Lathe work & boring bar deflection

How it works

The work (or bar) is treated as a round beam. Deflection δ = F × L³ ÷ (k × E × I), where I = π(d⁴ − bore⁴) ÷ 64 and k is 3 for a cantilever (chuck only), about 110 for chuck plus tailstock with the cut in the middle, and 48 between centres. Because it goes with L³ and d⁴, halving the overhang cuts deflection by 8×, and a 25% thicker bar is about 2.4× stiffer.

The cutting force estimate uses specific cutting force for the material group (the same data as the speeds & feeds calculator) × feed × depth of cut. The radial force that actually pushes the work away is usually smaller, roughly a third to a half of it, so this is a cautious upper figure EST.

Rules of thumb: keep chuck-only work under about 3 × diameter stick-out, support longer work with the tailstock, and keep steel boring bars under about 4 × diameter overhang (solid carbide about 6–8 ×) EST.