Diamond-like grooves

The Diamond Groove

The DiamondGroove class represents a rhombus shaped groove as shown in the figure.

diamond groove geometry

Mandatory measures of this groove are the two radii \(r_1\) and \(r_2\). To constrain geometry fully, any two of the following must be given:

  • usable width \(w_\mathrm{u}\)

  • tip depth \(d_\mathrm{t}\)

  • tip angle \(\delta\)

The radii are typically small, the depth is \(d_\mathrm{t}\) typically \(< \frac{b_\mathrm{kn}}{2}\) so that the tip angle \(\delta\) is larger than 90°. \(r_3\) and \(r_4\) are considered to be zero, as well as \(w_\mathrm{g}'\).

The tip depth \(d_\mathrm{t}\) was chosen in favor of the real depth \(d\), because it does not change, when the radii are modified. So the overall geometry remains the same if one modifies only the radii. The tip depth can be considered as the diagonal of the rhombus with sharp corners or the limit of the depth \(d\) for \(r_2 \rightarrow 0\).

class DiamondGroove(r1: float, r2: float, usable_width: float | None = None, tip_depth: float | None = None, tip_angle: float | None = None, pad_angle: float = 0)

Represent a diamond-shaped groove.

Exactly two of usable_width, tip_depth and tip_angle must be given. Widths are always measured at the intersection of the extrapolated ground, face and flanks. All angles are measured in ° (degree).

Parameters:

  • r1 – radius 1 (face/flank)

  • r2 – radius 2 (flank/ground)

  • usable_width – usable width of the groove

  • tip_depth – depth of the intersection of the extrapolated flanks

  • tip_angle – angle between the flanks

  • pad_angle – angle between z-axis and the roll face padding

Raises:

ValueError – if not exactly two of usable_width, tip_depth and tip_angle are given

property classifiers

A tuple of keywords to specify the type classifiers of this groove.

property tip_angle

Angle between the flanks.

property tip_depth

Depth of the intersection of the extrapolated flanks.

The Square Groove

The SquareGroove class represents a square shaped groove as shown in the figure.

square groove geometry

Mandatory measures of this groove are the two radii \(r_1\) and \(r_2\). To constrain geometry fully, any two of the following must be given:

  • usable width \(w_\mathrm{u}\)

  • tip depth \(d_\mathrm{t}\)

  • tip angle \(\delta\)

The radii are typically small, the depth is \(d_\mathrm{t}\) typically \(\approx \frac{w_\mathrm{u}}{2}\). The tip angle \(\delta\) is typically one or two degree larger than 90° for wear reasons. \(r_3\) and \(r_4\) are considered to be zero, as well as \(w_\mathrm{g}'\).

The tip depth \(d_\mathrm{t}\) was chosen in favor of the real depth \(d\), because it does not change, when the radii are modified. So the overall geometry remains the same if one modifies only the radii. The tip depth can be considered as the diagonal of the rhombus with sharp corners or the limit of the depth \(d\) for \(r_2 \rightarrow 0\).

The constructor will raise a warning, if the tip angle significantly deviates from 90°, consider to use a DiamondGroove instead.

class SquareGroove(r1: float, r2: float, usable_width: float | None = None, tip_depth: float | None = None, tip_angle: float | None = None, pad_angle: float = 0)

Represents a square-shaped groove (diamond with tip angle near 90°).

Exactly two of usable_width, tip_depth and tip_angle must be given. Widths are always measured at the intersection of the extrapolated ground, face and flanks. All angles are measured in ° (degree).

Parameters:

  • r1 – radius 1 (face/flank)

  • r2 – radius 2 (flank/ground)

  • usable_width – usable width of the groove

  • tip_depth – depth of the intersection of the extrapolated flanks

  • tip_angle – angle between the flanks

  • pad_angle – angle between z-axis and the roll face padding

Raises:

  • ValueError – if not exactly two of usable_width, tip_depth and tip_angle are given

  • ValueError – if tip angle is <85° or >95° (no matter if given or calculated internally)

property classifiers

A tuple of keywords to specify the type classifiers of this groove.

The Gothic Groove

The GothicGroove class represents oval-shaped groove standing on the edge as shown in the figure.

square groove geometry

Mandatory measures of this groove are the radii \(r_1\), \(r_2\) and \(r_3\), as well as the usable width \(w_\mathrm{u}\) and depth \(d\).

The radii \(r_1\) and \(r_3\) are typically small, the depth \(d\) is typically \(\ge w_\mathrm{u}\). The tip angle \(\delta\) is typically one or two degree larger than 90° for wear reasons. \(r_2\) is much larger than the other radii.

class GothicGroove(r1: float, r2: float, r3: float, depth: float, usable_width: float, pad_angle: float = 0)

Represents a square-shaped groove with curved flanks similar to a gothic arc.

Widths are always measured at the intersection of the extrapolated ground, face and flanks.

Parameters:

  • r1 – radius 1 (face/flank)

  • r2 – radius 2 (flank/ground)

  • r3 – radius 3 (ground)

  • depth – maximum depth

  • usable_width – usable width of the groove

  • pad_angle – angle between z-axis and the roll face padding

property classifiers

A tuple of keywords to specify the type classifiers of this groove.