gearbox.profile#

Transverse tooth form of an external cylindrical gear generated by a rack (hob).

The half tooth is drawn in a frame with the gear axis at the origin and the tooth axis along +y, on the side of negative x. It runs from the middle of the tooth gap on the root circle along

  • the root circle,

  • the root fillet, the trochoid-like curve that the rounded tip of the rack leaves,

  • the involute flank,

  • the tip circle,

to the tip on the tooth axis. The exporters and the finite-element meshes build on this form. Lengths are in millimetres.

class ToothProfile[source]#

Bases: object

Tooth form and main dimensions of an external gear cut by a rack.

data#

Dimensions by their usual symbol, the names used by the exporters, the meshes and the export templates: z, m_n, m_t, b, beta, alpha_n, alpha_t (degrees), x, d, d_b, d_a, d_f, d_Ff (root form diameter, where the involute starts), d_s (bore), rho_fP (tip radius of the rack), and s_p (tooth thickness on the reference circle, normal section).

formcoords#

Points [x, y] of the half tooth, from the middle of the gap to the tip.

shaftcoords#

Two points on the bore: on the tooth axis and in the middle of the gap.

rotate_ang#

Rotation [deg] that puts the tooth axis on the axis of symmetry of a gap, used by the export templates.

__init__(gear)[source]#

Generate the tooth form of gear.

Raises:

ValueError – For an internal gear, a tool tip radius too large for the gap, or a bore that does not fit inside the root circle.

half_angle(radius)[source]#

Half the angular tooth thickness of the involute at radius [rad].

(pi/2 + 2 x tan(alpha_n)) / z + inv(alpha_t) - inv(alpha_y), with cos(alpha_y) = r_b / r; radii below the base circle are taken on it.

Return type:

float | ndarray