Load Calculation of Hydrodynamic Journal Bearing

I have the pressure field generated in circumferencial and axial direction. But can't crack the double integration part. Can anybody help me with a code for that? It would be big help.

[Dyuman Joshi]

Is theta_prime related to theta? If yes, then how?

Are p and R constants?

[Adwait Mahajan]

R is a constant. p is a function of theta_prime and z.

theta_prime = theta - alpha

where, alpha is the attitude angle of the bearing.

Answer 1

[Hassaan]

you could use integral2 or dblquad function:

% Define the pressure function, replace this with your actual function
pressure = @(theta_prime, z) cos(theta_prime); % Example function

% Integration bounds
theta_prime_min = 0;
theta_prime_max = 2 * pi;
z_min = 0;
z_max = 1; % Replace with the actual length L of the bearing

% Radius R is a constant, replace with the actual radius of the bearing
R = 1;

% Radial load Wr calculation using double integration
Wr = integral2(@(theta_prime, z) pressure(theta_prime, z) .* R .* cos(theta_prime), ...
               z_min, z_max, theta_prime_min, theta_prime_max);

% Tangential load Wt calculation using double integration
Wt = integral2(@(theta_prime, z) pressure(theta_prime, z) .* R .* sin(theta_prime), ...
               z_min, z_max, theta_prime_min, theta_prime_max);

disp(Wr);

    4.5699

disp(Wt);

    2.2245

Replace the pressure function and the bounds with your actual function and bearing dimensions.

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[Adwait Mahajan]

Thanks a lot. I was trying to implement Simpson's integral rule. But this makes my work way easier.