KEVOS® MAKEOS · Manufacturing
Slender Work Turning Check (Work Deflection, Diameter Error, Steady Rest Spacing)
When turning a long, slender part, how far does the cutting force push the work away from the tool, how much diameter error does that cause, and how far apart must steady rests be to hold the tolerance?
Check of a slender round part turned between centres or held in a chuck only: the cutting and radial forces from the specific cutting force, depth of cut and feed, the deflection of the work at the worst tool position (mid-span between centres, or the free end in a chuck, as the beam deflection tool), the diameter error and the length-to-diameter ratio, the longest unsupported length that holds your allowance, the number of steady rests needed between centres, and the largest feed for the full length.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Work holding | choice | Between centres the worst deflection is at mid-span; in a chuck without tailstock support the worst is at the free end. |
| Work diameter at the cut | mm | Diameter of the work where the tool is cutting (use the smallest diameter along a stepped part for a cautious answer). |
| Length between centres, or overhang from the chuck | mm | Distance between the centres, or from the chuck jaws to the free end. |
| Work elastic modulus | GPa | Elastic modulus of the work material (steel about 210 GPa, aluminium about 70 GPa). |
| 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. |
| Depth of cut | mm | Depth of cut (radial). |
| 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. | |
| Tolerance | ||
| Diameter error the tolerance allows | µm | Part of the diameter tolerance you can give to work 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: Work holding
- What it is
- How the long part is supported while it is turned: between a headstock and a tailstock centre, or held only in the chuck with its other end unsupported.
- Units and format
- Choose one of 2 options from the list: Between centres (simply supported); In a chuck only (cantilever).
- Example
- The form opens with “Between centres (simply supported)” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Between centres the part is sixteen times stiffer than the same length overhanging from a chuck.
- Get it right
- If the part is in the chuck with a tailstock centre in the far end, between centres is the nearer case but the chuck stiffens it somewhat.
What this means: Work diameter at the cut
- What it is
- The diameter of the part where the tool is cutting, 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 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 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 thin sections deflect far more than their size suggests.
- Get it right
- On a stepped shaft use the smallest diameter in the span for a cautious answer.
What this means: Length between centres, or overhang from the ch…
- What it is
- The length of the part that bends: the distance between the centres, or the overhang from the chuck jaws to the free end.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 20000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 400 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 length.
- Get it right
- Measure between the actual support points; a steady rest or a tailstock centre shortens the span.
What this means: Work elastic modulus
- What it is
- The elastic modulus (Young’s modulus) of the work material, its stiffness before the shape of the part 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; an aluminium shaft deflects three times as much as steel.
- Get it right
- Steel is about 210 GPa, aluminium about 70 GPa and brass about 100 GPa.
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.
What this means: Depth of cut
- What it is
- The radial depth of cut, the amount removed from the radius in one pass along the part.
- 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 1.5 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
- Check the finishing pass separately; it is usually the one that sets the final size.
What this means: Feed per revolution
- What it is
- How far the tool advances along the part for each revolution, 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 0.2 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; the tool reports the largest feed that holds the allowance unsupported.
What this means: Radial force as a share of the cutting force
- What it is
- The radial (passive) force pushing the part away from the tool, as a share of the main tangential cutting force; it is the force that changes the diameter.
- 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.
- Get it right
- A small lead angle and nose radius keep it low; 0.2 to 0.6 is typical. Long, slender parts are often turned with a zero lead angle.
Tolerance
What this means: Diameter error the tolerance allows
- What it is
- The part of the diameter tolerance that you are willing to let work 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 30 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, the longest unsupported span and the number of steady rests.
- Get it right
- Leave room for tool wear, machine error and measurement; deflection should take only part of the tolerance.
Method and formulas
- Cutting force F_c = k_c × a_p × f; radial force F_r = share × F_c.
- Deflection at the worst tool position (as the beam deflection tool): between centres δ = F_r L³ ÷ (48 E I) at mid-span; in a chuck δ = F_r L³ ÷ (3 E I) at the free end; I = π d⁴ ÷ 64. Diameter error = 2δ.
- Longest unsupported length L_max = (C E I δ_allow ÷ F_r)^(1/3), C = 48 or 3; steady rests between centres = the number that divides the length into spans no longer than L_max.
- Largest feed for the full length = feed × allowance ÷ error, since the force is proportional to feed.
- Example: a 30 mm part over 400 mm deflects 38.324 µm, a diameter error of 76.649 µm; spans of up to 292.59 mm hold 30 µm, so 1 steady rest(s) are needed.
Limitations
- Treats the work as a uniform round beam on rigid supports; centres and chucks are less than rigid, and a hollow or stepped part needs its own section.
- Static deflection only: chatter, the part's own weight and heat from cutting are not included.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check whether a long shaft can be turned to tolerance without support
- Find how many steady rests a shaft needs
- Find the feed that keeps the error within the tolerance
Who it is for
- Machinists
- Process planners
- Manufacturing engineers
What you get
- Cutting and radial forces
- Work deflection at the worst position and diameter error
- Length-to-diameter ratio
- Longest unsupported length, steady rests needed and largest feed
Interpreting the result
- Between centres the error is largest at mid-length, so the part comes out barrel-shaped; in a chuck the error grows towards the free end, so the part comes out tapered.
- Halving the span cuts the deflection to an eighth, which is why one steady rest often solves the problem.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 232–244, 762, 1093–1094. 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.
Useful alongside · Library collection
Workholding and toolholding: vices, chucks, zero-point systems, tapers and holders
What it covers: How standard workholding and toolholding choices affect accuracy, tool life, set-up time and safety, from vices and chucks to zero-point pallets, spindle tapers, collets and shrink-fit holders.
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.