## Torque in journal bearing with large gap?

## Torque in journal bearing with large gap?

(OP)

I know how to calculate torque in a journal bearing filled with viscous fluid where the gap is small compared to the radial dimensions but need to do so where the gap is larger (say about 0.001" gap with inner radius of 0.0025"). The shaft is constrained to rotate in the center of the journal, so this is more of a rotary fluid damper than a bearing. Speed is slow enough to be laminar, and I'm not worried about local flows for now.

Is there a standard equation for this?

Thanks.

Is there a standard equation for this?

Thanks.

## RE: Torque in journal bearing with large gap?

Tau = 4*mu*pi^2*r^3*L*n_s / c_r

Where

Tau = torque, inch*lbf

mu = viscosity in reyns

pi = 3.14159

r = journal radius, inches

L = journal length, inches

n_s = rotational speed, revolutions/second

c_r = radial clearance, inches

## RE: Torque in journal bearing with large gap?

## RE: Torque in journal bearing with large gap?

However, the Petroff's equation assumes a constant velocity gradient in the radial direction. This gives a linear velocity profile. For larger gaps, the velocity gradient will not be constant. It will likely vary with radius, giving something like a parabolic velocity profile.

Surely there is a derivation in existence for an "infinite gap" solution, although I don't know what it is. Your correct answer may lie somewhere between Petroff's and infinite gap. As an approximation, I would use a parabolic velocity profile and derive the torque acting upon the journal. However, I don't have a design reference that goes through this or backs up my idea. I hope I've been helpful, and I'd like to hear from other what their thoughts are.

## RE: Torque in journal bearing with large gap?

Check out the following link:

http://scienceworld.wolfram.com/physics/CouetteFlow.html. It goes through the derivation of Taylor-Couette flow, which is essentially what you have. It is a little on the complex side of things.