How to solve for the torsional degrees of freedom
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I am trying to model the torsional degrees of freedom for a single stage helical gear system. My orignal code is here: https://uk.mathworks.com/matlabcentral/answers/1916150-keep-getting-a-blank-graph?s_tid=es_ans_avr_que_view
Please do not flag this question, I am trying to ask something different
For example- ![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1307315/image.jpeg)
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I_a = moment of inertia of smaller driver gear
I_p = moment of inertia of bigger driven gear
R_a = radius of smaller driver gear
Cs = meshing damping
theta_a = torsional angle of smaller driver gear
K_s = meshing stiffness
R_p = radius of bigger driven gear
theta_a = torsional angle of bigger driven gear
F_y = meshing excitation force
How can I solve for theta_a and theta_p using ode45 in a similar way as we solve for x in a simple mass spring damper system
function Ydot = num_for(t, Y)
Ydot = zeros(2,1);
m = 100;
k = 1000;
c = 160;
w = 5;
f = 160;
F = [0; (f/m)*cos(w*t)]; % input force vector
A = [0 1; -k/m -c/m]; % state matrix
Ydot = A*Y + F; % state-space model
end
function call-
Tspan = [0 10];
y0 = [0.01; 0.1];
[t, y] = ode45(@num_for, Tspan, y0);
figure
plot(t, y(:,1), 'linewidth', 1.5)
grid on
xlabel('Time, t [sec]')
ylabel({'displacement'})
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回答(1 个)
Sam Chak
2023-2-26
You can try modifying the following code to fit your application.
tspan = [0 0.1];
y0 = [0.1 0.2 0 0];
[t, y] = ode45(@heligear, tspan, y0);
for j = 1:4
figure(j)
plot(t, y(:,j), 'linewidth', 1.5), grid on
xlabel('Time, t [sec]'),
ystate = sprintf('y_{%d}', j);
ylabel(ystate)
end
function ydot = heligear(t, y)
ydot = zeros(4, 1);
% parameters
m_a = 0.5;
m_p = 0.5;
R_a = 51.19e-3;
R_p = 139.763e-3;
I_a = 0.5*m_a*(R_a^2);
I_p = 0.5*m_p*(R_p^2);
Freq = 1000*20/60;
Cs = 0.1 + 0.01*sin(2*pi*Freq*t);
Ks = 0.9e3 + 20*sin(2*pi*Freq*t);
% ODEs
% y1 is theta_a, y2 is theta_p
% y3 is thetaDot_a, y4 is thetaDot_p
ydot(1) = y(3);
ydot(2) = y(4);
ydot(3) = (- R_a*(Cs*(R_a*y(3) - R_p*y(4)) + Ks*(R_a*y(1) - R_p*y(2))))/I_a;
ydot(4) = ( R_p*(Cs*(R_a*y(3) - R_p*y(4)) + Ks*(R_a*y(1) - R_p*y(2))))/I_p;
end
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