diff --git a/ME3227_FinalProject.asv b/ME3227_FinalProject.asv deleted file mode 100644 index 691715f..0000000 --- a/ME3227_FinalProject.asv +++ /dev/null @@ -1,185 +0,0 @@ -% 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; - diff --git a/ME3227_FinalProject.m b/ME3227_FinalProject.m index 92ac1ba..a8945be 100644 --- a/ME3227_FinalProject.m +++ b/ME3227_FinalProject.m @@ -1,8 +1,14 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% ME 3227 Final Project +% This code allows the user to automatically calculate and visualize the +% required diameters if the design requirements change. The requirements that can be changed are the gear weight, the number of teeth, the pressure angle, and the diametric pitch. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + % 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) +sut = 118*10^3; %psi (ultimate strength) +sy = 102*10^3; %psi (yield strength) p = 0.3; %(poisson's ratio) ga_w = 4; %lbf - make as input value ga_t = 50; %teeth number - input @@ -49,6 +55,7 @@ c2z = 4.5*Fat - 3*c1z; x = linspace(0,9,10); for i=0:9 if i<(3) + q_xy(i+1) = 0; 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; @@ -56,6 +63,7 @@ for i=0:9 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 + q_xy(i+1) = -Fan*(i)^-1 + Rby*(i-3)^(-1); 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; @@ -63,6 +71,7 @@ for i=0:9 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 + q_xy(i+1) = -Fan*i^-1+Rby*(i-3)^-1-Fcn*(i-6)^-1; 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; @@ -70,6 +79,7 @@ for i=0:9 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 + q_xy(i+1) = -Fan*i^-1 +Rby*(i-3)^-1-Fcn*(i-6)^-1+Rdy*(i-9)^-1; 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; @@ -123,26 +133,26 @@ 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); +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); +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); +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); +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 +ka = (2.7)*(sut*10^-3)^-0.265; %Cold-Drawn +kb = 0.879*1^-0.107; %diameter guess of 1 in kc = 1; %due to combined loading kd = 1; %ambient temperature ke = 0.814; % 99% reliability @@ -159,7 +169,7 @@ 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; +kf_notch = q*(kt-1)+1; kfs =q*(kts-1)+1; syms d sig_a = (kf*M_max*32)/(pi*d^3); @@ -168,20 +178,24 @@ 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 +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); +d_shaft_5 = ((((32*M_max*kf_notch)/se)+(kfs*T*16*sqrt(3))/(sut))*(n/pi))^(1/3); % Critical speed of shaft % w_operating(shaft speed) *nd = w1; g = 386.24; % in/sec^2 nd = 1.5; -ss1 = ss*0.1047; +ss1 = ss*0.1047; % convert to rad/in w1 = ss1 * nd; y1 = -EIy_x(1); y2 = EIy_x(7); +d_shaft_6 = ((((w1)^2/g)*4096*(ga_w*y1^2+gc_w*y2^2))/((pi*E)*64*(ga_w*y1+gc_w*y2)))^(1/12); +% Determine required diameter for the shaft +d_shaft_total = [d_shaft_1,d_shaft_2,d_shaft_3,d_shaft_4,d_shaft_5,d_shaft_6]; +d_shaft_required = max(d_shaft_total); \ No newline at end of file diff --git a/parameters.m b/parameters.m deleted file mode 100644 index 4bf4136..0000000 --- a/parameters.m +++ /dev/null @@ -1,14 +0,0 @@ -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 -