2. SPM Rotor Thermal Analyzer

This analyzer determines the temperature distribution of a surface-mounted permanent magnet (SPM) rotor.

2.1. Model Background

The SPM rotor is modeled using a thermal resistance network as shown in the figure. The implementation of the resistances and nodal locations can be found in the source code of the create_resistance_network method of SPM_RotorThermalAnalyzer. This analyzer utilizes the Thermal Resistance Network Analyzer to solve for the temperature distribution in the rotor.

2.1.1. Geometric Dimensions

The required geometric dimensions and operating conditions needed to implement this model are shown in the following figure.

2.1.2. Nodal Locations

The location of the nodes and resistance network used in this analyzer are highlighted in the following figure. It should be noted that the iron losses are injected at node-3, and the magnet losses are injected at node-5. The convection resistance are shown as any resistance going to node-0. The numbering of the nodes corresponds with the index of the T vector returned by the analyzer (i.e. the magnet temperature would be provided by T[5]).

2.2. Inputs from User

The SPM_RotorThermalAnalyzer takes in a SPM_RotorThermalProblem with inputs listed in the following tables.

Material dictionary for rotor thermal problem – `mat_dict`
Variable/key_value name	Description	Units
shaft_therm_conductivity	Shaft Thermal Conductivity	W/m-k
core_therm_conductivity	Rotor Core Thermal Conductivity	W/m-k
magnet_therm_conductivity	Magnet Thermal Conductivity	W/m-k
sleeve_therm_conductivity	Sleeve Thermal Conductivity	W/m-k
rotor_hub_therm_conductivity	Rotor Hub Thermal Conductivity	W/m-k
air_therm_conductivity	Air Thermal Conductivity	W/m-k
air_viscosity	Viscosity of Air	m^2/s
air_cp	Specific Heat Capacity of Air	kJ/kg

Input losses for rotor thermal problem
Variable/key_value name	Description	Units
rotor_iron_loss	Iron losses in rotor back iron	W
magnet_loss	Magnet losses in rotor	W

Input dimensions and operating conditions for rotor thermal problem
Variable/key_value name	Description	Units
r_sh	Shaft radius	m
d_m	Magnet thickness	m
r_ro	Rotor outer radius	m
d_sl	Sleeve Thickness	m
l_st	Stack length	m
l_hub	Hub thickness	m
u_z	Axial Air Flow Rate	m/s
omega	Rotational Speed	rad/s
T_ref	Air Temperature	C

The following code-block demonstrates how to create a SPM_RotorThermalProblem and SPM_RotorThermalAnalyzer.

import numpy as np
from eMach.mach_eval.analyzers.mechanical.rotor_thermal import SPM_RotorThermalProblem,SPM_RotorThermalAnalyzer
# Example Machine Dimensions
r_sh=5E-3 # [m]
d_m=3E-3 # [m]
r_ro=12.5E-3 # [m]
d_ri=r_ro-r_sh - d_m # [m]
d_sl=1E-3 # [m]
l_st=50E-3 # [m]
l_hub=3E-3 # [m]
r_si=r_ro+d_sl+1E-3 # [m]

# Define Material Dictionary
mat_dict= {'shaft_therm_conductivity': 51.9, # W/m-k ,
           'core_therm_conductivity': 28, # W/m-k
           'magnet_therm_conductivity': 8.95, # W/m-k ,
           'sleeve_therm_conductivity': 0.71, # W/m-k,
           'air_therm_conductivity'     :.02624, #W/m-K
           'air_viscosity'              :1.562E-5, #m^2/s
           'air_cp'                     :1, #kJ/kg
           'rotor_hub_therm_conductivity':205.0} #W/m-K}
# Operating Conditions
T_ref=25 # [C]
omega=120E3*2*np.pi/60 # [rad/s]
losses={'rotor_iron_loss':.001,'magnet_loss':135}
u_z=0

prob=SPM_RotorThermalProblem(mat_dict,r_sh,d_ri,r_ro,d_sl,r_si,l_st,l_hub,T_ref,u_z,losses,omega)
ana=SPM_RotorThermalAnalyzer()

2.3. Outputs to User

The SPM_RotorThermalAnalyzer returns back

T a list of temperatures for each node (see this figure) defined by the resistance network.

T=ana.analyze(prob)