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Contact stress problem

  1. Apr 8, 2016 #1
    Hi All

    I am trying to validate a nylon (PA6 Guss) clamp which has a load of 166kN on a steel tube. I am only interested in validating the clamp.
    My analytical (MatLab-Octave) calculations give me a peak Von Misses stress of about 145MPa
    contact stress.png
    When comparing to FEM in ANSYS I only get about 30MPa
    Can someone shed light on why there is such a big difference?
    contact stress_b.png

    -Jesper Hemmlann
    M.Sc. Applied Mechanics
     
  2. jcsd
  3. Apr 8, 2016 #2

    billy_joule

    User Avatar
    Science Advisor

    Who knows? Show your code and we might able to comment.
     
  4. Apr 11, 2016 #3
    %%%Contact stress
    clear all
    clc
    close all
    graphics_toolkit('gnuplot')

    %%%Material parameters
    %Youngs Modulus
    E_1=2.62*10^9
    E_2=213*10^9
    %Poisson ratio
    nu_1=0.34
    nu_2=0.3


    %Cylinder radius
    %OBS (R_2= infity for a flat plate)
    %OBS (a cylindrical groove is a cylinder with a negative radius)
    R_1=0.055275
    R_2=0.055775
    L=0.2

    %Force
    F=166000


    %Contact area
    b=sqrt(4*F*((1-nu_1^2)/E_1+(1-nu_2^2)/E_2)/(pi*L*(1/R_1+1/R_2)))

    %maximum pressure
    P_max=2*F/(pi*b*L)


    %stresses
    i=50
    z=0.000000001:(b*3)/i:(b*3);

    for n=1:i
    sigma_1(n)=-2*nu_1*P_max*(sqrt(z(n)^2/b^2+1)-abs(z(n)/b));
    sigma_2(n)=-P_max*((2-(z(n)^2/b^2+1)^-1)*sqrt(z(n)^2/b^2+1)-2*abs(z(n)/b));
    sigma_3(n)=-P_max*(sqrt((z(n)^2/b^2)+1)^(-1));

    tau_1(n)=abs((sigma_2(n)-sigma_3(n))/2);
    tau_2(n)=abs((sigma_1(n)-sigma_3(n))/2);
    tau_3(n)=abs((sigma_1(n)-sigma_2(n))/2);
    sigma_vM(n)=sqrt(sigma_1(n)^2+sigma_2(n)^2+sigma_3(n)^2-sigma_1(n)*sigma_2(n)-sigma_2(n)*sigma_3(n)-sigma_3(n)*sigma_1(n)+3*(tau_1(n)^2+tau_2(n)^2+tau_3(n)^2));
    end

    figure
    hold on

    MPa=1/10^6;
    plot(z,abs(sigma_1)*MPa,'-ko', "markersize", 3)
    plot(z,abs(sigma_2)*MPa,'-m^', "markersize", 3)
    plot(z,abs(sigma_3)*MPa,'-.r*', "markersize", 3)
    plot(z,(tau_1)*MPa,'--yv', "markersize", 3)
    plot(z,(tau_2)*MPa,':bs', "markersize", 3)
    plot(z,(tau_3)*MPa,'-.go', "markersize", 3)
    plot(z,sigma_vM*MPa,'-bv',"markersize", 3)



    legend('\sigma_x', '\sigma_y', '\sigma_z', '\tau_1','\tau_2','\tau_3','\sigma_{vM}', "location",
    "northeast");
    xlabel('depth of surface [m]')
    ylabel('Stress [MPa]')
    title('Cylinder contact stress on clamp')
    grid on

    %Displacement in the center of the 2 cylinders
    delta_c=2*F*(1-nu_1^2)/(pi*L*E_1)*(2/3+log(4*R_1/b)+log(4*R_2/b))*(1000)
     
  5. Apr 13, 2016 #4
    I don't know ansys and have never actually done an fea but I know you can set one up in matlab so maybe try to do a simplified fea in matlab to see if your answers get closer? That would only confirm your ansys isnt setup right, though, if you know 30 isn't right
     
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