Roelands Pressure-Viscosity Estimator vs Barus
For tribology researchers evaluating EHL film thickness at 1–2 GPa contact pressures, where the Barus exponential runs away and a Roelands estimate — with z derived from the measured α — is the defensible alternative to quote. This tool provides both calculations side-by-side. The Roelands pressure-viscosity equation is used for EHL pressures, with the Barus equation η = η₀ exp(αp) presented beside it, and the Roelands index `z` is estimated from `α` when that mode is selected.
Lubricant Viscosity at Pressure
Results are for preliminary estimation only, not a substitute for review by a qualified/licensed engineer.
How to Use This Estimator
- Enter the base viscosity η₀ in Pa·s at atmospheric pressure, as given on the lubricant data sheet.
- Enter the contact pressure p in Pa (divide a GPa figure by 1e-9, i.e. 1 GPa = 1e9 Pa).
- Choose "enter z directly" and type the Roelands index, or choose "estimate z from α" and type α in 1/Pa so the tool derives z.
- Read η_R and η_B in Pa·s together with their η/η₀ ratios, and check the warning line before trusting the Barus value at high pressure.
FAQ
What is the difference between the Roelands and Barus pressure-viscosity equations?
Barus is the simple exponential η = η₀·exp(αp); Roelands uses η₀·exp((ln η₀ + 9.67)·(−1 + (1 + p/p₀)^z)) with p₀ = 1.96e8 Pa, so the two agree near zero pressure and diverge as p rises — this estimator shows both values at once.
How is the Roelands index z estimated from alpha?
z = α·p₀ / (ln η₀ + 9.67), with p₀ = 1.96e8 Pa, α entered in 1/Pa and η₀ in Pa·s; in α mode the tool computes z first and then evaluates the Roelands equation with it.
Why does the Barus equation overestimate viscosity at high pressure?
Its exponential growth keeps steepening with p, whereas the Roelands form includes the (1 + p/p₀)^z term that tempers the rise; the estimator flags pressures of 1 GPa and above, where the Barus value pulls far ahead of Roelands.
What units must I use for the 9.67 constant to be valid?
η₀ in Pa·s and p in Pa — the 9.67 constant and p₀ = 1.96e8 Pa assume a viscosity in Pa·s and a pressure in Pa, and α is entered in 1/Pa; using mPa·s or MPa gives a wrong z and a wrong viscosity.