Motor selection#
Written by Marc Budinger (INSA Toulouse), Scott Delbecq (ISAE-SUPAERO) and Félix Pollet (ISAE-SUPAERO), Toulouse, France.
Design graph#
The following diagram represents the design graph of the motor’s selection. The mean speed/thrust (Ωmoy & Tmoy), the max speed/thrust (Ωmax & Tmax) and the battery voltage are assumed to be known here.
Fig. 19 Motor design graph#
The design graphs for the overall drone system can be found in here.
Sizing code#
# Specifications
# Reference parameters for scaling laws
# Motor reference
# Ref : AXI 5325/16 GOLD LINE
T_nom_mot_ref = 2.32 # [N.m] rated torque
T_max_mot_ref = 85.0 / 70.0 * T_nom_mot_ref # [N.m] max torque
R_mot_ref = 0.03 # [Ohm] resistance
M_mot_ref = 0.575 # [kg] mass
K_T_ref = 0.03 # [N.m/A] torque coefficient
T_mot_fr_ref = 0.03 # [N.m] friction torque (zero load, nominal speed)
# Assumptions
T_pro_to = 0.5 # [N.m] Propeller Torque during takeoff
P_pro_to = 100 # [W] Propeller Power during takeoff
Omega_pro_to = 400.0 # [rad/s] Propeller speed during takeoff
T_pro_hov = 1.0 # [N.m] Propeller Torque during hover
P_pro_hov = 50 # [W] Propeller Power during hover
Omega_pro_hov = 0.22 # [rad/s] Propeller speed during hover
U_bat_est = 14.0 # [V] Battery voltage value (estimation)
# Design variables
k_vb = 1.0 # oversizing coefficient for voltage evaluation
k_mot = 1.0 # over sizing coefficient on the motor torque
k_speed_mot = 1.2 # adaption winding coef on the motor speed
# Equations
# Nominal torque selection with hover scenario
T_nom_mot = k_mot * T_pro_hov # [N*m] Motor nominal torque per propeller
# Torque constant selection with take-off scenario
U_bat = k_vb * 1.84 * P_pro_to ** (0.36) # [V] battery voltage estimation
K_T = U_bat / (k_speed_mot * Omega_pro_to) # [N*m/A] or [V/(rad/s)] Kt motor
# Estimation models
M_mot = M_mot_ref * (T_nom_mot / T_nom_mot_ref) ** (3.0 / 3.5) # [kg] Motor mass
R_mot = (
R_mot_ref * (T_nom_mot / T_nom_mot_ref) ** (-5.0 / 3.5) * (K_T / K_T_ref) ** 2.0
) # [ohm] motor resistance
T_mot_fr = T_mot_fr_ref * (T_nom_mot / T_nom_mot_ref) ** (3.0 / 3.5) # [N*m] Friction torque
T_max_mot = T_max_mot_ref * (T_nom_mot / T_nom_mot_ref) # [N*m] Max. torque
# Performance in various operating conditions
# Hover current and voltage
I_mot_hov = (T_pro_hov + T_mot_fr) / K_T # [A] Current of the motor per propeller
U_mot_hov = R_mot * I_mot_hov + Omega_pro_hov * K_T # [V] Voltage of the motor per propeller
P_el_mot_hov = U_mot_hov * I_mot_hov # [W] Hover : electrical power
# Takeoff current and voltage
I_mot_to = (T_pro_to + T_mot_fr) / K_T # [A] Current of the motor per propeller
U_mot_to = R_mot * I_mot_to + Omega_pro_to * K_T # [V] Voltage of the motor per propeller
P_el_mot_to = U_mot_to * I_mot_to # [W] Takeoff : electrical power
%whos
Variable Type Data/Info
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I_mot_hov float 50.43255613781267
I_mot_to float 25.57872068611814
K_T float 0.020117619309574616
K_T_ref float 0.03
M_mot float 0.279506832794264
M_mot_ref float 0.575
Omega_pro_hov float 0.22
Omega_pro_to float 400.0
P_el_mot_hov float 114.400456104866
P_el_mot_to float 235.20395039293444
P_pro_hov int 50
P_pro_to int 100
R_mot float 0.04489082730970943
R_mot_ref float 0.03
T_max_mot float 1.2142857142857142
T_max_mot_ref float 2.8171428571428567
T_mot_fr float 0.014582965189265948
T_mot_fr_ref float 0.03
T_nom_mot float 1.0
T_nom_mot_ref float 2.32
T_pro_hov float 1.0
T_pro_to float 0.5
U_bat float 9.656457268595815
U_bat_est float 14.0
U_mot_hov float 2.2683850446178813
U_mot_to float 9.195297656953668
k_mot float 1.0
k_speed_mot float 1.2
k_vb float 1.0