Shell four-ball tester — contact temperature from friction
Bulk and flash contact temperature rise in a Shell four-ball lubricant/EP-additive tester, from load, speed, ball size, friction coefficient and material properties.
Contact load per ball, F204.12414523193152 N
Sliding speed, v0.45344984105855446 m/s
Nominal contact radius, r₀0.15 mm
Real/nominal area ratio, Aᵣ/Aₙ0.4701729536403116
Real (junction) contact radius, r_j15.384615384615383 ×10⁻⁶ m
Bulk temperature rise, ΔT_bulk149.60359470226948 °C
Flash temperature rise, ΔT_flash44.6510509431516 °C
Total contact temperature rise, ΔT173.26092914033546 °C
Legacy reuses the variable name ArAn for two different area ratios (contact-radius sizing, then Hertzian-pressure-based); only the second feeds the reported output, per the original. Also reproduces the legacy fallback that zeroes ArAn/rj/dTbulk/dTflits/dT when the pressure-based ArAn exceeds 1 (invalid contact).
Method & references
- Ashby, M.F., Abulawi, J., Kong, H.S., 1991, "Temperature maps for Frictional Heating in Dry sliding", Tribology Transactions, Vol.34, Number 4, October 1991, pp577-587.
The computation is a literal port of the original client-side JavaScript from /calculators/e3_3.htm. Results are verified equal to the original by an automated golden-master test. No formula has been re-derived or “improved”.