Footstep Bearing – Power Absorbed by Viscous Resistance For a flat circular footstep bearing of radius R rotating at angular speed omega with oil film thickness h and viscosity mu, the power absorbed in viscous shear can be computed from the viscous torque acting on the plate.

Introduction:
Footstep bearings support axial loads using a thin lubricant film between a stationary base and a rotating circular face. Estimating viscous power loss is essential for heat generation calculations and lubricant selection in machine design.

Given Data / Assumptions:

• Flat circular disk of radius R rotates at angular speed omega over a stationary surface.
• Uniform lubricant film thickness h and Newtonian lubricant with viscosity mu.
• No slip at boundaries; velocity varies linearly across the film.

Concept / Approach:

At radius r, the circumferential velocity is v = omega * r. The shear rate across the film is dv/dy = v / h = (omega * r) / h, giving local shear stress tau = mu * (omega * r) / h. The viscous shear produces a torque dT on ring area at radius r which integrates over the disk.

Step-by-Step Solution:

Verification / Alternative check:

Dimensional check: mu has Ns/m^2, multiply by omega^2 (1/s^2) and R^4/h (m^4/m = m^3) to get Nm/s = W, confirming a power expression.

Why Other Options Are Wrong:

Option B: Missing one omega factor and wrong power dependence. Option C: Excess power of omega and radius. Option D: Missing geometric constants and radius dependence incorrect. Option E: Omits omega entirely, cannot be power loss for rotating shear.

Common Pitfalls:

Using mean radius incorrectly; forgetting the linear velocity distribution with r; mixing collar bearing friction models with dry friction instead of viscous shear.

Final Answer:

P = (pi * mu * omega^2 * R^4) / (2 * h)