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# Torque in journal bearing with large gap?

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## 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.
Replies continue below

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

For laminar flow, Petroff's equation gives torque for bearing running at 0% eccentricity.  The following equation comes from "Design of Machine Elements, 4th Ed., V. M. Faires.  The equation is:

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?

(OP)
Thanks, but that is the equation for thin gaps.  It does not hold when the gap is large compared to the radius as you will get quite different answers depending on what "nominal" radius you use.

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

According to my reference, the r in Petroff's equation is the journal radius, not the mean or outer radius.

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?

matlas,

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.

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