To develop this problem it is necessary to calculate the concepts related to the Torque given in a Journal bearing. A journal bearing is a hollow cylindrical enclosing a solid shaft that rotates about its axis at radial speed. The gap between bearing and shaft is filled by viscous oil. The Formula to find the torque is given by,
[tex]T= \mu \frac{4\pi^2R^3nL}{l}[/tex]
Where,
[tex]\mu =[/tex]viscosity of the oil
R = Radius of the shaft
n = Velocity of the shaft
l = gap between the shaft and the bearing
In the other hand our values are:
[tex]\mu = 0.1kg/ms[/tex]
[tex]R= 0.04m\\n=25rps\\L=0.55m\\l=0.0008m[/tex]
Replacing we have:
[tex]T_i = 0.1 * \frac{(4*\pi^2)(0.04^3)(25)(0.55)}{0.0008}[/tex]
[tex]T_i= 54.3426Nm \rightarrow[/tex] that is the torque required initially
We can now calculate the required torque during the steady operation:
[tex]T= \mu \frac{4\pi^2R^3nL}{l}[/tex]
But here our values are
[tex]\mu = 0.008kg/ms[/tex]
[tex]R= 0.04m[/tex]
[tex]n=25rps[/tex]
[tex]L=0.55m[/tex]
[tex]l=0.0008m[/tex]
[tex]T_f = 0.008* \frac{(4*\pi^2)(0.04^3)(25)(0.55)}{0.0008}[/tex]
[tex]T_f = 0.3474Nm \rightarrow[/tex] That is te torque requiered during the steady operation
