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MATISO_6336.m
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MATISO_6336.m
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classdef MATISO_6336 < ISO_6336
%MATISO_6336 do some calculations following the ISO 6336 standard.
% see also: ISO_6336, KSISO_6336, Gear_Set
%
% References:
% [1] Calculation of load capacity of spur and helical gears --
% Part 1: Basic principles, introduction and general influence factors,
% ISO 6336-1:2019, 2019.
% [2] Calculation of load capacity of spur and helical gears --
% Part 2: Calculation of surface durability (pitting),
% ISO 6336-2:2019, 2019.
% [3] Calculation of load capacity of spur and helical gears --
% Part 6: Calculation of service life under variable load,
% ISO 6336-6:2019, 2019.
% [4] Calculation of load capacity of spur and helical gears --
% Calculation examples for the application of ISO 6336 parts 1, 2, 3, 5,
% ISO/TR 6336-30:2017, 2017.
% [5] Arnaudov, K., Karaivanov, D. (2019). Planetary Gear Trains.
% Boca Raton: CRC Press, https://doi.org/10.1201/9780429458521
%
properties(Access = public)
nu_40; % [mm^2/s], Kinematic viscosity of the lubricant at 40 deg. C
C_a; % [um], Tip relief
end
properties(Access = private)
K_v_val;
end
properties(Dependent, Access = public)
S_H; % [-], Pitting safety factor
S_F; % [-], Tooth bending safety factor
sigma_H0; % [N/mm^2], Nominal contact stress
sigma_H; % [N/mm^2], Contact stress
sigma_HP; % [N/mm^2], Permissible contact stress
sigma_Hlim; % [N/mm^2], Allowable stress number
F_t; % [N], Transverse tangential load at reference cylinder (nominal, per mesh)
line_load; % [N/mm], Line load
v_pitch_line; % [m/s], Pitch line velocity
N_L; % [-], Number of load cycles
K_Falpha; % [-], Transverse load factor (root stress)
K_Fbeta; % [-], Face load factor (root stress)
K_Halpha; % [-], Transverse load factor (contact stress)
K_Hbeta; % [-], Face load factor (contact stress)
K_v; % [-], Dynamic factor
Z_beta; % [-], Helix angle factor
Z_eps; % [-], Contact ratio factor
Z_BD; % [-], Single pair tooth contact factor
Z_E; % [N^0.5/mm], Elasticity factor
Z_H; % [-], Zone factor
Z_L; % [-], Lubrication factor
Z_N; % [-], Life factor for contact stress
Z_NT; % [-], Life factor for contact stress for reference test conditions
Z_R; % [-], Roughness factor affecting surface durability
Z_v; % [-], Velocity factor (circumferential velocity at pitch line)
Z_W; % [-], Work hardening factor
Z_X; % [-], Size factor (pitting)
sigma_F;
sigma_F0;
sigma_FP;
sigma_Flim;
Y_B;
Y_DT;
Y_F;
Y_NT;
Y_RrelT;
Y_S;
Y_ST;
Y_X;
Y_beta;
end
methods
function obj = MATISO_6336(gset, varargin)
if(~exist('gset', "var"))
gset = Gear_Set();
elseif(~strcmp(class(gset), "Gear_Set"))
error('gset is not a Gear_Set object.');
end
T_1 = 9.0e3;
n_1 = 360.0;
P_r = 1.0e-3*T_1*n_1*pi/30.0;
C_ay = (1.0/18.0)*([gset.material(1:2).sigma_Hlim]./97.0 - 18.45).^2 + 1.5;
C_ay = mean(C_ay);
default = {'P_rated' , P_r, ...
'S_Hmin' , 1.0, ...
'S_Fmin' , 1.0, ...
'L_h' , 50.0e3, ...
'K_A' , 1.0, ...
'nu_40' , 320.0, ...
'n_nominal' , [n_1, NaN], ...
'C_a' , C_ay};
default = scaling_factor.process_varargin(default, varargin);
obj@ISO_6336(gset, 'P_rated' , default.P_rated, ...
'S_Hmin' , default.S_Hmin, ...
'S_Fmin' , default.S_Fmin, ...
'L_h' , default.L_h, ...
'K_A' , default.K_A, ...
'n_nominal' , default.n_nominal);
obj.nu_40 = default.nu_40;
obj.C_a = default.C_a;
obj.K_v_val = obj.dynamic_factor();
end
% function save_KS(obj, name)
% % do nothing...
% end
end
%% Calculation methods:
methods
function [SH, SF] = safety_factors(obj, varargin)
SH = obj.Pitting(varargin{:});
SF = nan(size(SH));
end
function SH = Pitting(obj, varargin)
% Safety factor for surface durability (against pitting):
SH = obj.S_Hmin*obj.sigma_HP./obj.sigma_H; % pinion/planet
end
% function SF = tooth_bending(obj, varargin)
% % to do...
% end
function ZN = life_factor(obj, N)
ZN = zeros(2, length(N));
for idx = 1:2
line = obj.material(idx).row;
ratio = obj.Z_NT(idx); % obj.sigma_HP_stat(idx)/obj.sigma_HP_ref(idx);
switch line
case 1
% St, V, GGG (perl. bai.), GTS (perl.), Eh, IF (when limited pitting is permitted)
val = power(3.0e8./6.0e5, 0.3705*log(ratio)).*( (N < 6.0e5)) + ... % if 1
power(3.0e8./N , 0.3705*log(ratio)).*((6.0e5 < N) & (N <= 1.0e7)) + ... % if 2
power(1.0e9./N , 0.2791*log(ratio)).*((1.0e7 < N) & (N <= 1.0e9)) + ...
1.0 .*((1.0e9 < N));
case 2
% St, V, GGG (perl. bai.), GTS (perl.), Eh, IF
val = power(5.0e7./1.0e5, 0.3705*log(ratio)).*( (N < 1.0e5)) + ... % if 1
power(5.0e7./N , 0.3705*log(ratio)).*((1.0e5 < N) & (N <= 5.0e7)) + ... % if 2
1.0 .*((5.0e7 < N));
case {3, 4}
% GG, GGG (ferr.), NT (nitr.), NV (nitr.)
% NV (nitrocar.)
val = power(2.0e6./1.0e5, 0.7686*log(ratio)).*( (N < 1.0e5)) + ... % if 1
power(2.0e6./N , 0.7686*log(ratio)).*((1.0e5 < N) & (N <= 2.0e6)) + ... % if 2
1.0 .*((2.0e6 < N));
otherwise
error("MATISO_6336:ZN", "Invalid input [%d].\nValid options are 1 to 4.\n", line);
end
ZN(idx, :) = val;
end
end
end
methods(Static)
function calc = example_01()
%EXAMPLE_01 runs the worked example 01 from [4], entitled
% 'Single helical case carburized gear pair', and compares the
% results against the values found in [4], Annex A.
%
% Results from 13.11.2020:
% - Z_NT was obtained using y_lim = 0.85, which is not the case
% for other systems.
% Parameter Symbol Problem Reference Calculated Rel_Error_pc
% _____________________________________________ _________________ _______ _________________ _________________ __________________
%
% {'Minimum safety factor (pitting)' } {'S_Hmin' } "" {[ 1.0000e+000]} {[ 1.0000e+000]} {[ 0.0000e+000]}
% {'Pitting safety factor for pinion' } {'S_H1' } "" {[ 1.0285e+000]} {[ 1.0299e+000]} {[-137.6429e-003]}
% {'Pitting safety factor for wheel' } {'S_H2' } "" {[ 1.0870e+000]} {[ 1.0885e+000]} {[-138.1352e-003]}
% {'Permissible contact stress for pinion' } {'sigma_HP1' } "" {[ 1.3385e+003]} {[ 1.3385e+003]} {[ -30.2347e-009]}
% {'Permissible contact stress for wheel' } {'sigma_HP2' } "" {[ 1.4145e+003]} {[ 1.4145e+003]} {[ 328.5801e-009]}
% {'Nominal contact stress' } {'sigma_H0' } "" {[ 1.2066e+003]} {[ 1.2065e+003]} {[ 8.1404e-003]}
% {'Contact stress for pinion' } {'sigma_H1' } "" {[ 1.3014e+003]} {[ 1.2996e+003]} {[ 137.4942e-003]}
% {'Contact stress for wheel' } {'sigma_H2' } "" {[ 1.3014e+003]} {[ 1.2996e+003]} {[ 137.4942e-003]}
% {'Nominal tangential load, [N]' } {'F_t' } "" {[127.3520e+003]} {[127.3524e+003]} {[-299.5607e-006]}
% {'Pitch line velocity, [m/s]' } {'v' } "" {[ 2.6640e+000]} {[ 2.6642e+000]} {[ -7.4461e-003]}
% {'Dynamic factor' } {'K_v' } "" {[ 1.0030e+000]} {[ 1.0005e+000]} {[ 246.6092e-003]}
% {'Transverse load factor (root stress)' } {'K_Falpha' } "" {[ 1.0000e+000]} {[ 1.0000e+000]} {[ 0.0000e+000]}
% {'Transverse load factor (contact stress)' } {'K_Halpha' } "" {[ 1.0000e+000]} {[ 1.0000e+000]} {[ 0.0000e+000]}
% {'Face load factor (root stress)' } {'K_Fbeta' } "" {[ 1.1280e+000]} {[ 1.1281e+000]} {[ -5.4065e-003]}
% {'Face load factor (contact stress)' } {'K_Hbeta' } "" {[ 1.1600e+000]} {[ 1.1596e+000]} {[ 30.8898e-003]}
% {'Virtual number of teeth for pinion' } {'z_n1' } "" {[ 18.9050e+000]} {[ 18.9051e+000]} {[-650.6211e-006]}
% {'Virtual number of teeth for wheel' } {'z_n2' } "" {[114.5430e+000]} {[114.5428e+000]} {[ 171.0638e-006]}
% {'Number of load cycles for pinion' } {'N_L1' } "" {[ 1.0800e+009]} {[ 1.0800e+009]} {[ 0.0000e+000]}
% {'Number of load cycles for wheel' } {'N_L2' } "" {[178.3000e+006]} {[178.2524e+006]} {[ 26.6813e-003]}
% {'Life factor for pinion' } {'Z_NT1' } "" {[910.0000e-003]} {[910.0545e-003]} {[ -5.9848e-003]}
% {'Life factor for wheel' } {'Z_NT2' } "" {[962.0000e-003]} {[961.7587e-003]} {[ 25.0846e-003]}
% {'Size factor' } {'Z_X' } "" {[ 1.0000e+000]} {[ 1.0000e+000]} {[ 0.0000e+000]}
% {'Work hardening factor' } {'Z_W' } "" {[ 1.0000e+000]} {[ 1.0000e+000]} {[ 0.0000e+000]}
% {'Roughness factor' } {'Z_R' } "" {[965.9900e-003]} {[965.9878e-003]} {[ 232.3318e-006]}
% {'Velocity factor' } {'Z_v' } "" {[969.1100e-003]} {[969.1142e-003]} {[-434.0740e-006]}
% {'Lubricant factor' } {'Z_L' } "" {[ 1.0474e+000]} {[ 1.0474e+000]} {[ 368.0474e-006]}
% {'Helix angle factor' } {'Z_beta' } "" {[ 1.0194e+000]} {[ 1.0194e+000]} {[-366.7828e-006]}
% {'Contact ratio factor' } {'Z_eps' } "" {[803.0000e-003]} {[803.3898e-003]} {[ -48.5416e-003]}
% {'Elasticity factor' } {'Z_E' } "" {[189.8117e+000]} {[189.8117e+000]} {[-230.5266e-009]}
% {'Single pair tooth contact factor' } {'Z_B' } "" {[ 1.0000e+000]} {[ 1.0000e+000]} {[ 0.0000e+000]}
% {'Single pair tooth contact factor' } {'Z_D' } "" {[ 1.0000e+000]} {[ 1.0000e+000]} {[ 0.0000e+000]}
% {'Zone factor' } {'Z_H' } "" {[ 2.3953e+000]} {[ 2.3953e+000]} {[-179.4571e-006]}
% {'Single stiffness, [N/(mm-um)]' } {'c'' } "" {[ 12.3705e+000]} {[ 12.3620e+000]} {[ 68.2642e-003]}
% {'Theoretical single stiffness, [N/(mm-um)]'} {'c_th'' } "" {[ 17.8558e+000]} {[ 17.8436e+000]} {[ 68.2770e-003]}
% {'Mesh stiffness, [N/(mm-um)]' } {'c_gamma_alpha'} "" {[ 17.4648e+000]} {[ 17.4553e+000]} {[ 54.8918e-003]}
% {'Mesh stiffness, [N/(mm-um)]' } {'c_gamma_beta' } "" {[ 14.8451e+000]} {[ 14.8370e+000]} {[ 54.8750e-003]}
%
mat = Material('row', 2);
mat = repmat(mat, 1, 2);
gset = Gear_Set('configuration', 'parallel', ... % configuration
'm_n' , 8.0, ... % normal module
'alpha_n' , 20.0, ... % pressure angle
'z' , [17 103], ... % number of teeth
'b' , 100.0, ... % face width
'x' , [0.145 0.0], ... % profile shift coefficient
'beta' , 15.8, ... % helix angle
'k' , [1 1]*0, ... % k
'bore_ratio' , [1 1]*0.5, ... % bore ratio
'N_p' , 1, ... % number of planets
'a_w' , 500.0, ... % center distance
'rack_type' , 'D', ... % rack type
'bearing' , Bearing(), ... %
'shaft' , Shaft(), ... %
'Q' , 5.0, ... % ISO accuracy grade
'R_a' , 1.0, ... % surface roughness flank
'material' , mat);
T_1 = 9.0e3;
n_1 = 360.0;
P_r = 1.0e-3*T_1*n_1*pi/30.0;
calc = MATISO_6336(gset, 'P_rated' , P_r, ...
'S_Hmin' , 1.0, ...
'S_Fmin' , 1.0, ...
'L_h' , 50.0e3, ...
'K_A' , 1.0, ...
'n_nominal' , [n_1 NaN], ...
'nu_40' , 320.0, ...
'C_a' , 70.0);
tab_set = {'Minimum safety factor (pitting)' , 'S_Hmin' , calc.S_Hmin , 1.0;
'Pitting safety factor for pinion' , 'S_H1' , calc.S_H(1) , 1.02853;
'Pitting safety factor for wheel' , 'S_H2' , calc.S_H(2) , 1.08696;
'Permissible contact stress for pinion' , 'sigma_HP1' , calc.sigma_HP(1) , 1338.48050;
'Permissible contact stress for wheel' , 'sigma_HP2' , calc.sigma_HP(2) , 1414.52551;
'Nominal contact stress' , 'sigma_H0' , calc.sigma_H0 , 1206.58207;
'Contact stress for pinion' , 'sigma_H1' , calc.sigma_H(1) , 1301.35343;
'Contact stress for wheel' , 'sigma_H2' , calc.sigma_H(2) , 1301.35343;
'Nominal tangential load, [N]' , 'F_t' , calc.F_t , 127352.0;
'Pitch line velocity, [m/s]' , 'v' , calc.v_pitch_line , 2.664;
'Dynamic factor' , 'K_v' , calc.K_v , 1.003;
'Transverse load factor (root stress)' , 'K_Falpha' , calc.K_Falpha , 1.0;
'Transverse load factor (contact stress)' , 'K_Halpha' , calc.K_Halpha , 1.0;
'Face load factor (root stress)' , 'K_Fbeta' , calc.K_Fbeta , 1.12803;
'Face load factor (contact stress)' , 'K_Hbeta' , calc.K_Hbeta , 1.16;
'Virtual number of teeth for pinion' , 'z_n1' , calc.z_n(1) , 18.905;
'Virtual number of teeth for wheel' , 'z_n2' , calc.z_n(2) , 114.543;
'Number of load cycles for pinion' , 'N_L1' , calc.N_L(1) , 1.080e9;
'Number of load cycles for wheel' , 'N_L2' , calc.N_L(2) , 1.783e8;
'Life factor for pinion' , 'Z_NT1' , calc.Z_NT(1) , 0.91;
'Life factor for wheel' , 'Z_NT2' , calc.Z_NT(2) , 0.962;
'Size factor' , 'Z_X' , calc.Z_X , 1.0;
'Work hardening factor' , 'Z_W' , calc.Z_W , 1.0;
'Roughness factor' , 'Z_R' , calc.Z_R , 0.96599;
'Velocity factor' , 'Z_v' , calc.Z_v , 0.96911;
'Lubricant factor' , 'Z_L' , calc.Z_L , 1.04739;
'Helix angle factor' , 'Z_beta' , calc.Z_beta , 1.01944;
'Contact ratio factor' , 'Z_eps' , calc.Z_eps , 0.803;
'Elasticity factor' , 'Z_E' , calc.Z_E , 189.81170;
'Single pair tooth contact factor' , 'Z_B' , calc.Z_BD(1) , 1.0;
'Single pair tooth contact factor' , 'Z_D' , calc.Z_BD(2) , 1.0;
'Zone factor' , 'Z_H' , calc.Z_H , 2.39533;
'Single stiffness, [N/(mm-um)]' , 'c''' , calc.cprime , 12.37047;
'Theoretical single stiffness, [N/(mm-um)]', 'c_th''' , calc.cprime_th , 17.85584;
'Mesh stiffness, [N/(mm-um)]' , 'c_gamma_alpha', calc.c_gamma_alpha, 17.46485;
'Mesh stiffness, [N/(mm-um)]' , 'c_gamma_beta' , calc.c_gamma_beta , 14.84512;
};
Parameter = tab_set(:, 1);
Symbol = tab_set(:, 2);
val_calc = tab_set(:, 3);
val_ref = tab_set(:, 4);
rel_err = (1.0 - cell2mat(val_calc)./cell2mat(val_ref))*100.0;
big_err = repmat("", length(rel_err), 1);
big_err(abs(rel_err) > 1.0) = 'YES';
rel_err = mat2cell(rel_err, ones(length(rel_err),1));
tab = table(Parameter, Symbol, big_err, val_ref, val_calc, rel_err, ...
'variableNames', ["Parameter", "Symbol", "Problem", "Reference", "Calculated", "Rel_Error_pc"]);
disp(tab)
end
function calc = example_load_spectra()
%EXAMPLE_LOAD_SPECTRA runs the example in [3], Annex C,
% entitled 'Example calculation for safety factor from given
% load spectrum', and compares the results against the values
% found in [3], Annex A.
%
%
% 'Dynamic factor' , 'K_v' , calc.K_v , 1.003;
% 'Nominal tangential load, [N]' , 'F_t' , calc.F_t , 127352.0;
% 'Pitch line velocity, [m/s]' , 'v' , calc.v_pitch_line , 2.664;
% 'Transverse load factor (root stress)' , 'K_Falpha' , calc.K_Falpha , 1.0;
% 'Transverse load factor (contact stress)' , 'K_Halpha' , calc.K_Halpha , 1.0;
% 'Face load factor (root stress)' , 'K_Fbeta' , calc.K_Fbeta , 1.12803;
% 'Face load factor (contact stress)' , 'K_Hbeta' , calc.K_Hbeta , 1.16;
% 'Virtual number of teeth for pinion' , 'z_n1' , calc.z_n(1) , 18.905;
% 'Virtual number of teeth for wheel' , 'z_n2' , calc.z_n(2) , 114.543;
% 'Number of load cycles for pinion' , 'N_L1' , calc.N_L(1) , 1.080e9;
% 'Number of load cycles for wheel' , 'N_L2' , calc.N_L(2) , 1.783e8;
% 'Helix angle factor' , 'Z_beta' , calc.Z_beta , 1.01944;
% 'Contact ratio factor' , 'Z_eps' , calc.Z_eps , 0.803;
% 'Elasticity factor' , 'Z_E' , calc.Z_E , 189.81170;
% 'Single pair tooth contact factor' , 'Z_B' , calc.Z_BD(1) , 1.0;
% 'Single pair tooth contact factor' , 'Z_D' , calc.Z_BD(2) , 1.0;
% 'Zone factor' , 'Z_H' , calc.Z_H , 2.39533;
% 'Single stiffness, [N/(mm-um)]' , 'c''' , calc.cprime , 12.37047;
% 'Theoretical single stiffness, [N/(mm-um)]', 'c_th''' , calc.cprime_th , 17.85584;
% 'Mesh stiffness, [N/(mm-um)]' , 'c_gamma_alpha', calc.c_gamma_alpha, 17.46485;
% 'Mesh stiffness, [N/(mm-um)]' , 'c_gamma_beta' , calc.c_gamma_beta , 14.84512;
%
mat = Material('row', 2);
mat = repmat(mat, 1, 2);
gset = Gear_Set('configuration', 'parallel' , ... % configuration
'm_n' , 8.467 , ... % normal module
'alpha_n' , 25.0 , ... % pressure angle
'z' , [17 60] , ... % number of teeth
'b' , 152.4 , ... % face width
'x' , [0.172 0.0015] , ... % profile shift coefficient
'beta' , 15.5 , ... % helix angle
'k' , [1 1]*0 , ... % k
'bore_ratio' , [1 1]*0.5 , ... % bore ratio
'N_p' , 1 , ... % number of planets
'a_w' , 339.727 , ... % center distance
'rack_type' , 'D' , ... % rack type
'bearing' , repmat(Bearing(), 1, 6), ... %
'shaft' , Shaft() , ... %
'Q' , 6.0 , ... % ISO accuracy grade
'R_a' , 1.0 , ... % surface roughness flank
'material' , mat);
T_1 = 25423.0; % [N-m], from [6], Table 4, bin 3
n_1 = 35.2; % [1.0/min.]
P_r = 1.0e-3*T_1*n_1*pi/30.0;
calc = MATISO_6336(gset, 'P_rated' , P_r , ...
'S_Hmin' , 1.0 , ...
'S_Fmin' , 1.0 , ...
'L_h' , 1.0e3 , ...
'K_A' , 1.0 , ...
'n_nominal' , [n_1 NaN], ...
'C_a' , 70.0);
tab_set = {'Minimum safety factor (pitting)' , 'S_Hmin' , calc.S_Hmin , 1.0;
'Pitting safety factor for pinion' , 'S_H1' , calc.S_H(1) , 1.374;
'Permissible contact stress for pinion' , 'sigma_HP1' , calc.sigma_HP(1) , 2400.0;
'Nominal contact stress' , 'sigma_H0' , calc.sigma_H0 , 1206.58207;
'Contact stress for pinion' , 'sigma_H1' , calc.sigma_H(1) , 1747.0;
'Life factor for pinion' , 'Z_NT1' , calc.Z_NT(1) , 0.91;
'Size factor' , 'Z_X' , calc.Z_X , 1.0;
'Work hardening factor' , 'Z_W' , calc.Z_W , 1.0;
'Roughness factor' , 'Z_R' , calc.Z_R , 1.01;
'Velocity factor' , 'Z_v' , calc.Z_v , 0.943;
'Lubricant factor' , 'Z_L' , calc.Z_L , 1.02;
};
tab_04 = readtable('table_04.csv');
torque_edges = tab_04.Torque_Max_Nm;
speed_Max = n_1*ones(size(torque_edges));
Max_power = torque_edges.*1.0e-3 .* ... % [kN-m]
speed_Max.*(pi/30.0); % [rad/s] = [kW]
L_h30y = 30.0*365.25*24.0;
n_30y = tab_04.load_cycles*L_h30y/sum(tab_04.time_h);
calc_tmp = calc;
calc_tmp.K_A = 1.0;
Khb = zeros(size(speed_Max));
SH = zeros(size(speed_Max));
ZNT = zeros(size(speed_Max));
sigmaH = zeros(2, size(speed_Max, 1));
range = 3:44; % Non-zero values
for idx = range %1:length(speed_Max)
calc_tmp.P_rated = Max_power(idx);
calc_tmp.n_nominal = calc_tmp.speed_ratio*abs(speed_Max(idx));
calc_tmp.L_h = sum(n_30y(1:idx));
sigmaH(:, idx) = calc_tmp.sigma_H';
Khb(idx) = calc_tmp.K_Hbeta;
SH(idx) = calc_tmp.S_H(1);
ZNT(idx) = calc_tmp.Z_NT(1);
end
sigmaHG = sigmaH.*1.275;
% Ni = nan(size(SH));
% Ui = Ni;
% tab_C2_calc = table(tab_04.num_bin, torque_edges*1.0e-3, tab_04.time_s , speed_Max , n_30y , Khb , sigmaH.*SH , ZNT , Ni , Ui, ...
% 'variableNames', {'Bin_No' , 'Pinion_Torque' , 'Operating_time_70d', 'Pinion_speed_rpm', 'Cycles_30y', 'K_Hbeta', 'sigma_HxS_H', 'Z_NT', 'N_i', 'U_i'});
num_cycle = [0.0; cumsum(n_30y)]';
[NN, sigHH] = calc.Pitting_SN_curve();
%% Plotting LDD:
torque_hist = [torque_edges; tab_04.Torque_min_Nm(end)];
torque_hist = flipud(torque_hist)*1.0e-3;
zdx = num_cycle == 0.0;
cycle_num = num_cycle;
cycle_num(zdx) = 1;
figure('unit', 'centimeters', 'position', [5, 5, 23, 16]);
subplot(211)
histogram('binEdges' , torque_hist', ...
'binCounts', flipud(tab_04.load_cycles));
title('ISO 6336-6:2019, Table 4 -- Histogram')
xlabel('T, [kN-m]');
ylabel('N, [-]');
subplot(212)
histogram('binEdges' , cycle_num, ...
'binCounts', torque_edges*1.0e-3);
title('ISO 6336-6:2019, Table 4 -- LDD');
set(gca, 'xScale', 'log')
xlabel('N, [-]');
ylabel('T, [kN-m]');
xlim([1e2 1e6]);
fig_axes = findobj(gcf, 'Type', 'Axes');
set(fig_axes, 'fontName', 'Times');
set(fig_axes, 'fontSize', 12);
set(fig_axes, 'box', 'on');
%% Figure C.1: Load Spectra and S-N Curve
fig_C1 = readtable('data_Fig_C1.csv');
figure('unit', 'centimeters', 'position', [5, 5, 23, 16]);
subplot(211)
hold on;
plot(NN, sigHH(1, :), 'k', 'lineWidth', 2.0);
histogram('binEdges' , cycle_num, ...
'binCounts', sigmaH(1, :)*1.275, ...
'displayStyle', 'stairs', ...
'edgeColor', 'r', ...
'lineWidth', 2.0);
histogram('binEdges' , cycle_num, ...
'binCounts', sigmaH(2, :), ...
'displayStyle', 'stairs', ...
'edgeColor', 'b', ...
'lineWidth', 2.0);
title('ISO 6336-6:2019, Fig. C.1 -- Load Spectra and S-N Curve (Obtained)')
ylabel('\sigma_H, [N/mm^2]');
subplot(212)
hold on;
plot(fig_C1.N_SN, fig_C1.sigma_SN, 'k-', 'lineWidth', 2.0);
plot(fig_C1.N_H1, fig_C1.sigma_H1, 'r', 'lineWidth', 2.0);
plot(fig_C1.N_H2, fig_C1.sigma_H2, 'b', 'lineWidth', 2.0);
xlabel('N, [-]');
ylabel('\sigma_H, [N/mm^2]');
title('ISO 6336-6:2019, Fig. C.1 -- Load Spectra and S-N Curve (Ref.)')
legend({'SN', '\sigma_{HG}', '\sigma_{H1}'}, 'location', 'best');
fig_axes = findobj(gcf, 'Type', 'Axes');
set(fig_axes, 'fontName', 'Times');
set(fig_axes, 'fontSize', 12);
set(fig_axes, 'box', 'on');
set(fig_axes, 'xScale', 'log');
set(fig_axes, 'yScale', 'log');
set(fig_axes, 'xlim', [1e2 1e10]);
set(fig_axes, 'ylim', [800.0 3.0e3]);
end
end
methods(Access = private)
function val = F_t_spectra(obj, torque)
val = 2.0e3*(torque/obj.d(1))/obj.N_p;
val = abs(val);
end
function val = F_tH_spectra(obj, torque)
val = 2.0e3*(torque/obj.d(1))/obj.N_p;
val = abs(val);
end
function val = dynamic_factor(obj)
z1 = obj.z(1);
uu = obj.u;
cond = (obj.v_pitch_line*z1/100.0)*sqrt((uu.^2)/(1.0 + uu.^2));
if(cond < 3.0) % [m/s]
warning('MATISO_6336:KV', ['Calculating K_v using method B', ...
' outside of its useful range. ', ...
'More info at the end of Sec. 6.3.2 of ISO 6336-1.']);
end
rho = [obj.material.rho];
% transverse base pitch deviation, [um]:
fpb = obj.f_pb;
% profile form deviation, [um]
f_falpha = max(obj.f_falpha);
% Estimated running allowance (pitch deviation):
y_p = obj.y_alpha;
% Estimated running allowance (flank deviation):
y_f = f_falpha*75.0e-3;
% transverse effective base pitch deviation after running-in, [um]:
f_pbeff = fpb - y_p;
% effective profile form deviation after running-in, [um]
f_falphaeff = f_falpha - y_f; % 0.925*y_f
if(strcmp(obj.configuration, 'parallel'))
% Based on Sec. 6.5.9 of ISO 6336-1, Eq. (30), assuming gears:
% - of solid construction, and
% - with the same density
num = pi*rho(1)*(obj.u^2)*obj.d_m(1)^4;
den = 8.0*(obj.u^2 + 1.0)*obj.d_b(1)^2;
m_red = num/den;
% Resonance running speed, Eq. (6) [1]:
n_E1 = 3.0e4*sqrt(obj.c_gamma_alpha/m_red)/(pi*obj.z(1)); % [1/min]
% Resonance ratio, Eq. (9) [1]:
N = obj.n_output/n_E1;
val = obj.dynamic_factor_from_range(N, obj.C_a, ...
f_pbeff, f_falphaeff);
elseif(strcmp(obj.configuration, 'planetary'))
m_sun = rho(1)*(pi/8.0)*(obj.d_m(1)^4)/(obj.d_b(1)^2); % sun
m_pla = rho(2)*(pi/8.0)*(obj.d_m(2)^4)/(obj.d_b(2)^2); % planet
m_red1 = (m_pla*m_sun)/(m_sun + m_pla*obj.N_p);
m_red2 = m_pla;
% Resonance running speed:
n_E11 = 3.0e4*sqrt(obj.cprime/m_red1)*1.0/(pi*obj.z(1)); % [1/min]
n_E12 = 3.0e4*sqrt(obj.cprime/m_red2)*1.0/(pi*obj.z(2)); % [1/min]
% Resonance ratio:
N_1 = obj.n_output/n_E11;
N_2 = (obj.n_output/obj.u)/n_E12;
K_v1 = obj.dynamic_factor_from_range(N_1, obj.C_a, ...
f_pbeff, f_falphaeff);
K_v2 = obj.dynamic_factor_from_range(N_2, obj.C_a, ...
f_pbeff, f_falphaeff);
val = max(K_v1, K_v2);
end
end
function K_v = dynamic_factor_from_range(obj, N, C_a, f_pbeff, f_falphaeff)
% Table 8, [1]:
C_v1 = 0.32;
C_v5 = 0.47;
% default values:
C_v2 = -1.0; C_v3 = -1.0;
C_v4 = -1.0; C_v6 = -1.0;
C_v7 = -1.0;
eps_g = obj.eps_gamma;
if((1.0 < eps_g) && (eps_g <= 2.0))
C_v2 = 0.34;
C_v3 = 0.23;
C_v4 = 0.90;
C_v6 = 0.47;
elseif(eps_g > 2.0)
C_v2 = 0.57 /(eps_g - 0.3);
C_v3 = 0.096/(eps_g - 1.56);
C_v4 = (0.57 - 0.05*eps_g)/(eps_g - 1.44);
C_v6 = 0.12/(eps_g - 1.74);
end
if((1.0 < eps_g) && (eps_g <= 1.5))
C_v7 = 0.75;
elseif((1.5 < eps_g) && (eps_g <= 2.5))
C_v7 = 0.125*sin(pi*(eps_g - 2.0)) + 0.875;
elseif(eps_g > 2.5)
C_v7 = 1.0;
end
cp = obj.cprime;
B_p = cp*f_pbeff/obj.line_load; % Eq. (15)
B_f = cp*f_falphaeff/obj.line_load; % Eq. (16)
B_k = abs(1.0 - cp*C_a/obj.line_load); % Eq. (17)
% Dynamic factor:
if(obj.line_load < 100) % [N/mm]
N_S = 0.5 + 0.35*sqrt(obj.line_load/100.0); % Eq. (11), [1]
else
N_S = 0.85; % Eq. (12) [1]
end
if(N <= N_S)
% Section 6.5.4, Eq. (13), [1]:
K = C_v1*B_p + C_v2*B_f + C_v3*B_k;
K_v = N*K + 1.0; % Eq. (14)
elseif((N_S < N) && (N <= 1.15))
% Section 6.5.5, Eq. (20), [1]:
K_v = C_v1*B_p + C_v2*B_f + C_v4*B_k + 1.0;
elseif((1.15 < N) && (N < 1.5))
K_vN115 = C_v1*B_p + C_v2*B_f + C_v4*B_k + 1.0;
K_vN15 = C_v5*B_p + C_v6*B_f + C_v7;
% Section 6.5.7, Eq. (22), [1]:
K_v = K_vN15 + (K_vN115 - K_vN15)*(1.5 - N)/0.35;
elseif(N >= 1.5)
% Section 6.5.6, Eq. (21), [1]:
K_v = C_v5*B_p + C_v6*B_f + C_v7;
end
end
end
%% Set methods:
methods
end
%% Get methods:
methods
function val = get.S_H(obj)
val = obj.S_Hmin.*obj.sigma_HP./obj.sigma_H;
if(all(isnan(val)))
val = -10.0*ones(size(val));
elseif(any(isnan(val)))
val(isnan(val)) = -10.0;
end
end
function val = get.S_F(obj)
val = nan(size(obj.S_H));
end
function val = get.sigma_H0(obj)
% Nominal contact stress at pitch point:
num = obj.F_t*(obj.u + 1.0);
den = obj.d(1)*obj.b*obj.u;
val = obj.Z_H * ...
obj.Z_E * ...
obj.Z_eps* ...
obj.Z_beta*sqrt(num/den);
end
function val = get.sigma_H(obj)
% Contact stress:
val = obj.sigma_H0*obj.Z_BD*sqrt(obj.K_gamma* ...
obj.K_A * ...
obj.K_v * ...
obj.K_Hbeta* ...
obj.K_Halpha); % pinion/wheel
end
function val = get.sigma_HP(obj)
% Permissible contact stress:
val = obj.sigma_Hlim.*obj.Z_NT* ...
obj.Z_L * ...
obj.Z_v * ...
obj.Z_R * ...
obj.Z_W * ...
obj.Z_X./obj.S_Hmin;
end
function val = get.sigma_Hlim(obj)
val = [obj.material(1:2).sigma_Hlim];
end
function val = get.F_t(obj)
% [N], Nominal tangential load:
val = 2.0e3*(obj.T_nominal(1)/obj.d(1))/obj.N_p;
val = abs(val);
end
function val = get.Z_NT(obj)
val = zeros(1, 2);
% assuming optimum lubrification, material, manufacturing and experience
% y_lim = 1.0;
y_lim = 0.85;
for idx = 1:2
line = obj.material(idx).row;
switch line
case 1
% St, V, GGG (perl. bai.), GTS (perl.), Eh, IF (when limited pitting is permitted)
x = [6.0e5 1.0e7 1.0e9 1.0e10];
y = [1.6 1.3 1.0 y_lim];
case 2
% St, V, GGG (perl. bai.), GTS (perl.), Eh, IF
x = [1.0e5 5.0e7 1.0e10];
y = [1.6 1.0 y_lim];
case 3
% GG, GGG (ferr.), NT (nitr.), NV (nitr.)
x = [1.0e5 2.0e6 1.0e10];
y = [1.3 1.0 y_lim];
case 4
% NV (nitrocar.)
x = [1.0e5 2.0e6 1.0e10];
y = [1.1 1.0 y_lim];
otherwise
error("MATISO_6336:ZNT", "Invalid input [%d].\nValid options are 1 to 4.\n", line);
end
jdx = find(y == 1, 1, 'first');
N_Lref = x(jdx);
N = obj.N_L(idx);
if(N <= x(1))
val(idx) = y(1);
elseif(N > x(end))
val(idx) = y(end);
else
if(N > N_Lref)
x = x([jdx end]);
y = y([jdx end]);
end
val(idx) = exp(interp1(log(x), log(y), log(N)));
end
end
end
function val = get.N_L(obj)
% Number of load cycles:
if(strcmp(obj.configuration, 'parallel'))
N_L1 = obj.n_input*60.0*obj.L_h; % pinion
val = N_L1*[1.0 1.0/obj.u];
elseif(strcmp(obj.configuration, 'planetary'))
n_rel = obj.n_nominal(1) - obj.n_nominal(4);
val = [obj.N_p obj.z(1)/obj.z(2)]*60.0*obj.L_h*n_rel;
end
end
function val = get.K_v(obj)
val = obj.K_v_val;
end
function val = get.line_load(obj)
val = obj.F_t*obj.K_A*obj.K_gamma/mean(obj.b);
end
function val = get.v_pitch_line(obj)
val = nan;
if(strcmp(obj.configuration, 'parallel'))
val = (pi*obj.n_input/60.0e3)*obj.d(1);
elseif(strcmp(obj.configuration, 'planetary'))
val = (pi*obj.n_output/60.0e3)*(obj.d(1) - obj.a_w/obj.u);
end
end
function val = get.K_Halpha(obj)
val = obj.K_Falpha;
% Section 8.3.4 of [1]:
% Transverse load factor (contact stress), Eq. (75):
K_Halpha_lim = obj.eps_gamma/(obj.eps_alpha*obj.Z_eps.^2);
if(val > K_Halpha_lim)
val = K_Halpha_lim;
elseif(val < 1.0)
val = 1.0;
end
end
function val = get.K_Falpha(obj)
term = obj.c_gamma_alpha*(obj.f_pb - obj.y_alpha)/(obj.F_tH/obj.b);
% Section 8.3.2 of [1]:
if(obj.eps_gamma <= 2.0) % Eq. (73)
val = (0.9 + 0.4*term)*(obj.eps_gamma/2.0);
else % Eq. (74)
val = 0.9 + 0.4*sqrt(2.0*(obj.eps_gamma - 1.0)/obj.eps_gamma)*term;
end
% Section 8.3.5 of [1]:
% Transverse load factor (root stress), Eq. (76):
K_Falpha_lim = obj.eps_gamma/(0.25*obj.eps_alpha + 0.75);
if(val > K_Falpha_lim)
val = K_Falpha_lim;
elseif(val < 1.0)
val = 1.0;
end
end
function val = get.K_Hbeta(obj)
% Alternative: according to [5], Eq.(17.14):
% val = 1.0 + 0.4*(obj.b/obj.d(1))^2;
% Mean transverse tangential load at the reference circle:
F_m = obj.F_t*obj.K_A*obj.K_gamma*obj.K_v;
k_unit = 0.023; % [mm-um/N]
B_star = 1.0 + 2.0*(obj.N_p - 1.0);
% Component of equivalent misalignment due to deformations of
% pinion and wheel shafts.
% Assumption made: Pinion offset is null, s = 0.
f_sh = (F_m/mean(obj.b))*k_unit*(abs(B_star - 0.3) + 0.3)*(mean(obj.b)/obj.d(1))^2;
% mesh misalignment due to manufacturing deviations:
f_ma = norm(obj.f_Hbeta);
% Initial equivalent misalignment (before running-in), assuming
% that no helix modification was applied:
F_betax = 1.33*f_sh + f_ma;
% Running-in allowance:
y_beta = 0.15*F_betax;
F_betay = F_betax - y_beta;
cond = (F_betay*obj.c_gamma_beta)/(2.0*F_m/mean(obj.b));
if(cond >= 1.0)
val = 2.0*sqrt(cond);
else
val = 1.0 + cond;
end
end
function val = get.K_Fbeta(obj)
% Method B, Sec. 7.6:
% h_1 = h_aP + h_fP + k_1*m_n;
h_1 = abs(obj.d_a(1) - obj.d_f(1))/2.0;
bh1 = obj.b/h_1;
h_2 = abs(obj.d_a(2) - obj.d_f(2))/2.0;
bh2 = obj.b/h_2;
bh = min(bh1, bh2);
if(bh < 3.0)
bh = 3.0;
end
N_F = (bh.^2)/(1.0 + bh + bh.^2);
val = power(obj.K_Hbeta, N_F);
end
function val = get.sigma_F(obj)
val = nan(size(obj.z));
end
function val = get.sigma_F0(obj)
val = nan(size(obj.z));
end
function val = get.sigma_FP(obj)
val = nan(size(obj.z));
end
function val = get.sigma_Flim(obj)
val = nan(size(obj.z));
end
function val = get.Y_B(obj)
val = nan(size(obj.z));
end
function val = get.Y_DT(obj)
val = nan(size(obj.z));
end
function val = get.Y_F(obj)
val = nan(size(obj.z));
end
function val = get.Y_NT(obj)
val = nan(size(obj.z));
end
function val = get.Y_RrelT(obj)
val = nan(size(obj.z));
end
function val = get.Y_S(obj)
val = nan(size(obj.z));
end
function val = get.Y_ST(~)
val = nan;
end
function val = get.Y_X(obj)
val = nan(size(obj.z));
end
function val = get.Y_beta(obj)
val = nan(size(obj.z));
end
function val = get.Z_E(obj)
% [N/mm^2], Young's modulus:
E = [obj.material.E];
% [-], Poisson's ratio:
nu = [obj.material.nu];
vec = (1.0 - nu.^2)./E;
val = sqrt(1.0/(pi*sum(vec(1:2))));
end
function val = get.Z_H(obj)
num = 2.0*cosd(obj.beta_b)*cosd(obj.alpha_wt);
den = sind(obj.alpha_wt)*cosd(obj.alpha_t).^2;
val = sqrt(num/den);
end
function val = get.Z_eps(obj)
eps_a = obj.eps_alpha;
eps_b = obj.eps_beta;
if(obj.beta == 0.0)
val = sqrt((4.0 - eps_a)/3.0);
else
if(eps_b < 1.0)
val = sqrt((1.0 - eps_b)*(4.0 - eps_a)/3.0 + eps_b/eps_a);
else
val = sqrt(1.0/eps_a);
end
end
end
function val = get.Z_beta(obj)
% Helix angle factor: (sec. 9)
val = 1.0/sqrt(cosd(obj.beta));
end
function val = get.Z_BD(obj)
M_1 = tand(obj.alpha_wt)/sqrt((sqrt((obj.d_a(1)/obj.d_b(1))^2 - 1.0) - ...
2.0*pi/obj.z(1))*(sqrt((obj.d_a(2)/obj.d_b(2))^2 - 1.0) - ...
(obj.eps_alpha - 1.0)*2.0*pi/obj.z(2)));
M_2 = tand(obj.alpha_wt)/sqrt((sqrt((obj.d_a(2)/obj.d_b(2))^2 - 1.0) - ...
2.0*pi/obj.z(2))*(sqrt((obj.d_a(1)/obj.d_b(1))^2 - 1.0) - ...
(obj.eps_alpha - 1.0)*2.0*pi/obj.z(1)));
M = [M_1 M_2];
val = nan(1, 2);
if((obj.eps_beta == 0.0) && (obj.eps_alpha > 1.0))
for idx = 1:2
if(M(idx) > 1.0)
val(idx) = M(idx);
else
val(idx) = 1.0;
end
end
elseif((obj.eps_alpha > 1.0) && (obj.eps_beta >= 1.0))
val = ones(1, 2);
elseif((obj.eps_alpha > 1.0) && (obj.eps_beta < 1.0))
for idx = 1:2
if(M(idx) > 1.0)
val(idx) = M(idx) + obj.eps_beta*(1.0 - M(idx));
else
val(idx) = 1.0;
end
end
end
end
function val = get.Z_R(obj)
rho_1 = 0.5*obj.d_b(1)*tand(obj.alpha_wt);
rho_2 = 0.5*obj.d_b(2)*tand(obj.alpha_wt);
rho_red = (rho_1*rho_2)/(rho_1 + rho_2);
R_z10 = obj.R_z*power(10.0/rho_red, 1.0/3.0);
sig_Hlim = min(obj.sigma_Hlim);