How to use this calculator
- Enter stickout. Use the free length from the holder or bore support to the cutting edge.
- Enter tool diameter. Use the round shank or boring bar diameter that resists bending.
- Enter radial force. Use a measured side load or a conservative estimate from the cut.
- Set limits. Enter Youngs modulus, allowable tip deflection and allowable bending stress.
- Read utilization. Use deflection utilization, stress utilization and L/D ratio to decide whether to shorten, stiffen or lighten the setup.
How it works
The tool is treated as a round solid cantilever with a radial point load at the cutting edge. The round-section area moment of inertia is I = pi · d⁴ / 64 and the static tip deflection is delta = F · L³ / (3 · E · I).
The same beam model gives the tip slope
theta = F·L²/(2·E·I) and the outer-fibre bending stress
sigma = 32·F·L/(pi·d³). The calculator also reports static stiffness
k = 3·E·I/L³, overhang ratio L/d, and the diameter required
to meet the entered deflection or stress limit.
This is useful when bore taper, chatter, chatter-like marks or poor finish might be caused by a long, flexible tool. It is not a dynamic stability model; use it as the first stiffness screen before tuning feed, speed, insert geometry or holder setup.
Worked example
Verified against the live calculator
Suppose a steel boring bar sticks out 4.000 in, has a
1.000 in diameter, carries an estimated 100 lbf
radial force and uses E = 29 Mpsi. With
I = pi × 1⁴ / 64 = 0.04909 in⁴, the static tip deflection is about
0.00150 in. If the allowable deflection is 0.00100 in,
deflection utilization is about 1.50x.
The same setup has L/d = 4.0 and a bending stress of about
4.08 ksi, so stiffness controls before strength. Reducing stickout to
3.000 in would cut the deflection by roughly
(3/4)³ = 0.422 for the same load and diameter.
Frequently asked questions
How do you calculate boring bar deflection?
Approximate the bar as a round cantilever with the radial cutting force at the tip. The area moment is I = pi*d^4/64 and the tip deflection is delta = F*L^3/(3*E*I), where F is side load, L is stickout, E is Youngs modulus and d is bar diameter.
What L/D ratio is acceptable for a boring bar?
A steel boring bar is often much happier around 3 to 4 L/D than 6 L/D or more. Carbide bars and damped bars can run farther out, but this calculator only screens static elastic stiffness; chatter can still govern before stress or static deflection.
Can this be used for end mill stickout deflection?
Yes as a first approximation if the cutter is treated as a solid round cantilever and you enter the cutter or shank diameter, stickout and radial force. It does not account for flute section stiffness, helix, holder grip, runout, axial force, chip load variation or dynamic chatter.
Why does diameter matter so much?
For a round bar, I = pi*d^4/64. Doubling the diameter increases bending stiffness by sixteen times, while doubling stickout increases deflection by eight times because delta scales with L^3.
How should I choose radial cutting force?
Use measured force data when available. Otherwise estimate it from material, chip load, engagement and depth of cut, then treat the result as a sensitivity screen. If a setup is marginal at a guessed force, reduce stickout or load before trusting finish and bore size.
Does this predict chatter?
No. Chatter depends on machine, holder, insert geometry, damping, cutting speed, material and process dynamics. This tool catches static stiffness and stress problems that often sit underneath chatter or taper, but it is not a stability-lobe model.
Method & assumptions
- Uses elastic, small-deflection Euler-Bernoulli cantilever beam theory.
- Assumes a prismatic, solid round bar or cutter shank with a radial point load at the tip.
- Does not include holder compliance, spindle bearings, collet grip, insert seat movement, runout, flute geometry, taper shanks, interrupted cuts or damping.
- Does not predict chatter or stability lobes; use the result as a stiffness and stress screen before process tuning.
- For carbide or damped bars, enter the effective modulus and still verify manufacturer guidance for allowable overhang.