This is a fatigue failure analysis of a shaft with an unknown diameter.
The issue being we have a lack of information.
So, we assume a diameter and perform multiple iterations to find the correct factor of safety. The factor of safety is given.
u = symunit; %Given information at the beginning of problem
Sy = 420e6*u.Pa; %Yield strength
Sut = 560e6*u.Pa; %Ultimate strength
TA = 340*u.N*u.m; %Given applied torque
d = .15*u.m ;theta = 20;BC = .25*u.m; CD = .1*u.m; n = 2.5;F = vpa(TA/(cosd(theta)*d/2),5); %Acting force.
%Sum of forces and Sum of moments to find the critical point of interest and the max bending moment.
C_z = vpa(F*sind(theta)*(BC+CD)/BC,4);B_z = vpa(F*sind(theta)-C_z ,4);M_z = abs(B_z*BC );C_y = vpa(F*cosd(theta)*(BC+CD)/BC,4);B_y = vpa(F*cosd(theta)-C_y ,4);M_y = abs(B_y*BC);M_max = vpa(sqrt(M_y^2 + M_z^2),4)%Torque on the whole system.
T = F*cosd(theta)*d/2 + TA;Se_p = .5*Sut;a = 3.04; b = -0.217; %kb, ka, kc constants help determine endurance strength
ka = a*separateUnits(Sut)^(b);Instead of doing multiplie iterations I just created a range of diameter values where it satisfied a factor of safety.
d = linspace(.04,.15)*u.m; %Here's my range of diametric values.
kb = 1.24.*separateUnits(d).^(-.107); kc = 1; Se = Se_p.*ka.*kb.*kc;% sharp fillet concentration factors
kt = 2.7; kts = 2.2;%inertia and polar moment of inertia.
I = pi.*d.^4./64;J = pi.*d.^4./32;%Alternating bending stress
sigma_alt = kt.*M_max.*32./(pi.*d.^3);%Mean bending stress
sigma_m = 0; % Alternating torsion stress
tao_alt = 0; %mean torsion stress
tao_m = kts.*16.*T./(pi.*d.^3);%Von mises alternating stress
sigma_altp = (sigma_alt.^2 + 3*tao_alt.^2).^(1/2);%Von mises mean stress
sigma_mp = (sigma_m^2 + 3.*tao_m.^2).^(1/2);A = sqrt(4*(kt*M_max)^2+3*(kts*0).^2); B = sqrt(4*(kt*0)^2+3*(kts*T).^2);%Goodman criteria for solving factor of safety
n = simplify(pi.*d.^3./16.*(A./Se + B./Sut).^(-1))Now that I have a range of values for the factor of safety, I can use polyfit function to find the coefficients to solve for an exact diameter.
When I apply the polyfit function it gives me coefficients.
x1 = polyfit(separateUnits(d),n,2)When I apply the polyval so that I can get the precise diameter value, it gives me an error.
polyval(x1,2.5)Specifically:
Error using filter
Invalid data type. Input
arrays must be numeric
or logical.
Error in polyval (line
56)
y = filter(1,[1
-x],p);
Error in Untitled (line
83)
polyval(x1,2.5)
Why doesn't this work? Thank you.
Best Answer