KEVOS® MAKEOS · Manufacturing
Boring Bar Overhang Check (Deflection, Diameter Error, Natural Frequency, Longest Overhang)
At this overhang and cut, how far does the boring bar deflect, how much diameter error does that cause, how stiff and how lively is the bar, and how long could the overhang be for the tolerance?
Check of a solid round boring bar: the cutting force from the specific cutting force, depth of cut and feed, the radial share of it, the tip deflection of the bar as a cantilever (as the boring bar deflection tool) and the diameter error it causes, the overhang ratio against your limit, the first natural frequency of the bar, the longest overhang and the largest feed that keep the diameter error within your allowance, and the same figures for a bar of a stiffer material such as carbide.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Bar | ||
| Bar diameter | mm | Diameter of the bar shank (a solid round bar; bars with coolant holes are slightly less stiff). |
| Overhang from the clamp to the cutting edge | mm | Distance from the face of the clamp or holder to the cutting edge. |
| Bar elastic modulus | GPa | Elastic modulus of the bar material (steel about 210 GPa; cemented carbide several times higher, from the bar maker). |
| Bar density | kg/m³ | Density of the bar material (steel about 7,850 kg/m³). |
| Cut | ||
| Specific cutting force | N/mm² | Specific cutting force for the work material at this chip thickness, from the tool maker or a cutting data handbook. |
| Radial depth of cut | mm | Radial depth of cut (half the change in diameter). |
| Feed per revolution | mm/rev | Feed per revolution. |
| Radial force as a share of the cutting force | Ratio of the radial (passive) force to the main cutting force; it depends on the lead angle and nose radius, often between about 0.2 and 0.6. | |
| Limits and alternative | ||
| Diameter error the tolerance allows | µm | Part of the diameter tolerance you can give to bar deflection. |
| Largest overhang ratio you accept for this bar material | Largest overhang-to-diameter ratio your practice accepts for this bar material (often about 4 for steel bars; higher for carbide or damped bars). | |
| Modulus of the alternative bar material | GPa | Elastic modulus of the stiffer alternative bar (cemented carbide is several hundred GPa). |
| Density of the alternative bar material | kg/m³ | Density of the alternative bar material. |
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.
Bar
What this means: Bar diameter
- What it is
- The diameter of the solid round shank of the boring bar, which sets its bending stiffness through the fourth power of the diameter.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Stiffness rises with D⁴, so a slightly larger bar cuts deflection sharply.
- Get it right
- Use the largest bar that fits the pre-bored hole with chip clearance; bars with coolant holes are a little less stiff than solid ones.
What this means: Overhang from the clamp to the cutting edge
- What it is
- The length of bar sticking out from the face of the clamp or holder to the cutting edge, the free length that bends under the cutting force.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 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 the overhang: doubling it multiplies the error by eight.
- Get it right
- Measure from the clamp face, not the back of the holder, and set the bar no longer than the bore depth needs.
What this means: Bar elastic modulus
- What it is
- The elastic modulus (Young’s modulus) of the bar material, the stiffness of the material itself before the bar’s shape is considered.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1500 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 proportion to the modulus, and the natural frequency rises with its square root.
- Get it right
- Steel is about 210 GPa; cemented carbide is roughly three times stiffer. Take the value from the bar maker for heavy-metal or composite bars.
What this means: Bar density
- What it is
- The density of the bar material, used with the stiffness to find how fast the bar would vibrate if it were struck.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 100 kg/m³ to 25000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7850 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A denser bar has a lower natural frequency; it does not change the static deflection.
- Get it right
- Steel is about 7,850 kg/m³; carbide is nearly twice as dense, which offsets part of its stiffness gain in frequency.
Cut
What this means: Specific cutting force
- What it is
- The specific cutting force of the work material: the cutting force per square millimetre of chip cross-section at the chip thickness being cut.
- Units and format
- Enter a number in N/mm²: newtons per square millimetre (equal to MPa). The form accepts 0.000001 N/mm² to 10000 N/mm². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2000 N/mm² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The cutting and radial forces, and so the deflection, rise in proportion.
- Get it right
- Take it from the insert maker’s data for the material group and chip thickness; harder and tougher materials have higher values.
What this means: Radial depth of cut
- What it is
- The radial depth of cut taken by the boring tool, half of the increase in bore diameter made by one pass.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 50 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Force and deflection rise in proportion to the depth of cut.
- Get it right
- For a finishing pass on a slender bar keep the depth small; the roughing passes can be checked separately.
What this means: Feed per revolution
- What it is
- How far the tool advances along the bore for each revolution of the work, which with the depth of cut sets the chip area.
- Units and format
- Enter a number in mm/rev: millimetres per revolution. The form accepts 0.000001 mm/rev to 5 mm/rev. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.15 mm/rev as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Force and deflection rise in proportion to the feed.
- Get it right
- Use the programmed feed for the pass being checked; the tool reports the largest feed that holds the allowance.
What this means: Radial force as a share of the cutting force
- What it is
- The radial (passive) force pushing the bar away from the bore wall, as a share of the main tangential cutting force; it is the force that changes the bore size.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 2. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.4 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The diameter error rises in proportion; the tangential deflection is unchanged.
- Get it right
- It depends on the lead angle and nose radius; small lead angles and small nose radii keep it low. 0.2 to 0.6 is a typical range.
Limits and alternative
What this means: Diameter error the tolerance allows
- What it is
- The part of the bore’s diameter tolerance that you are willing to let bar deflection use up, as a total on diameter.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts 0.000001 µm to 10000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the pass line and the longest overhang and largest feed the tool reports.
- Get it right
- Leave room in the tolerance for machine, tool wear and measurement errors; giving all of it to deflection is optimistic.
What this means: Largest overhang ratio you accept for this bar…
- What it is
- The largest ratio of overhang to bar diameter that your shop accepts for this bar material before switching to a stiffer or damped bar.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 20. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 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 overhang-ratio pass line; it does not change the deflection.
- Get it right
- Use your own experience or the bar maker’s guidance for the material; carbide and damped bars allow much higher ratios than steel.
What this means: Modulus of the alternative bar material
- What it is
- The elastic modulus of a stiffer bar you might use instead, such as cemented carbide, so the tool can show the gain from changing material.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1500 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 600 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes only the alternative-bar figures; a higher modulus shows a smaller error and a longer possible overhang.
- Get it right
- Take the modulus from the bar maker; carbide grades differ with their binder content.
What this means: Density of the alternative bar material
- What it is
- The density of the alternative bar material, used to find its natural frequency for comparison with the present bar.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 100 kg/m³ to 25000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 14500 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes only the alternative bar’s natural frequency.
- Get it right
- Carbide is about 14,000 to 15,000 kg/m³ depending on grade; use the maker’s value.
Method and formulas
- Cutting force F_c = k_c × a_p × f; radial force F_r = share × F_c.
- Bar stiffness k = 3 E I ÷ L³ with I = π D⁴ ÷ 64; tip deflections F ÷ k (as the boring bar deflection tool); diameter error = 2 × radial deflection.
- First natural frequency of a clamped cantilever f₁ = (1.8751² ÷ 2π) √(E I ÷ (ρ A L⁴)).
- Longest overhang L_max = (3 E I δ_allow ÷ F_r)^(1/3) with δ_allow = half the diameter allowance; largest feed scales the feed by allowance ÷ error, since the force is proportional to feed.
- Alternative material: deflection × E ÷ E_alt; frequency × √((E_alt ÷ ρ_alt) ÷ (E ÷ ρ)); L_max × (E_alt ÷ E)^(1/3).
- Example: a 25 mm bar at 100 mm overhang deflects 9.9337 µm radially, a diameter error of 19.867 µm; it could reach 100.22 mm for 20 µm, and 142.21 mm in the alternative material.
Limitations
- Static deflection of a solid round bar rigidly clamped; real clamps are less than rigid, so the bar behaves as if somewhat longer.
- The natural frequency is for the bar alone; chatter depends on the whole system, the cut and the lead angle, and is not predicted.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check whether a boring bar will hold a bore tolerance at a given overhang
- Find the longest overhang or the largest feed for a tolerance
- Compare a steel bar with a carbide bar of the same size
Who it is for
- Machinists
- Process planners
- Manufacturing engineers
What you get
- Cutting and radial forces
- Bar deflection, diameter error and overhang ratio
- First natural frequency
- Longest overhang and largest feed for the allowance
- The same for the alternative bar material
Interpreting the result
- Deflection rises with the cube of the overhang and falls with the fourth power of the diameter: the largest bar that fits the bore and the shortest overhang that reaches the depth matter more than anything else.
- A stiffer bar material reduces deflection in proportion to its modulus but extends the overhang only by the cube root of the ratio.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 197, 302, 762–790. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Method explained here · KEVOS® original book
Deflection, rigidity and chatter
What it covers: Estimate tool and workpiece deflection with cantilever formulas, see why overhang and diameter dominate, and recognise and reduce chatter before it limits accuracy and output.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.