3. SPM Airflow Analyzer

This analyzer is designed to determine how much supplemental axial airflow is needed to cool the rotor to a specified max_temp.

3.1. Model Background

The SPM rotor is modeled using the thermal resistance network described in SPM Rotor Thermal Analyzer. The implementation of the resistances and nodal locations can be found in the source code of the create_resistance_network method of SPM_RotorThemalAnalyzer. In this analyzer, the axial airflow is varied to increase the convection rate on the rotor in order to improve cooling.

The problem class for the AirflowAnalyzer contains the Rotor Thermal Analyzer which is used to calculate the magnet temperature as a function of the axial airflow. The AirflowAnalyzer solve a single objective minimization problem subject to a constraint that the magnet temperature is less than max_temp.

3.2. Inputs from User

The airflow analyzer utilizes the same mat_dict and losses dictionary as the SPM Rotor Thermal Analyzer (see here). In addition, the following inputs must be defined for the problem class. The location of these inputs are shown on this figure:

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
max_temp	Maximum allowable Rotor Temperature	C

The following code demonstrates how the eMach thermal analyzer for the rotor can be used to calculate the required airflow to cool a rotor.

import numpy as np
from eMach.mach_eval.analyzers.mechanical.rotor_thermal import AirflowProblem,AirflowAnalyzer

# 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}
max_temp=80

# Create an AirflowProblem object
afp=AirflowProblem(r_sh, d_ri, r_ro, d_sl, r_si, l_st, l_hub, T_ref, losses,
                   omega, max_temp, mat_dict)
# Create an Airflow Analyzer
ana=AirflowAnalyzer()

3.3. Outputs to User

The AirflowAnalyzer returns a results object with the following keys:

• Message: returns false if magnets exceed the specified maximum temperature.

• Magnet Temp: In Celsius

• Required Airflow: in m/s

The following code demonstrates how to use the airflow analyzer to solve the airflow problem.

# Analyze problem for required airflow
results=ana.analyze(afp)
print(results)

The results object returned by the analyzer for this example is shown below:

{'Message': True,
 'Magnet Temp': array([73.43703021]),
 'Required Airflow': array([1.23618711e-08])}