spiral-bevel-1755192689

Spiral Bevel

Spiral bevel equations for GearLab

Spiral bevel gears are a type of bevel gear with teeth that are curved and spiral-shaped, allowing for smoother engagement and higher load capacity compared to straight bevel gears. They are commonly used in applications where high speed and torque transmission is required, such as in automotive differentials and industrial machinery.

The main difference between spiral bevel gears and straight bevel gears is the shape of the teeth. Spiral bevel gears have teeth that are curved and angled, which allows for gradual engagement and smoother operation. This design reduces noise and vibration, making them suitable for high-speed applications.

The tooth design of spiral bevel gears also allows for higher load capacity and better strength compared to straight bevel gears. The curved teeth distribute the load more evenly, reducing stress concentrations and improving durability.

The equations for calculating the parameters of spiral bevel gears are similar to those for straight bevel gears, but with additional considerations for the curvature of the teeth and the spiral angle.

Equations for pitch angles, face angles and root angles are the same as those for straight bevel gears, but the calculations for the pitch diameters and other parameters take into account the curvature of the teeth.

Spherical involute geometry of spiral bevel gears just like straight bevel gears is driven by the three cone angles, the cone offset and the gear ratio. The addendum and dedendum are calculated based on the pitch cone distance, cone angles and the cone offsets.

Spherical Involute Geometry for Spiral Bevel Gears

The spherical involute geometry of spiral bevel gears is defined by the following parameters:

• ${\theta }_p^g$: Gear pitch angle
• ${\theta }_p^p$: Pinion pitch angle
• ${\theta }_s$: Shaft angle
• $z$: Gear ratio
• $z^g$: Gear teeth
• $z^p$: Pinion teeth
• ${\theta }_f$: Face angle
• ${\theta }_r$: Root angle
• $d_f$: Face cone offset
• $d_r$: Root cone offset
• $a$: Addendum
• $d$: Dedendum
• $d_i$: Inner pitch diameter
• $d_o$: Outer pitch diameter
• $L$: Pitch cone distance

Tooth microgeometry equations

The spherical involute curve equation is the same as a straight bevel gear however, the surface profile is rotated based on a function $F(r)$ instead of just radial extrusion to give the spiral geometry. (Al-Daccak et al., 1994)

The most common spiral equation is the logarithmic spiral, which ensures that the spiral angle is same at all points along the tooth. The equation for a logarithmic spiral is:

$F(r)=\frac{\tan (\psi )\ln (r/L)}{\sin ({\alpha }_p)}$

where:

• $\psi$ is the median spiral angle
• $r$ is the distance from the origin
• $L$ is the median cone distance
• ${\alpha }_p$ is the pressure angle

Al-Daccak, M. J., Angeles, J., & Gonza´lez-Palacios, M. A. (1994). The Modeling of Bevel Gears Using the Exact Spherical  Involute. Journal of Mechanical Design, 116(2), 364–368. https://doi.org/10.1115/1.2919387