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ME3227_finalproject/ME3227_FinalProject.asv
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% Given Parameters: | |
% Shaft Material - AISI 4130 Q&T CD | |
E = 29*10^6; %psi (Young's Modulus) | |
sut = 118*10^3; %psi (ultimate stress) | |
sy = 102*10^3; %psi (yield stress) | |
p = 0.3; %(poisson's ratio) | |
ga_w = 4; %lbf - make as input value | |
ga_t = 50; %teeth number - input | |
ga_a = 20; %deg - input | |
ga_d = 4; %diametric pitch - input | |
gc_w = 2; %lbf - make as input value | |
gc_t = 25; %teeth number - input | |
gc_a = 20; %deg - input | |
gc_d = 4; %diametric pitch - input | |
ss = 3000; %rpm (shaft speed) | |
T = 3500; %lbf-in (torque) | |
% Reliability for fatigue life = 0.99 | |
% nd, Safety factor for fatigue life = 2 | |
% nd, safety factor for all other criteria = 1 | |
% r/d = 0.02 - woodruff key | |
gear_def = 0.01; % deflection at gears - from table 7-2 | |
bearing_slope = 0.001; %rad | |
gear_slope = 0.005; %rad | |
d_a = ga_t/ga_d; % diameter of gear a | |
d_c = gc_t/gc_d; % diameter of gear c | |
Fct = T/(d_c/2); % tangential force on gear c | |
Fat = T/(d_a/2); % tangential force on gear a | |
Fcn = Fct * tand(gc_a); % Normal force on gear c | |
Fan = Fat * tand(ga_a); % Normal force on gear a | |
dtheta_dx = 0.00058; % rad/in | |
% Find Reaction Forces - XY plane | |
Rby = ((Fcn*3)+(Fan*9))/6; | |
Rdy = Fan + Fcn - Rby; | |
% Find Reaction Forces - XZ plane | |
Rbz = ((Fat*9)-(Fct*3))/6; | |
Rdz = Fat - Fct - Rbz; | |
% Calculate C1 and C2 - XY Plane | |
c1y = (117*Fan-36*Rby+4.5*Fcn)/6; | |
c2y = 4.5*Fan - 3*c1y; | |
% Calculate C1 and C2 - XZ Plane | |
c1z = (117*Fat-36*Rbz-4.5*Fct)/6; | |
c2z = 4.5*Fat - 3*c1z; | |
% Singularity Functions - x = 0 - 9 inches | |
x = linspace(0,9,10); | |
for i=0:9 | |
if i<(3) | |
M_xy(i+1) = 0; | |
EIdy_x(i+1) = -Fan/2*(i)^2+c1y; | |
EIy_x(i+1) = -Fan/6*(i)^3+c1y*i+c2y; | |
M_xz(i+1) = 0; | |
EIdz_x(i+1) = -Fat/2*(i)^2+c1z; | |
EIz_x(i+1) = -Fat/6*(i)^3+c1z*i+c2z; | |
elseif i>=3 && i<6 | |
M_xy(i+1) = -Fan*i + Rby*(i-3); | |
EIdy_x(i+1) = -Fan/2*(i)^2+Rby/2*(i-3)^2+c1y; | |
EIy_x(i+1) = -Fan/6*(i)^3+Rby/6*(i-3)^3+c1y*i+c2y; | |
M_xz(i+1) = -Fat*i + Rbz*(i-3); | |
EIdz_x(i+1) = -Fat/2*(i)^2+Rbz/2*(i-3)^2+c1z; | |
EIz_x(i+1) = -Fat/6*(i)^3+Rbz/6*(i-3)^3+c1z*i+c2z; | |
elseif i>=6 && i<9 | |
M_xy(i+1) = -Fan*i+Rby*(i-3)-Fcn*(i-6); | |
EIdy_x(i+1) = -Fan/2*(i)^2+Rby/2*(i-3)^2-Fcn/2*(i-6)^2+c1y; | |
EIy_x(i+1) = -Fan/6*(i)^3+Rby/6*(i-3)^3-Fcn/6*(i-6)^3+c1y*i+c2y; | |
M_xz(i+1) = -Fat*i+Rbz*(i-3)+Fct*(i-6); | |
EIdz_x(i+1) = -Fat/2*(i)^2+Rbz/2*(i-3)^2+Fct/2*(i-6)^2+c1z; | |
EIz_x(i+1) = -Fat/6*(i)^3+Rbz/6*(i-3)^3+Fct/6*(i-6)^3+c1z*i+c2z; | |
else | |
M_xy(i+1) = -Fan*i +Rby*(i-3)-Fcn*(i-6)+Rdy*(i-9); | |
EIdy_x(i+1) = -Fan/2*(i)^2+Rby/2*(i-3)^2-Fcn/2*(i-6)^2+Rdy/2*(i-9)^2+c1y; | |
EIy_x(i+1) = -Fan/6*(i)^3+Rby/6*(i-3)^3-Fcn/6*(i-6)^3+Rdy/2*(i-9)^3+c1y*i+c2y; | |
M_xz(i+1) = -Fat*i +Rbz*(i-3)+Fct*(i-6)+Rdz*(i-9); | |
EIdz_x(i+1) = -Fat/2*(i)^2+Rbz/2*(i-3)^2+Fct/2*(i-6)^2+Rdz/2*(i-9)^2+c1z; | |
EIz_x(i+1) = -Fat/6*(i)^3+Rbz/6*(i-3)^3+Fct/6*(i-6)^3+Rdz/2*(i-9)^3+c1z*i+c2z; | |
end | |
i = i+1; | |
end | |
%Create plots | |
figure(1) %position vs. deflection in xy plane | |
plot(x,EIy_x) | |
xlabel('Axial Postion') | |
ylabel('EI times Deflection') | |
figure(2) %position vs. deflection in xz plane | |
plot(x,EIz_x) | |
xlabel('Axial Postion') | |
ylabel('EI times Deflection') | |
figure(3) %position vs. slope in xy plane | |
plot(x,EIdy_x) | |
xlabel('Axial Postion') | |
ylabel('EI times Slope') | |
figure(4) %position vs. slope in xz plane | |
plot(x,EIdz_x) | |
xlabel('Axial Postion') | |
ylabel('EI times Slope') | |
% Find total slope and deflection | |
delta_prime = sqrt((EIdy_x).^2+(EIdz_x).^2); | |
delta = sqrt((EIz_x).^2+(EIy_x).^2); | |
% plot vs. axial position | |
figure(5) | |
plot(x,delta_prime) | |
xlabel('Axial Postion') | |
ylabel('EI times Slope') | |
figure(6) | |
plot(x,delta) | |
xlabel('Axial Postion') | |
ylabel('EI times Deflection') | |
% Calculate Resultant Slopes and Deflections | |
delta_a = delta(1); | |
delta_c = delta(7); | |
theta_a = delta_prime(1); | |
theta_b = delta_prime(4); | |
theta_c = delta_prime(7); | |
theta_d = delta_prime(10); | |
% Diameter of the shaft due to slope at the bearings - Points B/D | |
D_b = ((theta_b*64)/(E*pi*bearing_slope))^(1/4); | |
D_d = ((theta_d*64)/(E*pi*bearing_slope))^(1/4); | |
D_shaft_1 = max(D_b,D_d); | |
% Diameter of the shaft due to slope at the gears - Points A/C | |
D_a = ((theta_a*64)/(E*pi*gear_slope))^(1/4); | |
D_c = ((theta_c*64)/(E*pi*gear_slope))^(1/4); | |
D_shaft_2 = max(D_a,D_c); | |
% Diameter of the shaft due to deflection at the gears - Points A/C | |
D_a1 = ((delta_a*64)/(E*pi*gear_def))^(1/4); | |
D_c1 = ((delta_c*64)/(E*pi*gear_def))^(1/4); | |
D_shaft_3 = max(D_a1,D_c1); | |
%Diameter of the shaft due to torsional wind-up | |
G = E/(2*(1+p)); | |
D_shaft_4 = ((T*32)/(G*pi*dtheta_dx))^(1/4); | |
%Fatigue/Failure Criteria - Modified Goodman | |
% Modified Endurance Limit | |
ka = (2.7*10^3)*sut^-0.265; %Cold-Drawn | |
kb = 0.879^-0.107; %diameter guess of 1 in | |
kc = 1; %due to combined loading | |
kd = 1; %ambient temperature | |
ke = 0.814; % 99% reliability | |
kf = 1; %given | |
se_prime = 0.5*sut; | |
se=ka*kb*kc*kd*ke*kf*se_prime; | |
%Total Bending Moment | |
M_tot = sqrt((M_xy).^2+(M_xz).^2); | |
M_max = max(M_tot); %Occurs at Point C | |
% woodruff key: r/d = 0.02 | |
% diameter guess = 1 in., so r = 0.02 in | |
q = 0.7; %From chart 6-20 | |
qs = 0.77; % From chart 6-21 | |
kt = 2.14; %given | |
kts = 3.0; %given | |
kf = q*(kt-1)+1; | |
kfs =q*(kts-1)+1; | |
syms d | |
sig_a = (kf*M_max*32)/(pi*d^3); | |
sig_m = 0; | |
tau_a = 0; | |
tau_m = (16*kfs*T)/(pi*d^3); | |
sig_a_prime = sqrt((sig_a)^2+3*(tau_a)^2); | |
sig_m_prime = sqrt((sig_m)^2+3*(tau_m)^2); | |
n = 2; % design factor | |
%Modified Goodman | |
% (sig_a_prime/se)+(sig_m_prime/sut)=(1/n) | |
% ^ use this equation to derive diameter for d_shaft_5 | |
d_shaft_5 = ((n^2*(((kf^2*M_max^2*32^2)/(pi^2*se^2))+((3*16^2*kfs^2*T^2)/(pi^2*sut^2)))))^(1/9); | |
% Critical speed of shaft | |
% w_operating(shaft speed) *nd = w1; | |
g = 386.24; % in/sec^2 | |
nd = 1.5; | |
ss1 = ss*0.1047; | |
w1 = ss1 * nd; | |