Gear Hobbing Swivel & Feed Calculator

Determine exact hob head swivel tilt angles (Σ), worktable-to-hob rotational synchronization ratios, and axial feeds for spur and helical gear manufacturing.

Gear Module m (mm)

Gear Teeth Count (z_2)

Gear Helix Angle β (°)

Gear Hand of Helix

Hob Tool Parameters

Hob Outside Dia D_hob (mm):

Hob Starts / Threads (k_1):

Hob Lead Angle γ_hob (°):

Hob Thread Hand:

Cutting Speeds & Feeds

Hob Surface Speed V_c (m/min):

Axial Feed f_a (mm/rev work):

Face Width b (mm):

Hob Swivel & Kinematic Results

Hob Swivel Angle (Σ) -

Worktable RPM (n_work) -

Hob Spindle Speed (n_hob): -

Index Ratio (n_work / n_hob): -

Gear Pitch Diameter (d_p): -

Total Axial Travel (L_total): -

Machining Cycle Time: -

Hobbing Head Tilt Rule

Swivel Formula: -

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Principles of CNC & Manual Gear Hobbing

Gear hobbing is a continuous generating process where a worm-like cutting tool (the hob) and the blank workpiece rotate in continuous, synchronized engagement. As the hob rotates, its cutting flutes carve conjugate tooth profiles into the gear blank, while the tool carriage feeds axially across the gear face width.

Hob Swivel Angle ($Sigma$) Calculation

Because the hob's cutting teeth are arranged in a helical worm, the hob spindle must be swiveled on its trunnion to align the hob teeth with the gear tooth space. The swivel angle $Sigma$ depends on the gear helix angle $eta$ and the hob lead angle $gamma_{hob}$:

Spur Gears ($eta = 0^circ$): The head is tilted solely by the hob lead angle: \[ \Sigma = \gamma_{hob} \]
Helical Gears - Same Hand (e.g. RH Gear + RH Hob): The lead angles subtract: \[ \Sigma = \beta - \gamma_{hob} \]
Helical Gears - Opposite Hand (e.g. RH Gear + LH Hob): The lead angles add: \[ \Sigma = \beta + \gamma_{hob} \]

Kinematic Worktable Synchronization

For every full revolution of a single-start hob ($k_1 = 1$), the gear blank must index exactly one tooth. For a gear with $z_2$ teeth:

\[ n_{work} = n_{hob} \times \frac{k_1}{z_2} \]

In helical gear hobbing, as the tool feeds axially, the worktable receives an additional differential rotation (via electronic gear box EGB on CNCs or differential change gears on mechanical hobbers) to follow the gear helix.

Frequently Asked Questions

Why is it preferable to use a hob with the same hand as the gear helix?

When the hob and gear have the same helix hand, the required swivel angle is Sigma = beta - gamma_hob. This smaller tilt angle minimizes vertical overhang, increases machine rigidity, and reduces the required clearance envelope.

What is hob approach and overrun distance?

The hob cannot start cutting at full depth right at the gear edge because of its circular profile. The hob must start before the gear face by an approach distance L_app ≈ √(m · (D_hob - m)) and overrun by ~3-5 mm to finish the tooth profile across the entire face width.

When should multi-start hobs (k = 2 or 3) be used?

Multi-start hobs index 2 or 3 teeth per revolution, cutting cycle times by 50% to 65%. However, multi-thread hobs have larger lead angles (gamma), produce fewer generating cuts per tooth flank, and result in higher scallop roughness. They are commonly used for high-volume roughing, followed by single-thread finishing.