Boring Bar Deflection Calculator

Inputs

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Free length from the holder or bore support to the cutting edge.
in
Solid round shank diameter used in I = pi*d^4/64.
in
Side load at the cutting edge. If unknown, estimate from cut load, material, engagement and feed.
lbf
Steel is about 200 GPa (29 Mpsi). Carbide is much stiffer, often around 550-650 GPa.
Mpsi
Serviceability limit for tip movement. Use a tighter limit for finish bores and small tools.
in
Compare elastic bending stress with your material/design allowable.
ksi

Results

Default result
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Tip deflection(delta)
0.001498in
Caution

delta = F*L^3/(3*E*I).

Cantilever end-load deflection: delta = F*L^3/(3*E*I).

Also computed

Deflection utilization(U_delta)Caution1.5x

Bending stress(sigma)Pass4.074ksi

sigma = 32*F*L/(pi*d^3).

Stress utilization(U_sigma)Pass0.112x

Overhang ratio(L/d)Pass4L/D

Required diameter, deflection(d_delta)1.106in

Diameter that would meet the entered deflection limit for the same force and stickout.

Required diameter, stress(d_sigma)0.4826in

Method notes 4 notes
  • Tip deflection is above the entered allowable; reduce stickout, increase diameter, reduce side load or use a stiffer bar/material.
  • Modelled as a solid round cantilever with a radial point load at the cutting edge: I = pi*d^4/64 and delta = F*L^3/(3*E*I).
  • Static stiffness is k = 3*E*I/L^3. Because I scales with d^4 and deflection scales with L^3, short stickout and larger diameter dominate the result.
  • This is a static elastic screen. It does not predict chatter, holder compliance, spindle/runout, insert geometry, interrupted cuts, damping, built-up edge or cutting-force variation.

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