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TAPER TURNING ON LATHE MACHINE

4 Methods + Important Formulas + Real Calculations
Compound Rest Tailstock Offset Taper Attachment Form Tool
"Learn how to machine accurate tapered surfaces."
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Definition

What Is Taper Turning?

Taper turning is the operation of producing a conical surface on a cylindrical workpiece. The diameter gradually changes along its length.
⚙️ Machine tool spindles
🔩 Drill shanks
🔧 Tool holders
⚙️ Shafts & pins
🔧 Pipe fittings
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Geometry

Know the Taper Dimensions

DLarge diameter
dSmall diameter
LTaper length
αAngle with axis (compound rest)
θIncluded angle
θ = 2α
Set compound rest to α — not θ
This is the most common error in taper turning.
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Methods

4 Methods of Taper Turning

1. Compound Rest Method
Swivel top slide • manual feed • short tapers
2. Offset Tailstock Method
Between centres • shifted tailstock • long tapers
3. Taper Attachment Method
Guide bar • power feed • high accuracy
4. Form Tool Method
Shaped tool • single pass • short tapers
Choose the method by taper length, accuracy, and production volume.
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Method 1

Compound Rest Method

→ Swivel the compound rest
→ Set it to the calculated angle α
→ Feed the cutting tool manually
→ Best suited to short tapers
α = arctan((D − d) / (2L))
Compound rest setting angle
Manual feed limits length — usually up to ~75 mm of slide travel.
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Method 2

Tailstock Offset Method

→ Hold workpiece between centres
→ Shift tailstock off centreline
→ Feed tool parallel to the bed
→ Suitable for long tapers
Offset = (Ltot × (D − d)) / (2L)
Ltot = distance between centres
Ltot ≠ L. Do not confuse total length with taper length.
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Method 3

Taper Attachment

→ Set guide bar to required angle
→ Connect cross slide to attachment
→ Move carriage longitudinally
→ Guide bar controls cross slide
ACCURATE • REPEATABLE • LONG TAPERS
Best for production work — eliminates manual feeding errors.
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Method 4

Form Tool Method

→ Use a specially ground tool
→ Match tool profile to required taper
→ Produce short taper in one or few passes
FASTEST FOR SHORT TAPERS
Best for: short tapers and suitable production jobs where tool wear can be tolerated.
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Formulas

Master the Taper Formulas

T = (D − d) / L
Taper per unit length
α = arctan((D − d) / (2L))
Angle with axis
θ = 2 × α
Included angle
Dx = D − (D − d) × (x / L)
Diameter at any point x
Use consistent dimensions and units throughout.
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Worked Example

Calculate a Real Taper

D 50 mm
d 40 mm
L 100 mm
T = (50 − 40) / 100 0.10 mm/mm
θ = 2 × arctan(10/200) 5.724°
α = 5.724° / 2 2.862°
COMPOUND REST → 2.862°
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Offset Example

How Much Tailstock Offset?

Ltot 300 mm
L 200 mm
D 60 mm
d 50 mm
Offset = (300 × 10) / (2 × 200) = 3000/400
OFFSET = 7.5 MM
✓ Measure accurately ✓ Check centre alignment ✓ Secure workpiece ✓ Inspect finished taper
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Ready to Calculate Your Taper?

Enter your diameters and taper length. Calculate:
Taper Angle α Compound Rest Tailstock Offset
OPEN TAPER TURNING CALCULATOR READ THE FULL GUIDE →
Lathe Guide Bearing Decoder Hole Dividing Simple Indexing
Save this guide for your next taper turning job.
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