Steam Engine Reviews/Piston Head Stress

The following review is provided by Bastelmike

Stress Calculations
OSE Steam engine
Piston bolt

calculation in metric for bending piston force: F = A * p
A = 3,75” * 3,75” * 0,785 = 11,04 sq.inch = 71,2 cm² = 7120 mm²
p = 250 psi = 250 lbs / (25,4 * 25,4) = 0,387 lbs / mm² = 1,76 N / mm²

--> F = 7120 mm² * 1,76 N/mm² = 12531 N

assumed loose fit of the bolt in both parts

Mmax = F * (l + 2 * s) / 8 = 12531 N * (0,3” + 2* 0,1”) / 8
= 12531 N * 12,7 mm / 8 = 19893 Nmm

σ = M / W = M / 0,1 / d³ = 19893 / 0,1 / 6,35³ = 777 N / mm²

for mild steel St 37-2 allowable σ : 330 N/mm² STATIC
for tempered high grade steel 30 CrNiMo 8 allowable σ: 1440 N / mm² STATIC
only very high grade steel tempered will work, if just calculating static load

Dynamic calculation
σzul = σD * b1 * b2 / βk / ν
b1 : 0,88 for St 37-2 ( fine finished surface Ra 6,3)
b1 : 0,72 for 30CrNiMo 8
b2 : 1 (diameter below 10 mm)
βk : 1,3 for St37-2; 1,4 for 30CrNiMo8
ν : 1,5 average value
σDSch = 290 N/mm² for St37-2; σDSch = 1070 N/mm² for 30CrNiMo8

--> for St37-2: σzul = 131 N/mm²
--> for 30CrNiMo 8 σzul = 367 N/mm²

no steel will stand 777N/mm² longtime (fatigue)

Calculating area pressure
Aproj = d * l = 6,35mm * 7,62mm = 48,4mm² in stem
p = 12531N / 48,4mm² = 259 N/mm² in stem fit
Aproj = d * s * 2 = 6,35 mm * 5,04mm = 32mm² rod connector
p = 12531 / 32mm² = 392 N/mm² in fit to rod connector

tolerable pressure for non-sliding surfaces, mild steel, dynamic load: 75N/mm²
tolerable pressure for non-sliding surfaces,high grade steel, dynamic load: 150N/mm²

tolerable pressure for sliding surfaces, mild steel on steel: none. high rate of wear !!!
tolerable pressure for sliding surfaces, steel on bronze: 25 N/mm²

Both the stress through bending and the area pressure seem to be much over tolerable values.