ### S4: Intermittent periodic duty with starting --- # Duty Cycle ### S5: Intermittent periodic duty with Electric Braking -- ### S6: Continuous operation periodic duty -- ### S7: Continous Operation Periodic duty with electric braking -- ### S8: Continuous Operation Periodic Duty with Related Load/Speed Changes --- # Standards: IEC60034 -- ## Efficiency Standards ([IEC-60034-30](http://en.wikipedia.org/wiki/IEC_60034)) -- - ### IE1: Standard Efficiency -- - ### IE2: High Efficiency -- - ### IE3: Premium Efficiency -- - ### IE4: Super Premium Efficiency ### [More info](https://library.e.abb.com/public/1fd380f8ca8b4934ae3fa609d764fd33/21043_ABB_Motor_Guide_REV_D.pdf) --- # Standards: Efficiency <img src="http://www.elvem.it/wp-content/uploads/2014/10/ie-efficency-class-4-poles-motors.jpg" alt="Drawing" style="width: 500px;"/> #### Since 2015, all the motors between 7.5-375 kW sold in EU has to be IEC3! #### By 2021, motors between 0.75kW to 7.5kW should be IEC too! #### By [2023](https://ec.europa.eu/info/energy-climate-change-environment/standards-tools-and-labels/products-labelling-rules-and-requirements/energy-label-and-ecodesign/energy-efficient-products/electric-motors_en), motors between 75-200 kW must meet IE4 level! --- # Standards: Degrees of Protection -- ## IP 56 -- ## First Number (Particle/Person protection) - ### 2: Motors protected against solid objects greater than 12 mm -- - ### 4: Motors protected against solid objects greater than 1 mm -- - ### 5: Dust-protected motors -- - ### 6: Dust-tight motors --- # Standards: Degrees of Protection -- ## IP 56 -- ## Second Number (Water Ingress Protection) - ### 3: Motors protected against spraying water -- - ### 4: Motors protected against splashing water -- - ### 5: Motors protected against water jets -- - ### 6: Motors protected against heavy sea --- # Voltage Standards - ## 220-240 V (Delta) -- - ## 380-415 V (Wye) -- - ## 500 V (Delta) -- - ## 660-690 V (Wye) --- # Frame Sizes <img src="./images/ee564/frame_size.jpg" alt="Drawing" style="width: 750px;"> [More info](http://www.motology.co.th/download/motors/%282%29%20Standard%20Motor%20catalog.pdf) --- <img src="./images/ee564/frame_size2.jpg" alt="Drawing" style="width: 500px;"> --- # Design Procedure -- ## Starting Values -- - #### Motor Type and construction -- - #### Power, power factor -- - #### Rotational Speed -- - #### Rated frequency -- - #### Rated Voltage -- - #### Intended usage (duty cycle) -- - #### Enclosure Class --- # Design Procedure: -- - ## Define the magnetic loading and electric loading -- - ## Define the Diameter and axial length -- - ## Define the Airgap -- - ## Winding Type and number of coils --- # Design Procedure: - ## Determination of other dimensions (slot, tooth etc.) -- - ## Calculation of machine performance -- - ## Lots of iteration/optimization --- # Dimensions to Choose? -- ### Diameter (Outer-Airgap) -- ### Airgap clearance -- ### Stator Stack Length -- ### Number of Stator/Rotor Slots -- ### Slot-Teeth Dimensions -- ### Winding Schematic --- # Where to start? --- # Where is the torque generated? -- ### Maxwell Stress Tensor (textbook pg. 33) ## \\(\sigma_F = \dfrac{1}{2}\mu_0 H^2\\) or ## \\(\sigma_F = \dfrac{1}{2\mu_0} B^2\\) --- # Where is the torque generated? ## Which direction does it rotate? -- <img src="./images/ee564/maxwell_tensor.png" alt="Drawing" style="width: 750px;"> --- # Shear Stress [More info](http://www.eleceng.adelaide.edu.au/research/power/pebn/pebn009%20sizing%20of%20electrical%20machines.pdf) -- ## Average Shear Stress Values -- - ### Industrial Motor (<1 kW): 0.7 to 2 kPa -- - ### Industrial Motor (>1 kW): 4 to 15 kPa -- - ### High Performance Industrial Servo: 10 to 20 kPa -- - ### Liquid Cooled Machines: 20 to 100 kPa --- # Electric- Magnetic Loading [More info](http://www.eleceng.adelaide.edu.au/research/power/pebn/pebn009%20sizing%20of%20electrical%20machines.pdf) -- ## Specific Magnetic Loading (T) -- ### i.e. average airgap flux density over a pole -- ## \\(\bar{B} = \dfrac{p \Phi_p}{\pi D_i L}\\) --- # Typical Flux Density Values <img src="https://raw.githubusercontent.com/ozank/ozank.github.io/master/presentations/images/magnetic_loading.png" alt="Drawing" style="width: 750px;"/> --- # Typical Flux Density Values <img src="./images/typical_magnetic_loading.png" alt="Drawing" style="width: 750px;"/> Source: Traditional Design of Electrical Machines, Slide-12 --- # Specific Electric Loading (kA/m) -- ## RMS ampere turns per unit length of the airgap -- ## \\(\bar{A} = \dfrac{ N\_{turn,slot} I Q}{\pi D\_i}\\) -- ### \\(N\_{turn,slot}\\): Number of turns per slot ### \\(Q\\): Number of slots ### \\(I\\): RMS current for wire --- # Typical Electric Loading Values <img src="https://raw.githubusercontent.com/ozank/ozank.github.io/master/presentations/images/electric_loading.png" alt="Drawing" style="width: 750px;"/> --- # Typical Tangential Stress Values <img src="https://raw.githubusercontent.com/ozank/ozank.github.io/master/presentations/images/tangential_stress.png" alt="Drawing" style="width: 750px;"/> --- ## Electrical & Magnetic Loading vs Stress -- ## Local tangential stress -- ## \\(\sigma\_{tan}(x) = A(x) B(x) \\) -- ## Average Stress ### \\(\sigma\_{tan}(x) = \dfrac{\hat{A} \hat{B} cos (\phi)}{2} \\) -- \\(= \dfrac{A\_{rms} \hat{B} cos (\phi)}{\sqrt{2}} \\) #### Details and derivations are available in Design of Rotating Electrical Machines, Juha Pyrhonen. --- ## Torque vs Stress -- ## Torque = \\( \sigma\_{tan} r\_r S\_r\\) -- ## \\(r\_r\\): Rotor Radius (m) ## \\(S\_r\\): Rotor Surface Area (m2) ## \\(S\_r = (2 \pi r\_r l') \\) --- ## Torque vs Stress ## \\( T = \sigma\_{tan} r\_r (2 \pi r\_r l')\\) -- ## \\( T = \sigma\_{tan} 2 \pi r\_r^2 l'\\) -- ## \\( T = 2 \sigma\_{tan} V\_r \\) ## \\( V\_r = \pi r\_r^2 l' \\) : Rotor Volume ## Torque of a motor is proportional to rotor volume and tangential stress (i.e. electric loading x magnetic loading) --- # Specific Machine Constant (C) #### Full derivations available in in Design of Rotating Electrical Machines, Juha Pyrhonen. -- ### \\(S\_i = m E\_m I\_s\\) ### \\(S\_i\\): Apparent Power (kVA) ### \\(m\\): Number of Phases ### \\(E\_m\\): Induced Phase Voltage ### \\(I\_s\\): Stator Phase Current --- # Specific Machine Constant (C) #### Full derivations available in in Design of Rotating Electrical Machines, Juha Pyrhonen. ### \\(S\_i = m \dfrac{1}{\sqrt{2}} \omega N\_s k\_{w1} \hat{\Phi}\_m I\_s\\) -- ### \\(S\_i = m \dfrac{1}{\sqrt{2}} \omega N\_s k\_{w1} \hat{\Phi}\_m \dfrac{A \pi D}{2 m N\_s}\\) -- ### \\(\omega = 2 \pi p n\_{syn}\\) --- # Specific Machine Constant (C) -- ### \\(S\_i = \dfrac{1}{\sqrt{2}} 2 \pi p n\_{syn} k\_{w1} \dfrac{\pi D }{2p}\dfrac{2}{\pi} \hat{B} l'\dfrac{A \pi D}{2}\\) -- ### \\(S\_i = \dfrac{\pi^2}{\sqrt{2}} n\_{syn} k\_{w1} A \hat{B} D^2 l'\\) -- ### \\(S\_i = C D^2 l' n\_{syn}\\) ### \\(C = \dfrac{\pi^2}{2} k\_{w1} \hat{A} \hat{B} \\) --- # Specific Machine Constant (C) ### \\(S\_i = C D^2 l' n\_{syn}\\) ### \\(D^2 l'\\): Rotor Volume (m3) ### C: Specific Machine Constant ### \\(C = \dfrac{\pi^2}{2} k\_{w1} \hat{A} \hat{B} \\) ### A factor to evaluate a machine's performance that combines winding design, electric loading, magnetic loading --- # \\(C\_{mech}\\) <img src="./images/Cmech.png" alt="Drawing" style="width: 600px;"/> --- ## Exercise (Pyrhonen Ex 6.1) -- ### The diameter of a rotor of a 4 kW, 50 Hz, two-pole induction motor is 98 mm and the length is 82 mm. -- ### Assume 1% rated slip and calculate the machine constant and the average tangential stress. -- ### \\(P= T \omega \\) -- ### 50 Hz, 2 pole, 0.01 slip -- ### \\(\omega = 2 \pi f (1-s) = 2 \pi (1-0.01) = 99 \pi\\) --- ## Exercise (Pyrhonen Ex 6.1) ### \\( T = \dfrac{4 kW}{ 99 \pi} = 12.86\\) Nm -- ### Rotor Area: \\(S_r\\) -- \\(= \pi D_r l = \pi \, 0.098 \, 0.082 = 0.0252 m²\\) -- ### \\(F\_{tan}=\dfrac{Torque}{Radius} = \dfrac{12.86}{0.049} = 262 N\\) -- ### Stress \\( \sigma = \dfrac{F\_{tan}}{S\_r} = \dfrac{262}{0.0252} = 10.400 N/m² \\) --- ## Machine Constant ### \\(P\_{mech} = C\_{mech} D² l f\_{syn}\\) ### \\(C\_{mech} = \dfrac{4000}{0.098² \, 0.082 50 }\\) -- ### \\(C\_{mech} = 102 \, kWs/m³ \\) --- # Aspect Ratio -- ## Ratio of axial length to diameter in an electric machine ## \\(\chi = \dfrac{L'}{D}\\) --- # Aspect Ratio -- <img src="./images/ee564/aspect_ratio.png" alt="Drawing" style="width: 600px;"/> --- # Typical Aspect Ratios -- ### Asynchronous Machines: ### \\(\chi \approx \dfrac{\pi}{2p} \sqrt[3]{p}\\\) ### \\(p\\): pole pairs -- ### Synchronous Machines: ### \\(\chi \approx \dfrac{\pi}{4p} \sqrt{p}\\\) -- --- # 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\\)? -- <img src="./images/varying_number_of_poles.png" alt="Drawing" style="width: 800px;"/> --- # How to define \\(D_o\\)? -- <style type="text/css"> .tg {border-collapse:collapse;border-spacing:0;border-color:#bbb;margin:0px auto;} .tg td{font-family:Arial, sans-serif;font-size:32px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#bbb;color:#594F4F;background-color:#E0FFEB;} .tg th{font-family:Arial, sans-serif;font-size:32px;font-weight:normal;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#bbb;color:#493F3F;background-color:#9DE0AD;} </style> <table class="tg"> <tr> <th class="tg-031e">N Poles</th> <th class="tg-031e">2</th> <th class="tg-031e">4</th> <th class="tg-031e">6</th> <th class="tg-031e">8</th> <th class="tg-031e">10</th> <th class="tg-szh5">12</th> </tr> <tr> <td class="tg-031e">Do/Di</td> <td class="tg-031e">2 <br></td> <td class="tg-031e">1.88</td> <td class="tg-031e">1.78</td> <td class="tg-031e">1.66</td> <td class="tg-031e">1.54</td> <td class="tg-031e">1.43</td> </tr> </table> Source: T.Miller - Electric Machine Design Course, Lecture-5, Slide4 --- ## Example: -- ### Determine the main dimensions for a 30 kW, 690 V, 50 Hz four-pole, three-phase SCIG. -- ### Choose Cmech = 150 kW s/m3 -- ### \\(\chi \approx \dfrac{\pi}{2p} \sqrt[3]{p}\\\) -- ### \\(\chi \approx \dfrac{\pi}{4} \sqrt[3]{2} = 0.9895 \approx 1\\\) --- ### \\(P\_{mech}(kW) = C\_{mech} D² l n\_{syn}(Hz)\\) ### \\( D = \sqrt[3]{\dfrac{P\_{mech}(kW)}{\chi C\_{mech} n\_{syn}(Hz)}} = \sqrt[3]{\dfrac{30}{ 1 \, 150 \, 25}} \approx 200 mm \\) -- ### Tangential Stress if the speed is 1474 rpm -- ### \\(T=\dfrac{30k}{2\pi 1454/60}= 194.4 \\) Nm -- ### \\(\sigma = \dfrac{T}{r \, S\_r} = \dfrac{2 \, 194.4}{\pi 0.2² 0.2} = 15.5 \\) kPa --- --- # Stator Slot Pitch: -- - ## Induction Machines and small PMSMs: 7-45 mm -- - ## Synchronous Machines and large PMSMs: 14-75 mm -- - ## DC Machines: 10-30 mm -- ### Tooth thickness can be initially assumed as the half of the slot pitch -- ### Slot pitch gets bigger as the power rating of the machine increases --- ## Example: ### Define the rough dimensions, and a select suitable stator windings for the 30 kW, 4-pole induction machine. -- ### D= 200 mm, L= 200 mm, Stator circumference = 628 mm -- ### Assume q= 2, \\(N\_{slot} = 4 x 3 x 2 =24 \\) ### Tooth thickness: \\(\tau\_{teeth} = 0.5 \dfrac{628}{24} =13 \\)mm --- ## Example: ### Define the rough dimensions, and a select suitable stator windings for the 30 kW, 4-pole induction machine. ### D= 200 mm, L= 200 mm, Stator circumference = 628 mm ### Assume q= 3, \\(N\_{slot} = 4 x 3 x 3 =36 \\) ### Tooth thickness: \\(\tau\_{teeth} = 0.5 \dfrac{628}{36} =8 \\)mm --- ## Example: ### Define the rough dimensions, and a select suitable stator windings for the 30 kW, 4-pole induction machine. ### D= 200 mm, L= 200 mm, Stator circumference = 628 mm ### Assume q= 4, \\(N\_{slot} = 4 x 3 x 4 =48 \\) ### Tooth thickness: \\(\tau\_{teeth} = 0.5 \dfrac{628}{48} =6.5 \\)mm --- ## Example: ### Define the rough dimensions, and a select suitable stator windings for the 30 kW, 4-pole induction machine. ### D= 200 mm, L= 200 mm, Stator circumference = 628 mm ### q= 3 seems the best option ### Coil span: 9 slots ### A 8/9 or 7/9 short-pitched winding can be used. --- # Reading Assignment (Pyrhonen) -- ## Ch-7 Introduction summarizes the first steps in machine design --- # Where are we? Rough Design Steps -- <img src="./images/ee564/design_process.png" alt="Drawing" style="width: 800px;"/> --- --- ## You can download this presentation from: [keysan.me/ee564](http://keysan.me/ee564)