How to solve for the torsional degrees of freedom

Question

Siddharth Jain 2023-2-26

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1919040-how-to-solve-for-the-torsional-degrees-of-freedom

回答： Sam Chak 2023-2-26

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-

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'}) 