diff --git a/ME3227_FinalProject.asv b/ME3227_FinalProject.asv index 14b6148..691715f 100644 --- a/ME3227_FinalProject.asv +++ b/ME3227_FinalProject.asv @@ -1,8 +1,8 @@ % Given Parameters: % Shaft Material - AISI 4130 Q&T CD E = 29*10^6; %psi (Young's Modulus) -sut = 118*10^3; %psi (ultimate strength) -sy = 102*10^3; %psi (yield strength) +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 @@ -25,38 +25,161 @@ 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); -Fan = Fat * tand(ga_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 -c1 = (117*Fan-36*Rby+4.5*Fcn)/6; -c2 = 4.5*Fan - 3*c1; +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 -for i = 0:length(i) - if (0<=i) && (i<=3) - EIdy_x = -Fan/2*(i)^2+c1; - EIy_x = -Fan/6*(i)^3+c1*i+c2; - - elseif (3=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 - 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 -% Diameter of the shaft due to slope at the bearings - Points B,D +%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; diff --git a/ME3227_FinalProject.m b/ME3227_FinalProject.m index 8d93779..92ac1ba 100644 --- a/ME3227_FinalProject.m +++ b/ME3227_FinalProject.m @@ -25,37 +25,163 @@ 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); -Fan = Fat * tand(ga_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 -c1 = (117*Fan-36*Rby+4.5*Fcn)/6; -c2 = 4.5*Fan - 3*c1; +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 -for x = linspace(0,9,10) - if (0<=x) && (x<=3) - EIdy_x = -Fan/2*(x)^2+c1; - EIy_x = -Fan/6*(x)^3+c1*x+c2; - elseif (3=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 - 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 -% Diameter of the shaft due to slope at the bearings - Points B,D +%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; +y1 = -EIy_x(1); +y2 = EIy_x(7); diff --git a/parameters.m b/parameters.m new file mode 100644 index 0000000..4bf4136 --- /dev/null +++ b/parameters.m @@ -0,0 +1,14 @@ +function = parameters(ga_w,ga_t,ga_a,ga_d,gc_w,gc_t,gc_a,gc_d) +%UNTITLED3 Summary of this function goes here +% Detailed explanation goes here +%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 + +end +