Plain bearing operating clearance
Calculates diametral, radial and relative clearance of a plain bearing -- directly from two diameters or, optionally, with a thermal correction from a cold assembly clearance to an operating temperature.
Formula
s = dL - dW, psi = s / dL
Diametral clearance s is the difference between bush bore dL and journal diameter dW. Radial clearance s/2 is the one-sided gap between journal and bush. Relative (dimensionless) clearance psi = s/dL makes bearings of different sizes comparable and enters directly into the Sommerfeld number and film thickness. In thermal mode, the clearance change from differential thermal expansion of housing/bush versus shaft is computed as delta_s = d*(alphaL-alphaW)*(T-20 C).
What this model does not show
Historical guideline ranges for psi from experience tables are deliberately not automatically converted into a pass/fail verdict here -- they are a starting point for a full design per ISO 7902, not an approval criterion. The thermal model also assumes one common operating temperature for shaft and housing; with strongly different component temperatures a finer analysis is needed.
Worked example
Direct mode: bush bore dL = 50.08 mm, journal diameter dW = 50.00 mm. Diametral clearance s = 50.08 - 50.00 = 0.08 mm. Radial clearance s/2 = 0.04 mm. Relative clearance psi = 0.08/50.08 ~ 0.0016 (1.6 permille). Thermal mode: steel shaft (alphaW = 11e-6/K) in an aluminium housing (alphaL = 23e-6/K), d = 50 mm, cold clearance sE = 0.05 mm, heating from 20 C to 80 C: delta_s = 50 mm x (23-11)e-6/K x 60 K = 0.036 mm; operating clearance s = 0.05 + 0.036 = 0.086 mm -- clearance increases because the housing expands more than the shaft.
Common mistakes
- Confusing diametral and radial clearance -- radial clearance is only half the diametral clearance.
- Treating a historical guideline table for psi as a strict pass/fail criterion instead of a starting point for a full design.
- Swapping alphaL and alphaW in thermal mode, which flips the sign of the computed clearance change.
Frequently asked questions
What's the difference between diametral, radial and relative clearance?
Diametral clearance s = dL - dW is the full clearance across the diameter. Radial clearance s/2 is the one-sided gap between journal and bush at one point on the circumference. Relative clearance psi = s/dL is dimensionless and makes bearings of different sizes comparable.
What's the difference between cold assembly clearance and operating clearance?
Cold assembly clearance is measured or specified at assembly or at a reference temperature (usually 20 C). Operating clearance results from that via the differential thermal expansion of shaft and housing at operating temperature -- it can be larger or smaller than the cold clearance.
When does operating clearance shrink instead of grow?
When the shaft expands more than the housing (alphaW > alphaL), clearance falls as temperature rises and can, in an extreme case, cause seizure. The calculator raises an error if the computed operating clearance would be zero or negative.
Why is there no pass/fail verdict for psi here?
Guideline ranges for psi from the literature are experience values for starting a design, not normative limits. A reliable assessment needs the full hydrodynamic design per ISO 7902 including Sommerfeld number, eccentricity and film thickness.
Does the thermal calculation also apply with different shaft and housing temperatures?
Not directly -- the simplified model used here assumes one common operating temperature for both components. With significantly different component temperatures (e.g. from unequal heat dissipation) a finer, component-specific calculation is needed.
What comes after calculating clearance?
Relative clearance psi is needed directly for the Sommerfeld number (calculator 58) and minimum film thickness (calculator 59).