Boring Bar Max Overhang for a Deflection Limit
The longest a bar can stick out before its tip deflection reaches the allowable.
Example
You enter
- Bar / tool diameter d (in) 0.75
- Radial cutting force F (lb) 100
- Allowable tip deflection (in) 0.0154524
- Modulus E (psi: 30e6 steel, ~90e6 carbide) 30000000
You get
- Max overhang (deflection-limited) 6 in
- Overhang ratio L/D 8
Details, formula, and sources
L_max = (3 E I x deflection / F)^(1/3) with I = pi d^4/64. A 0.75 in steel bar under 100 lb held to 15 mil can reach 6.0 in (L/d 8); a stiffer carbide bar (90e6) reaches 8.6 in. It also flags the L/d against the chatter limit - if the deflection-limited overhang is past ~4:1 steel / 6-8:1 carbide, chatter governs and the real max is shorter. Answers 'how far can I stick out' instead of the deflection at one length. Static solid-round model. The tool and setup govern.
I = pi d^4/64; L_max = (3 E I delta_allow / F)^(1/3); L/d ratio for chatter risk. (E = 30e6 psi steel, ~90e6 carbide)
The cantilever tip-deflection model delta = F L^3/(3 E I) with I = pi d^4/64 solved for the overhang, a standard mechanics-of-materials result applied to tool overhang, by name.
The cantilever deflection formula is a public mechanics-of-materials result; the L/d overhang limits are standard machining guidance.
Estimate. AHJ and licensed professional govern.
Field names used by the API: d_in, f_lb, allowable_deflection_in, e_psi, max_overhang_in, ld
- Cantilever inverse L_max = (3 E I delta / F)^(1/3), I = pi d^4/64, uniform solid round bar under a tip loadmechanics of materials
- Chatter may govern check the L/d against ~4:1 steel / 6-8:1 carbide; if exceeded, the chatter limit sets a shorter max overhangmachining practice
- Static estimate static solid-round model, not a stability-lobe analysismachining practice