BIZOMAT MAKEOS · Manufacturing
Boring Bar Deflection
How far will this boring bar deflect under the cutting force, and is the overhang reasonable?
Tip deflection of a solid boring bar or long tool as a cantilever under the cutting force, with the overhang-to-diameter ratio, against an allowable deflection.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Bar diameter | mm | Diameter of the bar shank (use the flat-to-round equivalent for flats). |
| Overhang | mm | Length from the clamping face to the cutting edge. |
| Bar elastic modulus | GPa | Modulus of the bar: about 210 GPa for steel, about 550–630 GPa for solid carbide. |
| Cutting force on the tip | N | Resultant cutting force, roughly kc × depth × feed (see the turning power tool). |
| Allowable deflection | mm | Part of the bore tolerance you can accept from deflection. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Bar diameter
- What it is
- The diameter of the boring bar shank that overhangs the holder. For a bar with a flat ground on it, use an equivalent round diameter.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Deflection falls with the fourth power of diameter, so a slightly larger bar helps a lot.
- Get it right
- Use the shank diameter, not the bore diameter being cut.
What this means: Overhang
- What it is
- The free length of the bar from the face of the clamp or holder to the cutting edge.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Deflection rises with the cube of overhang, so small increases matter.
- Get it right
- Measure from where the bar is actually gripped, not from the end of the holder body.
What this means: Bar elastic modulus
- What it is
- The Young’s modulus of the bar material: how stiff it is in bending. It comes from the bar maker or material data, and differs widely between steel and carbide bars.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 210 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Deflection falls in direct proportion as modulus rises.
- Get it right
- Enter GPa, not MPa.
What this means: Cutting force on the tip
- What it is
- The cutting force acting sideways on the tip of the bar, from cutting force data or the turning power tool.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 10000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Deflection rises in direct proportion.
- Get it right
- Use the resultant force on the tip, not the spindle power; a worn insert raises it.
What this means: Allowable deflection
- What it is
- The largest tip deflection you can accept, usually the share of the bore tolerance you are willing to lose to bar bending.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.05 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pass or fail line; the deflection does not change.
- Get it right
- Enter millimetres; a few micrometres is a small fraction of a millimetre.
Method and formulas
- I = π D⁴ ÷ 64.
- Deflection δ = F L³ ÷ (3 E I); stiffness = 3EI ÷ L³.
- Overhang ratio = L ÷ D.
- Example: a 20 mm steel bar at 100 mm overhang deflects 40.42 µm under 200 N.
Limitations
- Static deflection only; chatter depends on dynamic stiffness and damping.
- Clamping is assumed rigid; real holders add compliance.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Choose bar diameter and material for a deep bore
- Estimate size error from tool deflection
- Compare steel and carbide bars
Who it is for
- Machinists
- CNC programmers
- Manufacturing engineers
What you get
- Tip deflection
- Overhang-to-diameter ratio
- Bar stiffness
Interpreting the result
- Common guidance: steel bars to about 4 × D, carbide to about 6 × D, damped bars to about 10 × D; check the supplier’s limits.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 762–790, 1300. Topic reference; no source tables or recommended settings are reproduced.
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